Entropic spring, flexible chain

Rubber materials are soft, elastic solids, made of mobile, flexible polymer chains (with a glass transition temperature (Tg) typically lower than 0 °C) which are linked together to form a three-dimensional network. They are characterised by a low, frequency independent elastic modulus (of the order 105 to 106 Pa) and usually by a large maximum reversible deformation (up to a few hundred per cent). Rubber elasticity is based on the properties of crosslinked polymer chains at large spatial scales, the presence of crosslinks ensures the reversibility of the deformation, while at short scales, mobile polymer chains behave as molecular, entropic springs. 

In dilute solutions in a theta solvent, flexible polymer chains are in an isolated, ideal random coil state. For description of the dynamics in such solutions, Zimm model subdivides the chain into subchains (cf Figure 2), represents the friction and elasticity of the subchain by a bead (friction center of the subchain) and the entropic springs conneaing the beads, respectively, and analyzes the motion of this bead-spring chain in the presence of hydrodynamic and thermal... 

It is worth recalling that any of the molecular force laws given by Eqs. (13-16) are derived within the framework of the freely-jointed model which considers the polymer chain as completely limp except for the spring force which resists stretching thus f(r) is purely entropic in nature and comes from the flexibility of the joints which permits the existence of a large number of conformations. With rodlike polymers, the statistical number of conformations is reduced to one and f(r) actually vanishes when the chain is in a fully extended state. 

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