We have studied a model of a complex fluid consisting of particles interacting through a hard core and a short range attractive potential of both Yukawa and square-well form. Using a hybrid method, including a self-consistent and quite accurate approximation for the liquid integral equation in the case of the Yukawa fluid, perturbation theory to evaluate the crystal free energies, and modecoupling theory of the glass transition, we determine both the equilibrium phase diagram of the system and the lines of equilibrium between the supercooled fluid and the glass phases. For these potentials, we study the phase diagrams for different values of the potential range, the ratio of the range of the interaction to the diameter of the repulsive core being the main control parameter. Our arguments are relevant to a variety of systems, from dense colloidal systems with depletion forces, through particle gels, nano-particle aggregation, and globular protein crystallization.

Using a simple mean-field density functional theory theory (DFT), we investigate the structure and phase behaviour of a model colloidal fluid composed of particles interacting via a pair potential which has a hard core of diameter σ, is attractive Yukawa at intermediate separations and repulsive Yukawa at large separations. We analyse the form of the asymptotic decay of the bulk fluid correlation functions, comparing results from our DFT with those from the self consistent Ornstein-Zernike approximation (SCOZA). In both theories we find rich crossover behaviour, whereby the ultimate decay of correlation functions changes from monotonic to long-wavelength damped oscillatory decay on crossing certain lines in the phase diagram, or sometimes from oscillatory to oscillatory with a longer wavelength. For some choices of potential parameters we find, within the DFT, a λ-line at which the fluid becomes unstable with respect to periodic density fluctuations. SCOZA fails to yield solutions for state points near such a λ-line. The propensity to clustering of particles, which is reflected by the presence of a long wavelength ≫ σ, slowly decaying oscillatory pair correlation function, and a structure factor that exhibits a very sharp maximum at small but non zero wavenumbers, is enhanced in states near the λ-line. We present density profiles for the planar liquid-gas interface and for fluids adsorbed at a planar hard wall. The presence of a nearby λ-transition gives rise to pronounced long-wavelength oscillations in the one-body densities at both types of interface.

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We study the phase behaviour of a fluid composed of particles which interact via a pair potential that is repulsive for large inter-particle distances, is attractive at intermediate distances and is strongly repulsive at short distances (the particles have a hard core). As well as exhibiting gasliquid phase separation, this system also exhibits phase transitions from the uniform fluid phases to modulated inhomogeneous fluid phases. Starting from a microscopic density functional theory, we develop an order parameter theory for the phase transition in order to examine in detail the phase behaviour. The amplitude of the density modulations is the order parameter in our theory. The theory predicts that the phase transition from the uniform to the modulated fluid phase can be either first order or second order (continuous). The phase diagram exhibits two tricritical points, joined to one another by the line of second order transitions.

The self-consistent Ornstein-Zernike approximation (SCOZA), the generalized mean spherical approximation (GMSA), the modified hypernetted chain (MHNC) approximation, and the hierarchical reference theory (HRT) are applied to the determination of thermodynamic and structural properties, and the phase diagram of the hard-core Yukawa fluid (HCYF). We investigate different Yukawa-tail screening lengths lambda, ranging from lambda=1.8 (a value appropriate to approximate the shape of the Lennard-Jones potential) to lambda=9 (suitable for a simple one-body modelization of complex fluids like colloidal suspensions and globular protein solutions). The comparison of the results obtained with computer simulation data shows that at relatively low lambda's all the theories are fairly accurate in the prediction of thermodynamic and structural properties; as far as the phase diagram is concerned, the SCOZA and HRT are able to predict the binodal line and the critical parameters in a quantitative manner. At lambda=4 some discrepancies begin to emerge in the performances of the different theoretical approaches: the MHNC remains, on the whole, reasonably accurate in predicting the energy and the contact value of the radial distribution function; the SCOZA predicts well the equation of state up to the highest lambda values investigated. The GMSA and the MHNC underestimate and overestimate, respectively, the liquid coexisting density, while the SCOZA and HRT yield liquid branches that fall between the two former theoretical predictions, although both appear to overestimate the critical temperature somewhat. At higher lambda's the GMSA and MHNC binodals further worsen, while the SCOZA appears to remain usefully predictive. In general, the predictions of all the theories tend to slightly worsen at low temperatures and high density. The determination of the freezing line, performed by means of a one-phase "freezing criterion" (due to other authors) is not particularly satisfactory within either the SCOZA or the MHNC; the GMSA prediction for the freezing line at lambda=7 and 9 is instead able to follow in a qualitative manner the pattern of the solid-vapor coexistence line as determined through computer simulation studies. The necessity of further assessments of the freezing predictions is also discussed. Finally, versions of the GMSA, SCOZA, and HRT that can be expected to be more accurate for interactions with extremely short-ranged attractions are identified.

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Colloidal fluids interacting via effective potentials which are attractive at the short range and repulsive at the long range have long been raising considerable attention because such an instance provides a simple mechanism leading to pattern formation even for isotropic interactions. If the competition between attraction and repulsion is strong enough, the gas-liquid phase transition is suppressed, and replaced by the formation of mesophases, i.e., inhomogeneous phases displaying periodic density modulations whose length, although being larger than the particle size, cannot nevertheless be considered macroscopic. We describe a fully numerical implementation of density-functional theory in three dimensions, tailored to periodic phases. The results for the equilibrium phase diagram of the model are compared with those already obtained in previous investigations for the present system as well as for other systems which form mesophases. The phase diagram which we find shows a strong similarity with that of block copolymer melts, in which self-assembly also results from frustration of a macroscopic phase separation. As the inhomogeneous region is swept by increasing the density from the low-density side, one encounters clusters, bars, lamellae, inverted bars, and inverted clusters. Moreover, a bicontinuous gyroid phase consisting of two intertwined percolating networks is predicted in a narrow domain between the bar and lamellar phases.

We consider symmetric binary mixtures consisting of spherical particles with equal diameters interacting via a hard-core plus attractive tail potential with strengths ǫ ij , i, j = 1, 2, such that ǫ 11 = ǫ 22 > ǫ 12 . The phase diagram of the system at all densities and concentrations is investigated as a function of the unlike-to-like interaction ratio δ = ǫ 12 /ǫ 11 by means of the hierarchical reference theory (HRT). The results are related to those of previous investigations performed at equimolar concentration, as well as to the topology of the mean-field critical lines. As δ is increased in the interval 0 < δ < 1, we find first a regime where the phase diagram at equal species concentration displays a tricritical point, then one where both a tricritical and a liquid-vapor critical point are present. We did not find any clear evidence of the critical endpoint topology predicted by mean-field theory as δ approaches 1, at least up to δ = 0.8, which is the largest value of δ investigated here. Particular attention was paid to the description of the critical-plus-tricritical point regime in the whole density-concentration plane. In this situation, the phase diagram shows, in a certain temperature interval, a coexistence region that encloses an island of homogeneous, one-phase fluid.