An elementary course on the continuum theory for nematic liquid crystals (Q2718645)

This book is devoted to the simplest expression of the theory of liquid crystals, i.e., the theory of nematic liquid crystals in the absence of flow. In other words, the medium considered is a crystal whose properties are purely elastic and are uniquely described by a unit-vector field \({\mathbf n}\) (a ``director'', although this wording from continuum mechanics is never used), and eventually by a second-order tensor \({\mathbf Q}\) that plays the role of an order parameter analogous to a conformation for macromolecules. This reduces drastically the scope of the book compared to now classical treatises on liquid crystals such as those of De Gennes and Prost, etc. Accordingly, viscous effects and the names of scientists such as Ericksen or Leslie or Martin and Parodi are not mentioned. The authors therefore focus on orientational effects on the director field, and on the resulting optical properties in electric and magnetic fields, since this is the only thing that can be envisaged. But no relaxation of this is even considered (in all, no dissipative effects of any kind). Many of the references are to the authors' and co-workers' works.NEWLINENEWLINENEWLINEThe book starts with a chapter on variational calculus. This looks more like a traditional mathematical introduction to undergraduate students in mathematics, although it directly paves the way for establishing admissible static configurations of the director field for prescribed geometries and boundary conditions. Chapter 2 deals per se with the modelling by consideration of an energy density depending on the first-, and sometimes higher-order gradient of \({\mathbf n}\), or on a second-order tensor \({\mathbf Q}\) in the manner of Maier and Saupe. There is an effort at some rationality in the reduction of the expression for energy density, of which the simplest one naturally is that of Frank. Chapter 3 provides a set of applications of the elasticity theory of nematic liquid crystals. This offers the opportunity to discuss thoroughly anchoring boundary conditions, various couplings with electric and magnetic fields, optical properties such as the rotation of polarization plane, and obviously the Fréedericksz transition. Chapter 4 provides an attempt at connecting together the phenomenological theory and the microscopic approach of Maier and Saupe (evaluation of material coefficients), and also deals with surface properties. As a matter of fact, further surface characteristics are examined in the last chapter 5, where various problems concerning the orientation of nematic liquid crystals at surfaces are examined.NEWLINENEWLINENEWLINEIn a general manner, many of the exposed points are presented in the form of queries and solutions, and this may be a good pedagogical approach accounting for the basic knowledge gained in the first chapter. Also, though the specific object of the book may appear as somewhat limited, it must be realized that this book is only one contribution to a series on liquid crystals managed by World Scientific. Accordingly, the book will find its place in an ensemble, and may be required reading to all those interested in the field of liquid crystals and their application to optical cells.