Electrophoretic properties of highly charged colloids: a hybrid molecular dynamics/lattice Boltzmann simulation study

Using computer simulations, the electrophoretic motion of a positively charged colloid (macroion) in an electrolyte solution is studied in the framework of the primitive model. In this model, the electrolyte is considered as a system of negatively and positively charged microions (counterions and coions, respectively) that are immersed into a structureless medium. Hydrodynamic interactions are fully taken into account by applying a hybrid simulation scheme, where the charged ions (i.e., macroion and electrolyte), propagated via molecular dynamics, are coupled to a lattice Boltzmann (LB) fluid. In a recent electrophoretic experiment by Martin-Molina et al. [J. Phys. Chem. B 106, 6881 (2002)], it was shown that, for multivalent salt ions, the mobility mu initially increases with charge density sigma, reaches a maximum, and then decreases with further increase of sigma. The aim of the present work is to elucidate the behavior of mu at high values of sigma. Even for the case of monovalent microions, a decrease of mu with sigma is found. A dynamic Stern layer is defined that includes all the counterions that move with the macroion while subjected to an external electrical field. The number of counterions in the Stern layer, q(0), is a crucial parameter for the behavior of mu at high values of sigma. In this case, the mobility mu depends primarily on the ratio q(0)/Q (with Q the valency of the macroion). The previous contention that the increase in the distortion of the electric double layer (EDL) with increasing sigma leads to the lowering of mu does not hold for high sigma. In fact, it is shown that the deformation of the EDL decreases with the increase of sigma. The role of hydrodynamic interactions is inferred from direct comparisons to Langevin simulations where the coupling to the LB fluid is switched off. Moreover, systems with divalent counterions are considered. In this case, at high values of sigma the phenomenon of charge inversion is found.     

Experimental study of electrostatically stabilized colloidal particles: colloidal stability and charge reversal

We consider the interaction of colloidal spheres in the presence of mono-, di-, and trivalent ions. The colloids are stabilized by electrostatic repulsion due to surface charges. The repulsive part of the interaction potential Ψ(d) is deduced from precise measurements of the rate of slow coagulation. These "microsurface potential measurements" allow us to determine a weak repulsion in which Ψ(d) is of the order of a few k(B)T. These data are compared to ζ potential measured under similar conditions. At higher concentrations both di- and trivalent counterions accumulate at the very proximity of the particle surface leading to charge reversal. The salt concentration c(cr) at which charge reversal occurs is found to be always above the critical coagulation concentration c(ccc). The analysis of Ψ(d) and of the ζ potential demonstrates, however, that adsorption of multivalent counterions starts far below c(cr). Hence, colloid stability in the presence of di- and trivalent ions cannot be described in terms of a DLVO ansatz assuming a surface charge that is constant with regard to the ionic strength.     

Dynamic electrophoretic mobility of spherical colloidal particles in a salt-free medium

A theory is proposed for the dynamic electrophoretic mobility mu(omega) of spherical colloidal particles in a salt-free medium containing only counterions in an oscillating electric field of frequency omega. The dynamic mobility depends on the frequency omega of the applied electric field and on the particle volume fraction as well as on the particle surface charge. It is found that as in the case of the static electrophoretic mobility mu(0) in salt-free media, there is a certain critical value of the particle surface charge separating two cases, that is, the low-surface-charge case and the high-surface-charge case (in the latter case the counterion condensation takes place near the particle surface). For the low-surface-charge case, the dynamic mobility agrees with that of a sphere in an electrolyte solution in the limit of very low electrolyte concentrations kappaa-->0 (Hückel's limit), where kappa is the Debye-Hückel parameter and a is the particle radius. For the high-surface-charge case, however, the dynamic mobility becomes constant independent of the particle surface charge, because of the counterion condensation effects. A simple expression for the ratio mu(omega)/mu(0) applicable for all cases is given.     

Electrophoretic mobility of a liquid drop in a salt-free medium

A theory is proposed for the electrophoretic mobility mu of dilute spherical liquid drops of radius a in salt-free media containing only counterions (e.g., nonaqueous media). As in the case of the electrophoretic mobility of rigid particle in salt-free media, there is a certain critical value of the drop surface charge separating two cases, that is, the low-surface-charge case and the high-surface-charge case. For the low-surface-charge case, mu coincides with that of a drop in an electrolyte solution in the limit of very low electrolyte concentrations kappaa-->0 (Hückel's limit), where kappa is the Debye-Hückel parameter. For the high-surface-charge case, however, mu becomes constant independent of the drop surface charge, since the counterion condensation takes place near the drop surface.     

Entropic effects in the electric double layer of model colloids with size-asymmetric monovalent ions

The structure of the electric double layer of charged nanoparticles and colloids in monovalent salts is crucial to determine their thermodynamics, solubility, and polyion adsorption. In this work, we explore the double layer structure and the possibility of charge reversal in relation to the size of both counterions and coions. We examine systems with various size-ratios between counterions and coions (ion size asymmetries) as well as different total ion volume fractions. Using Monte Carlo simulations and integral equations of a primitive-model electric double layer, we determine the highest charge neutralization and electrostatic screening near the electrified surface. Specifically, for two binary monovalent electrolytes with the same counterion properties but differing only in the coion's size surrounding a charged nanoparticle, the one with largest coion size is found to have the largest charge neutralization and screening. That is, in size-asymmetric double layers with a given counterion's size the excluded volume of the coions dictates the adsorption of the ionic charge close to the colloidal surface for monovalent salts. Furthermore, we demonstrate that charge reversal can occur at low surface charge densities, given a large enough total ion concentration, for systems of monovalent salts in a wide range of ion size asymmetries. In addition, we find a non-monotonic behavior for the corresponding maximum charge reversal, as a function of the colloidal bare charge. We also find that the reversal effect disappears for binary salts with large-size counterions and small-size coions at high surface charge densities. Lastly, we observe a good agreement between results from both Monte Carlo simulations and the integral equation theory across different colloidal charge densities and 1:1-electrolytes with different ion sizes.     

Stability of nanodispersions: a model for kinetics of aggregation of nanoparticles

In the course of aggregation of very small colloid particles (nanoparticles) the overlap of the diffuse layers is practically complete, so that one cannot apply the common DLVO theory. Since nanopoarticles are small compared to the extent of the diffuse layer, the process is considered in the same way as for two interacting ions. Therefore, the Br?nsted concept based on the Transition State Theory was applied. The charge of interacting nanoparticles was calculated by means of the Surface Complexation Model and decrease of effective charge of particles was also taken into account. Numerical simulations were performed using the parameters for hematite and rutile colloid systems. The effect of pH and electrolyte concentration on the stability coefficient of nanosystems was found to be more pronounced but similar to that for regular colloidal systems. The effect markedly depends on the nature of the solid which is characterized by equilibrium constants of surface reactions responsible for surface charge, i.e., by the point of zero charge, while the specificity of counterions is described by their association affinity, i.e., by surface association equilibrium constants. The most pronounced is the particle size effect. It was shown that extremely small particles cannot be stabilized by an electrostatic repulsion barrier. Additionally, at the same mass concentration, nanoparticles aggregate more rapidly than ordinary colloidal particles due to thier higher number concentration.     

Is there a ‘matrix suppression effect’ under fast‐atom bombardment liquid secondary ion mass spectrometry of ionic surfactants in glycerol?

Some features of a ‘matrix suppression effect’ caused by ionic surface‐active compounds under fast‐atom bombardment (FAB) liquid secondary ion mass spectrometry (LSIMS) are being revised. It is shown that abundant transfer of the glycerol matrix molecules to the gas phase does occur under FAB‐LSIMS of ionic surfactants, contrary to popular belief. This process can be obscure because of the dependence of the charge state of the glycerol‐containing cluster ions on the type of ionic surfactant. It is revealed that, while glycerol matrix signals are really completely suppressed in the positive ion mass spectra of cationic surfactants (decamethoxinum, aethonium), abundant deprotonated glycerol and glycerol‐anion clusters are recorded in the negative ion mode. In the case of an anionic surfactant (sodium dodecyl sulfate), on the contrary, glycerol is completely suppressed in the negative ion mode, but is present in the protonated and cationized forms in the positive ion mass spectra. It is suggested that such patterns of positive and negative ion FAB‐LSIMS spectra of ionic surfactants solutions reflect the structure and composition of the electric double layer formed at the vacuum‐liquid interface by organic cations or anions and their counterions. Processes leading to the formation of the glycerol‐containing ions preferentially of positive or negative charge are discussed. The most obvious of them is efficient binding of glycerol to inorganic counterions of the salts Cl^? or Na⁺, which is confirmed by data from quantum chemical calculations. The high content of the counterions and relatively small content of glycerol in the sputtered zone may be responsible for the charge‐selective suppression of neat glycerol clusters of opposite charge to the counterions. In the case of a mixture of cationic and anionic surfactants the substitution of inorganic counterions by organic ones was observed. The dependence of the exchange rate in the surface layer is not a linear function of the bulk solution concentration, and an effect of abrupt recharging of the surface can be registered. No both positively or negatively charged pure glycerol and glycerol‐inorganic counterion clusters are recorded for the mixture. Correlations between the mass spectrometric observations and some phenomena of surface and colloid chemistry and physics are discussed. Copyright © 2007 John Wiley & Sons, Ltd.     

Streaming potential generated by a long viscous drop in a capillary

The streaming potential generated by motion of a long drop of viscosity mu(d) = lambdamu in a uniform circular capillary filled with fluid of viscosity mu is investigated by means of a model previously used to study electrophoresis of a charged mercury drop in water. The capillary wall is at potential zeta c relative to the bulk fluid within it, and the surface of the drop is at potential zeta(d). Potentials are assumed to be sufficiently small so that the charge cloud is described by the linearized Poisson-Boltzmann equation, and the Debye length characterizing the thickness of the charge cloud is assumed to be thin compared with the gap h(0) between the drop and the capillary wall. Ions in the external fluid are not allowed to discharge at the surface of the drop, and the wall of the capillary has a nonzero surface conductivity sigma c. The drop is assumed to be sufficiently long so that end effects can be neglected. Recirculation of fluid within the drop gives rise to an enhanced streaming current when zeta(d) is nonzero, leading to an anomalously high streaming potential. This vanishes as the drop viscosity becomes large. If V is the velocity of the drop and gamma is the coefficient of interfacial tension between the two fluids, then the capillary number is Ca = mu V/gamma, and the gap varies as h(0)planck'sCa(2/3). When Ca is small, the gap h(0) is small and electrical conduction along the narrow gap is dominated by the surface conductivity sigma(c) of the capillary wall, which is constant. The electrical current convected by flowing fluid is proportional to Ca, as is the change in streaming potential caused by the presence of the drop. If sigma(c) = 0, then the electrical conductance of the gap depends on its width h(0) and on the bulk fluid conductivity sigma and becomes small as h(0) approximately equal to Ca(2/3) --> 0. The streaming potential required to cancel the O(Ca) convection current therefore varies as Ca(1/3). If sigma(c) = 0 and the drop is rigid (lambda --> infinity), then the change in streaming potential over and above that expected due to the change in pressure gradient is proportional to the difference in potentials zeta(c)-zeta(d).     

Electrophoretic mobility of a highly charged colloidal particle in a solution of general electrolytes.

For a highly charged particle in an electrolyte solution, counterions are condensed very near the particle surface. The electrochemical potential of counterions accumulated near the particle surface is thus not affected by the applied electric field, so that the condensed counterions do not contribute to the particle electrophoretic mobility. In the present paper we derive an expression for the electrophoretic mobility mu(infinity) of a highly charged spherical particle of radius a and zeta potential zeta in the limit of very high zeta in a solution of general electrolytes with large ka (where k is the Debye-Hückel parameter) on the basis of our previous theory for the case of symmetrical electrolytes (H. Ohshima, J. Colloid Interface Sci. 263 (2003) 337). It is shown that zeta can formally be expressed as the sum of two components: the co-ion component, zetaco-ion, and the counterion component, zetacounterion (where zeta = zetaco-ion + zetacounterion) and that the limiting electrophoretic mobility mu(infinity) is given by mu(infinity) = epsilonr epsilon0 zetaco-ion(infinity)/eta + 0(1/ka), where zetaco-ion(infinity) is the high zeta-limiting form of zetaco-ion, epsilonr and eta are, respectively, the relative permittivity and viscosity of the solution, and epsilon0 is the permittivity of a vacuum. That is, the particle behaves as if its zeta potential were zetaco-ion(infinity), independent of zeta. For the case of a positively charged particle in an aqueous electrolyte solution at 25 degrees C, the value of zetaco-ion(infinity) is 35.6 mV for 1-1 electrolytes, 46.0 mV for 2-1 electrolytes, and 12.2 mV for 1-2 electrolytes. It is also found that the magnitude of mu(infinity) increases as the valence of co-ions increases, whereas the magnitude of mu(infinity) decreases as the valence of counterions increases.     

Ionic condensation and charge renormalization in colloidal suspensions

The very popular notion of effective or renormalized polyion charge is a concept of fundamental importance in the field of highly charged colloidal or polyelectrolyte solutions. In such suspensions, the electrostatic coupling between oppositely charged species induces a strong accumulation (or electrostatic “condensation”) of counterions in the vicinity of the macroion surface. The basic idea is thus to consider the structural colloid and the condensed counterionic shell as a whole which carries an effective charge, Z^eff, much weaker than the structural one, Z^str. Consequently, as long as what happens far from the colloid is concerned, all Debye–Hückel-like linearized approaches which fail to correctly treat the nonlinear condensation phenomenon can still be used if Z^str is more or less replaced by Z^eff. Beyond this basic idea, it remains to estimate a priori the value of Z^eff. It will be discussed how to deduce simple laws for the effective charge of spherical colloids from the Poisson–Boltzmann approach, analogous to Manning's law for linear polyelectrolytes. The validity of these laws will be tested, against more complete treatments. Lastly, it will be shown that while the notion of colloidal charge renormalization remains clear for dilute suspensions, it becomes incorrect at higher densities where the condensed counterionic shells overlap.     

Counterion condensation on charged spheres, cylinders, and planes

We use the framework of counterion condensation theory, in which deviations from linear electrostatics are ascribed to charge renormalization caused by collapse of counterions from the ion atmosphere, to explore the possibility of condensation on charged spheres, cylinders, and planes immersed in dilute solutions of simple salt. In the limit of zero concentration of salt, we obtain Zimm-Le Bret behavior: a sphere condenses none of its counterions regardless of surface charge density, a cylinder with charge density above a threshold value condenses a fraction of its counterions, and a plane of any charge density condenses all of its counterions. The response in dilute but nonzero salt concentrations is different. Spheres, cylinders, and planes all exhibit critical surface charge densities separating a regime of counterion condensation from states with no condensed counterions. The critical charge densities depend on salt concentration, except for the case of a thin cylinder, which exhibits the invariant criticality familiar from polyelectrolyte theory.     

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).     

Phase diagram for the adsorption of weak polyelectrolytes at a soft charged surface

We have experimentally studied the adsorption of polyelectrolytes at oppositely charged surfaces. A weak flexible polyelectrolyte, poly(acrylic acid), was adsorbed from dilute solutions on a Langmuir film of a cationic amphiphile, dimethyldioctadecylammonium bromide. The polymer surface coverage, Gamma, at equilibrium was measured by two reflectivity techniques-ellipsometry and polarization modulated infrared reflection absorption spectroscopy (PM-IRRAS)-as a function of the surface charge density, sigma, and of the polymer ionization degree, alpha. Different adsorption regimes were evidenced. For weakly charged surfaces, sigma < sigma sat, Gamma increases with sigma and with 1/alpha, as expected for a neutralization of the surface by the adsorbed polymers. For highly charged surfaces, sigma > sigma sat, the adsorption of polyelectrolytes saturates. The mean orientation of the adsorbed chains also depends on the value of sigma: it is parallel to the surface for sigma < sigma (< sigma sat) and orthogonal to the surface for sigma > sigma. We have measured the values of sigma sat and sigma as a function of alpha and compared the results with existing theories.     

Charge injection across self-assembly monolayers in organic field-effect transistors: odd-even effects

We investigate the role of self-assembly monolayers in modulating the response of organic field-effect transistors. Alkanethiol monolayers of chain length n are self-assembled on the source and drain electrodes of pentacene field-effect transistors. The charge carrier mobility mu exhibits large fluctuations correlated with odd-even n. For n < 8, mu increases by 1 order of magnitude owing to the decrease of the hole injection barrier and the improved molecular order at the organic-metallic interface. For n > or = 8, mu decays exponentially with an inverse decay length beta = 0.6 A(-1). Our results show that (i) charge injection across the interface occurs by through-bond tunneling of holes mediated by the alkanethiol layer; (ii) in the long-chain regime, the charge injection across the alkanethiol monolayer completely governs the transistor response; (iii) the transistor is a sensitive gauge for probing charge transport across single monolayers. The odd-even effect is ascribed to the anisotropic coupling between the alkanethiol terminal sigma bond and the HOMO level of ordered pentacene molecules.     

Electrostatically stabilized metal oxide particle dispersions in carbon dioxide

We report electrostatic stabilization of micrometer-sized TiO(2) particles at long range (several micrometers) in liquid and supercritical CO(2) despite the ultralow dielectric constant, as low as 1.5. The counterions were solubilized in dry reverse micelles, formed with a low-molecular weight cationic perfluoropolyether trimethylammonium acetate surfactant, to prevent ion pairing with the particle surface. Dynamic light scattering and settling velocities indicate a particle diameter of 620-740 nm. The electrophoretic mobility of -2.3 x 10(-8) m(2)/V s indicated a particle charge on the order of -1.7 x 10(-17) C, or 105 elementary negative charges per particle. The balance of particle compression by an electric field versus electrostatic repulsion generated an amorphous arrangement of particles with 5-9 mum spacing, indicating Debye lengths greater than 1 mum. Scattering patterns also indicate that chains of particles may be achieved in CO(2) by dielectrophoresis with alternating fields. The electrostatic stabilization has been achieved by solubilizing a small concentration of counterions in only a small fraction of the reverse micelles in the double layer. Whereas many low-molecular weight surfactants have been shown to form reverse micelles in CO(2), very few polymers are able to stabilize micrometer-sized colloids sterically. Thus, electrostatic stabilization has the potential to expand markedly the domain of colloid science in apolar supercritical fluids.     

Electrophoretic mobility of a soft particle in a salt-free medium

A theory is presented for the electrophoretic mobility mu of dilute spherical soft particles (i.e., polyelectrolyte-coated particles) in salt-free media containing only counterions. As in the case of other types of particles (rigid particles and liquid drops) in salt-free media, there is a certain critical value of the particle charge separating two cases, the low-surface-charge case and the high-surface-charge case. For the low-charge case, the mobility is proportional to the particle charge and coincides with that of a soft particle in an electrolyte solution in the limit of very low electrolyte concentrations kappa-->0 (Hückel's limit), where kappa is the Debye-Hückel parameter. For the high-charge case, however, mu becomes essentially constant, independent of the particle charge, due to the counterion condensation effect.     

Colloido-chemical characteristics of nanoporous glasses with different compositions in solutions of simple and organic electrolytes. 2. Equilibrium electrochemical characteristics of membranes

The regularities of variations in the electrokinetic potential and surface charge of nanoporous glass membranes with different compositions have been studied as depending on the type of an electrolyte (sodium, potassium, ammonium, tetramethylammonium, and tetraethylammonium chlorides) and the structure of pore space. It has been shown that, in solutions containing specifically sorbed organic counterions, the range of positive values of electrokinetic potential arises due to the superequivalent absorption of counterions in the Stern layer. It has been found that the influence of the specific adsorption of counterions on the electrokinetic potential of porous glasses increases with the amount of secondary silica in the pore space. The effects of the counterion specificity, pore channel sizes, and composition of a porous glass on the value of the surface charge have been analyzed. The absolute value of the surface charge has been shown to significantly increase in the presence of organic counterions in comparison with inorganic ions throughout the examined range of background electrolyte concentrations.     

Effects of multivalent salt addition on effective charge of dilute colloidal solutions

The effective charge Z* is often invoked to account for the accumulation of counterions near the colloid with intrinsic charge Z. Although the ion concentrations c(i) are not uniform in the solution due to the presence of the charged particle, their chemical potentials are uniform everywhere. Thus, on the basis of ion chemical potential, effective ion concentrations c(i)*, which can be experimentally measured by potentiometry, are defined with the pure salt solution as the reference state. The effective charge associated with the charged particle can then be determined by the global electroneutrality condition. Monte Carlo simulations are performed in a spherical Wigner-Seitz cell to obtain the effective charge of the colloid. In terms of the charge ratio alpha=Z*/Z, the effects of added salt concentration, counterion valency, and particle charge are examined. The effective charge declines with increasing salt concentration and the multivalent salt is much more efficient in reducing the effective charge of the colloidal solution. Moreover, the extent of effective charge reduction is decreased with increasing intrinsic charge for a given concentration of added salt. Those results are qualitatively consistent with experimental observations by electrophoresis.     

Electrophoresis of a spherical dispersion of polyelectrolytes in a salt-free solution

The electrophoretic behavior of a spherical dispersion of polyelectrolytes of arbitrary concentration is analyzed theoretically under a salt-free condition, that is, the liquid phase contains only counterions which come from the dissociation of the functional groups of polyelectrolytes. We show that, in general, the surface potential of a polyelectrolyte increases nonlinearly with its surface charge. A linear relation exists between them, however, when the latter is sufficiently small; and the more dilute the concentration of polyelectrolytes, the broader the range in which they are linearly correlated. If the amount of surface charge is sufficiently large, counterion condensation occurs, and the rate of increase of surface potential as the amount of surface charge increases declined. Also, it leads to an inverse in the perturbed potential near the surface of a polyelectrolyte, and its mobility decreases accordingly. For a fixed amount of surface charge, the lower the concentration of polyelectrolytes and/or the lower the valence of counterions, the higher the surface potential. The qualitative behavior of the mobility of a polyelectrolyte as the amount of its surface charge varies is similar to that of its surface charge.     

Excluded volume driven counterion condensation inside nanotubes in a concave electrical double layer model

The physical properties of organic nanotubes attract increasing attention due to their potential benefit in technology, biology and medicine. We study the effect of ion size on the electrical properties of cylindrical nanotubes filled with electrolyte solution within a modified Poisson-Boltzmann (PB) approach. For comparison purposes, small hollow nanospheres filled with electrolyte solution are considered. The finite size of the particles in the inner electrolyte solution is described by the excluded volume effect within a lattice statistics approach. We found that an increased ion size reduces the number of counterions near the charged inner surface of the nanotube, leading to an enlarged electrostatic surface potential. The concentration of counterions close to the inner surface saturates for higher surface charge densities and larger ions. In the case of saturation, the closest counterion packing is achieved, all lattice sites near the surface are occupied and an actual counterion condensation is observed. By contrast, the counterion concentration at the axis of the nanotube steadily increases with increasing surface charge density. This growth is more pronounced for smaller nanotube radii and larger ions. At larger nanotube radii for small ion size counterion condensation may also be observed according to the Tsao criterion, i.e. the counterion concentration at the centre is independent of the number of counterions in the system. With decreasing radius the Tsao condensation effect is shifted towards physiologically unrealistic surface charge densities.