Diffuse Double-Layer Interaction between Two Identical Spherical Colloidal Particles

A simple method is given for calculating the potential energy of the diffuse double-layer interaction between two identical spherical colloidal particles in a symmetrical electrolyte solution with the help of Derjaguin's approximation. This method uses accurate analytic expressions for the corresponding interaction energy between two parallel similar plates obtained previously (Colloids Surf. A Physicochem. Eng. Asp. 146, 213 (1999); J. Colloid Interface Sci. 212, 130 (1999)). Agreement with numerical data provided by Honig and Mul (J. Colloid Interface Sci. 36, 258 (1971)) is excellent particularly for small particle separations. Copyright 2000 Academic Press.     

Electrostatic interaction between ion-penetrable membranes in a salt-free medium

A set of coupled equations is given which determines the distributions of the electric potential and counterions in a system of two interacting identical ion-penetrable membranes of thickness d at separation h immersed in a salt-free medium containing only counterions. The solution to these coupled equations also gives the electrostatic repulsive force between the membranes. It is shown that the interaction force remains finite at h-->0, unlike the case of the interaction between two planar charged surfaces (d-->0), and that the interaction force becomes independent of the membrane fixed charge and membrane thickness d at very large h. Finally, an approximate single transcendental equation giving the solution to the coupled equations is derived.     

Electrophoretic mobility of a cylindrical colloidal particle in a salt-free medium

Approximate expressions are derived for the electrophoretic mobility of dilute cylindrical colloidal particles in a salt-free medium containing only counterions. The cylinder is assumed to be infinitely long. It is shown that as in the case of a spherical particle, there is a certain critical value of the particle surface charge separating two cases. When the particle surface charge is lower than the critical value (case 1), the electrophoretic mobility increases with increasing particle surface charge per unit length. When the particle surface charge is higher than the critical value (case 2), the mobility becomes constant (for a cylinder in a transverse field) or the increase in the electrophoretic mobility with the particle surface charge becomes suppressed (for a cylinder in a tangential field). These phenomena are caused by the effect of counterion condensation in the vicinity of the particle surface. The critical value of the particle charge is essentially independent of the particle volume fraction phi for the dilute case, unlike the case of a sphere, in which case the critical charge value is proportional to ln(1/phi).     

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.     

An efficient 1,3-dipolar cycloaddition between aromatic selenoaldehydes and nitrile oxides or nitrile imines: an easy access to selenium-containing five-membered heterocyclic ring system

1,3-Dipolar cycloaddition between aromatic selenoaldehydes, generated by thermal retro Diels-Alder reaction of anthracene cycloadducts, and nitrile oxides or nitrile imines proceeded efficiently to give the corresponding [3+2] cycloadducts as a single isomer in good yields, being 1,4,2-oxaselenazoles or 1,3,4-selenadiazoles, respectively.     

Colloid vibration potential and ion vibration potential in a dilute suspension of spherical colloidal particles

A general electroacoustic theory is presented for the macroscopic electric field in a dilute suspension of spherical colloidal particles in an electrolyte solution, which consists of the colloid vibration potential (CVP) and the ion vibration potential (IVP), induced by an oscillating pressure gradient field due to an applied sound wave. This is a unified theory that unites previous theories for CVP and those for IVP. Approximate analytic expressions are derived for CVP and IVP. The obtained IVP expression agrees with Debye's formula that is corrected by taking into account the force acting on the electrolyte ions as a result of the pressure gradient in the sound wave. The obtained CVP expression is correct to the first order of the particle zeta potential and applicable for arbitrary kappaalpha, where kappa is the Debye-Hückel parameter and alpha is the particle radius. It is found that an Onsager relation holds between CVP and dynamic electrophoretic mobility. It is also shown that the CVP from particles with very small kappaalpha approaches IVP; that is, in the limit of very small kappaalpha a particle behaves like an ion.     

Surface charge density/surface potential relationship for a spherical colloidal particle in a salt-free medium

On the basis of a theory of Imai and Oosawa (Busseiron Kenkyu52, 42 (1952); 59, 99 (1953)), approximate analytic expressions for the surface charge density/surface potential relationship for a spherical colloidal particle in a salt-free (aqueous or nonaqueous) medium containing only counterions are derived. There is a certain critical value of the surface charge density (or the total surface charge) separating two distinct cases: low surface charge density case and high surface charge density case. In the latter case counterion condensation occurs in the vicinity of the particle surface. The results are in excellent agreement with numerical calculations for the case of dilute suspensions.     

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.     

Effect of Coriolis force on counter-current chromatographic separation by centrifugal partition chromatography

The effect of Coriolis force on the counter-current chromatographic separation was studied using centrifugal partition chromatography (CPC) with four different two-phase solvent systems including n-hexane-acetonitrile (ACN); tert-butyl methyl ether (MtBE)-aqueous 0.1% trifluoroacetic acid (TFA) (1:1); MtBE-ACN-aqueous 0.1% TFA (2:2:3); and 12.5% (w/w) polyethylene glycol (PEG) 1000-12.5% (w/w) dibasic potassium phosphate. Each separation was performed by eluting either the upper phase in the ascending mode or the lower phase in the descending mode, each in clockwise (CW) and counterclockwise column rotation. Better partition efficiencies were attained by the CW rotation in both mobile phases in all the two-phase solvent systems examined. The mathematical analysis also revealed the Coriolis force works favorably under the CW column rotation for both mobile phases. The overall results demonstrated that the Coriolis force produces substantial effects on CPC separation in both organic-aqueous and aqueous-aqueous two-phase systems.     

Electrostatic Interaction between Two Dissimilar Spheres with Constant Surface Charge Density

Explicit exact analytic expressions are obtained in the form of infinite series for the potential energy of the electrostatic interaction for the system of two dissimilar hard spheres with constant surface charge density in an electrolyte solution on the basis of the linearized Poisson-Boltzmann equation. The effects of the particle polarization, that is, the internal fields induced within tim interacting spheres, which are found to be of the order of instead of 1/κa (where κ is the Debye-Hückel parameter and a is the sphere radius), are taken into account. As in the case of the interaction at constant surface potential, the zeroth-order approximation to the interaction energy corresponds to the interaction energy that would be obtained if both spheres were ion-penetrable spheres ("soft" spheres) and to that obtained by the linear superposition approximation. The first-order approximation corresponds to the interaction energy that would be obtained if either sphere were a soft sphere, with the other being a hard sphere with constant surface charge density. The first-order correction term can be interpreted as the image interaction between the soft sphere and its image with respect to the hard sphere.