Interfacial tension and wetting in colloid-polymer mixtures

We calculate the interfacial tension and the wetting behavior in phase separated colloid-polymer mixtures both for ideal and excluded volume interacting polymers. Within the recently developed extension of the free volume theory to include polymer interactions the interfacial tension of the free interface is calculated by adding a van der Waals squared gradient term. The wetting behavior at a hard wall is calculated following a Cahn-Fisher-Nakanishi approach taking the one- and two-body colloid-wall interactions into account. Comparing results for interacting polymers with those for ideal polymers we find that for interacting polymers the interfacial tension does not increase as steeply as a function of the gas-liquid colloid density difference. Furthermore, the wetting transition shifts to higher polymer concentrations, even to above the triple line. The predictions for both the interfacial tension and the wetting are compared to recent experiments.     

Theoretical study of the three-phase contact line and its tension in adsorbed colloid-polymer mixtures

We perform a theoretical study of the three-phase contact line and the line tension in an adsorbed colloid-polymer mixture near a first-order wetting transition, employing an interface displacement model. We use a simple free-energy functional to describe a colloid-polymer mixture near a hard wall. The bulk phase behavior and the substrate-adsorbate interaction are modeled by the free-volume theory for ideal polymers. The large size of the colloidal particles and the suppression of the van der Waals interaction by optical matching of colloid and solvent justify the planar hard wall model for the substrate. Following the Fisher-Jin scheme, we derive from the free-energy functional an interface potential V(l) for these mixtures. For a particle diameter of 10-100 nm, the calculations indicate a line tension tau approximately 10(-12)-10(-13) N at room temperature. In view of the ultralow interfacial tension in colloid-polymer mixtures, gamma approximately 10(-7) Nm, this leads to a rather large characteristic length scale taugamma in the micrometer range for the three-phase contact zone width. In contrast with molecular fluids, this zone could be studied directly with optical techniques such as confocal scanning laser microscopy.     

Effect of excluded volume interactions on the interfacial properties of colloid-polymer mixtures

We report a numerical study of equilibrium phase diagrams and interfacial properties of bulk and confined colloid-polymer mixtures using grand canonical Monte Carlo simulations. Colloidal particles are treated as hard spheres, while the polymer chains are described as soft repulsive spheres. The polymer-polymer, colloid-polymer, and wall-polymer interactions are described by density-dependent potentials derived by Bolhuis and Louis [Macromolecules 35, 1860 (2002)]. We compared our results with those of the Asakura-Oosawa-Vrij model [J. Chem. Phys. 22, 1255 (1954); J. Polym Sci 33, 183 (1958); Pure Appl. Chem. 48, 471 (1976)] that treats the polymers as ideal particles. We find that the number of polymers needed to drive the demixing transition is larger for the interacting polymers, and that the gas-liquid interfacial tension is smaller. When the system is confined between two parallel hard plates, we find capillary condensation. Compared with the Asakura-Oosawa-Vrij model, we find that the excluded volume interactions between the polymers suppress the capillary condensation. In order to induce capillary condensation, smaller undersaturations and smaller plate separations are needed in comparison with ideal polymers.     

Miscibility of small colloidal spheres with large polymers in good solvent

Nearly athermal colloid-polymer mixtures were studied in the "protein limit." A fluid-fluid transition was observed in mixtures of stearyl-alcohol-coated silica particles and large polystyrene coils in toluene. The ratios of the polymer radius of gyration to the particle radii were q=4.1 and q=5.2. The binodal curves and the critical points were determined. Turbidity measurements and analysis for one set of particles allowed the systems to be mapped onto hard sphere-polymer mixtures. A comparison with recent predictions for the miscibility of model mixtures shows that the experimental binodals lie between the two extreme results for ideal and interacting polymers. The critical colloid volume fraction is also found to decrease with increasing size ratios.     

Demixing in athermal mixtures of colloids and excluded-volume polymers from density functional theory

We study the structure and interfacial properties of model athermal mixtures of colloids and excluded volume polymers. The colloid particles are modeled as hard spheres whereas the polymer coils are modeled as chains formed from tangentially bonded hard spheres. Within the framework of the nonlocal density functional theory we study the influence of the chain length on the surface tension and the interfacial width. We find that the interfacial tension of the colloid-interacting polymer mixtures increases with the chain length and is significantly smaller than that of the ideal polymers. For certain parameters we find oscillations on the colloid-rich parts of the density profiles of both colloids and polymers with the oscillation period of the order of the colloid diameter. The interfacial width is few colloid diameters wide and also increases with the chain length. We find the interfacial width for the end segments to be larger than that for the middle segments and this effect is more pronounced for longer chains.     

Depletion-induced phase separation in colloid-polymer mixtures

Phase separation can be induced in a colloidal dispersion by adding non-adsorbing polymers. Depletion of polymer around the colloidal particles induces an effective attraction, leading to demixing at sufficient polymer concentration. This communication reviews theoretical and experimental work carried out on the polymer-mediated attraction between spherical colloids and the resulting phase separation of the polymer-colloid mixture. Theoretical studies have mainly focused on the limits where polymers are small or large as compared to the colloidal size. Recently, however, theories are being developed that cover a wider colloid-polymer size ratio range. In practical systems, size polydispersity and polyelectrolytes (instead of neutral polymers) and/or charges on the colloidal surfaces play a role in polymer-colloid mixtures. The limited amount of theoretical work performed on this is also discussed. Finally, an overview is given on experimental investigations with respect to phase behavior and results obtained with techniques enabling measurement of the depletion-induced interaction potential, the structure factor, the depletion layer thickness and the interfacial tension between the demixed phases of a colloid-polymer mixture.     

Influence of solvent quality on polymer solutions: a Monte Carlo study of bulk and interfacial properties

The effect of solvent quality on dilute and semidilute regimes of polymers in solution is studied by means of Monte Carlo simulations. The equation of state, adsorption near a hard wall, wall-polymer surface tension, and effective depletion potential are all calculated as a function of concentration and solvent quality. We find important differences between polymers in good and theta solvents. In the dilute regime, the physical properties for polymers in a theta solvent closely resemble those of ideal polymers. In the semidilute regime, however, significant differences are found.     

Dendritic PtCo alloy nanoparticles as high performance oxygen reduction catalysts

We studied the physical properties and the concentration profile of benzene+water+caprolactam mixtures near the fluid-fluid interface using self-consistent field (SCF) theory. This yields the interfacial tension which plays an important role in describing the stability of transient liquid droplets of one phase in the other. The studies were performed at a fixed temperature of 313K. Flory-Huggins binary interaction parameters and the compound lattice segment numbers are input parameters for the applied SCF theory. These parameters were derived from activity coefficient relations, which are used to describe experimental liquid-liquid and vapor-liquid phase equilibrium measurements. Using first principles, the benzene-water interface was studied and the resulting interfacial tension was found to be in agreement with experimental values. This study illustrates that caprolactam accumulates at the benzene-water interface, acting as a weak surfactant. The interfacial tension is also demonstrated to be affected by the caprolactam concentration and the SCF results are in fair agreement with the experimental observations.     

Interfacial tension and interfacial profiles: an equation-of-state approach

A quasi-thermodynamic approach of inhomogeneous systems is used for modeling the fluid-fluid interface. It is based on the recently introduced QCHB (quasi-chemical hydrogen bonding) equation-of-state model of fluids and their mixtures, which is used for the estimation of the Helmholtz free energy density difference, Deltapsi(0), between the system with interface and another system of the same constitution but without interface. Consistent expressions for the interfacial tension and interfacial profiles for various properties are presented. The interfacial tension is proportional to the integral of Deltapsi(0) along the full height of the system, the proportionality constant being equal to 1, when no density gradient contributions are taken into consideration, 2, when the Cahn-Hilliard approximation is adopted, and 4, when the full density gradient contributions are taken into consideration. A satisfactory agreement is obtained between experimental and calculated surface tensions. Extension of the approach to mixtures is examined along with the associated problems for the numerical calculations of the interfacial profiles. A new equation is derived for the chemical potentials in the interfacial region, which facilitates very much the calculation of the composition profiles across the interface.     

Mixtures of charged colloid and neutral polymer: influence of electrostatic interactions on demixing and interfacial tension

The equilibrium phase behavior of a binary mixture of charged colloids and neutral, nonadsorbing polymers is studied within free-volume theory. A model mixture of charged hard-sphere macroions and ideal, coarse-grained, effective-sphere polymers is mapped first onto a binary hard-sphere mixture with nonadditive diameters and then onto an effective Asakura-Oosawa model [S. Asakura and F. Oosawa, J. Chem. Phys. 22, 1255 (1954)]. The effective model is defined by a single dimensionless parameter-the ratio of the polymer diameter to the effective colloid diameter. For high salt-to-counterion concentration ratios, a free-volume approximation for the free energy is used to compute the fluid phase diagram, which describes demixing into colloid-rich (liquid) and colloid-poor (vapor) phases. Increasing the range of electrostatic interactions shifts the demixing binodal toward higher polymer concentration, stabilizing the mixture. The enhanced stability is attributed to a weakening of polymer depletion-induced attraction between electrostatically repelling macroions. Comparison with predictions of density-functional theory reveals a corresponding increase in the liquid-vapor interfacial tension. The predicted trends in phase stability are consistent with observed behavior of protein-polysaccharide mixtures in food colloids.     

Surface tension of quantum fluids from molecular simulations

We present the first molecular simulations of the vapor-liquid surface tension of quantum liquids. The path integral formalism of Feynman was used to account for the quantum mechanical behavior of both the liquid and the vapor. A replica-data parallel algorithm was implemented to achieve good parallel performance of the simulation code on at least 32 processors. We have computed the surface tension and the vapor-liquid phase diagram of pure hydrogen over the temperature range 18-30 K and pure deuterium from 19 to 34 K. The simulation results for surface tension and vapor-liquid orthobaric densities are in very good agreement with experimental data. We have computed the interfacial properties of hydrogen-deuterium mixtures over the entire concentration range at 20.4 and 24 K. The calculated equilibrium compositions of the mixtures are in excellent agreement with experimental data. The computed mixture surface tension shows negative deviations from ideal solution behavior, in agreement with experimental data and predictions from Prigogine's theory. The magnitude of the deviations at 20.4 K are substantially larger from simulations and from theory than from experiments. We conclude that the experimentally measured mixture surface tension values are systematically too high. Analysis of the concentration profiles in the interfacial region shows that the nonideal behavior can be described entirely by segregation of H(2) to the interface, indicating that H(2) acts as a surfactant in H(2)-D(2) mixtures.     

Bulk and interfacial properties of binary polymer mixtures

A microscopic density functional theory is used to investigate a binary mixture of polymers, built of freely jointed tangent hard spheres. The difference in the chain length and in the segment diameter of polymers gives rise to a demixing transition. We evaluate the bulk fluid phase equilibria (binodal) and the limit of stability of a mixed state (spinodal) for selected systems, and analyze the decay of the critical packing fraction, critical mole fraction, and critical pressure with an increase of the chain length. The bulk results are subsequently used in the calculations of the density profiles across the fluid-fluid interface. The obtained profiles are smooth and do not exhibit any oscillations on the length scale of the segment diameter. Upon approaching the critical point the interfacial tension vanishes as (Deltarho)3, where Deltarho is the difference between bulk densities of one component in bulk phases rich and poor in that species. This indicates that the microscopic density functional theory applied here is of a mean-field type.     

Interfacial properties of colloid-polymer mixtures

Density functional theory and a virial approach are used to calculate the surface tension and bending rigidity of the interface between demixed fluid phases for a colloid-polymer mixture. The calculated surface tension compares well with results from computers simulations and experiments. The bending rigidity obtained from both theoretical approaches is negative (approximately equal to -0.1k(B)T), its magnitude increases away from the critical point and it is in reasonable agreement with computer simulations.     

Macroscopic modeling of the surface tension of polymer-surfactant systems

Polymer-surfactant mixtures are increasingly being used in a wide range of applications. Weakly interacting systems, such as SDS/PEO and SDS/PVP, comprise ionic surfactants and neutral polymers, while strongly interacting systems, such as SDS/POLYDMDAAC and C12TAB/NaPSS, comprise ionic surfactants and oppositely charged ionic polymers. The complex nature of interactions in the mixtures leads to interesting and surprising surface tension profiles as the concentrations of polymer and surfactant are varied. The purpose of our research has been to develop a model to explain these surface tension profiles and to understand how they relate to the formation of different complexes in the bulk solution. In this paper we show how an existing model based on the law of mass action can be extended to model the surface tension of weakly interacting systems, and we also extend it further to produce a model for the surface tension of strongly interacting systems. Applying the model to a variety of strongly interacting systems gives remarkable agreement with the experimental results. The model provides a sound theoretical basis for comparing and contrasting the behavior of different systems and greatly enhances our understanding of the features observed.     

Polydisperse telechelic polymers at interfaces: analytic results and density functional theory

We use a recently developed continuum theory to expand on an exact treatment of the interfacial properties of telechelic polymers displaying Schulz-Flory polydispersity. Our results are remarkably compact and can be derived from the properties of equilibrium, ideal polymers at interfaces. A new surface adsorption transition is identified for ideal telechelic chains, wherein the central block is an equilibrium polymer. This transition occurs in the limit of strong end adsorption. Additionally, closed expressions are derived for the ideal continuum telechelic chain in contact with two large spheres, using the Derjaguin approximation. We analyze the interactions between colloids as a function of polydispersity and molecular weight, and the results are compared with polymer density functional theory in the dilute limit. Significant variations in polymer mediated forces are observed as a function of polydispersity, molecuar weight, and chain stiffness.     

Surface tension of the Widom-Rowlinson model

We consider the computation of the surface tension of the fluid-fluid interface for the Widom-Rowlinson [J. Chem. Phys. 52, 1670 (1970)] binary mixture from direct simulation of the inhomogeneous system. We make use of the standard mechanical route, in which the surface tension follows from the computation of the normal and tangential components of the pressure tensor of the system. In addition to the usual approach, which involves simulations of the inhomogeneous system in the canonical ensemble, we also consider the computation of the surface tension in an ensemble where the pressure perpendicular (normal) to the planar interface is kept fixed. Both approaches are seen to provide consistent values of the interfacial tension. The issue of the system-size dependence of the surface tension is addressed. In addition, simulations of the fluid-fluid coexistence properties of the mixture are performed in the semigrand canonical ensemble. Our results are compared with existing data of the Widom-Rowlinson mixture and are also examined in the light of the vapor-liquid equilibrium of the thermodynamically equivalent one-component penetrable sphere model.     

Interfacial properties of water + alcohol mixtures

Mixtures of water with alcohol are important in numerous engineering applications. Caused by the polarity of water and alcohol self-association of water and alcohol as well cross-association between water and alcohol appear in such complex mixtures. These features show significant impact on physical and chemical properties, especially phase equilibrium behaviour and hence interfacial properties. The Cahn–Hilliard theory was combined with original statistical associated fluid theory equation of states (SAFT EOS) in order to describe both the phase behaviour and interfacial properties with respect of association. The paper focuses on theoretical investigations of surface tension, density profiles, surface thickness in vapour–liquid or vapour–liquid–liquid equilibrium of mixtures of water with ethanol or 1-butanol. Results of vapour–liquid equilibrium surface tension calculations were compared with experimental data taken from the literature.     

The QCHB model of fluids and their mixtures

The essentials of the QCHB (quasi-chemical hydrogen-bonding) equation-of-state model are presented along with some applications for calculations of phase equilibria and interfacial properties of fluids and their mixtures. This is a model applicable to non-polar systems as well as to highly non-ideal systems with strong specific interactions, to systems of small molecules as well as to macromolecules, including polydisperse polymers, glasses, and gels, to liquids as well as to vapours including supercritical systems, to homogeneous as well as to inhomogeneous systems. A quasi-thermodynamic approach of inhomogeneous systems is used for modeling the fluid–fluid interface. Consistent expressions for the interfacial tension and interfacial profiles for various properties are presented. A satisfactory agreement is obtained between experimental and calculated surface tensions. Extension of the approach to mixtures is examined along with the associated problems for the numerical calculations of the interfacial profiles. A new equation is derived for the chemical potentials in the interfacial region, which facilitates very much the calculation of the composition profiles across the interface. The relation of the model with the COSMO-RS approach is also discussed.