Davide Pini

Phase equilibria and glass transition in colloidal systems with short-ranged attractive interactions: Application to protein crystallization

We have studied a model of a complex fluid consisting of particles interacting through a hard-core and 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 mode-coupling 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, nanoparticle aggregation, and globular protein crystallization.

Model colloidal fluid with competing interactions: Bulk and interfacial properties

Using a simple mean field density functional theory (DFT), the authors investigate the structure and phase behavior of a model colloidal fluid composed of particles interacting via a pair potential which has a hard core of diameter sigma, is attractive Yukawa at intermediate separations, and is repulsive Yukawa at large separations. The authors analyze the form of the asymptotic decay of the bulk fluid correlation functions, comparing results from DFT with those from the self-consistent Ornstein-Zernike approximation (SCOZA). In both theories the authors find rich crossover behavior, 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 the authors find, within the DFT, a lambda line at which the fluid becomes unstable with respect to periodic density fluctuations. SCOZA fails to yield solutions for state points near such a lambda line. The propensity towards clustering of particles, which is reflected by the presence of a long wavelength (>>sigma) slowly decaying oscillatory pair correlation function, and a structure factor that exhibits a very sharp maximum at small but nonzero wave numbers, is enhanced in states near the lambda line. The authors present density profiles for the planar liquid-gas interface and for fluids adsorbed at a planar hard wall. The presence of a nearby lambda transition gives rise to pronounced long wavelength oscillations in the one-body density profiles at both types of interface.

Theory for the phase behaviour of a colloidal fluid with competing interactions

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 gas–liquid 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 each other by the line of second order transitions.

A simple approximation for fluids with narrow attractive potentials

A simple modification of the optimized random phase approximation (ORPA) has been made, aimed at improving the performance of the theory for interactions with a narrow attractive well by taking into account contributions to the direct correlation function that are nonlinear with respect to the interaction. The theory is applied to a hard core Yukawa and a square-well potential. Results for the equation of state, the correlations, and the critical point have been obtained for attractions within several ranges, and compared with Monte Carlo simulations. When the attractive interaction is narrow, the modified ORPA is a significant improvement over the plain one, especially with regard to the consistency between different routes to the thermodynamics, the two-body correlation function, and the critical temperature. However, although the spinodal curve of the modified theory is accessible, the liquid-vapour coexistence curve is not. A possible strategy to overcome this drawback is suggested.

Critical behavior in colloid-polymer mixtures: theory and simulation.

We extensively investigated the critical behavior of mixtures of colloids and polymers via the two-component Asakura-Oosawa model and its reduction to a one-component colloidal fluid using accurate theoretical and simulation techniques. In particular the theoretical approach, hierarchical reference theory [A. Parola and L. Reatto, Adv. Phys. 44, 211 (1995)], incorporates realistically the effects of long-range fluctuations on phase separation giving exponents which differ strongly from their mean-field values, and are in good agreement with those of the three-dimensional Ising model. Computer simulations combined with finite-size scaling analysis confirm the Ising universality and the accuracy of the theory, although some discrepancy in the location of the critical point between one-component and full-mixture description remains. To assess the limit of the pair-interaction description, we compare one-component and two-component results.

Liquid-gas phase behavior of an argon-like fluid modelled by the hard-core two-Yukawa potential

We study a model for an argon-like fluid parameterized in terms of a hard-core repulsion and a two-Yukawa potential. The liquid-gas phase behavior of the model is obtained from the thermodynamically Self-Consistent Ornstein–Zernike Approximation (SCOZA) of Hoye and Stell, the solution of which lends itself particularly well to a pair potential of this form. The predictions for the critical point and the coexistence curve are compared to new high resolution simulation data and to other liquid-state theories, including the hierarchical reference theory (HRT) of Parola and Reatto. Both SCOZA and HRT deliver results that are considerably more accurate than standard integral-equation approaches. Among the versions of SCOZA considered, the one yielding the best agreement with simulation successfully predicts the critical point parameters to within 1%.

Phase diagram of symmetric binary mixtures at equimolar and nonequimolar concentrations: A systematic investigation

We consider symmetric binary mixtures consisting of spherical particles with equal diameters interacting via a hard-core plus attractive tail potential with strengths epsilon(ij), i,j=1,2, such that epsilon(11)=epsilon(22)>epsilon(12). The phase diagram of the system at all densities and concentrations is investigated as a function of the unlike-to-like interaction ratio delta=epsilon(12)/epsilon(11) by means of the hierarchical reference theory. 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 delta is increased in the interval 0<delta<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 end point topology predicted by mean-field theory as delta approaches 1, at least up to delta=0.8, which is the largest value of delta 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.

Thermodynamic properties of short-range attractive Yukawa fluid: Simulation and theory

Coexistence properties of the hard-core attractive Yukawa potential with inverse-range parameter kappa=9, 10, 12, and 15 are calculated by applying canonical Monte Carlo simulation. As previously shown for longer ranges, we show that also for the ranges considered here the coexistence curves scaled by the critical density and temperature obey the law of corresponding states, and that a linear relationship between the critical density and the reciprocal of the critical temperature holds. The simulation results are compared to the predictions of the self-consistent Ornstein-Zernike approximation, and a good agreement is found for both the critical points and the coexistence curves, although some slight discrepancies are present.

Freezing and correlations in fluids with competing interactions

We consider fluids in which the attractive interaction at distances slightly larger than the particle size is dominated at larger distances by a repulsive contribution. A previous investigation of the effects of the competition between attraction and repulsion on the liquid–vapour transition and on the correlations is extended to the study of the stability of liquid–vapour phase separation with respect to freezing. We find that this long-range repulsive part of the interaction expands the region in which the fluid–solid transition preempts the liquid–vapour one, so the critical point becomes metastable at longer attraction ranges than those required for purely attractive potentials. Moreover, the large density fluctuations that occur near the liquid–vapour critical point are greatly enhanced by the competition between attractive and repulsive forces, and encompass a much wider region than in the attractive case. The decay of correlations for states in which the compressibility is large is governed by two characteristic lengths, and the usual Ornstein–Zernike picture breaks down except for the very neighbourhood of the critical point, where one length reduces to the commonly adopted correlation length, while the other one saturates at a finite value.

The smooth cut-off hierarchical reference theory of fluids

We provide a comprehensive presentation of the Hierarchical Reference Theory (HRT) in the smooth cut-off formulation. A simple and self-consistent derivation of the hierarchy of differential equations is supplemented by a comparison with the known sharp cut-off HRT. The theory is then applied to a hard core Yukawa fluid (HCYF): a closure, based on a mean spherical approximation ansatz, is studied in detail and its intriguing relationship to the self-consistent Ornstein–Zernike approximation is discussed. The asymptotic properties close to the critical point are investigated and compared with the renormalization group results both above and below the critical temperature. The HRT free energy is always a convex function of the density, leading to flat isotherms in the two-phase region with a finite compressibility at coexistence. This makes HRT the sole liquid-state theory able to obtain fluid–fluid phase equilibrium in homogeneous systems without resorting to the Maxwell construction. The way the mean field free energy is modified due to the inclusion of density fluctuations suggests how to identify the spinodal curve. Thermodynamic properties and correlation functions of the HCYF are investigated for three values of the inverse Yukawa range, z = 1.8, z = 4 and z = 7, where Monte Carlo simulations are available. The stability of the liquid–vapor critical point with respect to freezing is also studied.