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

Super-Arrhenius diffusion in a binary colloidal mixture at low volume fraction: an effect of depletion interaction due to an asymmetric barrier

We report results from the molecular dynamics simulations of a binary colloidal mixture subjected to an external potential barrier along one of the spatial directions at low volume fraction, ϕ = 0.2. The variations in the asymmetry of the external potential barrier do not change the dynamics of the smaller particles, showing Arrhenius diffusion. However, the dynamics of the larger particles shows a crossover from sub-Arrhenius to super-Arrhenius diffusion with the asymmetry in the external potential at the low temperatures and low volume fraction. Super-Arrhenius diffusion is generally observed in the high density systems where the transient cages are present due to dense packing, e.g., supercooled liquids, jammed systems, diffusion through porous membranes, dynamics within the cellular environment, etc. This model can be applied to study the molecular transport across cell membranes, nano-, and micro-channels which are characterized by spatially asymmetric potentials.

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.

Structure, thermodynamic properties, and phase diagrams of few colloids confined in a spherical pore

We study a system of few colloids confined in a small spherical cavity with event driven molecular dynamics simulations in the canonical ensemble. The colloidal particles interact through a short range square-well potential that takes into account the basic elements of attraction and excluded-volume repulsion of the interaction among colloids. We analyze the structural and thermodynamic properties of this few-body confined system in the framework of inhomogeneous fluids theory. Pair correlation function and density profile are used to determine the structure and the spatial characteristics of the system. Pressure on the walls, internal energy, and surface quantities such as surface tension and adsorption are also analyzed for a wide range of densities and temperatures. We have characterized systems from 2 to 6 confined particles, identifying distinctive qualitative behavior over the thermodynamic plane T - ρ, in a few-particle equivalent to phase diagrams of macroscopic systems. Applying the extended law of corresponding states, the square well interaction is mapped to the Asakura-Oosawa model for colloid-polymer mixtures. We link explicitly the temperature of the confined square-well fluid to the equivalent packing fraction of polymers in the Asakura-Oosawa model. Using this approach, we study the confined system of few colloids in a colloid-polymer mixture.

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 fluid with attractions near a planar wall

It is well known that a mixture of big and small hard spheres next to a planar wall will exhibit segregation based on their size difference. The larger spheres will tend to locate next to the substrate because the overall system entropy loss per unit area is less. In the present study we determine the role of attraction between the small particles and the wall to displace the larger particles. Both fluids density-functional theory and discontinuous molecular dynamics simulations demonstrate that at a certain attractive potential, which is on the order of the thermal energy, the large particles can indeed be dislodged from the surface layer so the small particles are now the major surface component. Exploration of a range of parameters, including relative sphere size and concentration, as well as attractions between the small spheres in the bulk, shows that the phenomenon is quite robust.

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.

Ultra-small-angle neutron scattering: a tool to study packing of relatively monodisperse polymer spheres and their binary mixtures

We measured ultra-small-angle neutron scattering (USANS) from polymethylmethacrylate spheres tamped down in air. Two slightly polydisperse pure sphere sizes (1.5 and 7.5 microm diameters) and five mixtures of these were used. All were loose packed (packing fractions of 0.3-0.6) with nongravitational forces (e.g., friction) important, preventing close packing. The USANS data are rich in information on powder packing. A modified Percus-Yevick fluid model was used to parametrize the data-adequately but not well. The modifications required the introduction of small voids, less than the sphere size, and a parameter reflecting substantial deviation from the Percus-Yevick prediction of the sphere-sphere correlation function. The mixed samples fitted less well, and two further modifying factors were necessary. These were local inhomogeneities, where the concentration of same-size spheres, both large and small, deviated from the mean packing, and a factor accounting for the presence within these "clusters" of self-avoidance of the large spheres (that is, large spheres coated with more small spheres than Percus-Yevick would predict). The overall deviations from the hard-sphere Percus-Yevick model that we find here suggest that fluid models of loose packed powders are unlikely to be successful but lay the ground work for future theoretical and computational works.

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 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.

Glass-liquid-glass reentrance in mono-component colloidal dispersions

The self-consistent generalized Langevin equation (SCGLE) theory of colloid dynamics is employed to describe the ergodic-non-ergodic transition in model mono-disperse colloidal dispersions whose particles interact through hard-sphere plus short-ranged attractive forces. The ergodic-non-ergodic phase diagram in the temperature-concentration state space is determined for the hard-sphere plus attractive Yukawa model within the mean spherical approximation for the static structure factor by solving a remarkably simple equation for the localization length of the colloidal particles. Finite real values of this property signals non-ergodicity and determines the non-ergodic parameters f(k) and f(s)(k). The resulting phase diagram for this system, which involves the existence of reentrant (repulsive and attractive) glass states, is compared with the corresponding prediction of mode coupling theory. Although both theories coincide in the general features of this phase diagram, there are also clear qualitative differences. One of the most relevant is the SCGLE prediction that the ergodic-attractive glass transition does not preempt the gas-liquid phase transition, but always intersects the corresponding spinodal curve on its high-concentration side. We also calculate the ergodic-non-ergodic phase diagram for the sticky hard-sphere model to illustrate the dependence of the predicted SCGLE dynamic phase diagram on the choice of one important constituent element of the SCGLE theory.