P. I. C. Teixeira

The effect of dipolar forces on the structure and thermodynamics of classical fluids

The present understanding of how dipolar forces affect the structure and phase behaviour of classical fluids is reviewed. We focus mainly on the apparent absence of a liquid-vapour phase transition for strongly polar spherical particles, and discuss how the same can be recovered. By concentrating on theoretical and simulation studies of simple models, the roles and interplay of dipolar and Van der Waals interactions and molecular shape can be clearly discerned. Connection is made with experimental work on ferrofluids. Finally, we discuss the theoretical and computational challenges that lie ahead.

Biaxial Nematic Order in the Hard-boomerang Fluid

Abstract We consider a fluid of hard boomerangs, each composed of two hard spherocylinders joined at their ends at an angle ψ. The resulting particle is nonconvex and biaxial. The occurence of nematic order in such a system has been investigated using Straleys theory, which is a simplificaton of Onsagers second-virial treatment of long hard rods, and by bifurcation analysis. The excluded volume of two hard boomerangs has been approximated by the sum of excluded volumes of pairs of constituent spherocylinders, and the angle-dependent second-virial coefficient has been replaced by a low-order interpolating function. At the so-called Landau point, ψ Landau ≈ 107.4°, the fluid undergoes a continuous transition from the isotropic to a biaxial nematic (B) phase. For ψ ≠ ψLandau ordering is via a first-order transition into a rod-like uniaxial nematic phase (N +) if ψ > ψLandau, or a plate-like uniaxial nematic (N−) phase if ψ < ψLandau. The B phase is separated from the N+ and N− phases by two lines of contin...

Density-functional theory for the interfacial properties of a dipolar fluid

The authors have studied the interfacial properties of a model dipolar fluid using a generalization of the density functional mean-field approximation. The generalization consists in weighting configurations in the mean-field average of the perturbative part of the energy by the low-density approximation of the radial distribution function. This leads to a bulk phase diagram which depends explicitly on the strength of the multipole moments, in contrast with the results of the simpler version of the theory. The calculated surface tension and density-orientational profile are in fair agreement with computer simulation (molecular dynamics) results: the addition of a dipole moment causes the surface tension to increase and there is interfacial ordering induced by purely multipolar forces. An extension of the theory to binary fluid mixtures is also briefly discussed.

Microscopic theory of anchoring transitions at the surfaces of pure liquid crystals and their mixtures. I. The Fowler approximation

We have generalized earlier work on anchoring of nematic liquid crystals by Sullivan, and Sluckin and Poniewierski, in order to study transitions which may occur in binary mixtures of nematic liquid crystals as a function of composition. Microscopic expressions have been obtained for the anchoring energy of (i) a liquid crystal in contact with a solid aligning surface; (ii) a liquid crystal in contact with an immiscible isotropic medium; (iii) a liquid crystal mixture in contact with a solid aligning surface. For (iii), possible phase diagrams of anchoring angle versus dopant concentration have been calculated using a simple liquid crystal model. These exhibit some interesting features including re‐entrant conical anchoring, for what are believed to be realistic values of the molecular parameters. A way of relaxing the most drastic approximation implicit in the above approach is also briefly discussed.

Equilibrium self-assembly of colloids with distinct interaction sites: Thermodynamics, percolation, and cluster distribution functions

We calculate the equilibrium thermodynamic properties, percolation threshold, and cluster distribution functions for a model of associating colloids, which consists of hard spherical particles having on their surfaces three short-ranged attractive sites (sticky spots) of two different types, A and B. The thermodynamic properties are calculated using Wertheims perturbation theory of associating fluids. This also allows us to find the onset of self-assembly, which can be quantified by the maxima of the specific heat at constant volume. The percolation threshold is derived, under the no-loop assumption, for the correlated bond model: In all cases it is two percolated phases that become identical at a critical point, when one exists. Finally, the cluster size distributions are calculated by mapping the model onto an effective model, characterized by a--state-dependent--functionality f and unique bonding probability p. The mapping is based on the asymptotic limit of the cluster distributions functions of the generic model and the effective parameters are defined through the requirement that the equilibrium cluster distributions of the true and effective models have the same number-averaged and weight-averaged sizes at all densities and temperatures. We also study the model numerically in the case where BB interactions are missing. In this limit, AB bonds either provide branching between A-chains (Y-junctions) if epsilon(AB)/epsilon(AA) is small, or drive the formation of a hyperbranched polymer if epsilon(AB)/epsilon(AA) is large. We find that the theoretical predictions describe quite accurately the numerical data, especially in the region where Y-junctions are present. There is fairly good agreement between theoretical and numerical results both for the thermodynamic (number of bonds and phase coexistence) and the connectivity properties of the model (cluster size distributions and percolation locus).

Ordering of hard particles between hard walls

The structure of a fluid of hard Gaussian overlap particles of elongation κ = 5, confined between two hard walls, has been calculated from density-functional theory and Monte Carlo simulations. By using the exact expression for the excluded volume kernel (Velasco E and Mederos L 1998 J. Chem. Phys. 109 2361) and solving the appropriate Euler-Lagrange equation entirely numerically, we have been able to extend our theoretical predictions into the nematic phase, which had up till now remained relatively unexplored due to the high computational cost. Simulation reveals a rich adsorption behaviour with increasing bulk density, which is described semi-quantitatively by the theory without any adjustable parameters.

A model calculation of the surface elastic constants of a nematic liquid crystal

We have evaluated the bulk and surface elastic constants of a nematic liquid crystal composed of Gay-Berne particles, using a generalization of earlier theories by Poniewierski and Stecki, and Lipkin, Rice and Mohanty. The ratios between surface and bulk elastic constants have been plotted as a function of temperature and at nematic-isotropic coexistence. In particular, the sign of the K 13 (splay-bend) constant has been shown to depend sensitively on details of the intermolecular potential. Results have been contrasted with those obtained from a different theory.

How patchy can one get and still condense? The role of dissimilar patches in the interactions of colloidal particles

We investigate the influence of strong directional, or bonding, interactions on the phase diagram of complex fluids, and in particular on the liquid–vapour critical point. To this end we revisit a simple model and theory for associating fluids which consist of spherical particles having a hard-core repulsion, complemented by three short-ranged attractive sites on the surface (sticky spots). Two of the spots are of type A and one is of type B; the interactions between each pair of spots have strengths , and . The theory is applied over the whole range of bonding strengths and results are interpreted in terms of the equilibrium cluster structures of the coexisting phases. In systems where unlike sites do not interact (i.e. where ), the critical point exists all the way to . By contrast, when , there is no critical point below a certain finite value of . These somewhat surprising results are rationalised in terms of the different network structures of the two systems: two long AA chains are linked by one BB bond (X-junction) in the former case, and by one AB bond (Y-junction) in the latter. The vapour–liquid transition may then be viewed as the condensation of these junctions and we find that X-junctions condense for any attractive (i.e. for any fraction of BB bonds), whereas condensation of the Y-junctions requires that be above a finite threshold (i.e. there must be a finite fraction of AB bonds).

Landau–de Gennes theory of anchoring transitions at a nematic liquid crystal–substrate interface

Abstract We have used Landau–de Gennes theory to study anchoring and anchoring transitions at the interface between a nematic liquid crystal and a smooth solid substrate. In contrast to earlier work by Sen and Sullivan, we allow for a spatially varying tilt angle and solve the Euler–Lagrange equations requiring that the order parameters be uniform far from the wall. We have found that temperature-driven anchoring transitions akin to those observed experimentally can be obtained either as a result of the change in the surface order parameter or due to competition between the ordering effects of the solid surface and the nascent isotropic–nematic interface as TNI is approached, in the regime of complete wetting by the isotropic phase. Predictions have also been made for the experimentally observable values of the anchoring energy.

Microscopic theory of anchoring transitions at the surfaces of pure liquid crystals and their mixtures. II: The effect of surface adsorption

We have extended our theory of anchoring transitions to take into account adsorption at the interface between a nematic–non‐nematic binary mixture and a solid aligning substrate. This was achieved by decoupling adsorption and anchoring and treating the former in the context of the Cahn theory of wetting, while the latter was studied using our previous anchoring theory. For ease of calculation, we mapped the relevant portion of the phase diagram of the mixture onto that of a (isotropic) regular solution. The anchoring angle has been calculated over the whole concentration range, in the partial wetting regime, and in the near saturation region, in the complete wetting regime. For realistic values of the molecular parameters, anchoring transitions have been found which exhibit a degree of temperature independence (‘universality’) akin to that observed experimentally. Ways of developing a fully consistent theory of anchoring transitions are also briefly discussed.