Analysis of the configurational temperature of polymeric liquids under shear and elongational flows using nonequilibrium molecular dynamics and Monte Carlo simulations

Abstract

We present a detailed analysis of the configurational temperature (Tconf) for its application to polymeric materials using nonequilibrium molecular dynamics (NEMD) and nonequilibrium Monte Carlo (NEMC) methods. Simulations were performed of linear polyethylene liquid C78H158 undergoing shear and elongational flows. At equilibrium, Tconf is equal to the set point temperature of the simulation. An aphysically large decrease in Tconf is observed in the NEMD simulations for both flows, especially at strong flow fields. By analyzing separately the individual contributions of the different potential interaction modes to the configurational temperature, it is found that the bonded modes (which constitutes almost 99.5% of the total) dominate the total Tconf over the nonbonded ones; i.e., bond-stretching (≈86.5%), bond-bending (≈11.8%), bond-torsional (≈1.2%), nonbonded intermolecular (≈0.4%), and intramolecular (≈0.1%) Lennard-Jones. The configurational temperature of the individual modes generally exhibits a nonmonotonic behavior with the flow strength and a dramatic change beyond a critical value of flow strength; this is mainly attributed to the dynamical effect of strong molecular collisions occurring at strong flow fields. In contrast, no such behavior is observed in the NEMC simulations where such dynamical effects are absent. Based on the principal physical concept of the configurational temperature, which represents the large-scale structural characteristics of the system, we propose to exclude the dynamical effects exhibited by the individual interaction modes, in obtaining a physically meaningful Tconf as the configurational entropy of the system should not be affected by such factors. Since (a) the main difference between equilibrium and nonequilibrium states lies in the change in the overall (global) structure (represented by the bond torsional and nonbonded modes), and (b) the local, very short structure (represented by the bond-stretching and bond-bending modes) is barely changing between equilibrium and nonequilibrium states and its contribution to the total system configurational entropy is negligible compared to the large-scale structural changes, in order to accurately describe the structural changes occurring at nonequilibrium states by use of the configurational temperature, we further propose that only the contributions from the bond-torsional and nonbonded modes to ΔTconf between equilibrium and nonequilibrium states should be taken into account to generate a physically meaningful ΔTconf. Applying the above hypothesis to the analysis of the simulation data, good agreement between the NEMD and NEMC simulations (and between NEMD simulations for different flows) is observed. Furthermore, the configurational temperature obtained in such way is found to match remarkably well with the heat capacity of amorphous polyethylene liquids and the flow-enhanced melting-point elevation reported in experiment.