Abstract
A review of the main elasticity models of flexible polymer networks is presented. Classical models of phantom networks suggest that the networks have a tree-like structure. The conformations of their strands are described by the model of a combined chain, which consists of the network strand and two virtual chains attached to its ends. The distribution of lengths of virtual chains in real polydisperse networks is calculated using the results of the presented replica model of polymer networks. This model describes actual networks having strongly overlapping and interconnected loops of finite sizes. The conformations of their strands are characterized by the generalized combined chain model. The model of a sliding tube is represented, which describes the general anisotropic deformations of an entangled network in the melt. I propose a generalization of this model to describe the crossover between the entangled and phantom regimes of a swollen network. The obtained dependence of the Mooney-Rivlin parameters and on the polymer volume fraction is in agreement with experiments. The main results of the theory of heterogeneities in polymer networks are also discussed.
Highlights
Polymer networks and gels belong to a unique class of materials that have the properties of both solids and liquids
The cumulative effect of a large number of strongly overlapping typical loops of finite size can be described in the effective mean-field approximation
This approximation works for polymer networks due to large overlap parameter of network strands, P(0) 1, see Equation (12)
Summary
Polymer networks and gels belong to a unique class of materials that have the properties of both solids and liquids. [2] suggests that polymer networks have a tree-like structure This theory takes into account the presence of loops in the network, it is assumed that they all are infinite in size. The conformations of the chains in the network are described by the combined chain model [3] This model is based on the concept of virtual chains, which determine the effective elasticity of the tree-like structures in the network. The structure of real networks differs significantly from the classical picture of ideal trees Typical loops of such networks have finite dimensions and strongly overlap with each other. Anisotropic deformations of the entangled network lead to slippage of chains along the contour of the entangled tube, which is described by the slip tube model [3].
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