Two-temperature activity induces liquid-crystal phases inaccessible in equilibrium

Jayeeta Chattopadhyay, Sriram Ramaswamy, Chandan Dasgupta, and Prabal K. Maiti

Phys. Rev. E 107, 024701 – Published 6 February 2023

Abstract

In equilibrium hard-rod fluids, and in effective hard-rod descriptions of anisotropic soft-particle systems, the transition from the isotropic (I) phase to the nematic phase (N) is observed above the rod aspect ratio $L / D = 3.70$ as predicted by Onsager. We examine the fate of this criterion in a molecular dynamics study of a system of soft repulsive spherocylinders rendered active by coupling half the particles to a heat bath at a higher temperature than that imposed on the other half. We show that the system phase-separates and self-organizes into various liquid-crystalline phases that are not observed in equilibrium for the respective aspect ratios. In particular, we find a nematic phase for $L / D = 3$ and a smectic phase for $L / D = 2$ above a critical activity.

Received 29 April 2022
Accepted 17 January 2023

DOI:https://doi.org/10.1103/PhysRevE.107.024701

Physics Subject Headings (PhySH)

Active nematics Liquid crystals Living matter & active matter

Polymers & Soft Matter

Authors & Affiliations

Jayeeta Chattopadhyay, Sriram Ramaswamy, Chandan Dasgupta , and Prabal K. Maiti^*

Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India

^*maiti@iisc.ac.in

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Vol. 107, Iss. 2 — February 2023

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Images

Figure 1
(a) Schematic diagram of SRSs. The dotted line segment joining the centers of the two hemispheres is known as the core of the spherocylinder. $u_{1}$ and $u_{2}$ represent the orientation vectors of spherocylinders 1 and 2, respectively. $r$ is the distance between their centers of mass, and $d_{m}$ is the shortest distance that determines the interaction potential between them. (b)–(e) Snapshots representing steady-state configurations of hot (red) and cold (green) particles before (middle panel) and after (right panel) phase separation for the aspect ratios (b), (c) $L / D = 2$ at a packing fraction $η = 0.45$ and activity $χ = 9$ and (d), (e) $L / D = 3$ at $η = 0.33$ and $χ = 4$ . Cold particles show (c) smectic ordering for $L / D = 2$ and (e) nematic ordering for $L / D = 3$ at the aforementioned activities.
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Figure 2
(a) Density order parameter $ϕ$ of the system and (b) nematic order parameter of the cold particles $S_{cold}$ vs activity $χ$ for different aspect ratios $L / D$ at their respective packing fractions: for $L / D = 5$ , $η = 0.36$ , for $L / D = 3$ , $η = 0.33$ , and for $L / D = 2$ , $η = 0.35$ . (c) Nematic order parameter of the cold and hot particles for $L / D = 2$ at a higher packing fraction $η = 0.45$ .
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Figure 3
Pair correlation functions for the cold particles at different activities $χ$ for $L / D = 3$ at the packing fraction $η = 0.33$ . (a) The center-of-mass pair radial distribution function $g (r)$ , (b) orientational pair distribution function $g_{2} (r)$ , and (c) projection of $g (r)$ along the direction parallel $[g_{∥} (r_{∥})]$ and (d) perpendicular $[g_{⊥} (r_{⊥})]$ to the director of the spherocylinders. The inset of (b) shows $g_{2} (r)$ at $χ = 7$ in a single cluster with a definite director. The distance between the two peaks in (c) is $4 D$ , which is the end-to-end distance of a spherocylinder with $L / D = 3$ .
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Figure 4
Pressure anisotropy and local heat flux across the hot-cold interface for $L / D = 3$ at $η = 0.33$ and $χ = 7$ . We plot (a) effective packing fraction $η$ , (b) normal ( $P_{n}$ ) and tangential ( $P_{t}$ ) components of the pressure, (c) pressure anisotropy $A = P_{n} - P_{t}$ , and (d) local heat flux $J$ along the direction perpendicular to the interfacial plane. The red dashed lines indicate boundaries of different zones. The black dashed lines in (d) indicate the location where the heat flux becomes 0. The arrows indicate the directions of the heat flow, depending on the sign of $J$ . We find a positive pressure anisotropy at the interface that extends in the cold zone and a finite heat flux flowing from the bulk hot zone to the bulk cold zone. Here, $S_{cold} = 0.42$ , $S_{hot} = 0.07$ .
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