Book Review

An Elementary Course on the Continuum Theory for Nematic Liquid Crystals

Chapter 1 deals with the calculus of variations in the context of nematic liquid crystal theory. As well as the usual standard variational problem, the topics include aspects such as strong and weak anchoring and the inclusion of second derivatives, all discussed in the context of the relevant variational theory of direct interest to liquid crystals. Discontinuous extremizing functions, functionals depending on two functions and other pertinent theory are also included in an appropriate fashion to be used in subsequent chapters.

Chapter 2 essentially discusses the elastic and electric energies for nematics. The elastic energy is first derived in terms of the director n and then derived in terms of the tensorial order parameter Qij and the scalar order parameter S. Also, the energy is given in the Nehring-Saupe form to include second derivatives via the K13 term. The electric energy is derived in a similarly lucid style. Many other topics are discussed, including quadrupolar properties induced by mechanical deformations, approximations for the constant and spatial variations of S, and the influence of ions on the anisotropic part of the surface tension of a nematic crystal. Some previous knowledge of indicial notation is required.

Chapter 3 is one of the key chapters on applications. After some introductory sections on anchoring and alignment in cells of nematic, it goes on to discuss the usual idea of the important Freedericksz transition. This chapter, over 100 pages long, is one to which I keep returning. It has an unprecedented wealth of novel and important problems, all expertly elucidated and explained. The problems are collected in a sensible order for discussion and include, among many other important features, the Freedericksz transition in strong and weak anchoring, hybrid cells, tilted magnetic fields, director orientation in a cholesteric liquid crystal, flexoelectric effects, rotation of the polarisation plane of a linearly polarised light beam on a cell submitted to electric or magnetic fields, and samples of nematic subjected to crossed electric and magnetic fields. This really is a chapter that will interest all researchers at every level.

Chapter 4 deals with molecular models. The classical interaction laws of Maier-Saupe, Nehring-Saupe and quadrupole-quadrupole are considered. The theories are developed and discussed in detail and bulk elastic properties are investigated. Both spherical and ellipsoidal approximations are introduced. Many advanced topics in this theory are expounded, including elastic properties limited by a surface, the generic two-body interaction problem and the bulk elastic properties of magnetic suspensions in lyotropic nematic liquid crystals.

Chapter 5 discusses the spontaneous deformations in nematics near a limiting surface. This is by far the most advanced chapter from a physical and mathematical viewpoint and requires quite extensive knowledge of the previous chapters. The influence of the K13 term upon the nematic orientation is discussed in great detail in sections 5.3 and 5.4. There is much controversy in the literature about the K13 term and these sections contribute positively to the debate, much of the work apparently being attributed to the authors and their co-workers. Other topics include the possible spatial dependence of the elastic constants near a boundary layer and the Freedericksz transition with a spatially dependent elastic constant.

There is, however, one minor point that the authors have overlooked: none of the references at the end of each chapter are cited within the text. This makes it difficult for novice readers to assess which references are directly relevant. None the less, this does not diminish the fact that this is an excellent text and, in conclusion, I thoroughly recommend this book to those interested in liquid crystal static continuum theory and its applications. It is written in a clear and straightforward manner and will appeal to workers at every level.
Iain Stewart, Strathclyde University

Date: October 2001

G. Barbero and L.R. Evangelista

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