Note: Formation of the nematic splay-bend in two-dimensional systems of bow-shaped particles

TL;DR

This paper develops a theoretical model using Onsager-type Density Functional Theory to describe the formation of the nematic splay-bend phase in two-dimensional bow-shaped particles, complementing previous simulation and experimental findings.

Contribution

It provides the first theoretical description of the nematic splay-bend phase in bow-shaped particles, filling a gap left by prior simulation and experimental studies.

Findings

The theory predicts conditions for nematic splay-bend formation.

Results depend on particle geometry such as segment length ratios and opening angles.

The model aligns with observed phases in simulations and experiments.

Abstract

Recently, Tavarone et al. (J. Chem. Phys. 143, 114505 (2015)) discussed phase behavior of zig-zag and bow-shaped particles composed of three needles. The authors presented very interesting results of extensive Monte Carlo simulations with periodic boundary conditions in the constant-NVT and the constant-NPT ensembles. In addition to isotropic, nematic, and smectic phases, they identified a modulated nematic, which is actually the nematic splay-bend phase ($N_{SB}$), long-anticipated for bent-core systems (Europhys. Lett. 56, 247 (2001)). They also described isotropic-nematic and nematic-smectic transitions using Density Functional Theory in mean-field approximation. The authors, however, did not provided a theoretical description of the $N_{SB}$. Here, we present a simple theory of a phase transition to the $N_{SB}$ phase to fill the gap. In our study, we use Onsager-type Density Functional Theory with perfect order approximation and Meyer parametrization of modulated structures. We present results for arbitrary ratios of the length of central and side segments and opening angles of bow-shaped particles.