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This work develops a probability-based numerical method for quantifying mechanical properties of non-Gaussian chains subject to uniaxial deformation, with the intention of being able to incorporate polymer-polymer and polymer-filler interactions. The numerical method arises from a probabilistic approach for evaluating the elastic free energy change of chain end-to-end vectors under deformation. The elastic free energy change, force, and stress computed by applying the numerical method to uniaxial deformation of an ensemble of Gaussian chains were in excellent agreement with analytical solutions that were obtained with a Gaussian chain model. Next, the method was applied to configurations of cis- and trans-1,4-polybutadiene chains of various molecular weights that were generated under unperturbed conditions over a range of temperatures with a Rotational Isomeric State (RIS) approach in previous work ( Polymer  2015 , 62 , 129-138). Forces and stresses increased with deformation, and further dependences on chain molecular weight and temperature were confirmed. Compression forces normal to the imposed deformation were much larger than tension forces on chains. Smaller molecular weight chains represent the equivalent of a much more tightly cross-linked network, resulting in greater moduli than larger chains. Young's moduli computed from the coarse-grained numerical model were in good agreement with experimental results.

Simulating Stress–Strain Behavior by Using Individual Chains: Uniaxial Deformation of Amorphous Cis- and Trans-1,4-Polybutadiene