Aspect-ratio-dependent void formation in active rhomboidal and elliptical particle systems

TL;DR

The paper addresses how particle shape and aspect ratio influence void formation in active nematics with excluded-volume interactions. It employs a 2D dry active nematic model with rhomboidal and elliptical particles, varying the aspect ratio $a$ while keeping area fixed, and analyzes local density, nematic order, topological defects, and void regions. The main findings are that void regions appear only at sufficiently high $a$; rhomboidal particles exhibit a characteristic void size that grows with $a$ and tracks the orientational correlation length, whereas elliptical particles show a broader size distribution with fewer voids, often constrained by the system size. Overall, the work highlights the crucial role of particle geometry, beyond aspect ratio, in determining pattern formation in dry active nematics and connects void dimensions to local orientational structure through correlation lengths.

Abstract

We execute a numerical simulation on active nematics with particles interacting by an excluded volume effect. The systems with rhomboidal particles and that with elliptical particles are considered in order to investigate the effect of the direct contact of particles. In our simulation, the void regions, where the local number density is almost zero, appear in both systems when the aspect ratio of the particles is high. We focused on the relationship between the void regions and the particle orientation of the bulk. The particle number density, particle orientation, topological defects, and void regions are analyzed for different aspect ratios in both systems. The systems with rhomboidal particles have characteristic void sizes, which increase with an increase in the aspect ratio. In contrast, the distribution of the void-region size in the systems with elliptical particles is broad. The present results suggest that the void size in the systems with rhomboidal particles is determined by the correlation length of the particle orientational field around the void regions, while that might be determined by the system size in the systems with elliptical particles.

Figures (9)

• Figure 1: Representative results of the numerical simulations for the systems with (a,c,e) rhomboidal and (b,d,f) elliptical particles at $t=1.9\times 10^7$. Aspect ratio is (i) $a=3.0$, (ii) $a=4.0$, and (iii) $a=5.0$. (a,b) Snapshots. The particle shape is illustrated on the upper side. (c,d) Local number density $\rho_{\boldsymbol{j},t} / \rho^{(\mathrm{sys})}$. (e,f) Local nematic order $P_{\boldsymbol{j},t}$, where white areas indicate the void regions in (e,f).
• Figure 2: The local mean orientations $\phi_{j,t}$ with the positions of the topological defects in the systems with (a) rhomboidal and (b) elliptical particles for $a=5.0$ at $t=1.9\times 10^7$. White areas indicate the void regions.
• Figure 3: Number density of the topological defects depending on the aspect ratio $a$ for the systems with (a) rhomboidal and (b) elliptical particles. The colors indicate the winding numbers. The fractions of the defects with winding numbers more than $+1/2$ or less than $-1/2$ are too small to recognize.
• Figure 4: Number density of the void regions depending on the aspect ratio $a$ for the systems with (a) rhomboidal and (b) elliptical particles. The colors indicate winding numbers.
• Figure 5: (a) Ensemble and time average of the void area $\left< \bar{S}^{(\mathrm{void})} \right>$. Error bars indicate standard deviation. Histogram of the void area $S^{(\mathrm{void})}$ for the systems with (b) rhomboidal and (c) elliptical particles. Aspect ratio is $a=5.0$. The fraction is weighted by the void region $S^{(\mathrm{void})}$. The fraction with respect to the count is shown in the inset.