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

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 modeling. 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 its 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 the 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.