Linear aggregation and liquid-crystalline order: comparison of Monte Carlo simulation and analytic theory

TL;DR

This study combines Monte Carlo simulations and analytic theory to explore how monomer aspect ratio and flexibility influence phase behavior in systems of aggregating rod-like particles, revealing phase diagrams similar to chromonic liquid crystals.

Contribution

It introduces a minimal model of sticky cylinders to analyze coupled aggregation and liquid-crystal ordering, highlighting the effects of aspect ratio and interaction potential on phase transitions.

Findings

Phase diagrams show isotropic-nematic-columnar triple points.

Triple point location depends on monomer aspect ratio.

Aggregate persistence length varies with temperature and interaction potential.

Abstract

Many soft-matter and biophysical systems are composed of monomers which reversibly assemble into rod-like aggregates. The aggregates can then order into liquid-crystal phases if the density is high enough, and liquid-crystal ordering promotes increased growth of aggregates. Systems that display coupled aggregation and liquid-crystal ordering include wormlike micelles, chromonic liquid crystals, DNA and RNA, and protein polymers and fibrils. Coarse-grained molecular models that capture key features of coupled aggregation and liquid-crystal ordering common to many different systems are lacking; in particular, the role of monomer aspect ratio and aggregate flexibility in controlling the phase behavior are not well understood. Here we study a minimal system of sticky cylinders using Monte Carlo simulations and analytic theory. Cylindrical monomers interact primarily by hard-core interactions but can stack and bind end to end. We present results for several different cylinder aspect ratios and a range of end-to-end binding energies. The phase diagrams are qualitatively similar to those of chromonic liquid crystals, with an isotropic-nematic-columnar triple point. The location of the triple point is sensitive to the monomer aspect ratio.We find that the aggregate persistence length varies with temperature in a way that is controlled by the interaction potential; this suggests that the form of the interaction potential affects the phase behavior of the system. Our analytic theory shows improvement compared to previous theory in quantitatively predicting the I-N transition for relatively stiff aggregates, but requires a better treatment of aggregate flexibility.