Variational design principles for nonequilibrium colloidal assembly

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.

13 pages, 8 figures

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• Principles of Low Dissipation Computing from a Stochastic Circuit Model
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• Shortcuts in stochastic systems and control of biophysical processes
• A large deviation theory perspective on nanoscale transport phenomena
• Thermodynamic Control of Activity Patterns in Cytoskeletal Networks
• Variational deep learning of equilibrium transition path ensembles
• Adaptive power method for estimating large deviations in Markov chains
• 2D capsid formation within an oscillatory energy landscape: orderly self-assembly depends on the interplay between a dynamic potential and intrinsic relaxation times
• Steering Active-Colloid Assembly by Biasing Dissipation