XI 9. PHOTOELASTIC PROPERTIES OF RUBBERS 9.1. Refractive index and polarizability 174 9.2. Optical properties of long-chain molecules 175 9.3. The Gaussian network 178 9.4. The effect of swelling 182 9.5. The non-Gaussian network 182 9.6. Measurement of birefringence 186 9.7. Investigations on natural rubber 189 9.8. The effect of the degree of cross-linking 195 9.9. Polyethylene 198 9.10. Optical properties of the monomer unit 202 9.11. The equivalent random link 204 9.12. The effect of swelling on stress-optical coefficient 206 9.13. Temperature dependence of optical anisotropy 209

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Stress-strain data are given for two types of vulcanized rubber: (1) an 8% S rubber, and (2) a latex rubber. The types of deformation studied were simple elongation, 2-dimensional extension (or compression), pure shear, and combined elongation and shear. Comparison with the theoretical relations based on the molecular-network model shows the agreement to be good for the 2-dimensional extension, but less good for simple elongation and shear. The effect of combined elongation and shear is satisfactorily accounted for. It is concluded that the theory provides a satisfactory explanation of rubberlike elasticity, and forms a useful basis for the description of the mechanical properties of rubber subjected to large deformations of any type.

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I n Section 1 the relation of rubbers to other classes of polymers and the molecular basis of rubber elasticity are briefly examined. I n Section 2 the methods used in the quantitative development of the statistical-thermodynamic theory of a molecular network are outlined, and the main conclusions, in the form of stressstrain relations, etc, are presented and compared with experimental data. Section 3 examines the photoelastic properties of rubbers from both theoretical and experimental standpoints and discusses in detail the evidence derived from photoelastic studies on the statistical segment length in the molecular chain and its relation to intramolecular energy barriers. Section 4 is concerned with the thermodynamic analysis of stress-temperature data for rubber and other polymers, with particular reference to the internal energy and entropy changes during extension under constant pressure or constant volume conditions. Methods of deriving these quantities are compared and the results related to the modified molecular network theory due to Flory. Section 5 deals with the phenomena of swelling in liquids and considers both the effect of swelling on the mechanical properties and the effect of different types of stress or strain on the swelling equilibrium. Sections 1-5 are concerned mainly with the statistical theory and its applications, T h e final section examines in considerable detail the formulation of more general theories of large elastic deformations on a purely empirical or phenomenological basis, so as to overcome some of the limitations of the statistical theory. T h e logical basis of these formulations is presented and the conclusions are discussed in relation to the available experimental evidence. Some common pitfalls to be avoided are emphasized.