Patent Publication Number: US-2005131126-A1

Title: Production of polymer nanocomposites using supercritical fluids

Description:
BACKGROUND OF THE INVENTION  
      1. Field of Invention  
      The present invention relates to a method for production of reinforced polymer nanocomposites comprising a polymer matrix having dispersed therein swellable clays. In particular, the present invention relates to the reinforced polymer composites having particular properties and the method for its production using preferentially selected polymers, supercritical fluids, and clay intercalants.  
      2. Related Art  
      Methods have been developed to facilitate the exfoliation of clays in polymer-clay mixtures to generate polymer nanocomposite compositions. However, none of the existing methods efficiently disperse the clay within the polymer. Therefore, a need exists for an exfoliation method for polymer-clay mixtures that will produce polymer nanocomposites having efficient dispersion of the clay throughout the polymer nanocomposite.  
     SUMMARY OF THE INVENTION  
      The present invention provides a method for the production of polymer nanocomposites which overcomes the aforementioned deficiencies and others inter alia provides a method for maximum and efficient dispersion of the clay throughout the reinforced polymer.  
      One aspect of the present invention is a method of forming a polymer nanocomposite comprising the steps of: selecting a clay having a layered structure and a polymer, said selecting satisfying |S p −S scf &gt;|S c −S scf | and |S c −S scf |≦2.0 (cal/cm 3 ) 0.5 , wherein S p  is a solubility parameter of the polymer, S c  is a solubility parameter of the clay; and S scf  is a solubility parameter of a supercritical fluid (SCF); mixing the polymer and the clay to form a polymer-clay mixture; melting the polymer-clay mixture to form a polymer-clay melt; initially contacting the polymer-clay melt with the SCF while the SCF is subject to an initial pressure exceeding the critical pressure of the SCF and to a temperature exceeding the critical temperature of the SCF; and after said initially contacting step, further contacting the polymer-clay melt with the SCF while the SCF is subject to a lower pressure that is less than the critical pressure of the SCF so as to exfoliate the clay to form the nanocomposite having the exfoliated clay being substantially dispersed throughout the polymer-clay melt.  
      A second aspect of the present invention is a system for forming a polymer nanocomposite, comprising: a polymer-clay melt of a clay having a layered structure and a polymer; and a supercritical fluid (SCF) in physical contact with the polymer-clay melt, wherein the clay, the polymer, and the SCF collectively satisfy |S p −S scf &gt;|S c −S scf | and |S c −S scf |≦2.0 (cal/cm 3 ) 0.5 , and wherein S p  is a solubility parameter of the polymer, S c  is a solubility parameter of the clay; and S scf  is a solubility parameter of the SCF. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
      The features of the present invention will best be understood from a detailed description of the invention and an embodiment thereof selected for the purpose of illustration and shown in the accompanying drawing in which:  
       FIG. 1  depicts a process schematic for mixing a polymer and clay, in accordance with embodiments of the present invention;  
       FIG. 2  depicts a process schematic for melting the polymer-clay mixture, in accordance with embodiments of the present invention;  
       FIG. 3  depicts a table of solubility parameters for polymers, supercritical fluids, and clays, in accordance with embodiments of the present invention;  
       FIG. 4  depicts dispersion curves denoting the degree of nonuniformity of a distribution of polymer particles in a polymer matrix, in accordance with embodiments of the present invention;  
       FIG. 5  is a flow chart of a method for making a polymer nanocomposite, in accordance with embodiments of the present invention;  
       FIG. 6  depicts an exfoliated polymer nanocomposite, in accordance with embodiments of the present invention; and  
       FIGS. 7A and 7B  depict an extruder of  FIG. 2  along with associated pressure profiles, in accordance-with embodiments of the present invention. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION  
      Although certain embodiments of the present invention will be shown and described in detail, it should be understood that various changes and modifications may be made without departing from the scope of the appended claims. The scope of the present invention will in no way be limited to the number of constituting components, the materials thereof, the shapes thereof, the relative arrangement thereof, etc. . . . , and are disclosed simply as an example of an embodiment. The features and advantages of the present invention are illustrated in detail in the accompanying drawing, wherein like reference numeral refer to like elements throughout the drawings. Although the drawings are intended to illustrate the present invention, the drawings are not necessarily drawn to scale.  
       FIG. 1  depicts a process schematic for mixing a polymer and a clay comprising a fully intermeshing, co-rotating twin extruder  15  and a convection oven  16 , in accordance with an embodiment of the present invention. The clay has a layered structure (e.g., a clay gallery). The extruder  15  may be a model such as the ZSK  30 , Werner &amp; Pfleiderer, and the like. The twin screw extruder  15  comprises an extruder hopper  19 , screws  20 , a vacuum port  21 , and an extruder die  22 . The length (L 1 ) to diameter (D 1 ) ratio (L 1 I/D 1 ) of the screw  20  may be in a range of 20 to 50 (e.g., 30).  
      As shown in  FIG. 1  and the step  63  of the  FIG. 5 , namely mixing the polymer and the clay to form a polymer-clay mixture, the step  63  is performed via the extruder  15 . A mixture  11  of the polymer and the clay is dry-blended and fed into the extruder  15  via the extruder hopper  19  along with thermal stabilizers and lubricants. The ratio of polymer to clay in the mixture may be in a range of from about 50/50 percent to about 99/1 percent, by weight. Alternatively, the polymer and clay may be fed into the extruder  15  separately giving a final percent by weight of the polymer-clay mixture ranging from about 50/50 percent to about 99/1 percent by weight.  
      The polymer-clay mixture is kneaded in the first kneading block zone  23  with complete melting of the polymer upon exiting the zone  23 . The polymer-clay mixture then enters the second kneading zone  24  where mechanical forces exerted by the extruder screws  20  of the extruder  15  disperse the clay within the polymer-clay mixture. As the polymer-clay mixture exits the kneading zone  24 , a vacuum is applied to the extruder  15  via the vent  21  to remove any volatiles that may be present in the polymer-clay mixture. The polymer-clay mixture then passes through the extruder die  22  preforming the mixture into polymer-clay pellets  25 . The pellets  25  are dried at a temperature from about 65° C. to about 85° C. for about 10 hrs to about 18 hrs in the convection oven  16  affording dried pellets  26 . The extruder  15  operates at a temperature from about 200° C. to about 250° C., with a screw speed from about 200 rpm to about 500 rpm, and a throughput from about 10 kg/hr to about 400 kg/hr. The extruder die  22  operates at a temperature from about 200° C. to about 270° C.  
       FIG. 2  depicts a process schematic for melting the polymer-clay mixture, i.e. polymer-clay pellets  26  and initially contacting a polymer-clay melt  42 , with a SCF  30  using a tandem single screw extrusion setup  31 , in accordance of the present invention. The setup  31  comprises a primary single screw extruder  32 , a secondary single screw extruder  33 , and a positive displacement pump  34 . The primary extruder  32  further comprises an extruder hopper  35 , a single screw  36 , and a delivery attachment  37 . The length to diameter ratio (L 2 /D 2 ) of the screw  36  may be in a range of 15 to 30 (e.g., L 2 =32.3 inches, D 2 =1.5 inches, L 2 /D 2 =21.5). The extruder  32  may have a compression ration of, inter alia, 2.5. The secondary single screw extruder  33  comprises a single screw  38 , an extruder die  39 , a torpedo type breaker plate  44 . The length to diameter ratio (L 3 /D 3 ) of the screw  38  maybe in a range of 5 to 15 (e.g., L 3 =17.2 inches, D 3 =2.0 inches, L 3 /D 3 =8.6).  
      As shown in  FIG. 2  and the step  64  of  FIG. 5 , namely melting said polymer-clay mixture to form a polymer-clay melt, the polymer-clay pellets  26  are fed into the extruder  32  via the extruder hopper  35 . The single screw  36  rotates from about  20  rpm to about 100 rpm. As the pellets  26  pass along the single screw  36 , the pellets  26  are heated from about 170° C. to about 250° C. melting the pellets  26  resulting in a polymer-clay melt  42 .  
      As shown in  FIG. 2  and the step  65  of  FIG. 5 , namely initially contacting the polymer-clay melt  42  with the SCF  30  while the SCF is subject to an initial pressure exceeding the critical pressure of the SCF  30  and to a temperature exceeding the critical temperature of the SCF  30 , the melt  42  then is delivered to the secondary single screw extruder  33  through the delivery attachment  37 , in accordance with the present invention. The secondary extruder  33  operates from about 20 rpm to about 100 rpm. The positive displacement pump  34  injects the SCF  30  into the upstream portion of the extruder  33 , via an injection valve assembly  43 . Injection of the SCF  30  occurs at a pressure from about 1,000 to about 3,500 pounds per square inch (psi) and at a speed from about 1.0 ml/min to about 10.0 ml/min.  
      When the SCF  30  is injected into the extruder  33 , a pressure gradient is created within the extruder  33 . An upstream pressure from about 1,000 psi to about 3,500 psi exists while a downstream pressure from about 500 psi to about 3,000 psi is initially maintained by the extruder die  39 . The extruder die  39  is able to control and maintain the pressure within the extruder  33  from about 500 psi to about 3,500 psi. Due to the pressure gradient, the SCF  30  depressurizes along the extruder screw  38  and contacts the polymer-clay melt  42 .  
      The SCF  30  preferentially migrates toward the clay gallery of the polymer-clay melt  42  because the SCF  30  is more soluble or thermodynamically miscible toward the clay than toward the polymer of the polymer-clay melt  42 . The preferential migration of the SCF  30  toward the clay results in the clay being dispersed throughout the polymer-clay melt  42 , i.e. exfoliation of the clay when the pressure is less than the critical pressure of the SCF  30 . As the SCF  30  and the polymer-clay melt  42  travel through the extruder  33 , the polymer-clay melt  42  is exfoliated and mixed as will be described infra in conjunction with  FIGS. 7A and 7B . After exfoliation, the polymer-clay melt  42  is extruded via the extruder die  39  and exits the extruder die  33 , resulting in a polymer nanocomposite  46  having the clay substantially dispersed throughout the polymer nanocomposite.  
      Using a co-rotating twin screw extruder and a tandem single screw extrusion line, as previously described, to form polymer nanocomposites is not meant to limit the scope of the production process in an embodiment of the present invention. Polymer nanocomposites can be produced using the co-rotating twin screw extruder and the tandem single screw extrusion line, the co-rotating twin screw extruder, the tandem single screw extruder, individually and combinations thereof in accordance with the method and system of the present invention.  
       FIG. 7A  depicts the secondary extruder  33  of  FIG. 2  along with an exemplary pressure profile P A  within the extruder  33 , in accordance with embodiments of the present invention. The extruder  33  includes the torpedo type breaker plate  44 . As shown in  FIG. 7A , the polymer-clay melt  42  enters the extruder  33  at (or in the vicinity of) entrance  40  and the resulting polymer nanocomposite  46  exits the extruder  33  at the exit surface  49 . The SCF  30  also enters the extruder  33  at (or in the vicinity of) entrance  40 . Within the extruder  33 , the SCF  30  is subject to the pressure P A  whose profile is depicted in  FIG. 7A . The pressure to which the SCF  30  in subjected at or in the vicinity of entrance  40 , and the pressure P A1  which the SCF  30  in subjected at the end  41  of the screw  38 , is above the critical pressure P CRIT  of the SCF  30 . The temperature to which the SCF  30  in subjected in the vicinity of entrance  40 , and the temperature at which the SCF  30  in subjected at the end  41  of the screw  38 , is above the critical temperature of the SCF  30 . Therefore, the SCF  30  is in its supercritical state at or in the vicinity of the entrance  40  and at the end  41  of the screw  38 .  
      In the example of  FIG. 7A , P A1 =3500 psi. For illustrative purposes, it is assumed that the P CRIT =3000 psi. The pressure P A  decreases along the screw  38  from P A1  to P A2 , wherein P A2  is the pressure at the end  18  of the screw  38 . Due to contact between the clay and the SCF  30  as facilitated by satisfying Equations (7)-(8), exfoliation of the clay in the polymer-clay melt  42  occurs when the pressure P A  is below P CRIT . Thus if P A2 &lt;P CRIT  (i.e., P A2 &lt;3000 psi wherein P CRIT =3000 psi) then the exfoliation will occur in region  28  along the portion of the screw  38  in which P A1 &lt;P CRIT . Region  28  exists between the screw  38  and the exterior surface  27  of the extruder  33 . Thus if P A2 &lt;P CRIT , then a pressure of P CRIT  and less than P CRIT  exists in region  28 .  
      However if P A2 ≧P CRIT , then the pressure exceeds P CRIT  throughout region  28  and exfoliation will occur exclusively between the end  18  of the screw  38  and the exit surface  49  where the pressure is less than P CRIT . Thus, the pressure is reduced to P CRIT  at some location between the end  18  of the screw  38  and the exit surface  49 . Note that the pressure profile P A  may have continuous portions (e.g., in region  28 ) and also be essentially discontinuous at discrete locations such as at the end  18  of the screw  38 .  
      The value of P A2  relative to the pressure P A1  at the end  41  of the screw  38  may be controlled by the volume of region  28 . |P A2 −P A1 | is a monotonically decreasing function of the volume in region  28 . Moreover, if the thickness (t) of the region  29  is diminished, then the magnitude of the pressure drop in region  29  in the vicinity of the end  18  of the screw  38  will be correspondingly reduced, so that the pressure drop in region  29  in the vicinity of the end  18  can be made as small as desired. Indeed, if the volume in region  28  is made sufficiently small to cause P A2 ≧P CRIT  and if the thickness (t) of the region  29  is made sufficiently small, then it may be possible to constrain the pressure P A  to be above P CRIT  throughout the extruder  33 , such that the exfoliation of the clay in the polymer-clay melt  42  occurs entirely outside of the extruder  33 . Thus for the case of exfoliation of the clay occurring entirely outside of the extruder  33 , the pressure is above P CRIT  throughout the extruder  33  and the SCF  30  is subject to a pressure below P CRIT  after exiting the extruder  33  at the exit surface  49 . Therefore, the user of the present invention may design the extruder  33  to adjust the pressure P A  profile such that the exfoliation of the clay in the polymer-clay melt  42  occurs wherever desired, such as along a portion of the screw  38 , between the end  18  of the screw  38  (a volume  12 ) and the exit surface  49 , outside the extruder  33 , etc.  
       FIG. 7B  depicts  FIG. 7A  with the torpedo breaker plate  44  replaced by a plug type breaker plate  47 , in accordance with embodiments of the present invention. As shown in  FIG. 7B  and the step  66 , after said initially contacting step, further contacting the polymer-clay melt with the SCF while the SCF is subject to a lower pressure that is less than the critical pressure of the SCF so as to exfoliate the clay to form the nanocomposite having the exfoliated clay being substantially dispersed throughout the polymer-clay melt, the pressure profile in  FIG. 7B  is denoted as P B .  
      The pressure P B  in  FIG. 7B  may be adjusted to control exfoliation of the clay in the polymer-clay melt  42  similar to the manner in which the pressure P A  in  FIG. 7A  may be adjusted to control said exfoliation, except that the volume  13  around the plug type breaker plate  47  in  FIG. 7B  may be substantially smaller than the volume  12  around the torpedo type breaker plate  44  in  FIG. 7A . Due to the relatively smaller volume  13  in  FIG. 7B  as compared with the volume  12  in  FIG. 7A , which facilitates a tendency toward higher pressure in the volume  13  than in the volume  12 , it is easier to maintain P A  above P CRIT  throughout the extruder  33  of  FIG. 7A  than to maintain P B  above P CRIT  throughout the extruder  33  of  FIG. 7B . Accordingly, it is easier to design the extruder  33  to have the exfoliation of the clay in the polymer-clay melt  42  occurring exclusively outside of the extruder  33  in the embodiment of  FIG. 7B  than in the embodiment of  FIG. 7A .  
      A necessary condition exists for efficient exfoliation of the polymer-clay mixture of the present invention and any polymer-clay mixture in general. The SCF  30  must preferentially migrate into the clay gallery of the polymer-clay mixture rather than migrate into the polymer matrix. Prior art does not address the migration phenomena. The SCF  30  is incorrectly assumed in the prior art to be in the clay gallery. Prior art neither provides any theoretical or experimental justification for the presence of the SCF  30  in the clay gallery nor explain or describe why such an environment, promoting preferential migration of a SCF  30 , would even exist. The preferential migration of the SCF  30  into the clay gallery rather than the polymer matrix is dependent upon satisfying the solubility relationships of Equations (7)-(8), described infra.  
       FIG. 3  depicts a table of solubility parameter values and absolute values of the difference of the solubility parameter values for polymers, supercritical fluids (SCF), and clays. Column  1  is a listing of polymers with column  2  listing the solubility parameter of the polymers (S p ). Column  4  is a listing of SCFs with column  5  listing the solubility parameter of the SCF (S scf ). Column  6  is a listing of clays with column  7  listing the solubility parameter of the clays (S c ). Column  3  is a listing of values resultant from the argument |S p −S scf |. Column  8  is a listing of values resultant from the argument |S c −S scf |. All solubility parameter values are given in units of (cal/cm 3 ) 0.5 .  
      The abbreviations for the polymers, SCFs, and clays are listed in  FIG. 2  are explained below:  
                                  Polymer                             PS   Polystyrene           HDPE   High Density Polyethylene           LDPE   Low Density Polyethylene           PP   Poly(propylene)           PVDF   Poly(vinylidene fluoride)           PET   Poly(ethylene teraphthalate)           PVA-VOH   Poly(vinyl acetate-co-vinyl alcohol)           POM   Poly(acetal)           PVDC   Poly(vinylidene chloride)           PVOH   Poly(vinyl alcohol)           PAN   Poly(acrylonitrile)                 Clay                             Fluoro-1   Aliphatic fluorocarbons           Fluoro-2   Perfluoroalkylpolyethers           Siloxane   Quarternary ammonium termintated               poly(dimethylsiloxane)           A-Ammonium   alkyl quarternary ammonium                 Supercritical Fluid (SCF)                             CO 2     Carbon dioxide           R-12   CF 2 Cl 2                        
 
      The solubility parameter (S) for organic liquids varies with temperature as shown by Eq. 1  
             S   =           Δ   ⁢           ⁢   H     -   RT     V               (   1   )             
 
 where ΔH is the molar enthalpy of vaporization, R is the gas constant, T is the temperature in Kelvin, and V is the molar volume. For gases with low critical temperatures such as N 2 , He, H 2 , and O 2 , the solubility of the gases increase with temperature. Conversely for gases with high critical temperatures such as CO 2 , the solubility decreases with temperature. 
 
      The solubility parameter of a polymer, a clay, or liquid can be calculated using the simple but powerful group contribution method as shown in Eq. (2)  
             S   =         ∑     i   =   1     j     ⁢           ⁢     E   i           ∑     i   =   1     j     ⁢           ⁢     V   i                 (   2   )             
 
 where E i  is the molar attraction constant and V i  is the molar volume constant for component i. Using the group contribution method, to a first approximation, the solubility parameters for many polymers can be estimated. For example, the solubility parameter for poly(methylmethacrylate) (PMMA)  
                 
 
      can be determined using Eq. (2) above and Table 1 below.  
               TABLE 1                          Molar Attraction and Volume Constants                                 Group   E [cal * cm 3 ) 0.5 /mol]   V (cm 3 /mol)                                             CH3   218   31.8           CH2   132   16.5           &lt;C&gt;   −97   −14.8           COO   298   19.6                                             S   =         132   +     2   ⁢     (   218   )       -   97   +   298       16.5   +     2   ⁢     (   31.8   )       -   14.8   +   19.6       =   9.1                    
 
 The solubility parameter of PMMA is determined to be 9.1 (cal/cm 3 ) 0.5  calculated by the group contribution method. 
 
      A supercritical fluid is any substance above its critical temperature and critical pressure. Supercritical fluids exhibit physicochemical properties intermediate between those of liquids and gases, i.e. solubilities approaching a liquid phase and diffusivities approaching a gas phase. The solubility parameter for CO 2  has been determined to be 3.5 (cal/cm 3 ) 0.5  at a typical processing temperature of 177° C. and a pressure of 3,500 psi. At a given pressure and temperature, the CO 2  solubility parameter was calculated with the help of molecular dynamics software, Materials Studio v2.2 (Accelrys, Inc.). The calculated value of 3.5 (cal/cm 3 ) 0.5  is in excellent agreement reported literature values. Table 2 lists properties of hydorchlorofluorocarbons (HCFCs) and chlorofluorocarbons (CFCs).  
                           TABLE 2                          Refrigerant   Chemical   Critical Points   S                                     Codes   Formula   T c     P c     ρ c     (cal/cm 3 ) 0.5                 R-11   CFCl 3     198   4.41   0.5539   7.6       R-12   CF 2 Cl 2     112   4.13   0.5572   5.5       R-21   CHFCl 2     178   5.18   0.5251   8.3       R-22   CHF 2 Cl    96   4.97   0.5209   8.3       R-112   C 2 Cl 4 F 2     N/A   N/A   N/A   7.8       R-123   CHCl 2 CF 3     184   3.67   N/A   7.8       R-142b   C 2 H 3 ClF 2     137   4.12   0.4351   8.1       —   CO 2      31   7.38   0.4682   —                  
 
 From table 2, the average solubility parameter for HCFC and CFC is 8.0 (cal/cm 3 ) 0.5  with R-12 being an exception. 
 
      The solubility parameter (S x ), is related to the Gibbs free energy of mixing equation, Eq. 3 
 
Δ G=ΔH−TΔS    (3) 
 
 where ΔG is the Gibbs free energy of mixing, ΔH is the enthalpy of mixing, and ΔS is the entropy of mixing. For a binary system, the heat of mixing per unit volume is 
 
Δ H/V =( S   1   −S   2 )Φ 1 Φ 2    (4) 
 
 where S is the solubility parameter and Φ is the volume fraction. For Eq. 3 to be less than zero, i.e. thermodynamically miscible system, the solubility parameters S 1  and S 2  of Eq. 4 must be close to each other. 
 
      For systems that exhibit strong interactions between system components, such as hydrogen bonding, if the difference between the solubility parameters of the system components is less than 2.0 (cal/cm 3 ) 0.5 , solubility can be expected. Strong solubility/affinity between system components would have solubility values that lie between 1.0 (cal/cm 3 ) 0.5  and 2.0 (cal/cm 3 ) 0.5 . The strongest solubility/affinity system components would have solubility values that are 1.0 (cal/cm 3 ) 0.5  or less. This concept can be represented mathematically by the Equations (5) and (6). 
 
| S   1   −S   2 |≦2.0   (5) 
 
| S   1   −s   2 |≦1.0   (6) 
 
      Applying Equations (5) and (6) to the preferential migration of the SCF into a clay gallery, Equations (7) and (8) can be derived to represent a condition that must be satisfied if preferential migration of the SCF into a clay gallery is to occur. 
 
| S   1   −S   2 |≦2.0   (7) 
 
 A second condition that must be satisfied for preferential migration of the SCF into a clay is represented by Eq. (8) 
 
| S   p   −s   scf   |&gt;|S   c   −S   scf |  (8) 
 
 where S c , S p , and S scf  are the solubility parameter of the clay, the polymer, and the supercritical fluid respectively. 
 
      As shown in  FIG. 3  and the step  62  of  FIG. 5 , selecting a clay having a layered structure and a polymer, said selecting satisfying |S p −S scf &gt;|S c −S scf | and |S c −S scf |≦2.0 (cal/cm 3 ) 0.5 , wherein S p  is a solubility parameter of the polymer, S c  is a solubility parameter of the clay; and S scf  is a solubility parameter of a supercritical fluid (SCF), of the method  60 , to be used in the production of a polymer nanocomposite, the polymer must satisfy Equations (7) and (8). 
 
| S   c   −S   scf |≦2.0   (7) 
 
| S   p   −S   scf   |&gt;|S   c   −S   scf  |  (8) 
 
      A candidate polymer for use in a polymer nanocomposite may be determined by substituting in Equations (7) and (8) the corresponding solubility parameter as well as the solubility parameters of the SCF and clay also to be used. If Equations (7) and (8) are satisfied, the polymer is considered to be a candidate polymer for use in a polymer nanocomposite. For example, to determine if PS would make a candidate polymer in a polymer nanocomposite with CO 2  as the SCF and a Fluoro-2 as the clay, the solubility parameters of the aforementioned would be substituted into the Equations (7) and (8). From  FIG. 3 , the solubility parameter of PS, CO 2 , and Fluoro-2 are 9.2, 3.5, and 4.5 respectively. Substitution into Equations (7) and (8) give: 
 
| S   p   −S   scf   |&gt;|S   c   −S   scf   | |S   c   −S   scf |≦2.0 
 
|9.2−3.5|&gt;|4.5−3.5| |4.5−3.5|≦2.0 
 
5.7&gt;1.0 1.0≦2.0 
 
 Having satisfied the Equations (7) and (8), PS is considered to be a candidate polymer for use in a polymer nanocomposite with CO 2  and Fluoro-1 as the SCF and the clay respectively. 
 
      Other examples of candidate polymers that satisfy Equations (7) and (8) are listed below with sample calculations. Solubility parameter values are from  FIG. 3 .  
      High Density Polyethylene (HDPE) with CO 2  and Fluoro-2 
 
| S   p   −S   scf   |&gt;|S   c   −S   scf   | |S   c   −S   scf |≦2.0 
 
|8.0−3.5|&gt;|4.5−3.5| |4.5−3.5|≦2.0 
 
4.5&gt;1.0 1.0≦2.0 
 
      Low Density Polyethylene (LDPE) with R-12 and Fluoro-1 
 
| S   p   −S   scf   |&gt;|S   c   −S   scf   | |S   c   −S   scf |≦2.0 
 
|8.0−5.5|&gt;|5.9−5.5| |5.9−5.5|≦2.0 
 
2.5&gt;0.4 0.4≦2.0 
 
      Poly(vinyl alcohol) (PVOH) with A-Ammonium and CFC |S p −S scf |&gt;|S c −S scf |
 
| S   c   −S   scf |2.0 
 
|12.6−8.0|&gt;|8.0−8.0| |8.0−8.0|≦2.0 
 
4.6&gt;0.0 0.0≦2.0 
 
      A table of candidate polymers for use in polymer nanocomposites along with compatible SCFs and clays is listed below in Table 3. All the polymers listed along with the corresponding variations of compatible SCFs and clays satisfy Equations (7) and (8).  
                               TABLE 3                                   Polymer   SCF   Clay           Type   Type   Type                          PS   CO 2     Fluora-2           PS   CO 2     Siloxane           HDPE   CO 2     Fluoro-2           HDPE   CO 2     Siloxane           LDPE   CO 2     Fluoro-2           LDPE   CO 2     Siloxane           PP   CO 2     Fluoro-2           PP   CO 2     Siloxane           PVDF   CO 2     Fluoro-2           PVDF   CO 2     Siloxane           PS   R-12   Fluoro-1           PS   R-12   Fluoro-2           PS   R-12   Siloxane           HDPE   R-12   Fluoro-1           HDPE   R-12   Fluoro-2           HDPE   R-12   Siloxane           LDPE   R-12   Fluoro-1           LDPE   R-12   Fluoro-2           LDPE   R-12   Siloxane           PP   R-12   Fluoro-1           PP   R-12   Fluoro-2           PP   R-12   Siloxane           nylon 6   HCFC, CFC   A-Ammonium           PET   HCFC, CFC   A-Ammonium           PVA-VOH   HCFC, CFC   A-Ammonium           POM   HCFC, CFC   A-Ammonium           PVDC   HCFC, CFC   A-Ammonium           PVOH   HCFC, CFC   A-Ammonium           nylon 6, 6   HCFC, CFC   A-Ammonium           PAN   HCFC, CFC   A-Ammonium                      
 
      If Equations (7) and (8) are not satisfied, the polymer is considered not to be a candidate polymer for use in a polymer nanocomposite. For example, from  FIG. 3 , the solubility parameter of PS (8.0), A-Ammonium (8.0), and CO 2  (3.5) would be substituted into the Equations (7) and (8). 
 
| S   p   −S   scf   |&gt;|S   c   −S   scf   | |S   c   −S   scf |≦2.0 
 
|8.0−3.5|&gt;|8.0−3.5| |8.0−3.5|≦2.0 
 
4.5≯1.0 4.5≮2.0 
 
 Not having satisfied Equations (7) and (8), PS is not considered to be a candidate polymer for use in a polymer nanocomposite with CO 2  and A-Ammonium as the SCF and the clay respectively. 
 
      Other examples of polymers that do not satisfy Equations (7) and (8) are listed below with sample calculations.  
      LDPE with CO 2  and A-Ammonium 
 
| S   p   −S   scf   |&gt;|S   c   −S   scf   | |S   c   −S   scf |≦2.0 
 
|8.0−3.5|&gt;|8.0−3.5| |8.0−3.5|≦2.0 
 
4.5≯4.5 4.5≮2.0 
 
      Poly(vinyldene fluoride) (PVDF) with CO 2  and A-Ammonium 
 
| S   p   −S   scf   |&gt;|S   c   −S   scf   | |S   c   −S   scf |≦2.0 
 
|8.0−3.5|&gt;|8.0−3.5| |8.0−3.5|≦2.0 
 
3.1≯4.5 4.5≮2.0 
 
      A table of polymers for that would not be candidates for use in polymer nanocomposites along with the SCFs and the clays is listed in Table 4 below.  
                               TABLE 4                                   Polymer   SCF   Clay                          PVDF   CO 2     A-Ammonium           HDPE   CO 2     A-Ammonium           LDPE   CO 2     A-Ammonium           PS   CO 2     A-Ammonium           PP   CO 2     A-Ammonium           nylon 6   CO 2     A-Ammonium           PET   CO 2     A-Ammonium           PVA-VOH   CO 2     A-Ammonium           POM   CO 2     A-Ammonium           PVDC   CO 2     A-Ammonium           PVOH   CO 2     A-Ammonium           nylon 6, 6   CO 2     A-Ammonium           PAN   CO 2     A-Ammonium                      
 
      In choosing the candidate polymers for the use in polymer nanocomposites, the polymers listed in  FIG. 3  and table 3 are not meant to limit the scope of the polymers that may be chosen in an embodiment of the present invention. Any polymer that has a solubility parameter satisfying Equations (7) and (8), whether measured or theoretically calculated, may be used in the method  1  for producing polymer nanocomposites.  
      The candidate polymers may be selected from a group including but not limited to high density polyethylene, low density polyethylene, nylon 6, nylon 6, 6, poly(acrylonitrile), poly(ethylene terephthalate), poly(acetal), poly(propylene), polystyrene, poly(vinyl acetate-co-vinyl alcohol), poly(vinylidene chloride), poly(vinylidene fluoride), poly(vinyl alcohol), and the like.  
      As shown in  FIG. 3  and the step  62  of  FIG. 5 , selecting a clay having a layered structure and a polymer, said selecting satisfying Equations (7) and (8). 
 
| S   c   −S   scf |≦2.0   (7) 
 
| S   c   −S   scf   |&lt;|S   p   −S   scf|   (8) 
 
 A candidate clay for use in a polymer nanocomposite may be determined by substituting in Equations (7) and (8) the corresponding solubility parameter of the clay as well as the solubility parameters of the SCF and the polymer also to be used. 
 
      If Equations (7) and (8) are satisfied, the clay is considered to be a candidate clay for use in a polymer nanocomposite. For example, to determine if A-Ammonium would make a candidate clay in a reinforced nanocomposite with CFC as the SCF and a nylon-6 as the polymer, the solubility parameters of the aforementioned would be substituted into the Equations (7) and (8). From  FIG. 3 , the solubility parameter of A-Ammonium, CFC, and nylon-6 are 8.0, 8.0, and 10.1 respectively. Substitution into Equations (7) and (8) give: 
 
| S   c   −S   scf   |&lt;|S   p   −S   scf   | |S   c   −S   scf |≦2.0 
 
|8.0−8.0|&lt;|10.1−3.5| |8.0−8.0|≦2.0 
 
0.0&lt;6.6 0.0≦2.0 
 
 Having satisfied the Equations (7) and (8), A-Ammonium is considered to be a candidate clay for use in a reinforced nanocomposite with CFC and nylon-6 as the SCF and polymer respectively. 
 
      Other examples of candidate clays that satisfy Equations (7) and (8) are listed below with sample calculations. The solubility parameter values are from  FIG. 3 .  
      Quarternary ammonium terminated PDMS (Siloxane) with R-12 and HDPE 
 
| S   c   −S   scf   | |S   p   −S   scf   | |S   c   −S   scf |≦2.0 
 
|5.4−5.5|&lt;|8.0−5.5| |5.4−5.5|≦2.0 
 
0.1&lt;2.5 0.1≦2.0 
 
      Fluoro-2 with CO 2  and Poly(propylene) (PP) 
 
| S   c   −S   scf   |&lt;|S   c   −S   scf   | |S   c   −S   scf |≦2.0 
 
|4.5−3.5|&lt;|8.0−3.5| |4.5−3.5|≦2.0 
 
1.0&lt;4.5 1.0≦2.0 
 
      A-Ammonium with HCFC and PVOH 
 
| S   c   −S   scf   |&lt;|S   c   −S   scf   | |S   c   −S   scf |≦2.0 
 
|8.0−8.0|&lt;|12.6−8.0| |8.0−8.0|≦2.0 
 
0.0&lt;4.6 0.0≦2.0 
 
      A table of candidate clays for use in polymer nanocomposites along with compatible SCFs and polymers is listed below in Table 5. All the clays listed along with the compatible SCFs and polymers satisfy Equations (7) and (8).  
                               TABLE 5                                   Clay   Supercritical Fluid   Polymer                          A-Ammonium   HCFC, CFC   nylon 6           A-Ammonium   HCFC, CFC   PET           A-Ammonium   HCFC, CFC   PVA-VOH           A-Ammonium   HCFC, CFC   POM           A-Ammonium   HCFC, CFC   PVDC           A-Ammonium   HCFC, CFC   PVOH           Fluoro-1   R-12   PS           Fluoro-1   R-12   HDPE           Fluoro-1   R-12   LDPE           Fluoro-1   R-12   PP           Fluoro-2   CO 2     PS           Fluoro-2   CO 2     HDPE           Fluoro-2   CO 2     LDPE           Fluoro-2   CO 2     PP           Fluoro-2   CO 2     PVDF           Fluoro-2   R-12   PS           Fluoro-2   R-12   HDPE           Fluoro-2   R-12   LDPE           Fluoro-2   R-12   PP           Siloxane   CO 2     PS           Siloxane   CO 2     HDPE           Siloxane   CO 2     LDPE           Siloxane   CO 2     PP           Siloxane   CO 2     PP           Siloxane   R-12   PS           Siloxane   R-12   HDPE           Siloxane   R-12   LDPE           Siloxane   R-12   PP                      
 
      If Equations (7) and (8) are not satisfied, the clay is not considered to be a candidate clay for use in a polymer nanocomposite. For example, to determine if the clay A-Ammonium is a candidate polymer; the solubility parameter of A-Ammonium (8.0), CO 2  (3.5), and PVDF (6.6) and would be substituted into the Equations (7) and (8). 
 
| S   c   −S   scf )&lt;|S p   −S   scf   | |S   c   −S   scf |≦2.0 
 
|8.0−3.5|&lt;|6.6−3.5| |8.0−3.5|≦2.0 
 
4.5≯4.1 4.5≮2.0 
 
 Not having satisfied the argument of Equations (7) and (8), A-Ammonium is not considered to be a candidate clay for use in a polymer nanocomposite with CO 2  and PVDF as the SCF and polymer respectively. 
 
      Other examples of clays that do not satisfy Equations (7) and (8) are listed below with sample calculations.  
      A-Ammonium with CO 2  and Nylon 6 
 
| S   c   −S   scf   |&lt;|S   c   −S   scf   | |S   c   −S   scf |≦2.0 
 
|8.0−3.5|&lt;|10.1−3.5| |8.0−3.5|≦2.0 
 
4.5&lt;6.6 4.5≮2.0 
 
      A-Ammonium with CO 2  and PVOH 
 
| S   c   −S   scf   |&gt;|S   p   −S   scf   | |S   c   −S   scf |≦2.0 
 
|8.0−3.5|&gt;|12.6−3.5| |8.0−3.5|≦2.0 
 
4.5&lt;9.1 4.5≮2.0 
 
      A table of clays for that would not be candidates for use in polymer nanocomposites along with the SCFs and polymers is listed below in Table 6.  
                               TABLE 6                                   Clay   SCF   Polymer                          A-Ammonium   CO 2     PVDF           A-Ammonium   CO 2     HDPE           A-Ammonium   CO 2     LDPE           A-Ammonium   CO 2     PS           A-Ammonium   CO 2     PP           A-Ammonium   CO 2     nylon 6           A-Ammonium   CO 2     PET           A-Ammonium   CO 2     PVA-VOH           A-Ammonium   CO 2     POM           A-Ammonium   CO 2     PVDC           A-Ammonium   CO 2     PVOH           A-Ammonium   CO 2     nylon 6, 6           A-Ammonium   CO 2     PAN                      
 
      In choosing the candidate clays for the use in polymer nanocomposites, the clays listed in  FIG. 3  and table 5 are not meant to limit the scope of the clays that may be chosen in an embodiment of the present invention. Any clay that has a solubility parameter satisfying Equations (7) and (8), whether measured or theoretically calculated, may be used in the method 60, for producing polymer nanocomposites.  
      The use of the term clay is not meant to limit the scope of the type of clay that may be selected for the method 60, producing polymer nanocomposites. The term clay, as used in the present invention, encompass clays that are modified as well as non-modified. Modified clays are clays that have an intercalant coupled to the clay by methods known to one ordinarily skilled in the art. The intercalant may be organic or inorganic in nature, and combinations thereof. The nature of the intercalant defines the nature of the modified clay. For example, a clay having an organic intercalant coupled to the clay is considered to be an organically modified clay. Analogously, a clay having an inorganic intercalant coupled to the clay is an inorganically modified clay. Generally, the solubility parameter of the clay is controlled by the solubility parameter of the intercalant coupled to the clay, i.e. the solubility of the intercalant is representative of the clay as whole.  
      A clay is but one member of larger category known as swelling material. Swelling materials are comprised of phyllosilicates such as smectite clays; naturally or synthetic, montmorillonite, saponite, hectorite, vermiculite, beidellite, stevensite, and the like. All of which may be used for producing polymer nanocomposites. Any swelling material that has a solubility parameter satisfying Equations (7) and (8), whether measured or theoretically calculated, and is capable of exfoliation by the methods presented in accordance with the present invention, may be used in the method 60, for producing polymer nanocomposites. A filler refers to a group of materials comprising glass fibers, carbon fibers, carbon nanotubes, talc, mica, and the like. Fillers may be used in combination with swelling agents, such as clays, for use in the production of polymer nanocomposites.  
      In selecting the SCFs for the use in producing polymer nanocomposites, the SCFs listed in  FIG. 3  are not meant to limit the scope of the SCFs that may be chosen in an embodiment of the present invention. Any SCF that has a solubility parameter satisfying Equations (7) and (8), whether measured or theoretically calculated, may be used in the method 60, for producing polymer nanocomposites  
      Examples of SCFs that may be selected include but are not limited to hydrocarbons such as propane, n-butane, iso-butane, n-pentane, iso-pentane, 2,2-dimethylpropane, 1-pentene, cyclopentene, n-hexane, 2-methylpentane, 3-methylpentane, 2,3-dimethylpentane, 2,2-dimethylbutane, 1-hexene, cyclohexane, n-heptane, 2-methylhexane, 2,2-dimethylpentane, 2,3-dimethylpentane, 2,4-dimethylpentane, 3,3-dimethylpentane, 3-ethylpentane, 2,3,3-trimethylbutane, 1-heptene, and the like; alcohols such as methanol, ethanol, 2-propanol, and the like; ketones such as acetone, methylethyl ketone, and the like; ethers such as ethyl ether, isopropyl ether, and the like; chlorinated hydrocarbons such as dichloromethane, trichloromethane, trichloroethylene, tetrachloromethane, 1,2-dichloroethane, and the like; fluorinated hydrocarbons such as tetrafluoromethane, triflouromethane, hexaflouroethane, difluoroethane, tetraflouroethane, and the like; and chlorofluorohydrocarbons such as trichlorofluoromethane, dichlorodifluoromethane, chlorotrifluoromethane, dichlorofluoromethane, chlorodifluoromethane, tetrachlorodifluoroethane, trichlorotrifluoroethane, dichlorotetrafluoroethane, chloropentafluoroethane, dichlorofluoroethane, chlorotetrafluoroethane, chlorodifluoroethane, and the like.  
      Selecting the polymer, the clay, and the SCF as previously described, to form polymer nanocomposites is not meant to limit the scope of the number of the aforementioned that may be used to form a polymer nanocomposite. For example, two polymers and one clay may be selected satisfying equations (7)-(8) inconjuntion with the SCF to form a polymer nanocomposite in accordance with the method and system of the present invention. Another example may be selecting one polymer and two clays that satisfy equations (7)-(8) inconjunction with the SCF to form a polymer nanocomposite. Polymer nanocomposites can be formed by selecting polymers and the clays satisfying equations (7)-(8) inconjucntion with the SCFs and combinations thereof in accordance with the method and system of the present invention. Generally, one or more clays may be used with one or more polymers in conjunction with one or more SCFs. Generally, each distinct combination of one clay, one polymer, and one SCF must satisfy Equation (7)-(8).  
      As explained supra, the present invention controls the uniformity of dispersion of the clay within the polymer matrix by adjusting the solubilities S p , S c , and S scf  in accordance with Equations (7)-(8). For convenience, Equation (7)-(8) can be rewritten in the following equivalent form: 
 
F 1 &lt;1   (9) 
 
F 2 ≦1   (10)
 
 where 
 
 F   1   =|S   c   −S   scf   |/|S   p   −S   scf |  (11) 
 
 F   2   =|S   c   −S   scf |/2   (12) 
 
      The extent to which the clay is uniformly dispersed in the polymer matrix by the exfoliation method of the present invention may be empirically determined as a function of F 1  and F 2  as follows. Let the σ represent the degree of dispersion of the clay within the polymer following the exfoliation. σ may be defined, inter alia, as the standard deviation of the distances between the centroids of the clay particles distributed within the polymer matrix; i.e., 
 
σ=[Σ I ( D ( I )− D   AVE ) 2   /N ] ½   (13) 
 
 D   AVE =[Σ I   D ( I )]/ N    (14) 
 
 where N is the number of pairs of clay particles in the polymer matrix, Σ I  denotes summation with respect to the index I from I=1 to I=N, D(I) is the distance between centroids of the two clay particles of the I th  pair of clay particles in the polymer matrix (I=1, 2, . . . , N), and D AVE  is the average of the N distances D(I). Alternatively, D AVE  could be computed as a weighted average for any purpose such as, inter alia, to differentiate the importance of different portions of the polymer matrix or to diminish the effect of outliers. The distances D(I) may be determined by measurement, through analysis of the locations of the clay particles within the polymer matrix following the exfoliation. It is not be necessary to analyze all pairs of clay particles in the polymer matrix, and the value of N reflects the number of such pairs of clay particles actually used in the numerical analysis. N should be large enough to assure the desired statistical accuracy in the calculation of σ. 
 
      To obtain a as a function of F 1  and F 2 , one could vary F 1  while holding F 2  constant. For example, one could select a first SCF (e.g., CO 2 ) and a first clay such that F 2  is 0.3 and select three different polymers such that F 1  is 0.3, 0.6, and 0.9, respectively, which enables σ to be determined by measurement, resulting in the curve  101  in  FIG. 4 , in accordance with embodiments with the present invention. Next, one could select the first SCF and a second clay such that F 2  is 0.6 and select another three different polymers such that F 1  is 0.3, 0.6, and 0.9, which enables σ to be determined by measurement, resulting in the curve  102  in  FIG. 4 . Again, one could select the second SCF and a third clay such that F 2  is 0.9 and select yet another three different polymers, which enables σ to be determined by measurement, resulting in the curve  103  in  FIG. 4 .  
      While the curves  101 ,  102 , and  103  are shown in  FIG. 4  as linear, the actual shapes of the σ versus F 1  curves  101 ,  102 , and  103  result from the empirically determined values of a for the fixed F 2  and varying F 1 . In practice, the curves  102 - 103  may be either linear or non-linear. Alternatively, each plotted curve could represent σ versus F 2  with F 1  being constant for each curve. In addition, one could repeat the preceding process for a second SCF (e.g., R-12) to obtain another set of curves analogous to the curves  101 ,  102 , and  103  of  FIG. 4 .  
      While F 1  has the same set of plotted values (i.e., 0.3, 0.6, 0.9) on each of curves  101 - 103  in  FIG. 4 , the selected polymers for curves  101 - 103  may result in a different set of plotted values of F 1  in each of curves  101 - 103 . Also, the number of plotted points on each of curves  101 - 103  may be the same number of plotted points (e.g., 3 as shown in  FIG. 4 ) or a different number of plotted points for each curve.  
       FIG. 5  depicts a flow chart of method  60 , forming a polymer nanocomposite comprising: the step  62 ; selecting a clay having a layered structure and a polymer, said selecting satisfying |S p −S scf |&gt;|S c   −S   scf | and |S c   −S   scf |≦2.0, wherein S p  is a solubility parameter of the polymer, S c  is a solubility parameter of the clay; and S scf  is a solubility parameter of a supercritical fluid (SCF); the step  63 , mixing the polymer and the clay to form a polymer-clay mixture; the step  64 , melting the polymer-clay mixture to form a polymer-clay melt; the step  65 , initially contacting the polymer-clay melt with the SCF while the SCF is subject to an initial pressure exceeding the critical pressure of the SCF and to a temperature exceeding the critical temperature of the SCF; and the step  66 , after said initially contacting step, further contacting the polymer-clay melt with the SCF while the SCF is subject to a lower pressure that is less than the critical pressure of the SCF so as to exfoliate the clay to form the nanocomposite having the exfoliated clay being substantially dispersed throughout the polymer-clay melt.  
       FIG. 6  depicts an embodiment of the present invention, polymer nanocomposite  46  in which the SCF  30  has been removed. The polymer-clay mixture, i.e. the polymer-clay melt  42 , comprising a polymer  56  and a layered clay  57 , is contacted with the supercritical fluid  30  at the supercritical pressure and the supercritical temperature of the fluid. The SCF  30  preferentially migrates to the clay gallery  58  and exfoliates the clay  57  of the clay gallery  58 . The result is a polymer nanocomposite  46  having the clay  57  dispersed uniformly throughout the polymer  56 .  
      The foregoing description of the embodiments of this invention has been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed, and obviously, many modifications and variations are possible. Such modifications and variations that may be apparent to a person skilled in the art are intended to be included withing the scope of this invention as defined by the accompanying claims.