Abstract Characterization of randomly crosslinked networks requires a topological description of imperfect network structure and a molecular-elasticity theory, preferably with a minimum number of adjustable parameters, relating macroscopic stress and strain or swelling ratios to molecular deformation. It is shown that simple relationships exist between the molecular weight between consecutive junctions, the molecular weight of linear precursor chains, the cycle rank, and the number of junctions for networks having no defects other than chain ends. The idealized affine deformation model (in which the constraints on junction fluctuations are infinite) and the idealized phantom-chain model (in which the constraints are absent) are inadequate for network characterization. The more realistic Flory-Erman constrained junction model is applied to the description of cis-polyisoprene cured with dicumyl peroxide. Swelling equilibrium experiments are in agreement with stress-strain measurements. Analysis of these stress-strain data with the constrained-junction and constrained-chain models gives similar results. This validates the Flory hypothesis that it is generally sufficient to concentrate the effects of the constraints on the junctions. Nevertheless, the constrained chain model proposed by Erman and Monnerie has the advantage of depending on one parameter, KG, instead of two, κ and ζ, for the constrained junction model.
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