Phase behavior of confined symmetric binary mixtures

Binding potential and wetting behavior of binary liquid mixtures on surfaces

We present a theory for the interfacial wetting phase behavior of binary liquid mixtures on rigid solid substrates, applicable to both miscible and immiscible mixtures. In particular, we calculate the binding potential as a function of the adsorptions, i.e., the excess amounts of each of the two liquids at the substrate. The binding potential fully describes the corresponding interfacial thermodynamics. Our approach is based on classical density functional theory. Binary liquid mixtures can exhibit complex bulk phase behavior, including both liquid-liquid and vapor-liquid phase separation, depending on the nature of the interactions among all the particles of the two different liquids, the temperature, and the chemical potentials. Here we show that the interplay between the bulk phase behavior of the mixture and the properties of the interactions with the substrate gives rise to a wide variety of interfacial phase behaviors, including mixing and demixing situations. We find situations where the final state is a coexistence of up to three different phases. We determine how the liquid density profiles close to the substrate change as the interaction parameters are varied and how these determine the form of the binding potential, which in certain cases can be a multivalued function of the adsorptions. We also present profiles for sessile droplets of both miscible and immiscible binary liquids.

Stability of nanoparticle laden aerosol liquid droplets

We develop a model for the thermodynamics and evaporation dynamics of aerosol droplets of a liquid, such as water, surrounded by gas. When the temperature and the chemical potential (or equivalently the humidity) are such that the vapor phase is in the thermodynamic equilibrium state, then, of course, droplets of the pure liquid evaporate over a relatively short time. However, if the droplets also contain nanoparticles or any other non-volatile solute, then the droplets can become thermodynamically stable. We show that the equilibrium droplet size depends strongly on the amount and solubility of the nanoparticles within, i.e., on the nature of the particle interactions with the liquid and, of course, also on the vapor temperature and chemical potential. We develop a simple thermodynamic model for such droplets and compare predictions with results from a lattice density functional theory that takes as input the same particle interaction properties, finding very good agreement. We also use dynamical density functional theory to study the evaporation/condensation dynamics of liquid from/to droplets as they equilibrate with the vapor, thereby demonstrating droplet stability.

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.

Paranematic-to-nematic ordering of a binary mixture of rodlike liquid crystals confined in cylindrical nanochannels

We explore the optical birefringence of the nematic binary mixtures 6CB_{1-x}7CB_{x} (0 ≤ x ≤ 1) embedded into parallel-aligned nanochannels of mesoporous alumina and silica membranes for channel radii of 3.4 ≤ R ≤ 21.0 nm. The results are compared with the bulk behavior and analyzed with a Landau-de Gennes model. Depending on the channel radius the nematic ordering in the cylindrical nanochannels evolves either discontinuously (subcritical regime, nematic ordering field σ<1/2) or continuously (overcritical regime, σ>1/2), but in both cases with a characteristic paranematic precursor behavior. The strength of the ordering field, imposed by the channel walls, and the magnitude of quenched disorder varies linearly with the mole fraction x and scales inversely proportionally with R for channel radii larger than 4 nm. The critical pore radius, R_{c}, separating a continuous from a discontinuous paranematic-to-nematic evolution varies linearly with x and differs negligibly between the silica and alumina membranes. We find no hints of preferred adsorption of one species at the channels walls. By contrast, a linear variation of the nematic-to-paranematic transition point T_{PN} and of the nematic ordering field σ versus x suggests that the binary mixtures of cyanobiphenyls 6CB and 7CB keep their homogeneous bulk stoichiometry also in nanoconfinement, at least for channel diameters larger than ∼7 nm.

Dynamic mean field theory for lattice gas models of fluid mixtures confined in mesoporous materials

We present the extension of dynamic mean field theory (DMFT) for fluids in porous materials (Monson, P. A. J. Chem. Phys. 2008, 128, 084701) to the case of mixtures. The theory can be used to describe the relaxation processes in the approach to equilibrium or metastable equilibrium states for fluids in pores after a change in the bulk pressure or composition. It is especially useful for studying systems where there are capillary condensation or evaporation transitions. Nucleation processes associated with these transitions are emergent features of the theory and can be visualized via the time dependence of the density distribution and composition distribution in the system. For mixtures an important component of the dynamics is relaxation of the composition distribution in the system, especially in the neighborhood of vapor-liquid interfaces. We consider two different types of mixtures, modeling hydrocarbon adsorption in carbon-like slit pores. We first present results on bulk phase equilibria of the mixtures and then the equilibrium (stable/metastable) behavior of these mixtures in a finite slit pore and an inkbottle pore. We then use DMFT to describe the evolution of the density and composition in the pore in the approach to equilibrium after changing the state of the bulk fluid via composition or pressure changes.

Phase separation of a binary liquid in anodic aluminium oxide templates: a structural study by small angle neutron scattering

The radial nanostructure of the binary liquid triethylamine/water confined in 60 nm diameter independent cylindrical pores of anodic aluminium oxide membranes is studied by small angle neutron scattering. It is shown that composition inhomogeneities are present in the confined mixtures well below the bulk critical point. An analysis of the neutron scattering form factor reveals the existence of an adsorbed water layer of a few nanometers at the liquid/alumina interface, coexisting with a TEA-rich phase in the core.

Adsorption of a Binary Mixture of Adhesive Fluids in Planar Pores: A Monte Carlo Study

Grand canonical Monte Carlo simulation is used to study the adsorption of a binary sticky hard-sphere fluid mixture in planar pores. The wall-component 1 and wall-component 2 contact densities are determined to calculate the pressure as a function of the composition of the mixture and the separation between the walls. From these data dependence of the solvation force between the plates on pore width is estimated. The simulation results are compared with the predictions of the Percus-Yevick approximation for planar pores. The density profiles of particular components show interesting shapes stemming from the interplay between the steric effects and the competitive adhesion among all possible species pairs. It is shown that narrowing of the pore causes selective partitioning of individual components of the mixture between the bulk phase and the interior of the pore. The agreement between the two methods is better at wider pores and for the component comprised of weakly adhesive 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.

Critical behavior of a colloid-polymer mixture confined between walls

We investigate the influence of confinement on phase separation in colloid-polymer mixtures. To describe the particle interactions, the colloid-polymer model of Asakura and Oosawa [J. Chem. Phys. 22, 1255 (1954)] is used. Grand canonical Monte Carlo simulations are then applied to this model confined between two parallel hard walls, separated by a distance D = 5 colloid diameters. We focus on the critical regime of the phase separation and look for signs of crossover from three-dimensional (3D) Ising to two-dimensional (2D) Ising universality. To extract the critical behavior, finite size scaling techniques are used, including the recently proposed algorithm of Kim et al [Phys. Rev. Lett. 91, 065701 (2003)]. Our results point to "effective" critical exponents that differ profoundly from 3D Ising values, and that are already very close to 2D Ising values. In particular, we observe that the critical exponent of the order parameter in the confined system is smaller than in 3D bulk, yielding a "flatter" binodal. Our results also show an increase in the critical colloid packing fraction in the confined system with respect to the bulk. The latter seems consistent with theoretical expectations, although subtleties due to singularities in the critical behavior of the coexistence diameter cannot be ruled out.

Soft core fluid in a quenched matrix of soft core particles: a mobile mixture in a model gel

We present a density-functional study of a binary phase-separating mixture of soft core particles immersed in a random matrix of quenched soft core particles of larger size. This is a model for a binary polymer mixture immersed in a cross-linked rigid polymer network. Using the replica "trick" for quenched-annealed mixtures we derive an explicit density functional theory that treats the quenched species on the level of its one-body density distribution. The relation to a set of effective external potentials acting on the annealed components is discussed. We relate matrix-induced condensation in bulk to the behavior of the mixture around a single large particle. The interfacial properties of the binary mixture at a surface of the quenched matrix display a rich interplay between capillary condensation inside the bulk matrix and wetting phenomena at the matrix surface.

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

We employ mean-field lattice density functional theory to calculate complete phase diagrams of binary fluid mixtures composed of molecules of equal size. We consider asymmetric binary mixtures in which the attraction strength between like molecules of either species differs as well as the attractivity between a pair of unlike molecules. Focusing on the topology of phase diagrams in the space spanned by the thermodynamic fields temperature , (mean) chemical potential , and incremental chemical potential (, are chemical potentials of pure mixture components A and B, respectively), we present an argument which precludes the existence of tricritical points (TCPs) in binary mixtures in general. This is a consequence of a purely geometrical argument based upon an analysis of the number of ways in which coexistence surfaces can be joined in the (Euclidian) space of , , and . However, we show that by the same token, TCPs may exist in cases where the mixture possesses some special symmetry. These latter results are in qualitative agreement with earlier works where, however, only special cuts through the complete phase diagrams were considered so that the important relation between existence of TCPs and symmetry properties of the mixture cannot be fully appreciated.

Phase and interfacial behavior of partially miscible symmetric Lennard-Jones binary mixtures

We have carried out extensive equilibrium molecular-dynamics simulations to study quantitatively the topology of the temperature versus density phase diagrams and related interfacial phenomena in a partially miscible symmetric Lennard-Jones binary mixture. The topological features are studied as a function of miscibility parameter, alpha = epsilonAB/epsilonAA. Here epsilonAA = epsilonBB and epsilonAB stand for the parameters related to the attractive part of the intermolecular interactions for similar and dissimilar particles, respectively. When the miscibility varies in the range 0 < alpha < 1, a continuous critical line of consolute points Tcons(rho)--critical demixing transition line--appears. This line intersects the liquid-vapor coexistence curve at different positions depending on the values of alpha, yielding mainly three different topologies for the phase diagrams. These results are in qualitative agreement to those found previously for square-well and hard-core Yukawa binary mixtures. The main contributions of the present paper are (i) a quantitative analysis of the phase behavior and (ii) a detailed study of the liquid-liquid interfacial and liquid-vapor surface tensions, as function of temperature and miscibility as well as its relationship to the topological features of the phase diagrams.

Phase behavior and local structure of a binary mixture in pores: Mean-field lattice model calculations for analyzing neutron scattering data

We investigate the phase behavior of an asymmetric binary liquid A-W mixture confined between two planar homogenous substrates (slit pore). Molecules of species W interact preferentially with the solid walls via a long-range potential. Assuming nearest-neighbor attractions between the liquid molecules, we employ a lattice-gas model and a mean-field approximation for the grand potential. Minimization of this potential yields the density profiles of thermodynamically stable phases for fixed temperature, chemical potentials of both species, pore width and strengths of attraction. This model is used to analyze experimental small-angle neutron-scattering (SANS) data on the microscopic structure of the binary system isobutyric acid (iBA)+heavy water (D2O) inside a mesoscopic porous matrix (controlled-pore glass of about 10 nm mean pore width). Confinement-independent model parameters are adjusted so that the theoretical liquid-liquid coexistence curve in the bulk matches its experimental counterpart. By choosing appropriate values of the pore width and the attraction strength between substrates and water we analyze the effect of confinement on the phase diagram. In addition to a depression of the liquid-liquid critical point we observe surface induced phase transitions as well as water-film adsorption near the walls. The temperature dependence of the structure of water-rich and iBA-rich phases of constant composition are discussed in detail. The theoretical predictions are consistent with results of the SANS study and assist their interpretation.

Modeling mercury porosimetry using statistical mechanics

We consider mercury porosimetry from the perspective of the statistical thermodynamics of penetration of a nonwetting liquid into a porous material under an external pressure. We apply density functional theory to a lattice gas model of the system and use this to compute intrusion/extrusion curves. We focus on the specific example of a Vycor glass and show that essential features of mercury porosimetry experiments can be modeled in this way. The lattice model exhibits a symmetry that provides a direct relationship between intrusion/extrusion curves for a nonwetting fluid and adsorption/desorption isotherms for a wetting fluid. This relationship clarifies the status of methods that are used for transforming mercury intrusion/extrusion curves into gas adsorption/desorption isotherms. We also use Monte Carlo simulations to investigate the nature of the intrusion and extrusion processes.

Confinement effect on the adsorption from a binary liquid system near liquid/liquid phase separation

The preferential adsorption of one component of a binary system at the inner surfaces of mesoporous silica glasses was studied in a wide composition range at temperatures close to liquid/liquid phase separation. Confinement effects on the adsorption were investigated by using three controlled-pore glass (CPG-10) materials of different mean pore size (10 to 50 nm). For the experimental system (2-butoxyethanol+water), which exhibits an upper miscibility gap, strong preferential adsorption of water occurs, as the coexistence curve is approached at bulk compositions, at which water is the minority component. In this strong adsorption regime the area-related surface excess amount of adsorbed water decreases with decreasing pore width, while the shift in the volume-related mean composition of the pore liquid shows an opposite trend, i.e., greatest deviation from bulk composition occurring in the most narrow pores. A simple mean-field lattice model of a liquid mixture confined by parallel walls is adopted to rationalize these experimental findings. This model reproduces the main findings of the confinement effect on the adsorption near liquid/liquid phase separation.

Density functional study of the phase behavior of asymmetric binary dipolar mixtures

Using density functional theory in the modified mean-field (MMF) approximation we study the phase behavior of asymmetric binary mixtures of equisized dipolar hard spheres with different dipole moments in the fluid phase regime. We focus on "dipole-dominated" systems where isotropic attractive interactions are absent. Despite these restrictions our results reveal complex fluid-fluid phase behavior involving demixing and first- and second-order isotropic-to-ferroelectric phase transitions the relative importance of which depends on two "tuning" parameters, that is, the parameter Gamma measuring the ratio of the dipolar coupling strengths, and the chemical potential difference Deltamu controlling the composition. The interplay of these effects then yields three different types of phase behavior differing in the degree to which demixing dominates the system. A generic feature of the resulting diagrams is that the isotropic-to-ferroelectric transition is shifted towards significantly higher densities compared to the one-component case, and is therefore destabilized. Furthermore, demixing in the MMF approach turns out to be always accompanied by spontaneous ferroelectricity, which is in contrast to recent integral equation and simulation results for the limiting case of a mixture of dipolar and pure hard spheres (Gamma=0).

Wetting of a selective solid surface by an asymmetric binary mixture

We consider a lattice-gas model of an asymmetric binary mixture in which the attraction between a pair of molecules of species A exceeds that between a pair of molecules of species B. The interaction between two molecules of species A and B is chosen to promote the formation of demixed A-rich liquid bulk phases. Molecules interact with a selective solid wall, preferentially adsorbing molecules of species B. Positions of molecules are restricted to sites on a simple-cubic lattice. We invoke a mean-field representation of the Hamiltonian governing all intermolecular interactions and assume only nearest-neighbor attractions. Minimizing the grand-potential functional of the lattice gas numerically, phase diagrams for films wetting the solid substrate are obtained. One of our key findings concerns B-rich mixed or demixed films forming in the vicinity of the solid surface and coexisting with demixed A-rich films. The formation of B-rich films can be understood as a result of the competition between the asymmetry of the (bulk) mixture and the selectivity of the solid surface. The concentration of component B in B-rich mixed films shows a peculiar temperature dependence. It first increases with temperature T until an "inversion" temperature T(inv) is reached, and then declines for T>or=T(inv) until the critical point between (demixed) A- and B-rich films is reached.

Continuous demixing at liquid-vapor coexistence in a symmetrical binary fluid mixture

We report a Monte Carlo finite-size scaling study of the demixing transition of a symmetrical Lennard-Jones binary fluid mixture. For equal concentration of species, and for a choice of the unlike-to-like interaction ratio delta=0.7, this transition is found to be continuous at liquid-vapor coexistence. The associated critical end point exhibits an Ising-like universality. These findings confirm those of earlier smaller scale simulation studies of the same model, but contradict the findings of recent integral equation and hierarchical reference theory investigations.