Topography of phase diagrams in binary fluid mixtures: a mean-field lattice density functional study

Efficient calculation of phase coexistence and phase diagrams: application to a binary phase-field-crystal model

We show that one can employ well-established numerical continuation methods to efficiently calculate the phase diagram for thermodynamic systems described by a suitable free energy functional. In particular, this involves the determination of lines of phase coexistence related to first order phase transitions and the continuation of triple points. To illustrate the method we apply it to a binary phase-field-crystal model for the crystallisation of a mixture of two types of particles. The resulting phase diagram is determined for one- and two-dimensional domains. In the former case it is compared to the diagram obtained from a one-mode approximation. The various observed liquid and crystalline phases and their stable and metastable coexistence are discussed as well as the temperature-dependence of the phase diagrams. This includes the (dis)appearance of critical points and triple points. We also relate bifurcation diagrams for finite-size systems to the thermodynamics of phase transitions in the infinite-size limit.

Dynamical Density Functional Theory for the Evaporation of Droplets of Nanoparticle Suspension

We develop a lattice gas model for the drying of droplets of a nanoparticle suspension on a planar surface, using dynamical density functional theory (DDFT) to describe the time evolution of the solvent and nanoparticle density profiles. The DDFT assumes a diffusive dynamics but does not include the advective hydrodynamics of the solvent, so the model is relevant to highly viscous or near to equilibrium systems. Nonetheless, we see an equivalent of the coffee-ring stain effect, but in the present model it occurs for thermodynamic rather the fluid-mechanical reasons. The model incorporates the effect of phase separation and vertical density variations within the droplet and the consequence of these on the nanoparticle deposition pattern on the surface. We show how to include the effect of slip or no-slip at the surface and how this is related to the receding contact angle. We also determine how the equilibrium contact angle depends on the microscopic interaction parameters.

Effects of geometrical and energetic nonadditivity on the phase behavior of two-component symmetric mixtures

Using Monte Carlo simulation methods in the grand-canonical ensemble, we have studied the phase behavior of three-dimensional symmetric binary mixtures of Lennard-Jones particles. We have also elucidated the effects of geometric and energetic nonadditivity on the phase behavior. Phase diagrams for several systems have been evaluated. We have demonstrated that in completely miscible mixtures the geometrical nonadditivity (negative as well as positive) stabilizes a liquid phase leading to a gradual increase of the critical temperature. The mechanism leading to such behavior is different when the system shows negative and positive geometrical nonadditivity. In the case of systems with negative energetic nonadditivity, which may exhibit demixing transition in the liquid phase, their phase behavior is also strongly affected by the geometric non-additivity. The systems with negative geometric nonadditivity have been demonstrated to show reentrant miscibility, while those with positive geometric nonadditivity show enhanced tendency toward mixing at sufficiently high temperatures. We have evaluated phase diagrams for several systems.

Sedimentation of a two-dimensional colloidal mixture exhibiting liquid-liquid and gas-liquid phase separation: a dynamical density functional theory study

We present dynamical density functional theory results for the time evolution of the density distribution of a sedimenting model two-dimensional binary mixture of colloids. The interplay between the bulk phase behaviour of the mixture, its interfacial properties at the confining walls, and the gravitational field gives rise to a rich variety of equilibrium and non-equilibrium morphologies. In the fluid state, the system exhibits both liquid-liquid and gas-liquid phase separation. As the system sediments, the phase separation significantly affects the dynamics and we explore situations where the final state is a coexistence of up to three different phases. Solving the dynamical equations in two-dimensions, we find that in certain situations the final density profiles of the two species have a symmetry that is different from that of the external potentials, which is perhaps surprising, given the statistical mechanics origin of the theory. The paper concludes with a discussion on this.

Reentrant miscibility in two-dimensional symmetrical mixtures

The Monte Carlo simulation method in the grand canonical ensemble is used to study the phase behavior of two-dimensional symmetrical binary mixtures of Lennard-Jones particles with negative nonadditivity and the weaker interaction between the pairs of unlike than between the pairs of like particles. We have determined the evolution of the phase diagram topology when the parameters describing the interaction between unlike particles vary. It has been found that such systems may exhibit reentrant miscibility in the liquid and the solid phases.

Exact density functional for hard-rod mixtures derived from Markov chain approach

Using a Markov chain approach we rederive the exact density functional for hard-rod mixtures on a one-dimensional lattice, which forms the basis of the lattice fundamental measure theory. The transition probability in the Markov chain depends on a set of occupation numbers, which reflects the property of a zero-dimensional cavity to hold at most one particle. For given mean occupation numbers (density profile), an exact expression for the equilibrium distribution of microstates is obtained, which means an expression for the unique external potential that generates the density profile in equilibrium. By considering the rod ends to fall onto lattice sites, the mixture is always additive.

Modelling the evaporation of thin films of colloidal suspensions using dynamical density functional theory

Recent experiments have shown that various structures may be formed during the evaporative dewetting of thin films of colloidal suspensions. Nanoparticle deposits of strongly branched 'flower-like', labyrinthine and network structures are observed. They are caused by the different transport processes and the rich phase behaviour of the system. We develop a model for the system, based on a dynamical density functional theory, which reproduces these structures. The model is employed to determine the influences of the solvent evaporation and of the diffusion of the colloidal particles and of the liquid over the surface. Finally, we investigate the conditions needed for 'liquid-particle' phase separation to occur and discuss its effect on the self-organized nanostructures.

The phase behavior of two-dimensional symmetrical mixtures

Using Monte Carlo simulation methods in the grand canonical and semigrand canonical ensembles, we study the phase behavior of two-dimensional symmetrical binary mixtures of Lennard-Jones particles. We discuss the interplay between the demixing transition in a liquid and the freezing in detail. Phase diagrams for several systems characterized by different parameters describing interactions in the system are presented. It is explicitly demonstrated that different scenarios involving demixing and freezing transitions, described in our earlier paper [A. Patrykiejew and S. Sokołowski, Phys. Rev. E, 81, 012501 (2010)], are possible. In one class of systems, the λ-line representing a continuous demixing transition in a liquid phase starts at the liquid side of either the vapor-liquid or liquid-solid coexistence. The second class involves the systems in which the λ-line begins at the liquid side of the vapor-liquid coexistence, in the lower critical end point, and then terminates at the liquid side of the liquid-solid coexistence, in the upper critical end point. It is also shown that in such systems the solid phase may undergo a demixing transition at the temperature above the upper critical end point.

Dynamical density functional theory for the dewetting of evaporating thin films of nanoparticle suspensions exhibiting pattern formation

Recent experiments have shown that the striking structure formation in dewetting films of evaporating colloidal nanoparticle suspensions occurs in an ultrathin "postcursor" layer that is left behind by a mesoscopic dewetting front. Various phase change and transport processes occur in the postcursor layer that may lead to nanoparticle deposits in the form of labyrinthine, network, or strongly branched "finger" structures. We develop a versatile dynamical density functional theory to model this system which captures all these structures and may be employed to investigate the influence of evaporation or condensation, nanoparticle transport, and solute transport in a differentiated way. We highlight, in particular, the influence of the subtle interplay of decomposition in the layer and contact line motion on the observed particle-induced transverse instability of the dewetting front.

Interplay between demixing and freezing in two-dimensional symmetrical mixtures

The interplay between demixing and freezing in two-dimensional symmetrical binary mixtures of Lennard-Jones particles is studied using Monte Carlo simulation. It is demonstrated that different scenarios are possible. For example, the line of continuous liquid demixing transition can start at the liquid side of the vapor-liquid coexistence at the lower critical end point and then it can terminate at the liquid side of the liquid-demixed solid coexistence at the upper critical end point. Other situations are also possible. We distinguish four different scenarios depending on the interactions between unlike particles.

Phase behavior of a symmetrical binary fluid mixture

We have investigated the phase behavior of a symmetrical binary fluid mixture for the situation where the chemical potentials mu(1) and mu(2) of the two species differ. Attention is focused on the set of interparticle interaction strengths for which, when mu(1)=mu(2), the phase diagram exhibits both a liquid-vapor critical point and a tricritical point. The corresponding phase behavior for the case mu(1) not equalmu(2) is investigated via integral-equation theory calculations within the mean spherical approximation and grand canonical Monte Carlo (GCMC) simulations. We find that two possible subtypes of phase behavior can occur, these being distinguished by the relationship between the triple lines in the full phase diagram in the space of temperature, density, and concentration. We present the detailed form of the phase diagram for both subtypes and compare with the results from GCMC simulations, finding good overall agreement. The scenario via which one subtype evolves into the other is also studied, revealing interesting features.