Electrophoretic mobility of a spherical colloidal particle

Abstract

The equations which govern the ion distributions and velocities, the electrostatic potential and the hydrodynamic flow field around a solid colloidal particle in an applied electric field are reexamined. By using the linearity of the equations which determine the electrophoretic mobility, we show that for a colloidal particle of any shape the mobility is independent of the dielectric properties of the particle and the electrostatic boundary conditions on the particle surface. The mobility depends only on the particle size and shape, the properties of the electrolyte solution in which it is suspended, and the charge inside, or electrostatic potential on, the hydrodynamic shear plane in the absence of an applied field or any macroscopic motion.New expressions for the forces acting on the particle are derived and a novel substitution is developed which leads to a significant decoupling of the governing equations. These analytic developments allow for the construction of a rapid, robust numerical scheme for the solution of the governing equations which we have applied to the case of a spherical colloidal particle in a general electrolyte solution. We describe a computer program for the conversion of mobility measurements to zeta potential for a spherical colloidal particle which is far more flexible than the Wiersema graphs which have traditionally been used for the interpretation of mobility data. Furthermore it is free of the high zeta potential convergence difficulties which limited Wiersema's calculations to moderate values of 5. Some sample computations in typical 1 : 1 and 2 : 1 electrolytes are exhibited which illustrate the existence of a maximum in the mobility at high zeta potentials. The physical explanation of this effect is given. The importance of the mobility maximum in testing the validity of the governing equations of electrophoresis and its implications for the colloid chemist's picture of the Stern layer are briefly discussed.

Cell Model of the Direct Current Electrokinetics in Salt-Free Concentrated Suspensions: The Role of Boundary Conditions

“…Despite the differences already described between salt and salt-free suspensions, the salt-free electrophoresis resembles in some sense the low κa regime of suspensions in electrolyte solutions, where no maxima in electrophoretic mobility versus surface potential are observed. 34 Influence on the Electrophoretic Mobility and Electrical Conductivity of the rp ≈ 0 Approximation. As already pointed out, previous salt-free electrophoresis models have used an approximation, valid in principle for those cases with low solid to solution permittivity ratios, to the true boundary condition for the perturbed electrical potential at the surface of the particles (compare eqs 43 and 44).…”

“…The drag coefficient λ c in eq 6 is related to the limiting ionic conductance Λ c 0 by 34 where N A is Avogadro's number. It is useful to apply a perturbation scheme as follows where quantities with the superscript "(0)" refer to equilibrium values, and for low applied field strengths the perturbations will be considered linearly dependent on the field, and second and higher orders are disregarded.…”

Carboxylated Ficolls: Preparation, Characterization, and Electrophoretic Behavior of Model Charged Nanospheres

“…at 70% ionization of all carboxyl groups), which implies that the mobility does not follow the increase of charge amount but becomes nonmonotonic at a critical surface charge density, as predicted by many theories. [1][2][3][4][5][6][7] The surface potential ψ 0 can be determined experimentally according to pK a -pK 0 ) 0.434eψ 0 (R)/kT (4) where K a and K 0 are the apparent and the intrinsic dissociation constants respectively, e is the electron charge, k is Boltzmann's constant, and T is absolute temperature. K a can be deduced from where pK 0 is obtained by extrapolating pK a to R ) 0.…”

Numerical and Analytical Studies of the Electrical Conductivity of a Concentrated Colloidal Suspension

“…At equilibrium, that is, when no electric field is applied, the distribution of electrolyte ions obeys the Boltzmann distribution and the equilibrium electrical potential, Ψ (0) , satisfies the Poisson-Boltzmann equation. 2 The boundary conditions at the slip plane and at the outer surface of the cell for the equilibrium electrical potential are given by or alternatively and where σ is the surface charge density of the particle. Equation 10 ensures the electroneutrality of the cell.…”