Coarse-Graining Based on Pair Interactions - Studies on Transferability and Dynamic Consistency in Coarse-Grained Models of Soft Matter

Abstract

Computer simulations of molecules and atoms are useful tools in soft matter research. Physical chemistry has profited significantly from the insight provided by the use of classical molecular dynamics simulations. In these simulations, atoms are modeled as point masses and their propagation in time and space is described by iterative solving of Newton’s equations of motion. A major challenge lies in the fact that the computational resources required to simulate systems at this resolution render atomistical simulations prohibitively expensive already at comparatively small time and length scales. One approach to make simulations of given systems more efficient in computational terms is to coarse-grain the model, i.e., to reduce the spatial resolution by merging atoms into larger interaction sites. The procedure of coarse-graining consists of two steps: the definition of a mapping between the scales of resolution and the determination of suitable potentials for the interactions between the sites of the coarse-grained model. Especially the second step is challenging because coarse-grained model needs to reproduce the physical behavior of the underlying (fine-grained) reference model as close as possible to retain its predictive quality. Several methods which share an approach described as systematic, bottom-up coarse-graining, have been published in the literature to determine interactions in the coarse-grained model from interactions in fine-grained (mostly atomistic) reference models of the systems of interest. The transferability of a coarse-grained model, i.e, the capability of accurately reproducing predictions of the reference model at varying state points is especially dependent on the method chosen for the parameterization of the coarse-grained model. Among the existing systematic coarse-graining methods, the conditional reversible work (CRW) method achieves a high degree of transferability, while being conceptually simple, straightforward to implement and computationally efficient. In this thesis, studies are presented which aim at an extension of the applications and systems of CRW-parameterized models. In a comparative study, the CRW method is used, among others, for the study of vapor-liquid equilibria and the thermodynamics of mixing with coarse-grained models of hexane and perfluorohexane. Results confirm the strong dependence of model transferability on the coarse-graining method chosen for its parameterization and show that the CRW models are transferable with respect to temperature, transfer from the interface to the bulk, transfer from the vapor to the liquid phase, and composition of a binary mixture. In the existing literature, the CRW method has only been applied to systems of apolar hydrocarbons. This thesis presents studies in which CRW models are parameterized for systems of weakly polar organic molecules and ionic liquids. The resulting CRW models are transferable to the same degree as those of apolar systems. Another major challenge in the simulation with coarse-grained models is the reproduction of dynamic properties in accordance with fine-grained reference models. In general, the time scales of relaxation are smaller in coarser models and this leads to an effective ‘speed-up’ of these simulations, a behavior which is related to a loss of dissipative degrees of freedom in the coarser model. The effective impact of these degrees of freedom on the dynamics of the system can be simulated through the insertion of dissipative pair interactions into the coarse-grained model. These interactions can be parameterized, like the interaction potential energy, in a bottom-up manner from simulations with the fine-grained model. This approach, which is based on the Mori-Zwanzig projection operator formalism, has been successfully utilized in several recent publications to parameterize coarse-grained models that consistently model the dynamics of model systems at low density. However, the approach relies on assumptions on the nature of the system which are not fully satisfied at the higher density typical for soft matter systems. Most importantly, it is assumed that the degrees of freedom removed from the model upon coarse-graining relax infinitely fast in comparison with those retained in the coarse-grained model (complete time scale separation). In this thesis, an application of such a procedure for a dynamically consistent coarse-grained model is presented for realistic model systems of soft matter. The aim of this study is to evaluate whether Mori-Zwanzig-based coarse-grained models can be used for the simulation of realistic soft matter systems, in which time scale separation is not complete. To this end, coarse-grained models are parameterized for model systems of different chain length and the predictions of the dynamics produced by the coarse-grained system are compared to those of an atomistic reference model. The self-diffusion coefficients of these systems can be reproduced to a good degree, whereas dynamics properties with a smaller characteristic time scale are less well reproduced with the Mori-Zwanzig coarse-grained model, a finding that can be related to the increasing deviation of the system’s state from the assumed complete time scale separation.