Entanglement model elastomeric networks

The deformation of polymer chains in stretched and swollen networks can be investigated by SANS, A few such studies have been carried out, and some theoretical results based on Gaussian models of networks have been presented. The possible defects in network formation may invalidate an otherwise well planned experiment, and because of this uncertainty, conclusions based on current experiments must be viewed as tentative. It is also true that theoretical calculations have been restricted thus far to only a few simple models of an elastomeric network. An appropriate method of calculation for trapped entanglements has not been constructed, nor has any calculation of the SANS pattern of a network which is constrained according to the reptation models of de Gennes (24) or Doi-Edwards (25,26) appeared. 

The molecular model of an elastomeric network with local intermolecular correlations, given by Flory, is used to calculate the components of the molecular deformation tensor and molecular orientation. Effects of molecTilar parameters such as severity of entanglements, network inhomogeneities and conditions during cross-linking are discussed. Components of molecular deformation and orientation are calculated for a network under uniaxial stress. 

A statistical mechanical model of an elastomeric network is proposed which takes into account that a chain in the network tends to follow the deformation of the macroscopic sample, but is restrained from doing so by the entanglement structures formed during crosslinking. 

The theoretical equations presented above can be used to interpret stress-strain measurements in uniaxial extension and thus to fully characterize elastomeric networks. In this regard, equations (124) and (125) are of particular interest since they relate the parameter k, quantifying the entanglement constraints in the Flory and Erman model, to the polymer microstructure and conformational properties and to the network topology. An illustrative analysis of stress-strain data due to Queslel, Thirion and Monnerie is reported below. 

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