Networks entropic springs

The above examples show that we can describe the network modulus of polymer gels by using the concept of entropic springs making up the network. In some cases corrections to the network are required to... 

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. 

The early molecular theories of rubber elasticity were based on models of networks of long chains in molecules, each acting as an entropic spring. That is, because the configurational entropy of a chain increased as the distance between the atoms decreased, an external force was necessary to prevent its collapse. It was understood that collapse of the network to zero volume in the absence of an externally applied stress was prevented by repulsive excluded volume (EV) interactions. The term nonbonded interactions was applied to those between atom pairs that were not neighboring atoms along a chain and interacting via a covalent bond. 

The resulting physical picture of a rubber-like system as a close-packed collection of mers is radically different from the two-phase image introduced by James and Guth [10]. The latter represents mbber as a network of chains, which act as entropic springs in tension, embedded in a bath of simple liquid. The bath gives rise to an isotropic pressure, whereas the network is responsible for the deviatoric stress. More recent physical pictures consider as well the distribution of network junctions in the liquid and the action of these junctions as constraints on the free motion of a generic chain of the network. The current description is on the mer or atomic level and treats the full stress tensor, both the mean and deviatoric portions, in terms of atomic interactions. 

Here we will discuss three groups of simulation. In all cases we consider only systems in which the role of the conserved topology is explicitly taken into account. First we discuss some work on short chain networks, where the crosslinks are fixed in space. These simulations were used to investigate to what extent the entropic spring concept, which is the basis of the theory of elasticity of networks, is valid in systems in which the excluded volume interactions are present. We then review some and... 

As discussed briefly in the introduction the elastic and relaxational properties of polymer networks are also expected to be influenced significantly by the presence of entanglements. The classical theories, the phantom network modeP and the affine deformation model, describe the two extreme points of view. In the first, at least in its original form, the network strands and the crosslinks are not subject to any constraint besides connectivity and functionality. The other extreme considers the crosslinks to be fixed in space and deform affinely under deformation. A number of modifications of these theories have been proposed in which the junction fluctuations are partially suppressed. All of these models however consider the network strands as entropic springs. The entropic force, as... 

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