Electrophoresis of Nonuniformly Charged Soft Particles

The value of 1/2, which is the reciprocal of the friction parameter 2, decreases as the drag exerted by the hydrogel layer on the liquid flow increases. In the limit of 1/2— 0, Eq. (21.55) tends to the well-known Smoluchowski s mobility formula for hard particles. In other words, as 1/2 increases, the hydrogel layer on the particle becomes softer. That is, the parameter 1/2 can be considered to characterize the softness of the hydrogel layer on the particle. The observed reduction of the softness parameter 1/2 (1.2 nm at 30°C to 0.9 nm at 35°C) implies that the hydrogel layer becomes harder, which is in accordance with the observed shrinkage of the hydrogel. 

Note that Makino et al. [57] found that Eq. (21.108) holds between the electro-osmotic velocity U o on a poly(N-isopropylacrylamide) hydrogel-coated solid surface and the electrophoretic mobility of a poly(N-isopropylacrylamide) hydrogel-coated latex particle. 

The surface potential of a uniformly charged soft particle in an electrolyte solution increase in magnitude with decreasing electrolyte concentration. This is not the case for a nonuniformly charged soft particle. The surface charge layer consists of a 

FIGURE 21.8 A surface charge layer consisting of two oppositely charged sublayers 1 and 2. 

The sign reversal takes place also in the electrophoretic mobility of a non-uniformly charged soft particles, as shown in this section. We treat a large soft particle. The x-axis is taken to be perpendicular to the soft surface with its origin at the front edge of the surface layer (Fig. 21.8). The soft surface consists of the outer layer —d x 0) and the inner layer (x —d), where the inner layer is sufficiently thick so that the inner layer can be considered practically to be infinitely thick. The liquid flow m(x) and equilibrium electric potential i//(x) satisfy the following planar Navier-Stokes equations and the Poisson-Boltzmann equations [39]  

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