Potential and Charge of a Soft Particle

In Chapter 1, we have discussed the potential and charge of hard particles, which colloidal particles play a fundamental role in their interfacial electric phenomena such as electrostatic interaction between them and their motion in an electric field [1 ]. In this chapter, we focus on the case where the particle core is covered by an ion-penetrable surface layer of polyelectrolytes, which we term a surface charge layer (or, simply, a surface layer). Polyelectrolyte-coated particles are often called soft particles [3-16]. It is shown that the Donnan potential plays an important role in determining the potential distribution across a surface charge layer. Soft particles serve as a model for biocolloids such as cells. In such cases, the electrical double layer is formed not only outside but also inside the surface charge layer Figure 4.1 shows schematic representation of ion and potential distributions around a hard surface (Fig. 4.1a) and a soft surface (Fig. 4.1b). 

The potential distribution outside the surface charge layer of a soft particle with surface potential j/g is the same as the potential distribution around a hard particle with a surface potential xj/g. The asymptotic behavior of the potential distribution around a soft particle and that for a hard particle are the same provided they have the same surface potential xj/o- The effective surface potential is an important quantity that determines the asymptotic behaviors of the electrostatic interaction between soft particles (see Chapter 15). 

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 ... 

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] ... 

Our findings for the weakly charged colloids suggest that even a slight softness of the intermolecular potential, has important consequences for the crystallization behavior. This effect could be relevant for experimental hard-sphere colloids, as these particles are, in fact, slightly soft. A particularly popular experimental hard-sphere colloid consists of a polymethylmethacrylate (PMMA) core coated with a thin layer of poly-12-hydroxystearic (PHSA). Due to the coating, the particles are slightly soft. We smdied the effect that such a softness has on the phase behavior and the crystallization kinetics [75]. 

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