Chapter 15
Liquid Crystals and Other
Anisotropic Fluids
Abstract This chapter deals with equilibrium properties of liquid crystals and other
anisotropic fluids. After some remarks on nematic, cholesteric and smectic liquid
crystals and blue phases, the second rank alignment tensor is introduced as the rele-
vant order parameter for the nematic state. Theories for the phase transition isotropic-
nematic are presented. The orientational elastic behavior of nematics and cholesterics
is firstly described by the director elasticity involving the Frank coefficients and then
by the alignment tensor elasticity theory. Systems with cubic and with tetrahedral
symmetry, referred to as cubatics and tetradics, are characterized by fourth and third
rank order parameter tensors. Some examples for the energetic coupling of order
parameter tensors of equal and of different ranks are considered.
Crystalline solids are anisotropic. Fluids in thermal equilibrium, on the other hand,
are commonly looked upon as isotropic substances. However, fluids can also become
anisotropic, be it through the application of external fields or by a spontaneous phase
transition into an state with orientational order.Liquid crystalsare the most prominent
anisotropic fluids. Here the emphasis is onnematic liquid crystals. Properties of
some other anisotropic fluids are discussed briefly. In any case, tensors are the tools
needed to characterize the anisotropy of these substances. This section is devoted
to equilibrium properties. Non-equilibrium phenomena are treated in Sect.16.4and
Chap. 17.
A standard publication for the physics of liquid crystals is the classic book of de
Gennes from 1973, a revised and extended second edition appeared in 1993 [67].
A good introduction is [68], for phase types and structures see also [69]. An extensive
survey of the literature up to 1980 is given in [70]. Concepts and experiments are
discussed in [71]. Classic papers on liquid crystals are reproduced and commented in
[72]. Optical experiments and their theoretical foundation are treated in [73] for equi-
librium and non-equilibrium properties of complex fluids, in particular for polymers
and liquid crystals.
© Springer International Publishing Switzerland 2015
S. Hess,Tensors for Physics, Undergraduate Lecture Notes in Physics,
DOI 10.1007/978-3-319-12787-3_15
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