Ion size effects on the electrokinetics of salt-free concentrated suspensions in ac fields

We analyze the influence of finite ion size effects in the response of a salt-free concentrated suspension of spherical particles to an oscillating electric field. Salt-free suspensions are just composed of charged colloidal particles and the added counterions released by the particles to the solution that counterbalance their surface charge. In the frequency domain, we study the dynamic electrophoretic mobility of the particles and the dielectric response of the suspension. We find that the Maxwell-Wagner-O’Konski process associated with the counterions condensation layer is enhanced for moderate to high particle charges, yielding an increment of the mobility for such frequencies. We also find that the increment of the mobility grows with ion size and particle charge. All these facts show the importance of including ion size effects in any extension attempting to improve standard electrokinetic models.     

Counterion condensation and release in micellar solutions

Counterion condensation and release in micellar solutions are investigated by direct measurement of counterion concentration with ion-selective electrode. Monte Carlo simulations based on the cell model are also performed to analyze the experimental results. The degree of counterion condensation is indicated by the concentration ratio of counterions in the bulk to the total ionic surfactant added, alpha< or =1. The ionic surfactant is completely dissociated below the critical micelle concentration (cmc). However, as cmc is exceeded, the free counterion ratio alpha declines with increasing the surfactant concentration and approaches an asymptotic value owing to counterion condensation to the surface of the highly charged micelles. Micelle formation leads to much stronger electrostatic attraction between the counterion and the highly charged sphere in comparison to the attraction of single surfactant ion with its counterion. A simple model is developed to obtain the true degree of ionization, which agrees with our Monte Carlo results. Upon addition of neutral polymer or monovalent salts, some of the surfactant counterions are released to the bulk. The former is due to the decrease of the intrinsic charge (smaller aggregation number) and the degree of ionization is increased. The latter is attributed to competitive counterion condensation, which follows the Hefmeister series. This consequence indicates that the specific ion effect plays an important role next to the electrostatic attraction.     

Wetting transitions of ionic solutions

Cahn's phenomenological theory of wetting of a solid substrate by a saturated vapor is generalized to the case where the substrate is charged and the wetting film contains counterions, with or without added salt. The electrostatic contribution to the grand potential associated with these ions is calculated within a nonlinear Poisson-Boltzmann theory. In the salt-free case, when the wetting film includes only counterions released by the substrate, the wetting transition is always first order, regardless of its nature in a neutral system. When salt is present, other wetting scenarios may arise, depending on the salt concentration and substrate surface charge. Over a restricted range of salt concentrations, a wetting scenario similar to that of prewetting, is predicted to occur along the liquid-vapor coexistence line. This scenario includes a discontinuous wetting transition between microscopic and mesoscopic film thicknesses, followed by a continuous divergence of the film thickness at higher temperatures.     

Theory of counter-ion condensation on flexible polyelectrolytes: adsorption mechanism

A new model is presented for counterion distribution around flexible polyelectrolytes by considering (i) free energy of the polyelectrolyte chain, (ii) translational entropy of adsorbed counterions, (iii) adsorption energy, (iv) translational entropy of unadsorbed counterions, (v) fluctuations of dissociated ions, and (vi) correlation among ion-pairs formed by adsorbed counterions on the polymer. The effective charge and size of the polymer are calculated self-consistently. The degree of ionization f of the polymer decreases continuously with 1/epsilonT (epsilon and T are the dielectric constant of the solvent and temperature, respectively), depending sensitively on local dielectric heterogeneity. Further, f decreases with an increase in salt concentration, monomer concentration, or chain flexibility. The polymer size, accompanying the changes in f, depends nonmonotonically on 1/epsilonT. The predictions of the model are consistent with all trends observed previously in simulations and are distinctly different from the Manning argument for rodlike chains.     

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).     

Optical absorption of semiconducting and metallic nanospheres with the confined electron-phonon coupling

We study the optical absorption, especially the (far-) infrared absorption by phonons, of semiconducting and metallic nanospheres. In the nanoscopic sphere, phonons as well as states of electronic excitations are quantized by confinement. It is also known that in the nanoscopic geometry, the confined electron-phonon interaction has a different form from the usual one in the bulk. First, we analyze the phonon and electron contributions to the dielectric response of nanospheres like epsilon(q,omega)=epsilon(ph)(q,omega)+epsilon(el)(q,omega) or 1epsilon(q,omega)=1epsilon(sc-ph)(q,omega)+1epsilon(el)(q,omega) from the confined electron-phonon interaction for three cases: the intrinsic semiconductor, the doped semiconductor, and the metal. From the dielectric response, the optical absorption spectra are calculated within the semiclassical framework concentrating on the (far-) infrared region and compared to the spectra without imposing confinement. Nontrivial differences of the spectra with confined phonons stem from two features: the electron-phonon coupling matrix has a different form and the phase space q of the confined phonon is reduced because of its quantization to q(n). Finally, size distribution effects in an ensemble of isolated nanospheres are briefly discussed. Those effects are found to be important in metallic spheres with rapid sweepings of resonances by a small change of the sphere size.     

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.     

Numerical calculation of the electrophoretic mobility of a spherical particle in a salt-free medium

By extending an approximate theory of the electrophoretic mobility of dilute spherical colloidal particles in a salt-free medium containing only counterions (H. Ohshima, J. Colloid Interface Sci. 248 (2002) 499--503), a systematic numerical method is given for the calculation of the electrophoretic mobility, which is based on an iteration method. We assume that each sphere is surrounded by a spherical free volume, within which counterions are distributed so that electro-neutrality is satisfied. The electrophoretic mobility is found to be determined mainly by the pressure due to the counterions at the outer surface of the free volume. It is shown how the mobility values deviate from those expected from Hückel's formula for high particle charges or zeta potentials because of the counterion condensation effect.     

Dielectric response of a polar fluid trapped in a spherical nanocavity

We present extensive molecular dynamics simulation results for the structure and the static and dynamical responses of a droplet of 1000 soft spheres carrying extended dipoles and confined to spherical cavities of radii R=2.5, 3, and 4 nm embedded in a dielectric continuum of permittivity epsilon(')>or=1. The polarization of the external medium by the charge distribution inside the cavity is accounted for by appropriate image charges. We focus on the influence of the external permittivity epsilon(') on the static and dynamic properties of the confined fluid. The density profile and local orientational order parameter of the dipoles turn out to be remarkably insensitive to epsilon('). Permittivity profiles epsilon(r) inside the spherical cavity are calculated from a generalized Kirkwood formula. These profiles oscillate in phase with the density profiles and go to a "bulk" value epsilon(b) away from the confining surface; epsilon(b) is only weakly dependent on epsilon('), except for epsilon(')=1 (vacuum), and is strongly reduced compared to the permittivity of a uniform (bulk) fluid under comparable thermodynamic conditions. The dynamic relaxation of the total dipole moment of the sample is found to be strongly dependent on epsilon(') and to exhibit oscillatory behavior when epsilon(')=1; the relaxation is an order of magnitude faster than in the bulk. The complex frequency-dependent permittivity epsilon(omega) is sensitive to epsilon(') at low frequencies, and the zero-frequency limit epsilon(omega=0) is systematically lower than the bulk value epsilon(b) of the static permittivity.     

Thermodynamic characterization of polyanetholesulfonic acid and its alkaline salts

Experimental and theoretical results for the thermodynamic properties of polyanetholesulfonic acid and its lithium, sodium, and cesium salts in aqueous solution at 298 K are presented. The osmotic pressure was measured using membrane and vapor pressure apparatus in the concentration range c(m) = 0.001-0.30 monomoles/dm(3). The osmotic coefficients obtained from these measurements were low, from 0.2 to 0.45 in this concentration range, indicating a strong interaction between counterions and polyions. The osmotic coefficients of the polyacid and its lithium and sodium salts appeared to be equal within experimental error, but the results for the cesium salt were lower. This indicates a somewhat stronger binding of cesium ions to the polyanion. In addition, enthalpies of dilution, DeltaH(D), from a certain concentration, m(m), to m(m) = 0.0044 monomoles/kg were measured. The measured heats of dilution were exothermic, with the acid producing the strongest and the cesium salt the weakest effect. These results were compared with previously published data for polyelectrolytes of similar structure, namely, polystyrenesulfonic acid and its alkaline salts. The osmotic pressure results indicate that polystyrenesulfonates bind the counterions more strongly than polyanetholesulfonic acid and its salts. Consistent with this finding, the enthalpies of dilution reveal that more heat is released upon dilution of polyanetholesulfonates (stronger exothermic effect) in comparison with the corresponding solutions of polystyrenesulfonic acid in its alkaline salts. These findings can be explained in terms of the structural differences between the two polyions. The experimental results were analyzed in relation to popular electrostatic theories such as the Manning condensation theory and the Poisson-Boltzmann cell model approach, where the polyion is pictured as a uniformly charged line or cylinder. In addition, we performed Monte Carlo simulations for a model polyanetholesulfonic anion having discrete charges. In all of the calculations, the solvent was treated as a continuum with the dielectric constant of pure water under the conditions of measurement. The theoretical considerations mentioned above yield results in semiquantitative agreement with the measured quantities.     

pePC-SAFT: Modeling of polyelectrolyte systems: 1. Vapor–liquid equilibria

A molecular thermodynamic model for polyelectrolyte systems—called pePC-SAFT—is proposed. The effect of charged monomers within the polyelectrolyte chain is explicitly taken into account in the reference term by replacing the hard-chain contribution of the PC-SAFT model by a charged-hard-chain contribution. Moreover, counterion condensation is accounted for to determine the effective number of charges along the polyion as well as of free counterions. The electrostatic contribution of the free counterions is described by a Debye–Hückel term.     

Line of charges in electrolyte solution near a half-space II. Electric field of a single charge

The electric potential of a single charge in electrolyte solution near a dielectric or a semiconducting half-space is determined in closed form when the electrostatics is described by the linear Debye-Hückel (D-H) equation. The electric potential strongly depends on the Debye length of the solution, the substrate-to-solution dielectric constant ratio, and the Debye length of the semiconductor. The technique of Hankel transforms is shown to be a useful tool in solving such axially symmetric boundary value problems for the D-H equation.     

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.     

Theoretical study of catalytic effects in micellar solutions

The catalytic effect of charged micelles as manifested through the increased collision frequency between the counterions of an electrolyte in the presence of such micelles is explored by the Monte Carlo simulation technique and various theoretical approaches. The micelles and ions are pictured as charged hard spheres embedded in a dielectric continuum with the properties of water at 298 K with the charge on micelles varying from zero to z(m) = 50 negative elementary charges. Analytical theories such as (i) the symmetric Poisson-Boltzmann theory, (ii) the modified Poisson-Boltzmann theory, and (iii) the hypernetted-chain integral equation are applied and tested against the Monte Carlo data for micellar ions (m) with up to 50 negative charges in aqueous solution with monovalent counterions (c; z(c) = +1) and co-ions (co; z(co) = -1). The results for the counterion-counterion pair correlation function at contact, g(cc)(sigma(cc)), are calculated in a micellar concentration range from c(m) = 5 x 10(-)(6) to 0.1 mol/dm(3) with an added +1:-1 electrolyte concentration of 0.005 mol/dm(3) (for most cases), and for various model parameters. Our computations indicate that even a small concentration of a highly charged polyelectrolyte added to a +1:-1 electrolyte solution strongly increases the probability of finding two counterions in contact. This result is in agreement with experimental data. For low charge on the micelles (z(m) below -8), all the theories are in qualitative agreement with the new computer simulations. For highly charged micelles, the theories either fail to converge (the hypernetted-chain theory) or, alternatively, yield poor agreement with computer data (the symmetric Poisson-Boltzmann and modified Poisson-Boltzmann theories). The nonlinear Poisson-Boltzmann cell model results yield reasonably good agreement with computer simulations for this system.     

Optical study of porphyrin-doped carbon nanotubes

Porphyrin-doped carbon nanotubes in sodium dodecylbenzenesulfonate (NaDDBS) aqueous solution were obtained from NaDDBS/carbon nanotube aqueous dispersions. Several phonon-assisted absorption and recombination processes seem to occur, including one-phonon and two-phonon processes, and remain present even upon porphyrin doping. Power-law scaling of exciton binding energies and environmental dielectric screening effects are used to infer the doping from photoluminescence maps. The dielectric constant of the 5,10,15,20-tetrakis(4-trimethylammonium phenyl) porphyrin (H₂TTMAPP) in NaDDBS aqueous solution seems to be higher than the one of NaDDBS/aqueous solution apparently because the counterions have opposite net charges.     

Counterion condensation in hydrosols of single-crystalline detonation nanodiamond particles obtained by air annealing of their agglomerates

The pattern of previously recorded dependences of the specific surface charge and electrophoretic mobility of monodisperse detonation nanodiamond particles on pH of aqueous KCl solutions suggests that counterions are condensed on the particle surface. Counterion condensation is considered in terms of the Levin model, and the experimental ratios between the densities of the electrokinetic and surface charges of dispersed particles, as well as the fractions of condensed counterions, are calculated as depending on pH and KCl concentration in nanodiamond hydrosols. The obtained dependences lead to the conclusion that counterion condensation on the surface of detonation nanodiamond particles does indeed take place.     

Theory of competitive counterion adsorption on flexible polyelectrolytes: divalent salts

The counterion distribution around an isolated flexible polyelectrolyte in the presence of a divalent salt is evaluated using the adsorption model [M. Muthukumar, J. Chem. Phys. 120, 9343 (2004)] that considers the Bjerrum length, salt concentration, and local dielectric heterogeneity as physical variables in the system. Self-consistent calculations of effective charge and size of the polymer show that divalent counterions replace condensed monovalent counterions in competitive adsorption. The theory further predicts that at modest physical conditions for a flexible polyelectrolytes such as sodium polystyrene sulfonate in aqueous solutions polymer charge is compensated and reversed with increasing divalent salt. Consequently, the polyelectrolyte shrinks and reswells. Lower temperatures and higher degrees of dielectric heterogeneity between chain backbone and solvent enhance condensation of all species of ions. Complete diagrams of states for the effective charge calculated as functions of the Coulomb strength and salt concentration suggest that (a) overcharging requires a minimum Coulomb strength and (b) progressively higher presence of salt recharges the polymer due to either electrostatic screening (for low Coulomb strengths) or coion condensation (for high Coulomb strengths). Consideration of ion-bridging by divalent counterions leads to a first-order collapse of polyelectrolytes in modest presence of divalent salts and at higher Coulomb strengths. The authors' theoretical predictions are in agreement with the generic results from experiments and simulations.     

Counterion release from adsorbed highly charged polyelectrolyte: an electrooptical study

The adsorption of sodium poly(4-styrene sulfonate) on oppositely charged beta-FeOOH particles is studied by electrooptics. The focus of this paper is on the release of condensed counterions from adsorbed polyelectrolyte upon surface charge overcompensation. The fraction of condensed Na+ counterions on the adsorbed polyion surface is estimated according to the theory of Sens and Joanny and it is compared with the fraction of condensed counterions on nonadsorbed polyelectrolyte. The relaxation frequency of the electrooptical effect from the polymer-coated particle is found to depend on the polyelectrolyte molecular weight. This is attributed to polarization of the layer from condensed counterions on the polyion surface, being responsible for creation of the effect from particles covered with highly charged polyelectrolyte. The number of the adsorbed chains is calculated also assuming counterion condensation on the adsorbed polyelectrolyte and semiquantative agreement is found with the result obtained from the condensed counterion polarizability of the polymer-coated particle. Our findings are in line with theoretical predictions that the fraction of condensed counterions remains unchanged due to the adsorption of highly charged polyelectrolyte onto weakly charged substrate.     

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.