Chapter 8
Fréedericksz-Like Positional Transition
Triggered by An External Electric Field
Ke Xiao and Chen-Xu Wu
Abstract Microparticles (colloidal particles) of different shapes suspended in an
anisotropic nematic liquid crystal (NLC) host medium are important soft matter systems which behave quite differently from those simply composed of microparticles or
conventional isotropic liquids. The embedded microparticles disturb the alignment
of LC molecules and induce elastic distortions, generating long-range anisotropic
interactions and topological defects. The replacement of isotropic liquids with NLC
medium gives rise to abundant physical behaviors of the microparticles, which leads
to a broad range of practical applications ranging from biological detectors to new
display and topological memory devices. This chapter is devoted to the new dynamic
behaviors of a microparticle suspended in a uniform nematic liquid crystal (NLC) cell
in the presence of an external electric field, an important tool in soft matter systems
to manipulate microparticles. Investigating the basic dependence of critical electric value on cell thickness, Frank elastic constant, microparticle size and density is
essential for understanding the dynamical behaviors of micropartices. This chapter is
organized as follows. We start with a short introduction on liquid crystal together with
a review of the related literature on microparticle-suspended liquid crystal (Sect. 8.1).
The theoretical background of liquid crystals with particular focus on order parameter, Frank-Oseen free energy, surface anchoring free energy, Fréedericksz transition,
and multipole expansion is described in Sect. 8.2. The main theoretical model and
tools are then outlined in Sect. 8.3 to study the properties of a single particle in a
uniform nematic liquid crystal cell in the presence of an external electric field. The
main results and discussions based on the theoretical model we proposed in Sect. 8.3
are presented in Sect. 8.4. In Sect. 8.5 a brief summary is made.
Keywords Nematic liquid crystal · Positional transition · Effective elastic
energy · Green’s function method
K. Xiao · C.-X. Wu (B)
Department of Physics, College of Physical Science and Technology,
Xiamen University, Fujian, People’s Republic of China
e-mail: cxwu@xmu.edu.cn
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
X.-Y. Liu (ed.), Frontiers and Progress of Current Soft Matter Research,
Soft and Biological Matter, https://doi.org/10.1007/978-981-15-9297-3_8
323
Fréedericksz-Like Positional Transition
Triggered by An External Electric Field
Ke Xiao and Chen-Xu Wu
Abstract Microparticles (colloidal particles) of different shapes suspended in an
anisotropic nematic liquid crystal (NLC) host medium are important soft matter systems which behave quite differently from those simply composed of microparticles or
conventional isotropic liquids. The embedded microparticles disturb the alignment
of LC molecules and induce elastic distortions, generating long-range anisotropic
interactions and topological defects. The replacement of isotropic liquids with NLC
medium gives rise to abundant physical behaviors of the microparticles, which leads
to a broad range of practical applications ranging from biological detectors to new
display and topological memory devices. This chapter is devoted to the new dynamic
behaviors of a microparticle suspended in a uniform nematic liquid crystal (NLC) cell
in the presence of an external electric field, an important tool in soft matter systems
to manipulate microparticles. Investigating the basic dependence of critical electric value on cell thickness, Frank elastic constant, microparticle size and density is
essential for understanding the dynamical behaviors of micropartices. This chapter is
organized as follows. We start with a short introduction on liquid crystal together with
a review of the related literature on microparticle-suspended liquid crystal (Sect. 8.1).
The theoretical background of liquid crystals with particular focus on order parameter, Frank-Oseen free energy, surface anchoring free energy, Fréedericksz transition,
and multipole expansion is described in Sect. 8.2. The main theoretical model and
tools are then outlined in Sect. 8.3 to study the properties of a single particle in a
uniform nematic liquid crystal cell in the presence of an external electric field. The
main results and discussions based on the theoretical model we proposed in Sect. 8.3
are presented in Sect. 8.4. In Sect. 8.5 a brief summary is made.
Keywords Nematic liquid crystal · Positional transition · Effective elastic
energy · Green’s function method
K. Xiao · C.-X. Wu (B)
Department of Physics, College of Physical Science and Technology,
Xiamen University, Fujian, People’s Republic of China
e-mail: cxwu@xmu.edu.cn
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
X.-Y. Liu (ed.), Frontiers and Progress of Current Soft Matter Research,
Soft and Biological Matter, https://doi.org/10.1007/978-981-15-9297-3_8
323