Statistical mechanics of a polymer chain

Thermal effects strongly influence both the elastic and viscoelastic parts of the behavior. Thus, the thermo-mechanical modeling of polymers remains a challenge. In collaboration with my advisor at University of California Berkeley, I performed a study of a polymer chain under thermomechanical loading in the framework of statistical mechanics. 

The goal was to determine a general structure of the elastic temperature-dependent free energy of a polymer in finite deformation. In theory, the formal free energy structure is linear according to temperature apart from an integral of the deformation- and temperature- dependent heat capacity. This quantity is generally assumed constant with respect to deformation for simplicity. We aimed at verifying this assumption by:

(i) calculating the theoretical response of a polymer chain in the stress ensemble through statistical mechanics, 

(ii) simulating the resulting heat capacity using a Monte-Carlo algorithm, and 

(iii) compare with experimental results measuring the thermal behavior of a polymer with respect to deformation. 

Numerical and experimental results showed that the heat capacity is linear with respect to the end-to-end distance in the direction of the loading until the chain maximum stretch.