Networks with Semi-Flexible Chains

Abstract

Classical theories of rubber elasticity¹ are based on the flexible-chain model. A flexible chain may be classified as one with a characteristic ratio of the order of unity. The elasticity of the network is primarily of intramolecular origin arising from the entropy of the individual chains. Intermolecular contributions are of secondary importance. The phantom network model in which the chains do not experience any interaction with their neighbors seems to be a good firstorder approximation for real networks that consist of flexible chains. Recently, a large body of experimental work has been reported on networks made by crosslinking semi-flexible or semi-rigid chains. Stress-strain, swelling and birefringence measurements on these networks show significant deviations from the predictions of the classical network model. Among these networks are those prepared from aromatic polyamide chains^2,3 from cellulose and amylose^4–6 and from side-chain and main-chain liquid-crystalline systems.^7–11 The chains constituting these networks have characteristic ratios which are several orders of magnitude larger than those of classical flexible chains. The networks are marked with very high degree of segmental orientability under macroscopic deformation and a discontinuous stress-strain behavior indicating a phase transition under external stress. These experimental observations can not be predicted by the classical network theories. Instead, a theory recognizing the reduced flexibility of these semi-rigid chains is required.