Glass transition and reversible gelation in asymmetric binary mixtures: A study by mode coupling theory and molecular dynamics.

The glass transition and the binodals of asymmetric binary mixtures are investigated from the effective fluid approach in the mode coupling theory and by molecular dynamics. Motivated by previous theoretical predictions, the hard-sphere mixture and the Asakura-Oosawa models are used to analyze experimental results from the literature, relative to polystyrene spheres mixed either with linear polymers or with dense microgel particles. In agreement with the experimental observations, the specificity of the depletant particles is shown to favor lower density gels. It further favors equilibrium gelation by reducing also the tendency of the system to phase separate. These results are confirmed by a phenomenological modification of the mode coupling theory in which the vertex functions are computed at an effective density lower than the actual one. A model effective potential in asymmetric mixtures of hard particles is used to further check this phenomenological modification against molecular dynamics simulation.

α-relaxation, shear viscosity, and elastic moduli of hard-particle fluids from a mode-coupling theory with a retarded vertex.

The recently proposed modification of the mode-coupling theory (MCT) in which the static structure used in the vertex is computed at a lower density than the actual one is tested on several dynamics-related properties. The predictions from this modified version of MCT calibrated on the one-component hard-sphere fluid are found in very good agreement with simulation data for one-component and binary hard-sphere fluids. They are also relevant for the stress moduli for models with attractive tails beyond the hard core. The clear improvement observed on several properties should give a new impetus to the use of MCT as a quantitative tool.

Dynamics of field-driven population inversion in a confined colloidal mixture.

We study, using Langevin dynamics simulations, the change in composition of a binary colloidal mixture confined in a finite-length channel, induced by an external field. The field-induced transition from a near-bulk composition to an inverted population is studied as a function of time, for different field strengths and system parameters. For state points corresponding to reversible field cycles, the cyclic filling and emptying of the channel by the minority species are compared. Extrapolation of the physical relaxation times to the colloidal regime is performed through a series of simulations at increasing value of the damping parameter. For state points at which the mixture is unstable at zero field, reproducible irreversible cycles are illustrated. For reversible field cycles, the scaling with the particles size of the characteristic cycling time is discussed.

Glass transition in hard-core fluids and beyond, using an effective static structure in the mode coupling theory.

The dynamical arrest in classical fluids is studied using a simple modification of the mode coupling theory (MCT) aimed at correcting its overestimation of the tendency to glass formation while preserving its overall structure. As in previous attempts, the modification is based on the idea of tempering the static pair correlations used as input. It is implemented in this work by computing the static structure at a different state point than the one used to solve the MCT equation for the intermediate scattering function, using the pure hard-sphere glass for calibration. The location of the glass transition predicted from this modification is found to agree with simulations data for a variety of systems --pure fluids and mixtures with either purely repulsive interaction potentials or ones with attractive contributions. Besides improving the predictions in the long-time limit, and so reducing the non-ergodicity domain, the same modification works as well for the time-dependent correlators.

Bond lifetime and diffusion coefficient in colloids with short-range interactions.

We use molecular dynamics simulations to study the influence of short-range structures in the interaction potential between hard-sphere-like colloidal particles. Starting from model potentials and effective potentials in binary mixtures computed from the Ornstein-Zernike equations, we investigate the influence of the range and strength of a possible tail beyond the usual core repulsion or the presence of repulsive barriers. The diffusion coefficient and mean "bond" lifetimes are used as indicators of the effect of this structure on the dynamics. The existence of correlations between the variations of these quantities with the physical parameters is discussed to assess the interpretation of dynamics slowing down in terms of long-lived bonds. We also discuss the question of a universal behaviour determined by the second virial coefficient B ((2)) and the interplay of attraction and repulsion. While the diffusion coefficient follows the B ((2)) law for purely attractive tails, this is no longer true in the presence of repulsive barriers. Furthermore, the bond lifetime shows a dependence on the physical parameters that differs from that of the diffusion coefficient. This raises the question of the precise role of bonds on the dynamics slowing down in colloidal gels.

Non-ergodicity transition and multiple glasses in binary mixtures: on the accuracy of the input static structure in the mode coupling theory.

We examine the question of the accuracy of the static correlation functions used as input in the mode coupling theory (MCT) of non-ergodic states in binary mixtures. We first consider hard-sphere mixtures and compute the static pair structure from the Ornstein-Zernike equations with the Percus-Yevick closure and more accurate ones that use bridge functions deduced from Rosenfeld's fundamental measures functional. The corresponding MCT predictions for the non-ergodicity lines and the transitions between multiple glassy states are determined from the long-time limit of the density autocorrelation functions. We find that while the non-ergodicity transition line is not very sensitive to the input static structure, up to diameter ratios D(2)/D(1) = 10, quantitative differences exist for the transitions between different glasses. The discrepancies with the more accurate closures become even qualitative for sufficiently asymmetric mixtures. They are correlated with the incorrect behavior of the PY structure at high size asymmetry. From the example of ultra-soft potential it is argued that this issue is of general relevance beyond the hard-sphere model.

Mode-coupling theory for the glass transition: test of the convolution approximation for short-range interactions.

We reexamine the convolution approximation commonly used in the mode-coupling theory (MCT) of nonergodic states of classical fluids. This approximation concerns the static correlation functions used as input in the MCT treatment of the dynamics. Besides the hard-sphere model, we consider interaction potentials that present a short-range tail, either attractive or repulsive, beyond the hard core. By using accurate static correlation functions obtained from the fundamental measures functional for hard spheres, we show that the role of three-body direct correlations can be more significant than what is inferred from previous simple ansatzs for pure hard spheres. This may in particular impact the location of the glass transition line and the nonergodicity parameter.

Binary mixture of nonadditive hard spheres adsorbed in a slit pore: a study of the population inversion by the integral equations theory.

The structure of a binary mixture of nonadditive hard spheres confined in a slit pore is studied by the integral equations method in which the confining medium acts as a giant particle at infinite dilution. The adsorption/desorption curves are studied as a function of the composition and density, when the homogeneous bulk mixture is near the demixing instability. The Ornstein-Zernike integral equations are solved with the reference functional approximation closure in which the bridge functions are derived from Rosenfeld's hard sphere functional for additive hard sphere. To study the high composition asymmetry regime in which a population inversion occurs, we developed an approximate closure that overcomes the no solution problem of the integral equation. By comparison with simulation data, this method is shown to be sufficiently accurate for predicting the threshold density for the population inversion. The predictions of simpler closure relations are briefly examined.

Binary mixture adsorbed in a slit pore: Field-induced population inversion near the bulk instability.

The recently proposed method for modulating through an external field the composition of a binary fluid mixture adsorbed in a slit pore is discussed. The population inversion near the bulk (demixing) instability is first analyzed in the case of a symmetric mixture of nonadditive hard spheres, without field. It is next investigated for a mixture comprising dipolar particles subject to an external field. The influence of several factors on the adsorption curves including bulk composition, pore width, field direction, polarizability versus permanent dipoles, and temperature on this field induced population inversion is shown by Monte Carlo simulation.

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.

Generalization of Rosenfeld's functional to non-additive hard-spheres: pair structure and test-particle consistency.

The accuracy of the structural data obtained from the recently proposed generalization to non-additive hard-spheres (Schmidt 2004 J. Phys.: Condens. Matter 16 L351) of Rosenfeld's functional is investigated. The radial distribution functions computed from the direct correlation functions generated by the functional, through the Ornstein-Zernike equations, are compared with those obtained from the density profile equations in the test-particle limit, without and with test-particle consistency. The differences between these routes and the role of the optimization of the parameters of the reference system when the functional is used to obtain the reference bridge functional are discussed in the case of symmetric binary mixtures of non-additive hard-spheres. The case of highly asymmetric mixtures is finally briefly discussed.

Adsorption of Zn2+ ions onto NaA and NaX zeolites: kinetic, equilibrium and thermodynamic studies.

The adsorption of Zn(2+) onto NaA and NaX zeolites was investigated. The samples were synthesized according to a hydrothermal crystallization using aluminium isopropoxide (Al[OCH(CH(3))(2)](3)) as a new alumina source. The effects of pH, initial concentration, solid/liquid ratio and temperature were studied in batch experiments. The Freundlich and the Langmuir models were applied and the adsorption equilibrium followed Langmuir adsorption isotherm. The uptake distribution coefficient (K(d)) indicated that the Zn(2+) removal was the highest at minimum concentration. Thermodynamic parameters were calculated. The negative values of standard enthalpy of adsorption revealed the exothermic nature of the adsorption process whereas the negative activation entropies reflected that no significant change occurs in the internal structure of the zeolites solid matrix during the sorption of Zn(2+). The negative values of Gibbs free energy were indicative of the spontaneity of the adsorption process. Analysis of the kinetic and rate data revealed that the pseudo second-order sorption mechanism is predominant and the intra particle diffusion was the determining step for the sorption of zinc ions. The obtained optimal parameters have been applied to wastewater from the industrial zone (Algeria) in order to remove the contained zinc effluents.

Controlling the composition of a confined fluid by an electric field.

Starting from a generic model of a pore/bulk mixture equilibrium, we propose a novel method for modulating the composition of the confined fluid without having to modify the bulk state. To achieve this, two basic mechanisms-sensitivity of the pore filling to the bulk thermodynamic state and electric field effect-are combined. We show by Monte Carlo simulation that the composition can be controlled both in a continuous and in a jumpwise way. Near the bulk demixing instability, we demonstrate a field induced population inversion in the pore. The conditions for the realization of this method should be best met with colloids, but being based on robust and generic mechanisms, it should also be applicable to some molecular fluids.

Structure of highly confined fluids: mixture of polar and nonpolar macroparticles in an external field.

In this paper we study the structure of highly confined mixtures of polar and nonpolar macroparticles in an external field by Monte Carlo simulation in the canonical ensemble. Without attempting a systematic investigation of the model, several effects including confinement, polarization, and solvation forces are considered. In particular, we show that layering at different length scales can be obtained in mixtures of differently sized particles subject to an external electric field.

Equilibrium route to colloidal gelation: mixtures of hard-sphere-like colloids.

The binodals and the nonergodicity lines of a binary mixture of hard-sphere-like particles with a large size ratio are computed for studying the interplay between dynamic arrest and phase separation in depletion-driven colloidal mixtures. Contrary to the case of hard core plus short-range effective attraction, physical gelation without competition with the fluid-phase separation can occur in such mixtures. This behavior due to the oscillations in the depletion potential should concern all simple mixtures with a nonideal depletant, justifying further studies of their dynamic properties.

Optimum free energy in the reference functional approach for the integral equations theory.

We investigate the question of determining the bulk properties of liquids, required as input for practical applications of the density functional theory of inhomogeneous systems, using density functional theory itself. By considering the reference functional approach in the test particle limit, we derive an expression of the bulk free energy that is consistent with the closure of the Ornstein-Zernike equations in which the bridge functions are obtained from the reference system bridge functional. By examining the connection between the free energy functional and the formally exact bulk free energy, we obtain an improved expression of the corresponding non-local term in the standard reference hypernetted chain theory derived by Lado. In this way, we also clarify the meaning of the recently proposed criterion for determining the optimum hard-sphere diameter in the reference system. This leads to a theory in which the sole input is the reference system bridge functional both for the homogeneous system and the inhomogeneous one. The accuracy of this method is illustrated with the standard case of the Lennard-Jones fluid and with a Yukawa fluid with very short range attraction.

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.

Phase transitions in highly asymmetric binary hard-sphere fluids: Fluid-fluid binodal from a two-component mixture theory.

Fluid-fluid binodals of binary hard-sphere mixtures are computed from the recently proposed fundamental measure functional-mean spherical approximation closure of the two-component Ornstein-Zernike equation. The results, especially in the dense fluid region that was not accessible by previous theoretical methods, are compared with the corresponding ones for the one-component fluid of big spheres with effective potential obtained from the same closure. The general trends are those expected for hard-sphere potentials but small difference are detectable. The overall agreement found validates the equivalence of the two descriptions for size ratios R = 8.5 or greater.

Structure of highly asymmetric hard-sphere mixtures: an efficient closure of the Ornstein-Zernike equations.

A simple modification of the reference hypernetted chain (RHNC) closure of the multicomponent Ornstein-Zernike equations with bridge functions taken from Rosenfeld's hard-sphere bridge functional is proposed. Its main effect is to remedy the major limitation of the RHNC closure in the case of highly asymmetric mixtures--the wide domain of packing fractions in which it has no solution. The modified closure is also much faster, while being of similar complexity. This is achieved with a limited loss of accuracy, mainly for the contact value of the big sphere correlation functions. Comparison with simulation shows that inside the RHNC no-solution domain, it provides a good description of the structure, while being clearly superior to all the other closures used so far to study highly asymmetric mixtures. The generic nature of this closure and its good accuracy combined with a reduced no-solution domain open up the possibility to study the phase diagram of complex fluids beyond the hard-sphere model.

Potential of mean force in confined colloids: integral equations with fundamental measure bridge functions.

The potential of mean force for uncharged macroparticles suspended in a fluid confined by a wall or a narrow pore is computed for solvent-wall and solvent-macroparticle interactions with attractive forces. Bridge functions taken from Rosenfeld's density-functional theory are used in the reference hypernetted chain closure of the Ornstein-Zernike integral equations. The quality of this closure is assessed by comparison with simulation. As an illustration, the role of solvation forces is investigated. When the "residual" attractive tails are given a range appropriate to "hard sphere-like" colloids, the unexpected role of solvation forces previously observed in bulk colloids is confirmed in the confinement situation.