Theory and Simulations of Hybrid Networks
M Jacobs and HY Liang and AV Dobrynin, MACROMOLECULES, 54, 7337-7346 (2021).
Hybrid networks are made of different types of polymer strands, which could differ by their degrees of polymerization (DPs), chemical structure, or rigidity (Kuhn length). Examples of such networks include biological networks and gels crosslinked by binding proteins and networks of graft polymers cross-linked by their side chains. Here, we report on a theoretical model and coarse-grained molecular dynamics simulations of hybrid networks made of two types of strands. The networks are made by cross-linking precursor chains of type 1 by shorter chains of type 2, which results in a trifunctional network with junction points having two strands of type 1 and one strand of type 2. The developed approach, based on the phantom network model and the nonlinear elasticity of the network strands, self-consistently accounts for entropic elasticity, bond deformation, and the continuous redistribution of stress between different network strands as they undergo nonlinear deformation. Analysis of the different deformation regimes shows that at small deformations the network elastic response is controlled by the elasticity of the longest network strands. However, in the nonlinear network deformation regime, the network mechanical properties are determined by nonlinear deformation of the strands of the first kind constituting the majority of the network strands. The model predictions are in excellent agreement with molecular dynamics simulations of hybrid networks in the linear and nonlinear deformation regimes. Furthermore, the model provides a theoretical foundation for the analysis of strain stiffening observed in networks of graft polymers and networks with a bimodal distribution of strands.
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