Variational design principles for nonequilibrium colloidal assembly

TL;DR

This paper develops a variational framework using large deviation theory and stochastic control to design optimal forces for targeted nonequilibrium colloidal self-assembly, demonstrating high-yield cluster formation under shear flow.

Contribution

It introduces a variational principle for inverse design of nonequilibrium assembly processes and provides an optimization algorithm to determine forces for targeted self-assembly.

Findings

High-yield assembly of colloidal clusters achieved with specific short-range interactions.

Shear flow influences cluster yields, decreasing for rigid and increasing for nonrigid clusters.

Generalized linear response theory explains the effects of shear on assembly yields.

Abstract

Using large deviation theory and principles of stochastic optimal control, we show that rare molecular dynamics trajectories conditioned on assembling a specific target structure encode a set of interactions and external forces that lead to enhanced stability of that structure. Such a relationship can be formulated into a variational principle, for which we have developed an associated optimization algorithm and have used it to determine optimal forces for targeted self-assembly within nonequilibrium steady-states. We illustrate this perspective on inverse design in a model of colloidal cluster assembly within linear shear flow. We find that colloidal clusters can be assembled with high yield using specific short-range interactions of tunable complexity. Shear decreases the yields of rigid clusters, while small values of shear increase the yields of nonrigid clusters. The enhancement or suppression of the yield due to shear is rationalized with a generalized linear response theory. By studying 21 unique clusters made of 6, 7 or 8 particles, we uncover basic design principles for targeted assembly out of equilibrium.