Mass dependence of the activation enthalpy and entropy of unentangled linear alkane chains

The mass scaling of the self-diffusion coefficient D of polymers in the liquid state, D ∼ M(β), is one of the most basic characteristics of these complex fluids. Although traditional theories such as the Rouse and reptation models of unentangled and entangled polymer melts, respectively, predict that β is constant, this exponent for alkanes has been estimated experimentally to vary from -1.8 to -2.7 upon cooling. Significantly, β changes with temperature T under conditions where the chains are not entangled and at temperatures far above the glass transition temperature Tg where dynamic heterogeneity does not complicate the description of the liquid dynamics. Based on atomistic molecular dynamics simulations on unentangled linear alkanes in the melt, we find that the variation of β with T can be directly attributed to the dependence of the enthalpy ΔHa and entropy ΔSa of activation on the number of alkane backbone carbon atoms, n. In addition, we find a sharp change in the melt dynamics near a "critical" chain length, n ≈ 17. A close examination of this phenomenon indicates that a "buckling transition" from rod-like to coiled chain configurations occurs at this characteristic chain length and distinct entropy-enthalpy compensation relations, ΔSa ∝ ΔHa, hold on either side of this polymer conformational transition. We conclude that the activation free energy parameters exert a significant influence on the dynamics of polymer melts that is not anticipated by either the Rouse and reptation models. In addition to changes of ΔHa and ΔSa with M, we expect changes in these free energy parameters to be crucial for understanding the dynamics of polymer blends, nanocomposites, and confined polymers because of changes of the fluid free energy by interfacial interactions and geometrical confinement.