Soft particle electrophoresis

This section deals with a general theory of electrophoresis of soft particles and approximate analytic expressions for the mobility of soft particles [30-51]. This theory unites the electrophoresis theories of hard particles [1-29] and of polyelec-trolytes [52], since a soft particle tends to a hard particle in the absence of the polymer layer and to a polyelectrolyte in the absence of the particle. 

Electrokinetic equations describing the electrical conductivity of a suspension of colloidal particles are the same as those for the electrophoretic mobility of colloidal particles and thus conductivity measurements can provide us with essentially the same information as that from electrophoretic mobihty measurements. Several theoretical studies have been made on dilute suspensions of hard particles [1-3], mercury drops [4], and spherical polyelectrolytes (charged porous spheres) [5], and on concentrated suspensions of hard spherical particles [6] and mercury drops [7] on the basis of Kuwabara s cell model [8], which was originally applied to electrophoresis problem [9,10]. In this chapter, we develop a theory of conductivity of a concentrated suspension of soft particles [11]. The results cover those for the dilute case in the limit of very low particle volume fractions. We confine ourselves to the case where the overlapping of the electrical double layers of adjacent particles is negligible. 

Ohshima [42-45] presented a theory for electrophoresis of a soft particle. The general mobility expression of a soft particle that consists of the hard particle core of radius a covered with a layer of polyelectrolytes of thickness d (=b — a) and moves in an electrolyte solution of viscosity tj is given... 

For the case where the hxed charges are not uniformly distributed in the polyelectrolyte layer and that the relative permittivity in the poly electrolyte layer does not take the same value as that in the bulk solution phase, the above theory must be modihed as discussed by Ohshima and Kondo [52] and Hsu et al. [54]. Tseng et al. [55] considered the effects of charge regulation on the mobility in the polyelectrolyte layer. The case where the polyelectrolyte layer is not fully ion-penetrable is considered in Ref. [56]. Varoqui [57] considered the case where electrically neutral polymers are adsorbed with an exponential segment density distribution onto the particle surface with a charge density. Ohshima [58] extended Varoqui s theory [57] to the case where adsorbed polymers are charged. Saville [59] and Hill et al. [60] considered the relaxation effects of soft particles in electrophoresis. 

The above theory can be extended to electrophoresis of liquid drops [70] and soft particles [71a,b] in salt-free media. The result for liquid drops of viscosity is as follows [70] ... 

As in the case of electrophoresis of hard cylindrical particles, the electrophoretic mobility of a soft cylinder depends on the orientation of the particle [44, 47]. 

The second problem of interest is that of the electrophoresis of soft (polyelectrolyte-covered) particles. This problem is not merely of academic interest polyelectrolytes are often used to control the surface charge of the particles and hence the stability and other properties of their suspensions. In the presence of such polyelectrolytes, the particles get covered by a layer of the polymer in an amount controlled by its interactions with the solid and by the quahty of the solvent for the polyelectrolyte used. 

Duval, J. F. L. 2007. Electrophoresis of soft colloids Basic principles and applications. In Environmental Colloids and Particles Behaviour, Separation and Characterisation, ed. K. J. Wilkinson and J. R. Lead, 315-344. 1st ed. Chichester, UK Wdey. 

---