Cylindrical Soft Particles

Consider a cylindrical soft particle, that is, an infinitely long cylindrical hard particle of core radius a covered with an ion-penetrable layer of polyelectrolytes of thickness d in a symmetrical electrolyte solution of valence z and bulk concentration (number density) n. The polymer-coated particle has thus an inner radius a and an outer radius b = a + d. The origin of the cylindrical coordinate system (r, z, cp) is held fixed on the cylinder axis. We consider the case where dissociated groups of valence Z are distributed with a uniform density N in the polyelectrolyte layer so that the density of the fixed charges in the surface layer is given by pgx = ZeN. We assume that the potential i/ (r) satisfies the following cylindrical Poisson-Boltz-mann equations  

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Consider the electrostatic interaction between two parallel dissimilar cylindrical soft particles 1 and 2. We denote by di and d2 the thicknesses of the surface charge layers of cylinders 1 and 2, respectively. Let the radius of the core of soft cylinder 1 be fli and that for soft cylinder 2 be U2- We imagine that each surface layer is uniformly charged. Let Z and N, respectively, be the valence and the density of fixed-charge layer of cylinder 1, and Z2 and N2 for cylinder 2. 

The electrophoretic mobility fiuoi an infinitely long cylindrical soft particle in a tangential field for the case where Xa l,Ka, Xd , Kd, is given by Eq. (21.55), namely. 

For cylindrical soft particles, Ohshima [49,50] derived the following mobility expressions ... 

Ohshima, H., Electrophoretic mobility of cylindrical soft particles. Colloid Polym. ScL, 275, 480,... 

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]. 

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