Stress-optical coefficient/measurements

Figure 5.9. Effect of strain history on the stress-optical coefficient (measured at 10% strain) for a segmented polyester-urethane at various temperatures. (Estes et al, 1969.)...

The photoelastic measurements were carried out in simple extension using strip specimens. In addition to the force/ also the optical retardation S (hence also the birefringence An <5) could be determined and the modulus G, the deformational-optical function A and the stress-optical coefficient C = A/G were calculated using the equations [31]... 

A special advantage of this method is that the high shear rate range becomes available. It appears that one can measure nu — n33 up to the critical shear stress, at which extrusion defect (melt-fracture) occurs. On the other hand, entrance effects can also be studied, when the windows are located sufficiently close to the entrance. With the aid of the stress-optical coefficient, the corresponding normal stress difference can be... 

From the foregoing it becomes evident that only a measure of the magnitude of the form birefringence, but not of its influence on the extinction angle, can be given. For this purpose the reader may be reminded that the stress-optical coefficient of an infinitely dilute solution can be expressed by one half of the ratio of Maxwell constant to intrinsic viscosity [eq. (2.33)]. In the absence of the form birefringence the limiting... 

Dynamic viscoelastic and stress-optical measurements are reported for blends of crosslinked random copolymers of butadiene and styrene prepared by anionic polymerization. Binary blends in which the components differ in composition by at least 20 percentage units give 2 resolvable loss maxima, indicative of a two-phase domain structure. Multiple transitions are also observed in multicomponent blends. AU blends display an elevation of the stress-optical coefficient relative to simple copolymers of equivalent over-all composition. This elevation is shown to be consistent with a multiphase structure in which the domains have different elastic moduli. The different moduli arise from increased reactivity of the peroxide crosslinking agent used toward components of higher butadiene content. 

As discussed in section 7.1.6.4, semidilute solutions of rodlike polymers can be expected to follow the stress-optical rule as long as the concentration is sufficiently below the onset of the isotropic to nematic transition. Certainly, once such a system becomes nematic and anisotropic, the stress-optical rule cannot be expected to apply. This problem was studied in detail using an instrument capable of combined stress and birefringence measurements by Mead and Larson [109] on solutions of poly(y benzyl L-glutamate) in m-cresol. A pretransitional increase in the stress-optical coefficient was observed as the concentration approached the transition to a nematic state, in agreement of calculations based on the Doi model of polymer liquid crystals [63]. In addition to a dependence on concentration, the stress-optical coefficient was also seen to be dependent on shear rate, and on time for transient shear flows. 

The stress-optical coefficient C is defined by equation (10.27) and the relaxation times t,1 and t][ are defined by relations (2.30). One can see that the dynamo-optical coefficient of dilute polymer solutions depends on the non-dimensional frequency t w, the measure of internal viscosity ip and indices zv and 6... 

The molecular deformation ratio K in the directions I and II can be estimated in the following way the difference Aa between the principal stresses in the x-y plane can be readily calculated from the birefringence A (measured parallel and perpendicular to the direction of extinction) and the stress-optical coefficient C for molten polystyrene (C= 4.8xlO Pa , see Chapter III.l). According to the classical network theory, the stress tensor is proportional to the Cauchy deformation tensor which means that the network deformation along the principal directions of the stress tensor are X and 1/ where ... 

The relationship between the measured relative retardation (R) and the stress-induced birefringence (An) is given by R = fAn (2), in which t is the sample thickness. The stress optical coefficient C is defined by An = Ct (2), in which t is the true stress (t = f/A f is the force in newtons per square millimeter, and A is the cross-sectional area of the network sample). This coefficient is thus simply the slope of the line in a plot of An versus t. Finally, the optical configuration parameter An is defined by... 

From these measured values of x and An, along with the stress-optical coefficient C, calculate cti2 and. ... 

Table 8.1. Stress-optic coefficients Ca of glassy and rubbery amorphous polymers, and of melts of semicrystalline polymers, in Brewsters (=1(H2 Pa). T denotes the measurement temperature. 

Strain and Stress Optical Coefficients. The relationship between A and is usually defined in terms of results obtained in the customary stress relaxation experiment in which a specimen is deformed to a constant strain, and a (or in this case A) is measured as a function of time. The strain optical coefficient, K(t), is defined as... 

In Figure 11, the calculated stress at the freeze point is plotted versus the measured birefringence of as-spun fibers for several IV levels of PET. The three lines represent various other workers measurements of the stress-optical coefficient by various techniques, and are all in excellent agreement with the model calculations. This plot demonstrates the bridge between process conditions and polymer properties and developed structure as measured by birefringence. It is Interesting to note that this curve is essentially linear over the entire range of experimental conditions in spite of the fact that... 

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