(200d) Uniaxial, 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 Floryâ??s 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 uniaxially deformed along the x-direction and consequently compressed along the y and z directions. For comparative analysis, Gaussian chains were generated and compared with RIS chains. Variation in probability density distribution of chain vectors with deformation was observed. Changes in elastic free energy of the chain vectors under deformation were studied for chains of different number of repeat units at a single temperature and for chains at different temperatures for the same number of repeat units. Change in elastic free energy of a system increased with increasing deformation. At a particular deformation, RIS chains showed higher elastic free change 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. Cis chains showed higher deformation force and stress than trans. For chains at a single temperature and varying number of repeat units, deformation force and stress decreased with increasing number of repeat units while for chains at a single repeat unit with varying temperature, the deformation force and stress decreased with increasing temperature. The study was then extended towards analyzing biaxial and shear deformations on ensembles of chains. Moduli of chains were computed under undeformed and deformed conditions.