Nematic ordering of hard rods under strong confinement in a dense array of nanoposts

Kye Hyoung Kil, Arun Yethiraj, and Jun Soo Kim

Phys. Rev. E 101, 032705 – Published 18 March 2020

Abstract

The effect of confinement on the behavior of liquid crystals is interesting from a fundamental and practical standpoint. In this work, we report Monte Carlo simulations of hard rods in an array of hard nanoposts, where the surface-to-surface separations between nanoposts are comparable to or less than the length of hard rods. This particular system shows promise as a means of generating large-scale organization of the nematic liquid by introducing an entropic external field set by the alignment of nanoposts. The simulations show that nematic ordering of hard rods is enhanced in the nanopost arrays compared with that in bulk, in the sense that the nematic order is significant even at low concentrations at which hard rods remain isotropic in bulk, and the enhancement becomes more significant as the passage width between two nearest nanoposts decreases. An analysis of local distribution of hard-rod orientations at low concentrations with weak nematic ordering reveals that hard rods are preferentially aligned along nanoposts in the narrowing regions between two curved surfaces of nearest nanoposts; hard rods are less ordered in the passages and in the centers of interpost spaces. It is concluded that at low concentrations the confinement in a dense array of nanoposts induces the localized nematic order first in the narrowing regions and, as the concentration further increases, the nematic order spreads over the whole region. The formation of a well-ordered phase at low concentrations of hard rods in a dense array of nanoposts can provide a new route to the low-concentration preparation of nematic liquid crystals that can be used as anisotropic dispersion media.

Received 7 August 2019
Revised 29 January 2020
Accepted 26 February 2020

DOI:https://doi.org/10.1103/PhysRevE.101.032705

Physics Subject Headings (PhySH)

Confinement

Liquid crystals Rodlike polymer

Monte Carlo methods

Polymers & Soft Matter

Authors & Affiliations

Kye Hyoung Kil ¹, Arun Yethiraj^2,*, and Jun Soo Kim ^1,†

¹Department of Chemistry and Nanoscience, Ewha Womans University, Seoul 03760, Republic of Korea
²Department of Chemistry, University of Wisconsin-Madison, Wisconsin 53706, USA

^*yethiraj@chem.wisc.edu
^†jkim@ewha.ac.kr

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Issue

Vol. 101, Iss. 3 — March 2020

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Images

Figure 1
(a) Top view of the rectangular nanopost array with diameter $D_{p}$ and spacing $L_{p}$ . The distance $W_{p}$ is referred to as the passage width. With periodic boundary conditions the nanoposts are infinitely long in the $z$ direction. (b) A representative snapshot of nematic ordering of hard rods in a nanopost array with $(L_{p}, D_{p}) = (30, 21)$ at a volume fraction of $ϕ = 0.10$ .
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Figure 2
Average order parameter $〈 S_{2} 〉$ as a function of volume fraction for several values of $D_{p}$ and (a) $L_{p} = 20$ , (b) $L_{p} = 30$ , and (c) $L_{p} = 40$ . Simulation results for the bulk liquid (gray triangles) are included for comparison.
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Figure 3
Spatial distribution of order parameter $S_{2 z}^{'}$ at the volume fraction $ϕ = 0.07$ with $L_{p} = 40$ and (a) $D_{p} = 35$ , (b) $D_{p} = 31$ , and (c) $D_{p} = 27$ . The value of overall average $〈 S_{2 z}^{'} 〉$ is specified at the upper right corner of each figure, and three values of local average $S_{2 z}^{'}$ (as given in Table 1) are specified on the corresponding regions of the passages, narrowing regions, and centers of interpost spaces (from top to bottom). The value of $S_{2 z}^{'}$ at each location is also indicated by the color in the scale bar on the right (of the color online figure).
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Figure 4
Spatial distribution of order parameter $S_{2 x}^{'}$ at the volume fraction $ϕ = 0.07$ with $L_{p} = 40$ and (a) $D_{p} = 35$ , (b) $D_{p} = 31$ , and (c) $D_{p} = 27$ . The value of $S_{2 x}^{'}$ at each location is indicated by the color in the scale bar on the right (of the color online figure). Those in the passages along the $x$ -axis, for instance, at (X,Y) $=$ (40, 20) are positive and those in the passages along the $y$ axis, including the region at (20, 40), are negative.
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Figure 5
Spatial distribution of (a) order parameter $S_{2 z}^{'}$ at each location and (b) the deviation $Δ S_{2 z}^{'}$ from the average order parameter at the volume fraction $ϕ = 0.10$ for a nanopost array with $(L_{p}, D_{p}) = (40, 35)$ . $Δ S_{2 z}^{'} = S_{2 z}^{'} - 〈 S_{2 z}^{'} 〉$ and $〈 S_{2 z}^{'} 〉 = 0.6877$ . The values of the order parameter $S_{2 z}^{'}$ in (a) are uniformly positive and are close to the average value $〈 S_{2}^{'} 〉$ in all regions. The values of the deviation $Δ S_{2 z}^{'}$ in (b) are negative in the passages and centers of the interpost spaces whereas those in the narrowing regions are positive.
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Figure 6
Spatial distribution of (a) order parameter $S_{2 z}^{'}$ at each location and (b) the deviation $Δ S_{2 z}^{'}$ from the average order parameter at the volume fraction $ϕ = 0.07$ for a nanopost array with $(L_{p}, D_{p}) = (20, 15)$ . $Δ S_{2 z}^{'} = S_{2 z}^{'} - 〈 S_{2 z}^{'} 〉$ and $〈 S_{2 z}^{'} 〉 = 0.5008$ . The values of the order parameter $S_{2 z}^{'}$ in (a) are all positive with small spatial variations around the average value $〈 S_{2}^{'} 〉$ . The values of the deviation $Δ S_{2 z}^{'}$ in (b) are negative in the passages whereas those in the diagonal regions of the interpost spaces are positive.
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