# Geometrically Frustrated Assembly at Finite Temperature: Phase Transitions from Self-Limiting to Bulk States

## TL;DR

This study uses Monte Carlo simulations to explore phase transitions in a 2D model of geometrically frustrated assembly, revealing how concentration and temperature influence the shift from self-limiting to bulk states with defect structures.

## Contribution

It provides a detailed phase diagram of frustrated assembly, identifying mechanisms of transition driven by concentration and temperature, and highlights the roles of entropy and model parameters.

## Key findings

- Percolation of worm-like domains leads to a heterogeneous network.
- Transition thresholds depend on frustration and stiffness ratios.
- Self-limiting phase persists at higher frustrations and temperatures.

## Abstract

Geometric frustration is recognized to generate complex morphologies in self-assembling particulate and molecular systems. In bulk states, frustrated drives structured arrays of topological defects. In the dilute limit, these systems have been shown to form a novel state of self-limiting assembly, in which the equilibrium size of multi-particle domains are finite and well-defined. In this article, we employ Monte Carlo simulations of a recently developed 2D lattice model of geometrically frustrated assembly~\cite{HackneyPhysRevX.13.041010} to study the phase transitions between the self-limiting and defect bulk phase driven by two distinct mechanisms: (i) increasing concentration and (ii) decreasing temperature or frustration. The first transition is mediated by a concentration-driven percolation transition of self-limiting, worm-like domains into an intermediate heterogeneous network mesophase, which gradually fills in at high concentration to form a quasi-uniform defect bulk state. We find that the percolation threshold is weakly dependent on frustration and shifts to higher concentration as frustration is increased, but depends strongly on the ratio of cohesion to elastic stiffness in the model. The second transition takes place between self-limiting assembly at high-temperature/frustration and phase separation into a condensed bulk state at low temperature/frustration. We consider the competing influences that translational and conformational entropy have on the critical temperature/frustration and show that the self-limiting phase is stabilized at higher frustrations and temperatures than previously expected. Taken together, this understanding of the transition pathways from self-limiting to bulk defect phases of frustrated assembly allows us to map the phase behavior of this 2D minimal model over the full range of concentration.