(196j) Biaxial and Shear Deformation of Simulated Amorphous Cis-, Trans-1, 4-Polybutadiene Chains
Rolling resistance in rubber tires leads to losses in vehicle fuel economy. We hypothesize the rolling resistance on the macroscale connects directly to deformation-induced changes in elastomer chain conformations on the microscale through changes in elastic free energy. To study this phenomenon, random chain conformations were generated using Floryâs Rotational Isomeric State (RIS) Approach, which weights particular torsional states along the backbone of polymer chains. Polybutadiene chains were generated under unperturbed conditions where chain size and shape characteristics were studied. Ensembles of unperturbed chains were then subjected to three separate deformation conditions: uniaxial along the x-direction, biaxial, and shear. For comparative analysis, Gaussian chains were generated and RIS chains were analyzed against them. The end-to-end distance vectors of the chains were computed before and after deformation, and the probability distribution of these vectors led to computations of elastic free energy. Changes in elastic free energy were studied for chain vectors under deformation at a single temperature with varying number of repeat units and for a single number of repeat units at varying temperatures. Change in elastic free energy of a system increased with increasing deformation. At a particular deformation, RIS chains showed higher elastic free energy changes than Gaussian chains. These changes in elastic free energy were then quantified to compute deformation force and stress acting on ensembles of chains. Good agreement was observed between deformation forces computed numerically and analytically for Gaussian chains. Under all conditions, RIS chains showed higher deformation force and stress as compared to Gaussian chains, and cis chains showed higher deformation force and stress than trans chains. For chains at a single temperature and varying number of repeat units, deformation force and stress decreased with increasing number of repeat units. For chains at a single repeat unit with varying temperature, the deformation force and stress decreased with increasing temperature. This approach allows for including specific chemistry effects on chain conformation and deformation by analyzing the stress-strain behavior of chains that surround filler particles.