Coarse-Graining Approach to Infer Mesoscale Interaction Potentials from Atomistic Interactions for Aggregating Systems

Abstract

A coarse-graining (CG) approach is developed to infer mesoscale interaction potentials in aggregating systems, resulting in an improved potential of mean force for Langevin dynamics (LD) and Brownian dynamics (BD) simulations. Starting from the evolution equation for the solute pair correlation function, this semi-analytical CG approach identifies accurate modeling of the relative acceleration between solute particles in a solvent bath as a reliable route to predicting the time-evolving structural properties of nonequilibrium aggregating systems. Noting that the solute-solvent pair correlation function attains a steady state rapidly as compared to characteristic aggregation time scales, this CG approach derives the effective relative acceleration between a pair of solute particles in the presence of this steady solute-solvent pair correlation by formally integrating the solvent force on each solute particle. This results in an improved potential of mean force that explicitly depends on the solute-solute and solute-solvent pair potentials, with the capability of representing both solvophilic and solvophobic interactions that give rise to solvation forces. This approach overcomes the difficulty in specifying the LD/BD potential of mean force in aggregating systems where the solute pair correlation function evolves in time, and the Kirkwood formulaU(r) = −kBT ln g(r) that is applicable in equilibrium diffusion problems cannot be used. LD simulations are compared to molecular dynamics (MD) simulations for a model colloidal system interacting with Lennard-Jones pair potentials to develop and validate the improved potential of mean force. LD simulations using the improved potential of mean force predict a solute pair correlation function that is in excellent match with MD in all aggregation regimes, whereas using the unmodified MD solute-solute pair potential in LD results in a poor match in the reactionlimited aggregation regime. The improved potential also dramatically improves the predicted extent of aggregation and evolution of cluster size distributions that exhibit the same self-similar scaling found in MD. This technique of coarse-graining MD potentials to obtain an improved potential of mean force can be applied in a general multiscale framework for nonequilibrium systems where the evolution of aggregate structure is important. ABSTRACT: A coarse-graining (CG) approach is developed to infer mesoscale interaction potentials in aggregating systems, resulting in an improved potential of mean force for Langevin dynamics (LD) and Brownian dynamics (BD) simulations. Starting from the evolution equation for the solute pair correlation function, this semi-analytical CG approach identifies accurate modeling of the relative acceleration between solute particles in a solvent bath as a reliable route to predicting the time-evolving structural properties of nonequilibrium aggregating systems. Noting that the solute−solvent pair correlation function attains a steady state rapidly as compared to characteristic aggreg...

Characterization of sheared colloidal aggregation using Langevin dynamics simulation

“…In earlier work [13] it was shown that although molecular dynamics (MD) simulations of aggregation in dilute systems with full solvent interactions are still too computationally expensive, mesoscale methods such as LD with modeled solvent interactions scale favorably to larger systems while retaining the capability of representing structure in aggregating systems. A coarse-graining procedure recently developed in our group to specify the potential of mean force in LD for aggregating systems yields time-evolving structure in nonequilibrium aggregating systems that matches very well with MD simulations in both diffusion-limited and reaction-limited regimes [14]. With this improved potential of mean force, the authors have confidence that LD simulations of aggregation can reliably predict important aggregation statistics such as the extent of aggregation, time-evolving solute pair correlation function, and dynamically scaled cluster size distribution that have been compared with MD simulations of smaller model systems [14].…”

“…A coarse-graining procedure recently developed in our group to specify the potential of mean force in LD for aggregating systems yields time-evolving structure in nonequilibrium aggregating systems that matches very well with MD simulations in both diffusion-limited and reaction-limited regimes [14]. With this improved potential of mean force, the authors have confidence that LD simulations of aggregation can reliably predict important aggregation statistics such as the extent of aggregation, time-evolving solute pair correlation function, and dynamically scaled cluster size distribution that have been compared with MD simulations of smaller model systems [14]. The essential features of this improved LD model that is used to study sheared aggregating systems in this work are described in Sec.…”

A coarse-graining approach for molecular simulation that retains the dynamics of the all-atom reference system by implementing hydrodynamic interactions

“…It is shown that the random fluctuation forces arise naturally as an output of the coarse-graining procedure, and, furthermore, can be used with second fluctuation-dissipation theorem to compute the friction tensor components. This procedure for parameterizing the Langevin equation is in contrast to other examples 24,25,28,42,43 where the frictional force is first determined and then used to derive the random fluctuation force. The PDF-based CG approach is tested for water and a dilute glucose solution, and the results show remarkable agreement with the dynamics obtained from reference all-atom simulations.…”

“…Equation (2) was originally derived to describe the dynamics of a Brownian particle across time scales 39,40 and it has been successfully used to model the dynamics of many other systems. [41][42][43] Unfortunately, by replacing the complete friction tensor (Eq. (1)) with a diagonal friction tensor, Eq.…”

Constitutive modeling of dense granular flow based on discrete element method simulations

“…Relative acceleration is the key to capturing structure dependent rheology. The relative acceleration based coarse graining approach (Markutsya, 2010;Markutsya et al, 2012) based on transport equation for two-particle density has been successfully used to model the solute interactions in the presence of solvent, leading to accurate prediction of nanoparticle aggregation using Brownian dynamics simulations. The crucial unclosed term that needs to be modeled in the two-particle transport equation is the relative acceleration between two particles conditional on their relative separation and relative velocity.…”