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Nanodrops of discotic liquid crystals: a Monte Carlo study Luis F. Rull, and José Manuel Manuel Romero-Enrique Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b02347 • Publication Date (Web): 12 Sep 2017 Downloaded from http://pubs.acs.org on September 15, 2017
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Langmuir
Nanodrops of discotic liquid crystals: a Monte Carlo study Luis F. Rull
∗
and Jose M. Romero-Enrique
Departamento de Física Atómica, Molecular y Nuclear, Área de Física Teórica, Universidad de Sevilla, Avenida de Reina Mercedes s/n 41012 Sevilla (Spain)
E-mail:
[email protected] Abstract We study the morphologies of nematic nanodrops in a vapor of a discotic nematogen by Monte Carlo simulations. The uid interactions are modeled by a Gay-Berne model with molecular elongations κ = 0.3 and 0.5, and dierent values of the energy anisotropy parameter κ0 in the range of temperatures T in which the nematic coexists with a vapor phase. We considered nanodrops of N = 4000 and N = 32000 particles. For κ > κ0 we observe that nanodrops are quite spherical (even for N = 4000 nanodrops), with a homogeneous director eld for κ = 0.3 and a bipolar nematic con guration with tangential anchoring for κ = 0.5. By increasing the value of κ0 , nanodrops change from spherical to lens-shaped for κ = 0.3, and for κ = 0.5 spherical nanodrops with homeotropic anchoring and a disclination ring located on its equatorial plane are observed. Although no radial nanodrops are observed, isotropic liquid nanodrops with a paranematic shell and radial texture are observed slightly above the vapor-isotropicnematic triple point when the vapor-isotropic interface is completely wet by the nematic phase.
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Introduction Nematic liquid crystal drops have been extensively studied in the last few years by their fascinating properties, which are of interest not only from a fundamental point of view, but also by their possible applications. In these systems, geometrical frustration plays a relevant role, since the topological constraints induced by the shape of the drop may prevent the homogeneous orientational order favored by physical interactions.
As a result, there may
appear defects in the order, i.e. spatial regions where the nematic director is not de ned, or elastic distortions may even alter the otherwise typical spherical shape for drops of simple uids. Drops of nematic liquid crystals have been proposed as key ingredients for applications as privacy windows and other electro-optic devices. For example, polymer dispersed liquid crystals can switch between scattering and transparent states after application of an external electric eld,
1
and holographic polymer dispersed liquid crystals can switch between
diracting and transparent states.
27
There are many possible drop con gurations for either tangential or perpendicular alignment of the molecules at the bounding surface.
1
In some situations, the shape of the drop
is xed, because the surrounding media is polymerized. In addition, even if this is not the case, surface tension tends to make everything spherical. However, since the seminal work by Bernal and Fankuchen on plant virus tactoids
8
there is experimental evidence indicating that
the shape of a nematic drop can change either if it is small enough are applied;
10
9
or if external electric elds
this suggests an interesting interplay between minimization of the free energy
and the shape of the drop. Continuum theory has been extensively applied in the literature to predict the shape of nematic drops.
1119
In this approach the nematic director distortions
are modeled by the Frank-Oseen elastic functional with a Rapini-Papoular coupling with the nematic-isotropic interface, while the drop shape is controlled by a surface tension term. The elements which are essential to describe the nematic drop phenomenology are the drop volume
V,
the bare surface tension
K1 , K2 , K3 ,
γ,
the anchoring strength
w
and the elastic constants
associated to splay, twist and bend bulk distortions, respectively,
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and
K24 ,
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associated to saddle-splay distortions. For rod-like nematogens with planar anchoring the shape of the drop and the nematic drop texture are controlled mainly by the ratios and
∆ = wV 1/3 /K , 18,19
respectively, where the latter is the ratio between the typical drop
size and the extrapolation length So, small large
ω
ω
and large
∆
20
and
K = (K1 − K24 ) is the relevant bulk elastic constant.
would correspond to spherical and homogeneous drops, while for
the nematic texture becomes bipolar, and elongated drops correspond to small
A small value of
K3
with respect to
and a small value of
K2
K1
with respect
may induce the emergence of toroidal textures,
K1
and
breaking from a bipolar to a twisted texture.
K3
14,25
is generally irrelevant, since typically
K2
2124
Similar arguments have been applied to
26
In thermotropic liquid crystals
K1 ≈ K2 > K3 , 27,28
liquid crystals have extremely small values of
∆.
may induce a spontaneous symmmetry
tactoids of discotic nematics with homeotropic anchoring.
K2
ω = w/γ
althought lyotropic chromonic
which induce twisted textures.
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Formation of drops of spherical particles interacting with a Lennard-Jones potential has been extensively studied theoretically neering work of Thompson
29,30
and by computer simulations
3139
since the pio-
et al. 31 In the case of nematic drops, most computer simulations
are performed on spherical nematic drops.
4045
However, computer simulations addresing
the formation of nematic drops in monocomponent nematogens in equilibrium with its vapor and from binary mixtures of spherical and rod-like particles indicate that the drops are non-spherical.
4652
In contact with at surfaces the drops are also anisotropic.
shape may be spheroidal or spindle-like, drop has also been reported.
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53
The drop
and a bipolar to twisted texture transition in the
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Herein we address the problem of the morphologies of a nematic drop in a vapor for discotic Gay-Berne models by Monte Carlo simulations.
The procedure to generate the
drop is similar to the reported for prolate Gay-Berne models. elongations
κ = 0.3
and
κ = 0.5,
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We focus on two molecular
which from previous studies there is a vapor-nematic
transition in a range of temperatures.
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We investigate the drop shape and nematic textures
for dierent temperatures and interfacial anchoring conditions, which are correlated with
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intermolecular potential features.
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Methodology The Gay-Berne model
The Gay-Berne potential
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describes the intermolecular interactions in nematogen uids by
a suitable modi cation of the Lennard-Jones potential:
−6 Uij (rij , ui , uj ) = 4ε(ˆrij , ui , uj ) ρ−12 ij − ρij
(1)
with
ρij = where
ui
rij − σ(ˆrij , ui , uj ) + σ0 σ0
is the unit vector along the symmetry axis of particle
distance along the intermolecular vector
j,
and
ˆrij = rij /rij .
interaction energy,
rij
breath ratio of the particle,
i, rij = |ri − rj |
joining the centers of mass of particles
The anisotropic contact distance,
ε(ˆrij , ui , uj ),
(2)
σ(ˆrij , ui , uj ),
is the
i
and
and the depth of the
depend on the orientational unit vectors, the length-to-
κ = σee /σss ,
and the energy depth anisotropy,
κ0 = ee /ss ,
which are both de ned as the ratio of the size and energy interaction parameters in the end-to-end (ee) and side-by-side ( ss) con gurations, respectively.
κ>1
corresponds to prolate particles while
κ
