Abstract:
The present invention relates to a single layer mixed cellulose ester film having a reversed optical dispersion. The mixed cellulose ester material has a DS OH  from 0.35 to 1.35. By manipulating the thickness of the film, and the film stretching conditions, desirable optical retardation and optical dispersion properties can be obtained. The film can be used as an optical waveplate in liquid crystal displays to improve viewing angle, contrast ratio, and color shift.

Description:
CROSS REFERENCES TO RELATED APPLICATIONS 
       [0001]    This application is a continuation-in-part of U.S. Ser. No. 13/157,580, filed Jun. 10, 1011 and claims the benefit of U.S. Provisional Application Ser. No. 61/360,941 filed Jul. 2, 2010. 
     
    
     FIELD OF THE INVENTION 
       [0002]    The present invention generally relates to cellulose ester films. In particular, the invention relates to multilayer cellulose ester films having reversed optical dispersion. The invention also relates to single layer cellulose ester films having reversed optical dispersion. The films are particularly suitable for use as an optical waveplate in liquid crystal displays. 
       BACKGROUND OF THE INVENTION 
       [0003]    An optical waveplate (also known as an optical retarder) is one of the key optical components to control the polarization state of polarized light. It has been widely used in different kinds of polarizing optical systems, such as optical imaging, fiber optical telecommunication, wave front correction, polarization controller, and liquid crystal displays (LCDs). Two important characteristics of a waveplate are its optical retardation and optical dispersion. A waveplate can have a strong or weak optical retardation value as well as a normal, flat, or reversed optical dispersion. 
         [0004]      FIG. 1  shows a waveplate  3  sandwiched between two crossed polarizers  1  and  2 . For normal incident light, the transmission T (output light) depends on following relationship: 
         [0000]        T ∝ sin 2  2β sin 2    [πΔnd/λ   0 ]  (1)
 
         [0000]    where d is the waveplate thickness; Δn=n x −n y  where n x  and n y  are the refractive indices of the waveplate in x and y directions (in-plane); β is the angle between the waveplate optical axis (i.e., the n x  axis) and the polarizer  1  transmission axis; and λ 0  is the wavelength in free space of the input light. The transmission axis of the polarizer  1  is in the horizontal direction, while the transmission axis of the polarizer  2  is in the vertical direction. The input light can be polarized or non-polarized. The output light T is always polarized and its transmission depends on two terms: (i) sin 2  2β; and (ii) sin 2 (πΔnd/λ 0 ). 
         [0005]    If the second term has a constant value, T only depends on the orientation of the waveplate. When β=0° or 90°, T is minimum; when β=45°, T is maximum. On the other hand, if the first term has a constant value, such as 1.0, which corresponds to β=45°, T only depends on Δnd/λ 0 . The term Δnd is defined as the waveplate in-plane retardation, R e : 
         [0000]        R   e   =Δnd =( n   x   −n   y ) d   (2)
 
         [0000]    Therefore, for normal incident light, the transmission T depends on R e /λ 0 . The related out-of-plane retardation R th  is defined as: 
         [0000]    
       
         
           
             
               
                 
                   
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         [0000]    where n z  is the waveplate refractive index in the z direction (out-of-plane). 
         [0006]    If the incident light contains multiple wavelengths, to achieve the same transmission for all wavelengths, such as red (R), green (G), and blue (B) light, R e /λ 0  must be a constant. For example, R e (R)/λ 0 (R)=R e (G)/λ 0 (G)=R e (B)/λ 0 (B)=¼, which is termed as an achromatic or a broadband quarter waveplate.  FIG. 2  shows an ideal achromatic quarter waveplate plot between R e  and λ. 
         [0007]    If R e  of a waveplate decreases as the wavelength λ increases, this waveplate has normal optical dispersion. Most polymers such as polyethylene, polypropylene, polycarbonate, and polystyrene, exhibit this kind of dispersion. If R e  of a waveplate increases as the wavelength λ increases, this waveplate has reversed optical dispersion. 
         [0008]      FIG. 2  indicates that an ideal achromatic waveplate should have reversed optical dispersion. In reality, this is very difficult to achieve (cf. Masayuki Yamaguchi et al.,  Macromolecules  2009, 42, 9034-9040; Akihiko Uchiyama et al.,  Jpn. J. Appl. Phys., Vol.  42 (2003) 3503-3507; Akihiko Uchiyama et al.,  Jpn. J. Appl. Phys., Vol.  42 (2003) 6941-6945). To improve the image quality of LCDs, controlling the optical dispersion of a waveplate plays an important role and a waveplate exhibiting reversed optical dispersion is highly desirable. Furthermore, considering the complexity of a typical LCD and dispersions of the other layers, a waveplate often needs to have optimized optical dispersion properties. 
         [0009]    A useful way to quantify optical dispersion is by the parameters A Re , B Re , A Rth  and B Rth : 
         [0000]        A   Re   =R   e (450)/ R   e (550)  (4)
 
         [0000]      B Re   =R   e (650)/ R   e (550)  (5)
 
         [0000]        A   Rth   =R   th (450)/ R   th (550)  (6)
 
         [0000]      B Rth   =R   th (650)/ R   th (550)  (7)
 
         [0000]    where 450, 550, and 650 in the parentheses are the wavelength in nanometers. For an ideal achromatic waveplate, A Re =A Rth =0.818, and B Re =B Rth =1.182, and the dispersion curve is a linear straight line as shown in  FIG. 2 . If a waveplate has non-ideal reversed dispersion, A Re  and A Rth  have to be less than 1.0, and B Re  and B Rth  have to be greater than 1.0. In reality, most materials with reversed dispersion do not have linear relation. If A Re , A Rth , B Re  and B Rth  are all equal to 1.0, the waveplate has flat dispersion. If A Re  and A Rth  is greater than 1.0, and B Re  and B Rth  is less than 1.0, the waveplate has normal dispersion. 
         [0010]    Unlike most other polymers, waveplates made from cellulose esters such as cellulose acetate (CA), cellulose acetate propionate (CAP), and cellulose acetate butyrate (CAB), often have reversed optical dispersions because of their polymer chain conformation and chemical compositions. But the values of A Re , B Re , A Rth  and B Rth  also depend on other factors such as plasticizers, additives, and processing conditions for making the waveplate. Also, cellulose esters with very low hydroxyl level could exhibit normal optical dispersions. 
         [0011]    In some LCD applications, waveplates with higher optical retardation and more reversed dispersion are desired, where A Re , B Re , A Rth  and B Rth  are close to an ideal achromatic waveplate. However, our studies have found that, typically, there is a tradeoff between having a higher optical retardation and more reversed dispersion. In general, we have found that when a waveplate has higher optical retardation values, the waveplate often exhibits relatively flat dispersion curves. On the other hand, when the waveplate exhibits a more reversed dispersion, the retardation is relatively low and cannot meet some requirements for certain applications. As an illustration,  FIGS. 3(   a ) and  3 ( b ) show the in-plane and out-of-plane optical dispersion curves of two types of cellulose esters (CEs). CE1, which has a low optical retardation (R e (550) CE1 =31.35 nm and R th (550) CE1 =−60.32 nm), has a more reversed optical dispersion than CE2. CE2, which has a high optical retardation (R e (550) CE2 =88.40 nm and R th (550) CE2 =−211.20 nm), has a more flat optical dispersion relative to CE1. 
         [0012]    Thus, there is a need in the art for an optical waveplate that has both high optical retardation and more reversed optical dispersion at the same time. The present invention addresses this need as well as others that will become apparent from the following description and claims. 
       SUMMARY OF THE INVENTION 
       [0013]    It has been surprisingly discovered that waveplates with both high optical retardation and reversed dispersion can be obtained. Such waveplates are composed of multiple layers of cellulose ester film. The cellulose ester materials for layer A should have low hydroxyl content, while the cellulose ester materials for layer B should have high hydroxyl content. By varying the thickness of layers A and B, and the film stretching conditions, films with the desired optical retardations and optical dispersions can be obtained. 
         [0014]    In one aspect, the invention provides a multilayer film having reversed optical dispersion. The film comprises: 
         [0015]    (a) a layer (A) comprising cellulose ester having a degree of substitution of hydroxyl groups (DS OH ) of 0 to 0.5; and 
         [0016]    (b) a layer (B) comprising cellulose ester having a DS OH  of 0.5 to 1.3, provided that when the DS OH  of layer (A) and layer (B) are both 0.5, the cellulose ester of layer (A) is different from the cellulose ester of layer (B). 
         [0017]    In a second aspect, the invention provides an optical waveplate for a liquid crystal display. The waveplate has reversed optical dispersion and comprises the multilayer film as described herein. 
         [0018]    In a third aspect, the invention provides a liquid crystal display. The display comprises an optical waveplate as described herein. 
         [0019]    In one aspect, the invention provides an optical waveplate comprising a single layer film with reversed optical dispersions comprised of cellulose ester film have a R e  from about 55 to 400 nm and a R th  from about −40 to −400 nm. 
         [0020]    In one aspect, the invention provides an optical waveplate comprising a single layer film comprising a cellulose ester with a total DS from about 1.65 to about 2.65, or DS OH  from 0.35 to 1.35. 
         [0021]    In one aspect, the invention provides an optical waveplate comprising a single layer film comprising cellulose esters that are randomly substituted copolymers having a total DS from about 1.65 to about 2.65. 
         [0022]    In one aspect, the invention provides an optical waveplate comprising a film comprising a cellulose ester film that is annealed and uniaxially or biaxially stretched and has reverse optical dispersion. 
         [0023]    In another aspect of this invention, the cellulose ester film after uniaxial or biaxial stretching has R e (589) from about 55 nm to 400 nm, R th (589) from about −40 nm to −400 nm, A Re  and A Rth  are from about 0.85 to 1.0, B Re  and B Rth  are from about 1.0 to 1.15. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0024]      FIG. 1  is an illustration of an optical waveplate sandwiched between two crossed polarizers. 
           [0025]      FIG. 2  is an ideal achromatic quarter waveplate optical dispersion graph. 
           [0026]      FIG. 3(   a ) is an in-plane optical dispersion graph of two different cellulose ester films. 
           [0027]      FIG. 3(   b ) is an out-of-plane optical dispersion graph of two different cellulose ester films. 
           [0028]      FIG. 4(   a ) shows a multilayer film according to the invention in an A-B configuration. 
           [0029]      FIG. 4(   b ) shows a multilayer film according to the invention in an A-B-A configuration. 
           [0030]      FIG. 5  shows the structure of a broadband quarter waveplate according to the prior art. 
           [0031]      FIG. 6  is an ideal achromatic quarter and half waveplate optical dispersion graph. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0032]    In accordance with the present invention, there is provided a multilayer film having reversed optical dispersion. The film comprises: 
         [0033]    (a) a layer (A) comprising cellulose ester having a degree of substitution of hydroxyl groups (DS OH ) of 0 to 0.5; and 
         [0034]    (b) a layer (B) comprising cellulose ester having a DS OH  of 0.5 to 1.3, provided that when the DS OH  of layer (A) and layer (B) are both 0.5, the cellulose ester of layer (A) is different from the cellulose ester of layer (B). 
         [0035]    The cellulose esters making up the individual layers (A) and (B) may be randomly or regioselectively substituted. Regioselectivity can be measured by determining the relative degree of substitution (RDS) at C 6 , C 3 , and C 2  in the cellulose ester by carbon 13 NMR ( Macromolecules,  1991, 24, 3050-3059). In the case of one acyl substituent or when a second acyl substituent is present in a minor amount (DS&lt;0.2), the RDS can be most easily determined directly by integration of the ring carbons. When 2 or more acyl substituents are present in similar amounts, in addition to determining the ring RDS, it is sometimes necessary to fully substitute the cellulose ester with an additional substituent in order to independently determine the RDS of each substituent by integration of the carbonyl carbons. In conventional cellulose esters, regioselectivity is generally not observed and the RDS ratio of C 6 /C 3 , C 6 /C 2 , or C 3 /C 2  is generally near 1 or less. In essence, conventional cellulose esters are random copolymers. In contrast, when adding one or more acylating reagents to cellulose dissolved in an appropriate solvent, the C 6  position of cellulose are acylated much faster than C 2  and C 3 . Consequentially, the C 6 /C 3  and C 6 /C 2  ratios are significantly greater than 1, which is characteristic of a 6,3- or 6,2-enhanced regioselectively substituted cellulose ester. 
         [0036]    The cellulose esters useful in the present invention can be prepared by any known means for preparing cellulose esters. 
         [0037]    Examples of randomly substituted cellulose esters having a DS OH  from about 0.0 to about 0.5 useful for layer A are described in US 2009/0054638 and US 2009/0050842; the contents of which are hereby incorporated by reference with the exception of blends of two or more cellulose esters. 
         [0038]    The cellulose esters of US 2009/0054638 and US 2009/0050842 are mixed esters, based for example, on acetyl, propionyl, and/or butyryl, but longer chain acids can also be used. Mixed esters can provide adequate solubility for processing and reduce gel formation. The non-acetyl degree of substitution is termed as DS NAC . The propionyl/butyryl degree of substitution (DS (PR+Bu) ) is a subgenus of DS NAC , and refers to the non-acetyl degree of substitution wherein the non-acetyl groups are propionyl and/or butyryl groups. In one embodiment, acetyl is the primary ester forming group. In another embodiment, the cellulose ester is a cellulose acetate propionate (CAP) ester. In another embodiment, the cellulose ester is a cellulose acetate butyrate (CAB) ester. In another embodiment, the cellulose ester is a cellulose acetate propionate butyrate (CAPB) ester. In another embodiment, the cellulose ester is a mixed cellulose ester of acetate and comprises at least one ester residue of an acid chain having more than 4 carbon atoms, such as, for example, pentonoyl or hexanoyl. Such higher acid chain ester residues may include, but are not limited to, for example acid chains esters with 5, 6, 7, 8, 9, 10, 11, and 12 carbon atoms. They may also include acid chains esters with more than 12 carbon atoms. In another embodiment, the mixed cellulose acetate ester that comprises at least one ester residue of an acid chain having more than 4 carbon atoms may also comprise propionyl and/or butyryl groups. 
         [0039]    In one embodiment, the mixed ester system has a total degree of substitution of from 2.8 to 3 (i.e., the hydroxyl DS is between 0 and 0.2). In another embodiment, the total degree of substitution is from 2.83 to 2.98, and in yet another embodiment, the total degree of substitution is from 2.85 to 2.95. In another embodiment of the invention, the total degree of substitution is such that the total hydroxyl level is low enough to produce the desired retardation behavior. 
         [0040]    The cellulose esters described in US 2009/0054638 and US 2009/0050842 can be prepared by a number of synthetic routes, including, but not limited to, acid-catalyzed esterification and hydrolysis of cellulose. 
         [0041]    For example, as described in US 2009/0054638 and US 2009/0050842, cellulose (75 g) was fluffed in a metal lab blender in three batches. This fluffed cellulose was treated in one of the following four pretreatments. 
         [0042]    Pretreatment A: The fluffed cellulose was soaked in mixtures of acetic acid and propionic acid. Then the reaction was carried out as shown below. 
         [0043]    Pretreatment B: The fluffed cellulose was soaked in 1 liter of water for about 1 hour. The wet pulp was filtered and washed four times with acetic acid to yield acetic acid wet pulp and the reaction carried out as shown below. 
         [0044]    Pretreatment C: The fluffed cellulose was soaked in about 1 liter of water for about 1 hour. The wet pulp was filtered and washed four times with propionic acid to yield propionic acid wet pulp and the reaction carried out as shown below. 
         [0045]    Pretreatment D: The fluffed cellulose was soaked in about 1 liter of water for about 1 hour. The wet pulp was filtered and washed three times with acetic acid and three times with propionic acid to yield propionic wet pulp and the reaction carried out as shown below. 
         [0046]    Reaction: The acid wet pulp from one of the pretreatments above was then placed in a 2-liter reaction kettle and acetic or propionic acid was added. The reaction mass was cooled to 15° C., and a 10° C. solution of acetic anhydride and propionic anhydride, and 2.59 g of sulfuric acid were added. After the initial exotherm, the reaction mixture was held at about 25° C. for 30 minutes and then the reaction mixture was heated to 60° C. When the proper viscosity of the mixture was obtained, a 50-60° C. solution of 296 mL of acetic acid and 121 mL of water was added. This mixture was allowed to stir for 30 minutes and then a solution of 4.73 g of magnesium acetate tetrahydrate in 385 mL of acetic acid and 142 mL of water was added. This reaction mixture was then precipitated by one of the methods shown below. 
         [0047]    Precipitation Method A: The reaction mixture was precipitated by the addition of 8 L of water. The resulting slurry was filtered and washed with water for about four hours and then dried in a 60° C. forced air oven to yield cellulose acetate propionate. 
         [0048]    Precipitation Method B: The reaction mixture was precipitated by the addition of 4 L of 10% acetic acid and then hardened by addition of 4 L of water. The resulting slurry was filtered and washed with water for about four hours and then dried in a 60° C. forced air oven to yield cellulose acetate propionate. 
         [0049]    Examples of regioselectively substituted cellulose esters having a DS OH  from about 0.0 to about 0.5 useful for layer A and regioselectively substituted cellulose esters having a DS OH  from about 0.5 to about 1.3 useful for layer B are described in US 2010/0029927, U.S. patent application Ser. No. 12/539,817, and WO 2010/019245; the contents of which are hereby incorporated by reference. 
         [0050]    In general, US 2010/0029927, U.S. patent application Ser. No. 12/539,817, and WO 2010/019245 concern dissolution of cellulose in an ionic liquid, which is then contacted with an acylating reagent. Accordingly, for the present invention, cellulose esters can be prepared by contacting the cellulose solution with one or more C 1 -C 20  acylating reagents at a contact temperature and contact time sufficient to provide a cellulose ester with the desired degree of substitution (DS) and degree of polymerization (DP). The cellulose esters thus prepared generally comprise the following structure: 
         [0000]    
       
                 
         
             
             
         
       
     
         [0000]    where R 2 , R 3 , and R 6  are hydrogen (with the proviso that R 2 , R 3 , and R 6  are not hydrogen simultaneously) or C 1 -C 20  straight- or branched-chain alkyl or aryl groups bound to the cellulose via an ester linkage. 
         [0051]    The cellulose esters prepared by these methods may have a DS from about 0.1 to about 3.0, preferably from about 1.7 to about 3.0, more preferably from about 1.65 to about 2.65, and yet more preferably from about 1.85 to about 2.35. The degree of polymerization (DP) of the cellulose esters prepared by these methods will be at least 10. More preferred is when the DP of the cellulose esters is at least 50. Yet further preferred is when the DP of the cellulose esters is at least 100. Most preferred is when the DP of the cellulose esters is at least 250. In yet another embodiment, the DP of the cellulose esters is from about 5 to about 100. More preferred is when the DP of the cellulose esters is from about 10 to about 50. 
         [0052]    The preferred acylating reagents are one or more C 1 -C 20  straight- or branched-chain alkyl or aryl carboxylic anhydrides, carboxylic acid halides, diketene, alkyl diketene, or acetoacetic acid esters. Examples of carboxylic anhydrides include, but are not limited to, acetic anhydride, propionic anhydride, butyric anhydride, isobutyric anhydride, valeric anhydride, hexanoic anhydride, 2-ethylhexanoic anhydride, nonanoic anhydride, lauric anhydride, palmitic anhydride, stearic anhydride, benzoic anhydride, substituted benzoic anhydrides, phthalic anhydride, and isophthalic anhydride. Examples of carboxylic acid halides include, but are not limited to, acetyl, propionyl, butyryl, hexanoyl, 2-ethylhexanoyl, lauroyl, palmitoyl, benzoyl, substituted benzoyl, and stearoyl chlorides. Examples of acetoacetic acid esters include, but are not limited to, methyl acetoacetate, ethyl acetoacetate, propyl acetoacetate, butyl acetoacetate, and tert-butyl acetoacetate. The most preferred acylating reagents are C 2 -C 9  straight- or branched-chain alkyl carboxylic anhydrides selected from the group acetic anhydride, propionic anhydride, butyric anhydride, 2-ethylhexanoic anhydride, nonanoic anhydride, and stearic anhydride. The acylating reagents can be added after the cellulose has been dissolved in the ionic liquid. If so desired, the acylating reagent can be added to the ionic liquid prior to dissolving the cellulose in the ionic liquid. 
         [0053]    In the esterification of cellulose dissolved in ionic liquids, the preferred contact temperature is from about 20° C. to about 140° C. A more preferred contact temperature is from about 50° C. to about 100° C. The most preferred contact temperature is from about 60° C. to about 80° C. 
         [0054]    In the esterification of cellulose dissolved in ionic liquids, the preferred contact time is from about 1 min to about 48 h. A more preferred contact time is from about 10 min to about 24 h. The most preferred contact time is from about 30 min to about 5 h. 
         [0055]    Examples of randomly substituted cellulose esters having a DS OH  from about 0.5 to about 1.3 useful for layer B are described in US 2009/0096962, which is hereby incorporated by reference. 
         [0056]    The cellulose esters described in US 2009/0096962 can be prepared by a number of synthetic routes, including, but not limited to, acid-catalyzed hydrolysis of a previously prepared cellulose ester in an appropriate solvent or mixture of solvents and base-catalyzed hydrolysis of a previously prepared cellulose ester in an appropriate solvent or mixture of solvents. Additionally, high DS OH  cellulose esters can be prepared from cellulose by a number of known methods. For additional details on synthetic routes for preparing high DS OH  cellulose esters, see U.S. Pat. No. 2,327,770; S. Gedon et al., “Cellulose Esters, Organic Esters,” from Kirk-Othmer Encyclopedia of Chemical Technology, Fifth Edition, Vol. 5, pp. 412-444, 2004, John Wiley &amp; Sons, Hoboken, N.J.; and D. Klemm et al., “Comprehensive Cellulose Chemistry: Volume 2 Functionalization of Cellulose,” Wiley-VCH, New York, 1998. 
         [0057]    In one embodiment, conventional cellulose esters (for example, but not limited to CAB-381-20 and CAP-482-20, commercially available from Eastman Chemical Company) are dissolved in an organic carboxylic acid, such as acetic acid, propionic acid, or butyric acid, or mixture of organic carboxylic acids, such as acetic acid, propionic acid, or butyric acid to form a dope. The resulting cellulose ester dopes can be treated with water and an inorganic acid catalyst, including, but not limited to, sulfuric acid, hydrochloric acid, and phosphoric acid, to hydrolyze the ester groups to increase the DS OH . 
         [0058]    The same hydrolysis protocols described above can be accomplished with non-acidic catalysts, such as bases. Additionally, solid catalysts such as ion exchange resins can be used. Additionally, the solvent used to dissolve the initial cellulose ester prior to hydrolysis can be an organic solvent that is not an organic acid solvent; examples of which include, but are not limited to, ketones, alcohols, dimethyl sulfoxide (DMSO), and N,N-dimethylformamide (DMF). 
         [0059]    Additional methods for preparing high DS OH  cellulose esters include preparation of the high DS OH  cellulose esters from cellulose from wood or cotton. The cellulose can be a high-purity dissolving grade wood pulp or cotton linters. The cellulose can, alternatively, be isolated from any of a number of biomass sources including, but not limited to, corn fiber. 
         [0060]    In one embodiment of this invention, additives such as plasticizers, stabilizers, UV absorbers, antiblocks, slip agents, lubricants, dyes, pigments, retardation modifiers, etc. may be mixed with the cellulose esters. Examples of these additives are found in US 2009/0050842, US 2009/0054638, and US 2009/0096962; the contents of which are hereby incorporated by reference. 
         [0061]    Examples of plasticizers include but are not limited to one or more of the following, phosphoric acid-based plasticizers, phthalic acid ester-based plasticizers, glycolate-based plasticizers, and citric acid ester-based plasticizers, carbohydrate ester-based plasticizers, and alditol ester-based plasticizers. 
         [0062]    Examples of phosphoric acid ester-based plasticizers include but are not limited to triphenyl phosphate (TPP), tricresyl phosphate, cresyl phenyl phosphate, octyl diphenyl phosphate, diphenyl biphenyl phosphate, trioctyl phosphate, and tributyl phosphate. Phthalic acid ester-based plasticizers include but are not limited to diethyl phthalate, dimethoxyethyl phthalate, dimethyl phthalate, dioctyl phthalate, dibutyl phthalate, di-2-ethyl hexyl phthalate, butyl benzyl phthalate, di-2-ethylhexyl phthalate, butyl benzyl phthalate, and dibenzyl phthalate. Citric acid ester-based plasticizers include but are not limited to acetyl trimethyl citrate, and acetyl tributyl citrate. Glycolate-based plasticizers include but are not limited to alkyl phthalyl alkyl glycolate, such as methyl phthalyl methyl glycolate, ethyl phthalyl ethyl glycolate (EPEG), propyl phthalyl propyl glycolate, butyl phthalyl butyl glycolate, octyl phthalyl octyl glycolate, methyl phthalyl ethyl glycolate, ethyl phthalyl methyl glycolate, ethyl phthalyl propyl glycolate, propyl phthalyl ethyl glycolate, methyl phthalyl propyl glycolate, methyl phthalyl butyl glycolate, ethyl phthalyl butyl glycolate, butyl phthalyl methyl glycolate, butyl phthalyl ethyl glycolate, propyl phthalyl butyl glycolate, butyl phthalyl propyl glycolate, methyl phthalyl octyl glycolate, ethyl phthalyl octyl glycolate, octyl phthalyl methyl glycolate, and octyl phthalyl ethyl glycolate. Other useful plasticizers include, but are not limited to, butyl oleate, methyl acetyl ricinolate, dibutyl sebacate, and triacetin. Carbohydrate ester-based plasticizers include, but are not limited to, esters of 6-carbon aldose sugars, such as glucose pentapropionate, glucose pentaisobutyrate, and glucose pentatbutyrate; esters of 6-carbon ketose sugars such as fructose pentapropionate, fructose pentaisobutyrate, fructose pentatbutyrate; esters of 5-carbon aldose sugars, such as xylose tetrapropionate, xylose tetraisobutyrate, and xylose tetrabutryate. Alditol ester-based plasticizers include but are not limited to 5-carbon alditol esters, such as xylitol pentapropionate, xylitol pentaisobutryate, and xylitol pentabutyrate; 6-carbon alditol esters, such as mannitol hexapropionate, mannitol hexaisobutyrate, and mannitol hexabutyrate. Other useful plasticizers include triphenyl phosphate, xylitol pentaacetate, trimethyl pentanoyl diisobutyrate, 2-naphthyl benzoate or mixtures thereof. 
         [0063]    The multilayer film according to the invention can be made by solvent co-casting, melt co-extrusion, lamination, or a coating process. These procedures are generally known in the art. Examples of solvent co-casting, melt co-extrusion, lamination, and coating methods to form multilayer structures are found in US 2009/0050842, US 2009/0054638, and US 2009/0096962. 
         [0064]    Further examples of solvent co-casting, melt co-extrusion, lamination, and coating methods to form a multilayer structure are found in U.S. Pat. No. 4,592,885; U.S. Pat. No. 7,172,713; US 2005/0133953; and US 2010/0055356, the contents of which are hereby incorporated by reference in their entirety. 
         [0065]    The multilayer film may be configured in an A-B structure or an A-B-A structure ( FIGS. 4(   a ) and  4 ( b ), respectively). In the case of a bi-layer structure, the layers are made using different cellulose esters. For the tri-layer structure, the top and bottom layers are made using the same cellulose ester and the middle layer is made using a different cellulose ester. Other configurations are possible such as A-X-B where X is an adhesive or tie layer, and B-A-B. The thickness of each layer can be the same or different. By varying the thickness of each layer, the desired optical retardation and reversed optical dispersion can be obtained. The thickness of layer A before stretching can range from 5 μm to 50 μm, and the thickness of layer B before stretching can range from 30 μm to 100 μm. 
         [0066]    To obtain certain in-plane retardation (R e ) values, the multilayer film may be stretched. By adjusting the stretch conditions such as stretch temperature, stretch ratio, stretch type—uniaxial or biaxial, pre-heat time and temperature, and post-stretch annealing time and temperature; the desired R e , R th , and reverse optical dispersion can be achieved. The stretching temperature can range from 130° C. to 200° C. The stretch ratio can range from 1.0 to 1.4 in the machine direction (MD) and can range from 1.1 to 2.0 in the transverse direction (TD). The pre-heat time can range from 10 to 300 seconds, and the pre-heat temperature can be the same as the stretch temperature. The post-annealing time can range from 0 to 300 seconds, and the post-annealing temperature can range from 10° C. to 40° C. below the stretching temperature. 
         [0067]    For applications such as an optical waveplate for LCDs, certain optical retardations R e  and R th  as well as optical dispersion are desired. Hence, in one embodiment of this invention, a single-layer film of layer A after uniaxial or biaxial stretching has an R e (550) from −80 nm to −10 nm, an R th (550) from 0 nm to 100 nm, A Re  and A Rth  from about 1.0 to 1.6, and B Re  and B Rth  from about 1.0 to 0.6. In another embodiment, a single-layer film of layer A after stretching in at least one direction has an R e (550) from about 10 nm to 60 nm, R th (550) from about 0 nm to −60 nm, A Re  and A Rth  from about 0.5 to 1.0, and B Re  and B Rth  from about 1.0 to 1.3. In yet another embodiment, a single-layer film of layer A after uniaxial or biaxial stretching has an R e (550) from −60 nm to −20 nm, R th (550) from 0 nm to 60 nm, A Re  and A Rth  from 1.2 to 1.6, and B Re  and B Rth  from 0.5 to 0.8. In another embodiment, a single-layer film of layer A after stretching in at least one direction has an R e (550) from about 10 nm to 40 nm, R th (550) from 0 nm to −40 nm, A Re  and A Rth  from about 0.5 to 0.8, and B Re  and B Rth  from about 1.1 to 1.3. In still yet another embodiment, a single-layer film of layer A after uniaxial or biaxial stretching has an R e (550) from about −50 nm to −30 nm, R th (550) from about 0 nm to 40 nm, A Re  and A Rth  from about 1.4 to 1.6, and B Re  and B Rth  from about 0.5 to 0.7. In another embodiment, a single-layer film of layer A after stretching in at least one direction has an R e (550) from about 15 nm to 30 nm, R th (550) from about 0 nm to −30 nm, A Re  and A Rth  from about 0.5 to 0.7, and B Re  and B Rth  from about 1.2 to 1.3. 
         [0068]    In embodiment of this invention, a single-layer film of layer B after uniaxial or biaxial stretching has an R e (550) from about 10 nm to 350 nm, R th (550) from about −100 nm to −400 nm, A Re  and A Rth  from about 0.97 to 1.1, and B Re  and B Rth  from about 0.97 to 1.05. In another embodiment, a single-layer film of layer B after uniaxial or biaxial stretching has an R e (550) from about 45 nm to 300 nm, R th (550) from about −150 nm to −350 nm, A Re  and A Rth  from about 0.97 to 1.0, and B Re  and B Rth  from about 1.0 to 1.05. In another embodiment, a single-layer film of layer B after uniaxial or biaxial stretching has R e (550) from about 55 nm to 280 nm, R th (550) from about −180 nm to −300 nm, A Re  and A Rth  from about 0.97 to 0.99, and B Re  and B Rth  from about 1.0 to 1.06. 
         [0069]    In another aspect of this invention, the cellulose ester single layer film after uniaxial or biaxial stretching has R e (589) from about 100 nm to 400 nm, R th (589) from about −40 nm to −400 nm, A Re  and A Rth  are from about 0.85 to 1.0, B Re  and B Rth  are from about 1.0 to 1.15. In another embodiment of the invention, the cellulose ester single layer film after uniaxial or biaxial stretching has R e (589) from about 120 nm to 300 nm, R th (589) from about −60 nm to −280 nm, A Re  and A Rth  are from about 0.880 to 0.99, B Re  and B Rth  are from about 1.0 to 1.10. In another embodiment of the invention, the cellulose ester single layer film after uniaxial or biaxial stretching has R e (589) from about 140 nm to 270 nm, R th (589) from about −70 nm to −200 nm; A Re  and A Rth  are from about 0.93 to 0.98, B Re  and B Rth  are from about 1.0 to 1.06. 
         [0070]    After uniaxial or biaxial stretching, the multilayer film according to the invention can have an R e (550) from about 10 nm to 300 nm, R th (550) from about −50 nm to −300 nm, A Re  and A Rth  from about 0.95 to 1.0, and B Re  and B Rth  from about 1.0 to 1.06. In another embodiment, the multilayer film after uniaxial or biaxial stretching can have an R e (550) from about 40 nm to 280 nm, R th (550) from about −70 nm to −300 nm, A Re  and A Rth  from about 0.90 to 0.97, and B Re  and B Rth  from about 1.05 to 1.1. In another embodiment, the multilayer film after uniaxial or biaxial stretching can have an R e (550) from about 55 nm to 250 nm, R th (550) from about −70 nm to −280 nm, A Re  and A Rth  from about 0.82 to 0.95, and B Re  and B Rth  are from about 1.06 to 1.18. 
         [0071]    The R e  and R th  values reported above for wavelength 550 nm are based on a film thickness of 30 to 120 μm. 
         [0072]    In yet another embodiment, layer A and layer B each can have an R e  of 0 to 280 nm and an R th  of −400 to +200 nm, measured at a film thickness of 30 to 120 μm and at a light wavelength of 550 nm. 
         [0073]    Currently, it is common practice to use two or more compensation films to obtain LCDs with adequate viewing angles, contrast ratios, and color shifts. For example, a broadband quarter waveplate is achieved by combining one half-waveplate with one quarter-waveplate. This is shown in  FIG. 5 . (Cf. Pancharatnam,  Proceedings of the Indian Academy of Science , Sec. A., Vol. 41., 130-136 (1955); Tae-Hoon Yoon et al.,  Optics Letters , Vol. 25, No. 20 1547-1549, 2000.) Both the half-waveplate and the quarter-waveplate in  FIG. 5  have normal optical dispersion. After laminating them together with certain orientation, the combination has the retardation of a quarter-waveplate and reversed optical dispersion. This practice, however, is undesirable because it consumes more materials, is complicated to construct, and results in a thick display. In contrast, we have surprisingly found that the multilayer films of the present invention (such as shown in  FIGS. 4(   a ) and  4 ( b )) can provide optical waveplates with excellent viewing angles, contrast ratios, and color shifts when used as a single waveplate in LCDs. Moreover, the individual layers of the films of the present invention do not need special orientation relative to each other in order to have reversed optical dispersion. 
         [0074]    Thus, in another aspect, the present invention provides an optical waveplate for a liquid crystal display. The optical waveplate has a reversed optical dispersion and is composed of the multilayer films according to the present invention. 
         [0075]    Thus, in another aspect, the present invention provides an optical waveplate for a liquid crystal display. The optical waveplate has a reversed optical dispersion and is composed of the single layer films according to the present invention. 
         [0076]    In yet another aspect, the present invention provides a liquid crystal display which comprises the optical waveplate according to the present invention. The optical waveplate comprises a single layer film according to the present invention. 
         [0077]    Thus, in another aspect, the present invention provides an optical waveplate for a circular polarizer for an Organic light emitting diode (OLED) display. The optical waveplate has a reversed optical dispersion and is composed of the single layer films according to the present invention. 
         [0078]    Thus, in another aspect, the present invention provides an optical waveplate for a three-dimensional (3-D) display. The optical waveplate has a reversed optical dispersion and is composed of the single layer films according to the present invention. 
         [0079]    Thus, in another aspect, the present invention provides an optical waveplate for glasses for watching a three-dimensional (3-D) display. The optical waveplate has a reversed optical dispersion and is composed of the single layer films according to the present invention. 
         [0080]    This invention can be further illustrated by the following working examples, although it should be understood that these examples are included merely for purposes of illustration and are not intended to limit the scope of the invention. 
       EXAMPLES 
     General Procedures 
       [0081]    Solution preparation: Cellulose ester solids and 10 wt % plasticizer (based on the total weight of solids) were added to a 87/13 wt % solvent mixture of CH 2 Cl 2 /methanol (or ethanol) to give a final concentration of 5-30 wt % based on cellulose ester+plasticizer. The mixture was sealed, placed on a roller, and mixed for 24 hours to create a uniform solution. 
         [0082]    Solvent casting of a single-layer film: The solution prepared above was cast onto a glass plate using a doctor blade to obtain a film with the desired thickness. Casting was conducted in a fume hood with relative humidity controlled at 45%-50%. After casting, the film was allowed to dry for 45 minutes under a cover pan to reduce the rate of solvent evaporation before the pan was removed. The film was allowed to dry for 15 minutes, then the film was peeled from the glass and annealed in a forced air oven for 10 minutes at 100° C. After annealing at 100° C., the film was annealed at a higher temperature (120° C.) for another 10 minutes. 
         [0083]    Film uniaxial or biaxial stretching was carried out on a Brückner Karo IV laboratory film stretcher. Constrained uniaxial stretch means the film is held by the tenter frame on all sides; non-constrained uniaxial stretch means the film is held only in the stretching direction, which allows the film to neck in during stretching. Stretching conditions, such as stretch ratio (MD: machine direction, TD: transverse direction), stretch temperature, and pre-heating and post-annealing time and temperature, will affect the film final optical retardations and dispersion. These conditions can be varied to achieve specific optical retardation and dispersion according to the requirements of the application. 
         [0084]    Film optical retardation and dispersion measurements were made using a J.A. Woollam M-2000V Spectroscopic Ellipsometer having a spectral range from 370 to 1000 nm. RetMeas (Retardation Measurement) program from J.A. Woollam Co., Inc. was used to obtain optical film in-plane (R e ) and out-of-plane (R th ) retardations. Unless specified otherwise, all reported values were measured at 589 nm. 
         [0085]    Film haze was measured by UltraScan XE from HunterLab using standard calibration and measurement procedures. 
       Example 1 
     Comparative 
       [0086]    This example shows the optical retardation and dispersion of a single-layer film suitable for layer B in an optical waveplate. 
         [0087]    Following the general solution preparation, a randomly substituted cellulose acetate propionate (DS Ac =0.14, DS Pr =1.71, DS OH =1.15) was used to prepare the following solution for Example 1: 
         [0000]    
       
         
               
               
               
               
             
           
               
                   
                   
               
             
             
               
                   
                 Total solids 
                 24 
                 g 
               
               
                   
                 Cellulose ester 
                 21.6 
                 g 
               
               
                   
                 Plasticizer 
                 2.4 
                 g triphenyl phosphate 
               
               
                   
                 Total solvent 
                 176 
                 g 
               
               
                   
                 Methylene chloride 
                 153.12 
                 g 
               
               
                   
                 Methanol 
                 22.88 
                 g 
               
               
                   
                   
               
             
          
         
       
     
         [0088]    Following the general solvent cast procedures described above, the solution for Example 1 was used to obtain single-layer films. The films were annealed at 100° C. and 120° C. for 10 minutes, respectively, before they were uniaxially or simultaneous biaxially stretched under different stretching conditions. The stretching conditions and optical and film data of these films are listed in Table 1. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Optical properties for a single-layer cellulose acetate propionate film 
               
               
                 (DS Ac  = 0.14, DS Pr  = 1.71, DS OH  = 1.15). 
               
             
          
           
               
                   
                   
                 Stretch 
                   
                   
                   
                   
                   
                   
                 Film 
               
               
                   
                   
                 Temp. 
                 R e   
                 R th   
                   
                   
                   
                   
                 Thickness 
               
               
                 Run 
                 MD × TD 
                 (° C.) 
                 (nm) 
                 (nm) 
                 A Re   
                 B Re   
                 A Rth   
                 B Rth   
                 (micron) 
               
               
                   
               
             
          
           
               
                 1 
                 1.00 × 1.40 
                 175 
                 152.31 
                 −301.86 
                 0.993 
                 1.001 
                 0.999 
                 0.994 
                 68 
               
               
                 2 
                 1.00 × 1.45 
                 180 
                 146.67 
                 −271.03 
                 0.993 
                 1.002 
                 0.998 
                 0.995 
                 68 
               
               
                 3 
                 1.00 × 1.40 
                 180 
                 135.07 
                 −275.95 
                 0.992 
                 1.002 
                 0.998 
                 0.994 
                 70 
               
               
                 4 
                 1.00 × 1.35 
                 177 
                 105.94 
                 −248.51 
                 0.994 
                 1.002 
                 0.998 
                 0.995 
                 70 
               
               
                 5 
                 1.00 × 1.35 
                 180 
                 120.68 
                 −257.34 
                 0.994 
                 1.002 
                 1.000 
                 0.994 
                 72 
               
               
                 6 
                 1.04 × 1.26 
                 175 
                 73.08 
                 −297.34 
                 0.991 
                 1.002 
                 0.995 
                 1.000 
                 74 
               
               
                   
               
             
          
         
       
     
         [0089]    Relative to an ideal achromatic waveplate in which A Re =A Rth =0.818 and B Re =B Rth =1.182, the data in Table 1 indicate that these films exhibited only a slight reversed dispersion. That is, the dispersion curves of these films were essentially flat. 
       Example 2 
     Comparative 
       [0090]    This example shows the optical retardation and dispersion of a single-layer film suitable for layer A in an optical waveplate. 
         [0091]    Following the general solution preparation, a randomly (RDS: C 6 =0.92, C 3 =1.00, C 2 =0.96) substituted cellulose acetate propionate (DS Ac =1.49, DS Pr =1.44, DS OH =0.07) was used to prepare the following solution for Example 2: 
         [0000]    
       
         
               
               
               
               
             
           
               
                   
                   
               
             
             
               
                   
                 Total solids 
                 24 
                 g 
               
               
                   
                 Cellulose ester 
                 21.6 
                 g 
               
               
                   
                 Plasticizer 
                 2.4 
                 g Triphenyl phosphate 
               
               
                   
                 Total solvent 
                 176 
                 g 
               
               
                   
                 Methylene chloride 
                 153.12 
                 g 
               
               
                   
                 Methanol 
                 22.88 
                 g 
               
               
                   
                   
               
             
          
         
       
     
         [0092]    Following the general solvent cast procedures described above, the solution for Example 2 was used to obtain single-layer films. The films were annealed at 100° C. and 120° C. for 10 minutes, respectively, before they were uniaxially or simultaneous biaxially stretched under different stretching conditions. The stretching conditions and optical and film data of these films are listed in Table 2. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 Optical properties for a single-layer cellulose acetate propionate film 
               
               
                 (DS Ac  = 1.49, DS Pr  = 1.44, DS OH  = 0.07). 
               
             
          
           
               
                   
                   
                 Stretch 
                   
                   
                   
                   
                   
                   
                 Film 
               
               
                   
                   
                 Temp. 
                 R e   
                 R th   
                   
                   
                   
                   
                 Thickness 
               
               
                 Run 
                 MD × TD 
                 (° C.) 
                 (nm) 
                 (nm) 
                 A Re   
                 B Re   
                 A Rth   
                 B Re   
                 (micron) 
               
               
                   
               
             
          
           
               
                 7 
                 1.00 × 1.50 
                 160 
                 −9.56 
                 11.15 
                 1.536 
                 0.706 
                 1.471 
                 0.593 
                 58 
               
               
                 8 
                 1.00 × 1.60 
                 160 
                 −11.83 
                 12.93 
                 1.511 
                 0.729 
                 1.413 
                 0.648 
                 56 
               
               
                 9 
                 1.00 × 1.70 
                 160 
                 −12.59 
                 10.40 
                 1.476 
                 0.737 
                 1.409 
                 0.606 
                 48 
               
               
                 10  
                 1.00 × 1.80 
                 160 
                 −16.48 
                 10.87 
                 1.427 
                 0.766 
                 1.476 
                 0.638 
                 48 
               
               
                 11* 
                 1.00 × 1.80 
                 160 
                 −53.48 
                 31.32 
                 1.337 
                 0.815 
                 1.228 
                 0.791 
                 80 
               
               
                 12* 
                 1.00 × 1.90 
                 160 
                 −57.66 
                 32.71 
                 1.347 
                 0.811 
                 1.225 
                 0.784 
                 86 
               
               
                 13* 
                 1.00 × 2.00 
                 160 
                 −55.74 
                 27.57 
                 1.362 
                 0.803 
                 1.249 
                 0.761 
                 80 
               
               
                   
               
               
                 *= The film was not constrained in the MD while stretching. 
               
             
          
         
       
     
         [0093]    Relative to an ideal achromatic waveplate in which A Re =A Rth =0.818 and B Re =B Rth =1.182, the data in Table 2 show that these films did not exhibit a reversed dispersion. In fact, A Re  and A Rth  are all greater than 1, while B Re  and B Rth  are less than one, which is characteristic of a normal dispersion. 
       Example 3 
     Comparative 
       [0094]    This example shows the optical retardation and dispersion of a single-layer film suitable for layer A in an optical waveplate. 
         [0095]    A regioselectively substituted cellulose benzoate propionate in which the benzoate was primarily located on C 2  and C 3  was prepared according to U.S. patent application Ser. No. 12/539,817. 325.26 g of tributylmethylammonium dimethylphosphate ([TBMA]DMP) was added to a 3-neck 1 L round bottom flask equipped with mechanical stirring, a N 2 /vacuum inlet, and an iC10 diamond tipped infrared probe (Mettler-Toledo AutoChem, Inc., Columbia, Md., USA). The flask was placed in a 100° C. oil bath and the [TBMA]DMP was stirred 17 h under vacuum (0.8-1.4 mm Hg). 139.4 g of NMP (30 wt %) was added to the [TBMA]DMP, and then the mixture was cooled to room temperature. While stirring rapidly at room temperature, 34.97 g of cellulose (7 wt %, DPv (degree of polymerization as determined from Cuene viscosity) 1080) was added to the solution (9 min addition). The mixture was stirred for an additional 3 min to insure that the cellulose was well dispersed before raising a preheated 100° C. oil bath to the flask. Sixty minutes after raising the oil bath, there were no visible particles and the solution was light amber. To insure complete cellulose dissolution, stirring was continued for an additional 70 minutes. 2.1 equivalents of Pr 2 O (propionic anhydride) was added drop-wise (28 min addition) to the cellulose solution at 100° C. Ten minutes after the end of Pr 2 O addition, a total of 3 equivalents of benzoic anhydride was added as a liquid (melted at 85° C.). The contact mixture was stirred for 80 minutes before the IR probe was removed from the contact mixture. The contact mixture was immediately poured into 2.5 L of MeOH while mixing with a homogenizer. The solids were isolated by filtration then washed 10× with 2 L portions of MeOH before drying overnight at 10 mm Hg, 50° C. Analysis by  1 H NMR revealed that the cellulose ester had a DS Bz =0.29, DS Pr =2.26, DS OH =0.45. Analysis by quantitative carbon 13 NMR showed that the product was regioselectively substituted having a ring RDS of: C 6 =1.00, C 3 =0.68, C 2 =0.84. 
         [0096]    Following the general solution preparation, the regioselectively substituted cellulose benzoate propionate was used to prepare the following solution for Example 3: 
         [0000]    
       
         
               
               
               
               
             
           
               
                   
                   
               
             
             
               
                   
                 Total solids 
                 24 
                 g 
               
               
                   
                 Cellulose ester 
                 21.6 
                 g 
               
               
                   
                 Plasticizer 
                 2.4 
                 g triphenyl phosphate 
               
               
                   
                 Total solvent 
                 176 
                 g 
               
               
                   
                 Methylene chloride 
                 153.12 
                 g 
               
               
                   
                 Methanol 
                 22.88 
                 g 
               
               
                   
                   
               
             
          
         
       
     
         [0097]    Following the general solvent cast procedures described above, the solution for Example 3 was used to obtain single-layer films. The films were annealed at 100° C. and 120° C. for 10 minutes, respectively, before they were uniaxially or simultaneous biaxially stretched under different stretching conditions. The stretching conditions and optical and film data of these films are listed in Table 3. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 Optical properties for a single-layer cellulose benzoate propionate film 
               
               
                 (DS Bz  = 0.29, DS Pr  = 2.26, DS OH  = 0.45). 
               
             
          
           
               
                   
                   
                 Stretch 
                   
                   
                   
                   
                   
                   
                 Film 
               
               
                   
                   
                 Temp. 
                 R e   
                 R th   
                   
                   
                   
                   
                 Thickness 
               
               
                 Run 
                 MD × TD 
                 (° C.) 
                 (nm) 
                 (nm) 
                 A Re   
                 B Re   
                 A Rth   
                 B Rth   
                 (micron) 
               
               
                   
               
             
          
           
               
                 14 
                 1.00 × 1.30 
                 165 
                 −32.47 
                 −6.76 
                 1.207 
                 0.898 
                 −19.350 
                 16.300 
                 58 
               
               
                 15 
                 1.00 × 1.40 
                 165 
                 −41.56 
                 −22.05 
                 1.194 
                 0.900 
                 0.262 
                 1.542 
                 56 
               
               
                 16 
                 1.00 × 1.50 
                 165 
                 −55.67 
                 −24.66 
                 1.185 
                 0.903 
                 0.330 
                 1.494 
                 54 
               
               
                 17 
                 1.00 × 1.60 
                 165 
                 −83.05 
                 −17.31 
                 1.190 
                 0.905 
                 −0.436 
                 2.081 
                 64 
               
               
                  18* 
                 1.00 × 1.40 
                 165 
                 −110.71 
                 57.08 
                 1.251 
                 0.873 
                 1.257 
                 0.800 
                 88 
               
               
                  19* 
                 1.00 × 1.50 
                 165 
                 −125.81 
                 59.83 
                 1.242 
                 0.878 
                 1.260 
                 0.799 
                 86 
               
               
                  20* 
                 1.00 × 1.60 
                 165 
                 −156.69 
                 75.23 
                 1.228 
                 0.885 
                 1.243 
                 0.814 
                 90 
               
               
                   
               
               
                 *= The film was not constrained in the MD while stretching. 
               
             
          
         
       
     
         [0098]    Relative to an ideal achromatic waveplate in which A Re =A Rth =0.818 and B Re =B Rth =1.182, the data in Table 2 show that these films did not exhibit a reversed dispersion. In fact, the values for A Re  and B Re  indicate that the films exhibited a normal dispersion. 
       Example 4 
     Comparative 
       [0099]    This example shows the optical retardation and dispersion of a single-layer film suitable for layer A in an optical waveplate. 
         [0100]    Following the general solution preparation, a randomly (RDS: C 6 =0.85, C 3 =0.92, C 2 =0.90) substituted cellulose acetate propionate (DS Ac =0.79, DS Pr =2.00, DS OH =0.21) was used to prepare the following solution for Example 4: 
         [0000]    
       
         
               
               
               
               
             
           
               
                   
                   
               
             
             
               
                   
                 Total solids 
                 24 
                 g 
               
               
                   
                 Cellulose ester 
                 21.6 
                 g 
               
               
                   
                 Plasticizer 
                 2.4 
                 g Triphenyl phosphate 
               
               
                   
                 Total solvent 
                 176 
                 g 
               
               
                   
                 Methylene chloride 
                 153.12 
                 g 
               
               
                   
                 Methanol 
                 22.88 
                 g 
               
               
                   
                   
               
             
          
         
       
     
         [0101]    Following the general solvent cast procedures described above, the solution for Example 4 was used to obtain single-layer films. The films were annealed at 100° C. and 120° C. for 10 minutes, respectively, before they were uniaxially or simultaneous biaxially stretched under different stretching conditions. The stretching conditions and optical and film data of these films are listed in Table 4. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 4 
               
             
             
               
                   
               
               
                 Optical properties for a single-layer cellulose acetate propionate film 
               
               
                 (DS Ac  = 0.79, DS Pr  = 2.00, DS OH  = 0.21). 
               
             
          
           
               
                   
                   
                 Stretch 
                   
                   
                   
                   
                   
                   
                 Film 
               
               
                   
                   
                 Temp. 
                 R e   
                 R th   
                   
                   
                   
                   
                 Thickness 
               
               
                 Run 
                 MD × TD 
                 (° C.) 
                 (nm) 
                 (nm) 
                 A Re   
                 B Re   
                 A Rth   
                 B Rth   
                 (micron) 
               
               
                   
               
               
                 21  
                 1.00 × 1.50 
                 150 
                 12.81 
                 −30.81 
                 0.577 
                 1.226 
                 0.807 
                 1.158 
                 64 
               
               
                 22  
                 1.00 × 1.60 
                 150 
                 14.25 
                 −31.83 
                 0.538 
                 1.251 
                 0.807 
                 1.161 
                 58 
               
               
                 23  
                 1.00 × 1.70 
                 150 
                 15.26 
                 −30.57 
                 0.494 
                 1.270 
                 0.810 
                 1.170 
                 58 
               
               
                 24* 
                 1.00 × 1.70 
                 150 
                 33.70 
                 −23.44 
                 0.522 
                 1.260 
                 0.644 
                 1.297 
                 82 
               
               
                 25* 
                 1.00 × 1.80 
                 150 
                 33.49 
                 −23.39 
                 0.542 
                 1.245 
                 0.682 
                 1.296 
                 72 
               
               
                 26* 
                 1.00 × 1.90 
                 150 
                 35.07 
                 −23.43 
                 0.516 
                 1.259 
                 0.656 
                 1.305 
                 74 
               
               
                 27* 
                 1.00 × 2.00 
                 150 
                 34.31 
                 −21.65 
                 0.505 
                 1.267 
                 0.623 
                 1.391 
                 72 
               
               
                   
               
               
                 *= The film was not constrained in the MD while stretching. 
               
             
          
         
       
     
         [0102]    Relative to an ideal achromatic waveplate in which A Re =A Rth =0.818 and B Re =B Rth =1.182, the data in Table 4 show that these films did exhibit a reversed dispersion. However, the smaller values for A Re  (0.49-0.58) and the larger values for B Re  (1.22-1.27) showed that the slopes were much larger than that of an ideal achromatic waveplate (cf.  FIG. 2 ). Moreover, the R th  values (−22 to −32) were too small to be suitable for use in certain LCDs. 
       Example 5 
     Comparative 
       [0103]    This example shows the optical retardation and dispersion of a single-layer film suitable for layer A in an optical waveplate. 
         [0104]    Following the general solution preparation, a randomly (RDS: C 6 =0.84, C 3 =0.92, C 2 =0.88) substituted cellulose acetate propionate (DS Ac =0.04, DS Pr =2.69, DS OH =0.27) was used to prepare the following solution for Example 5: 
         [0000]    
       
         
               
               
               
               
             
           
               
                   
                   
               
             
             
               
                   
                 Total solids 
                 24 
                 g 
               
               
                   
                 Cellulose ester 
                 21.6 
                 g 
               
               
                   
                 Plasticizer 
                 2.4 
                 g Triphenyl phosphate 
               
               
                   
                 Total solvent 
                 176 
                 g 
               
               
                   
                 Methylene chloride 
                 153.12 
                 g 
               
               
                   
                 Methanol 
                 22.88 
                 g 
               
               
                   
                   
               
             
          
         
       
     
         [0105]    Following the general solvent cast procedures described above, the solution for Example 5 was used to obtain single-layer films. The films were annealed at 100° C. and 120° C. for 10 minutes, respectively, before they were uniaxially or simultaneous biaxially stretched under different stretching conditions. The stretching conditions and optical and film data of these films are listed in Table 5. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 5 
               
             
             
               
                   
               
               
                 Optical properties for a single-layer cellulose acetate propionate film 
               
               
                 (DS Ac  = 0.04, DS Pr  = 2.69, DS OH  = 0.27). 
               
             
          
           
               
                   
                   
                 Stretch 
                   
                   
                   
                   
                   
                   
                 Film 
               
               
                   
                   
                 Temp. 
                 R e   
                 R th   
                   
                   
                   
                   
                 Thickness 
               
               
                 Run 
                 MD × TD 
                 (° C.) 
                 (nm) 
                 (nm) 
                 A Re   
                 B Re   
                 A Rth   
                 B Re   
                 (micron) 
               
               
                   
               
               
                 28  
                 1.00 × 1.50 
                 135 
                 19.55 
                 −45.12 
                 0.762 
                 1.127 
                 0.903 
                 1.083 
                 60 
               
               
                 29  
                 1.00 × 1.60 
                 135 
                 21.48 
                 −43.29 
                 0.738 
                 1.139 
                 0.893 
                 1.091 
                 56 
               
               
                 30* 
                 1.00 × 1.60 
                 135 
                 46.57 
                 −30.96 
                 0.775 
                 1.121 
                 0.818 
                 1.150 
                 76 
               
               
                 31* 
                 1.00 × 1.70 
                 135 
                 49.39 
                 −30.41 
                 0.763 
                 1.129 
                 0.804 
                 1.162 
                 74 
               
               
                 32* 
                 1.00 × 1.80 
                 135 
                 48.19 
                 −29.15 
                 0.749 
                 1.135 
                 0.799 
                 1.173 
                 72 
               
               
                 33  
                 1.00 × 1.70 
                 135 
                 34.88 
                 −38.98 
                 0.742 
                 1.141 
                 0.856 
                 1.118 
                 68 
               
               
                 34* 
                 1.00 × 2.00 
                 135 
                 47.98 
                 −29.41 
                 0.722 
                 1.147 
                 0.773 
                 1.197 
                 72 
               
               
                   
               
               
                 *= The film was not constrained in the MD while stretching. 
               
             
          
         
       
     
         [0106]    Relative to an ideal achromatic waveplate in which A Re =A Rth =0.818 and B Re =B Rth =1.182, the data in Table 5 show that these films did exhibit a reversed dispersion, but with a different slope (cf.  FIG. 2 ). Again, the R th  values (−29 to −45) were too small to be suitable for use in certain LCDs. 
       Example 6 
       [0107]    This example shows the optical retardation and dispersion of a bi-layer optical waveplate prepared by solvent co-casting. 
         [0108]    A randomly (RDS: C 6 =0.92, C 3 =1.00, C 2 =0.96) substituted cellulose acetate propionate (DS Ac =1.49, DS Pr =1.44, DS OH =0.07) was used to prepare the following solution for layer A for Example 6: 
         [0000]    
       
         
               
               
               
               
             
               
               
               
             
               
               
               
               
             
           
               
                   
                   
               
             
             
               
                   
                 Total solids 
                 24 
                 g 
               
               
                   
                 Cellulose ester 
                 21.6 
                 g 
               
             
          
           
               
                   
                 Plasticizer 
                 2.4 g Xylitol Pentaacetate 
               
             
          
           
               
                   
                 Total solvent 
                 276 
                 g 
               
               
                   
                 Methylene chloride 
                 240.12 
                 g 
               
               
                   
                 Methanol 
                 35.88 
                 g 
               
               
                   
                   
               
             
          
         
       
     
         [0109]    A randomly substituted cellulose acetate propionate (IDS Ac =0.14, DS Pr =1.71, DS OH =1.15) was used to prepare the following solution for layer B for Example 6: 
         [0000]    
       
         
               
               
               
               
             
               
               
               
             
               
               
               
               
             
           
               
                   
                   
               
             
             
               
                   
                 Total solids 
                 24 
                 g 
               
               
                   
                 Cellulose ester 
                 21.6 
                 g 
               
             
          
           
               
                   
                 Plasticizer 
                 2.4 g Triphenyl phosphate 
               
             
          
           
               
                   
                 Total solvent 
                 176 
                 g 
               
               
                   
                 Methylene chloride 
                 153.12 
                 g 
               
               
                   
                 Methanol 
                 22.88 
                 g 
               
               
                   
                   
               
             
          
         
       
     
         [0110]    Following the general procedure for solution preparation, solutions for layers A and B were independently prepared. The solution for layer B was first cast on a glass plate with a doctor blade at a certain thickness and covered by a pan for 5 minutes. The solution for layer A was then cast on top of the layer B and covered by a pan for 45 minutes. The cover pan was removed and the bi-layer film was left on the glass plate for an additional 15 minutes. The film was peeled from the glass plate then annealed at 100° C. and 120° C. for 10 minutes, respectively. Films made in this manner were uniaxially or simultaneous biaxially stretched under different stretching conditions. The stretching conditions and optical and film data of these films are listed in Table 6. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 6 
               
             
             
               
                   
               
               
                 Optical properties for a bi-layer optical waveplate prepared by co-casting. 
               
             
          
           
               
                   
                   
                 Stretch 
                   
                   
                   
                   
                   
                   
                 Film 
                   
               
               
                   
                   
                 Temp. 
                 R e   
                 R th   
                   
                   
                   
                   
                 Thickness 
                 Haze 
               
               
                 Run 
                 MD × TD 
                 (° C.) 
                 (nm) 
                 (nm) 
                 A Re   
                 B Re   
                 A Rth   
                 B Rth   
                 (micron) 
                 (%) 
               
               
                   
               
             
          
           
               
                 35 
                 1.00 × 1.30 
                 165 
                 116.85 
                 −266.08 
                 0.972 
                 1.015 
                 0.975 
                 1.016 
                 100 
                 0.44 
               
               
                 36 
                 1.10 × 1.40 
                 170 
                 80.86 
                 −268.99 
                 0.964 
                 1.020 
                 0.973 
                 1.018 
                 80 
                 0.47 
               
               
                 37 
                 1.00 × 1.27 
                 165 
                 97.43 
                 −241.59 
                 0.972 
                 1.015 
                 0.971 
                 1.020 
                 88 
                 0.56 
               
               
                 38 
                 1.05 × 1.40 
                 170 
                 94.07 
                 −266.24 
                 0.966 
                 1.017 
                 0.978 
                 1.014 
                 84 
                 0.42 
               
               
                 39 
                 1.03 × 1.40 
                 175 
                 92.83 
                 −206.28 
                 0.965 
                 1.017 
                 0.973 
                 1.017 
                 82 
                 0.36 
               
               
                   
               
             
          
         
       
     
         [0111]    As shown in Example 1, as a single-layer film, the cellulose ester used to make layer B exhibited large positive values for R e  and large negative values for R th , but the film exhibited a flat dispersion. As shown in Example 2, as a single-layer film, the cellulose ester used to make layer A exhibited negative R e  values and positive R th  values, and the film exhibited a normal dispersion. 
         [0112]    In accordance with this invention, when the two cellulose esters were used to construct a bi-layer optical waveplate, the R e  and R th  values of the two cellulose esters were additive. As used herein, the term “additive” does not necessarily refer to the arithmetic sum of the two values, but is simply used in the sense that the absolute value of R e  decreased relative to Example 1 and increased relative to Example 2. Similarly, the absolute value for R th  decreased relative to Example 1 and increased relative to Example 2. Significantly, the bi-layer optical waveplate now exhibited a reversed dispersion. It is important to note that layers A and B did not have a special orientation with respect to each other. Furthermore, as the data in Table 6 show, these films have very low haze. Hence, the bi-layer optical waveplate simultaneously provided high optical retardation and a reversed dispersion. 
       Example 7 
       [0113]    This example shows the optical retardation and dispersion of a tri-layer optical waveplate prepared by solvent co-casting. 
         [0114]    The solutions for layer A and layer B were the same as those in Example 6. 
         [0115]    The solution for layer A was first cast on a glass plate with a doctor blade at a certain thickness and covered by a pan for 4 minutes. The solution for layer B was then cast on top of the layer A and covered by a pan for 4 minutes. Then a third layer using solution A was cast on top of the layer B and covered by a pan for 45 minutes. The cover pan was removed and the tri-layer film was left on the glass plate for an additional 15 minutes. The film was peeled from the glass plate then annealed at 100° C. and 120° C. for 10 minutes, respectively. Films made in this manner were uniaxially or simultaneous biaxially stretched under different stretching conditions. The stretching conditions and optical and film data of these films are listed in Table 7. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 7 
               
             
             
               
                   
               
               
                 Optical properties for a tri-layer optical waveplate prepared by co-casting. 
               
             
          
           
               
                   
                   
                 Stretch 
                   
                   
                   
                   
                   
                   
                 Film 
                   
               
               
                   
                   
                 Temp. 
                 R e   
                 R th   
                   
                   
                   
                   
                 Thickness 
                 Haze 
               
               
                 Run 
                 MD × TD 
                 (° C.) 
                 (nm) 
                 (nm) 
                 A Re   
                 B Re   
                 A Rth   
                 B Rth   
                 (micron) 
                 (%) 
               
               
                   
               
             
          
           
               
                 40 
                 1.00 × 1.30 
                 170 
                 90.86 
                 −251.57 
                 0.971 
                 1.015 
                 0.981 
                 1.009 
                 80 
                 0.33 
               
               
                 41 
                 1.00 × 1.30 
                 170 
                 85.73 
                 −244.95 
                 0.971 
                 1.016 
                 0.983 
                 1.010 
                 78 
                 0.35 
               
               
                 42 
                 1.00 × 1.35 
                 175 
                 114.23 
                 −276.40 
                 0.967 
                 1.018 
                 0.981 
                 1.011 
                 88 
                 0.36 
               
               
                 43 
                 1.00 × 1.35 
                 175 
                 100.41 
                 −249.56 
                 0.971 
                 1.016 
                 0.980 
                 1.011 
                 78 
                 0.32 
               
               
                   
               
             
          
         
       
     
         [0116]    Similar to Example 6, when the two cellulose esters were used to construct a tri-layer optical waveplate, the R e  and R th  values of the two cellulose esters were additive, and reversed dispersion and low haze were obtained. Thus, the tri-layer optical waveplate simultaneously provided high optical retardation and a reversed dispersion. By varying the cellulose ester for each layer, layer thickness, and stretching and annealing conditions, it was possible to construct optical waveplates with a range of R e  and R th  values, and reversed dispersion. 
       Example 8 
       [0117]    This example shows the optical retardation and dispersion of a bi-layer optical waveplate prepared by solvent coating. 
         [0118]    The solutions for layer A and layer B were the same as those of Example 6. 
         [0119]    The solution for layer B was first cast on a glass plate with a doctor blade at a certain thickness and covered by a pan for 45 minutes. The cover pan was removed and the film was left on the glass plate for an additional 15 minutes. The solution for layer A was then coated on top of layer B at a thickness much less than layer B. The coated film was then covered by a pan for 20 minutes. The cover pan was removed and the coated film was left on the glass plate for an additional 20 minutes. The film was peeled from the glass plate then annealed at 100° C. and 120° C. for 10 minutes, respectively. Films made in this manner were uniaxially or simultaneous biaxially stretched under different stretching conditions. The stretching conditions and optical and film data of these films are listed in Table 8. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 8 
               
             
             
               
                   
               
               
                 Optical retardation and dispersion of a bi-layer 
               
               
                 optical waveplate prepared by solvent coating. 
               
             
          
           
               
                   
                   
                 Stretch 
                   
                   
                   
                   
                   
                   
                 Film 
                   
               
               
                   
                   
                 Temp. 
                 R e   
                 R th   
                   
                   
                   
                   
                 Thickness 
                 Haze 
               
               
                 Run 
                 MD × TD 
                 (° C.) 
                 (nm) 
                 (nm) 
                 A Re   
                 B Re   
                 A Rth   
                 B Rth   
                 (micron) 
                 (%) 
               
               
                   
               
             
          
           
               
                 44 
                 1.00 × 1.30 
                 175 
                 89.43 
                 −263.71 
                 0.979 
                 1.011 
                 0.982 
                 1.009 
                 66 
                 0.73 
               
               
                 45 
                 1.00 × 1.40 
                 175 
                 114.57 
                 −274.07 
                 0.976 
                 1.014 
                 0.981 
                 1.009 
                 64 
                 1.89 
               
               
                 46 
                 1.00 × 1.30 
                 175 
                 96.81 
                 −253.28 
                 0.979 
                 1.012 
                 0.983 
                 1.009 
                 72 
                 0.46 
               
               
                 47 
                 1.00 × 1.35 
                 180 
                 112.35 
                 −260.85 
                 0.979 
                 1.012 
                 0.980 
                 1.012 
                 70 
                 0.56 
               
               
                 48 
                 1.00 × 1.40 
                 180 
                 122.34 
                 −293.01 
                 0.978 
                 1.012 
                 0.979 
                 1.012 
                 66 
                 0.91 
               
               
                   
               
             
          
         
       
     
         [0120]    Similar to Example 6, when the two cellulose esters were used to construct a bi-layer optical waveplate, the R e  and R th  values of the two cellulose esters were additive. In Example 6, the bi-layer optical waveplate was prepared by solvent co-casting while in this example, the bi-layer optical waveplate was prepared by coating dried layer B with the solution of layer A. Comparing the data in Table 8 with those in Table 6, it is evident the optical retardations and dispersions are very similar. Namely, both bi-layer optical waveplates simultaneously provided high optical retardation and a reversed dispersion. Further, the haze in both examples was low. Hence, this example shows that optical waveplates with a reversed dispersion can be prepared by a coating process. 
       Example 9 
     Comparative 
       [0121]    This example shows the optical retardation and dispersion of a film prepared by solvent blending and casting. 
         [0122]    A single solution comprising two cellulose esters was prepared according to the general solution preparation process. The cellulose esters in the solution were the same as those in Example 6: 
         [0000]    
       
         
               
               
               
               
             
               
               
               
             
               
               
               
               
             
           
               
                   
                   
               
             
             
               
                   
                 Total solids 
                 24 
                 g 
               
             
          
           
               
                   
                 Cellulose ester A 
                 2.16 g or 4.32 g of a randomly 
               
               
                   
                   
                 substituted cellulose acetate 
               
               
                   
                   
                 propionate (DS Ac  = 1.49, 
               
               
                   
                   
                 DS Pr  = 1.44, DS OH  = 0.07) 
               
               
                   
                 Cellulose ester B 
                 19.44 g or 17.28 g of a randomly 
               
               
                   
                   
                 substituted cellulose acetate 
               
               
                   
                   
                 propionate (DS Ac  = 0.14, 
               
               
                   
                   
                 DS Pr  = 1.71, DS OH  = 1.15) 
               
               
                   
                 Plasticizer 
                 2.4 g Triphenyl phosphate 
               
             
          
           
               
                   
                 Total solvent 
                 176 
                 g 
               
               
                   
                 Methylene chloride 
                 153.12 
                 g 
               
               
                   
                 Methanol 
                 22.88 
                 g 
               
               
                   
                   
               
             
          
         
       
     
         [0123]    Following the general solvent cast procedures described above, the solution was used to obtain single-layer films. The films were annealed at 100° C. and 120° C. for 10 minutes, respectively, before they were uniaxially or simultaneous biaxially stretched under different stretching conditions. The stretching conditions and optical and film data of these films are listed in Table 9. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 9 
               
             
             
               
                   
               
               
                 Optical retardation and dispersion of film prepared by solvent blending and casting. 
               
             
          
           
               
                   
                   
                   
                 Stretch 
                   
                   
                   
                   
                   
                   
                 Film 
                   
               
               
                   
                 Ester A 
                   
                 Temp. 
                 R e   
                 R th   
                   
                   
                   
                   
                 Thickness 
                 Haze 
               
               
                 Run 
                 (wt %) 
                 MD × TD 
                 (° C.) 
                 (nm) 
                 (nm) 
                 A Re   
                 B Re   
                 A Rth   
                 B Rth   
                 (micron) 
                 (%) 
               
               
                   
               
             
          
           
               
                 49 
                 10 
                 1.00 × 1.30 
                 165 
                 88.74 
                 −277.78 
                 0.984 
                 1.009 
                 1.010 
                 0.983 
                 60 
                 3.78 
               
               
                 50 
                   
                 1.00 × 1.27 
                 165 
                 89.63 
                 −286.97 
                 0.983 
                 1.009 
                 1.013 
                 0.981 
                 76 
                 4.5 
               
               
                 51 
                   
                 1.00 × 1.27 
                 165 
                 95.23 
                 −315.38 
                 0.984 
                 1.008 
                 1.036 
                 0.964 
                 76 
                 5.67 
               
               
                 52 
                   
                 1.00 × 1.30 
                 170 
                 83.44 
                 −242.84 
                 0.984 
                 1.009 
                 1.012 
                 0.983 
                 58 
                 4.52 
               
               
                 53 
                 20 
                 1.00 × 1.35 
                 165 
                 88.46 
                 −297.08 
                 0.977 
                 1.010 
                 1.108 
                 0.909 
                 62 
                 13.61 
               
               
                 54 
                   
                 1.00 × 1.40 
                 170 
                 96.47 
                 −279.68 
                 0.977 
                 1.012 
                 1.108 
                 0.907 
                 60 
                 13.4 
               
               
                 55 
                   
                 1.00 × 1.35 
                 165 
                 88.43 
                 −296.38 
                 0.976 
                 1.013 
                 1.110 
                 0.906 
                 60 
                 12.81 
               
               
                   
               
             
          
         
       
     
         [0124]    Similar to Examples 6 and 8, the R e  and R th  of these single-layer blended films showed an additive effect. However, the film haze was much higher in this example than in Examples 6 and 8. The higher film haze would not be acceptable in LCDs where clarity is important. The higher haze in this example is believed to be a result of the two cellulose esters being incompatible as a blend. 
         [0125]    This example also illustrates that it is not necessary to intimately blend the two cellulose esters in order to obtain the R e  and R th  additive effect. Discrete layers formed by co-casting or coating processes without specific orientation with respect to each layer can lead to the same R e  and R th  additive effect. By having discrete layers, issues such as incompatibility can be avoided. 
       Example 10 
       [0126]    This example shows the optical retardation and dispersion of a tri-layer optical waveplate prepared by solvent co-casting. 
         [0127]    A randomly (RDS: C 6 =0.92, C 3 =1.00, C 2 =0.96) substituted cellulose acetate propionate (DS Ac =1.49, DS Pr =1.44, DS OH =0.07) was used to prepare the following solution for layer A for Example 10: 
         [0000]    
       
         
               
               
               
               
             
               
               
               
             
               
               
               
               
             
           
               
                   
                   
               
             
             
               
                   
                 Total solids 
                 24 
                 g 
               
               
                   
                 Cellulose ester 
                 21.6 
                 g 
               
             
          
           
               
                   
                 Plasticizer 
                 2.4 g Xylitol Pentaacetate 
               
             
          
           
               
                   
                 Total solvent 
                 276 
                 g 
               
               
                   
                 Methylene chloride 
                 240.12 
                 g 
               
               
                   
                 Methanol 
                 35.88 
                 g 
               
               
                   
                   
               
             
          
         
       
     
         [0128]    A randomly (RDS: C 6 =0.55, C 3 =0.69, C 2 =0.68) substituted cellulose acetate propionate (DS Ac =1.41, DS Pr =0.61, DS OH =0.98) was used to prepare the following solution for layer B for Example 10: 
         [0000]    
       
         
               
               
               
               
             
               
               
               
             
               
               
               
               
             
           
               
                   
                   
               
             
             
               
                   
                 Total solids 
                 24 
                 g 
               
               
                   
                 Cellulose ester 
                 21.6 
                 g 
               
             
          
           
               
                   
                 Plasticizer 
                 2.4 g Triphenyl phosphate 
               
             
          
           
               
                   
                 Total solvent 
                 176 
                 g 
               
               
                   
                 Methylene chloride 
                 153.12 
                 g 
               
               
                   
                 Methanol 
                 22.88 
                 g 
               
               
                   
                   
               
             
          
         
       
     
         [0129]    Following the general procedure for solution preparation, solutions for layers A and B were independently prepared. The solution for layer A was first cast on a glass plate with a doctor blade at a certain thickness and covered by a pan for 4 minutes. The solution for layer B was then cast on top of the layer A and covered by a pan for 4 minutes. Then a third layer using solution A was cast on top of the layer B and covered by a pan for 45 minutes. The cover pan was removed and the tri-layer film was left on the glass plate for an additional 15 minutes. The film was peeled from the glass plate then annealed at 100° C. and 120° C. for 10 minutes, respectively. Films made in this manner were uniaxially or simultaneous biaxially stretched under different stretching conditions. The stretching conditions and optical and film data of these films are listed in Table 10. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 10 
               
             
             
               
                   
               
               
                 Optical retardation and dispersion of a tri-layer 
               
               
                 optical waveplate prepared by solvent co-casting. 
               
             
          
           
               
                   
                   
                 Stretch 
                   
                   
                   
                   
                   
                   
                 Film 
               
               
                   
                   
                 Temp. 
                 R e   
                 R th   
                   
                   
                   
                   
                 Thickness 
               
               
                 Run 
                 MD × TD 
                 (° C.) 
                 (nm) 
                 (nm) 
                 A Re   
                 B Re   
                 A Rth   
                 B Rth   
                 (micron) 
               
               
                   
               
             
          
           
               
                 56 
                 1.00 × 1.30 
                 180 
                 64.19 
                 −85.87 
                 0.945 
                 1.031 
                 0.927 
                 1.059 
                 126 
               
               
                 57 
                 1.00 × 1.40 
                 180 
                 116.18 
                 −227.82 
                 0.946 
                 1.030 
                 0.956 
                 1.030 
                 128 
               
               
                 58 
                 1.00 × 1.35 
                 180 
                 83.61 
                 −183.41 
                 0.943 
                 1.032 
                 0.953 
                 1.034 
                 102 
               
               
                   
               
             
          
         
       
     
         [0130]    The cellulose ester used in layer B in this example was similar to the cellulose ester of Example 1 in that as a single-layer film the cellulose ester exhibited large positive values for R e  and large negative values for R th , but the film exhibited a flat dispersion. As shown in Example 2, as a single-layer film, the cellulose ester used to make layer A exhibited negative R e  values and positive R th  values, and the film exhibited a normal dispersion. Similar to Example 7, when the two cellulose esters here were used to construct a tri-layer optical waveplate, the R e  and R th  values of the two cellulose esters were additive. In addition, the tri-layer optical waveplate simultaneously provided high optical retardation and a reversed dispersion. 
         [0131]    Comparing the data in Table 10 to those in Table 7, it can be seen that the values for A Re  and B Re  as well as for A Rth  and B Rth  in this example were closer to those of an ideal achromatic waveplate. This example illustrates that the cellulose ester in each layer is a factor in constructing optical waveplates. 
       Example 11 
       [0132]    This example shows the optical retardation and dispersion of a tri-layer optical waveplate prepared by solvent co-casting. 
         [0133]    A regioselectively (RDS: C 6 =1.00, C 3 =0.68, C 2 =0.84) substituted cellulose benzoate propionate in which the benzoate was primarily located on C 2  and C 3  (DS Bs =0.29, DS Pr =2.26, DS OH =0.45) (which was prepared according to U.S. patent application Ser. No. 12/539,817) was used to prepare the following solution for layer A for Example 11: 
         [0000]    
       
         
               
               
               
               
             
               
               
               
             
               
               
               
               
             
           
               
                   
                   
               
             
             
               
                   
                 Total solids 
                 24 
                 g 
               
               
                   
                 Cellulose ester 
                 21.6 
                 g 
               
             
          
           
               
                   
                 Plasticizer 
                 2.4 g Triphenyl phosphate 
               
             
          
           
               
                   
                 Total solvent 
                 276 
                 g 
               
               
                   
                 Methylene chloride 
                 240.12 
                 g 
               
               
                   
                 Methanol 
                 35.88 
                 g 
               
               
                   
                   
               
             
          
         
       
     
         [0134]    A randomly (RDS: C 6 =0.55, C 3 =0.69, C 2 =0.68) substituted cellulose acetate propionate (DS Ac =1.41, DS Pr =0.61, DS OH =0.98) was used to prepare the following solution for layer B for Example 11: 
         [0000]    
       
         
               
               
               
               
             
               
               
               
             
               
               
               
               
             
           
               
                   
                   
               
             
             
               
                   
                 Total solids 
                 24 
                 g 
               
               
                   
                 Cellulose ester 
                 21.6 
                 g 
               
             
          
           
               
                   
                 Plasticizer 
                 2.4 g Triphenyl phosphate 
               
             
          
           
               
                   
                 Total solvent 
                 176 
                 g 
               
               
                   
                 Methylene chloride 
                 153.12 
                 g 
               
               
                   
                 Methanol 
                 22.88 
                 g 
               
               
                   
                   
               
             
          
         
       
     
         [0135]    Following the general procedure for solution preparation, solutions for layers A and B were independently prepared. The solution for layer A was first cast on a glass plate with a doctor blade at a certain thickness and covered by a pan for 4 minutes. The solution for layer B was then cast on top of the layer A and covered by a pan for 4 minutes. Then a third layer using solution A was cast on top of the layer B and covered by a pan for 45 minutes. The cover pan was removed and the tri-layer film was left on the glass plate for an additional 15 minutes. The film was peeled from the glass plate then annealed at 100° C. and 120° C. for 10 minutes, respectively. Films made in this manner were uniaxially or simultaneous biaxially stretched under different stretching conditions. The stretching conditions and optical and film data of these films are listed in Table 11. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 11 
               
             
             
               
                   
               
               
                 Optical retardation and dispersion of a tri-layer 
               
               
                 optical waveplate prepared by solvent co-casting. 
               
             
          
           
               
                   
                   
                 Stretch 
                   
                   
                   
                   
                   
                   
                 Film 
               
               
                   
                   
                 Temp. 
                 R e   
                 R th   
                   
                   
                   
                   
                 Thickness 
               
               
                 Run 
                 MD × TD 
                 (° C.) 
                 (nm) 
                 (nm) 
                 A Re   
                 B Re   
                 A Rth   
                 B Rth   
                 (micron) 
               
               
                   
               
             
          
           
               
                 59 
                 1.00 × 1.25 
                 180 
                 70.72 
                 −309.59 
                 0.936 
                 1.031 
                 0.971 
                 1.017 
                 102 
               
               
                 60 
                 1.00 × 1.30 
                 180 
                 92.13 
                 −314.29 
                 0.930 
                 1.033 
                 0.971 
                 1.018 
                 104 
               
               
                 61 
                 1.00 × 1.30 
                 180 
                 87.60 
                 −292.64 
                 0.933 
                 1.035 
                 0.971 
                 1.019 
                 98 
               
               
                 62 
                 1.00 × 1.35 
                 180 
                 98.41 
                 −297.14 
                 0.925 
                 1.038 
                 0.967 
                 1.021 
                 102 
               
               
                   
               
             
          
         
       
     
         [0136]    The cellulose ester used in layer B of this example was the same cellulose ester used in Example 10, and it is similar to the cellulose ester of Example 1 in that as a single-layer film, the cellulose ester exhibited large positive values for R e  and large negative values for R th , but the film exhibited a flat dispersion. As shown in Example 3, as a single-layer film, the cellulose ester used to make layer A exhibited negative R e  values and positive or negative R th  values depending upon stretching conditions and the film exhibited a normal dispersion. Similar to Examples 7 and 10, when the two cellulose esters here were used to construct a tri-layer optical waveplate, the R e  and R th  values of the two cellulose esters were additive. 
         [0137]    Comparing the data in Table 11 with those in Table 10, it can be seen that larger R th  values were obtained in this example. The values for A Re  and B Re  as well as for A Rth  and B Rth  in this example indicate that the optical waveplate exhibited a reversed dispersion with a slope different from that found in Example 10. This example illustrates that the cellulose ester of each layer is a factor in constructing optical waveplates. 
       Example 12 
       [0138]    This example shows the optical retardation and dispersion of a tri-layer optical waveplate prepared by solvent co-casting. 
         [0139]    A randomly (RDS: C 6 =0.92, C 3 =1.00, C 2 =0.96) substituted cellulose acetate propionate (DS Ac =1.49, DS Pr =1.44, DS OH =0.07) was used to prepare the following solution for layer A for Example 12: 
         [0000]    
       
         
               
               
               
               
             
               
               
               
             
               
               
               
               
             
           
               
                   
                   
               
             
             
               
                   
                 Total solids 
                 24 
                 g 
               
               
                   
                 Cellulose ester 
                 21.6 
                 g 
               
             
          
           
               
                   
                 Plasticizer 
                 2.4 g Xylitol Pentaacetate 
               
             
          
           
               
                   
                 Total solvent 
                 276 
                 g 
               
               
                   
                 Methylene chloride 
                 240.12 
                 g 
               
               
                   
                 Methanol 
                 35.88 
                 g 
               
               
                   
                   
               
             
          
         
       
     
         [0140]    A randomly (RDS: C 6 =0.61, C 3 =0.72, C 2 =0.74) substituted cellulose acetate propionate (DS Ac =1.24, DS Pr =0.95, DS OH =0.81) was used to prepare the following solution for layer B for Example 12: 
         [0000]    
       
         
               
               
               
               
             
               
               
               
             
               
               
               
               
             
           
               
                   
                   
               
             
             
               
                   
                 Total solids 
                 24 
                 g 
               
               
                   
                 Cellulose ester 
                 21.6 
                 g 
               
             
          
           
               
                   
                 Plasticizer 
                 2.4 g Triphenyl phosphate 
               
             
          
           
               
                   
                 Total solvent 
                 176 
                 g 
               
               
                   
                 Methylene chloride 
                 153.12 
                 g 
               
               
                   
                 Methanol 
                 22.88 
                 g 
               
               
                   
                   
               
             
          
         
       
     
         [0141]    Following the general procedure for solution preparation, solutions for layers A and B were independently prepared. The solution for layer A was first cast on a glass plate with a doctor blade at a certain thickness and covered by a pan for 4 minutes. The solution for layer B was then cast on top of the layer A and covered by a pan for 4 minutes. Then a third layer using solution A was cast on top of the layer B and covered by a pan for 45 minutes. The cover pan was removed and the tri-layer film was left on the glass plate for an additional 15 minutes. The film was peeled from the glass plate then annealed at 100° C. and 120° C. for 10 minutes, respectively. Films made in this manner were uniaxially or simultaneous biaxially stretched under different stretching conditions. The stretching conditions and optical and film data of these films are listed in Table 12. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 12 
               
             
             
               
                   
               
               
                 Optical retardation and dispersion of a tri-layer 
               
               
                 optical waveplate prepared by solvent co-casting. 
               
             
          
           
               
                   
                   
                 Stretch 
                   
                   
                   
                   
                   
                   
                 Film 
               
               
                   
                   
                 Temp. 
                 R e   
                 R th   
                   
                   
                   
                   
                 Thickness 
               
               
                 Run 
                 MD × TD 
                 (° C.) 
                 (nm) 
                 (nm) 
                 A Re   
                 B Re   
                 A Rth   
                 B Rth   
                 (micron) 
               
               
                   
               
             
          
           
               
                 63 
                 1.00 × 1.40 
                 177 
                 65.90 
                 −144.63 
                 0.936 
                 1.037 
                 0.943 
                 1.043 
                 102 
               
               
                 64 
                 1.00 × 1.50 
                 177 
                 82.34 
                 −144.90 
                 0.930 
                 1.037 
                 0.940 
                 1.044 
                 94 
               
               
                 65 
                 1.00 × 1.40 
                 180 
                 62.98 
                 −125.11 
                 0.939 
                 1.033 
                 0.938 
                 1.050 
                 98 
               
               
                 66 
                 1.00 × 1.50 
                 180 
                 71.68 
                 −129.04 
                 0.941 
                 1.034 
                 0.938 
                 1.047 
                 94 
               
               
                   
               
             
          
         
       
     
         [0142]    The cellulose ester used in layer B of this example was similar to the cellulose ester of Example 1 in that as a single-layer film, the cellulose ester exhibited large positive values for R e  and large negative values for R th , but the film exhibited a flat dispersion. As shown in Example 2, as a single-layer film, the cellulose ester used to make layer A exhibited negative R e  values and positive R th  values, and the film exhibited a normal dispersion. Layer A in this example was the same as that used in Example 10. Similar to Example 10, when the cellulose esters here were used to construct a tri-layer optical waveplate, the R e  and R th  values of the two cellulose esters were additive. 
         [0143]    In this example, the tri-layer optical waveplate simultaneously provided high optical retardation and a reversed dispersion. Comparing the data in Table 12 with those in Table 10, it can be seen that the values for A Re  and B Re  in this example indicate that the dispersion was more reversed relative to Example 10. This example illustrates that the cellulose ester for each layer is a factor in constructing optical waveplates with desired optical retardation and a reversed dispersion. 
       Example 13 
       [0144]    This example shows the optical retardation and dispersion of a tri-layer optical waveplate prepared by solvent co-casting. 
         [0145]    A regioselectively (RDS: C 6 =1.00, C 3 =0.68, C 2 =0.84) substituted cellulose benzoate propionate in which the benzoate was primarily located on C 2  and C 3  (DS Bz =0.29, DS Pr =2.26, DS OH =0.45), prepared according to U.S. patent application Ser. No. 12/539,817, was used to prepare the following solution for layer A for Example 13: 
         [0000]    
       
         
               
               
               
               
             
               
               
               
             
               
               
               
               
             
           
               
                   
                   
               
             
             
               
                   
                 Total solids 
                 24 
                 g 
               
               
                   
                 Cellulose ester 
                 21.6 
                 g 
               
             
          
           
               
                   
                 Plasticizer 
                 2.4 g Triphenyl phosphate 
               
             
          
           
               
                   
                 Total solvent 
                 276 
                 g 
               
               
                   
                 Methylene chloride 
                 240.12 
                 g 
               
               
                   
                 Methanol 
                 35.88 
                 g 
               
               
                   
                   
               
             
          
         
       
     
         [0146]    A randomly (RDS: C 6 =0.61, C 3 =0.72, C 2 =0.74) substituted cellulose acetate propionate (DS Ac =1.24, DS Pr =0.95, DS OH =0.81) was used to prepare the following solution for layer B for Example 13: 
         [0000]    
       
         
               
               
               
               
             
               
               
               
             
               
               
               
               
             
           
               
                   
                   
               
             
             
               
                   
                 Total solids 
                 24 
                 g 
               
               
                   
                 Cellulose ester 
                 21.6 
                 g 
               
             
          
           
               
                   
                 Plasticizer 
                 2.4 g Triphenyl phosphate 
               
             
          
           
               
                   
                 Total solvent 
                 176 
                 g 
               
               
                   
                 Methylene chloride 
                 153.12 
                 g 
               
               
                   
                 Methanol 
                 22.88 
                 g 
               
               
                   
                   
               
             
          
         
       
     
         [0147]    Following the general procedure for solution preparation, solutions for layers A and B were independently prepared. The solution for layer A was first cast on a glass plate with a doctor blade at a certain thickness and covered by a pan for 4 minutes. The solution for layer B was then cast on top of the layer A and covered by a pan for 4 minutes. Then a third layer using solution A was cast on top of the layer B and covered by a pan for 45 minutes. The cover pan was removed and the tri-layer film was left on the glass plate for an additional 15 minutes. The film was peeled from the glass plate then annealed at 100° C. and 120° C. for 10 minutes, respectively. Films made in this manner were uniaxially or simultaneous biaxially stretched under different stretching conditions. The stretching conditions and optical and film data of these films are listed in Table 13. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 13 
               
             
             
               
                   
               
               
                 Optical retardation and dispersion of a tri-layer 
               
               
                 optical waveplate prepared by solvent co-casting. 
               
             
          
           
               
                   
                   
                 Stretch 
                   
                   
                   
                   
                   
                   
                 Film 
               
               
                   
                   
                 Temp. 
                 R e   
                 R th   
                   
                   
                   
                   
                 Thickness 
               
               
                 Run 
                 MD × TD 
                 (° C.) 
                 (nm) 
                 (nm) 
                 A Re   
                 B Re   
                 A Rth   
                 B Rth   
                 (micron) 
               
               
                   
               
             
          
           
               
                 67 
                 1.00 × 1.40 
                 177 
                 64.07 
                 −242.78 
                 0.865 
                 1.070 
                 0.958 
                 1.030 
                 96 
               
               
                 68 
                 1.00 × 1.40 
                 180 
                 70.28 
                 −261.71 
                 0.898 
                 1.052 
                 0.956 
                 1.028 
                 100 
               
               
                 69 
                 1.00 × 1.45 
                 180 
                 75.19 
                 −242.92 
                 0.872 
                 1.066 
                 0.955 
                 1.032 
                 100 
               
               
                   
               
             
          
         
       
     
         [0148]    The cellulose ester used in layer B of this example was the same cellulose ester used in Example 12 and it was similar to the cellulose ester of Example 1 in that as a single-layer film, the cellulose ester exhibited large positive values for R e  and large negative values for R th , but the film exhibited a flat dispersion. As shown in Example 3, as a single-layer film, the cellulose ester used to make layer A exhibited negative R e  values and positive or negative R th  values depending upon stretching conditions and the film exhibited a normal dispersion. Similar to Example 12, when the cellulose esters here were used to construct a tri-layer optical waveplate, the R e  and R th  values of the two cellulose esters were additive. 
         [0149]    Comparing the data in Table 13 with those in Table 12, it can be seen that larger absolute R th  values were obtained in this example. The values for A Re  and B Re  in this example indicate that the optical waveplate exhibited a reversed dispersion that is very close to that of an ideal achromatic waveplate (A Re =A Rth =0.818 and B Re =B Rth =1.182). This example illustrates that the cellulose ester of each layer is a factor in constructing optical waveplates. In this case, substitution of the regioselective substituted cellulose benzoate propionate in layer A for the randomly substituted CAP of Example 12 significantly altered the R th , A Re , and B Re  values. 
       Examples 70-112 
     Optical Retardation and Dispersion of Uniaxially Stretched Film 
       [0150]    Following the general solution preparation, a randomly substituted cellulose acetate propionate (DS Ac =0.14, DS Pr =1.71, DS OH =1.15) was used to prepare the following solution for Example 1: 
         [0000]    
       
         
               
               
               
               
             
               
               
               
             
               
               
               
               
             
           
               
                   
                   
               
             
             
               
                   
                 Total solids 
                 24 
                 g 
               
               
                   
                 Cellulose ester 
                 21.6 
                 g 
               
             
          
           
               
                   
                 Plasticizer 
                 2.4 g triphenyl phosphate (TPP) 
               
             
          
           
               
                   
                 Total solvent 
                 176 
                 g 
               
               
                   
                 Methylene chloride 
                 153.12 
                 g 
               
               
                   
                 Methanol 
                 22.88 
                 g 
               
               
                   
                   
               
             
          
         
       
     
         [0151]    Following the general solvent cast procedures described above, the solution for Examples 70-112 was used to obtain single layer films. The films were annealed at 100° C. and 120° C. for 10 minutes, respectively, before they were uniaxially stretched under the different stretching conditions. Some optical data are listed in Table 14. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 14 
               
             
             
               
                   
               
               
                 Optical properties for an uniaxial stretched cellulose acetate propionate film 
               
               
                 (DS Ac  = 0.14, DS Pr  = 1.71, DS OH  = 1.15) with TPP. 
               
             
          
           
               
                   
                 Re(589) 
                 Rth(589) 
                 Thickness 
                   
                   
                   
                   
                 Stretch 
                 Stretch 
               
               
                 Entry 
                 (nm) 
                 (nm) 
                 (micron) 
                 A Re   
                 B Re   
                 A Rth   
                 B Rth   
                 Temp (C.) 
                 Ratio 
               
               
                   
               
             
          
           
               
                 70 
                 105.11 
                 −207.42 
                 50 
                 0.996 
                 1.004 
                 0.988 
                 1.001 
                 180 
                 1 × 1.4  
               
               
                 71 
                 130.05 
                 −200.39 
                 47 
                 0.996 
                 1.003 
                 0.984 
                 1.006 
                 180 
                 1 × 1.5  
               
               
                 72 
                 137.57 
                 −195.50 
                 46 
                 0.996 
                 1.003 
                 0.990 
                 1.004 
                 180 
                 1 × 1.55 
               
               
                 73 
                 112.23 
                 −201.80 
                 48 
                 0.996 
                 1.004 
                 0.995 
                 1.004 
                 180 
                 1 × 1.45 
               
               
                 74 
                 106.94 
                 −181.26 
                 44 
                 0.997 
                 1.002 
                 0.992 
                 1.002 
                 185 
                 1 × 1.5  
               
               
                 75 
                 120.08 
                 −179.60 
                 46 
                 0.996 
                 1.002 
                 0.990 
                 1.006 
                 185 
                 1 × 1.55 
               
               
                 76 
                 121.84 
                 −181.69 
                 46 
                 0.996 
                 1.003 
                 0.989 
                 1.005 
                 185 
                 1 × 1.55 
               
               
                 77 
                 129.37 
                 −177.99 
                 45 
                 0.996 
                 1.002 
                 0.990 
                 1.008 
                 185 
                 1 × 1.6  
               
               
                 78 
                 144.10 
                 −182.79 
                 47 
                 0.997 
                 1.002 
                 0.997 
                 0.994 
                 185 
                 1 × 1.65 
               
               
                 79 
                 118.85 
                 −149.96 
                 46 
                 0.996 
                 1.002 
                 0.990 
                 1.006 
                 190 
                 1 × 1.65 
               
               
                 80 
                 122.53 
                 −147.39 
                 44 
                 0.996 
                 1.004 
                 0.987 
                 1.004 
                 190 
                 1 × 1.7  
               
               
                 81 
                 135.15 
                 −221.12 
                 50 
                 0.996 
                 1.003 
                 0.989 
                 1.004 
                 180 
                 1 × 1.5  
               
               
                 82 
                 144.35 
                 −216.48 
                 49 
                 0.996 
                 1.003 
                 0.991 
                 1.005 
                 180 
                 1 × 1.55 
               
               
                 83 
                 145.56 
                 −212.19 
                 49 
                 0.996 
                 1.002 
                 0.984 
                 1.000 
                 180 
                 1 × 1.55 
               
               
                 84 
                 163.25 
                 −219.39 
                 50 
                 0.996 
                 1.003 
                 0.993 
                 0.997 
                 180 
                 1 × 1.6  
               
               
                 85 
                 123.92 
                 −185.92 
                 49 
                 0.996 
                 1.003 
                 0.985 
                 1.000 
                 185 
                 1 × 1.55 
               
               
                 86 
                 132.63 
                 −183.69 
                 47 
                 0.997 
                 1.004 
                 0.987 
                 1.007 
                 185 
                 1 × 1.6  
               
               
                 87 
                 142.08 
                 −181.07 
                 46 
                 0.996 
                 1.002 
                 0.997 
                 0.998 
                 185 
                 1 × 1.65 
               
               
                 88 
                 122.30 
                 −170.42 
                 50 
                 0.997 
                 1.003 
                 0.990 
                 1.002 
                 190 
                 1 × 1.65 
               
               
                 89 
                 126.77 
                 −154.14 
                 46 
                 0.996 
                 1.003 
                 0.988 
                 1.003 
                 190 
                 1 × 1.70 
               
               
                 90 
                 136.55 
                 −153.47 
                 45 
                 0.997 
                 1.003 
                 0.982 
                 1.001 
                 190 
                 1 × 1.75 
               
               
                 91 
                 133.99 
                 −148.52 
                 43 
                 0.997 
                 1.002 
                 1.000 
                 1.000 
                 190 
                 1 × 1.8  
               
               
                 92 
                 144.87 
                 −229.59 
                 54 
                 0.996 
                 1.003 
                 0.994 
                 1.006 
                 180 
                 1 × 1.5  
               
               
                 93 
                 146.79 
                 −224.97 
                 52 
                 0.996 
                 1.004 
                 0.990 
                 1.007 
                 180 
                 1 × 1.55 
               
               
                 94 
                 163.19 
                 −221.34 
                 52 
                 0.996 
                 1.002 
                 0.996 
                 1.001 
                 180 
                 1 × 1.6  
               
               
                 95 
                 126.08 
                 −216.47 
                 56 
                 0.996 
                 1.005 
                 0.998 
                 1.004 
                 180 
                 1 × 1.45 
               
               
                 96 
                 135.77 
                 −202.20 
                 52 
                 0.996 
                 1.003 
                 0.992 
                 1.004 
                 185 
                 1 × 1.55 
               
               
                 97 
                 140.67 
                 −197.17 
                 49 
                 0.996 
                 1.003 
                 0.992 
                 1.005 
                 185 
                 1 × 1.6  
               
               
                 98 
                 155.19 
                 −199.85 
                 48 
                 0.996 
                 1.001 
                 0.998 
                 0.992 
                 185 
                 1 × 1.65 
               
               
                 99 
                 166.74 
                 −203.45 
                 47 
                 0.997 
                 1.001 
                 1.010 
                 0.982 
                 185 
                 1 × 1.7  
               
               
                 100 
                 132.24 
                 −170.71 
                 50 
                 0.997 
                 1.002 
                 0.992 
                 1.005 
                 190 
                 1 × 1.65 
               
               
                 101 
                 148.28 
                 −161.37 
                 47 
                 0.997 
                 1.002 
                 0.990 
                 1.003 
                 190 
                 1 × 1.7  
               
               
                 102 
                 138.58 
                 −167.34 
                 46 
                 0.996 
                 1.002 
                 0.987 
                 0.999 
                 190 
                 1 × 1.75 
               
               
                 103 
                 143.44 
                 −160.76 
                 46 
                 0.997 
                 1.003 
                 0.997 
                 0.992 
                 190 
                 1 × 1.8  
               
               
                 104 
                 165.84 
                 −157.12 
                 52 
                 0.996 
                 1.001 
                 1.034 
                 0.954 
                 190 
                 1 × 1.95 
               
               
                 105 
                 170.00 
                 −156.93 
                 48 
                 0.997 
                 1.002 
                 1.059 
                 0.945 
                 190 
                 1 × 2.0  
               
               
                 106 
                 165.85 
                 −191.40 
                 60 
                 0.996 
                 1.001 
                 0.990 
                 0.999 
                 190 
                 1 × 1.75 
               
               
                 107 
                 149.20 
                 −163.97 
                 45 
                 0.996 
                 1.002 
                 0.986 
                 0.995 
                 190 
                 1 × 1.8  
               
               
                 108 
                 164.00 
                 −160.76 
                 43 
                 0.996 
                 1.001 
                 1.021 
                 0.981 
                 190 
                 1 × 1.9  
               
               
                 109 
                 259.64 
                 −132.47 
                 96 
                 0.996 
                 1.001 
                 0.994 
                 1.003 
                 185 
                 1 × 1.45 
               
               
                 110 
                 375.86 
                 NA 
                 96 
                 0.996 
                 1.002 
                 NA 
                 NA 
                 185 
                 1 × 1.50 
               
               
                 111 
                 308.40 
                 −162.67 
                 88 
                 0.995 
                 1.001 
                 0.989 
                 1.002 
                 185 
                 1 × 1.55 
               
               
                 112 
                 310.00 
                 −160.34 
                 88 
                 0.995 
                 1.001 
                 0.989 
                 1.002 
                 185 
                 1 × 1.60 
               
               
                   
               
             
          
         
       
     
         [0152]    Examples 70-108 are constrained and examples 109-112 are not constrained. 
         [0153]    Relative to an ideal achromatic waveplate in which A Re =A Rth =0.818 and B Re =B Rth =1.182, the data in Table 14 indicate that the films exhibit only a slight reverse dispersion. That is, the dispersion curves obtained with these films essentially are flat. 
       Examples 113-138 
     Optical Retardation and Dispersion of Uniaxially Stretched Film 
       [0154]    Following the general solution preparation, a randomly substituted cellulose acetate propionate (DS Ac =0.14, DS Pr =1.71, DS OH =1.15) was used to prepare the following solution for Examples 114-: 
         [0000]    
       
         
               
               
               
             
               
               
             
               
               
               
             
           
               
                   
               
             
             
               
                 Total solids 
                 24 
                 g 
               
               
                 Cellulose ester 
                 21.6 
                 g 
               
             
          
           
               
                 Plasticizer 
                 2.4 g Trimethyl Pentanyl Diisobutyrate(TXIB) 
               
             
          
           
               
                 Total solvent 
                 176 
                 g 
               
               
                 Methylene chloride 
                 153.12 
                 g 
               
               
                 Methanol 
                 22.88 
                 g 
               
               
                   
               
             
          
         
       
     
         [0155]    Following the general solvent cast procedures described above, the solution for Example 2 was used to obtain single layer films. The films were annealed at 100° C. and 120° C. for 10 minutes, respectively, before they were uniaxially stretched under the different stretching conditions. Some optical data are listed in Table 2. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 15 
               
             
             
               
                   
               
               
                 Optical properties for an uniaxial stretched cellulose acetate propionate film 
               
               
                 (DS Ac  = 0.14, DS Pr  = 1.71, DS OH  = 1.15) with TXIB. 
               
             
          
           
               
                   
                 Re (589) 
                 Rth (589) 
                 Thickness 
                   
                   
                   
                   
                 Stretch 
                 Stretch Ratio 
               
               
                 Entry 
                 (nm) 
                 (nm) 
                 (micron) 
                 A Re   
                 B Re   
                 A Rth   
                 B Rth   
                 Temp (C.) 
                 MD × TD 
               
               
                   
               
             
          
           
               
                 113 
                 82.16 
                 −175.89 
                 49 
                 0.985 
                 1.005 
                 0.995 
                 1.007 
                 178 
                 1 × 1.40 
               
               
                 114 
                 87.57 
                 − 182.94 
                 48 
                 0.985 
                 1.005 
                 0.991 
                 1.002 
                 178 
                 1 × 1.45 
               
               
                 115 
                 97.61 
                 − 187.67 
                 48 
                 0.985 
                 1.006 
                 0.990 
                 1.001 
                 178 
                 1 × 1.50 
               
               
                 116 
                 108.65 
                 − 192.26 
                 47 
                 0.985 
                 1.007 
                 0.997 
                 0.998 
                 178 
                 1 × 1.55 
               
               
                 117 
                 117.66 
                 − 200.04 
                 50 
                 0.985 
                 1.007 
                 1.008 
                 0.987 
                 178 
                 1 × 1.60 
               
               
                 118 
                 132.20 
                 − 200.90 
                 52 
                 0.985 
                 1.006 
                 1.018 
                 0.976 
                 178 
                 1 × 1.65 
               
               
                 119 
                 96.35 
                 − 203.83 
                 54 
                 0.985 
                 1.006 
                 0.988 
                 0.999 
                 178 
                 1 × 1.45 
               
               
                 120 
                 110.50 
                 − 207.82 
                 54 
                 0.986 
                 1.005 
                 0.992 
                 1.001 
                 178 
                 1 × 1.50 
               
               
                 121 
                 115.58 
                 − 200.88 
                 52 
                 0.985 
                 1.005 
                 0.992 
                 0.997 
                 178 
                 1 × 1.55 
               
               
                 122 
                 122.76 
                 − 215.89 
                 56 
                 0.986 
                 1.005 
                 0.991 
                 1.002 
                 178 
                 1 × 1.50 
               
               
                 123 
                 132.53 
                 − 239.12 
                 56 
                 0.986 
                 1.006 
                 0.991 
                 1.000 
                 178 
                 1 × 1.50 
               
               
                 124 
                 115.57 
                 − 210.77 
                 58 
                 0.985 
                 1.005 
                 0.992 
                 1.002 
                 178 
                 1 × 1.50 
               
               
                 125 
                 114.89 
                 − 211.82 
                 56 
                 0.986 
                 1.006 
                 0.989 
                 1.002 
                 178 
                 1 × 1.50 
               
               
                 126 
                 120.79 
                 − 228.44 
                 56 
                 0.986 
                 1.006 
                 0.991 
                 1.001 
                 178 
                 1 × 1.50 
               
               
                 127 
                 128.82 
                 − 214.20 
                 56 
                 0.986 
                 1.005 
                 0.983 
                 0.998 
                 178 
                 1 × 1.55 
               
               
                 128 
                 132.03 
                 − 221.51 
                 56 
                 0.986 
                 1.006 
                 0.995 
                 0.999 
                 178 
                 1 × 1.60 
               
               
                 129 
                 175.18 
                 − 252.72 
                 56 
                 0.987 
                 1.005 
                 1.051 
                 0.944 
                 178 
                 1 × 1.65 
               
               
                 130 
                 125.99 
                 − 219.40 
                 54 
                 0.985 
                 1.006 
                 1.025 
                 0.966 
                 178 
                 1 × 1.60 
               
               
                 131 
                 198.88 
                 − 128.08 
                 84 
                 0.990 
                 1.003 
                 0.990 
                 1.004 
                 175 
                 1 × 1.11 
               
               
                 132 
                 228.87 
                 − 134.05 
                 84 
                 0.990 
                 1.003 
                 0.987 
                 1.006 
                 175 
                 1 × 1.15 
               
               
                 133 
                 238.02 
                 − 137.21 
                 78 
                 0.991 
                 1.003 
                 0.985 
                 1.007 
                 175 
                 1 × 1.2  
               
               
                 134 
                 262.30 
                 − 151.23 
                 76 
                 0.990 
                 1.003 
                 0.985 
                 1.008 
                 175 
                 1 × 1.25 
               
               
                 135 
                 283.24 
                 − 166.63 
                 74 
                 0.989 
                 1.003 
                 0.989 
                 1.006 
                 175 
                 1 × 1.3  
               
               
                 136 
                 289.19 
                 − 169.95 
                 72 
                 0.988 
                 1.003 
                 0.987 
                 1.007 
                 175 
                 1 × 1.35 
               
               
                 137 
                 304.52 
                 − 171.98 
                 76 
                 0.988 
                 1.003 
                 0.984 
                 1.010 
                 175 
                 × 1 × .4 
               
               
                 138 
                 312.54 
                 − 217.77 
                 68 
                 0.987 
                 1.005 
                 0.990 
                 1.003 
                 175 
                 1 × 1.5  
               
               
                   
               
             
          
         
       
     
         [0156]    Examples 113-130 are constrained and examples 131-138 are not constrained. 
         [0157]    The only difference between Examples 70-112 and Examples 113-138 is plasticizer TPP and TXIB. Because of the plasticizer effect, the wave plate dispersion from Example 113-138 is more reversed than Examples 70-112, which are relatively flat. 
       Examples 139-145 
     Optical Retardation and Dispersion of Uniaxially Stretched Film 
       [0158]    Following the general solution preparation, a randomly substituted cellulose acetate propionate (DS Ac =1.24, DS Pr =0.95, DS OH =0.81) was used to prepare the following solution for Example 3: 
         [0000]    
       
         
               
               
               
               
             
               
               
               
             
               
               
               
               
             
           
               
                   
                   
               
             
             
               
                   
                 Total solids 
                 24 
                 g 
               
               
                   
                 Cellulose ester 
                 21.6 
                 g 
               
             
          
           
               
                   
                 Plasticizer 
                 2.4 g triphenyl phosphate (TPP) 
               
             
          
           
               
                   
                 Total solvent 
                 176 
                 g 
               
               
                   
                 Methylene chloride 
                 153.12 
                 g 
               
               
                   
                 Methanol 
                 22.88 
                 g 
               
               
                   
                   
               
             
          
         
       
     
         [0159]    Following the general solvent cast procedures described above, the solution for Examples 139-145 was used to obtain single layer films. The films were annealed at 100° C. and 120° C. for 10 minutes, respectively, before they were uniaxially stretched under the different stretching conditions. Some optical data are listed in Table 16. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 16 
               
             
             
               
                   
               
               
                 Optical properties for an uniaxial stretched cellulose acetate 
               
               
                 propionate film (DS Ac  = 1.24, DS Pr  = 0.95, DS OH  = 0.81) with TPP. 
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Stretch 
                 Stretch 
               
               
                   
                 Re (589) 
                 Rth (589) 
                 Thickness 
                   
                   
                   
                   
                 Temp 
                 Ratio 
               
               
                 Entry 
                 (nm) 
                 (nm) 
                 (micron) 
                 A Re   
                 B Re   
                 A Rth   
                 B Rth   
                 (C.) 
                 MD × TD 
               
               
                   
               
             
          
           
               
                 139 
                 251.64 
                 −242.21 
                 90 
                 0.974 
                 1.012 
                 0.977 
                 1.014 
                 170 
                 1 × 1.2 
               
               
                 140 
                 91.70 
                 −248.56 
                 68 
                 0.973 
                 1.014 
                 0.989 
                 1.002 
                 170 
                 1 × 1.3 
               
               
                 141 
                 282.33 
                 −177.55 
                 94 
                 0.977 
                 1.011 
                 0.976 
                 1.015 
                 172 
                  1 × 1.35 
               
               
                 142 
                 270.26 
                 −191.33 
                 82 
                 0.976 
                 1.012 
                 0.978 
                 1.014 
                 172 
                 1 × 1.3 
               
               
                 143 
                 239.77 
                 −143.41 
                 96 
                 0.978 
                 1.010 
                 0.980 
                 1.014 
                 170 
                 1 × 1.3 
               
               
                 144 
                 196.29 
                 −116.63 
                 104 
                 0.980 
                 1.011 
                 0.976 
                 1.015 
                 175 
                 1 × 1.1 
               
               
                 145 
                 108.03 
                 −256.07 
                 74 
                 0.975 
                 1.015 
                 0.977 
                 1.014 
                 175 
                  1 × 1.35 
               
               
                   
               
             
          
         
       
     
         [0160]    Examples 140 and 145 are constrained and examples 139 and 141-144 are not constrained. 
       Examples 146-156 
     Optical Retardation and Dispersion of Uniaxially Stretched Film 
       [0161]    Following the general solution preparation, a randomly substituted cellulose acetate propionate (DS Ac =0.53, DS Pr =1.46, DS OH =1.01) was used to prepare the following solution for Examples 147-: 
         [0000]    
       
         
               
               
               
               
             
               
               
               
             
               
               
               
               
             
           
               
                   
                   
               
             
             
               
                   
                 Total solids 
                 24 
                 g 
               
               
                   
                 Cellulose ester 
                 21.6 
                 g 
               
             
          
           
               
                   
                 Plasticizer 
                 2.4 g triphenyl phosphate (TPP) 
               
             
          
           
               
                   
                 Total solvent 
                 176 
                 g 
               
               
                   
                 Methylene chloride 
                 153.12 
                 g 
               
               
                   
                 Methanol 
                 22.88 
                 g 
               
               
                   
                   
               
             
          
         
       
     
         [0162]    Following the general solvent cast procedures described above, the solution for Examples 146-156 was used to obtain single layer films. The films were annealed at 100° C. and 120° C. for 10 minutes, respectively, before they were uniaxially stretched under the different stretching conditions. Some optical data are listed in Table 17. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 17 
               
             
             
               
                   
               
               
                 Optical properties for an uniaxial stretched cellulose acetate 
               
               
                 propionate film (DS Ac  = 0.53, DS Pr  = 1.46, DS OH  = 1.01) with TPP. 
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Stretch 
                 Stretch 
               
               
                   
                 Re (589) 
                 Rth (589) 
                 Thickness 
                   
                   
                   
                   
                 Temp 
                 Ratio 
               
               
                 Entry 
                 (nm) 
                 (nm) 
                 (micron) 
                 A Re   
                 B Re   
                 A Rth   
                 B Rth   
                 (C.) 
                 MD × TD 
               
               
                   
               
               
                 146 
                 211.25 
                 −144.08 
                 92 
                 0.993 
                 1.003 
                 0.991 
                 1.003 
                 170 
                 1 × 1.1 
               
               
                 147 
                 366.47 
                 NA 
                 78 
                 0.990 
                 1.003 
                 NA 
                 NA 
                 172 
                 1 × 1.5 
               
               
                 148 
                 260.16 
                 −169.71 
                 84 
                 0.991 
                 1.002 
                 0.991 
                 1.004 
                 170 
                 1 × 1.2 
               
               
                 149 
                 337.65 
                 NA 
                 78 
                 0.990 
                 1.004 
                 NA 
                 NA 
                 172 
                 1 × 1.4 
               
               
                 150 
                 137.83 
                 −278.88 
                 64 
                 0.989 
                 1.004 
                 0.995 
                 0.998 
                 172 
                 1 × 1.4 
               
               
                 151 
                 376.10 
                 NA 
                 90 
                 0.990 
                 1.003 
                 NA 
                 NA 
                 170 
                 1 × 1.4 
               
               
                 152 
                 152.30 
                 −254.15 
                 58 
                 0.989 
                 1.005 
                 0.996 
                 0.997 
                 172 
                  1 × 1.45 
               
               
                 153 
                 331.50 
                 NA 
                 86 
                 0.991 
                 1.003 
                 NA 
                 NA 
                 172 
                 1 × 1.3 
               
               
                 154 
                 209.69 
                 −127.70 
                 94 
                 0.992 
                 1.002 
                 0.990 
                 1.002 
                 172 
                 1 × 1.1 
               
               
                 155 
                 274.77 
                 −168.35 
                 90 
                 0.991 
                 1.002 
                 0.989 
                 1.006 
                 172 
                 1 × 1.2 
               
               
                 156 
                 151.09 
                 −299.90 
                 64 
                 0.989 
                 1.006 
                 0.998 
                 0.997 
                 170 
                 1 × 1.4 
               
               
                   
               
             
          
         
       
     
         [0163]    Examples 150, 152 and 156 are constrained and examples 146-149, 151 and 153-155 are not constrained. 
       Examples 157-169 
     Optical Retardation and Dispersion of Uniaxially Stretched Film 
       [0164]    Following the general solution preparation, a randomly substituted cellulose acetate propionate (DS Ac =1.41, DS Pr =0.61, DS OH =0.98) was used to prepare the following solution for Example 5: 
         [0000]    
       
         
               
               
               
               
             
           
               
                   
                   
               
             
             
               
                   
                 Total solids 
                 24 
                 g 
               
               
                   
                 Cellulose ester 
                 21.6 
                 g 
               
               
                   
                 Plasticizer 
                 2.4 
                 g triphenyl phosphate (TPP) 
               
               
                   
                 Total solvent 
                 176 
                 g 
               
               
                   
                 Methylene chloride 
                 153.12 
                 g 
               
               
                   
                 Methanol 
                 22.88 
                 g 
               
               
                   
                   
               
             
          
         
       
     
         [0165]    Following the general solvent cast procedures described above, the solution for Examples −169 was used to obtain single layer films. The films were annealed at 100° C. and 120° C. for 10 minutes, respectively, before they were uniaxially stretched under the different stretching conditions. Some optical data are listed in Table 18. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 18 
               
             
             
               
                   
               
               
                 Optical properties for an uniaxial stretched cellulose acetate 
               
               
                 propionate film (DS Ac  = 1.41, DS Pr  = 0.61, DS OH  = 0.98) with TPP. 
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Stretch 
                 Stretch 
               
               
                   
                 Re(589) 
                 Rth(589) 
                 Thickness 
                   
                   
                   
                   
                 Temp 
                 Ratio MD × 
               
               
                 Entry 
                 (nm) 
                 (nm) 
                 (micron) 
                 A Re   
                 B Re   
                 A Rth   
                 B Rth   
                 (C.) 
                 TD 
               
               
                   
               
             
          
           
               
                 157 
                 58.96 
                 −238.89 
                 70 
                 0.990 
                 1.004 
                 0.990 
                 1.004 
                 170 
                 1 × 1.1 
               
               
                 158 
                 153.15 
                 −260.02 
                 62 
                 0.988 
                 1.005 
                 0.992 
                 1.000 
                 170 
                 1 × 1.2 
               
               
                 159 
                 205.39 
                 −270.97 
                 60 
                 0.987 
                 1.004 
                 1.003 
                 0.993 
                 170 
                 1 × 1.3 
               
               
                 160 
                 125.47 
                 −412.16 
                 80 
                 0.985 
                 1.007 
                 1.004 
                 0.992 
                 172 
                 1 × 1.3 
               
               
                 161 
                 54.76 
                 −348.03 
                 72 
                 0.985 
                 1.003 
                 0.993 
                 1.001 
                 172 
                 1 × 1.35 
               
               
                 162 
                 121.78 
                 −384.26 
                 70 
                 0.985 
                 1.006 
                 1.002 
                 0.994 
                 172 
                 1 × 1.3 
               
               
                 163 
                 129.27 
                 −369.92 
                 72 
                 0.984 
                 1.006 
                 1.002 
                 0.995 
                 175 
                 1 × 1.32 
               
               
                 164 
                 120.43 
                 −405.60 
                 70 
                 0.985 
                 1.005 
                 0.999 
                 0.994 
                 170 
                 1 × 1.3 
               
               
                 165 
                 167.82 
                 −278.59 
                 90 
                 0.989 
                 1.004 
                 0.994 
                 0.999 
                 175 
                 1 × 1.1 
               
               
                 166 
                 39.54 
                 −323.39 
                 74 
                 0.987 
                 1.007 
                 0.993 
                 1.000 
                 175 
                 1 × 1.35 
               
               
                 167 
                 243.78 
                 −287.04 
                 84 
                 0.989 
                 1.004 
                 0.992 
                 1.002 
                 175 
                 1 × 1.2 
               
               
                 168 
                 327.08 
                 −337.81 
                 80 
                 0.989 
                 1.004 
                 0.992 
                 1.002 
                 175 
                 1 × 1.4 
               
               
                 169 
                 316.48 
                 −309.32 
                 84 
                 0.988 
                 1.004 
                 0.993 
                 1.001 
                 175 
                 1 × 1.3 
               
               
                   
               
             
          
         
       
     
         [0166]    Examples 160-164 and 166 are constrained and examples 157-159, 165 and 167-169 are not constrained. 
         [0167]    Following the general solvent cast procedures described above, the solution for Examples 170-174 was used to obtain single layer films. The films were annealed at 100° C. and 120° C. for 10 minutes, respectively, before they were uniaxially stretched under the different stretching conditions. Some optical data are listed in Table 19. 
         [0000]    
       
         
               
               
               
             
           
               
                   
               
             
             
               
                 Total solids 
                 48.0 
                 g 
               
               
                 Cellulose ester 
                 43.2 
                 g 
               
               
                 Plasticizer 
                 2.4 
                 g 2,2,4-trimethyl-1,3-pentanediol (TXIB) 
               
               
                 Plasticizer 
                 2.4 
                 g 2-naphthyl benzoate 
               
               
                 Total solvent 
                 352 
                 g 
               
               
                 Methylene chloride 
                 316.8 
                 g 
               
               
                 Methanol 
                 35.20 
                 g 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 19 
               
             
             
               
                   
               
               
                 Optical properties for an uniaxial stretched cellulose acetate 
               
               
                 propionate film (DS Ac  = 1.90, DS Pr  = 0.72, DS OH  = 0.38) with TXIB and 
               
               
                 2-naphthyl benzoate. 
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 Stretch 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Stretch 
                 Ratio 
               
               
                   
                 Re (589) 
                 Rth (589) 
                 Thickness 
                   
                   
                   
                   
                 Temp 
                 MD × 
               
               
                 Entry 
                 (nm) 
                 (nm) 
                 (micron) 
                 A Re   
                 B Re   
                 A Rth   
                 B Rth   
                 (C.) 
                 TD 
               
               
                   
               
             
          
           
               
                 170 
                 133.84 
                 −105.89 
                 76 
                 0.969 
                 1.024 
                 0.970 
                 1.025 
                 160 
                 1 × 1.40 
               
               
                 171 
                 128.79 
                 −101.96 
                 78 
                 0.969 
                 1.023 
                 0.968 
                 1.029 
                 160 
                 1 × 1.35 
               
               
                 172 
                 122.81 
                 −106.74 
                 76 
                 0.970 
                 1.023 
                 0.968 
                 1.029 
                 160 
                 1 × 1.30 
               
               
                 173 
                 125.54 
                 −89.72 
                 76 
                 0.966 
                 1.026 
                 0.963 
                 1.033 
                 165 
                 1 × 1.30 
               
               
                 174 
                 120.33 
                 −91.34 
                 74 
                 0.967 
                 1.024 
                 0.964 
                 1.031 
                 165 
                 1 × 1.25 
               
               
                   
               
             
          
         
       
     
         [0168]    Examples 170-174 are not constrained. 
         [0169]    Following the general solvent cast procedures described above, the solution for Examples 175-178 was used to obtain single layer films. The films were annealed at 100° C. and 120° C. for 10 minutes, respectively, before they were uniaxially stretched under the different stretching conditions. Some optical data are listed in Table 20. 
         [0000]    
       
         
               
               
               
             
           
               
                   
               
             
             
               
                 Total solids 
                 48.0 
                 g 
               
               
                 Cellulose ester 
                 43.2 
                 g 
               
               
                 Plasticizer 
                 1.92 
                 g 2,2,4-trimethyl-1,3-pentanediol (TXIB) 
               
               
                 Plasticizer 
                 2.88 
                 g 2-naphthyl benzoate 
               
               
                 Total solvent 
                 352 
                 g 
               
               
                 Methylene chloride 
                 316.8 
                 g 
               
               
                 Methanol 
                 35.20 
                 g 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 20 
               
             
             
               
                   
               
               
                 Optical properties for an uniaxial stretched cellulose acetate 
               
               
                 propionate film (DS Ac  = 1.90, DS Pr  = 0.72, DS OH  = 0.38) with TXIB and 
               
               
                 2-naphthyl benzoate. 
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Stretch 
                 Stretch 
               
               
                   
                 Re (589) 
                 Rth (589) 
                 Thickness 
                   
                   
                   
                   
                 Temp 
                 Ratio 
               
               
                 Entry 
                 (nm) 
                 (nm) 
                 (micron) 
                 A Re   
                 B Re   
                 A Rth   
                 B Rth   
                 (C.) 
                 MD × TD 
               
               
                   
               
               
                 175 
                 121.39 
                 −81.82 
                 76 
                 0.936 
                 1.039 
                 0.940 
                 1.051 
                 165 
                 1 × 1.40 
               
               
                 176 
                 109.25 
                 −75.75 
                 78 
                 0.935 
                 1.041 
                 0.940 
                 1.051 
                 165 
                 1 × 1.35 
               
               
                 177 
                 107.93 
                 −72.46 
                 80 
                 0.937 
                 1.040 
                 0.938 
                 1.053 
                 165 
                 1 × 1.30 
               
               
                 178 
                 120.93 
                 −81.21 
                 72 
                 0.937 
                 1.039 
                 0.939 
                 1.052 
                 165 
                 1 × 1.40 
               
               
                   
               
             
          
         
       
     
         [0170]    Examples 175-178 are not constrained. 
         [0171]    Following the general solvent cast procedures described above, the solution for Examples 179-185 was used to obtain single layer films. The films were annealed at 100° C. and 120° C. for 10 minutes, respectively, before they were uniaxially stretched under the different stretching conditions. Some optical data are listed in Table 21. 
         [0000]    
       
         
               
               
               
             
           
               
                   
               
             
             
               
                 Total solids 
                 48.0 
                 g 
               
               
                 Cellulose ester 
                 43.2 
                 g 
               
               
                 Plasticizer 
                 1.44 
                 g 2,2,4-trimethyl-1,3-pentanediol (TXIB) 
               
               
                 Plasticizer 
                 3.36 
                 g 2-naphthyl benzoate 
               
               
                 Total solvent 
                 352 
                 g 
               
               
                 Methylene chloride 
                 316.8 
                 g 
               
               
                 Methanol 
                 35.20 
                 g 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 21 
               
             
             
               
                   
               
               
                 Optical properties for an uniaxial stretched cellulose acetate 
               
               
                 propionate film (DS Ac  = 1.90, DS Pr  = 0.72, DS OH  = 0.38) with TXIB and 
               
               
                 2-naphthyl benzoate. 
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Stretch 
                 Stretch 
               
               
                   
                 Re (589) 
                 Rth (589) 
                 Thickness 
                   
                   
                   
                   
                 Temp 
                 Ratio 
               
               
                 Entry 
                 (nm) 
                 (nm) 
                 (micron) 
                 A Re   
                 B Re   
                 A Rth   
                 B Rth   
                 (C) 
                 MD × TD 
               
               
                   
               
             
          
           
               
                 179 
                 94.99 
                 −64.49 
                 78 
                 0.892 
                 1.063 
                 0.909 
                 1.079 
                 165 
                 1 × 1.35 
               
               
                 180 
                 93.74 
                 −68.36 
                 74 
                 0.895 
                 1.062 
                 0.914 
                 1.073 
                 165 
                 1 × 1.40 
               
               
                 181 
                 99.08 
                 −63.24 
                 78 
                 0.892 
                 1.063 
                 0.902 
                 1.083 
                 165 
                 1 × 1.35 
               
               
                 182 
                 105.78 
                 −68.09 
                 76 
                 0.893 
                 1.062 
                 0.905 
                 1.080 
                 165 
                 1 × 1.45 
               
               
                 183 
                 107.91 
                 −69.46 
                 74 
                 0.890 
                 1.064 
                 0.903 
                 1.082 
                 165 
                 1 × 1.50 
               
               
                 184 
                 110.14 
                 −70.34 
                 72 
                 0.894 
                 1.063 
                 0.905 
                 1.080 
                 165 
                 1 × 1.55 
               
               
                 185 
                 109.50 
                 −67.42 
                 74 
                 0.888 
                 1.065 
                 0.900 
                 1.084 
                 165 
                 1 × 1.40 
               
               
                   
               
             
          
         
       
     
         [0172]    Examples 179-185 are not constrained. 
         [0173]    Following the general solvent cast procedures described above, the solution for Examples 186-200 was used to obtain single layer films. The films were annealed at 100° C. and 120° C. for 10 minutes, respectively, before they were uniaxially stretched under the different stretching conditions. Some optical data are listed in Table 22. 
         [0000]    
       
         
               
               
               
             
           
               
                   
               
             
             
               
                 Total solids 
                 52.8 
                 g 
               
               
                 Cellulose ester 
                 48.0 
                 g 
               
               
                 Plasticizer 
                 2.40 
                 g 2,2,4-trimethyl-1,3-pentanediol (TXIB) 
               
               
                 Plasticizer 
                 2.40 
                 g 2-naphthyl benzoate 
               
               
                 Total solvent 
                 352 
                 g 
               
               
                 Methylene chloride 
                 316.8 
                 g 
               
               
                 Methanol 
                 35.20 
                 g 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 22 
               
             
             
               
                   
               
               
                 Optical properties for an uniaxial stretched cellulose acetate 
               
               
                 propionate film (DS Ac  = 1.58, DS Pr  = 0.85, DS OH  = 0.57) with TXIB and 
               
               
                 2-naphthyl benzoate. 
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Stretch 
                 Stretch 
               
               
                   
                 Re (589) 
                 Rth (589) 
                 Thickness 
                   
                   
                   
                   
                 Temp 
                 Ratio 
               
               
                 Entry 
                 (nm) 
                 (nm) 
                 (micron) 
                 A Re   
                 B Re   
                 A Rth   
                 B Rth   
                 (C.) 
                 MD × TD 
               
               
                   
               
             
          
           
               
                 186 
                 92.29 
                 −151.85 
                 58 
                 1.002 
                 1.004 
                 1.001 
                 1.000 
                 175 
                 1 × 1.40 
               
               
                 187 
                 87.37 
                 −144.81 
                 46 
                 0.999 
                 1.005 
                 0.995 
                 0.997 
                 175 
                 1 × 1.45 
               
               
                 188 
                 92.05 
                 −147.76 
                 47 
                 1.000 
                 1.007 
                 0.991 
                 0.991 
                 175 
                 1 × 1.50 
               
               
                 189 
                 219.98 
                 −117.70 
                 84 
                 1.007 
                 0.999 
                 1.003 
                 1.003 
                 175 
                 1 × 1.20 
               
               
                 190 
                 251.06 
                 −130.36 
                 82 
                 1.007 
                 1.000 
                 1.001 
                 1.001 
                 175 
                 1 × 1.30 
               
               
                 191 
                 266.77 
                 −141.47 
                 78 
                 1.007 
                 1.000 
                 1.001 
                 1.003 
                 175 
                 1 × 1.35 
               
               
                 192 
                 262.53 
                 −137.51 
                 80 
                 1.005 
                 1.001 
                 0.991 
                 1.004 
                 175 
                 1 × 1.40 
               
               
                 193 
                 188.34 
                 −103.66 
                 86 
                 1.007 
                 0.998 
                 1.002 
                 1.003 
                 175 
                 1 × 1.10 
               
               
                 194 
                 129.80 
                 −69.53 
                 84 
                 1.006 
                 1.000 
                 0.980 
                 1.010 
                 180 
                 1 × 1.10 
               
               
                 195 
                 171.33 
                 −88.11 
                 84 
                 1.004 
                 1.000 
                 0.994 
                 1.007 
                 180 
                 1 × 1.20 
               
               
                 196 
                 186.93 
                 −95.87 
                 82 
                 1.003 
                 1.001 
                 0.997 
                 1.005 
                 180 
                 1 × 1.30 
               
               
                 197 
                 214.89 
                 −110.58 
                 78 
                 1.004 
                 1.000 
                 1.000 
                 1.005 
                 180 
                 1 × 1.40 
               
               
                 198 
                 95.52 
                 −126.79 
                 58 
                 1.001 
                 1.005 
                 0.997 
                 1.001 
                 180 
                 1 × 1.50 
               
               
                 199 
                 87.98 
                 −126.18 
                 50 
                 1.000 
                 1.006 
                 0.997 
                 1.001 
                 180 
                 1 × 1.60 
               
               
                 200 
                 79.96 
                 −104.35 
                 42 
                 0.993 
                 1.010 
                 1.027 
                 0.965 
                 180 
                 1 × 1.70 
               
               
                   
               
             
          
         
       
     
         [0174]    Examples 186-188 and 198-200 are constrained and examples 189-197 are not constrained. 
         [0175]    Following the general solvent cast procedures described above, the solution for Examples 201-215 was used to obtain single layer films. The films were annealed at 100° C. and 120° C. for 10 minutes, respectively, before they were uniaxially stretched under the different stretching conditions. Some optical data are listed in Table 23. 
         [0000]    
       
         
               
               
               
             
           
               
                   
               
             
             
               
                 Total solids 
                 52.8 
                 g 
               
               
                 Cellulose ester 
                 43.2 
                 g 
               
               
                 Plasticizer 
                 1.92 
                 g 2,2,4-trimethyl-1,3-pentanediol (TXIB) 
               
               
                 Plasticizer 
                 2.88 
                 g 2-naphthyl benzoate 
               
               
                 Total solvent 
                 352 
                 g 
               
               
                 Methylene chloride 
                 316.8 
                 g 
               
               
                 Methanol 
                 35.20 
                 g 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 23 
               
             
             
               
                   
               
               
                 Optical properties for an uniaxial stretched cellulose acetate 
               
               
                 propionate film (DS Ac  = 1.58, DS Pr  = 0.85, DS OH  = 0.57) with TXIB and 
               
               
                 2-naphthyl benzoate. 
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Stretch 
                 Stretch 
               
               
                   
                 Re (589) 
                 Rth (589) 
                 Thickness 
                   
                   
                   
                   
                 Temp 
                 Ratio MD × 
               
               
                 Entry 
                 (nm) 
                 (nm) 
                 (micron) 
                 A Re   
                 B Re   
                 A Rth   
                 B Rth   
                 (C.) 
                 TD 
               
               
                   
               
             
          
           
               
                 201 
                 183.27 
                 −97.92 
                 86 
                 0.992 
                 1.005 
                 0.990 
                 1.009 
                 175 
                 1 × 1.10 
               
               
                 202 
                 193.86 
                 −102.90 
                 84 
                 0.992 
                 1.005 
                 0.988 
                 1.012 
                 175 
                 1 × 1.20 
               
               
                 203 
                 256.07 
                 −135.54 
                 84 
                 0.992 
                 1.007 
                 0.990 
                 1.010 
                 175 
                 1 × 1.30 
               
               
                 204 
                 238.81 
                 −125.97 
                 78 
                 0.990 
                 1.006 
                 0.991 
                 1.010 
                 175 
                 1 × 1.40 
               
               
                 205 
                 287.25 
                 −160.35 
                 72 
                 0.991 
                 1.008 
                 0.946 
                 1.026 
                 175 
                 1 × 1.60 
               
               
                 206 
                 274.21 
                 −160.52 
                 68 
                 0.987 
                 1.010 
                 0.932 
                 1.003 
                 175 
                 1 × 1.80 
               
               
                 207 
                 125.40 
                 −68.69 
                 86 
                 0.994 
                 1.005 
                 0.979 
                 1.012 
                 180 
                 1 × 1.10 
               
               
                 208 
                 180.04 
                 −95.53 
                 84 
                 0.992 
                 1.005 
                 0.989 
                 1.013 
                 180 
                 1 × 1.20 
               
               
                 209 
                 182.80 
                 −99.59 
                 82 
                 0.993 
                 1.005 
                 0.987 
                 1.013 
                 180 
                 1 × 1.30 
               
               
                 210 
                 202.76 
                 −106.16 
                 78 
                 0.992 
                 1.006 
                 0.986 
                 1.013 
                 180 
                 1 × 1.40 
               
               
                 211 
                 221.23 
                 −115.96 
                 74 
                 0.990 
                 1.006 
                 0.986 
                 1.008 
                 180 
                 1 × 1.60 
               
               
                 212 
                 238.60 
                 −135.74 
                 66 
                 0.988 
                 1.008 
                 0.925 
                 1.010 
                 180 
                 1 × 1.80 
               
               
                 213 
                 74.50 
                 −118.25 
                 56 
                 0.989 
                 1.012 
                 0.990 
                 1.006 
                 180 
                 1 × 1.50 
               
               
                 214 
                 85.97 
                 −127.06 
                 52 
                 0.984 
                 1.012 
                 0.995 
                 1.000 
                 180 
                 1 × 1.60 
               
               
                 215 
                 87.20 
                 −112.41 
                 48 
                 0.981 
                 1.012 
                 0.997 
                 1.000 
                 180 
                 1 × 1.70 
               
               
                   
               
             
          
         
       
     
         [0176]    Examples 201-212 are constrained and examples 213-215 are not constrained. 
         [0177]    Following the general solvent cast procedures described above, the solution for Examples 216-230 was used to obtain single layer films. The films were annealed at 100° C. and 120° C. for 10 minutes, respectively, before they were uniaxially stretched under the different stretching conditions. Some optical data are listed in Table 24. 
         [0000]    
       
         
               
               
               
             
           
               
                   
               
             
             
               
                 Total solids 
                 52.8 
                 g 
               
               
                 Cellulose ester 
                 43.2 
                 g 
               
               
                 Plasticizer 
                 1.44 
                 g 2,2,4-trimethyl-1,3-pentanediol (TXIB) 
               
               
                 Plasticizer 
                 2.36 
                 g 2-naphthyl benzoate 
               
               
                 Total solvent 
                 352 
                 g 
               
               
                 Methylene chloride 
                 316.8 
                 g 
               
               
                 Methanol 
                 35.20 
                 g 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 24 
               
             
             
               
                   
               
               
                 Optical properties for an uniaxial stretched cellulose acetate 
               
               
                 propionate film (DS Ac  = 1.58, DS Pr  = 0.85, DS OH  = 0.57) with TXIB and 
               
               
                 2-naphthyl benzoate. 
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Stretch 
                 Stretch 
               
               
                   
                 Re (589) 
                 Rth (589) 
                 Thickness 
                   
                   
                   
                   
                 Temp 
                 Ratio MD × 
               
               
                 Entry 
                 (nm) 
                 (nm) 
                 (micron) 
                 A Re   
                 B Re   
                 A Rth   
                 B Rth   
                 (C.) 
                 TD 
               
               
                   
               
             
          
           
               
                 216 
                 158.42 
                 −83.62 
                 86 
                 0.977 
                 1.012 
                 0.967 
                 1.020 
                 175 
                 1 × 1.10 
               
               
                 217 
                 173.42 
                 −90.71 
                 86 
                 0.975 
                 1.012 
                 0.971 
                 1.022 
                 175 
                 1 × 1.20 
               
               
                 218 
                 202.54 
                 −105.94 
                 82 
                 0.974 
                 1.013 
                 0.974 
                 1.022 
                 175 
                 1 × 1.30 
               
               
                 219 
                 216.11 
                 −113.55 
                 76 
                 0.973 
                 1.013 
                 0.977 
                 1.021 
                 175 
                 1 × 1.40 
               
               
                 220 
                 241.30 
                 −126.32 
                 72 
                 0.972 
                 1.015 
                 0.970 
                 1.021 
                 175 
                 1 × 1.60 
               
               
                 221 
                 252.99 
                 −142.79 
                 68 
                 0.969 
                 1.017 
                 0.935 
                 1.019 
                 175 
                 1 × 1.80 
               
               
                 222 
                 69.82 
                 −121.46 
                 58 
                 0.969 
                 1.020 
                 0.979 
                 1.014 
                 175 
                 1 × 1.40 
               
               
                 223 
                 124.19 
                 −67.29 
                 86 
                 0.978 
                 1.012 
                 0.965 
                 1.021 
                 180 
                 1 × 1.10 
               
               
                 224 
                 163.57 
                 −86.10 
                 84 
                 0.976 
                 1.012 
                 0.966 
                 1.024 
                 180 
                 1 × 1.20 
               
               
                 225 
                 174.44 
                 −90.87 
                 82 
                 0.974 
                 1.012 
                 0.967 
                 1.025 
                 180 
                 1 × 1.30 
               
               
                 226 
                 194.23 
                 −103.64 
                 76 
                 0.973 
                 1.013 
                 0.975 
                 1.023 
                 180 
                 1 × 1.40 
               
               
                 227 
                 230.94 
                 −117.91 
                 72 
                 0.972 
                 1.014 
                 0.973 
                 1.021 
                 180 
                 1 × 1.60 
               
               
                 228 
                 67.57 
                 −109.32 
                 52 
                 0.966 
                 1.024 
                 0.974 
                 1.014 
                 180 
                 1 × 1.50 
               
               
                 229 
                 76.91 
                 −105.80 
                 48 
                 0.968 
                 1.022 
                 0.978 
                 1.016 
                 180 
                 1 × 1.60 
               
               
                 230 
                 78.10 
                 −114.86 
                 45 
                 0.966 
                 1.023 
                 0.999 
                 0.980 
                 180 
                 1 × 1.70 
               
               
                   
               
             
          
         
       
     
         [0178]    Examples 222 and 228-230 are constrained and examples 216-221 and 223-227 are not constrained. 
         [0179]    Following the general solvent cast procedures described above, the solution for Examples 231-242 was used to obtain single layer films. The films were annealed at 100° C. and 120° C. for 10 minutes, respectively, before they were uniaxially stretched under the different stretching conditions. Some optical data are listed in Table 25. 
         [0000]    
       
         
               
               
               
             
           
               
                   
               
             
             
               
                 Total solids 
                 52.8 
                 g 
               
               
                 Cellulose ester 
                 43.2 
                 g 
               
               
                 Plasticizer 
                 0.96 
                 g 2,2,4-trimethyl-1,3-pentanediol (TXIB) 
               
               
                 Plasticizer 
                 3.84 
                 g 2-naphthyl benzoate 
               
               
                 Total solvent 
                 352 
                 g 
               
               
                 Methylene chloride 
                 316.8 
                 g 
               
               
                 Methanol 
                 35.20 
                 g 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 25 
               
             
             
               
                   
               
               
                 Optical properties for an uniaxial stretched cellulose acetate 
               
               
                 propionate film (DS Ac  = 1.58, DS Pr  = 0.85, DS OH  = 0.57) with TXIB and 
               
               
                 2-naphthyl benzoate. 
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Stretch 
                 Stretch 
               
               
                   
                 Re (589) 
                 Rth (589) 
                 Thickness 
                   
                   
                   
                   
                 Temp 
                 Ratio 
               
               
                 Entry 
                 (nm) 
                 (nm) 
                 (micron) 
                 A Re   
                 B Re   
                 A Rth   
                 B Rth   
                 (C.) 
                 MD × TD 
               
               
                   
               
             
          
           
               
                 231 
                 134.07 
                 −71.00 
                 86 
                 0.954 
                 1.021 
                 0.944 
                 1.035 
                 175 
                 1 × 1.10 
               
               
                 232 
                 158.67 
                 −83.41 
                 84 
                 0.953 
                 1.022 
                 0.949 
                 1.035 
                 175 
                 1 × 1.20 
               
               
                 233 
                 204.61 
                 −112.31 
                 84 
                 0.950 
                 1.023 
                 0.954 
                 1.033 
                 175 
                 1 × 1.30 
               
               
                 234 
                 206.95 
                 −109.06 
                 82 
                 0.950 
                 1.023 
                 0.955 
                 1.033 
                 175 
                 1 × 1.40 
               
               
                 235 
                 225.95 
                 −117.64 
                 74 
                 0.945 
                 1.026 
                 0.946 
                 1.039 
                 175 
                 1 × 1.60 
               
               
                 236 
                 224.50 
                 −121.11 
                 70 
                 0.943 
                 1.027 
                 0.931 
                 1.032 
                 175 
                 1 × 1.80 
               
               
                 237 
                 100.11 
                 −54.32 
                 86 
                 0.959 
                 1.022 
                 0.954 
                 1.029 
                 180 
                 1 × 1.10 
               
               
                 238 
                 167.09 
                 −90.08 
                 86 
                 0.955 
                 1.021 
                 0.953 
                 1.033 
                 180 
                 1 × 1.20 
               
               
                 239 
                 146.09 
                 −76.72 
                 82 
                 0.956 
                 1.022 
                 0.947 
                 1.034 
                 180 
                 1 × 1.30 
               
               
                 240 
                 205.06 
                 −108.43 
                 80 
                 0.949 
                 1.023 
                 0.954 
                 1.035 
                 180 
                 1 × 1.40 
               
               
                 241 
                 170.53 
                 −87.35 
                 74 
                 0.948 
                 1.024 
                 0.945 
                 1.038 
                 180 
                 1 × 1.60 
               
               
                 242 
                 215.23 
                 −113.65 
                 68 
                 0.943 
                 1.027 
                 0.934 
                 1.026 
                 180 
                 1 × 1.80 
               
               
                   
               
             
          
         
       
     
         [0180]    Examples 231-242 are not constrained. 
         [0181]    Following the general solvent cast procedures described above, the solution for Examples 243-256 was used to obtain single layer films. The films were annealed at 100° C. and 120° C. for 10 minutes, respectively, before they were uniaxially stretched under the different stretching conditions. Some optical data are listed in Table 26. 
         [0000]    
       
         
               
               
               
             
           
               
                   
               
             
             
               
                 Total solids 
                 52.8 
                 g 
               
               
                 Cellulose ester 
                 43.2 
                 g 
               
               
                 Plasticizer 
                 0.48 
                 g 2,2,4-trimethyl-1,3-pentanediol (TXIB) 
               
               
                 Plasticizer 
                 4.32 
                 g 2-naphthyl benzoate 
               
               
                 Total solvent 
                 352 
                 g 
               
               
                 Methylene chloride 
                 316.8 
                 g 
               
               
                 Methanol 
                 35.20 
                 g 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 26 
               
             
             
               
                   
               
               
                 Optical properties for an uniaxial stretched cellulose acetate 
               
               
                 propionate film (DS Ac  = 1.58, DS Pr  = 0.85, DS OH  = 0.57) with TXIB and 
               
               
                 2-naphthyl benzoate. 
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Stretch 
                 Stretch 
               
               
                   
                 Re (589) 
                 Rth (589) 
                 Thickness 
                   
                   
                   
                   
                 Temp 
                 Ratio 
               
               
                 Entry 
                 (nm) 
                 (nm) 
                 (micron) 
                 A Re   
                 B Re   
                 A Rth   
                 B Rth   
                 (C.) 
                 MD × TD 
               
               
                   
               
             
          
           
               
                 243 
                 140.03 
                 −77.42 
                 86 
                 0.934 
                 1.031 
                 0.927 
                 1.045 
                 175 
                 1 × 1.10 
               
               
                 244 
                 146.71 
                 −77.87 
                 82 
                 0.932 
                 1.031 
                 0.925 
                 1.048 
                 175 
                 1 × 1.20 
               
               
                 245 
                 174.36 
                 −91.09 
                 80 
                 0.926 
                 1.033 
                 0.925 
                 1.050 
                 175 
                 1 × 1.30 
               
               
                 246 
                 180.62 
                 −93.43 
                 78 
                 0.926 
                 1.034 
                 0.928 
                 1.049 
                 175 
                 1 × 1.40 
               
               
                 247 
                 222.70 
                 −115.51 
                 74 
                 0.919 
                 1.037 
                 0.925 
                 1.051 
                 175 
                 1 × 1.60 
               
               
                 248 
                 199.32 
                 −103.71 
                 66 
                 0.915 
                 1.039 
                 0.915 
                 1.051 
                 175 
                 1 × 1.80 
               
               
                 249 
                 111.23 
                 −58.32 
                 86 
                 0.940 
                 1.030 
                 0.932 
                 1.041 
                 180 
                 1 × 1.10 
               
               
                 250 
                 121.61 
                 −63.71 
                 86 
                 0.936 
                 1.031 
                 0.930 
                 1.044 
                 180 
                 1 × 1.20 
               
               
                 251 
                 155.72 
                 −81.53 
                 82 
                 0.931 
                 1.030 
                 0.927 
                 1.045 
                 180 
                 1 × 1.30 
               
               
                 252 
                 146.88 
                 −78.58 
                 76 
                 0.931 
                 1.031 
                 0.925 
                 1.049 
                 180 
                 1 × 1.40 
               
               
                 253 
                 187.23 
                 −96.12 
                 72 
                 0.922 
                 1.036 
                 0.921 
                 1.054 
                 180 
                 1 × 1.60 
               
               
                 254 
                 177.27 
                 −92.05 
                 66 
                 0.919 
                 1.037 
                 0.921 
                 1.051 
                 180 
                 1 × 1.80 
               
               
                 255 
                 65.09 
                 −105.47 
                 62 
                 0.917 
                 1.043 
                 0.947 
                 1.035 
                 180 
                 1 × 1.50 
               
               
                 256 
                 57.33 
                 −82.54 
                 52 
                 0.917 
                 1.043 
                 0.944 
                 1.038 
                 180 
                 1 × 1.60 
               
               
                   
               
             
          
         
       
     
         [0182]    Examples 243-254 are constrained and examples 255-256 are not constrained. 
         [0183]    Following the general solvent cast procedures described above, the solution for Examples 257-266 was used to obtain single layer films. The films were annealed at 100° C. and 120° C. for 10 minutes, respectively, before they were uniaxially stretched under the different stretching conditions. Some optical data are listed in Table 27. 
         [0000]    
       
         
               
               
               
             
           
               
                   
               
             
             
               
                 Total solids 
                 48.0 
                 g 
               
               
                 Cellulose ester 
                 43.2 
                 g 
               
               
                 Plasticizer 
                 2.4 
                 g 2,2,4-trimethyl-1,3-pentanediol (TXIB) 
               
               
                 Plasticizer 
                 2.4 
                 g 2-naphthyl benzoate 
               
               
                 Total solvent 
                 352 
                 g 
               
               
                 Methylene chloride 
                 316.8 
                 g 
               
               
                 Methanol 
                 35.20 
                 g 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 27 
               
             
             
               
                   
               
               
                 Optical properties for an uniaxial stretched cellulose acetate 
               
               
                 butyrate film (DS Ac  = 2.25, DS Bu  = 0.21, DS OH  = 0.54) with TXIB and 2- 
               
               
                 naphthyl benzoate. 
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Stretch 
                 Stretch 
               
               
                   
                 Re (589) 
                 Rth (589) 
                 Thickness 
                   
                   
                   
                   
                 Temp 
                 Ratio 
               
               
                 Entry 
                 (nm) 
                 (nm) 
                 (micron) 
                 A Re   
                 B Re   
                 A Rth   
                 B Rth   
                 (C.) 
                 MD × TD 
               
               
                   
               
               
                 257 
                 253.60 
                 −147.81 
                 78 
                 1.009 
                 0.999 
                 1.008 
                 0.999 
                 175 
                 1 × 1.10 
               
               
                 258 
                 252.14 
                 −139.26 
                 80 
                 1.008 
                 1.000 
                 1.006 
                 1.000 
                 180 
                 1 × 1.10 
               
               
                 259 
                 270.03 
                 −143.27 
                 82 
                 1.009 
                 1.000 
                 1.000 
                 1.001 
                 180 
                 1 × 1.20 
               
               
                 260 
                 189.01 
                 −104.49 
                 84 
                 1.008 
                 0.998 
                 1.003 
                 0.997 
                 185 
                 1 × 1.10 
               
               
                 261 
                 230.30 
                 −121.28 
                 84 
                 1.008 
                 0.999 
                 1.000 
                 1.003 
                 185 
                 1 × 1.20 
               
               
                 262 
                 108.23 
                 −205.03 
                 54 
                 1.007 
                 1.002 
                 1.010 
                 0.992 
                 175 
                 1 × 1.40 
               
               
                 263 
                 108.39 
                 −195.36 
                 50 
                 1.005 
                 1.003 
                 1.023 
                 0.980 
                 175 
                 1 × 1.45 
               
               
                 264 
                 101.89 
                 −168.59 
                 47 
                 1.003 
                 1.004 
                 1.022 
                 0.977 
                 180 
                 1 × 1.50 
               
               
                 265 
                 112.54 
                 −196.07 
                 42 
                 1.001 
                 1.008 
                 1.118 
                 0.896 
                 180 
                 1 × 1.60 
               
               
                 266 
                 166.19 
                 −207.17 
                 56 
                 1.004 
                 1.003 
                 0.997 
                 0.986 
                 180 
                 1 × 1.80 
               
               
                   
               
             
          
         
       
     
         [0184]    Examples 257-261 are constrained and examples 262-266 are not constrained. 
         [0185]    Following the general solvent cast procedures described above, the solution for Examples 267-277 was used to obtain single layer films. The films were annealed at 100° C. and 120° C. for 10 minutes, respectively, before they were uniaxially stretched under the different stretching conditions. Some optical data are listed in Table 28. 
         [0000]    
       
         
               
               
               
             
           
               
                   
               
             
             
               
                 Total solids 
                 48.0 
                 g 
               
               
                 Cellulose ester 
                 43.2 
                 g 
               
               
                 Plasticizer 
                 1.92 
                 g 2,2,4-trimethyl-1,3-pentanediol (TXIB) 
               
               
                 Plasticizer 
                 2.88 
                 g 2-naphthyl benzoate 
               
               
                 Total solvent 
                 352 
                 g 
               
               
                 Methylene chloride 
                 316.8 
                 g 
               
               
                 Methanol 
                 35.20 
                 g 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 28 
               
             
             
               
                   
               
               
                 Optical properties for an uniaxial stretched cellulose acetate 
               
               
                 butyrate film (DS Ac  = 2.25, DS Bu  = 0.21, DS OH  = 0.54) with TXIB and 2- 
               
               
                 naphthyl benzoate. 
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Stretch 
                 Stretch 
               
               
                   
                 Re (589) 
                 Rth (589) 
                 Thickness 
                   
                   
                   
                   
                 Temp 
                 Ratio MD × 
               
               
                 Entry 
                 (nm) 
                 (nm) 
                 (micron) 
                 A Re   
                 B Re   
                 A Rth   
                 B Rth   
                 (C.) 
                 TD 
               
               
                   
               
             
          
           
               
                 267 
                 239.07 
                 −131.15 
                 84 
                 0.991 
                 1.007 
                 0.990 
                 1.010 
                 180 
                 1 × 1.10 
               
               
                 268 
                 264.48 
                 −139.15 
                 84 
                 0.992 
                 1.007 
                 0.987 
                 1.010 
                 180 
                 1 × 1.20 
               
               
                 269 
                 169.86 
                 −88.79 
                 82 
                 0.992 
                 1.006 
                 0.986 
                 1.013 
                 185 
                 1 × 1.10 
               
               
                 270 
                 236.82 
                 −123.03 
                 84 
                 0.990 
                 1.006 
                 0.991 
                 1.009 
                 185 
                 1 × 1.20 
               
               
                 271 
                 253.54 
                 −130.37 
                 84 
                 0.990 
                 1.007 
                 0.988 
                 1.011 
                 185 
                 1 × 1.30 
               
               
                 272 
                 288.46 
                 −147.92 
                 82 
                 0.989 
                 1.009 
                 0.981 
                 1.013 
                 185 
                 1 × 1.40 
               
               
                 273 
                 262.81 
                 −135.18 
                 76 
                 0.987 
                 1.009 
                 0.977 
                 1.010 
                 185 
                 1 × 1.60 
               
               
                 274 
                 99.13 
                 −186.32 
                 62 
                 0.988 
                 1.009 
                 0.980 
                 1.011 
                 180 
                 1 × 1.40 
               
               
                 275 
                 97.83 
                 −167.71 
                 58 
                 0.982 
                 1.014 
                 0.996 
                 0.987 
                 185 
                 1 × 1.60 
               
               
                 276 
                 85.86 
                 −130.02 
                 42 
                 0.980 
                 1.016 
                 1.030 
                 0.973 
                 185 
                 1 × 1.70 
               
               
                 277 
                 83.65 
                 −142.85 
                 58 
                 0.985 
                 1.013 
                 0.989 
                 1.007 
                 185 
                 1 × 1.50 
               
               
                   
               
             
          
         
       
     
         [0186]    Examples 267-273 are constrained and examples 274-277 are not constrained. 
         [0187]    Following the general solvent cast procedures described above, the solution for Examples 278-288 was used to obtain single layer films. The films were annealed at 100° C. and 120° C. for 10 minutes, respectively, before they were uniaxially stretched under the different stretching conditions. Some optical data are listed in Table 29. 
         [0000]    
       
         
               
               
               
             
           
               
                   
               
             
             
               
                 Total solids 
                 48.0 
                 g 
               
               
                 Cellulose ester 
                 43.2 
                 g 
               
               
                 Plasticizer 
                 1.92 
                 g 2,2,4-trimethyl-1,3-pentanediol (TXIB) 
               
               
                 Plasticizer 
                 2.88 
                 g 2-naphthyl benzoate 
               
               
                 Total solvent 
                 352 
                 g 
               
               
                 Methylene chloride 
                 316.8 
                 g 
               
               
                 Methanol 
                 35.20 
                 g 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 29 
               
             
             
               
                   
               
               
                 Optical properties for an uniaxial stretched cellulose acetate 
               
               
                 butyrate film (DS Ac  = 2.25, DS Bu  = 0.21, DS OH  = 0.54) with TXIB and 2- 
               
               
                 naphthyl benzoate. 
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Stretch 
                 Stretch 
               
               
                   
                 Re (589) 
                 Rth (589) 
                 Thickness 
                   
                   
                   
                   
                 Temp 
                 Ratio MD × 
               
               
                 Entry 
                 (nm) 
                 (nm) 
                 (micron) 
                 A Re   
                 B Re   
                 A Rth   
                 B Rth   
                 (C.) 
                 TD 
               
               
                   
               
             
          
           
               
                 278 
                 197.86 
                 −106.67 
                 84 
                 0.975 
                 1.012 
                 0.981 
                 1.013 
                 180 
                 1 × 1.10 
               
               
                 279 
                 247.09 
                 −131.27 
                 82 
                 0.974 
                 1.014 
                 0.976 
                 1.019 
                 180 
                 1 × 1.30 
               
               
                 280 
                 178.49 
                 −93.43 
                 86 
                 0.974 
                 1.013 
                 0.967 
                 1.025 
                 185 
                 1 × 1.10 
               
               
                 281 
                 189.52 
                 −99.20 
                 84 
                 0.975 
                 1.012 
                 0.969 
                 1.022 
                 185 
                 1 × 1.20 
               
               
                 282 
                 239.24 
                 −126.20 
                 82 
                 0.972 
                 1.015 
                 0.973 
                 1.023 
                 185 
                 1 × 1.30 
               
               
                 283 
                 243.28 
                 −128.16 
                 80 
                 0.974 
                 1.014 
                 0.978 
                 1.020 
                 185 
                 1 × 1.40 
               
               
                 284 
                 266.76 
                 −143.26 
                 76 
                 0.970 
                 1.017 
                 0.965 
                 1.024 
                 185 
                 1 × 1.60 
               
               
                 285 
                 286.43 
                 −154.83 
                 72 
                 0.968 
                 1.018 
                 0.947 
                 1.025 
                 185 
                 1 × 1.80 
               
               
                 286 
                 70.37 
                 −129.61 
                 47 
                 0.968 
                 1.020 
                 0.966 
                 1.015 
                 185 
                 1 × 1.50 
               
               
                 287 
                 95.41 
                 −146.78 
                 54 
                 0.972 
                 1.020 
                 0.961 
                 1.010 
                 185 
                 1 × 1.60 
               
               
                 288 
                 93.37 
                 −132.20 
                 44 
                 0.971 
                 1.021 
                 0.967 
                 1.011 
                 185 
                 1 × 1.70 
               
               
                   
               
             
          
         
       
     
         [0188]    Examples 278-285 are constrained and examples 286-288 are not constrained. 
         [0189]    Following the general solvent cast procedures described above, the solution for Examples 289-303 was used to obtain single layer films. The films were annealed at 100° C. and 120° C. for 10 minutes, respectively, before they were uniaxially stretched under the different stretching conditions. Some optical data are listed in Table 30. 
         [0000]    
       
         
               
               
               
             
           
               
                   
               
             
             
               
                 Total solids 
                 48.0 
                 g 
               
               
                 Cellulose ester 
                 43.2 
                 g 
               
               
                 Plasticizer 
                 1.92 
                 g 2,2,4-trimethyl-1,3-pentanediol (TXIB) 
               
               
                 Plasticizer 
                 2.88 
                 g 2-naphthyl benzoate 
               
               
                 Total solvent 
                 352 
                 g 
               
               
                 Methylene chloride 
                 316.8 
                 g 
               
               
                 Methanol 
                 35.20 
                 g 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 30 
               
             
             
               
                   
               
               
                 Optical properties for an uniaxial stretched cellulose acetate 
               
               
                 butyrate film (DS Ac  = 2.25, DS Bu  = 0.21, DS OH  = 0.54) with TXIB and 2- 
               
               
                 naphthyl benzoate. 
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Stretch 
                 Stretch 
               
               
                   
                 Re (589) 
                 Rth (589) 
                 Thickness 
                   
                   
                   
                   
                 Temp 
                 Ratio 
               
               
                 Entry 
                 (nm) 
                 (nm) 
                 (micron) 
                 A Re   
                 B Re   
                 A Rth   
                 B Rth   
                 (C.) 
                 MD × TD 
               
               
                   
               
             
          
           
               
                 289 
                 193.25 
                 −105.94 
                 86 
                 0.951 
                 1.023 
                 0.948 
                 1.036 
                 180 
                 1 × 1.10 
               
               
                 290 
                 234.23 
                 −127.35 
                 84 
                 0.950 
                 1.023 
                 0.957 
                 1.034 
                 180 
                 1 × 1.20 
               
               
                 291 
                 241.55 
                 −135.48 
                 82 
                 0.953 
                 1.023 
                 0.958 
                 1.032 
                 180 
                 1 × 1.30 
               
               
                 292 
                 263.21 
                 −155.36 
                 82 
                 0.952 
                 1.024 
                 0.959 
                 1.031 
                 180 
                 1 × 1.40 
               
               
                 293 
                 280.57 
                 −155.02 
                 78 
                 0.949 
                 1.026 
                 0.943 
                 1.036 
                 180 
                 1 × 1.60 
               
               
                 294 
                 287.67 
                 −157.92 
                 76 
                 0.946 
                 1.028 
                 0.911 
                 1.053 
                 180 
                 1 × 1.80 
               
               
                 295 
                 158.49 
                 −86.52 
                 86 
                 0.959 
                 1.020 
                 0.953 
                 1.032 
                 185 
                 1 × 1.10 
               
               
                 296 
                 196.83 
                 −101.94 
                 86 
                 0.954 
                 1.021 
                 0.950 
                 1.036 
                 185 
                 1 × 1.20 
               
               
                 297 
                 198.92 
                 −105.41 
                 84 
                 0.953 
                 1.022 
                 0.952 
                 1.035 
                 185 
                 1 × 1.30 
               
               
                 298 
                 232.48 
                 −121.33 
                 84 
                 0.953 
                 1.022 
                 0.957 
                 1.031 
                 185 
                 1 × 1.40 
               
               
                 199 
                 281.16 
                 −151.21 
                 78 
                 0.953 
                 1.024 
                 0.950 
                 1.030 
                 185 
                 1 × 1.60 
               
               
                 300 
                 285.10 
                 −153.23 
                 74 
                 0.946 
                 1.027 
                 0.948 
                 1.032 
                 185 
                 1 × 1.80 
               
               
                 301 
                 72.58 
                 −121.31 
                 54 
                 0.945 
                 1.029 
                 0.965 
                 1.021 
                 185 
                 1 × 1.50 
               
               
                 302 
                 91.20 
                 −158.00 
                 52 
                 0.941 
                 1.029 
                 0.985 
                 1.002 
                 185 
                 1 × 1.60 
               
               
                 303 
                 90.58 
                 −123.29 
                 47 
                 0.943 
                 1.032 
                 0.942 
                 1.014 
                 185 
                 1 × 1.70 
               
               
                   
               
             
          
         
       
     
         [0190]    Examples 289-300 are constrained and examples 301-303 are not constrained. 
         [0191]    Following the general solvent cast procedures described above, the solution for Examples 304-319 was used to obtain single layer films. The films were annealed at 100° C. and 120° C. for 10 minutes, respectively, before they were uniaxially stretched under the different stretching conditions. Some optical data are listed in Table 31. 
         [0000]    
       
         
               
               
               
             
           
               
                   
               
             
             
               
                 Total solids 
                 48.0 
                 g 
               
               
                 Cellulose ester 
                 43.2 
                 g 
               
               
                 Plasticizer 
                 0.48 
                 g 2,2,4-trimethyl-1,3-pentanediol (TXIB) 
               
               
                 Plasticizer 
                 4.32 
                 g 2-naphthyl benzoate 
               
               
                 Total solvent 
                 352 
                 g 
               
               
                 Methylene chloride 
                 316.8 
                 g 
               
               
                 Methanol 
                 35.20 
                 g 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 31 
               
             
             
               
                   
               
               
                 Optical properties for an uniaxial stretched cellulose acetate 
               
               
                 butyrate film (DS Ac  = 2.25, DS Bu  = 0.21, DS OH  = 0.54) with TXIB and 2- 
               
               
                 naphthyl benzoate. 
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Stretch 
                 Stretch 
               
               
                   
                 Re (589) 
                 Rth (589) 
                 Thickness 
                   
                   
                   
                   
                 Temp 
                 Ratio 
               
               
                 Entry 
                 (nm) 
                 (nm) 
                 (micron) 
                 A Re   
                 B Re   
                 A Rth   
                 B Rth   
                 (C.) 
                 MD × TD 
               
               
                   
               
             
          
           
               
                 304 
                 186.06 
                 −86.39 
                 86 
                 0.935 
                 1.029 
                 0.891 
                 1.071 
                 180 
                 1 × 1.10 
               
               
                 305 
                 192.70 
                 −92.15 
                 84 
                 0.931 
                 1.030 
                 0.874 
                 1.081 
                 180 
                 1 × 1.20 
               
               
                 306 
                 216.06 
                 −115.11 
                 78 
                 0.927 
                 1.034 
                 0.916 
                 1.059 
                 180 
                 1 × 1.30 
               
               
                 307 
                 223.97 
                 −118.94 
                 78 
                 0.925 
                 1.034 
                 0.929 
                 1.051 
                 180 
                 1 × 1.40 
               
               
                 308 
                 261.94 
                 −146.31 
                 70 
                 0.920 
                 1.037 
                 0.925 
                 1.047 
                 180 
                 1 × 1.60 
               
               
                 309 
                 257.65 
                 −145.68 
                 66 
                 0.918 
                 1.038 
                 0.926 
                 1.047 
                 180 
                 1 × 1.80 
               
               
                 310 
                 91.28 
                 −149.04 
                 56 
                 0.917 
                 1.040 
                 0.946 
                 1.033 
                 180 
                 1 × 1.50 
               
               
                 311 
                 169.52 
                 −84.34 
                 86 
                 0.929 
                 1.031 
                 0.904 
                 1.062 
                 185 
                 1 × 1.10 
               
               
                 312 
                 177.78 
                 −94.66 
                 80 
                 0.934 
                 1.029 
                 0.931 
                 1.047 
                 185 
                 1 × 1.20 
               
               
                 313 
                 231.36 
                 −123.23 
                 82 
                 0.930 
                 1.032 
                 0.940 
                 1.044 
                 185 
                 1 × 1.30 
               
               
                 314 
                 208.45 
                 −109.55 
                 76 
                 0.925 
                 1.034 
                 0.931 
                 1.049 
                 185 
                 1 × 1.40 
               
               
                 315 
                 246.22 
                 −133.14 
                 72 
                 0.920 
                 1.037 
                 0.919 
                 1.053 
                 185 
                 1 × 1.60 
               
               
                 316 
                 207.56 
                 −116.00 
                 64 
                 0.914 
                 1.038 
                 0.932 
                 1.043 
                 185 
                 1 × 1.80 
               
               
                 317 
                 67.79 
                 −115.60 
                 48 
                 0.916 
                 1.044 
                 0.947 
                 1.029 
                 185 
                 1 × 1.50 
               
               
                 318 
                 60.09 
                 −99.08 
                 40 
                 0.912 
                 1.045 
                 0.954 
                 1.022 
                 185 
                 1 × 1.60 
               
               
                 319 
                 70.29 
                 −110.31 
                 41 
                 0.913 
                 1.045 
                 0.966 
                 1.012 
                 185 
                 1 × 1.70 
               
               
                   
               
             
          
         
       
     
         [0192]    Examples 304-309 and 311-316 are not constrained. Examples 310 and 317-319 are constrained. 
         [0193]    The invention has been described in detail with particular reference to preferred embodiments thereof, but it will be understood that variations and modifications can be effected within the spirit and scope of the invention.