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

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 formula U(r) = -k(B)T 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 reaction-limited 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.