Soft repulsive mixtures under gravity: brazil-nut effect, depletion bubbles, boundary layering, nonequilibrium shaking

A binary mixture of particles interacting via long-ranged repulsive forces is studied in gravity by computer simulation and theory. The more repulsive A-particles create a depletion zone of less repulsive B-particles around them reminiscent to a bubble. Applying Archimedes' principle effectively to this bubble, an A-particle can be lifted in a fluid background of B-particles. This "depletion bubble" mechanism explains and predicts a brazil-nut effect where the heavier A-particles float on top of the lighter B-particles. It also implies an effective attraction of an A-particle towards a hard container bottom wall which leads to boundary layering of A-particles. Additionally, we have studied a periodic inversion of gravity causing perpetuous mutual penetration of the mixture in a slit geometry. In this nonequilibrium case of time-dependent gravity, the boundary layering persists. Our results are based on computer simulations and density functional theory of a two-dimensional binary mixture of colloidal repulsive dipoles. The predicted effects also occur for other long-ranged repulsive interactions and in three spatial dimensions. They are therefore verifiable in settling experiments on dipolar or charged colloidal mixtures as well as in charged granulates and dusty plasmas.     

Depletion potentials induced by charged colloidal rods

We present direct depletion potential measurements for a single colloidal sphere close to a wall in suspensions of charged colloidal rods. In contrast to earlier studies of purely entropic systems (Helden et al. Phys. Rev. Lett. 2003, 90, 048301), here electrostatic interactions are important. These enhance the depletion attraction and lead to repulsive parts in the interaction potentials, indicating correlation effects between the rods.     

Effect of grafting on nanoparticle segregation in polymer/nanoparticle blends near a substrate

Nanoparticles in polymer films have shown the tendency to migrate to the substrate due to an entropic-based attractive depletion interaction between the particles and the substrate. It is also known that polymer-grafted nanoparticles show better dispersion in a polymer matrix. Here, molecular dynamics simulations are employed to study the effect of grafting on the nanoparticle segregation to the substrate. The nanoparticles were modeled as spheres and the polymers as bead-spring chains. The polymers of the grafts and the matrix are identical in nature. For a purely repulsive system, the nanoparticle density near the surface was found to decrease as the length of grafted chains and the number of grafts increased and in the bulk, the nanoparticles are well-dispersed. Whereas, in case of attractive systems with interparticle interactions on the order of thermal energy, the nanoparticles segregated to the substrate even more strongly, essentially forming clusters on the wall and in the bulk. However, due to the presence of grafted chains on the nanoparticles, the clusters formed in the bulk are structurally anisotropic. The effect of grafts on nanoparticle segregation to the surface was found to be qualitatively similar to the purely repulsive case.     

Prediction and measurement of the interparticle depletion interaction next to a flat wall

A theoretical and experimental study was performed to investigate the depletion interaction between two colloidal particles next to a solid wall in a solution of nonadsorbing macromolecules. By calculating the change in free volume available to the macromolecules upon approach of the two particles, a relatively simple expression was developed for the interparticle depletion attraction in hard sphere systems as a function of the particle-particle and particle-plate spacing. Perhaps the most useful result obtained from this analysis was that the wall has no effect whenever the ratio of the particle radius to the macromolecule radius is greater than four. (In charged systems, this ratio would apply to the effective particle and macromolecule sizes.) A series of experiments was then performed in which the hydrodynamic force balance (HFB) apparatus was used to measure the shear force needed to separate a colloidal doublet consisting of two particles trapped in a secondary energy well formed by a repulsive electrostatic force and an attractive depletion force. The macromolecules used here were small, nanometer-sized spheres of either silica or polystyrene. Agreement between the measured separation forces and those predicted using the force balance model of J. Y. Walz and A. Sharma (J. Colloid Interface Sci. 168, 485 (1994)) was within a factor of 1.3 using no adjustable parameters and accounting for polydispersity and uncertainty in the macromolecule size. It is shown that this remaining discrepancy could be caused by the Brownian (stochastic) nature of the doublet breakup process.     

Internal and free energy in a pair of like-charged colloids: Monte Carlo simulations

The effective interaction between two colloidal particles in a bath of monovalent co- and counterions is studied by means of lattice Monte Carlo simulations with the primitive model. The internal electrostatic energy as a function of the colloid distance is studied fixing the position of the colloids. The free energy of the whole system is obtained introducing a bias parabolic potential, that allows us to sample efficiently small separations between the colloidal particles. For small charges, both the internal and free energy increase when the colloids approach each other, resulting in an effective repulsion driven by the electrostatic repulsion. When the colloidal charge is large enough, on the other hand, the colloid-ion coupling is strong enough to form double layers. The internal energy in this case decreases upon approaching the colloids because more ions enter the double layer. This attractive contribution to the interaction between the colloids is stronger for larger charges and larger ionic concentrations. However, the total free energy increases due to the loss of ionic entropy, and resulting finally in a repulsive interaction potential driven by the entropic contributions. The loss of ionic entropy can be almost quantitatively reproduced with the ideal contribution, the same level of approximation as the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. The overall behavior is captured by the DLVO theory qualitatively, and a comparison is made with the functional form predicted by the theory, showing moderate agreement.     

Interaction forces measured between poly(N-isopropylacrylamide) grafted surface and hydrophobic particle

The interaction forces between poly(N-isopropylacrylamide) (PNIPAAm)-grafted surfaces and colloidal particles in an aqueous solution were investigated using an atomic force microscope. Measurements were conducted between smooth silicon wafers on which PNIPAAm was terminally grafted and silica particles hydrophobized with a silanating reagent in an aqueous electrolyte solution under controlled temperature. Below the lower critical solution temperature (LCST) of PNIPAAm, there were large repulsive forces between the surfaces, both on approach and separation of the surfaces. On the other hand, above LCST, attractive forces were observed both in approaching and in separating force curves. When surface hydrophobicity of the particles increased, the maximum attractive force tended to increase. The changes of hydration state of the grafted PNIPAAm chains depending on temperature are considered to greatly alter the interaction force properties. The role of the intermolecular interaction between the PNIPAAm chains and the hydrophobic particles in the interaction forces is discussed.     

Interactions between polymer brushes in solvents of variable quality: a density functional theory study

We present a density functional theory study of interactions between sterically stabilized colloidal particles in solvents of variable quality. Both flat and spherical polymer brushes are considered, as well as both monatomic and polymeric solvents. It is shown that the interaction between sterically stabilized particles can be tuned from repulsive to attractive by varying the solvent quality, the relative length of free and grafted chains, and by employing a mixed brush consisting of both well and poorly solvated chains.     

Depletion-induced phase separation in colloid-polymer mixtures

Phase separation can be induced in a colloidal dispersion by adding non-adsorbing polymers. Depletion of polymer around the colloidal particles induces an effective attraction, leading to demixing at sufficient polymer concentration. This communication reviews theoretical and experimental work carried out on the polymer-mediated attraction between spherical colloids and the resulting phase separation of the polymer-colloid mixture. Theoretical studies have mainly focused on the limits where polymers are small or large as compared to the colloidal size. Recently, however, theories are being developed that cover a wider colloid-polymer size ratio range. In practical systems, size polydispersity and polyelectrolytes (instead of neutral polymers) and/or charges on the colloidal surfaces play a role in polymer-colloid mixtures. The limited amount of theoretical work performed on this is also discussed. Finally, an overview is given on experimental investigations with respect to phase behavior and results obtained with techniques enabling measurement of the depletion-induced interaction potential, the structure factor, the depletion layer thickness and the interfacial tension between the demixed phases of a colloid-polymer mixture.     

Direct measurement of weak depletion force between two surfaces

In a mixture of colloidal particles and polymer molecules,the particles may experience an attractive"depletion force"if the size of the polymer molecule is larger than the interparticle separation.This is because individual polymer molecules experience less conformational entropy if they stay between the particles than they escape the inter-particle space, which results in an osmotic pressure imbalance inside and outside the gap and leads to interparticle attraction.This depletion force has been the subject of several studies since the 1980s,but the direct measurement of this force is still experimentally challenging as it requires the detection of energy variations of the order of k_BT and beyond.We present here our results for applying total internal reflection microscopy(TIRM) to directly measure the interaction between a free-moving particle and a flat surface in solutions consisting of small water-soluble organic molecules or polymeric surfactants.Our results indicate that stable nanobubbles(ca.150 nm) exist free in the above aqueous solutions.More importantly,the existence of such nanobubbles induces an attraction between the spherical particle and flat surface.Using TIRM,we are able to directly measure such weak interaction with a range up to 100 nm.Furthermore,we demonstrate that by employing thermo-sensitive microgel particles as a depleting agent,we are able to quantitatively measure and reversibly control k_BYT-scale depletion attraction as function of solution pH.     

Direct imaging of repulsive and attractive colloidal glasses

Coherent anti-Stokes Raman scattering microscopy is performed on glassy systems of poly(methylmethacrylate) colloidal particles in density- and refractive-index-matched solvents. Samples are prepared with varying amounts of linear polystyrene, which induces a depletion driven attraction between the nearly hard-sphere particles. Images collected over several hours confirm the existence of a reentrant glass transition. The images also reveal that the dynamics of repulsive and attractive glasses are qualitatively different. Colloidal particles in repulsive glasses exhibit cage rattling and escape, while those in attractive glasses are nearly static while caged but exhibit large displacements upon (infrequent) cage escape.     

Potential barrier gravitational field-flow fractionation based on the variation of the pH solution for the analysis of colloidal materials

Summary Potential barrier gravitational field-flow fractionation (PBGFFF) is a new technique for the separation and characterization of colloidal materials. It consists in changing the potential energy of interaction between the colloidal particles and the channel wall by varying the solution ionic strength or the Hamaker constant and the surface potential of the particles. In this work the PBGFFF technique based on the particles' surface potential variation, by varying the pH, is presented. Polydisperse colloidal particles of the sulphide CuZnS (with molar ratio Cu/Zn-10/90) are used as a model sample. Comparison of the results obtained by PBGFFF with those given by conventional gravitational fieldflow fractionation and laser counter measurements, shows that one could use PBGFFF not only for the separation and characterization of colloidal materials, but also for the investigation of the interactions between colloids and solid surfaces.     

Thermodynamically stable dispersions induced by depletion interactions

When small particles are added to a colloidal dispersion of large particles, a depletion interaction between large particles occurs because the small ones are depleted from the gaps between the former particles. In the present paper, a cell model is employed to examine the behavior of a dispersion of large particles immersed in an electrolyte solution containing small particles. In this model, each cell consists of one large particle in its center and an associated atmosphere. Double-layer, van der Waals, and depletion interactions, as well as entropic effects, have been taken into account. When the change of the free energy with respect to that of the electrolyte solution is negative (and this happens in most cases), the dispersions of large particles are stable from a thermodynamic point of view. With increasing volume fraction of the small particles, the free energy change becomes more negative. The formation of gels observed experimentally in concentrated emulsions is explained through the formation of a thermodynamically stable dispersion.     

Cylindrical inclusions in a copolymer membrane

The membrane-mediated interaction between two parallel, cylindrical inclusions is investigated by using the self-consistent field theory (SCFT). The rodlike inclusions are located within the interior of the bilayer and are enveloped by two monolayers. They may exhibit one of the two basic types of behaviors involving pinching two monolayers together and swelling them outward. For different parameters, we calculate the density profile of the deformation membrane, the associated interaction free energy, as well as the conformational entropy of polymer chains. The similarity of the two types of interaction potentials is the qualitative characteristics. An energy barrier separates an attractive from a repulsive region; the repulsive region is preceded by a weak attraction at a large distance. The difference between them, which is due to the different contact environments around the rods, lies in the appearance of a small barrier at a short distance in the pinching structure. Particular emphasis is put on the closely energetic and entropic analyses of the interaction potential. We show that the chemical potential energy has provided a qualitative trend and roughly dominated the basic shape of the interaction potential; the amphiphile entropy in the swelling structure and the solvent entropy in the pinching structure, combined with the corresponding chemical potential energy, are responsible for the repulsive barrier at an intermediate distance and for the weak attraction at a large distance, respectively. The influence of inclusion hydrophobicity on the interaction potential is taken into account. In particular, the pinching and swelling structures can appear and can transform into each other in a system at intermediate hydrophobicity.     

Dielectrophoretic levitation in the presence of shear flow: implications for colloidal fouling of filtration membranes

The ability of dielectrophoretic (DEP) forces created using a microelectrode array to levitate particles in a colloidal suspension is studied experimentally and theoretically. The experimental system employs microfabricated electrode arrays on a glass substrate to apply repulsive DEP forces on polystyrene latex particles suspended in an aqueous medium. A numerical model based on the convection-diffusion-migration equation is presented to calculate the concentration distribution of colloidal particles in shear flow under the influence of a repulsive DEP force field. The results obtained from the numerical simulations are compared against trajectory analysis results and experimental data. The results indicate that by incorporating ac electric field-induced DEP forces in a shear flow, particle accumulation and deposition on the flow channel surfaces can be significantly reduced or even completely averted. The mathematical model is then used to indicate how the deposition behavior is modified in the presence of a permeable substrate, representative of tangential flow membrane filtration operations. The results indicate that the repulsive dielectrophoretic (DEP) forces imparted to the particles suspended in the feed can be employed to mitigate membrane fouling in a cross-flow filtration process.     

Steric stabilization of spherical colloidal particles: Implicit and explicit solvent

We present the results of Monte Carlo simulations and density functional theory treatment of interactions between spherical colloidal brushes both in implicit (good) solvent and in an explicit polymeric solution. Overall, theory is seen to be in good agreement with simulations. We find that interactions between hard-sphere particles grafted with hard-sphere chains are always repulsive in implicit solvent. The range and steepness of the repulsive interaction is sensitive to the grafting density and the length of the grafted chains. When the brushes are immersed in an explicit solvent of hard-sphere chains, a weak mid-range attraction arises, provided the length of the free chains exceeds that of the grafted chains.     

The influence of micelle formation on the stability of colloid surfactant mixtures

The stability of colloidal dispersions can be severely affected by the presence of surfactants. Because surfactants can adsorb at colloidal surfaces as well as form micelles, one can expect an interplay between both phenomena. Using grand-canonical coarse-grained Monte Carlo simulations on surfactant solutions confined between two surfaces, we investigate how adsorption and micelle formation affects the effective interaction between two colloidal particles, and hence, the stability of the colloidal dispersion. For solvophilic colloidal surfaces, we observe a short-ranged oscillatory solvation pressure that is hardly affected by the presence of surfactants in the system. The effective surface-surface interaction, however, reveals a decrease in solvophilic stabilization as a function of surfactant chemical potential. For solvophobic surfaces, we find that the capillary evaporation observed in a confined pure solvent, is counteracted by the addition of surfactants. Around the critical micelle concentration (CMC), the surface-surface interaction even becomes repulsive, enhancing stabilization of the colloidal dispersion. In contrast, the formation of micelles at concentrations above the CMC causes an additional depletion effect, resulting in an effective attraction, which in turn can destabilize a colloidal dispersion.     

分散体系中任意形状的胶粒模型与相互作用能——Ⅲ. 园柱体型颗粒

在分散体系的研究中,也经常遇到园柱体型胶粒,例如蛋白质分子,海泡石和凸凹棒石粘土颗粒,它们都能用带电的园柱体型采近似处理。这种类型的颗粒以往研究不多,其原因大约有二,一是处理这类颗粒时,数学上的困难很大;二是这类颗粒之间的相互作用,和它们之间的取向有关。Sparnaay首先用Derjaguin法得出园柱体型颗粒处于平行和垂直位置时,相互排斥能的近似表达式。Brenner和McQuarrie(BM)对颗粒外的电位分布采     

Relationships between the single particle barrier hopping theory and thermodynamic, disordered media, elastic, and jamming models of glassy systems

The predictions of the ultralocal limit of the activated hopping theory of highly viscous simple fluids and colloidal suspensions [K. S. Schweizer and G. Yatsenko, J. Chem. Phys. 127, 164505 (2007), preceding paper] for the relaxation time and effective activation barrier are compared with those of diverse alternative theoretical approaches and computer simulation. A nonlinear connection between the barrier height and excess pressure as empirically suggested by simulations of polydisperse repulsive force fluids is identified. In the dense normal and weakly dynamical precursor regime, where entropic barriers of hard spheres are nonexistent or of order the thermal energy, agreement with an excess entropy ansatz is found. In the random close packing or jamming limit, the barrier hopping theory predicts an essential singularity stronger than the free volume model, which is in agreement with the simplest entropic droplet nucleation and replica field theoretic approaches. Upon further technical simplification of the theory, close connections with renormalization group and nonperturbative memory function based studies of activated transport of a Brownian particle in a disordered medium can been identified. Several analytic arguments suggest a qualitative consistency between the barrier hopping theory and solid-state elastic models based on the high frequency shear modulus and a molecular-sized apparent activation volume. Implications of the analysis for the often high degeneracy of conflicting explanations of glassy dynamics are discussed.     

Electrical double-layer effects on the deposition of zeolite A on surfaces

Zeolite particles formed from an aluminosilicate solution possess a negative surface charge due to the substitution of aluminum atoms into a SiO4 tetrahedral structure making it difficult to form a continuous layer in solution. The particle interactions with surfaces and each other can be studied using the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. The interaction energy between zeolite-zeolite and zeolite-substrate on various materials can be estimated in this fashion. The zeolite LTA particles show a stronger repulsion interaction on all substrates and on the each other as compared to the ZSM-5 particles. This repulsive energy also increases as the particles size increases. This results in the formation of conglomerate in the solution rather than forming an adhered layer on the substrate.