Dissipative self-assembly of particles interacting through time-oscillatory potentials.

Dissipative self-assembly is the emergence of order within a system due to the continuous input of energy. This form of nonequilibrium self-organization allows the creation of structures that are inaccessible in equilibrium self-assembly. However, design strategies for dissipative self-assembly are limited by a lack of fundamental understanding of the process. This work proposes a novel route for dissipative self-assembly via the oscillation of interparticle potentials. It is demonstrated that in the limit of fast potential oscillations the structure of the system is exactly described by an effective potential that is the time average of the oscillatory potential. This effective potential depends on the shape of the oscillations and can lead to effective interactions that are physically inaccessible in equilibrium. As a proof of concept, Brownian dynamics simulations were performed on a binary mixture of particles coated by weak acids and weak bases under externally controlled oscillations of pH. Dissipative steady-state structures were formed when the period of the pH oscillations was smaller than the diffusional timescale of the particles, whereas disordered oscillating structures were observed for longer oscillation periods. Some of the dissipative structures (dimers, fibers, and honeycombs) cannot be obtained in equilibrium (fixed pH) simulations for the same system of particles. The transition from dissipative self-assembled structures for fast oscillations to disordered oscillating structures for slow oscillations is characterized by a maximum in the energy dissipated per oscillation cycle. The generality of the concept is demonstrated in a second system with oscillating particle sizes.