Abstract:
An extensional rheometer comprises a drive shaft connected to an armature, wherein the armature is further connected to a torque shaft, and two rotatable drums are mounted in the armature. One end of a sample is connected to each drum, and the drums are rotated, stretching the sample until the sample breaks. The torque in the apparatus caused by the stretching of the sample is measured. Environmental control may be provided for testing samples under different conditions.

Description:
TECHNICAL FIELD  
         [0001]    The invention relates to a rheometer or rheometer attachment which is used to measure the viscosity and stress relaxation of polymers, elastomers, and rubber compounds in simple extension.  
         BACKGROUND ART  
         [0002]    Joachim Meissner, in the review article “Polymer Melt Elongation-Methods, Results, and Recent Developments” in Polymer Engineering and Science, April 1987, Vol. 27, No. 8, pp. 537-546 describes different extensional rheometers that have been developed in the prior art. Meissner is also the author of several patents on the subject including U.S. Pat. No. 3,640,127, dated Feb.8, 1972, German 2138504, dated Aug. 02, 1971, German 2243816, dated Sep. 07, 1972 and U.K. 1287367.  
           [0003]    Extensional rheometer designs by Cogswell, Vinogradov, and later Münstedt had in common that one end of the polymer fiber or filament that was used for testing was fixed to a load cell/indicator, while the other end was stretched by mechanical means to a finite maximum elongation. Accordingly, these rheometers operated with a non-uniform extensional rate throughout the sample particularly near the clamped ends of the fiber. Meissner overcame these difficulties with his dual rotary clamp design in which rotary clamps stretched the fiber at either end over a fixed gauged length. See, for example, “Rotary Clamp and Uniaxial and Biaxial Extensional Rheometry of Polymer Melts” by J. Meissner, et al., Journal of Rheology, Vol. 25, pp. 1-28 (1981) and “Development of a Universal Extensional Rheometer for the Uniaxial Extension of Polymer Melts”, by J Meissner, Transactions of the Society of Rheology, Vol. 16, No. 3, pp. 405-420 (1972). In a further development of this type of rheometer, in order to improve the transfer of the circumferential speed of the clamps to the local speed of the sample at the location of clamping (strain rate lag), two rotary clamps in the prior art devices were replaced by Meissner and Hostettler as illustrated in “A New Elongational Rheometer for Polymer Melts and other Highly Viscoelastic Liquids”, Rheological Acta, Vol. 33, pp. 1-21 (1994) with matched/grooved, metal conveyor belts. With this design, however, a measurement was limited to a single rotation of the clamps corresponding to a Hencky strain of seven, and the maximum extensional rate was limited to 1/s (a reciprocal second). The extensional viscosity was determined from the force required to deform the fiber, which was measured by the deflection of leaf springs supporting one set of rotating clamps.  
           [0004]    Other techniques used to measure extensional viscosity involved winding one end of a fiber around a drum and measuring the resultant stretching force at the other fixed end of the fiber, as illustrated in U.S. Pat. No. 3,693,425 (1972) by J M Starita et al. Like the earlier designs, this method imparted a non-uniform extensional deformation to the free gauge length of the stretched fiber, particularly at the fixed end of the fiber. Further, the windup was uncontrolled and precautions had to be taken to ensure that windup did not take place over a portion of previously wound fiber.  
         DISCLOSURE OF THE INVENTION.  
         [0005]    An apparatus for measuring the rate of extensional flow of low modulus solids comprises; (a) a drive shaft mounted in an armature, the armature being connected to a torque shaft, and (b) two rotatable drums in proximity to one another, wherein a first drum is mounted in the armature substantially in alignment with the torque and drive shafts, and a second drum is adjacent thereto.  
           [0006]    In the illustrated embodiment, the first and second drums are in substantially parallel alignment, are mounted on bearings, and may have associated therewith means for directing the windup of a sample on the drums. The drums may be geared to be counter rotating or co-rotating. In the illustrated embodiment, the drums are geared such that the drums rotate at the same speed.  
           [0007]    Also provided is a method for measuring the rate of flow of low modulus solids comprising the steps of, a) providing an apparatus for measuring the rate of extensional flow of low modulus solids comprising a drive shaft mounted in an armature wherein the armature is further connected to a torque shaft, two rotatable drums in proximity to one another wherein the first drum is mounted in the armature substantially in alignment with the torque and drive shafts and the second drum is adjacent thereto, b) fixing a sample to both drums, one end of said sample being attached to each drum, c) causing the two ends of the sample to be pulled away from each other by rotation of the drums, and d) measuring the torque created in the torque shaft by the drawing of the sample.  
           [0008]    The method may further comprise the steps of measuring the maximum torque achieved by the sample and measuring the lapsed time from the start of the measurement to the breaking of the sample. In the illustrated embodiment of the method, the two rotatable drums are mounted substantially in parallel alignment on bearings, and the drums have associated therewith means for directing the windup of a sample on the drums.  
           [0009]    The dual windup threaded drum extensional rheometer illustrated, makes possible the windup of each end of a fiber and imparts a uniform extensional deformation to the unsupported pre gauge length of the fiber, and allows for large extensional deformations by allowing multiple drum rotations with a threaded drum design.  
           [0010]    The rheometer provides a simple design and method to measure the extensional flow properties of polymers, elastomers and compounds. The rheometer of the invention can be attached to any commercially available rotational rheometer, and can be made small enough to fit within the environmental chamber of a rotational rheometer in order to measure extensional flow properties as a function of temperature. The invention may also be part of, or be incorporated into a new type of rheometer. The apparatus can also be used to measure the extensional properties of viscoelastic solids. 
       
    
    
     BRIEF DESCRIPTION OF DRAWINGS  
       [0011]    [0011]FIG. 1 illustrates a side view of the apparatus of the invention illustrating the armature and two parallel rotating drums.  
         [0012]    [0012]FIG. 2 illustrates the apparatus of FIG. 1 rotated 90 degrees.  
         [0013]    [0013]FIG. 3 illustrates an enlarged view of the armature and the rotation drums.  
         [0014]    [0014]FIG. 4 illustrates the apparatus of FIG. 3 rotated 90 degrees.  
         [0015]    [0015]FIG. 5, FIG. 6 and FIG. 6A illustrate the apparatus of the invention contained in an environmental chamber, wherein FIG. 6A illustrates a top of view of an alternative embodiment of the apparatus where the drums are co-rotating.  
         [0016]    [0016]FIG. 7, FIG. 8 and FIG. 8A illustrate an alternative embodiment of the apparatus of the invention.  
         [0017]    [0017]FIG. 9 is a graphic illustration of the top view of the primary and secondary drums as a sample is stretched. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0018]    With reference now to FIGS.  1 - 4 , the apparatus  10  comprises a drive shaft  14 , which is mounted on bearings  28  that are attached to armature  16 , armature  16  further being attached to torque shaft  12 . Mounted within armature  16  are primary windup drum  18  and secondary windup drum  20 .  
         [0019]    Although primary windup drum  18  and secondary windup drum  20  are illustrated as being mounted parallel to one another and directly adjacent to one another, those skilled in the art will recognize that said drums can be mounted at different angles relative to one another, and different angles relative to the torque and drive shafts. Such angular mounting may affect how calculations are done in determining results, but would not affect the results achieved by the apparatus.  
         [0020]    In the illustrated embodiment, primary windup drum  18  is illustrated as being in direct alignment with drive shaft  14  and torque shaft  12 . Those skilled in the art will recognize that this alignment is not necessary for operation of the apparatus, but is preferred to make construction easier and simplify the calculations of torque.  
         [0021]    Each of the windup drums  18 ,  20  have associated therewith means for securing a filament to the drum as required to carry out the measurements desired. In the illustrated embodiment the securing means is filament securing clamp  22 .  
         [0022]    Windup drums  18 ,  20  are mounted on armature  16  through ball bearings  28  and are further connected to gears  36  and  26  respectively. Drive shaft  14  turns gear  36 , gear  36  turns gear  26  which causes rotation of secondary windup drum  20 . The resistance provided by the stretched sample to the turning of secondary windup drum  20  imparts a force to the intermeshing gears  36  and  26 , which in turn imparts a force to armature  16 . This force tends to turn the armature in a direction opposite the direction of rotation of secondary windup drum  20 , wherein the tendency of the armature to turn creates a torque in torque shaft  12  that can be measured.  
         [0023]    In the operation of the apparatus of the invention, the ends of a fiber sample are secured to the windup drums, and constant rotation of the drums imparts a constant, uniform extensional deformation rate to the unsupported pre gauge length of the fiber. The extensional deformation of the fiber offers a resistance to deformation which is related to the extensional viscosity of the sample, which in turn offers a resistance to the drum rotation in the form of a resultant torque on the torque armature. By measuring the resultant torque on the armature, the extensional viscosity of the fiber may be calculated for a given extensional deformation rate and temperature.  
         [0024]    With reference specifically to FIGS. 3 and 4, in an enlarged view of the apparatus, details of the construction of the apparatus can be seen. To those skilled in the mechanical art, other mechanical embodiments of the inventive concepts described herein will be readily apparent.  
         [0025]    The same type of filament securing clamp  22  is used with both primary windup drum  18  and secondary windup drum  20 . Accordingly, filament securing clamp  22  for primary windup drum  18  is illustrative for the method used to secure a filament to both drums in the illustrated embodiment. Filament securing clamp  22  has associated therewith a filament securing clamp knob  40  which is used by the operator to secure a filament  34  or  34 A (see FIGS. 5 and 6A) to a windup drum  18 ,  20 . By depressing the securing clamp knob  40 , the guide hole  41  in the filament securing clamp  22  aligns with the guide hole  42  of the windup drum (see FIG. 4) and the filament  34 ,  34 A is threaded through said aligned holes  41  and  42 . Releasing the clamp knob  40  relieves the securing clamp compression spring  44  causing the edge of the filament securing clamp guide hole  41  to bear against the filament  34 ,  34 A, thus securing the filament in said windup drum guide hole  42 .  
         [0026]    Filament guide means are used to control the manner in which the filament is wound up on the drums, and in the illustrated embodiment the filament guide means is provided by the helical threading  50  on the drums. Thus, in operation, when the windup drums  18 ,  20  are turned, the filament is guided into the helical threads on the drums so that there is no overlap of the filament and there is no distortion in the extensional measurements.  
         [0027]    With reference now to FIGS. 5, 6 and  6 A, the apparatus is illustrated as being contained within an environmental chamber  32  which can be used to heat or cool the sample as desired. In the operation of the apparatus, after a filament is secured to primary windup drum  18  and secondary windup drum  20 , drive shaft  14  is rotated in the direction of arrow C, which causes primary windup drum  18  to rotate in the direction of arrow A. Since, in the embodiment illustrated in FIG. 5, gear  36  and gear  26  are intermeshing, turning of gear  36  causes secondary windup drum  20  to rotate the opposite direction, i.e., in the direction of arrow B. When filament  34  is secured to primary windup drum  18  and secondary drum  20  as illustrated in FIG. 5, the counter rotation of drums  18 ,  20  cause filament  34  to be stretched. As filament  34  is stretched, its resistance to the turning of drums  18  and  20  increases, wherein the resistance of the filament is transferred to secondary windup drum  20  which has a tendency to turn armature  16  in the opposite direction, thereby creating a resultant torque on torque shaft  12  in the direction of arrow F.  
         [0028]    The apparatus is designed so that torque shaft  12  does not actually move, but a torque on torque shaft  12  activates a force rebalance transducer which, through a closed feedback loop in the apparatus, develops a current which tends to counteract the torque imposed on torque shaft  12  by the secondary windup drum, and the current required to counteract this torque is measured, thereby measuring the torque created. Such force rebalance transducers are well known to those skilled in the art.  
         [0029]    Other techniques of measuring torque are known to those skilled in the art, and such other techniques can be used with the apparatus of the invention.  
         [0030]    Environmental chamber  32  is designed to measure the rheology of samples from −70 degrees centigrade to 300 degrees centigrade. Measurements at lower temperatures are designed to measure extensional rheology as it relates to the T g  (glass transition) of the sample, and the extensional flow of the materials at higher temperatures is related to the melt/viscosity of the sample. Environmental chamber  32  can be in the form of an oven or an oil bath, or any other means known to those skilled in the art for controlling the physical state of a sample.  
         [0031]    An embodiment is illustrated in FIG. 6A wherein the primary windup drum  18  and the secondary windup drum  20  are co-rotational. Co-rotation of drums  18  and  20  can be achieved simply by adding an additional gear (not shown) between spur gears  26  and  36 . When co-rotational primary windup drums  18  and second windup drums  20  are used, the sample filament  34 A will be attached to the drums as illustrated in FIG. 6A i.e., between the drums. The resultant torque in such an embodiment will be opposite the resultant torque illustrated in FIG. 5. The same principles of operation as described with respect to an apparatus with counter rotating drums apply.  
         [0032]    With reference again to FIG. 5, a sample  34  in its original state has a relatively substantial thickness as represented by the thick line in the drawing. After the secondary and the primary windup drums have been rotated, the sample is stretched over the diameter of the drums, and accordingly, its cross-sectional thickness is substantially reduced. It is the resistance of the material to stretch, and continued stretching that creates a force on the armature, which transmits a torque to torque shaft  12 .  
         [0033]    With reference now to FIGS. 7, 8, and  8 A, in an alternative embodiment, primary drum  94  and secondary drum  100  of apparatus  90  of the invention can be made smooth, without sample guiding means since many samples are not long enough to survive one rotation of the drums. The securing clamp  102  of each drum can be spring-loaded and fashioned to slide up and down primary drive shaft  92  and secondary shaft  93  of the apparatus during fiber loading and unloading. Also, the torque armature  96  can be made to house intermeshing gears  95  and  97  and to support the ends of the primary and secondary shafts of the apparatus with radial ball bearings  98 , rather than having the shafts cantilevered as in the embodiment earlier described.  
         [0034]    When the invention is used as a fixture on a commercial rotational rheometer in which one of the fixture adapters is affixed to a reciprocating, movable stage, a miniature telescoping ball spline  106  can be incorporated onto the torque shaft  104 . This telescoping ball spline ensures the translation of torque, but not compressive loads, to the torque transducer. Such telescoping ball spines are available from Sterling Instruments, as illustrated in the Handbook of Shafts, Bearings and Couplings, (1995) p. 4-9. The alternative embodiment of the apparatus  90  functions in the same manner described above with respect to apparatus  10 .  
         [0035]    The invention is further illustrated with reference to the following example.  
       EXAMPLE 1  
       [0036]    The apparatus shown in FIGS.  1 - 5  is used for illustrative purposes in this example.  
         [0037]    Both ends of an uncured polymer filament  34  are secured by the spring-loaded fiber securing clamps of the equal diameter windup drums  18 ,  20  of the extensional rheometer  10 . A motor rotating at a fixed rotational rate drives the primary windup drum  18  and a fine toothed spur gear  36  on the same shaft  14 . This spur gear  36  intermeshes with a similar spur gear  26  on the shaft  26   a  connected to the secondary windup drum  20 .  
         [0038]    Since both spur gears are similar, motion of the primary drum  18  drives an equal but opposite rotation of the secondary drum  20 . The shafts of both drums are affixed with precision radial ball bearings  28  housed in the torque armature  16 . The constant rotational speed (Ω) of the drums of equal radius (R) imparts a constant, uniform extensional deformation rate ({acute over (ε)}) to the unsupported length (L) of the fiber  34  such that: 
         {acute over (ε)}=2Ω R/L   
         [0039]    as illustrated graphically in FIG. 9.  
         [0040]    The extension of the fiber offers a resistance to deformation due to the extensional viscosity η E  (t) of the fiber, which in turn offers a resistance to the drum rotation in the form of torque T E . The extensional viscosity of the fiber can be expressed in the following relationship: 
         η E  ( t )=σ E ( t )/{acute over (ε)}= F   E ( t )/ A ( t )/{acute over (ε)} 
         [0041]    Where σ E  (t) is the instantaneous extensional stress in the unsupported fiber, F E  (t) is the instantaneous force required to stretch the unsupported fiber, and A(t) is the instantaneous cross-sectional area of unsupported fiber. The resultant torque acting on the drums may then be expressed as: 
           T   E ( t )= F   E ( t ) 2 R   
         [0042]    Both of these expressions may be combined to yield: 
         η E  ( t )= T   E  ( t )/(2 R {acute over (ε)} A ( t )) 
         [0043]    By measuring the resultant torque on the armature, the extensional viscosity of the fiber may be calculated for a given extensional deformation rate and temperature.  
         [0044]    T E  can be resolved by a summation of torques about point 0 from FIG. 9. Thus, the resistance of the fiber to extend imparts a torque on the gear teeth which in turn imparts a resultant torque, T R , on the torque armature. Since the bearings and intermeshing gears also offer resistance to rotation, a summation of torques yields: 
         Σ  T   O =0= T   R   −T   E   −T   Gears   −T   Bearings   =T   R   −T   E   −T   Friction   
         [0045]    Thus, the above expression for η E  (t) can be rewritten as: 
         η E  ( t )=( T   R ( t )− T   Friction )/ (2 R {acute over (ε)} A ( t )) 
         [0046]    where T R (t) is the resultant torque measured on the torque armature shaft by the torque transducer as a function of time, and T Friction  is the torque losses from the bearings and gears which can be determined from calibration.  
         [0047]    Now for a fiber in simple extension, A(t) can be expressed as: 
           A ( t )= A   o  exp (−{acute over (ε)}  t ) 
         [0048]    where A o  is the original cross-sectional area prior to fiber extension. Substituting the initial expression for {acute over (ε)}, A(t) can be rewritten as: 
           A ( t )= A   o  exp (−2Ω R t )/ L   
         [0049]    Since Ω=d(θ(t))/dt where θ(t) is the angular rotation of the primary windup drum as a function of time, then for a constant rotational drum speed, Ω may be expressed as: 
         Ω=(θ 2 −θ 1 )/( t   2   −t   1 ) 
         [0050]    If it is assumed that θ 1 =0 at t 1 =0 and that a constant rotational speed is achieved instantaneously then the expression for Ω simplifies to: 
         Ω=θ 2   /t   2 =θ( t )/ t   
         [0051]    Assuming no-slip of the fiber on the drum, the above expression can be substituted into the expression for A(t) and the following can be obtained: 
           A ( t )= A   o  exp (−2θ( t ) R t ) /( tL )= A   o exp (−2θ( t )  R/L   
         [0052]    Thus, the resulting expression for the instantaneous cross-sectional area of the fiber sample is only a function of the angular rotation of the primary windup drum at a given time, t. Beyond the realm of validity of the aforementioned assumptions, however, more rigorous empirical methods for determining instantaneous fiber cross-sectional area should be applied and are well known to those skilled in the art.  
         [0053]    Note that each windup drum can be threaded to allow for fiber alignment and multiple drum rotations to allow for very large Hencky strains. In doing so, however, the increaed extensional deformation per drum revolution must be accounted for in the expression for extensional deformation rate, {acute over (ε)}. In addition, a non-circumferential force component must be accounted for in the torque measurement, T R (t).  
         [0054]    While the invention has been specifically illustrated and described, those skilled in the art will recognize that the invention may be variously modified and practiced without departing from the concepts of the invention. The scope of the invention is limited only by the following claims.