Theory of Strain Birefringence of Amorphous Polymer Networks

Abstract

Recent rubber elasticity theory, according to which departures from relationships derived for phantom networks originate in constraints on the fluctuations of network junctions, is applied to the treatment of strain birefringence. The strain birefringence of phantom networks is first considered. It is smaller than for networks in which the transformation of chain vectors is affine in the macroscopic strain, as assumed in all previous treatments of strain birefringence in rubber elastic systems. The relationship of birefringence to the stress is the same, however. Real networks, in which the constraints on fluctuations impart a pattern of behavior intermediate between the extremes of phantom and affine networks, are treated in detail by extension of rubber elasticity theory. Illustrative numerical calculations are presented. Contributions of the constraints to the birefringence An are somewhat larger, relatively, than their contributions to the stress τ. In contrast to theories of phantom and of affine networks, An for the real network is predicted to be nonlinear with τ for uniaxial extension; i.e., the stress-optical coefficient Δn/τ should decrease with elongation. © 1983, American Chemical Society. All rights reserved.