Cross-Correlation Contributions to Orientational Relaxations in Primitive Chain Network Simulations

Abstract

Models for entangled polymer dynamics can be conveniently thought of as belonging to two major categories - multichain models, such as the Kremer-Grest model simulated using molecular dynamics and single chain models, such as the tube and sliplink models. The single chain models typically assume that each polymer chain moves essentially independently of the other chains in the system. Hence they also assume that the cross-correlations between the different chains make negligible contribution to the various physical quantities (for e.g., the time-dependent relaxation modulus). However, Cao and Likhtman [Phys Rev Lett 104, 207801 (2010)] using molecular dynamics simulations have shown that there exist significant cross-correlation contributions to the time-dependent orientational relaxation function. In this study, the effect of cross-correlation was investigated using the primitive chain network model, a multi-chain sliplink model. Orientational relaxation functions for both the subchain vectors between entanglements and also for the end-to-end vector of whole chain were evaluated. In the case of the subchain relaxation function (and which corresponds to the time-dependent relaxation modulus by the stress-optical rule), the cross-correlation contribution to the total relaxation function appears to progressively increase with time. Further, the ratio of the cross-correlation function to the total relaxation function reaches a maximum value of approximately 40 % in the terminal region. Besides indicating that the cross-correlation contributions to the total relaxation function are non-negligible, this also demonstrates that the relaxation spectrum itself is modified if the cross-correlation contribution is neglected from the total relaxation. Specifically, the cross-correlation contribution affects the relaxation spectrum in the time range where the effect of the constraint release process is expected to be important. On the other hand, the results indicate that effect of cross-correlations on the shape of the relaxation curve is not significant at long times around the terminal region and that the autocorrelation and the total correlation functions can be superimposed by rescaling the unit of modulus. In contrast, the contribution from cross-correlation to the end-to-end relaxation (that corresponds to the dielectric relaxation of type-A polymers) is less significant than that for the subchain relaxation. In fact, no significant difference was found in the prediction of dielectric relaxation between the end-to-end relaxation functions with and without the contribution of the cross-correlations.