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K. Xiao and C.-X. Wu
8.1 Introduction
Liquid crystals (LCs) are soft materials made of organic molecules with rodlike,
disclike or banana shapes, a mesophase intermediate between the crystalline and
isotropic liquid state formed at a certain temperature or molecular concentration
range [1, 2]. In the undeformed ground state, uniaxial molecules in nematic liquid
crystal (NLC) phase, the simplest type of all orientational orders, prefer an orientation
with their molecular long axes aligning along a common direction n called director.
It is widely accepted that the NLCs possess many anisotropic physical properties
that are easy to control by external stimuli owing to their long-range orientational
order rather than translational order. Colloids, which are widely used in our daily
life, including milk, ink, paint, cream and fog, are dispersions of solid, liquid or gas
particles with typical size ranging from a few nanometers up to a few micrometers in
a host surrounding medium [3, 4]. When dispersed in a NLC, the colloidal particles
disturb the alignment of LC molecules and induce elastic distortions which give rise
to long-range anisotropic interactions and topological defects. The generated longrange force leads to the self-assembly of molecules in such system, a topological
phenomenon offering the possibility to control and design anticipated function for
novel composite materials and diverse topology materials with similar features. One
of the main themes of liquid crystal is to study the properties and behaviors of colloids
suspended in nematic liquid crystal (NLC), and a wide range of promising practical applications have been realized, such as new display and topological memory
devices [5–7], new materials [8], external triggers and release microcargo [9], and
biological detectors [10, 11]. Over the past two decades, many experimental, theoretical and computer simulation studies have been focused on the physical properties
of colloidal particles embedded within NLCs [12–25].
At the experimental level, diverse methods and techniques have been developed
to measure the interaction force between particles in NLC in a direct manner [12,
26–29]. It has been found that the interaction force of spherical particles suspended
in NLC is associated not only with interparticle distance and geological confinement [13], but also with the shape of particles which plays a crucial role in pair interaction and aggregation behaviors [17]. Whereas, in the presence of the electric field,
fruitful fascinating physical phenomena such as levitation, lift, bidirectional motion,
aggregation, Electrokinetic and superdiffusion [24, 30–32] have been observed for
colloids dispersed in NLCs. On the other hand, theoretical modeling and computer
simulation as useful complements to experiments, such as Landau-de Gennes (LdG)
theory and elastic free energy method, have been carried out to interpret the nature
of colloidal particles dispersed in NLCs. Generally Monte Carlo simulation [23,
33], lattice Boltzmann method [34, 35] and finite element method [13, 36–39] are
common adopted techniques to minimize the LdG free energy functional. Except
for the methods mentioned above, recently S. B. Chernyshuk and coauthors studied
the interaction between colloidal particles in NLCs with or without external field
by using Green’s function method, and obtained general formulae for interaction
energy between colloidal particles [40–42]. In the liquid crystal and particles coex-
K. Xiao and C.-X. Wu
8.1 Introduction
Liquid crystals (LCs) are soft materials made of organic molecules with rodlike,
disclike or banana shapes, a mesophase intermediate between the crystalline and
isotropic liquid state formed at a certain temperature or molecular concentration
range [1, 2]. In the undeformed ground state, uniaxial molecules in nematic liquid
crystal (NLC) phase, the simplest type of all orientational orders, prefer an orientation
with their molecular long axes aligning along a common direction n called director.
It is widely accepted that the NLCs possess many anisotropic physical properties
that are easy to control by external stimuli owing to their long-range orientational
order rather than translational order. Colloids, which are widely used in our daily
life, including milk, ink, paint, cream and fog, are dispersions of solid, liquid or gas
particles with typical size ranging from a few nanometers up to a few micrometers in
a host surrounding medium [3, 4]. When dispersed in a NLC, the colloidal particles
disturb the alignment of LC molecules and induce elastic distortions which give rise
to long-range anisotropic interactions and topological defects. The generated longrange force leads to the self-assembly of molecules in such system, a topological
phenomenon offering the possibility to control and design anticipated function for
novel composite materials and diverse topology materials with similar features. One
of the main themes of liquid crystal is to study the properties and behaviors of colloids
suspended in nematic liquid crystal (NLC), and a wide range of promising practical applications have been realized, such as new display and topological memory
devices [5–7], new materials [8], external triggers and release microcargo [9], and
biological detectors [10, 11]. Over the past two decades, many experimental, theoretical and computer simulation studies have been focused on the physical properties
of colloidal particles embedded within NLCs [12–25].
At the experimental level, diverse methods and techniques have been developed
to measure the interaction force between particles in NLC in a direct manner [12,
26–29]. It has been found that the interaction force of spherical particles suspended
in NLC is associated not only with interparticle distance and geological confinement [13], but also with the shape of particles which plays a crucial role in pair interaction and aggregation behaviors [17]. Whereas, in the presence of the electric field,
fruitful fascinating physical phenomena such as levitation, lift, bidirectional motion,
aggregation, Electrokinetic and superdiffusion [24, 30–32] have been observed for
colloids dispersed in NLCs. On the other hand, theoretical modeling and computer
simulation as useful complements to experiments, such as Landau-de Gennes (LdG)
theory and elastic free energy method, have been carried out to interpret the nature
of colloidal particles dispersed in NLCs. Generally Monte Carlo simulation [23,
33], lattice Boltzmann method [34, 35] and finite element method [13, 36–39] are
common adopted techniques to minimize the LdG free energy functional. Except
for the methods mentioned above, recently S. B. Chernyshuk and coauthors studied
the interaction between colloidal particles in NLCs with or without external field
by using Green’s function method, and obtained general formulae for interaction
energy between colloidal particles [40–42]. In the liquid crystal and particles coex-