J. M. Tavares

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.

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).

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).

Self-assembly in chains, rings, and branches: a single component system with two critical points

We study the interplay between phase separation and self-assembly in chains, rings, and branched structures in a model of particles with dissimilar patches. We extend Wertheims first order perturbation theory to include the effects of ring formation and to theoretically investigate the thermodynamics of the model. We find a peculiar shape for the vapor-liquid coexistence, featuring reentrant behavior in both phases and two critical points, despite the single-component nature of the system. The emergence of the lower critical point is caused by the self-assembly of rings taking place in the vapor, generating a phase with lower energy and lower entropy than the liquid. Monte Carlo simulations of the same model fully support these unconventional theoretical predictions.

Quantitative description of the self-assembly of patchy particles into chains and rings

We numerically study a simple fluid composed of particles having a hard-core repulsion complemented by two patchy attractive sites on the particle poles. An appropriate choice of the patch angular width allows for the formation of ring structures which, at low temperatures and low densities, compete with the growth of linear aggregates. The simplicity of the model makes it possible to compare simulation results and theoretical predictions based on the Wertheim perturbation theory, specialized to the case in which ring formation is allowed. Such a comparison offers a unique framework for establishing the quality of the analytic predictions. We find that the Wertheim theory describes remarkably well the simulation results.

Structural and conformational properties of a quasi-two-dimensional dipolar fluid

A survey of the structural properties of a quasi-two-dimensional dipolar fluid is given with emphasis on the low-density regime where particles self-assemble into clusters. The internal energy, conformational properties and equilibrium length distributions of the clusters are measured by means of Monte Carlo simulation and compared with equilibrium polymer theory. The scaling forms of the length distribution functions predicted by theory are found to describe the simulation results adequately. The existence and mechanisms of phase transitions in dilute dipolar fluids are discussed.

Properties of patchy colloidal particles close to a surface: A Monte Carlo and density functional study

We investigate the behavior of a patchy particle model close to a hard-wall via Monte Carlo simulation and density functional theory (DFT). Two DFT approaches, based on the homogeneous and inhomogeneous versions of Wertheims first order perturbation theory for the association free energy are used. We evaluate, by simulation and theory, the equilibrium bulk phase diagram of the fluid and analyze the surface properties for two isochores, one of which is close to the liquid side of the gas-liquid coexistence curve. We find that the density profile near the wall crosses over from a typical high-temperature adsorption profile to a low-temperature desorption one, for the isochore close to coexistence. We relate this behavior to the properties of the bulk network liquid and find that the theoretical descriptions are reasonably accurate in this regime. At very low temperatures, however, an almost fully bonded network is formed, and the simulations reveal a second adsorption regime which is not captured by DFT. We trace this failure to the neglect of orientational correlations of the particles, which are found to exhibit surface induced orientational order in this regime.

Bicontinuous and mixed gels in binary mixtures of patchy colloidal particles

We investigate the thermodynamics and percolation regimes of model binary mixtures of patchy colloidal particles. The particles of each species have three sites of two types, one of which promotes bonding of particles of the same species while the other promotes bonding of different species. We find up to four percolated structures at low temperatures and densities: two gels where only one species percolates, a mixed gel where particles of both species percolate but neither species percolates separately, and a bicontinuous gel where particles of both species percolate separately forming two interconnected networks. The competition between the entropy and the energy of bonding drives the stability of the different percolating structures. Appropriate mixtures exhibit one or more connectivity transitions between the mixed and bicontinuous gels, as the temperature and/or the composition changes.

Phase diagrams of binary mixtures of patchy colloids with distinct numbers of patches: the network fluid regime

We calculate the network fluid regime and phase diagrams of binary mixtures of patchy colloids, using Wertheims first order perturbation theory and a generalization of Flory–Stockmayers theory of polymerization. The colloids are modelled as hard spheres with the same diameter and surface patches of the same type, A. The only difference between species is the number of their patches – or functionality – f(1)A and f(2)A (with f(2)A > f(1)A). We have found that the difference in functionality is the key factor controlling the behaviour of the mixture in the network (percolated) fluid regime. In particular, when f(2)A ≥ 2f(1)A the entropy of bonding drives the phase separation of two network fluids, which is absent in other mixtures. This drastically changes the critical properties of the system and drives a change in the topology of the phase diagram (from type I to type V) when f(1)A > 2. The difference in functionality also determines the miscibility at high (osmotic) pressures. If f(2)A − f(1)A = 1, the mixture is completely miscible at high pressures, while closed miscibility gaps at pressures above the highest critical pressure of the pure fluids are present if f(2)A − f(1)A > 1. We argue that this phase behaviour is driven by a competition between the entropy of mixing and the entropy of bonding, as the latter dominates in the network fluid regime.

Three-dimensional patchy lattice model: Ring formation and phase separation

We investigate the structural and thermodynamic properties of a model of particles with 2 patches of type A and 10 patches of type B. Particles are placed on the sites of a face centered cubic lattice with the patches oriented along the nearest neighbor directions. The competition between the self-assembly of chains, rings, and networks on the phase diagram is investigated by carrying out a systematic investigation of this class of models, using an extension of Wertheims theory for associating fluids and Monte Carlo numerical simulations. We varied the ratio r ≡ εAB/εAA of the interaction between patches A and B, εAB, and between A patches, εAA (εBB is set to 0) as well as the relative position of the A patches, i.e., the angle θ between the (lattice) directions of the A patches. We found that both r and θ (60°, 90°, or 120°) have a profound effect on the phase diagram. In the empty fluid regime (r < 1/2) the phase diagram is reentrant with a closed miscibility loop. The region around the lower critical point exhibits unusual structural and thermodynamic behavior determined by the presence of relatively short rings. The agreement between the results of theory and simulation is excellent for θ = 120° but deteriorates as θ decreases, revealing the need for new theoretical approaches to describe the structure and thermodynamics of systems dominated by small rings.