Molecular origins of anisotropy in the thermal conductivity of deformed polymer melts: stress versus orientation contributions

Abstract

Amorphous polymer melts, and polymer networks exhibit anisotropic thermal transport when deformed. Moreover, a ‘stress-thermal rule’, a linear proportionality between the stress tensor and the thermal conductivity tensor, is observed, with a proportionality constant called the ‘stress-thermal coefficient’ C_t. When this coefficient is made dimensionless by the plateau modulus G⁰_N of the polymer melt, a universal value of approximately 0.05 has been observed for polymers of different chemistries. Such universality is surprising, given that thermal properties are determined by small-scale properties, unlike stress, which has entropic origins. Seeking insight into this observation, we examine independently the contributions to anisotropy in thermal conductivity from both stress and polymer orientation. Using an optical technique, we measure components of the thermal conductivity of polystyrene and polymethylmethacrylate with orientation, but no stress, and of samples that have stress, but no orientation. Consistent with polymer orientation dominating the effect, we find for the former samples that C_tG⁰_N ∼ 0.04 ± 0.01, and that the latter samples have a stress-thermal coefficient of opposite sign, and whose magnitude is a factor of 100 smaller. These results are not consistent with the “minimum thermal conductivity” model.