Asymmetric Binary Mixtures Research Articles

Impact of Polymer Graft Characteristics and Evaporation Rate on the Formation of 2-D Nanoparticle Assemblies

The effect of polymer functionalization on the two-dimensional (2-D) assembly of uniform as well as highly asymmetric binary colloidal mixtures with both neutral and incompatible polymer grafts is presented. In ordered assemblies of uniform particle brush systems, the observed size-segregation is analogous to that of hard sphere colloidal systems, suggesting that lateral capillary interactions are responsible for the crystal nucleation in the early stages of assembly formation. Structure formation in binary blends of asymmetric particle brush systems is found to be strongly influenced by three major energetic contributions, that is, the interfacial energies associated with the particle brush/air boundaries, the interfacial energies between the distinct brush components, as well as the elastic energy associated with the stretching of the polymer-brush to fill the interstitial regions within locally ordered particle arrays. Our results demonstrate the relevance of capillary interactions in soft particle brush systems but also highlight distinctive differences in the order formation as compared to hard sphere colloidal systems. In particular, the compliant response of grafted polymer chains is shown to promote phase separation in binary blends of incompatible and asymmetric colloidal systems.

Thermodynamic consistency of experimental VLE data for asymmetric binary mixtures at high pressures

A thermodynamic consistency of isothermal vapor–liquid equilibrium data for 9 non-polar and 8 polar binary asymmetric mixtures at high pressures has been evaluated. A method based on the isothermal Gibbs–Duhem equation was used for the test of thermodynamic consistency using a Φ–Φ approach. The Peng–Robinson equation of state coupled with the Wong–Sandler mixing rules were used for modeling the vapor–liquid equilibrium (VLE) within the thermodynamic consistency test. The VLE parameters calculations for asymmetric mixtures at high pressures were highly dependent on bubble pressure calculation, making more convenient to eliminate the data points yielding the highest deviations in pressure. However the results of the thermodynamic consistencies test of experimental data for many cases were found not fully consistent. As a result, the strategies for solving these problems were discussed in detailed.

Gelation and phase coexistence in colloidal suspensions with short-range forces: Generic behavior versus specificity

The interplay between physical gelation and equilibrium phase transitions in asymmetric binary mixtures is analyzed from the effective fluid approach, in which the big particles interact via a short-range effective attraction beyond the core due to the depletion mechanism. The question of the universality of the scenario for dynamical arrest is then addressed. The comparison of the phase diagrams of the hard-sphere mixture and the Asakura-Oosawa models at various size ratios shows that strong specificity is observed for nonideal depletants. In particular, equilibrium gelation, without the competition with fluid-fluid transition is possible in mixtures of hard-sphere colloids. This is interpreted from the specificities of the effective potential, such as its oscillatory behavior and its complex variation with the physical parameters. The consequences on the dynamical arrest and the fluid-fluid transition are then investigated by considering in particular the role of the well at contact and the first repulsive barrier. This is done for the actual effective potential in the hard-sphere mixture and for a square well and shoulder model, which allows a separate discussion of the role of the different parameters, in particular on the localization length and the escape time. This study is next extended to mixtures of "hard-sphere-like" colloids with residual interactions. It confirms the trends relative to equilibrium gelation and illustrates a diversity of the phase behavior well beyond the scenarios expected from simple models.

Interfacial properties of selected binary mixtures containing n-alkanes

We report the correlation and prediction of the subcritical vapour–liquid interfacial properties of three asymmetric binary mixtures composed of long n-alkanes in equilibria with a smaller solvent: hexane + decane, carbon dioxide + decane, and ethane + eicosane. The interfacial region is described by the complementary use of the Square Gradient Theory (SGT) and molecular dynamics (MD) simulations that allow the prediction of both the macroscopic and molecular level properties of the binary fluid mixtures. Calculations with SGT rely on the description of the vapour–liquid equilibria (VLE) by means of the Statistical Associated Fluid Theory (SAFT) equation of state. MD simulations are performed in the canonical ensemble using united-atom potentials to probe coexisting phases and the accompanying interface simultaneously. In addition to the phase equilibrium compositions and interfacial tensions, other interfacial properties, such as concentration profiles along the interfacial region, surface activities, and relative Gibbs adsorption isotherms at the interfaces have been obtained from a combination of SGT and MD. The entropy and surface enthalpy change of surface formation are also calculated for the case of ethane + eicosane mixture, where we report three different isothermal conditions. While pure component data are used to fit model parameters, mixture results are predictions. When possible, results are compared to available experimental data and quantitative agreement is observed throughout. The particularly high excess adsorption in the interface of the smaller solvents, CO 2 and ethane, is noted.

Parameters estimation and VLE calculation in asymmetric binary mixtures containing carbon dioxide + n-alkanols

In the present work, the estimation of the parameters for asymmetric binary mixtures of carbon dioxide + n-alkanols has been developed. The binary interaction parameter k 12 of the second virial coefficient and non-random two liquid model parameters τ 12 and τ 21 were obtained using Peng–Robinson equation of state coupled with the Wong–Sandler mixing rules. In all cases, Levenberg–Marquardt minimization algorithm was used for the parameters optimization employing an objective function based on the calculation of the distribution coefficients for each component. Vapor–liquid equilibrium for binary asymmetric mixtures (CO 2 + n-alkanol, from methanol to 1-decanol) was calculated using the obtained values of the mentioned parameters. The agreement between calculated and experimental values was satisfactory.

Simulating asymmetric colloidal mixture with adhesive hard sphere model

Monte Carlo simulation and Percus-Yevick (PY) theory are used to investigate the structural properties of a two-component system of the Baxter adhesive fluids with the size asymmetry of the particles of both components mimicking an asymmetric binary colloidal mixture. The radial distribution functions for all possible species pairs, g(11)(r), g(22)(r), and g(12)(r), exhibit discontinuities at the interparticle distances corresponding to certain combinations of n and m values (n and m being integers) in the sum nsigma(1)+msigma(2) (sigma(1) and sigma(2) being the hard-core diameters of individual components) as a consequence of the impulse character of 1-1, 2-2, and 1-2 attractive interactions. In contrast to the PY theory, which predicts the delta function peaks in the shape of g(ij)(r) only at the distances which are the multiple of the molecular sizes corresponding to different linear structures of successively connected particles, the simulation results reveal additional peaks at intermediate distances originating from the formation of rigid clusters of various geometries.

Theoretical studies of the correlations in moderately asymmetric binary hard-sphere solid mixtures

A theoretical approach to calculate the correlation functions in binary hard-sphere (HS) solid mixtures is developed. The method is motivated by the theory of correlations in one-component HS solids [Rascon, Phys. Rev. E 54, 1261 (1996)] and the Kirkwood-Buff theory for solutions. Combined with the fundamental measure density functional theory the approach provides correlation functions in good agreement with the numerical simulations results for the moderately asymmetric mixtures.

Diffusion processes in homogeneous and phase-separated binary fluid mixtures.

Diffusion processes in dynamically asymmetric binary fluid mixtures made of monodisperse polystyrene (PS) and a rodlike nematogen molecule (5CB) are studied by pulsed-field gradient spin echo NMR in the vicinity of the phase-separation/phase-dissolution temperature. The phase-separation process and the loss of mobility of polymer chains at Tg take place simultaneously evidencing the strong effect of elasticity on the sample morphology. Below the instability point of the mixture, two self-diffusion coefficients, named Dfast and Dslow, are observed and assigned to mobile molecules i) dissolved in the polymeric matrix and ii) phase-separated in isolated or interconnected domains, respectively. The temperature dependence of Dfast exhibits an Arrhenius-like behaviour when the mixture is submitted to a slow cooling rate whereas a Vogel-Fulcher-Tamman-Hesse law is obeyed for deep quenches. These results show the dynamic heterogeneities existing in the PS/5CB system below the UCST. Characteristic length scales are estimated from modelling echo attenuation curves exhibiting diffraction-like patterns.

Ions in a binary asymmetric dipolar mixture: Mole fraction dependent Born energy of solvation and partial solvent polarization structure

Mean spherical approximation (MSA) for electrolyte solution has been extended to investigate the role of partial solvent polarization densities around an ion in a completely asymmetric binary dipolar mixture. The differences in solvent diameters, dipole moments, and ionic size are incorporated systematically within the MSA framework in the present theory for the first time. In addition to the contributions due to difference in dipole moments, the solvent-solvent and ion-solvent size ratios are found to significantly affect the nonideality in binary dipolar mixtures. Subsequently, the theory is used to investigate the role of ion-solvent and solvent-solvent size ratios in determining the nonideality in Born free energy of solvation of a unipositive rigid ion in alcohol-water and dimethyl sulfoxide-acetonitrile mixtures, where the solvent components are represented only by their molecular diameters and dipole moments. Nonideality in Born free energy of solvation in such simplified mixtures is found to be stronger for smaller ions. The slope of the nonideality for smaller alkali metal ions in methanol-water mixture is found to be opposite to that for larger ion, such as quaternary tertiary butyl ammonium ion. For ethanol-water mixtures, the slopes are in the same direction for all the ions studied here. These results are in qualitative agreement with experiments, which is surprising as the present MSA approach does not include the hydrogen bonding and hydrophobic interactions present in the real mixtures. The calculated partial polarization densities around a unipositive ion also show the characteristic deviation from ideality and reveal the microscopic origin of the ion and solvent size dependent preferential solvation. Also, the excess free energy of mixing (in the absence of any ion) for these binary mixtures has been calculated and a good agreement between theory and experiment has been found.

Equilibrium and glassy states of the Asakura-Oosawa and binary hard sphere mixtures: Effective fluid approach

Motivated by recent experimental results on model binary colloidal mixtures, especially for the glass transition, we investigate the phase diagram of two models of asymmetric binary mixtures: the hard sphere and the Asakura-Oosawa mixtures. This includes the binodals and the glass transition line, computed in the effective one-component representation using the corresponding potentials of mean force at infinite dilution. The reference hypernetted chain approximation is used for computing the static properties and the glass transition line is computed in the mode coupling approximation. The similarities and the differences between the two models are discussed for different size ratios. It is shown that while both models follow a universal behavior at large asymmetry, the hard sphere mixture model leads to more original results at moderate size ratio. These results show that a modeling beyond generic effective potentials might be necessary for an appropriate description of the complete phase diagram.

VLE Predictions of Strongly Non-Ideal Binary Mixtures by Modifying Van Der Waals and Orbey-Sandler Mixing Rules

By proposing a predictive method with no adjustable parameter and by using infinite dilution activity coefficients of components in binary mixtures obtained from UNIFAC model, the binary interaction parameters (k12) in van der Waals mixing rule (vdWMR) and Orbey-Sandler mixing rule (OSMR) have been evaluated. The predicted binary interaction parameters are used in Peng-Robinson-Stryjek-Vera equation of state (PRSV-EoS) to obtain the vapor-liquid equilibrium (VLE) for six strongly polar and asymmetric binary mixtures. The binary interaction parameters evaluated by correlation of VLE experimental data and by PRSV EoS are also used in VLE calculations of the same binary mixtures. The average absolute deviations (AADs%) of the calculated results by both predictive and correlative methods are reported. The results indicate that although the correlative method has a more flexibility to fit the VLE experimental data, the AAD% of the predictive method is comparable and in some cases even better than that of correlative method.

Computer simulation of phase separation under a double temperature quench

The authors numerically study a two-step quench process in an asymmetric binary mixture. The mixture is first quenched to an unstable state in the two-phase region. After a large phase-separated structure is formed, the authors again quench the system deeper. The second quench induces the formation of small secondary droplets inside the large domains created by the first quench. The authors characterize this secondary droplet growth in terms of the temperature of the first quench as well as the depth of the second one.

Transport in a highly asymmetric binary fluid mixture

We present molecular dynamics calculations of the thermal conductivity and viscosities of a model colloidal suspension with colloidal particles roughly one order of magnitude larger than the suspending liquid molecules. The results are compared with estimates based on the Enskog transport theory and effective medium theories (EMT) for thermal and viscous transport. We find, in particular, that EMT remains well applicable for predicting both the shear viscosity and thermal conductivity of such suspensions when the colloidal particles have a "typical" mass, i.e., much larger than the liquid molecules. Very light colloidal particles on the other hand yield higher thermal conductivities, in disagreement with EMT. We also discuss the consequences of these results for some proposed mechanisms for thermal conduction in nanocolloidal suspensions.

Investigation of phase separation within the generalized Lin–Taylor model for a binary liquid mixture of large hexagonal and small triangular particles

The generalized Lin–Taylor model defined on the hexagonal lattice is used to investigate the phase separation in an asymmetric binary liquid mixture consisting of large A (hexagons) and small B (triangles) particles. By considering interaction energies between A–A and A–B pairs of particles that occupy nearest-neighbour cells of the hexagonal lattice, we have derived an exact solution for the considered model system having established a mapping correspondence with the two-dimensional Ising model on its dual triangular lattice. Altogether, six different types of coexistence curves including those with re-entrant miscibility regions (i.e. closed-loop coexistence curves) were found with dependence on the relative strength between both coupling constants.

Ornstein–Zernike equations for highly asymmetric mixtures: confronting the no-solution challenge

The question of the absence of a solution to the Ornstein–Zernike integral equations for the pair structure of asymmetric binary mixtures is discussed. The behaviour of a recently proposed closure with a reduced no-solution domain in the case of highly asymmetric hard sphere mixtures is considered. The modifications that are required to treat non-hard-sphere interactions are examined. A possible implementation of the same strategy is illustrated for the potential of the mean force for solvophilic macroparticles in a Lennard–Jones fluid.

A combined determination of phase diagrams of asymmetric binary mixtures by equations of state and transitiometry

Transitiometric investigations of the pure compounds tetracosane and anhydrous caffeine as well as of the mixtures ( methane + tetracosane ) and ( carbon dioxide + caffeine ) are reported for pressures up to 180 MPa. The results are compared with calculations from equations of state; the selection of reference data and the fitting of parameters is explicitly discussed. It is demonstrated how the calculations can aid the interpretation of transitiometric signals, and how the combination of transitiometry and thermodynamic modelling can be used to construct and understand high-pressure phase diagrams of asymmetric mixtures.

Objective functions analysis in the minimization of binary VLE data for asymmetric mixtures at high pressures

Five different objective functions were studied with the purpose of analyzing their performance for parameters estimation of vapor–liquid equilibrium models for a series of 13 non-polar and 13 polar asymmetric binary mixtures at high pressures. Peng–Robinson equation of state coupled with the Wong–Sandler mixing rules were used for modeling the VLE in all cases. The first two objective functions are based on the calculation of the distribution coefficients for each component in the mixture and the remaining objective functions involve additional calculations of other quantities such as the bubble point pressure. In general, the optimal parameters obtained from all objective functions showed a good prediction capacity of the behavior of the vapor phase. It is also demonstrated that a good prediction of the pressure depends on the form of the objective function. It was found that one objective function has slight advantages over the other analyzed objective functions: first, it does not involve additional iterative calculations as the bubble point or isothermal flash for each data point; second, the optimal second virial coefficient interaction parameter shows to be in concordance with the statistical thermodynamic postulates; and finally, VLE predictions using the optimal parameters obtained with the help of this objective function show very good representations of both the vapor phase and pressure.

Influence of polydispersity on the critical parameters of an effective-potential model for asymmetric hard-sphere mixtures

We report a Monte Carlo simulation study of the properties of highly asymmetric binary hard-sphere mixtures. This system is treated within an effective fluid approximation in which the large particles interact through a depletion potential [R. Roth, Phys. Rev. E 62 5360 (2000)] designed to capture the effects of a virtual sea of small particles. We generalize this depletion potential to include the effects of explicit size dispersity in the large particles and consider the case in which the particle diameters are distributed according to a Schulz form having a degree of polydispersity 14%. The resulting alteration (with respect to the monodisperse limit) of the metastable fluid-fluid critical point parameters is determined for two values of the ratio of the diameters of the small and large particles: q(triple bond)sigma(s)/(-)sigma(b)=0.1 and q=0.05. We find that the inclusion of polydispersity moves the critical point to lower reservoir volume fractions of the small particles and high volume fractions of the large ones. The estimated critical point parameters are found to be in good agreement with those predicted by a generalized corresponding states argument which provides a link to the known critical adhesion parameter of the adhesive hard-sphere model. Finite-size scaling estimates of the cluster percolation line in the one phase fluid region indicate that inclusion of polydispersity moves the critical point deeper into the percolating regime. This suggests that phase separation is more likely to be preempted by dynamical arrest in polydisperse systems.

Aggregation Kinetics in a Model Colloidal Suspension

We present molecular dynamics simulations of aggregation kinetics in a colloidal suspension modeled as a highly asymmetric binary mixture. Starting from a configuration with largely uncorrelated colloidal particles the system relaxes by coagulation-fragmentation dynamics to a structured state of low-dimensionality clusters with an exponential size distribution. The results show that short-range repulsive interactions alone can give rise to so-called cluster phases. For the present model and probably other, more common colloids, the observed clusters appear to be equilibrium phase fluctuations induced by the entropic intercolloidal attractions.

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.