Colloidal flocculation in near-critical binary mixtures

Colloidal suspensions in one-phase mixed solvents under shear flow

We numerically studied the behaviour of colloidal suspensions in one-phase binary liquid mixtures under shear flows. Far from the phase-separation point, the colloidal particles are well dispersed and the suspension exhibits a Newtonian viscosity. When the mixture is close to the coexistence curve, the colloidal particles aggregate by attractive interactions due to the concentration heterogeneity caused by surface wetting, and the viscosity of the suspension increases. Near the phase-separation point, the viscosity increases when the fraction of species favoured by the surface of a colloid particle is small. The mixture also exhibits shear thinning behaviour, since the aggregated structure is rearranged into small clusters due to the shear flow. Our simulations indicate that the concentration profile around each particle is not significantly disturbed by the shear flow at the onset of the structural rearrangements. The effective interaction is independent of the shear flow and remains isotropic.

Fluctuating hydrodynamics of multicomponent membranes with embedded proteins

A simulation method for the dynamics of inhomogeneous lipid bilayer membranes is presented. The membrane is treated using stochastic Saffman-Delbrück hydrodynamics, coupled to a phase-field description of lipid composition and discrete membrane proteins. Multiple applications are considered to validate and parameterize the model. The dynamics of membrane composition fluctuations above the critical point and phase separation dynamics below the critical point are studied in some detail, including the effects of adding proteins to the mixture.

Hydrodynamics in bridging and aggregation of two colloidal particles in a near-critical binary mixture

We investigate bridging and aggregation of two colloidal particles in a near-critical binary mixture when the fluid far from the particles is outside the coexistence (CX) curve and is rich in the component disfavored by the colloid surfaces. In such situations, the adsorption-induced interaction is enhanced, leading to bridging and aggregation of the particles. We realize bridging firstly by changing the temperature with a fixed interparticle separation and secondly by letting the two particles aggregate. The interparticle attractive force dramatically increases upon bridging. The dynamics is governed by hydrodynamic flow around the colloid surfaces. In aggregation, the adsorption layers move with the particles and squeezing occurs at narrow separation. These results suggest relevance of bridging in the reversible colloid aggregation observed so far. We use the local functional theory [J. Chem. Phys., 2012, 136, 114704] to take into account the renormalization effect and the simulation method [Phys. Rev. Lett., 2000, 85, 1338] to calculate the hydrodynamic flow around the colloidal particles.

Attractive interaction and bridging transition between neutral colloidal particles due to preferential adsorption in a near-critical binary mixture

We examine the solvent-mediated interaction between two neutral colloidal particles due to preferential adsorption in a near-critical binary mixture. We take into account the renormalization effect due to the critical fluctuations using the recent local functional theory [J. Chem. Phys. 136, 114704 (2012)]. We calculate the free energy and the force between two colloidal particles as functions of the temperature T, the composition far from the colloidal particles c(∞), and the colloid separation ℓ. The interaction is much enhanced when the component favored by the colloid surfaces is poor in the reservoir. For such off-critical compositions, we find a surface of a first-order bridging transition ℓ=ℓ(cx)(T,c(∞)) in the T-c(∞)-ℓ space in a universal, scaled form, across which a discontinuous change occurs between separated and bridged states. This surface starts from the bulk coexistence surface (CX) and ends at a bridging critical line where ℓ is determined by T as ℓ=ℓ(c)(T). On approaching the critical line, the discontinuity vanishes and the derivatives of the force with respect to T and ℓ both diverge. Furthermore, bridged states continuously change into separated states if c(∞) (or T) is varied from a value on CX to a value far from CX with ℓ kept smaller than ℓ(c)(T).

Phase behavior of colloidal suspensions with critical solvents in terms of effective interactions

We study the phase behavior of colloidal suspensions the solvents of which are considered to be binary liquid mixtures undergoing phase segregation. We focus on the thermodynamic region close to the critical point of the accompanying miscibility gap. There, due to the colloidal particles acting as cavities in the critical medium, the spatial confinements of the critical fluctuations of the corresponding order parameter result in the effective, so-called critical Casimir forces between the colloids. Employing an approach in terms of effective, one-component colloidal systems, we explore the possibility of phase coexistence between two phases of colloidal suspensions, one being rich and the other being poor in colloidal particles. The reliability of this effective approach is discussed.

Membrane composition-mediated protein-protein interactions

The authors investigate membrane composition-mediated interactions between proteins adsorbed onto a two-component lipid bilayer close to critical demixing using coarse-grained molecular dynamics simulations and a phenomenological Ginzburg-Landau theory. The simulations consist of three-bead lipids and platelike proteins, which adsorb onto the membrane by binding preferentially to one of the two lipid species. The composition profile around one protein and the pair correlation function between two proteins are measured and compared to the analytical predictions. The theoretical framework is applicable to any scalar field embedded in the membrane, and although in this work the authors treat flat membranes, the methodology extends readily to curved geometries. Neglecting fluctuations, both lipid composition profile and induced protein pair potential are predicted to follow a zeroth order modified Bessel function of the second kind with the same characteristic decay length. These predictions are consistent with our molecular dynamics simulations, except that the interaction range is found to be larger than the single profile correlation length.

Effect of surface curvature on critical adsorption

We studied critical adsorption on curved surfaces by utilizing spherical nanoparticles immersed in a critical binary liquid mixture of 2,6 lutidine+water. The temperature dependence of the adsorbed film thickness and excess adsorption was determined from fluorescence correlation spectroscopy measurements of the enlarged effective hydrodynamic radius of the particles. Our results indicated that the adsorbed film thickness is of the order of correlation length associated with concentration fluctuations. The excess adsorption per unit area increases following a power law in reduced temperature with an exponent of -1, which is the mean-field value for the bulk susceptibility exponent. This has been confirmed with silica particles of two different radii, 10 and 25 nm. The results were also compared with the theoretical mean-field scaling function.

Direct observation of colloidal aggregation by critical Casimir forces

We present a refractive-index-matched colloidal system that allows direct observation of critical Casimir induced aggregation with a confocal microscope. We show that in this system, in which van der Waals forces are negligible, a simple competition between repulsive screened Coulomb and attractive critical Casimir forces can account quantitatively for the reversible aggregation. Above the temperature T(a), the critical Casimir force drives aggregation of the particles into fractal clusters, while below T(a), the electrostatic repulsion between the particles breaks up the clusters, and the particles resuspend by thermal diffusion. The aggregation is observed in a remarkably wide temperature range of as much as 15 degrees. We derive a simple expression for the particle pair potential that accounts quantitatively for the temperature-dependent aggregation and aggregate breakup.

Wetting-induced depletion interaction between particles in a phase-separating liquid mixture

Inclusion of solid particles drastically affects the pattern evolution of phase separation of a binary fluid mixture, via preferential wetting of one of the phases to the particles. Here we study this problem by numerical simulation, which incorporates interparticle hydrodynamic interactions properly. When particles favor one of the components of a mixture, wetting layers are quickly formed on the particle surfaces and all particles are eventually included into the more wettable phase. For immobile particles, domains of the more wettable phase are pinned to the particles and the domain growth is thus suppressed. For this case, the domain size at a certain phase-separation time decreases monotonically with increasing the particle concentration. For mobile particles, on the other hand, the reentrant morphological transformation is observed as a function of the particle concentration: With an increase in the particle concentration, the domain morphology of the more wettable phase sequentially changes from network, droplet to network. We found that the final morphological transition is induced by wetting-induced depletion interaction: strong attractive interactions act among particles when the total volume of the more wettable phase is not enough to cover all the particles by wetting layers.

Colloidal aggregation in polymer blends

We consider here a low-density assembly of colloidal particles immersed in a critical polymer mixture of two chemically incompatible polymers. We assume that, close to the critical point of the free mixture, the colloids prefer to be surrounded by one polymer (critical adsorption). As result, one is assisted to a reversible colloidal aggregation in the nonpreferred phase, due the existence of a long-range attractive Casimir force between particles. This aggregation is a phase transition driving the colloidal system from dilute to dense phases, as the usual gas-liquid transition. We are interested in a quantitative investigation of the phase diagram of the immersed colloids. We suppose that the positions of particles are disordered, and the disorder is quenched and follows a Gaussian distribution. To apprehend the problem, use is made of the standard phi(4) theory, where the field phi represents the composition fluctuation (order parameter), combined with the standard cumulant method. First, we derive the expression of the effective free energy of colloids and show that this is of Flory-Huggins type. Second, we find that the interaction parameter u between colloids is simply a linear combination of the isotherm compressibility and specific heat of the free mixture. Third, with the help of the derived effective free energy, we determine the complete shape of the phase diagram (binodal and spinodal) in the (Psi,u) plane, with Psi as the volume fraction of immersed colloids. The continuous "gas-liquid" transition occurs at some critical point K of coordinates (Psi(c) = 0.5,u(c) = 2). Finally, we emphasize that the present work is a natural extension of that, relative to simple liquid mixtures incorporating colloids.

Domain formation induced by the adsorption of charged proteins on mixed lipid membranes

Peripheral proteins can trigger the formation of domains in mixed fluid-like lipid membranes. We analyze the mechanism underlying this process for proteins that bind electrostatically onto a flat two-component membrane, composed of charged and neutral lipid species. Of particular interest are membranes in which the hydrocarbon lipid tails tend to segregate owing to nonideal chain mixing, but the (protein-free) lipid membrane is nevertheless stable due to the electrostatic repulsion between the charged lipid headgroups. The adsorption of charged, say basic, proteins onto a membrane containing anionic lipids induces local lipid demixing, whereby charged lipids migrate toward (or away from) the adsorption site, so as to minimize the electrostatic binding free energy. Apart from reducing lipid headgroup repulsion, this process creates a gradient in lipid composition around the adsorption zone, and hence a line energy whose magnitude depends on the protein's size and charge and the extent of lipid chain nonideality. Above a certain critical lipid nonideality, the line energy is large enough to induce domain formation, i.e., protein aggregation and, concomitantly, macroscopic lipid phase separation. We quantitatively analyze the thermodynamic stability of the dressed membrane based on nonlinear Poisson-Boltzmann theory, accounting for both the microscopic characteristics of the proteins and lipid composition modulations at and around the adsorption zone. Spinodal surfaces and critical points of the dressed membranes are calculated for several different model proteins of spherical and disk-like shapes. Among the models studied we find the most substantial protein-induced membrane destabilization for disk-like proteins whose charges are concentrated in the membrane-facing surface. If additional charges reside on the side faces of the proteins, direct protein-protein repulsion diminishes considerably the propensity for domain formation. Generally, a highly charged flat face of a macroion appears most efficient in inducing large compositional gradients, hence a large and unfavorable line energy and consequently lateral macroion aggregation and, concomitantly, macroscopic lipid phase separation.

Macroion-induced compositional instability of binary fluid membranes

Macroion adsorption on a mixed, fluid, lipid membrane containing oppositely charged lipids induces local changes in lipid composition at the interaction zones, and gradients at their boundaries. Including these effects in the free energy of the macroion-dressed membrane we derive its spinodal equation, and show that nonideal lipid mixing can lead to (lipid-mediated) attraction between macroions and lateral phase separation in the composite membrane. The critical nonideality for this transition is substantially smaller than that of the bare lipid membrane, decreasing with macroion size and charge. That is, the lipid membrane is destabilized by macroion adsorption.

Contribution of physical clusters to phase behavior

In a multicomponent fluid mixture, each physical cluster generated as an ensemble consisting of particles joined by each particle pair characterized by a bound state E(ij)+u(ij)</=0 can contribute towards prohibiting a transition from its macroscopically homogeneous phase to its macroscopically inhomogeneous phase. Here, E(ij) and u(ij) represent the relative kinetic energy and the pair potential for the pair of i and j particles, respectively. Branches constructing such physical clusters can confine unbound particles (i.e., particles constituting pairs characterized by an unbound state E(ij)+u(ij)>0) within regions surrounded by the branches, and can prohibit the boundaries of the regions from expanding freely. Particles belonging to one of the two groups characterizing constituents of a multicomponent fluid mixture (particles of A) should have a tendency to satisfy the condition E(ij)+u(ij)</=0; particles belonging to the other group (particles of B) should have a tendency to satisfy the condition E(ij)+u(ij)>0. The pair connectedness P(ij)(sigma) proportional to the probability that a particle of A is bound near another particle of A hardly varies as densities of particles of A increase, although the mean physical cluster size diverges to infinity as the densities approach values specified at the percolation threshold. Thus, each physical cluster should grow toward that having a larger span as densities of particles of A increase. According to this growth of physical clusters, the number of unbound particles confined by branches of the physical clusters is enhanced. The formation of physical clusters of particles of A can be considered as a primary phenomenon resulting in density fluctuations. Their formation results in the confinement of particles of B and A within regions surrounded by the branches of the physical clusters.

Geometric view on colloidal interactions above the nematic-isotropic phase transition

Particles dispersed in a liquid crystal above the nematic-isotropic phase transition are surrounded by a surface-induced nematic wetting layer. When the nematic coronas of two particles overlap, they experience a strong attraction since the volume of nematic ordering and therefore the free energy is reduced. For normal anchoring of the liquid-crystal molecules on the particles' surfaces, we demonstrate that the implementation of this geometric view reproduces the Yukawa interaction derived by Galatola and Fournier in a recent paper [Phys. Rev. Lett. 86, 3915 (2001)], however with half the strength. To understand the factor 2, we rederive the Yukawa potential with the approximation of linear superposition of two one-particle profiles. At the end, we comment on the similarities of our approach to the screened electrostatic interaction of charged colloids.

Determination of the interaction force between two adsorptive surfaces delimiting a critical binary polymer blend

We consider a mixture of two incompatible polymers A and B, confined between two parallel surfaces of the same chemical nature, separated by a distance L. It is assumed that both surfaces strongly adsorb one of the species (A) at high temperature. It is also assumed that a demixing transition occurs at a critical temperature T(c) below the adsorption temperature T(a). The strong adsorption implies that the composition of species A on surfaces is quenched even when the temperature is lowered. The presence of strong density fluctuations near the critical point induces an interaction between the surfaces. We reexamine this attractive force and determine its dependence with the thickness L, when the latter is smaller than the thermal correlation length. We find that, in the vicinity of the critical point, this force decreases with distance as L-4. We show that the corresponding amplitude is a universal number, independent of the value of the composition on surfaces, and we give its exact expression. Finally, we note that the present system may be considered as a typical model enabling one to understand qualitatively and quantitatively the flocculation of colloids embedded in critical binary polymer blends.

Wetting-induced effective interaction potential between spherical particles

Using a density-functional-based interface displacement model, we determine the effective interaction potential between two spherical particles which are immersed in a homogeneous fluid such as the vapor phase of a one-component substance or the A-rich liquid phase of a binary liquid mixture composed of A and B particles. If this solvent is thermodynamically close to a first-order fluid-fluid phase transition, the spheres are covered with wetting films of the incipient bulk phase, i.e., the liquid phase or the B-rich liquid, respectively. Below a critical distance between the spheres their wetting films snap to a bridgelike configuration. We determine phase diagrams for this morphological transition, and analyze its repercussions on the effective interaction potential. Our results are accessible to various types of force microscopy and scattering experiments, and may be relevant to flocculation in colloidal suspensions.

Critical adsorption on curved objects

A systematic field-theoretical description of critical adsorption on curved objects such as spherical or rodlike colloidal particles immersed in a fluid near criticality is presented. The temperature dependence of the corresponding order parameter profiles and of the excess adsorption are calculated explicitly. Critical adsorption on elongated rods is substantially more pronounced than on spherical particles. It turns out that, within the context of critical phenomena in confined geometries, critical adsorption on a microscopically thin "needle" represents a distinct universality class of its own. Under favorable conditions the results are relevant for the flocculation of colloidal particles.