Excess Entropy and Dynamics in Coarse-Grained Models

Coarse-graining modeling is a leading technique in multiscale simulations that has been continuously developed and applied in the past three decades. With coarse-graining, it is possible to simulate significantly larger systems than in purely atomistic systems and for time scales that cannot be reached with all-atom models. Such enhancements arise from removing unnecessary degrees of freedom to study the problem at hand. Consequently, molecular friction is removed from the system, and the potential energy surfaces become smoother and less intricate, leading to a significant acceleration of the overall dynamics. Even though this acceleration is favorable and desirable in achieving larger length scales and longer time scales, it inevitably affects the dynamical properties extracted from the simulations and thus makes it difficult to compare these quantities with experimental data. For example, self-diffusion coefficients of coarse-grained systems increase by up to three orders of magnitude with respect to the corresponding atomistic systems or experimental values. Other dynamical properties such as shear viscosities or local relaxation times are also significantly influenced. The lack of accurate dynamics is scientifically unsatisfactory. It also precludes the application of multiscale concepts to the predictive calculation of technologically important dynamical and transport properties. Examples include rheological properties that play a crucial role in extrusion and injection molding of polymer melts. This thesis addresses whether the artificially accelerated dynamics of coarse-grained models can be quantified in terms of the variation of excess entropy between bead-spring polymer models at different modeling resolutions. The acceleration of the dynamics of coarse-grained models, and thus the decrease of monomer friction, is cast in terms of excess entropy differences of different coarse-grained resolutions. Starting with an elementary bead-spring model of unentangled chains in a melt state, we derive two less-detailed models following a systematic approach using bottom-up coarse-graining techniques. The exact entropy is calculated for the three models using a rigorous approach based on thermodynamic integration and an approximation that only includes contributions of pair correlations to the excess entropy. The excess entropy differences across the resolutions are then correlated with the rate of dynamics acceleration. Among the findings of this project, it is remarkable that the excess entropy differences between the coarser and finer models correlate significantly with the logarithm of the ratio of dynamical properties quantifying the acceleration upon changing the model resolution. The results indicate that it is possible to understand the acceleration driven by coarse-graining in terms of excess entropy differences for unentangled polymers. These correlations may open new possibilities for simple empirical methods to perform a posteriori corrections of the coarse-grained dynamics