Coarse-Graining Frequency-Dependent Phenomena and Memory in Soft Matter Systems
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Abstract
In recent years, the focus of soft matter science has shifted more and more from equilibrium to non-equilibrium systems. One of the best examples for this trend is the popularity of active matter and microswimmers in modern research. One major feature of non-equilibrium processes is their strong dependence on the dynamical properties of the system. This complicates the construction of coarse-grained models for these systems, because the coarse-graining inherently changes their dynamics. In this thesis, we investigate and coarse-grain frequency-dependent phenomena in soft matter science. The methods proposed in this work are still restricted to systems in equilibrium, however, they represent an important first step to develop coarse-graining techniques for non-equilibrium simulations.
In the first part of this thesis we investigate the dielectric properties of flexible polyelectrolytes in ionic solution. We can demonstrate that the electric polarizability strongly depends on the solvent quality. Due to the overlapping of different relaxation times, it is also revealed that the dielectric properties depend non-monotonically on the frequency of the externally applied electric field. Afterwards, the hydrodynamic interactions of dispersed nanocolloids are analyzed. Similar to the observation made for the previous system, the study shows that physical processes on different but overlapping time scales induce significant memory effects in the system. The movement of a nanocolloid in dispersion, e.g., generates fluid vortices that affect its own dynamics and the movement of other nearby nanocolloids at later times. These memory effects can be described with a generalized Langevin equation by including frequency-dependent friction kernels and time-correlated stochastic forces.
To utilize these insights for dynamic coarse-graining, we develop two novel methods: the iterative memory reconstruction'' to systematically determine memory kernels from microscopic systems, and the generalized Brownian dynamics'' technique to integrate the generalized Langevin equation. The combination of these tools enables the construction of a non-Markovian coarse-grained model for the dispersed nanocolloids that perfectly reproduces the dynamics of the underlying microscopic system. The distinct feature of this model is that it not only includes the hydrodynamic self-diffusion of the colloids but it also incorporates the correct frequency-dependent pair-correlations between different particles. Additionally, we can show that the time-integration of this transferable coarse-grained model is roughly 10000 times faster than the original molecular dynamics simulations.