Computer simulation of thermal conductivity in vulcanized polyisoprene at variable strain and temperature

We study the thermal conductivity tensor in an atomistic model of vulcanized cis-1,4-polyisoprene (PI) rubber via molecular dynamics simulations. Our polymer force field is based on V. A. Harmandaris et al. [J. Chem. Phys. 116, 436 (2002)], whereas the polymerization algorithm follows the description in J. Hager et al. [Macromolecules 48, 9039 (2015)]. The polymer chains are chemically cross linked via sulfur bridges of adjustable cross-link density. A volume-conserving uniaxial strain of up to 200% is applied to the systems. The widely used GROMACS simulation package is adapted to allow using the Green-Kubo approach to calculate the thermal conductivity tensor components. Our analysis of the heat flux autocorrelation functions leads to the conclusion that the thermal conductivity in PI is governed by short-lived phonon modes at low wave numbers due to deformation of the monomers along the polymer backbone. Applying uniaxial strain causes increased orientation of monomers along the strain direction, which enhances the attendant thermal conductivity component. We find an exponential increase of the conductivity in stretch direction in terms of an attendant orientation order parameter. This is accompanied by a simultaneous decline of thermal conductivity in the orthogonal directions. Increase of the cross-link density only has a weak effect on thermal conductivity in the unstrained system, even at high cross-link density. In the strained system we do observed a rising thermal conductivity in the limit of high stress. This increase is attributed to enhanced coupling between chains rather than to their orientation.