Langmuir 1992,8, 2850-2854
2850
Art i d e s Electrophoresis of Heterogeneous Colloids: Doublets of Dissimilar Particles Mark C. Fair and John L. Anderson* Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 Received April 1 , 1992. In Final Form: June 15, 1992 The electrophoretic dynamics of colloidal particles possessing a distribution of zeta potential can be significantlydifferent than the dynamics of uniformly charged particles. Microelectrophoresis experiments using heterogeneous doublets formed in a suspension of amidine- and carboxylate-modified polystyrene particles demonstrate some of these differences and support the theoretical analysis applicable to these colloids. An applied electric field of a few volts per centimeter caused the heterogeneous doublets to not only translate but also rotate into alignment with the field. Reversing the field direction caused the doublets to rotate end-for-end and realign with the applied field. These observations provide the first experimental demonstration of electrophoreticrotation of colloidal particles. The mobility of the aligned doublets agrees quantitatively with theoretical calculations based on the size and zeta potential of each of the two spheres comprising the doublets.
Introduction Electrophoresis is the movement of a colloidal particle through a liquid in an electric field. Measurement of the electrophoretic mobility, defined as the ratio of particle velocity (v) to applied electric field ( E ) ,is an important technique for characterizing the charge on the surface of colloids. These measurements are generally interpreted with the Smoluchowski equation
where { is the zeta potential of the surface, often taken as the electrical potential at the particle’s surface relative to the fluid, and e and q are the dielectric constant and coefficient of viscosity for the fluid, respectively. (Note that we use the “esu” system of electrostatic units.) The charge density of the surface can be estimated from {by using the Gouy-Chapman theory of the electrical double layer or other more sophisticated models. Electrophoresis differs from electromigration of “point charges”in that the charged surface of a particle is screened by the counterion cloud in the adjacent electrolyte solution, giving rise to a diffuse “double layer” of charge. The thickness of the double layer is of order K - ~ , the Debye screening length which is inversely proportional to the square root of the ionic strength of the solution; K - ~= 10 A for a 0.1 mol/L solution of NaCl in water at room temperature. Taken together, the particle and its double layer are a neutral mass, albeit not a rigid body, and hence the applied electric field produces no net force on the material contained within a boundary enclosing the particle and double layer. This means that the particle moves such that the total viscous force of the fluid on the particle plus its double layer is zero, which leads to hydrodynamically interesting p h e n ~ m e n a . ~For ? ~ example, Smoluchowski’s equation applies to a particle of any shape,
* Author to whom correspondence should be addressed.
(1) Hunter, R. J. Zeta Potential in Colloid Science; Academic Press: New York, 1981. (2) Anderson, J. L. Annu. Reu. Fluid Mech. 1989,21, 61.
particles do not rotate no matter what their shape, and each particle in a cluster of particles having the same zeta potential moves at the same velocity, given by Smoluchowski’s equation, no matter how many particles are in the cluster and how they are spaced. The validity of Smoluchowski’s equation rests on four criteria: (1)the Debye screening length must be very small compared to the radius of curvature (R) at all points on the particle’s surface (KR >> 1);(2) polarization of the double layer is negligible, exp(elfl/2kT)
