Optical coefficient, stress

More recently, test products were created of a blend of PMMA with a phenyl-substituted methacrylate these products have a glass-transition temperature of around 125°C, a significantly reduced water absorption compared to pure PMMA of about 0.32%, but also a higher birefringence (a stress-optic coefficient of 5.2 X 10 , compared with 0.3 X 10 for PMMA and 6.8 x 10 for BPA-PC). 

V. Galiatsatos, R.O. Neaffer, S. Sen and B.J. Sherman, Refractive index, stress optical coefficient, and optical configuration parameter of polymers. In J.E. Mark (Ed.), Physical Properties of Polymers Handbook, Springer-Verlag, New York, 1996, p. 535. 

In observing the time dependent changes in birefringence and stress-optical coefficient, for elongated samples at 25 C, it was found that the rate of crystallization of high trans SBR s was very much faster, some 10 times more rapid, than that for NR (8). This is consistent with the reported rates of isothermal crystallization for NR (2.5 hours at -26°C) and for 807. trans-1,4 polybutadiene (0.3 hours at -3°C) in the relaxed state (12). 

Birefringence. The birefringence of a crosslinked Gaussian rubber subjected to an affine deformation is described by the theories of Kuhn and Grun (1 ) and Treloar (2). These predict a stress-optical coefficient given by... 

Figures 6 and 7 give the data of Fukuda et al. (3) and that of Saunders (52). The variation of stress optical coefficient of the high cis and high trans, 1,4-polybutadiene is plotted against Me in Figure 6, where it is compared with...

Figure 6. PIP after Saunders, 1956. Stress optical coefficient as a function of molecular weight between cross-links (3, 52). PBD is polybutadiene. PIP is polyisoprene.

Figure 7. Stress optical coefficient X temperature as a function of temperature (3). PBD is poly butadiene. Key O, p-xylene A. toluene , benzene CClt all of swollen trans-/,4 PBD.

Birefringence induced by applied stress is caused by the two components of the refracted light traveling at different velocities. This generates interference which is characteristic of the material. The change in refractive index, An, produced by a stress S is often related by a factor C called the stress-optical coefficient as follows ... 

C Partial volume Capacity Concentration Compliance Stress-optical coefficient... 

Today generator matrices F are known for many properties,10 among them the population of different conformers, the relative stability of macromolecular diastereoisomers, the mean-square end-to-end distance, the radius of gyration, the molecular dipole moment, the molecular optical anisotropy (and, with it, the stress-optical coefficient, the Kerr effect, depolarized light scattering, and the... 

Expressions for the optical anisotropy AT of Kuhn s random link (an equivalent to the stress-optical coefficient) of stereo-irregular and multirepeat polymers are derived on the basis of the additivity principle of bond polarizabilities and the RIS approximation for rotations about skeletal bonds. Expressions for the unperturbed mean-square end-to-end distance , which are required in the calculation of Ar, are also obtained. 

The stress-optical coefficient of PE networks is calculated, and results are compared with experimental data. Observed temperature coefficients of AT and the optical anisotropy for unswollen samples are much larger than those calculated using acceptable values of E(g), the energy of the gauche conformation, relative to that of Vans. It is concluded that observed temperature coefficients should Include some contributions other than those implied in the theory, i.e., those arising from the conformational change with temperature. 

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]... 

The photoelastic behavior of nonionized PAAm network and ionized P(AAm/MNa) network prepared by the copolymerization of AAm with MNa ( MNa = 0.05) was investigated in water-acetone mixtures [31]. For a pure PAAm network, the dependences of all photoelastic functions (see Eqs. (15) and (16)), i.e. modulus G, strain-optical function A and stress-optical coefficient C, on the acetone concentration in the mixtures are continuous (Fig. 17). At ac = 54 vol %, the ionized network undergoes a transition which gives rise to jumpwise change in G, A and C also the refractive index of the gel n8 changes discontinuously. While in the collapsed state the optical functions A and C are negative, in the expanded state they are positive. 

In addition, the optical anisotropy of the statistical segment Aa calculated [50, 51] from the stress-optical coefficient C,... 

A jumpwise volume change in the transition correlates with a jumpwise change in the shear equilibrium modulus, the refractive index, the stress-optical coefficient and in the components of complex permittivity e and complex modulus G. ... 

Flory has recently summarized the experimental evidence pertaining to local correlation and their effects on chain dimensions (49). There is experimental support for local alignment from optical properties such as stress-optical coefficients in networks (both unswelled and swelled in solvents of varying asymmetry), and from the depolarization of scattered light in the undiluted state and at infinite dilution. The results for polymers however, turn out to be not greatly different from those for asymmetric small molecule liquids. The effect of... 

A final piece of evidence against both finite extensibility and internal viscosity is provided by flow birefringence studies. One would expect each to produce variations in the stress optical coefficient with shear rate, beginning near the onset of shear rate dependence in the viscosity (307). Experimentally, the stress-optical coefficient remains constant well beyond the onset of shear rate dependence in r for all ranges of polymer concentration (18,340). 

Quantitative data, as to the magnitude of the stress-optical coefficient for various polymer systems, will be given in Chapter 2, where other properties of this coefficient will be discussed. 

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... 

As is well-known, the stress-optical coefficient for permanent rubberlike networks reads (6) ... 

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