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.     

Active colloids on fluid interfaces

We review recent work on active colloids at interfaces, including self-propelled colloids that move by generating a propulsive force, and driven colloids that move under external fields. Features unique to fluid interfaces alter the flows generated at interfaces by active colloid motion, and hydrodynamic interactions with these layers. We emphasize recent observations of natural swimmers, like bacteria, and bio-mimetic colloids including self-propelled phoretic and Marangoni swimmers, and magnetically driven colloids. We discuss active colloid interaction with boundaries and with each other. We conclude with a discussion of open issues and opportunities to design active colloids as active surface agents that manipulate interfacial properties and the transport in the vicinity of interfaces.     

Effects of colloid polydispersity on the phase behavior of colloid-polymer mixtures

We study theoretically the equilibrium phase behavior of a mixture of polydisperse hard-sphere colloids and monodisperse polymers, modeled using the Asakura-Oosawa model [S. Asakura and F. Oosawa, J. Chem. Phys. 22, 1255 (1954)] within the free volume approximation of H. N. W. Lekkerkerker, W. C. K. Poon, P. N. Pusey, A. Stroobants, and P. B. Warren [Europhys. Lett. 20, 559 (1992)]. We compute full phase diagrams in the plane of colloid and polymer volume fractions, using the moment free energy method. The intricate features of phase separation in pure polydisperse colloids combine with the appearance of polymer-induced gas-liquid coexistence to give a rich variety of phase diagram topologies as the polymer-colloid size ratio xi and the colloid polydispersity delta are varied. Quantitatively, we find that polydispersity disfavors fluid-solid against gas-liquid separation, causing a substantial lowering of the threshold value xi(c) above which stable two-phase gas-liquid coexistence appears. Phase splits involving two or more solids can occur already at low colloid concentration, where they may be kinetically accessible. We also analyze the strength of colloidal size fractionation. When a solid phase separates from a fluid, its polydispersity is reduced most strongly if the phase separation takes place at low colloid concentration and high polymer concentration, in agreement with experimental observations. For fractionation in gas-liquid coexistence we likewise find good agreement with experiment, as well as with perturbative theories for near-monodisperse systems.     

Ligand-receptor interactions in chains of colloids: when reactions are limited by rotational diffusion

We discuss the theory of ligand receptor reactions between two freely rotating colloids in close proximity to one other. Such reactions, limited by rotational diffusion, arise in magnetic bead suspensions where the beads are driven into close contact by an applied magnetic field as they align in chainlike structures. By a combination of reaction-diffusion theory, numerical simulations, and heuristic arguments, we compute the time required for a reaction to occur in a number of experimentally relevant situations. We find in all cases that the time required for a reaction to occur is larger than the characteristic rotation time of the diffusion motion tau(rot). When the colloids carry one ligand only and a number n of receptors, we find that the reaction time is, in units of tau(rot), a function simply of n and of the relative surface alpha occupied by one reaction patch alpha = pirC2/(4pir2), where rC is the ligand receptor capture radius and r is the radius of the colloid.     

Distribution of counterions around lignosulfonate macromolecules in different polar solvent mixtures

Lignosulfonate is a colloidal polyelectrolyte that is obtained as a side product in sulfite pulping. In this work we wanted to study the noncovalent association of the colloids in different solvents, as well as to find out how the charged sulfonate groups are organized on the colloid surface. We studied sodium and rubidium lignosulfonate in water-methanol mixtures and in dimethyl formamide. The number average molecular weights of the Na- and Rb-lignosulfonate fractions were 7600 g/mol and 9100 g/mol, respectively, and the polydispersity index for both was 2. Anomalous small-angle X-ray scattering (ASAXS) was used for determining the distribution of counterions around the Rb-lignosulfonate macromolecules. The scattering curves were fitted with a model constructed from ellipsoids of revolution of different sizes. Counterions were taken into account by deriving an approximative formula for the scattering intensity of the Poisson-Boltzmann diffuse double layer model. The interaction term between the spheroidal particles was estimated using the local monodisperse approximation and the improved Hayter-Penfold structure factor given by the rescaled mean spherical approximation. Effective charge of the polyelectrolyte and the local dielectric constant of the solvent close to the globular polyelectrolyte were followed as a function of the methanol content in the solvent and lignosulfonate concentration. The lignosulfonate macromolecules were found to aggregate noncovalently in water-methanol mixtures with increasing methanol or lignosulfonate content in a specific directional manner. The flat macromolecule aggregates had a nearly constant thickness of 1-1.4 nm, while their diameter grew when counterion association onto the polyelectrolyte increased. These results indicate that the charged groups in lignosulfonate are mostly at the flat surfaces of the colloid, allowing the associated lignosulfonate complexes to grow further at the edges of the complex.     

Janus and multiblock colloidal particles

We review recent developments in the synthesis and self-assembly of Janus and multiblock colloidal particles, highlighting new opportunities for colloid science and technology that are enabled by encoding orientational order between particles as they self-assemble. Emphasizing the concepts of molecular colloids and colloid valence unique to such colloids, we describe their rational self-assembly into colloidal clusters, taking monodisperse tetrahedra as an example. We also introduce a simple method to lock clusters into permanent shapes. Extending this to 2D lattices, we also review recent progress in assembling new open colloidal networks including the kagome lattice. In each application, areas of opportunity are emphasized.     

Long-time self-diffusion of charged colloidal particles: electrokinetic and hydrodynamic interaction effects

The authors analyze the long-time self-diffusion of charge-stabilized colloidal macroions in nondilute suspensions using a mode-coupling scheme developed for multicomponent suspensions of interacting Brownian spheres. In this scheme, all ionic species, including counterions and electrolyte ions, are treated on an equal footing as charged hard spheres undergoing overdamped Brownian motion. Hydrodynamic interactions between all ions are accounted for on the far-field level. We show that the influence on the colloidal long-time self-diffusion coefficient arising from the relaxation of the microionic atmosphere surrounding the colloids, the so-called electrolyte friction effect, is usually insignificant in comparison with the friction contributions arising from direct and hydrodynamic interactions between the colloidal particles. This finding is true even for small colloid concentrations unless the mobility difference between colloidal particles and microions is not large. Furthermore, we observe an interesting nonmonotonic density dependence of the colloidal long-time self-diffusion coefficient in suspensions with low amount of added salt. We show that this unusual density dependence is due to colloid-colloid hydrodynamic interactions.     

Two-fluid model for the simultaneous flow of colloids and fluids in porous media

To describe the velocities of particles such as ions, protein molecules and colloids dispersed or dissolved in a fluid, it is important to also describe the forces acting on the fluid, including pressure gradients and friction of the fluid with the particles and with the porous media through which the fluid flows. To account for this problem, the use of a two-fluid model is described, familiar in the field of fluid mechanics, extended to include osmotic effects. We show how familiar relationships follow in various situations and give examples of combined fluid/particle transport in neutral and charged membranes driven by a combination of electrostatic, diffusional and pressure forces. The analysis shows how the same modeling framework can be generally used both for multidimensional electrokinetic flow through macroscopic channels and around macroscopic objects, as well as for mean-field modeling of transport through porous media such as gels and membranes.     

Colloid dispersion in a uniform-aperture fracture

This research investigates the dispersion of colloids through fracture systems by exploring experimentally and numerically the transport and dispersion of 1.0-, 0.11-, and 0.043-mum diameter fluorescent carboxylate-modified microspheres and chloride at various flow rates through variable-length, synthetic Plexiglas fractures (flow cells). A dimensionless number describing each experiment is varied by changing the colloid size, flow rate, and fracture length. Surface characteristics of the microspheres and Plexiglas favor repulsive interactions, thereby minimizing the chance of colloid filtration and remobilization. Full recovery of the colloids is typically observed, thereby supporting the assumption of negligible colloid filtration. In comparison to chloride transport, there is increased tailing for colloid plumes traveling through the flow cell. This increased tailing is attributed to Taylor dispersion phenomena (dispersion due to an advection gradient). In the synthetic fractures investigated here, colloid dispersion due to the velocity gradient is evident, but fully developed Taylor conditions are not realized. A particle-tracking algorithm is run inversely to estimate the effective dispersion rate for the colloid plume in each experiment as a function of the experimental parameters (flow rate, fracture length, and colloid size). Results suggest that the log of the effective dispersion rate of the colloid plume increases linearly with the log of the dimensionless number comprising experimental parameters.     

Sedimentation–diffusion profiles and layered sedimentation of charged colloids at low ionic strength

We report the formation of strongly inflated sedimentation–diffusion concentration profiles for charged monodisperse colloidal spheres in absolute ethanol. Various additional experiments, such as light scattering, confirm that the very dilute supernatants, left behind by the majority of settling colloids, contain spheres that repel each other at distances of micrometers. We attribute these unusual profiles to a significant counter-ion contribution to the osmotic pressure and to the Debye screening length. An approximate osmotic equation-of-state at the level of the second virial coefficient for dispersions at very low ionic strength indeed implies an algebraic long-distance decay of sedimentation–diffusion profiles, together with significant lowering of the effective colloid mass by an entropic lift due to counter-ions. We have also observed that sedimenting dispersions sometimes demix into two layers, which are both disordered fluids. Since the colloids are clearly repulsive on the DLVO pair level, this layering possibly manifests a phase transition driven by many-body attractions.     

Detachment of colloids from a solid surface by a moving air-water interface

Colloid attachment to liquid–gas interfaces is an important process used in industrial applications to separate suspended colloids from the fluid phase. Moving gas bubbles can also be used to remove colloidal dust from surfaces. Similarly, moving liquid–gas interfaces lead to colloid mobilization in the natural subsurface environment, such as in soils and sediments. The objective of this study was to quantify the effect of moving air–water interfaces on the detachment of colloids deposited on an air-dried glass surface, as a function of colloidal properties and interface velocity. We selected four types of polystyrene colloids (positive and negative surface charge, hydrophilic and hydrophobic). The colloids were deposited on clean microscope glass slides using a flow-through deposition chamber. Air–water interfaces were passed over the colloid-deposited glass slides, and we varied the number of passages and the interface velocity. The amounts of colloids deposited on the glass slides were visualized using confocal laser scanning microscopy and quantified by image analysis. Our results showed that colloids attached under unfavorable conditions were removed in significantly greater amounts than those attached under favorable conditions. Hydrophobic colloids were detached more than hydrophilic colloids. The effect of the air–water interface on colloid removal was most pronounced for the first two passages of the air–water interface. Subsequent passages of air–water interfaces over the colloid-deposited glass slides did not cause significant additional colloid removal. Increasing interface velocity led to decreased colloid removal. The force balances, calculated from theory, supported the experimental findings, and highlight the dominance of detachment forces (surface tension forces) over the attachment forces (DLVO forces).     

Melting line of charged colloids from primitive model simulations

We develop an efficient simulation method to study suspensions of charged spherical colloids using the primitive model. In this model, the colloids and the co- and counterions are represented by charged hard spheres, whereas the solvent is treated as a dielectric continuum. In order to speed up the simulations, we restrict the positions of the particles to a cubic lattice, which allows precalculation of the Coulombic interactions at the beginning of the simulation. Moreover, we use multiparticle cluster moves that make the Monte Carlo sampling more efficient. The simulations are performed in the semigrand canonical ensemble, where the chemical potential of the salt is fixed. Employing our method, we study a system consisting of colloids carrying a charge of 80 elementary charges and monovalent co- and counterions. At the colloid densities of our interest, we show that lattice effects are negligible for sufficiently fine lattices. We determine the fluid-solid melting line in a packing fraction eta-inverse screening length kappa plane and compare it with the melting line of charged colloids predicted by the Yukawa potential of the Derjaguin-Landau-Verwey-Overbeek theory. We find qualitative agreement with the Yukawa results, and we do not find any effects of many-body interactions. We discuss the difficulties involved in the mapping between the primitive model and the Yukawa model at high colloid packing fractions (eta>0.2).     

Interaction between colloids with grafted diblock polyampholytes

The interaction between composite colloidal particles composed of a spherical core and grafted AB-diblock polyampholytes (diblock copolymers with oppositely charged blocks) are investigated by using a coarse-grained model solved with Monte Carlo simulations. The B block is end-grafted onto the core of the colloid and its linear charge density is varied, whereas the linear charge density of the A block is fixed. The brush structure of a single colloid, the mean force between two colloids, and the structure of solutions of such colloids have been determined for different linear charge densities of the B blocks and block lengths. Many features of the present system are controlled by the charge of the B blocks. In the limit of uncharged B blocks, (i) the grafted chains are stretched and form an extended polyelectrolyte brush, (ii) a strong repulsive force is operating between two colloids, (iii) and the solution is thermodynamic stable and displays strong spatial correlation among the colloids. In the limit where the charges of the two types of blocks exactly compensate each other, (i) the chains are collapsed and form a polyelectrolyte complex surrounding the cores, (ii) an attractive force appears between two colloids, and (iii) strong colloid clustering appears in the solution. These features become more pronounced as the length of the polymer blocks is increased, and a phase instability occurs at sufficiently long chains. A comparison with properties for other related colloidal particles is also provided.     

Effective interactions in colloid-semipermeable membrane systems

We investigate effective interactions between a colloidal particle, immersed in a binary mixture of smaller spheres, and a semipermeable membrane. The colloid is modeled as a big hard sphere, and the membrane is represented as an infinitely thin surface, which is fully permeable to one of the smaller spheres and impermeable to the other one. Within the framework of the density functional theory, we evaluate depletion potentials and we consider two different approximate theories: the simple Asakura-Oosawa approximation and the accurate White-Bear version of the fundamental measure theory. The effective potentials are compared with the corresponding potentials for the hard, nonpermeable wall. Using statistical-mechanical sum rules, we argue that the contact value of the depletion potential between a colloid and a semipermeable membrane is smaller in magnitude than the potential between a colloid and a hard wall. A heuristic argument is provided that the colloid-semipermeable membrane effective interactions are generally weaker than these near a hard nonpermeable wall. These predictions are confirmed by explicit calculations, and the effect is more pronounced for smaller osmotic pressures. The depletion potential for a colloidal particle inside a semipermeable vesicle is stronger than the potential for the colloidal particle located outside of a vesicle. We find that the asymptotic decay of the depletion potential for the semipermeable membrane is similar to that for the nonpermeable wall and reflects the asymptotics of the total correlation function of the corresponding binary mixture of smaller spheres. Our results demonstrate that the ability of the membrane to change its shape as well as specific interactions constitute an important factor in determining the effective interactions between the semipermeable membrane and the colloidal macroparticle.     

Aqueous suspensions of charged spherical colloids: dependence of the surface charge on ionic strength, acidity, and colloid concentration

We theoretically investigate the dependence of the surface charge developed on charged spherical colloids upon several environmental parameters: the ionic strength of the monovalent added electrolyte, acidity (stabilized by a pH buffer solution), and colloid concentration. In the framework of the mean-field Poisson-Boltzmann spherical cell model, we include the charged colloid-microion correlations into the buffer equation, and we allow for the specific binding of ions to the ionizable groups on the colloid surface. Theoretical predictions are compared to the results obtained under the planar-symmetry Gouy-Chapman approximation and analyzed for the experimental conditions of an aqueous dispersion of the phospholipid dimyristoyl phosphatidylglycerol (DMPG). Experimental measurements of the partition ratio of an aqueous soluble cationic spin label on buffered dispersions of polyanionic unilamellar vesicles of DMPG in the presence of added monovalent salt are theoretically interpreted in terms of ion partition due to electrostatic interactions. We show that the specific binding of the probe must be admitted to explain the experimental results.     

Interactions between two bubbles on a hot or cold wall

A temperature gradient normal to a planar wall produces two-dimensional motion and aggregation or separation of bubbles on the hot or cold wall, respectively. The origin of the motion is fluid convection driven by the thermal Marangoni stress on the surface of the bubbles. Previous theories for the dynamics of two or more bubbles have been based on an analysis of flow about a single bubble and the resulting convection that entrains its neighbors. Here we extend the theory by solving the quasi-steady equations for the temperature and velocity fields for two bubbles. The result is a quantitative model for the relative velocity between two bubbles as a function of both the distance between them and the gap between each bubble and the surface. Interactions between the bubbles strongly increase the approach velocity, which is counter-intuitive because the hydrodynamic resistance increases as the bubbles approach each other. An asymptotic analysis indicates the thermocapillary force bringing them together or pushing them apart is singular in the separation when the bubbles are close to each other. The two-bubble theory agrees reasonably well with the experimentally measured velocities of pairs of bubbles on hot or cold surfaces, though it slightly overestimates the velocities.     

Structure-defined c60/polymer colloids supramolecular nanocomposites in water

We report a new supramolecular method for the synthesis of well-defined pristine C 60/polymer colloid nanocomposites in water. The colloids include polymer micelles and emulsion particles. To a polymer colloid solution in water or alcohol, we introduced C 60 solution in a solvent that is miscible with water or alcohol. After the two solutions mixed, polymer colloids and C 60 spontaneously assembled into stable colloidal nanocomposites. After a dialysis process, a nanocomposite dispersion in pure water was obtained. As characterized by DLS and (Cryo-)TEM, the nanocomposites have a core-shell structure with C 60 aggregated on the surface of emulsion particles or micellar cores. The resulting nanocomposites have many potential applications such as biomedicals and photovoltaics.     

Detachment of deposited colloids by advancing and receding air-water interfaces

Moving air-water interfaces can detach colloidal particles from stationary surfaces. The objective of this study was to quantify the effects of advancing and receding air-water interfaces on colloid detachment as a function of interface velocity. We deposited fluorescent, negatively charged, carboxylate-modified polystyrene colloids (diameter of 1 μm) into a cylindrical glass channel. The colloids were hydrophilic with an advancing air-water contact angle of 60° and a receding contact angle of 40°. After colloid deposition, two air bubbles were sequentially introduced into the glass channel and passed through the channel at different velocities (0.5, 7.7, 72, 982, and 10,800 cm/h). The passage of the bubbles represented a sequence of receding and advancing air-water interfaces. Colloids remaining in the glass channel after each interface passage were visualized with confocal microscopy and quantified by image analysis. The advancing air-water interface was significantly more effective in detaching colloids from the glass surface than the receding interface. Most of the colloids were detached during the first passage of the advancing air-water interface, while the subsequent interface passages did not remove significant amounts of colloids. Forces acting on the colloids calculated from theory corroborate our experimental results, and confirm that the detachment forces (surface tension forces) during the advancing air-water interface movement were stronger than during the receding movement. Theory indicates that, for hydrophilic colloids, the advancing interface movement generally exerts a stronger detachment force than the receding, except when the hysteresis of the colloid-air-water contact angle is small and that of the channel-air-water contact angle is large.     

Surface charge property governing co-transport of illite colloids and Eu(III) in saturated porous media

The transport of colloids and radionuclides is sophisticated because of the variety of charge properties between colloidal particles and host subsurface media, which causes great difficulty in establishing a reliable model of radionuclides migration by taking the colloid phase into consideration. In this work, the co-transport of illite colloids (IC) and Eu(III) in the quartz sand and iron-coated sand porous media was investigated by column experiments to address the predominant mechanism of charge properties on co-transport. Results showed that Eu(III) transport was driven by the illite colloids and electrostatic interaction was critical in governing the co-transport patterns. The promotion of Eu(III) transport by IC was attenuated in the iron-coated sand systems; more IC-Eu(III) complexes were retained uniformly in the column. The pore throat shrinkage caused by electrostatic attachment between aggregated IC and iron oxides exacerbated the physical straining and size exclusion effect of IC-Eu(III) complexes. An aggravated irreversible retention of IC-Eu(III) was detected in iron-coated sand column due to the electrostatic attraction of IC-Eu(III) to host media. The findings are essential for improving the understanding on the potential transport, retention and release risk of colloids associated radionuclides, and imply that the positively charged permeable reactive barrier is an effective strategy to reduce the transport risk of colloid associated radionuclides.     

Interactions between colloidal particles in polymer solutions: A density functional theory study

We present a density functional theory study of colloidal interactions in a concentrated polymer solution. The colloids are modeled as hard spheres and polymers are modeled as freely jointed tangent hard sphere chains. Our theoretical results for the polymer-mediated mean force between two dilute colloids are compared with recent simulation data for this model. Theory is shown to be in good agreement with simulation. We compute the colloid-colloid potential of mean force and the second virial coefficient, and analyze the behavior of these quantities as a function of the polymer solution density, the polymer chain length, and the colloid/polymer bead size ratio.