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.     

Spinodal decomposition in asymmetric polymer mixtures

We present a preliminary numerical study of spinodal decomposition in an asymmetric polymer mixture, i.e., of polymer with different chain lengths, in three dimensions with full Flory-Huggins-de Gennes free energy, numerically integrating the time evolution equations for the conserved order parameter. For the sake of comparison, we also present a numerical study of the symmetric polymer mixture. The results indicate that the scaled structure factor for the asymmetric polymer mixture is much broader than that of a symmetric polymer mixture. It is interesting that the growth exponents are not symmetric around the critical quench, i.e., growth exponents on the two sides of the critical composition are different. In addition to that, the magnitudes of the pair correlation functions of asymmetric mixtures are very small for x larger than the characteristic domain size r_g and the oscillations seen in the symmetric mixture are almost absent. We have attributed this finding to the rough interfaces and broader domain size distribution in the phase separated asymmetric polymer mixtures. Therefore, the simulation reveals that the asymmetry plays an important role for the spinodal decomposition dynamics of polymer mixtures.     

Highly asymmetric electrolytes in the primitive model: Hypernetted chain solution in arbitrary spatial dimensions

The pair‐correlation functions for fluid ionic mixtures in arbitrary spatial dimensions are computed in hypernetted chain (HNC) approximation. In the primitive model (PM), all ions are approximated as nonoverlapping hyperspheres with Coulomb interactions. Our spectral HNC solver is based on a Fourier‐Bessel transform introduced by Talman (J. Comput. Phys. 1978, 29, 35), with logarithmically spaced computational grids. Numeric efficiency for arbitrary spatial dimensions is a commonly exploited virtue of this transform method. Here, we highlight another advantage of logarithmic grids, consisting in efficient sampling of pair‐correlation functions for highly asymmetric ionic mixtures. For three‐dimensional fluids, ion size and charge‐ratios larger than 1000 can be treated, corresponding to hitherto computationally not accessed micrometer‐sized colloidal spheres in 1‐1 electrolyte. Effective colloidal charge numbers are extracted from our PM results. For moderately large ion size and charge‐asymmetries, we present molecular dynamics simulation results that agree well with the approximate HNC pair correlations. © 2013 Wiley Periodicals, Inc.     

Structure and phase behavior of Widom-Rowlinson model calculated from a nonuniform Ornstein-Zernike equation

The second-order integral-equation formalism of [Attard J. Chem. Phys. 91, 3072 (1989); 95, 4471 (1991)], applied previously to one-component hard spheres and Lennard-Jones fluids, as well as to their mixtures, is used to binary Widom-Rowlinson mixtures. Comparison with Monte Carlo simulations of the pair correlation functions and of the demixing phase diagram shows that this method is also quite accurate in the case of highly nonadditive mixtures. Moreover, the results of the second-order theory are compared with previous theoretical predictions. Our interest is also in the calculation of the bridge functions, i.e., parts of the radial distribution functions either not included or simply approximated in the usual theories.     

Monte Carlo study of four dimensional binary hard hypersphere mixtures

A multithreaded Monte Carlo code was used to study the properties of binary mixtures of hard hyperspheres in four dimensions. The ratios of the diameters of the hyperspheres examined were 0.4, 0.5, 0.6, and 0.8. Many total densities of the binary mixtures were investigated. The pair correlation functions and the equations of state were determined and compared with other simulation results and theoretical predictions. At lower diameter ratios the pair correlation functions of the mixture agree with the pair correlation function of a one component fluid at an appropriately scaled density. The theoretical results for the equation of state compare well to the Monte Carlo calculations for all but the highest densities studied.     

Ultrafast electron-transfer and solvent adiabaticity effects in viologen charge-transfer complexes

We report ultrafast electron transfer (ET) in charge-transfer complexes that shows solvent relaxation effects consistent with adiabatic crossover models of nonadiabatic ET. The complexes of either dimethyl viologen (MV) or diheptyl viologen (HV) with 4,4'-biphenol (BP) (MVBP or HVBP complexes) have identical charge-transfer spectra and kinetics in ethylene glycol with approximately 900 fs ET decay. We assign this decay time as largely due to adiabatic control of a predicted approximately 40 fs nonadiabatic ET. The MVBP decay in methanol of 470 fs is reduced in mixtures having low (2-20%) concentrations of acetonitrile to as short as 330 fs; these effects are associated with faster relaxation time in methanol and its mixtures. In contrast, HVBP has much longer ET decay in methanol (730 fs) and mixture effects that only reduce its decay to 550 fs. We identify the heptyl substituent as creating major perturbations to solvent relaxation times in the methanol solvation shell of HVBP. These charge-transfer systems have reasonably well-defined geometry with weak electronic coupling where the electronic transitions are not dependent on intramolecular motions. We used a nonadiabatic ET model with several models for adiabatic crossover predictions to discuss the small variation of energy gap with solvent and the ET rates derived from adiabatic solvent control. A time correlation model of solvent relaxation was used to define the solvent relaxation times for this case of approximately zero-barrier ET.     

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.     

Thermodynamics of dipolar hard sphere mixtures

The thermodynamic properties of mixtures of hard spheres with imbedded point dipoles are investigated by an extension of the perturbation theory used by Rushbrooke et al. for pure fluids. Equations are presented for the general multicomponent mixture in which all the hard spheres have the same diameter. Numerical calculations are presented of the phase behaviour and excess thermodynamic mixing functions for the special case of the binary mixture in which only one species is polar. A brief discussion is given of the relationship of this model to experimental results for real fluid mixtures and of possible extensions of this work.     

Large attractive depletion interactions in soft repulsive-sphere binary mixtures

We consider binary mixtures of soft repulsive spherical particles and calculate the depletion interaction between two big spheres mediated by the fluid of small spheres, using different theoretical and simulation methods. The validity of the theoretical approach, a virial expansion in terms of the density of the small spheres, is checked against simulation results. Attention is given to the approach toward the hard-sphere limit and to the effect of density and temperature on the strength of the depletion potential. Our results indicate, surprisingly, that even a modest degree of softness in the pair potential governing the direct interactions between the particles may lead to a significantly more attractive total effective potential for the big spheres than in the hard-sphere case. This might lead to significant differences in phase behavior, structure, and dynamics of a binary mixture of soft repulsive spheres. In particular, a perturbative scheme is applied to predict the phase diagram of an effective system of big spheres interacting via depletion forces for a size ratio of small and big spheres of 0.2; this diagram includes the usual fluid-solid transition but, in the soft-sphere case, the metastable fluid-fluid transition, which is probably absent in hard-sphere mixtures, is close to being stable with respect to direct fluid-solid coexistence. From these results, the interesting possibility arises that, for sufficiently soft repulsive particles, this phase transition could become stable. Possible implications for the phase behavior of real colloidal dispersions are discussed.     

Computer simulations of catanionic surfactants adsorbed at air/water interfaces

Structural properties pertaining to the solvation of mixtures of dodecytrimethylammonium/dodecylsulfate adsorbed at water/air interfaces were studied using molecular dynamics techniques. Two different surfactant coverages, both in the submonolayer regime, were considered: an infinite-diluted catanionic pair and an equimolar mixture, at a surface concentration of 78.7 A2/headgroup. The most stable solvated structures for the single surfactant pair correspond to contact-head-ion-pairs (CHIP) at a distance close to 5 A. In addition, marginally stable solvent-separated-head-ion-pairs (SSHIP) at distances approximately 7 A were also observed. The mean free energy for the dissociation of CHIP was estimated to be approximately 1 kcal/mol. At finite surfactant concentrations, one observes a considerable degree of clustering between the amphiphiles, due to the strong Coulomb coupling between headgroups. The resulting spatial domains show asymmetric structures with linear dimensions comparable to the simulation box, suggesting the onset of percolative structures. The connectivity pattern of these domains was interpreted in terms of a simplified model consisting of two-dimensional charged Lennard-Jones spheres.     

Structure, phase behavior, and inhomogeneous fluid properties of binary dendrimer mixtures

The effective pair potentials between different kinds of dendrimers in solution can be well approximated by appropriate Gaussian functions. We find that in binary dendrimer mixtures the range and strength of the effective interactions depend strongly upon the specific dendrimer architecture. We consider two different types of dendrimer mixtures, employing the Gaussian effective pair potentials, to determine the bulk fluid structure and phase behavior. Using a simple mean field density functional theory (DFT) we find good agreement between theory and simulation results for the bulk fluid structure. Depending on the mixture, we find bulk fluid-fluid phase separation (macrophase separation) or microphase separation, i.e., a transition to a state characterized by undamped periodic concentration fluctuations. We also determine the inhomogeneous fluid structure for confinement in spherical cavities. Again, we find good agreement between the DFT and simulation results. For the dendrimer mixture exhibiting microphase separation, we observe a rather striking pattern formation under confinement.     

Integral equation theory for symmetric nonadditive hard sphere mixtures

An integral equation theory is presented for the pair correlation functions and phase behavior of symmetric nonadditive hard sphere mixtures with hard sphere diameters given by sigma(A)(A)() = sigma(BB) = lambdad and sigma(AB) = d. This mixture exhibits a fluid-fluid phase separation into an A-rich phase and a B-rich phase at high densities. The theory incorporates, into the closure approximation, all terms that can be calculated exactly in the density expansion of the direct correlation functions. We find that the closure approximation developed in this work is accurate for the structure and phase behavior over the entire range of lambda, when compared to computer simulations, and is significantly more accurate than the previous theories.     

Pair correlation functions in mixtures of Lennard-Jones particles

The pair correlation functions for a mixture of two Lennard-Jones particles were computed by both the Percus-Yevick equations and by molecular dynamics. The changes in the pair correlation function resulting from changes in the composition of the mixtures are quite unexpected. Essentially, identical changes are obtained from the Percus-Yevick equations and from molecular dynamics simulations. The molecular reason for this unexpected behavior is discussed.     

Phase diagrams of binary mixtures of oppositely charged colloids

Phase diagrams of binary mixtures of oppositely charged colloids are calculated theoretically. The proposed mean-field-like formalism interpolates between the limits of a hard-sphere system at high temperatures and the colloidal crystals which minimize Madelung-like energy sums at low temperatures. Comparison with computer simulations of an equimolar mixture of oppositely charged, equally sized spheres indicate semiquantitative accuracy of the proposed formalism. We calculate global phase diagrams of binary mixtures of equally sized spheres with opposite charges and equal charge magnitude in terms of temperature, pressure, and composition. The influence of the screening of the Coulomb interaction upon the topology of the phase diagram is discussed. Insight into the topology of the global phase diagram as a function of the system parameters leads to predictions on the preparation conditions for specific binary colloidal crystals.     

Phase diagram of hard snowman-shaped particles

We present the phase diagram of hard snowman-shaped particles calculated using Monte Carlo simulations and free energy calculations. The snowman particles consist of two hard spheres rigidly attached at their surfaces. We find a rich phase behavior with isotropic, plastic crystal, and aperiodic crystal phases. The crystalline phases found to be stable for a given sphere diameter ratio correspond mostly to the close packed structures predicted for equimolar binary hard-sphere mixtures of the same diameter ratio. However, our results also show several crystal-crystal phase transitions, with structures with a higher degree of degeneracy found to be stable at lower densities, while those with the best packing are found to be stable at higher densities.     

Theory of gelation, vitrification, and activated barrier hopping in mixtures of hard and sticky spheres

Naive mode coupling theory (NMCT) and the nonlinear stochastic Langevin equation theory of activated dynamics have been generalized to mixtures of spherical particles. Two types of ideal nonergodicity transitions are predicted corresponding to localization of both, or only one, species. The NMCT transition signals a dynamical crossover to activated barrier hopping dynamics. For binary mixtures of equal diameter hard and attractive spheres, a mixture composition sensitive "glass-melting" type of phenomenon is predicted at high total packing fractions and weak attractions. As the total packing fraction decreases, a transition to partial localization occurs corresponding to the coexistence of a tightly localized sticky species in a gel-like state with a fluid of hard spheres. Complex behavior of the localization lengths and shear moduli exist because of the competition between excluded volume caging forces and attraction-induced physical bond formation between sticky particles. Beyond the NMCT transition, a two-dimensional nonequilibrium free energy surface emerges, which quantifies cooperative activated motions. The barrier locations and heights are sensitive to the relative amplitude of the cooperative displacements of the different species.     

Multiphase coexistence in polydisperse colloidal mixtures

The authors study the phase behavior of mixtures of monodisperse colloidal spheres with a depletion agent which can have arbitrary shape and can possess a polydisperse size or shape distribution. In the low concentration limit considered here, the authors can employ the free-volume theory and take the geometry of particles of the depletion agent into account within the framework of fundamental measure theory. The authors apply their approach to study the phase diagram of a mixture of (monodisperse) colloidal spheres and two polydisperse polymer components. By fine tuning the distribution of the polymer, it is possible to construct a complex phase diagram which exhibits two stable critical points.     

Fluid-phase diagrams of binary mixtures from constant pressure integral equations

A new algorithm for solving integral equations of the theory of liquids at fixed pressure is introduced. Combining this technique with the Lee's star function approximation for the chemical potentials, we obtain an efficient method to investigate fluid-phase diagrams of binary mixtures. We have tested the capabilities of such technique to study symmetric and asymmetric phase diagrams in nonadditive hard spheres and Lennard-Jones mixtures. We find that the integral equation theories, although approximate, can provide a flexible tool to determine the fluid-phase diagrams whose accuracy is critically dependent on the quality of the closure and of the resulting chemical potentials.     

Virial coefficients and demixing of athermal nonadditive mixtures

We compute the fourth virial coefficient of a binary nonadditive, hard-sphere mixture over a wide range of deviations from diameter additivity and size ratios. Hinging on this knowledge, we build up a y expansion (Barboy, B.; Gelbart, W. N. J. Chem. Phys. 1979, 71, 3053) in order to trace the fluid-fluid coexistence lines, which we then compare with the available Gibbs-ensemble Monte Carlo data and with the estimates obtained through two refined integral-equation theories of the fluid state. We find that in a regime of moderately negative nonadditivity and largely asymmetric diameters, relevant to the modeling of sterically and electrostatically stabilized colloidal mixtures, the fluid-fluid critical point is unstable with respect to crystallization.