Discrete state model of a self-aggregating colloidal system with directional interactions

TL;DR

This paper introduces a discrete state Markov model for self-aggregating colloidal particles under external fields, capturing the dynamics of multiple aggregate formations and their evolution, validated against detailed simulations.

Contribution

It develops a novel coarse-grained Markov state model for colloidal self-assembly that accounts for multiple aggregate formation and dynamic transition changes.

Findings

Model accurately predicts state populations compared to simulations.

The approach captures the evolution of aggregate sizes over time.

Detailed balance condition validity varies during aggregation stages.

Abstract

The construction of coarse-grained descriptions of a system's kinetics is well established in biophysics. One prominent example is Markov state models in protein folding dynamics. In this paper, we develop a coarse-grained, discrete state model of a self-aggregating colloidal particle system inspired by the concepts of Markov state modelling. The specific self-aggregating system studied here involves field-responsive colloidal particles in orthogonal electric and magnetic fields. Starting from particle-resolved (Brownian dynamics) simulations, we define the discrete states by categorizing each particle according to it's local structure. We then describe the kinetics between these states as a series of stochastic, memoryless jumps. In contrast to other works on colloidal self-assembly, our coarse-grained approach describes the simultaneous formation and evolution of multiple aggregates from single particles. Our discrete model also takes into account the changes in transition dynamics between the discrete states as the size of the largest cluster grows. We validate the coarse-grained model by comparing the predicted population fraction in each of the discrete states with those calculated directly from the particle-resolved simulations as a function of the largest cluster size. We then predict population fractions in presence of noise-averaging and in a situation where a model parameter is changed instantaneously after a certain time. Finally, we explore the validity of the detailed balance condition in the various stages of aggregation.