Modelling liquid crystalline ordering in anisotropic and inhomogeneous fluids: From simple models of rod- and disc-like particles to polypeptides
Author(s)
Wu, Liang
Type
Thesis or dissertation
Abstract
A liquid crystal (LC) is a substance that exhibits phases intermediate between a crystal
and a disordered liquid state. LCs have attracted longstanding research interest because
of their potential commercial applications in opto-electronics, pharmaceuticals and surfactants
but also because ordered soft matter is prevalent in bio-molecular systems such
as DNA and lipid cell membranes. In liquid-crystalline systems, both molecular shape
and asymmetric attractive interactions contribute to the formation and ultimate stability
of anisotropic phases. The research outlined in this thesis provides a fundamental understanding
of these systems by developing theoretical models and undertaking detailed
molecular simulation studies.
In the first part of this thesis, prototype oblate models for LCs are studied: cut spheres
and cylindrical discs. Coupled with a scaled Onsager approach, a general equation of state
(EoS) for hard-core discotic LCs is developed that allows for an accurate description of the
isotropic and nematic phases of oblate discs by introducing a correction to incorporate the
negative contributions from high-order virial coefficients. Combining the above mentioned
approach with an extended cell approach, the isotropic-nematic-columnar phase diagram
of cut spheres is determined. The accuracy of the EoS is assessed by comparison with the
more traditional Parsons-Lee description and existing simulation data.
Although the anisotropic athermal hard-body fluid is a reasonable representation of lyotropic
or colloidal LCs, for thermotropic LC systems temperature plays a key role. In
the second part of this thesis a model of hard-core particles incorporating additional
anisotropic attractive interactions is proposed to describe thermotropic LCs. Based on a
perturbation theory and the Onsager-Parsons-Lee approach, a van der Waals-type (meanfield
level) theory of attractive hard-core particles is formulated in a compact algebraic
form. The phase diagrams of model attractive prolate (spherocylinder) and oblate (cylindrical
disc) molecules are calculated in order to examine the separate effects of molecular
shape and anisotropic attractive interactions. As a practical example, a coarse-grained
model comprising an attractive spherocylinder is employed to describe phase behaviour of
solutions of the polypeptide poly-(γ-benzyl-L-glutamate) (PBLG) in dimethylformamide
(DMF). Quantitative agreement between the results obtained from the EoS and experimental
data is obtained.
In the final part of the thesis, a detailed Monte Carlo (MC) simulation study of athermal
mixtures of hard spherocylinders and hard spheres between two well separated parallel
hard walls is performed. A combination of constant volume (canonical ensemble) and
constant (normal) pressure (isobaric-isothermal ensemble) simulations are carried out.
With these simulations, the bulk phase behaviour as well as surface-induced LC ordering
are explored. The phase diagram of binary mixtures of hard spherocylinders and hard
spheres is presented and is compared with the predictions of the one-fluid Parsons-Lee
and many-fluid theories. Rich phase behaviour is exhibited on the surface of the walls:
drying (de-wetting), isotropic wetting, and nematic wetting are all observed. A previously
unreported entropy-driven transition from a bulk nematic state to a homeotropic smectic
surface ordering (with particles arranged in a perpendicular orientation relative to the
surface plane) is seen in for both the pure hard rod system and the mixture of hard rods
and hard spheres as the density is increased (high pressure states).
and a disordered liquid state. LCs have attracted longstanding research interest because
of their potential commercial applications in opto-electronics, pharmaceuticals and surfactants
but also because ordered soft matter is prevalent in bio-molecular systems such
as DNA and lipid cell membranes. In liquid-crystalline systems, both molecular shape
and asymmetric attractive interactions contribute to the formation and ultimate stability
of anisotropic phases. The research outlined in this thesis provides a fundamental understanding
of these systems by developing theoretical models and undertaking detailed
molecular simulation studies.
In the first part of this thesis, prototype oblate models for LCs are studied: cut spheres
and cylindrical discs. Coupled with a scaled Onsager approach, a general equation of state
(EoS) for hard-core discotic LCs is developed that allows for an accurate description of the
isotropic and nematic phases of oblate discs by introducing a correction to incorporate the
negative contributions from high-order virial coefficients. Combining the above mentioned
approach with an extended cell approach, the isotropic-nematic-columnar phase diagram
of cut spheres is determined. The accuracy of the EoS is assessed by comparison with the
more traditional Parsons-Lee description and existing simulation data.
Although the anisotropic athermal hard-body fluid is a reasonable representation of lyotropic
or colloidal LCs, for thermotropic LC systems temperature plays a key role. In
the second part of this thesis a model of hard-core particles incorporating additional
anisotropic attractive interactions is proposed to describe thermotropic LCs. Based on a
perturbation theory and the Onsager-Parsons-Lee approach, a van der Waals-type (meanfield
level) theory of attractive hard-core particles is formulated in a compact algebraic
form. The phase diagrams of model attractive prolate (spherocylinder) and oblate (cylindrical
disc) molecules are calculated in order to examine the separate effects of molecular
shape and anisotropic attractive interactions. As a practical example, a coarse-grained
model comprising an attractive spherocylinder is employed to describe phase behaviour of
solutions of the polypeptide poly-(γ-benzyl-L-glutamate) (PBLG) in dimethylformamide
(DMF). Quantitative agreement between the results obtained from the EoS and experimental
data is obtained.
In the final part of the thesis, a detailed Monte Carlo (MC) simulation study of athermal
mixtures of hard spherocylinders and hard spheres between two well separated parallel
hard walls is performed. A combination of constant volume (canonical ensemble) and
constant (normal) pressure (isobaric-isothermal ensemble) simulations are carried out.
With these simulations, the bulk phase behaviour as well as surface-induced LC ordering
are explored. The phase diagram of binary mixtures of hard spherocylinders and hard
spheres is presented and is compared with the predictions of the one-fluid Parsons-Lee
and many-fluid theories. Rich phase behaviour is exhibited on the surface of the walls:
drying (de-wetting), isotropic wetting, and nematic wetting are all observed. A previously
unreported entropy-driven transition from a bulk nematic state to a homeotropic smectic
surface ordering (with particles arranged in a perpendicular orientation relative to the
surface plane) is seen in for both the pure hard rod system and the mixture of hard rods
and hard spheres as the density is increased (high pressure states).
Version
Open Access
Date Issued
2013-07
Online Publication Date
2014-07-18T11:17:15Z
Date Awarded
2013-07
Advisor
Jackson, George
Muller, Erich
Publisher Department
Chemical Engineering
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)