Decay of correlation functions in hard-sphere mixtures: structural crossover

We investigate the decay of pair correlation functions in a homogeneous (bulk) binary mixture of hard spheres. At a given state point the asymptotic decay r-->infinity of all three correlation functions is governed by a common exponential decay length and a common wavelength of oscillations. Provided the mixture is sufficiently asymmetric, size ratios q less than or approximately 0.7, we find that the common wavelength reflects either the size of the small or that of the big spheres. By analyzing the (complex) poles of the partial structure factors we find a sharp structural crossover line in the phase diagram. On one side of this line the common wavelength is approximately the diameter of the smaller sized spheres whereas on the other side it is approximately the diameter of the bigger ones; the wavelength of the longest ranged oscillations changes discontinuously at the structural crossover line. Using density functional theory and Monte Carlo simulations we show that structural crossover also manifests itself in the intermediate range behavior of the pair correlation functions and we comment on the relevance of this observation for real (colloidal) mixtures. In highly asymmetric mixtures, q< or =0.1, where there is metastable fluid-fluid transition, we find a Fisher-Widom line with two branches. This line separates a region of the phase diagram where the decay of pair correlations is oscillatory from one in which it is monotonic.     

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.     

Investigation of the local composition enhancement and related dynamics in supercritical CO2-cosolvent mixtures via computer simulation: the case of ethanol in CO2

The supercritical mixture ethanol-carbon dioxide (EtOH-CO2) with mole fraction of ethanol X(EtOH) congruent with 0.1 was investigated at 348 K, by employing the molecular dynamics simulation technique in the canonical ensemble. The local intermolecular structure of the fluid was studied in terms of the calculated appropriate pair radial distribution functions. The estimated average local coordination numbers and mole fractions around the species in the mixture reveal the existence of local composition enhancement of ethanol around the ethanol molecules. This finding indicates the nonideal mixing behavior of the mixture due to the existence of aggregation between the ethanol molecules. Furthermore, the local environment redistribution dynamics have been explored by analyzing the time correlation functions (TCFs) of the total local coordination number (solvent, cosolvent) around the cosolvent molecules in appropriate parts. The analysis of these total TCFs in the auto-(solvent-solvent, cosolvent-cosolvent) and cross-(solvent-cosolvent, cosolvent-solvent) TCFs has shown that the time dependent redistribution process of the first solvation shell of ethanol is mainly determined by the redistribution of the CO2 solvent molecules. These results might be explained on the basis of the CO2-CO2 and EtOH-CO2 intermolecular forces, which are sufficiently weaker in comparison to the EtOH-EtOH hydrogen bonding interactions, creating in this way a significantly faster redistribution of the CO2 molecules in comparison with EtOH. Finally, the self-diffusion coefficients and the single reorientational dynamics of both the cosolvent and solvent species in the mixture have been predicted and discussed in relationship with the local environment around the species, which in the case of the EtOH molecules seem to be strongly affected.     

Negative azeotropy in mixed adsorption of hexanol and dodecylammonium chloride at water/air interface

Miscibility of hexanol and dodecylammonium chloride (DAC) in adsorbed films and micelles was investigated by evaluating the compositions of the adsorbed films and micelles from surface tension measurements. Judging from the phase diagram of adsorption, negative azeotropy of adsorption was observed for the mixed adsorption of hexanol and DAC at water/air interfaces. The nonideal mixing in the adsorbed film was clarified using excess functions of adsorption. Interaction between hexanol and DAC in the adsorbed film was compared with that between other alkanols and surfactants. It was found that the range of azeotropes is narrower for the hexanol-DAC mixture than for the heptanol-octylsulfinylethanol mixture, because interaction between different species in an adsorbed film is weaker in the former than in the latter.     

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.     

Molecular models for 267 binary mixtures validated by vapor–liquid equilibria: A systematic approach

By assessing a large number of binary systems, it is shown that molecular modeling is a reliable and robust route to vapor–liquid equilibria (VLE) of mixtures. A set of simple molecular models for 78 pure substances from prior work is taken to systematically describe all 267 binary mixtures of these components for which relevant experimental VLE data is available. The mixture models are based on the modified Lorentz–Berthelot combining rule. Per binary system, one state independent binary interaction parameter in the energy term is adjusted to a single experimental vapor pressure. The unlike energy parameter is altered usually by less than 5% from the Berthelot rule. The mixture models are validated regarding the vapor pressure at other state points and also regarding the dew point composition, which is a fully predictive property in this work. In almost all cases, the molecular models give excellent predictions of the mixture properties.     

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.     

Gel to glass transition in simulation of a valence-limited colloidal system

We numerically study a simple model for thermoreversible colloidal gelation in which particles can form reversible bonds with a predefined maximum number of neighbors. We focus on three and four maximally coordinated particles, since in these two cases the low valency makes it possible to probe, in equilibrium, slow dynamics down to very low temperatures T. By studying a large region of T and packing fraction phi we are able to estimate both the location of the liquid-gas phase separation spinodal and the locus of dynamic arrest, where the system is trapped in a disordered nonergodic state. We find that there are two distinct arrest lines for the system: a glass line at high packing fraction, and a gel line at low phi and T. The former is rather vertical (phi controlled), while the latter is rather horizontal (T controlled) in the phi-T plane. Dynamics on approaching the glass line along isotherms exhibit a power-law dependence on phi, while dynamics along isochores follow an activated (Arrhenius) dependence. The gel has clearly distinct properties from those of both a repulsive and an attractive glass. A gel to glass crossover occurs in a fairly narrow range in phi along low-T isotherms, seen most strikingly in the behavior of the nonergodicity factor. Interestingly, we detect the presence of anomalous dynamics, such as subdiffusive behavior for the mean squared displacement and logarithmic decay for the density correlation functions in the region where the gel dynamics interferes with the glass dynamics.     

Vapor pressure of R227ea + ethanol at 343.13 K by molecular simulation

A new molecular model for 1,1,1,2,3,3,3-heptafluoropropane (R227ea) was developed on the basis of quantum chemical calculations and optimized using experimental vapor pressure and bubble density data. In combination with an existing model for ethanol, a molecular model for the binary mixture R227ea + ethanol was defined, using the Lorentz–Berthelot combining rule. It was validated at 283.17 K, where, considering the statistical uncertainties, it agrees to the experimental vapor pressure. The vapor–liquid equilibrium, comprising both bubble line and dew line data, was predicted at 343.13 K by molecular simulation. The Peng–Robinson equation of state fails for this system.     

EFFECT OF DILUENTS ON CRYSTALLIZATION OF POLY(VINYLIDENE FLUORIDE) AND PHASE SEPARATED STRUCTURE IN A TERNARY SYSTEM via THERMALLY INDUCED PHASE SEPARATION

The phase diagram of a ternary system of PVDF,dibutyl phthalate (DBP) and di(2-ethylhexyl) phthalate (DEHP) was determined in terms of a pseudo binary system with the same polymer concentration and different DBP content in diluent mixture.The experimental results showed that as the DBP content increased in diluent mixture,the phase separation changed from liquid-liquid phase separation to solid-liquid phase separation,and both the cloudy point for L-L phase separation and crystallization temperature shif...     

Effects of Polydispersity on the Phase Behavior of Additive Hard Spheres in Solution

The ability to separate enzymes, nucleic acids, cells, and viruses is an important asset in life sciences. This can be realised by using their spontaneous asymmetric partitioning over two macromolecular aqueous phases in equilibrium with one another. Such phases can already form while mixing two different types of macromolecules in water. We investigate the effect of polydispersity of the macromolecules on the two-phase formation. We study theoretically the phase behavior of a model polydisperse system: an asymmetric binary mixture of hard spheres, of which the smaller component is monodisperse and the larger component is polydisperse. The interactions are modelled in terms of the second virial coefficient and are assumed to be additive hard sphere interactions. The polydisperse component is subdivided into sub-components and has an average size ten times the size of the monodisperse component. We calculate the theoretical liquid–liquid phase separation boundary (the binodal), the critical point, and the spinodal. We vary the distribution of the polydisperse component in terms of skewness, modality, polydispersity, and number of sub-components. We compare the phase behavior of the polydisperse mixtures with their concomittant monodisperse mixtures. We find that the largest species in the larger (polydisperse) component causes the largest shift in the position of the phase boundary, critical point, and spinodal compared to the binary monodisperse binary mixtures. The polydisperse component also shows fractionation. The smaller species of the polydisperse component favor the phase enriched in the smaller component. This phase also has a higher-volume fraction compared to the monodisperse mixture.     

Equilibrium domains on heterogeneously charged surfaces

Recent experiments have shown that salt solutions containing surfaces with two oppositely charged species show stable, possibly equilibrium, structures with finite domain sizes. The short-range interactions between the two species would normally result in phase separation that is driven by the line tension with macroscopically large domains of each species. In this paper, we show that, when at least one of the charged species is mobile, finite domains can occur in equilibrium. The domain size is determined by a competition of the electrostatic free energy that promotes charge mixing and small domains, with the line tension that promotes macroscopic phase separation. We calculate the equilibrium patch size as a function of the surface charge and the concentration of dissolved monovalent salts in the bulk phase. An important finding is the prediction of a first-order transition from finite patches to macroscopic phase separation of the two charge species as the salt concentration is increased.     

Phase behavior of a blend of polymer-tethered nanoparticles with diblock copolymers

Using the self-consistent field theory (SCFT), we investigate the phase behavior of a mixture of diblock copolymers and nanoparticles with monodisperse polymer chains tethered to their surfaces. We assume the size of the nanoparticles to be much smaller than that of the attached polymer chains and therefore model the particles with their grafted polymer "shell" as star polymers. The polymer chains attached to the particles are of the same species as one of the blocks of the symmetric diblock copolymer. Of primary interest is how to tune the shell of the particle by changing both the length and number of tethered polymers in order to achieve higher loading of nanoparticles within an ordered structure without macrophase separation occurring. We find that the phase behavior of the system is very sensitive to the size of the particle including its tethered shell. The region of microphase separation is increased upon decreasing the star polymer size, which may be achieved by shortening and/or removing tethered polymer chains. To explore the possible structures in these systems we employ SCFT simulations that provide insight into the arrangement of the different species in these complex composites.     

Surface phase separation in complex mixed adsorbing systems: an interface-bulk coupling effect

The interfacial thermodynamics and structure of ternary mixtures of the type A+B+solvent are investigated. According to the Gibbs phase rule, the coupling between the bulk phase and the interfacial region-which is related to the reversibility of the adsorption of the corresponding species-is a determinant as to whether phase separation can be observed at the interface. For an n-component adsorbing solution, at least one of the species has to adsorb irreversibly over the experimental time scales in order not to fix more intensive variables than those required to observe surface phase separation. We present results for a lattice model planar interface consisting of the ternary mixture A+B+solvent. The solvent molecules and the type A molecules have fixed chemical potentials at the interface since they are equilibrated with a bulk solution. In contrast, the type B molecules are irreversibly adsorbed at the interface and do not equilibrate with the bulk. Mean-field theory is compared with Monte Carlo simulation. Interestingly, the spinodal line in the interaction-composition plane shows a reentrant on the B-rich phase side. We discuss the implications of these results for surface phase separation of adsorbing mixtures of proteins and low-molecular-weight surfactants.     

Adsorption and mixing behavior of ethers and alkanes at the solid/liquid interface

The behavior of binary mixtures of linear symmetrical ethers and alkanes adsorbed to a graphite surface from the bulk liquid mixtures is described on the basis of differential scanning calorimetry (DSC) data. Both the ethers and the alkanes are found to form solid monolayers when adsorbed from the liquid. In addition, the monolayer mixing behavior is addressed. The results indicate that there is good, essentially ideal, mixing in the monolayers for ethers and alkanes of the same overall chain length, where the chain length is equal to the total number of carbon and oxygen atoms in the molecule. However, a difference in chain length of more than one atom results in a variation of mixing behavior from nonideal mixing (for long pairs) to phase separation (for short pairs) on the graphite surface. Hence, we conclude that it is the relative chain lengths that control mixing behavior. The results are quantified using a regular solution model with a correction for preferential adsorption. The phase behavior of the mixed monolayers is also compared to the behavior of the bulk. Interestingly, we observe mixtures where the bulk and monolayer behavior are quite different, for example, phase separation in the bulk but essentially ideal mixing in the monolayer for mixtures of ethers and alkanes with the same chain lengths. At present, we attribute this mixing in the monolayer to dilution of the unfavorable ether oxygen-ether oxygen lone pair interactions by the coadsorbed alkanes. In addition, we find evidence for the preferential adsorption of the alkane over the ether. For example, heptane is preferentially adsorbed over dibutyl ether even though it contains two fewer atoms in the molecular chain. This contrasts with the preferential adsorption of alcohols over alkanes reported previously (Messe, L.; Perdigon, A.; Clarke, S. M.; Inaba, A.; Arnold, T. Langmuir 2005, 21, 5085-5093).     

Solvent mediated interactions close to fluid-fluid phase separation: microscopic treatment of bridging in a soft-core fluid

Using density functional theory we calculate the density profiles of a binary solvent adsorbed around a pair of big solute particles. All species interact via repulsive Gaussian potentials. The solvent exhibits fluid-fluid phase separation, and for thermodynamic states near to coexistence the big particles can be surrounded by a thick adsorbed "wetting" film of the coexisting solvent phase. On reducing the separation between the two big particles we find there can be a "bridging" transition as the wetting films join to form a fluid bridge. The effective (solvent mediated) potential between the two big particles becomes long ranged and strongly attractive in the bridged configuration. Within our mean-field treatment the bridging transition results in a discontinuity in the solvent mediated force. We demonstrate that accounting for the phenomenon of bridging requires the presence of a nonzero bridge function in the correlations between the solute particles when our model fluid is described within a full mixture theory based upon the Ornstein-Zernike equations.     

Non-Lorentz–Berthelot Lennard-Jones mixtures: A systematic study

Binary mixtures of two identical Lennard-Jones fluids with non-Lorentz–Berthelot combining rules have been simulated over the entire concentration range at three state points in order to examine the effect of cross interactions on the mixing properties, excess volumes and enthalpies, and partial molar volumes, and on the structure. Various combinations of deviations, in both the energy and size cross parameters, from the Lorentz–Berthelot rule, have been considered and the results analyzed using a recently proposed method based on the Tikhonov regularization. It is found that the most important is the size cross parameter and that by varying the combining rules a variety of qualitatively different behavior can be produced including, e.g., a minimum in the partial molar volumes observed otherwise only in complex mixtures of associating fluids; occurrence of this minimum seems to be associated with changes in the second coordination shell as witnessed by the pair correlation function.     

Applicability of cubic equation of state mixing rules on correlation of excess molar volume of Non-Electrolyte binary mixtures

The excess molar volume V ^E data of the binary liquid systems were correlated by the Peng–Robinson–Stryjek–Vera equation of state coupled with two different types of mixing rules: composition dependent van der Waals mixing rule (vdW) and the mixing rule based on the Gupta–Rasmussen–Fredenslund method (GRF), with the NRTL equation as G ^E model. The results obtained by these models show that type of applied mixing rule, a number and position of interaction parameters are of great importance for a satisfactory correlation of V ^E data. The GRF mixing rules coupled with the NRTL model gave mostly satisfactory results for V ^E correlation of the nonideal binary systems of diverse complexity.     

Calorimetric and dielectric effects during polymerization of an elastomer‐containing mixture and liquid‐liquid phase separation

Calorimetry and dielectric spectroscopy of an elastomer, amine terminated butadiene acrylonitrile (ATBN), dissolved in a stoichiometric mixture of ethylene diamine and diglycidyl ether of bisphenol‐A, were studied in real time during the polymerization and phase separation of the mixture. In the two polymer compositions containing 8 w/w % ATBN and 20 w/w % ATBN, the total enthalpy released per mole of DGEBA's reaction was the same, indicating indetectably small changes in molecular interactions before and after the phase separation. The dielectric relaxation spectra showed no evidence for phase separation, which indicated a gradual phase separation with time and the extent of polymerization, and relatively small differences in the permittivity and conductivity between the ATBN particles and the network matrix at the time of phase separation. The equilibrium permittivity and dc conductivity showed a nonideal mixing of ATBN. The stretched exponential relaxation parameter remained at 0.36, but the characteristic dielectric relaxation time and the dc conductivity increased on addition of ATBN. An increase in the temperature had a greater effect on the relaxation time than the increase in the extent of polymerization. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1911–1919, 1999