Effect of ionic sizes on the stability ratio of a dispersion of particles with a charge-regulated surface

The influence of the ionic sizes on the stability of a dispersion of particles, which have an amphoteric, charged-regulated surface, is discussed. A modified Poisson-Boltzmann equation, which takes into account the sizes of ionic species, is adopted to describe the electrical field. An extended DLVO theory, which takes into account the electrical, the van der Waals, and the hydration energies, is used to estimate the stability of a colloidal dispersion. The effects of the key parameters, including ionic strength, pH, and density of surface sites, on the behavior of problem under consideration are examined. The results obtained are qualitatively consistent with experimental findings in the literature.     

Sedimentation of concentrated spherical particles with a charge-regulated surface

The sedimentation of a concentrated colloidal dispersion is examined for the case of an arbitrary double-layer thickness. Here, a general mixed-type condition on particle surface is assumed, and the classic models, which assume constant surface properties, can be recovered as the special cases of the present analysis. In particular, the behavior of biological cells, which carry dissociable functional groups on their surfaces, and particles, which are capable of exchanging ions with the surrounding medium, can be simulated by the present model. The mixed-type boundary condition leads to several interesting results in both sedimentation velocity and sedimentation potential as double-layer thickness and the concentration of particles vary.     

Effect of multiple ionic species on the electrophoretic behavior of a charge-regulated particle

It is often assumed in the conventional electrophoresis analysis that the liquid phase contains only one kind of each cation and anion. That analysis is extended to the case where the liquid phase contains multiple ionic species in this study so that the conditions considered are closer to reality. Using a dispersion of SiO(2) particles, which is of a charge-regulated nature, as an example, where the dispersion pH is adjusted by HCl and NaOH, numerical simulation is conducted to examine the electrophoretic behaviors of the particle under various conditions. We show that the presence of multiple ionic species is capable of yielding profound and interesting electrophoretic behaviors, which are justified by the experimental data in the literature. In addition, we show that two types of double-layer polarization (DLP) are present that have not been reported previously in the electrophoresis analyses. Type I DLP, which reduces the mobility of a particle, occurs inside the double layer, and type II DLP, which raises that mobility, occurs immediately outside the double layer.     

Stability of a dispersion of particles covered by a charge-regulated membrane: effect of the sizes of charged species

The influence of the sizes of charged species on the stability of a colloidal dispersion is investigated theoretically. We consider the case where a particle comprises a rigid core and an amphoteric, charge-regulated membrane layer, which simulates biocolloids and particles covered by artificial membranes. A modified Poisson-Boltzmann equation, which takes the sizes of all the charged species into account, is adopted to describe the electrical field. The effects of other key parameters such as electrolyte concentration, pH, and the valence of counterions on the behavior of a dispersion are also examined. We show that the larger the effective size of the counterions, the greater the stability ratio, which is consistent with experimental observations in the literature.     

Dynamic electrophoretic mobility of a concentrated dispersion of particles with a charge-regulated surface at arbitrary potential

The dynamic electrophoretic mobility of a concentrated dispersion of biocolloids such as cells and microorganisms is modeled theoretically. Here, a biological particle is simulated by a particle, the surface of which contains dissociable functional groups. The results derived provide basic theory for the quantification of the surface properties of a biocolloid through an electroacoustic device, which has the merit of making direct measurement on a concentrated dispersion without dilution. Two key parameters are defined to characterize the phenomenon under consideration: the first, A, is associated with the pH of the dispersion, and the second, B, is associated with the equilibrium constant of the dissociation reaction of the functional group. We show that if A is large and/or B is small, the surface potential is high, and the effect of double-layer polarization becomes significant. In this case the dynamic electrophoretic mobility may have a local maximum and a phase lead as the frequency of the applied electric field varies. Due to the hydrodynamic interaction between neighboring particles, the dynamic electrophoretic mobility decreases with the concentration of dispersion.     

Aspects of ionic diffusion through thick matrices of charged particles

A review of the literature on ionic diffusion through matrices of charged particles shows that many workers have reported higher diffusivity of co-ions than of counterions. If these observations are correct then the requirement of electroneutrality of bulk solutions is violated. In those experiments other, not looked for, ions must have been taking part. It therefore appears that complete chemical analyses of solutions of both up- and downstream sides should be carried out, otherwise misleading inferences may be drawn, with practical consequences. Some researchers have studied transport of water under osmotic pressure differentials across clay membranes. However, a diffusing ion, during its transport from higher concentration to lower concentration, always carries its water of hydration. This second water transport process has not received attention. This suggests that at a critical concentration two transport processes will cancel each other. Attention has been drawn to this second type of water flow and its consequences. In ionic diffusion, each side of the membrane-outside solution interface is subject to the effects of the Nernst layer and Donnan zone. However, these layers and zones are seldom treated quantitatively. This has been carried out in this paper by two different methods. Both methods give identical thicknesses of the Nernst layer and Donnan zone. Finally, the effects of the presence of soluble bivalent salts on the diffusivity of different types of ions have been commented up on. In these cases some of the co-ions diffuse to the upstream side.     

Importance of temperature effect on the electrophoretic behavior of charge-regulated particles

The Joule heating effect is inevitable in electrophoresis operations. To assess its influence on the performance of electrophoresis, we consider the case of a charge-regulated particle in a solution containing multiple ionic species at temperatures ranging from 298 to 308 K. Using an aqueous SiO(2) dispersion as an example, we show that an increase in the temperature leads to a decrease in both the dielectric constant and the viscosity of the liquid phase, and an increase in both the diffusivity of ions and the particle surface potential. For a particle having a constant surface potential, its electrophoretic mobility is most influenced by the variation in the liquid viscosity as the temperature varies, but for a charged-regulated particle both the liquid viscosity and the surface potential can play an important role. Depending upon the level of pH, the degree of increase in the mobility can be on the order of 40% for a 5 K increase in the temperature. The presence of double-layer polarization, which is significant when the surface potential is sufficiently high, has the effect of inhibiting that increase in the mobility. This implies that the influence of the temperature on the mobility of the particle is most significant when the pH is close to the point of zero charge.     

Electrophoresis of ionic microgel particles: from charged hard spheres to polyelectrolyte-like behavior

We perform electrophoretic mobility measurements of ionic microgel particles in the deswollen and swollen phases. The results show that microgels behave as charged hard spheres in the first case and as free-draining spherical polyelectrolytes in the latter. A unified theory for the electrophoresis of polyelectrolyte-coated particles [H. Ohshima, Adv. Colloid Interface Sci. 62, 189 (1995)] is shown to contain the essential physics for describing the experiments, upon adequate consideration of the particles swelling behavior and network-solvent friction variations.     

Electrophoretic mobility of concentrated spheres with a charge-regulated surface

The electrophoretic behavior of a concentrated spherical colloidal particle is modeled theoretically under the Debye-Hückel condition. The surface of a particle contains dissociable functional groups, the dissociation of which yields negative fixed charges. The model derived is applicable to an arbitrarily thick double layer. We show that the absolute surface potential decreases with the increase in kappa(a); kappa and a are the reciprocal Debye length and the radius of a particle, respectively. Moreover, the variation of the absolute electrophoretic mobility as a function of kappa(a) has a maximum.     

Electrophoresis of a charge-regulated sphere at an arbitrary position in a charged spherical cavity

The electrophoresis of a charge-regulated spherical particle at an arbitrary position in a charged spherical cavity is modeled under conditions of low surface potential (<25 mV) and weak applied electric field (<25 kV/m). The charged cavity allows us to simulate the effect of electroosmotic flow, and the charge-regulated nature of the particle permits us to model various types of surface. The problem studied previously is reanalyzed based on a more rigorous electric force formula. In particular, the influences of various types of charged conditions on the electrophoretic behavior of a particle and the roles of all the relevant forces acting on the particle are examined in detail. Several new results are found. For instance, the mobility of a particle has a local minimum as the thickness of a double layer varies, which is not seen in the cases where the surface of a particle is maintained at a constant potential and at a constant charge density.     

Electrostatic behavior of the charge-regulated bacterial cell surface

The electrostatic behavior of the charge-regulated surfaces of Gram-negative Escherichia coli and Gram-positive Bacillus brevis was studied using numerical modeling in conjunction with potentiometric titration and electrophoretic mobility data as a function of solution pH and electrolyte composition. Assuming a polyelectrolytic polymeric bacterial cell surface, these experimental and numerical analyses were used to determine the effective site numbers of cell surface acid-base functional groups and Ca(2+) sorption coefficients. Using effective site concentrations determined from 1:1 electrolyte (NaCl) experimental data, the charge-regulation model was able to replicate the effects of 2:1 electrolyte (CaCl(2)), both alone and as a mixture with NaCl, on the measured zeta potential using a single Ca(2+) surface binding constant for each of the bacterial species. This knowledge is vital for understanding how cells respond to changes in solution pH and electrolyte composition as well as how they interact with other surfaces. The latter is especially important due to the widespread use of the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory in the interpretation of bacterial adhesion. As surface charge and surface potential both vary on a charge-regulated surface, accurate modeling of bacterial interactions with surfaces ultimately requires use of an electrostatic model that accounts for the charge-regulated nature of the cell surface.     

Structure and rheological behavior of highly charged colloidal particles in a cylindrical pore I. Effect of pore size

In this work we performed nonequilibrium Brownian dynamics (NEBD) computer simulations of highly charged colloidal particles in diluted suspension under a parabolic flow in cylindrical pores. The influence of charged and neutral cylindrical pores on the structure and rheology of suspensions is analyzed. A shear-induced disorder-order-disorder-like transition was monitored for low shear rates and small pore diameters. We calculate the concentration profiles, axial distribution functions, and axial-angular pair correlation functions to determine the structural properties at steady state for a constant shear flow for different pore sizes and flow strengths. Similar behavior has been observed in a planar narrow channel in the case of charged interacting colloidal particles (M.A. Valdez, O. Manero, J. Colloid Interface Sci. 190 (1997) 81). The mobility of the particles in the radial direction decreases rapidly with the flow and becomes practically frozen. The flow exhibits non-Newtonian shear thinning behavior due to interparticle interactions and particle-wall interaction; the apparent viscosity is lower as the pore diameter decreases, giving rise to an apparent slip in the colloidal suspension. The calculated slip velocity was higher than that obtained in a rectangular slit under shear flow.     

Control of the water permeability of polyelectrolyte multilayers by deposition of charged paraffin particles

We present a new way to protect polyelectrolyte multilayers from water, consisting in the adsorption and subsequent fusing of charged wax particles atop a multilayer. The formation of the wax layer is demonstrated by different techniques such as ellipsometry, contact angle measurements, and atomic force microscopy. The diffusion of water in protected and unprotected multilayers is studied by in situ neutron reflectometry. Whereas a top layer of wax crystals already allows substantial reduction of the diffusion, the fusion of this top layer leads to the dominating exclusion of water from the multilayers when dipped in water. This method opens up new interesting avenues for polyelectrolyte multilayers in practical applications where permeability of water, ions, or hydrophilic drugs is an issue.     

Effect of dextran on the deposition of latex on a glass surface

Adsorption of dextran on hairy latex particles affects the electrophoretic mobility differently, depending on the salt concentration. At a low salt concentration, dextran adsorbs between the hairs, and the expected decrease of mobility with dextran concentration is observed. When the thickness of the dextran layer is greater than the length of the hairs, the anomalous deposition of latex on glass, thought to be caused by the hairs, is eliminated.     

Importance of electroosmotic flow and multiple ionic species on the electrophoresis of a rigid sphere in a charge-regulated zwitterionic cylindrical pore

The influence of electroosmotic flow (EOF) on the electrophoretic behavior of a particle is investigated by considering a rigid sphere in a charge-regulated, zwitterionic cylindrical pore filled with an aqueous solution containing multiple ionic species. This extends conventional analyses to a more general and realistic case. Taking a pore with pK(a) = 7 and pK(b) = 2 (point of zero charge is pH = 2.5) filled with an aqueous NaCl solution as an example, several interesting results are observed. For instance, if pH < 5.5, the particle mobility is influenced mainly by boundary effect, and is influenced by both EOF and boundary effects if pH ≥ 5.5. If pH is sufficiently high, the particle behavior is dominated by EOF, which might alter the direction of electrophoresis. The ratio of (pore radius/particle radius) influences not only the boundary effect, but also the strength of EOF. If the boundary effect is insignificant, the mobility varies roughly linearly with log(bulk salt concentration). These findings are of practical significance to both the interpretation of experimental data and the design of electrophoresis devices.     

Double layer interactions between charge-regulated colloidal surfaces: pair potentials for spherical particles bearing ionogenic surface groups

The variational approach of Reiner and Radke (1990) is employed to investigate the effect of surface charge regulation upon the double layer interaction free energy V_e of pairs of colloidal particles immersed in an electrolyte. A model for dissociating surface groups that permits the consideration of an arbitrary number ofion-complexation reactions is introduced. The variational method is then used to derive (in the Poisson-Boltzmann approximation) the configurational free energy functional Ω of an ensemble of particles bearing such groups. The Debye-Hückel (DH) linearization process is applied to this functional, and ensuing consistency issues are examined.The DH free energy is extremized for a configuration of two interacting flat plates, and Derjaguin's (1934 and 1939) method is used to obtain an approximate analytical form for V_e for two different-sized spherical particles bearing different surface groups. This second problem is next considered from the perspective ofLevine's (1934, 1939b) exact multipole expansion of the electrostatic potential surrounding two axisymmetric particles. It is shown that the linear superposition approximation (LSA) for V_e developed by Levine (1939c) and Verwey and Overbeek (1948) emerges rigorously from this formulation in the limit of large interparticle separations. The interaction free energy from Levine's expansion is calculated te a six digit accuracy for identical spheres over the range of regulated behavior from fixed surface charge density q_s to fixed surface potential ψ_s for surface-surface separation h to Debye length λ ratios from 0 to 2 and ratios of the particle radius a to λ of 0.1, 1, and 10. These results are compared to those obtained from Derjaguin's method and the linear superposition approximation. Derjaguin's method is only quantitatively accurate (in error by less than 10%) for the largest value of a/λ and becomes progressively less so as the boundary is changed from perfectly regulating (constant ψ_s) to unregulated (constant q_s). Agreement of the LSA with the exact V_e is good over a wide range of parameters, but worsens for large a/λ and small h/λ. Appendices present extensions of our approach to surfaces bearing more than one type of complexing group and to the consideration of Stern layer formation at the particle-electrolyte boundary in the context of a standard model for metal oxide-aqueous interfaces.