Self-assembly of frustrated and disordered systems -- equilibrium microphases and out-of-equilibrium active matter

Abstract

The potential for matter to self-assemble in complex morphologies and to follow intricate dynamics is of great fundamental interest as well as for a broad array of applications in nanotechnology, catalysis, drug delivery, and beyond. The inherent complexity of these processes, however, is a challenge both to theories and to numerical simulations. This dissertation focuses on two such complex systems: (i) equilibrium microphases and (ii) out-of-equilibrium active matter. In the first part, a model of microphase formers with short-range attractive and long-range repulsive (SALR) interactions is investigated. First, using various advanced Monte Carlo methods, a thorough characterization of the disordered regime of this model is obtained. Given that this regime had thus far eluded systematic characterization, the results serve as a benchmark for evaluating algorithmic performances. Around the order-disorder transition, existing algorithms nevertheless remain inefficient at sampling configurations, due to the severe critical slowdown. To understand the limitations of these algorithms in microphase formers, simple spin models are studied in a one-dimensional chain, on a two-dimensional square lattice and on the Bethe lattice. The results reveal that the existing cluster algorithms overestimate the correlation length, and therefore its divergence no longer coincides with the critical point. In fact, because frustration depresses the correlation length, a negative bonding probability would formally be needed for a cluster scheme to succeed. Two cluster algorithms that approximate this effect are proposed and shown markedly to improve sampling, albeit only for small to moderate system sizes. In the second part, the out-of-equilibrium nature of active matter is confronted with the goal of obtaining first-principle descriptions of its behavior. Sluggish dynamics (and arrest) at high densities in these systems is a particularly challenging concern. To obtain insight into the thus-far unsolved dynamic mean-field theory (DMFT), which is exact in the high-dimensional limit $d\rightarrow\infty$, I have conducted simulations of active Brownian particles (ABP) in the heterogeneous random Lorentz gas environment, using event-driven Brownian dynamics algorithm in $d$ spatial dimension. The results reveal that activity shifts the glass transition to higher density and saturates around the percolation threshold. The non-Gaussian parameter is also markedly different from that of the passive systems. These findings suggest that non-trivial processes might be at play in the arrest of active matter, which helps chart the way for eventually solving and extending the DMFT.