Rubber Elasticity

Abstract

Rubbers are lightly cross-linked amorphous polymers with a glass transition temperature considerably lower than the usage temperature. The elasticity of rubbers is predominantly entropy-driven which leads to several remarkable phenomena: the stiffness increases with increasing temperature and heat is reversibly generated by mechanical work done on the rubber; a deformed piece of rubber is warm and, on unloading, temperature drops instantaneously. A more detailed analysis shows that the elastic force originates from both changes in conformational entropy and changes in the internal energy. The latter are normally small and at constant volume, it relates to changes in conformational energy. Statistical mechanical models equating the Helmholtz free energy are useful in describing the stress-strain behaviour of rubbers. The affine network model assumes that the network consists of phantom Gaussian chains, and that the positions of the junction points are fixed and prescribed by the macroscopic deformation. The phantom network model assumes that the positions of the junctions fluctuate about their mean positions prescribed by the macroscopic deformation ratio. This constrain is achieved by giving some of the crosslinks a precise position according to the macroscopic deformation. The non-Gaussian chain statistics limiting the extensibility of the network and network “defects” such as loose chain ends, intramolecular crosslinks and trapped entanglements (e.g. according to the Langley method) are thoroughly treated. Other topics presented are the very useful Mooney equation, the effect of solvents on the stress-strain behaviour expressed by the Flory-Rehner equation and rubbers present in nature and in biological systems, viz. protein rubbers and hydrogels based on polysaccharides.