A Monte Carlo study of the elastic behavior of polymethylene chains

The rubber elastic behaviors of long polymethylene (PM) chains are investigated using Monte Carlo simulations and considering the rotational-isomeric-state model. Through the Monte Carlo method we can generate many PM chains in the equilibrium states, and obtain the average Helmholtz free energy (A) and average energy [U]. Chain dimensions and thermodynamic statistical properties of long PM chains under various elongation ratios lambda are also calculated. We find that the elastic force f increases with elongation ratio lambda, and that energy contribution f(u) to the elastic force is negative and significant. The ratio f(u)/f ranges from -0.37 to -0.32 at T = 300 K and from -0.53 to -0.40 at T = 413 K, and decreases with increasing temperature, which agrees with the experimental data. Our calculations may provide some insights into the macroscopic phenomena of rubber elasticity.