Understanding elasticity of polydisperse polymer networks by a stochastic method

Elasticity of polymer network origins from the microscopic connectivity of its constituent polymer chains. Classical theory, like affine and phantom models, is well established and has enjoyed great success, with an assumption that the network comprises only of monodisperse polymer chains. However, variation of chain-length, i.e., polydispersity, is present in a wide range of applications and affects the elasticity of the network. On the other hand, it is possible to tune the elasticity of the network by controlling the polydispersity since sophisticated methods have been developed. Therefore, understanding the structure-property relationship of the polydisperse network is highly valuable. Although efforts have been devoted to clarifying this relationship, most of them rely on phenomenological extensions of the classical theory, usually with extra unphysical assumptions. These extensions might be sufficient to explain certain experimental observations, but do not necessarily elucidate how the polydispersity inherently affects the network elasticity. In order to shed light on the structure-property relationship, we propose a stochastic sampling method that is capable of predicting the elastic moduli of polydisperse polymer networks explicitly. Based on the graph representation of network connectivity, this method effectively estimates junctional fluctuations of chains in the network and predicts the moduli accurately. Large-scale molecular dynamics simulations, with up to over 30 million monomers, are conducted to verify the proposed method. Consistency between theoretical and computational results suggests that the stochastic method is not only efficient but also powerful in evaluation of the elasticity of polymer network with complex microstructures.