Polymer physics and dynamics

An early model based on crosslinked rubbers put forward by Flory and Rehner (1943) assumed that chain segments deform independently and in the same manner as the whole sample (affine deformation) where crosslinks were fixed in space. James and Guth (1943) then described a phantom-network model that allowed free motion of crosslinks about the average affine deformation. The stress (cr) described from these theories can be described in the following equations  

Modifications to these classical statistical models can also be made, such as by the incorporation of loose chains (non-load-bearing chains), physical crosslinks (temporary or permanent) and intramolecular crosslinks (loops). At higher deformations (strains) or increasing crosslink densities, it may be necessary to use a non-Gaussian statistical treatment that considers the finite extensibility of the chain. Non-Gaussian models are reviewed extensively by Treloar (1975). 

In reality, of course, polymer systems are varied and consist of polymer solutions, polymer melts, and polymer networks and gels, and the polymer dynamics of these systems should be examined in detail. 

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