E. F. Gramsbergen

Abstract: A review is given of the wide variety of predictions that results from a Landau-type of description of the nematic-isotropic phase transition. This includes a discussion of the nature of the order parameter and of the various types of possible phases, of the influence of external fields, and of the effect of inclusion of spatial variations of the order parameter. The various predictions are compared with the available experimental results. It is concluded that there is still no clear picture about the nature of the singularity near the nematic-isotropic phase transition. Though the assumption of classical (mean-field) critical behaviour seems to be incorrect, there is no conclusive proof which alternative applies.

Abstract: The birefringence of mixtures of homologues from the terminally non-polar series of p,p′-dialkylazoxybenzenes has been studied. The birefringence is used as a probe of the orientational order parameter, which is coupled to the translational (smectic) order parameter. The tricritical nematic to smectic-A point which results from this coupling is found at a McMillan ratio TAN/TNI= 0.977. This is similar to the values reported for terminally polar systems and is higher than predicated by theory. The critical exponent for the variation of the order parameter across the SA–N phase transition obeys the expected trend.

Abstract: The X-ray reflectivity form the surface of a liquid crystal with terminally polar (cyano substituted) molecules has been studied using a high-resolution triple-axis X-ray spectrometer in combination with a synchrotron source. It is demonstrated that at the surface of the smectic A1 phase a few antiferroelectric double layers develop that can be distinguished from the bulk single layer structure. A model is developed that separates the electron density in a contribution from the molecular form factor, and from the structure factor of the mono- and the bilayers, respectively. With only a few adjustable parameters it accounts for the rather complex observed reflection curve. It shows that (i) the first molecular layer has tails up rather than heads up, (ii) the smectic order parameter of the first mono- and bilayer is saturated, (iii) the antiferroelectric bilayering does decay rather abruptly and not exponentially Etude RX de la surface d'un cristal liquide pres de la transition nematique-smectique A1. Developpement en surface de quelques doubles couches antiferroelectriques qui peuvent etre distinguees de la structure en simples couches du materiau massif

Abstract: Results are given for the elastic constants in the nematic phase of some molecules with a curved (banana-like) molecular shape. In principle this could lead to a reduced bend elastic constant due to the possibility of adjusting to a bend deformation by a redistribution of the molecules. However, the elastic constants turn out to have quite normal values as compared with similar non-curved molecules.

Abstract: As their name indicates, liquid crystals simultaneously exhibit some characteristics common to both ordinary isotropic liquids and solid crystals. This ambivalence is also found in the effects of surfaces on these systems which lead to a great diversity of phenomena. These phenomena are reviewed focusing on nematic liquid crystals which have the simplest structure among the many existing types and which have been the most extensively studied. Three main kinds of effects can be distinguished. The first concerns the perturbation of the liquid crystalline structure close to the surface. Beyond this transition region, the bulk liquid crystalline structure is recovered with an orientation which is fixed by the surface: this phenomenon of orientation of liquid crystals by surfaces is the so-called anchoring. Finally, close to bulk phase transitions, critical adsorption or wetting can occur at surfaces as is also seen in isotropic systems.

Abstract: This article reviews the physics of colloidal dispersions in nematic liquid crystals as a novel challenging type of soft matter We first investigate the nematic environment of one particle with a radial anchoring of the director at its surface Three possible structures are identified and discussed in detail; the dipole, the Saturn-ring and the surface-ring configuration Secondly, we address dipolar and quadrupolar two-particle interactions with the help of a phenomenological theory Thirdly, we calculate the anisotropic Stokes drag of a particle in a nematic environment which determines the Brownian motion of particles via the Stokes–Einstein relation We then turn our interest towards colloidal dispersions in complex geometries where we identify the dipolar configuration and study its formation Finally, we demonstrate that surface-induced nematic order above the nematic-isotropic phase transition results in a strongly attractive but short-range two-particle interaction Its strength can be controlled by temperature and thereby induce flocculation in an otherwise stabilized dispersion

Abstract: Mesogenic materials exhibit a multitude of transitions involving new phases. Studies of these phases are of importance in a wide range of scientific fields and as such have stimulated considerable theoretical and experimental efforts over the decades. This review article presents a comprehensive overview until this date of the developments in this subject. An attempt is made to identify the essential key concepts and points of difficulty associated with the study of phase transitions. The article begins with a brief introduction about the symmetry, structure and types of liquid crystalline phases. This is followed by a discussion of the distribution functions and order parameters which are considered as the basic knowledge essential for the study of ordered phases. A brief discussion of the thermodynamic properties at and in the vicinity of phase transitions, which are required to understand the molecular structure phase stability relationship, is given. The most widely used experimental techniques for measuring these transition properties are critically examined. The remaining parts of the article are concerned with the current status of the theoretical developments and experimental studies in this field. The application of the various theories to the description of isotropic liquid-uniaxial nematic, uniaxial nematic-smectic A, uniaxial nematic-biaxial nematic, smectic A–smectic C phase transitions are reviewed comprehensively. The basic ideas of Landau–de Gennes theory and its applications to study these transitions are discussed. Since the formation of liquid crystals depends on the anisotropy in the intermolecular interactions, questions concerning its role in the mesophase transitions are addressed. The hard particle, Maier-Saupe and van der Waals types of theories are reviewed. The application of density functional theory in studying mesophase transitions is described. A critical assessment of the experimental investigations concerning reentrant phase transitions in liquid crystals is made and the factors which impede its proper understanding are identified. A survey is given of existing computer simulation studies of the isotropic to nematic transition, the nematic to smectic A transition, the smectic A to hexatic S B transition, the smectic A to reentrant nematic transition, and transitions to the discotic phase. The current status of the study of phase transitions involving hexatic smectic, cholesteric, polymeric and ferroelectric liquid crystals is outlined. Finally, a range of unexplored problems and some of the areas which are in greatest need of future attention are identified.

Abstract: Based on the distorted wave Born approximation we derive a general expression for the kinematic scattering cross-section of X-rays and neutrons impinging on an arbitrary interfacial structure. The scattering intensity is expressed in terms of the two-point correlation function of the atomic number densities. Since our approach takes fully into account the refraction at the corresponding smooth mean interface profile, our results offer the basis for an accurate analysis of the diffuse scattering intensity, which allows one to extract the lateral correlations. As an illustration of this formalism, we discuss applications to particularly interesting systems such as liquid-vapor interfaces, thin films, and multilayers. The systematic separation of the contributions to the scattering intensity which are proportional to the volume of the sample and those scaling with the area of the illuminated surface yields a detailed description of the truncation rod scattering of crystals. In the case of fluctuating interfaces, we provide a systematic derivation for the expression of the scattering cross-section. We show which approximations are necessary in order to recover those formulae which are commonly used to describe the scattering intensity caused by fluctuating interfaces. Therefore, we are able to assess their range of validity and their limitations. Beyond that, we discuss cases in which the vector character of X-rays cannot be ignored or where the atomic form factors and the correlation functions do not factorize.