Book review by J. W. Emsley

 

Biaxial nematic liquid crystals: theory, simulation and experiment, edited by Geoffrey R. Luckhurst and Timothy J. Sluckin, Chichester, John Wiley & Sons, 2015, 383 p., £120 ($160, 135 Euro) hardback, ISBN 9780470871959

Those drawn to read this review are surely interested in, and probably involved with liquid crystals, but for different motives. All of you could gain from reading the articles in this edited collection covering all aspects of the biaxial nematic phase. I have been guiltily aware that this excellent book has been sitting on my bookshelf unread since a copy was given to me by Geoffrey Luckhurst shortly after its publication in 2015. I surely intended to read it sometime, but not until I could find a space in my busy life in retirement. I therefore did not need much persuading when asked to review this book to read the 15 articles, written by 23 authors, and covering the theory, methods of characterisation, chemical synthesis and possible applications. And now that I have read them I am very impressed. The articles represent a classic case of a problem posed initially by a theorist, Marvin Freiser in 1970, that since the molecules which form a nematic phase have at most biaxial symmetry, why are nematic phases characterised until that time invariably of uniaxial symmetry? This may now seem an obvious conjecture to make, but it perturbed a strongly held view that apart from the cholesteric liquid crystals formed by chiral compounds, thermotropic liquid crystals formed from achiral rod-like molecules, produce nematic phases which are optically uniaxial. Molecules with disc-like shapes were shown to form thermotropic nematic phases a little later, but these phases are also of uniaxial symmetry. Of course, chemists at this time knew that although classic thermotropic, nematogens, such as PAA, could be thought of as rods (they are elongated), they have no symmetry, and have shapes that fluctuate because of various forms of intramolecular motion. Freiser suggested that molecules which are closer to being board-like rather than rod-like might form a biaxial nematic phase having D2h rather than D∞h symmetry, and have two distinguishable director axes. The challenge was to find such an NB phase. This was achieved 10 years later by Yu and Saupe for an amphiphilic system containing three components: a surfactant, potassium laurate; a co-surfactant, decanol; and water. In these systems, the liquid crystallinity originates from the formation of micelles with anisotropic shapes. Yu and Saupe found that at certain relative concentrations of the three components changing the temperature produced an NB phase bounded on one side by an  and the other by an , the + and − referring to the sign of Δχ, the anisotropy in the bulk magnetic susceptibility. This change in sign of Δχ could be followed conveniently by deuterium NMR spectroscopy, and is attributed to the two NU phases as being comprised of micelles with spheroidal shapes, either prolate (rod-like) for  and oblate (disc-like) for . The small number of amphiphilic systems which have been found to display the NB phase are described here in Chapter 11 by Neto and Galerne, and they remain the best examples of this elusive biaxial phase.

Experimentalists, guided by theoreticians, have searched diligently for a low-molar-mass thermotropic system which shows the NB phase. The various theoretical approaches are described by Luckhurst (Chapter 2, ‘Biaxial nematics: order parameters and distribution functions’), Virga (Chapter 3, ‘Molecular field theory’), Longa (Chapter 5, ‘Landau theory of nematic phases’), and these are an excellent combined introduction to these topics. Berardi and Zannoni describe computer simulation experiments in Chapter 6, and there follows a long chapter (Chapter 10) on ‘Characterisation’, subdivided into sections of five principal methods used.

Taking just one theme on the interaction of theory with experiment illustrates why I am thrilled by the work described in this book. It seems obvious to look for molecules of strongly anisotropic shape when searching for a thermotropic biaxial nematic phase. Both rod-like and disc-like molecules form the NU phase, but what will be formed by mixing these different shaped mesogens? Theory suggests that they will probably de-mix, and experiment verifies this depressing prediction. But what would happen if rod and disc fragments are combined in one molecule? Many relatively low-molar-mass rod-disc molecules were made but most did not show the NB phase. The one exception was a tetrapode, in which an NB phase was identified by infrared absorbance and described here in Chapter 10.3 by Vij and Kocot. This technique can also be used to measure the set of parameters, S, P, D and C, which are necessary to characterise molecular orientational order in an NB phase of D2h symmetry. Moreover, the temperature dependences of these order parameters throughout both NB and NU were obtained, and, as pointed out in Chapter 10.3, and in Chapter 3 on ‘Molecular field theory’ by Virga, there is a major difference between experiment and theory for the temperature dependence of C. Both theory and experiment could be wrong, and one way of resolving such a dilemma is to conduct a computer simulation experiment on a model system, as described by Virga in Chapter 3, which supported the predictions of theory rather than the result from experiment. The authors of Chapter 10.3 recognise the importance of this disagreement between theory and experiment, and describe how this has stimulated proposals of how it may be resolved.

One final example of how there is much to learn by reading this book concerns the molecules with an average, pronounced, bent shape, which have been shown to produce a variety of new translationally ordered liquid crystal phases. Do they also form the NB phase? In 2004 the answer seemed to be yes! A molecule with this shape, based on an oxadiazole-biphenol (ODBP) was assigned an NB phase on the basis of NMR experiments on deuterated probe molecules, as described by the Madsen in Chapter 10.4. Bingo! But then a curious and fascinating development occurred. The NMR experiments involve the presence of a magnetic field in competition with a viscous torque produced by sample rotation. The effect of a magnetic field, of intensity B on an NU phase is simply to align the single director axis either parallel or perpendicular to B depending on the sign of the anisotropy in the magnetic susceptibility, but clearly the biaxial nematic phase presents more possibilities, as described in Chapter 8 by Photinos. NMR studies on an ODBP sample containing deuterium in the mesogen and not in a probe molecule lead to the discovery that the NB phase is of monoclinic rather than orthorhombic symmetry. But there was still a further surprise. An NB phase when aligned by a magnetic field should show an X-ray scattering pattern with four spots near the beam centre, as described here in Chapter 10.5 by Davidson, and this was indeed observed for the ODBC sample. However, more detailed studies (summarised by Dingemans et al. Liquid Crystals, 40 (2013) 1655) concluded that this pattern was not because the phase was an NB, indeed it was now assigned uniaxial symmetry, but was diagnostic of the presence of clusters of molecules with overall biaxial symmetry, a so-called, cybotactic cluster. Clearly, the stimulus produced by the suggestion that an NB phase might exist has considerably enhanced our understanding of liquid crystal phases.

Persuading a large group of scientists to produce articles on a common theme, in a timely fashion, is not an easy task, and Geoffrey Luckhurst and Timothy Sluckin are to be thanked for doing so, particularly when the result is such a good read.