Effect of discrete macroion charge distributions in solutions of like-charged macroions

The effect of replacing the conventional uniform macroion surface charge density with discrete macroion charge distributions on structural properties of aqueous solutions of like-charged macroions has been investigated by Monte Carlo simulations. Two discrete charge distributions have been considered: point charges localized on the macroion surface and finite-sized charges protruding into the solution. Both discrete charge distributions have been examined with fixed and mobile macroion charges. Different boundary conditions have been applied to examine various properties. With point charges localized on the macroion surface, counterions become stronger accumulated to the macroion and the effect increases with counterion valence. As a consequence, with mono- and divalent counterions the potential of mean force between two macroions becomes less repulsive and with trivalent counterions more attractive. With protruding charges, the excluded volume effect dominates over the increased correlation ability; hence the counterions are less accumulated near the macroions and the potential of mean force between two macroions becomes more repulsive/less attractive.     

Molecular Dynamics Simulation of the Electrical Double Layer of Spherical Macroion

The structure of the electrical double layer (EDL) of a spherical macroion with a total charge of 60 elementary charges is studied by molecular dynamics methods. In calculations we used two models: continuous and discrete. In the continuous model, the total charge was concentrated in the center of the macroion; in the discrete model, elementary charges were randomly distributed over the surface of the macroion. The radial profiles of local densities and electric potential in EDL, as well as the degree of counterion binding by the macroion, are calculated with allowance for the Lennard-Jones and electrostatic interactions. It is established that the character of charge distribution significantly affects the EDL structure near the macroion, whereas its effect is much weaker at larger distances. The results obtained are compared with the experimental data on the surface potential and the diffuse part of EDL of sodium dodecyl sulfate micelles in aqueous solution, as well as on the micelle-bound charge. It is shown that even weak specific interaction between counterions and a macroion can substantially influence the structure of its EDL.     

Effects of image charges, interfacial charge discreteness, and surface roughness on the zeta potential of spherical electric double layers

We investigate the effects of image charges, interfacial charge discreteness, and surface roughness on spherical electric double layer structures in electrolyte solutions with divalent counterions in the setting of the primitive model. By using Monte Carlo simulations and the image charge method, the zeta potential profile and the integrated charge distribution function are computed for varying surface charge strengths and salt concentrations. Systematic comparisons were carried out between three distinct models for interfacial charges: (1) SURF1 with uniform surface charges, (2) SURF2 with discrete point charges on the interface, and (3) SURF3 with discrete interfacial charges and finite excluded volume. By comparing the integrated charge distribution function and the zeta potential profile, we argue that the potential at the distance of one ion diameter from the macroion surface is a suitable location to define the zeta potential. In SURF2 model, we find that image charge effects strongly enhance charge inversion for monovalent interfacial charges, and strongly suppress charge inversion for multivalent interfacial charges. For SURF3, the image charge effect becomes much smaller. Finally, with image charges in action, we find that excluded volumes (in SURF3) suppress charge inversion for monovalent interfacial charges and enhance charge inversion for multivalent interfacial charges. Overall, our results demonstrate that all these aspects, i.e., image charges, interfacial charge discreteness, their excluding volumes, have significant impacts on zeta potentials of electric double layers.     

Simulation of the electrical double layer of a macroion with different counterion charges

An electrical double layer of a spherical macroion with single-, double-, and triple-charged counterions in aqueous solution of 1: 1 background electrolyte at different concentrations are studied by the molecular dynamics method for models with discrete and continuous surface charge distribution. Radial profiles of ion partial densities and the electric potential distribution in the double layer are calculated. The degree of counterion binding with a macroion is determined. The effect of water permittivity on the structure of electrical double layer is studied.     

Macroion solutions in the cell model studied by field theory and Monte Carlo simulations

Aqueous solutions of charged spherical macroions with variable dielectric permittivity and their associated counterions are examined within the cell model using a field theory and Monte Carlo simulations. The field theory is based on separation of fields into short- and long-wavelength terms, which are subjected to different statistical-mechanical treatments. The simulations were performed by using a new, accurate, and fast algorithm for numerical evaluation of the electrostatic polarization interaction. The field theory provides counterion distributions outside a macroion in good agreement with the simulation results over the full range from weak to strong electrostatic coupling. A low-dielectric macroion leads to a displacement of the counterions away from the macroion.     

Electric transport and ion binding in solutions of fullerenehexamalonic acid Th-C66(COOH)12 and its alkali and calcium salts

The transport numbers of the macroion constituent in aqueous solutions of fullerenehexamalonic acid, C66(COOH)12, and its lithium, sodium, cesium, and calcium salts were determined by the indirect moving boundary method. By combining the transport data with the literature data for the electrical conductivity of the same solutions, the fraction of bound counterions to the fullerenehexamalonate macroion was calculated. It was found that about 20-40% of counterions are associated with the macroion in the concentration range from about 0.1 to 0.002 mol COO-/L. Consequently, under the influence of a potential field, these counterions move toward the anode as an integral part of the migrating macroion in opposition to the electrical field. Therefore, the absolute values of the macroion constituent transport numbers are relatively high. The experimental values of the fractions of bound counterions were compared with the theoretical predictions based on the solution of the Poisson-Boltzmann equation for the spherical cell model, and a reasonable agreement was obtained.     

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.     

Effect of Complexation on the Zeta Potential of Titanium Dioxide Dispersions

Abstract

The present paper deals with the surface charge properties and the dispersion stability of an aqueous titania suspension. Generally the titania powder surface is negatively charged. The dispersion stability of TiO₂ suspension is governed by the value of zeta potential. The zeta potential was measured as a function of barium acetate and zinc acetate concentrations, at pH 6.0, and the addition of electrolytes caused sharp decrease of surface charge. Ethylenediaminetetraacetic acid (EDTA) was used to chelate the bivalent metal ions, so that the charge of counterions was reduced. The complexation of bivalent counterions favors the increase of the negative zeta potential and the dispersion stability of aqueous TiO₂ suspension.     

Breakdown of the Gouy-Chapman model for highly charged Langmuir monolayers: counterion size effect

Deviations from the classic Gouy-Chapman (GC) model due to the finite size of hydrated counterions were tested for negatively charged Langmuir monolayers with different surface charge densities. Monolayers with the largest charge density (>0.6 C.m(-2)) show an increase of the surface potential for a series of alkali metal cations from Li(+) to Cs(+) by 200-250 mV. The increase is similar for different monolayers and suggests that this effect is independent of the particular type of headgroup. The magnitude of variation is comparable with model estimations of the electrical double layer (EDL) potential implying that the deviation from the GC model is drastic. Deviations from the GC model rapidly vanish with decreasing monolayer charge density and become hardly observable below 0.3 C.m(-2). For monolayers with a high charge density on subphases containing different sized counterions, preferential participation of the smallest ions in the EDL should be favorable in terms of electrostatic free energy because of packing density limitations. This effect was demonstrated for behenyl sulfate (BS) monolayers (0.64 C.m(-2)) with the X-ray reflectivity technique. For the Cs(+)-Li(+) system, the fraction of Cs(+) in the EDL is 50-60% compared with only 10% of Cs(+) in the subphase. Providing high surface charge density, a small univalent Cs(+) is capable to compete even with a bulky divalent Mg(2+). For equal concentrations of Cs(+) and Mg(2+) in the subphase, the Cs(+)/Mg(2+) ratio in EDL of BS monolayer is 1.3 to 2.0 (in contrast to 0.04, predicted by the GC model). All experimental results of this study are described in terms of packing density limitations for hydrated counterions in the EDL.     

Macroion adsorption: the crucial role of excluded volume and co-ions

The adsorption of charged colloids (macroions) onto an oppositely charged planar substrate is investigated theoretically. Taking properly into account the finite size of the macroions, unusual behaviors are reported. It is found that the role of the co-ions (the little salt-ions carrying the same sign of charge as that of the substrate) is crucial in understanding the mechanisms involved in the process of macroion adsorption. In particular, the co-ions can accumulate near the substrate's surface and lead to a counterintuitive surface charge amplification.     

Effect of multivalent ions on electroosmotic flow in micro- and nanochannels

In this work, the effect of multivalent ions on electroosmotic flow is investigated for multiple electrolyte components. The cases studied include incorporating Ca2+ and HPO4(2-) and other monovalent ions, such as K+ and H2PO4-, into an aqueous NaCl solution. The governing equations are derived and solved numerically. The boundary conditions for the governing equations are obtained from the electrochemical equilibrium requirements. In comparison with monovalent ions, the results show that in micro- and nanochannels having fixed surface charges, multivalent counterions, even in very small amounts, reduce electroosmotic flow significantly, while the multivalent co-ions have little effect on the electroosmotic flow. Due to the enhanced ion-wall interactions multivalent counterions compose the majority of ions in the electric double layer (EDL), causing a decrease of net charge at the surface.     

The influence of discrete surface charges on the force between charged surfaces

The force between two parallel charged flat surfaces, with discrete surface charges, has been calculated with Monte Carlo simulations for different values of the electrostatic coupling. For low electrostatic coupling (small counterion valence, small surface charge, high dielectric constant, and high temperature) the total force is dominated by the entropic contribution and can be described by mean field theory, independent of the character of the surface charges. For moderate electrostatic coupling, counterion correlation effects lead to a smaller repulsion than predicted by mean field theory. This correlation effect is strengthened by discrete surface charges and the repulsive force is further reduced. For large electrostatic coupling the total force for smeared out surface charges is known to be attractive due to counterion correlations. If discrete surface charges are considered the attractive force is weakened and can even be turned into a repulsive force. This is due to the counterions being strongly correlated to the discrete surface charges forming effective, oppositely directed, dipoles on the two walls.     

Surface properties of fluids of charged platelike colloids

Surface properties of mixtures of charged platelike colloids and salt in contact with a charged planar wall are studied within density functional theory. The particles are modeled by hard cuboids with their edges constrained to be parallel to the Cartesian axes corresponding to the Zwanzig model [J. Chem. Phys. 39, 1714 (1963)] and the charges of the particles are concentrated at their centers. The density functional applied is an extension of a recently introduced functional for charged platelike colloids. It provides a qualitative approach because it does not determine the relation between the actual and the effective charges entering into the model. Technically motivated approximations, such as using the Zwanzig model, are expected not to influence the results qualitatively. Analytically and numerically calculated bulk and surface phase diagrams exhibit first-order wetting for sufficiently small macroion charges and isotropic bulk order as well as first-order drying for sufficiently large macroion charges and nematic bulk order. The asymptotic wetting and drying behaviors are investigated by means of effective interface potentials which turn out to be asymptotically the same as for a suitable neutral system governed by isotropic nonretarded dispersion forces. Wetting and drying points as well as predrying lines and the corresponding critical points have been located numerically. A crossover from monotonic to nonmonotonic electrostatic potential profiles upon varying the surface charge density has been observed. Nonmonotonic electrostatic potential profiles are equivalent to the occurrence of charge inversion. Due to the presence of both the Coulomb interactions and the hard-core repulsions, the surface potential and the surface charge do not vanish simultaneously, i.e., the point of zero charge and the isoelectric point of the surface do not coincide.     

The electrical double layer of micelles in ionic surfactant solutions in the presence of a background electrolyte: 1. Diluted micellar solutions of sodium dodecyl sulfate

The structure of the electrical double layer (EDL) of micelles in dilute micellar solutions in the presence of a background electrolyte is studied within the framework of the Gouy-Chapman-Stern theory. On the basis of the Stern isotherm for counterion adsorption, conditions of electroneutrality, and the Gauss condition at the interface between the diffuse and dense parts of EDL, three equations are derived for the electrostatic potentials of the surface of micelle cores and the diffuse part of EDL as well as for the potential of the specific adsorption of counterions. Model parameters are verified by the example of sodium dodecyl sulfate (SDS). Potentials of the diffuse part of EDL, the degree of binding of counterions with micelles, and the specific adsorption potential are calculated from the experimental data on the potential of the surface of SDS micelle cores and their sizes, critical micellization concentration, aggregation numbers, and the constants of premicellar association. The specific adsorption potential of SDS is found to be ?(4.6 ± 0.1)?, where ? is the product of Boltzmann’s constant and absolute temperature. The specific adsorption potential is independent of the background electrolyte concentration, remains constant within the determination error of the parameters, and substantially contributes to the formation of EDL of micelles.     

Correlations and Fluctuations of Charged Colloids as Determined by Anomalous Small‐Angle X‐Ray Scattering

Summary: We performed molecular dynamics simulation of a charged colloidal particle with explicit counterions. Our work provides a direct comparison between simulations and ASAXS‐experiments, offering insight into the counterion distribution of charged colloidal suspensions. We give a detailed constitution of the appearing scattering terms with their physical meaning. It is shown that the cross‐correlation between a macroion and its counterions gives the meanfield approximation of the counterion density even if the counterion system is highly fluctuating. Furthermore, it is shown that cross‐correlations can be negative due to oscillations of the density amplitudes of the macroion and counterions and, therefore, must be distinguished from other scattering contributions. These oscillations become more pronounced if the counterions exhibit a fixed shape and if the size of the macroion and that of the counterion system are different.

Simulation sanpshot of a charged colloid (big central sphere) with counterions (small spheres).     

Electric double layers with electrolyte mixtures: integral equations theories and simulations

A study of a planar electric double layer (EDL) in the presence of mixtures of electrolyte is presented. In particular, results from the Hyper-Netted-Chain/Mean-Spherical-Approximation (HNC/MSA) theory are compared with Monte Carlo (MC) simulations. In this way, the charge inversion induced by mixtures of multivalent and monovalent counterions is probed. Since overcharging phenomena in nature emerge under such conditions, the role of ion-ion correlations in the EDL appears as a crucial point in this kind of study. Unlike previous related works, a realistic hydrated ion size is used in the HNC/MSA calculations and simulations. In this way, a qualitative agreement between the results obtained from the theory and MC simulations is found. However, some discrepancies arise when the charge inversion is expected to be more noticeable, namely at high surface charges and/or elevated concentrations of multivalent electrolytes. Such differences are explained in terms of an overestimation of the charge inversion by the integral equation (IE) formalism.     

Rheological Properties of SiC Suspensions with a Compound Surface Modification Using Ethyl Orthosilicate and Ethylene Glycol

Ultrafine silicon carbide (SiC) powders were surface-modified using ethyl orthosilicate (TEOS) combined with ethylene glycol. SiC suspensions with favorable rheological properties, low viscosity, and high solid loading were successfully obtained. The mechanisms of the compound surface modification for SiC powders as well as the influences of the compound surface modification not only on functional groups and charge state of the surface for SiC powders but also on the rheological properties of SiC suspensions were investigated in the present study. The results show that under alkaline conditions and acidic conditions, the surface charge states of SiC powders were [Si-OCH₂CH₂O]^? and [Si-OCH₂CH₂OH₂]⁺, respectively. The absolute value of zeta potential reached the maximum value of 22.69 mV at pH 11. Additionally, with added 1 wt% TEOS and 3 wt% ethylene glycol, the SiC suspensions exhibited good rheological properties, low viscosity and high stability due to the steric hindrance and electrostatic repulsion offered by the [Si-OCH₂CH₂O]^- with a high concentration.