Reversible coagulation of colloidal suspension in shallow potential wells: Direct numerical simulation

Brownian dynamics computer simulations of aggregation in 2D colloidal suspensions are discussed. The simulations are based on the Langevin equations, pairwise interaction between colloidal particles and take into account Brownian, hydrodynamic and colloidal forces. The chosen mathematical model enables to predict the correct values of diffusion coefficient of freely moving particle, the mean value of kinetic energy for each particle in ensemble of interacting colloidal particles and residence times of colloidal particles inside the potential wells of different depths. The simulations allow monitoring formation and breakage of clusters in a suspension as well as time dependence of the mean cluster size. The article is published in the original.     

Corrected results for the influence of size,zeta potential,and state of motion of dispersed particles on the conductivity of a colloidal suspension

A correction of a recent work on the dependence of the DC conductivity of diluted colloidal suspensions on the size, zeta potential, and state of motion of dispersed particles (C. Grosse, S. Pedrosa, V.N. Shilov, J. Colloid Interface Sci. 251 (2002) 304) is presented. It is shown that the procedure used in that work to calculate the contribution of the particles to the conductivity of the suspension leads to a result that includes the variation of the conductivity of the dispersion medium. Revised analytical and numerical calculations are presented, which strongly reinforce the conclusions reached in the original work: The expression for the conductivity increment based on the value of the dipolar coefficient of the suspended particles (calculated taking into account their electrophoretic motion) appears to be valid over the whole range of particle sizes.     

Structural properties of charge-stabilized ferrofluids under a magnetic field: a Brownian dynamics study

We present Brownian dynamics simulations of real charge-stabilized ferrofluids, which are stable colloidal dispersions of magnetic nanoparticles, with and without the presence of an external magnetic field. The colloidal suspensions are treated as collections of monodisperse spherical particles, bearing point dipoles at their centers and undergoing translational and rotational Brownian motions. The overall repulsive isotropic interactions between particles, governed by electrostatic repulsions, are taken into account by a one-component effective pair interaction potential. The potential parameters are fitted in order that computed structure factors are close to the experimental ones. Two samples of ferrofluid differing by the particle diameter and consequently by the intensity of the magnetic interaction are considered here. The magnetization and birefringence curves are computed: a deviation from the ideal Langevin behaviors is observed if the dipolar moment of particles is sufficiently large. Structure factors are also computed from simulations with and without an applied magnetic field H: the microstructure of the repulsive ferrofluid becomes anisotropic under H. Even our simple modeling of the suspension allows us to account for the main experimental features: an increase of the peak intensity is observed in the direction perpendicular to the field whereas the peak intensity decreases in the direction parallel to the field.     

On the influence of size, zeta potential, and state of motion of dispersed particles on the conductivity of a colloidal suspension

The dependence of the DC conductivity of diluted colloidal suspensions on the size, zeta potential, and state of motion of the dispersed particles is analyzed both theoretically and numerically. It is shown that the simple formula that represents the conductivity as a sum of products: charge times mobility, taken over all the carriers present in the suspension, is only valid for exceedingly low values of the product kappaa. In contrast, the formulation based on the value of the dipolar coefficient of the suspended particles seems to be valid for all the range of particle sizes. This assertion is only true if the dipolar coefficient is calculated taking into account the electrophoretic motion of the particles. For very low values of the product kappaa, the dipolar coefficient of particles free to move can be several orders of magnitude larger than that of immobile particles.     

Simulations of the PDF functions for dilute colloidal suspensions of molecular particles flowing in mesopores with rough surface boundaries

Simulations have been carried out to analyze the dynamics of dilute colloidal suspensions of macromolecular particles in solutions flowing in pores, subject to hydrodynamic forces, Brownian motion and stochastic collisions at rough pore boundaries in a two-dimensional spatial frame. A theoretical model is developed and intensively analyzed for the treatment of the mechanical restitution of the particles due to dynamic collisions at these boundaries. In particular we are able to calculate the Probability distribution functions for the spatial positions and the orientations of rod-like particles inside the pores. The results are presented for different widths of pore channels referenced to the size of a rod-like particle. These simulations are general in the sense that they are developed for confining and open pore channels, rough at the nano scale. The simulations also permit calculating the nematic order parameters for colloidal suspensions; the model calculation is applied for dilute colloidal suspensions of carbon nano-tubes in an aqueous single-stranded DNA solution flowing inside pores. Our calculated nematic order results for dilute suspensions of particles of known lengths flowing inside porous systems should indicate, when coupled to birefringence and dichroism experimental results, the possibility to estimate the pore widths for these systems.     

Modeling real dynamics in the coarse-grained representation of condensed phase systems

This work presents a systematic multiscale methodology to provide a more faithful representation of real dynamics in coarse-grained molecular simulation models. The theoretical formalism is based on the recently developed multiscale coarse-graining (MS-CG) method [S. Izvekov and G. A. Voth, J. Phys. Chem. B. 109, 2469 (2005); J. Chem. Phys. 123, 134105 (2005)] and relies on the generalized Langevin equation approach and its simpler Langevin equation limit. The friction coefficients are determined in multiscale fashion from the underlying all-atom molecular dynamics simulations using force-velocity and velocity-velocity correlation functions for the coarse-grained sites. The diffusion properties in the resulting CG Brownian dynamics simulations are shown to be quite accurate. The time dependence of the velocity autocorrelation function is also well-reproduced relative to the all-atom model if sufficient resolution of the CG sites is implemented.     

Light-scattering form factors of asymmetric particle dimers from heteroaggregation experiments

Measurements of form factors of asymmetric particle dimers composed of oppositely charged polystyrene latex particles are presented. These measurements are based on time-resolved static and dynamic light scattering on dilute aggregating aqueous suspensions. The experimental form factors are compared with independent calculations based on the superposition T-matrix method and Rayleigh-Debye-Gans (RDG) approximation. While the RDG approximation is found to be reliable only up to particle diameters of about 250 nm, the superposition T-matrix method is very accurate for all types of dimers investigated. The present results show clearly the appropriateness of the superposition T-matrix method to estimate the optical properties of colloidal particles in the micrometer range reliably.     

Numerical calculation of the electrophoretic mobility of concentrated suspensions of soft particles

The electrophoretic mobility of spherical soft particles in concentrated colloidal suspensions is numerically calculated. The particle is modeled as a hard core coated with an ion-penetrable membrane bearing a uniform distribution of fixed charges, while the high particle concentration is taken into account by means of a cell model. The network simulation method used makes it possible to solve the problem without any restrictions on the values of the parameters such as particle concentration, membrane thickness, fixed charge density in the membrane, viscous drag in the membrane, number and valence of ionic species, electrolyte concentration, etc. The theoretical model used is similar to the one presented by Ohshima [H. Ohshima, J. Colloid Interface Sci. 225 (2000) 233], except for the use of the Shilov-Zharkikh, rather than the Levine-Neale, boundary condition for the electric potential, and the inclusion in the force balance equation of an additional term corresponding to the force exerted by the liquid on the core of the moving particle [J.J. López-García, C. Grosse, J. Horno, J. Colloid Interface Sci. 265 (2003) 327]. The obtained results only coincide with existing analytical expressions for low particle concentrations, low particle charge, and when the electrolyte concentration is high, the membrane is thick, and its resistance to the fluid flow is high. This suggests that most interpretations of the electrophoretic mobility of soft particles in concentrated suspensions require numerical calculations.     

Dynamics of swelling/contracting hard spheres surmised by an irreversible Langevin equation

The diffusion of molecules through uniform homogeneous materials can readily be described by Brownian motion or generalizations thereof. The further generalization of these models to describe molecular diffusion through heterogeneous and nonstationary solvents is much less understood. Phenomenological nonstationary generalizations of the generalized Langevin equation (GLE) have earlier been developed satisfying the fluctuation-dissipation relationship in quasi-equilibrium limits while exhibiting somewhat complex behavior away from equilibrium. This reduced-dimensional representation should be capable of describing the diffusion of a particle through a colloidal suspension whose average particle size is tuned by an external driving force such as pH. A simple particle model of such a process involves the motion of a hard-sphere particle in an explicit environment of swelling hard spheres. The velocity autocorrelation functions observed in a large number of simulations of the particle model under various swelling rates agree precisely with those of a single form of the nonstationary phenomenological model. Though this procedure is not an explicit projection of the mechanical system onto the nonstationary GLE, it does show that the latter correctly describes the dynamics of the projected coordinate--namely, diffusion of the solute--under nonequilibrium conditions. Both nonequilibrium solvent models lead to behavior reminiscent of beta-relaxation processes at packing fractions substantially below that of the glass transition.     

Improved theory of cyclical electrical field flow fractionation

Previously reported theories for cyclical electrical field flow fractionation (CyElFFF) are severely limited in that they do not account for diffusion, steric, or electric double layer effects. Experiments have shown that these theories overpredict the retention of particles in CyElFFF. In this work, we present a model for prediction of steric, diffusion, and electrical effects. The electrical double layer effects are treated using a lumped electrical circuit model that accounts for the field shielding by the electrical double layer formed at the electrode-carrier interface. The electrical effects are shown to dominate retention times and outweigh the contributions of diffusion and particle size. Detailed results from the simulations are presented in this work, and a comparison between the theoretical and experimental results obtained from the retentions of polystyrene particle standards is presented in this paper. The models are shown to correctly predict the retention of the polystyrene standards in CyElFFF with a reasonable error, while existing models are shown to have significant failings.     

Flow‐induced particle orientation and rheological properties of suspensions of organoclays in thermoplastic resins

The influence of nano‐scale particles on the viscoelastic properties of polymer suspensions is investigated. We have developed a simulation technique for the particle orientation and polymer conformation tensors to study various features of the suspensions. The nano‐particles are modeled as thin rigid oblate spheroid particles and the polymers as FENE‐P type viscoelastic and Newtonian fluid. Both interparticle and polymer‐particle interactions have been taken into account in our numerical computations. The nonlinear viscoelastic properties of nanocomposites of layered silicate particles in non‐Newtonian fluids are examined at the start‐up of shear flow and are interpreted using the model to examine the effects of model parameters as well as flow conditions on particle orientation, viscosity, and first normal stress difference of the suspensions. We have studied the microstructure of polymer‐clay nanocomposites using X‐ray diffraction (XRD) scattering and transmission electron microscopy (TEM). The rheology of these nanocomposites in step‐shear is shown to be fairly well predicted by the model. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 2003–2011, 2010     

Experimental verification of an exact evanescent light scattering model for TIRM

Total internal reflection microscopy (TIRM) is a method for the precise measurement of interaction potentials between a spherical colloidal particle and a wall. The method is based on single-particle evanescent wave light scattering. The well-established model used to interpret TIRM data is based on an exponential relation between scattering intensity and particle wall distance. However, applying this model for a certain range of experimental parameters leads to significant distortions of the measured potentials. Using a TIRM setup based on a two-wavelength illumination technique, we were able to directly measure the intensity distance relation revealing deviations from an exponential decay. The intensity-distance relations could be compared to scattering simulations taking into account exact experimental parameters and multiple reflections between a particle and the wall. Converging simulation results were independently obtained by the T-matrix method and the discrete sources method (DSM) and show excellent agreement with experiments. Using the new scattering model for data evaluation, we could reconstruct the correct potential shape for distorted interaction potentials as we demonstrate. The comparison of simulations to experiment intrinsically yields a new method to determine absolute particle-wall distances, a highly desired quantity in TIRM experiments.     

One-dimensional cluster growth and branching gels in colloidal systems with short-range depletion attraction and screened electrostatic repulsion

We report extensive numerical simulations of a simple model for charged colloidal particles in suspension with small nonadsorbing polymers. The chosen effective one-component interaction potential is composed of a short-range attractive part complemented by a Yukawa repulsive tail. We focus on the case where the screening length is comparable to the particle radius. Under these conditions, at low temperature, particles locally cluster into quasi one-dimensional aggregates which, via a branching mechanism, form a macroscopic percolating gel structure. We discuss gel formation and contrast it with the case of longer screening lengths, for which previous studies have shown that arrest is driven by the approach to a Yukawa glass of spherical clusters. We compare our results with recent experimental work on charged colloidal suspensions (Phys. Rev. Lett. 2005, 94, 208301).     

Electric double layer for spherical particles in salt-free concentrated suspensions including ion size effects

The equilibrium electric double layer (EDL) that surrounds colloidal particles is essential for the response of a suspension under a variety of static or alternating external fields. An ideal salt-free suspension is composed of charged colloidal particles and ionic countercharges released by the charging mechanism. Existing macroscopic theoretical models can be improved by incorporating different ionic effects usually neglected in previous mean-field approaches, which are based on the Poisson-Boltzmann equation (PB). The influence of the finite size of the ions seems to be quite promising because it has been shown to predict phenomena like charge reversal, which has been out of the scope of classical PB approximations. In this work we numerically obtain the surface electric potential and the counterion concentration profiles around a charged particle in a concentrated salt-free suspension corrected by the finite size of the counterions. The results show the high importance of such corrections for moderate to high particle charges at every particle volume fraction, especially when a region of closest approach of the counterions to the particle surface is considered. We conclude that finite ion size considerations are obeyed for the development of new theoretical models to study non-equilibrium properties in concentrated colloidal suspensions, particularly salt-free ones with small and highly charged particles.     

Magnetophoresis, sedimentation, and diffusion of particles in concentrated magnetic fluids

A dynamic mass transfer equation for describing magnetophoresis, sedimentation, and gradient diffusion of colloidal particles in concentrated magnetic fluids has been derived. This equation takes into account steric, magnetodipole, and hydrodynamic interparticle interactions. Steric interactions have been investigated using the Carnahan-Starling approximation for a hard-sphere system. In order to study the effective interparticle attraction, the free energy of the dipolar hard-sphere system is represented as a virial expansion with accuracy to the terms quadratic in particle concentration. The virial expansion gives an interpolation formula that fits well the results of computer simulation in a wide range of particle concentrations and interparticle interaction energies. The diffusion coefficient of colloidal particles is written with regard to steric, magnetodipole and hydrodynamic interactions. We thereby laid the foundation for the formulation of boundary-value problems and for calculation of concentration and magnetic fields in the devices (for example, magnetic fluid seals and acceleration sensors), which use a concentrated magnetic fluid as a working fluid. The Monte-Carlo methods and the analytical approach are employed to study the magnetic fluid stratification generated by the gravitational field in a cylinder of finite height. The coefficient of concentration stratification of the magnetic fluid is calculated in relation to the average concentration of particles and the dipolar coupling constant. It is shown that the effective particle attraction causes a many-fold increase in the concentration inhomogeneity of the fluid if the average volume fraction of particles does not exceed 30%. At high volume concentrations steric interactions play a crucial role.     

Adsorption of colloidal particles to curved interfaces

As a simple model for a Pickering emulsion droplet, we consider the adsorption of spherical particles to a spherical liquid-liquid interface in order to investigate the curvature effect on the particle adsorption. By taking into account both the surface and the volume energies due to the presence of a particle, we show that the equilibrium contact angle is determined by the classical Young's equation although the adsorption energy depends on the curvature. We also calculate the partitioning of the colloidal particles among the two liquids and the interface. The distribution of colloidal particles is expressed in terms of the interfacial curvature as well as the relative wettability of the particle.     

Viscosity of concentrated colloidal suspensions: comparison of bidisperse models

In this paper, recent advances in the study of rheological behavior of concentrated bimodal suspensions are briefly reviewed. The predictive models are divided into two categories, namely, the effective volume fraction (or hard sphere scaling) approach and the separation of contributions approach. Predictions of both approaches are compared with experimental data of electrostatically and sterically stabilized suspensions. It is shown that the predictions of both hard sphere scaling and the scaling method of Zaman and Moudgil (J. Colloid Interface Sci. 212 (1999) 167) to separate the contributions of fine and coarse particles are in good agreement with the experimentally observed results. The approach by Dames, Morrison, Wilenbacher (Rheol. Acta 40 (2001) 434) to separate the hard-sphere and non-hard-sphere contributions is investigated using the aqueous silica and polystyrene suspensions respectively. A good agreement is shown for aqueous silica suspensions. However, significant differences between the predictions and experimental data are found for the sterically stabilized polystyrene suspensions, suggesting a more generalized expression is needed. As an attempt to classify the models on the viscosity of colloidal suspensions, the present study will provide guidelines for interpretation of experimental results and for the development of more comprehensive predictive methodologies for polydispersed colloidal dispersions.     

Simple analytic solution of the rate equations for the early-stage aggregation kinetics of colloidal particles

The potential energy of the interaction between two approaching colloidal particles obtained by the DLVO theory can exhibit a maximum, a primary minimum, and a secondary minimum on the potential curve of the interparticle interaction energy. Behrens and Borkovec (J Colloid Interface Sci 225: 460, 2000) considered a set of coupled nonlinear differential rate equations for the early-stage aggregation kinetics of colloidal particles by taking into account the influence of the secondary minimum and derived an approximate solution to the rate equations as well as their exact numerical solutions. In the present article, an improved simple analytic solution is derived for these rate equations. The obtained solution, which involves two distinct (fast and slow) exponentially decay constants, is found to be in excellent agreement with numerical solutions to the rate equations with negligible errors.     

Dielectric properties of aqueous zwitterionic liposome suspensions

The dielectric spectra of aqueous suspensions of unilamellar liposomial vesicles built up by zwitterionic phospholipids (dipalmitoylphosphatidyl-choline, DPPC) were measured over the frequency range extending from 1 kHz to 10 MHz, where the interfacial polarization effects, due to the highly heterogeneous properties of the system, prevail. The dielectric parameters, i.e., the permittivity epsilon'(omega) and the electrical conductivity sigma(omega), have been analyzed in terms of dielectric models based on the effective medium approximation theory, considering the contribution associated with the bulk ion diffusion on both sides of the aqueous interfaces. The zwitterionic character of the lipidic bilayer has been modeled by introducing an "apparent" surface charge density at both the inner and outer aqueous interface, which causes a tangential ion diffusion similar to the one occurring in charged colloidal particle suspensions. A good agreement with the experimental results has been found for all the liposomes investigated, with size ranging from 100 to 1000 nm in diameter, and the most relevant parameters have briefly discussed in the light of the effective medium approximation theory.     

Fast evaporation of spreading droplets of colloidal suspensions

When a coffee droplet dries on a countertop, a dark ring of coffee solute is left behind, a phenomenon often referred to as the coffee-ring effect. A closely related yet less-well-explored phenomenon is the formation of a layer of particles, or skin, at the surface of the droplet during drying. In this work, we explore the behavior of a mathematical model that can qualitatively describe both phenomena. We consider a thin axisymmetric droplet of a colloidal suspension on a horizontal substrate undergoing spreading and evaporation. In contrast to prior work, precursor films (rather than pinned contact lines) are present at the droplet edge, and evaporation is assumed to be limited by how quickly molecules can transfer out of the liquid phase (rather than by how quickly they can diffuse through the gas phase). The lubrication approximation is applied to simplify the mass and momentum conservation equations, and the colloidal particles are allowed to influence the droplet rheology through their effect on the viscosity. By describing the transport of the colloidal particles with the full convection-diffusion equation, we are able to capture depthwise gradients in particle concentration and thus describe skin formation, a feature neglected in prior models of droplet evaporation. The highly coupled model equations are solved for a range of problem parameters using a finite-difference scheme based on a moving overset grid. The presence of evaporation and a large particle Peclet number leads to the accumulation of particles at the liquid-air interface. Whereas capillarity creates a flow that drives particles to the droplet edge to produce a coffee ring, Marangoni flows can compete with this and promote skin formation. Increases in viscosity due to particle concentration slow down droplet dynamics and can lead to a reduction in the spreading rate.