Soft particle double layer interaction between

In Chapter 11, we derived the double-layer interaction energy between two parallel plates with arbitrary surface potentials at large separations compared with the Debye length 1/k with the help of the linear superposition approximation. These results, which do not depend on the type of the double-layer interaction, can be applied both to the constant surface potential and to the constant surface charge density cases as well as their mixed case. In addition, the results obtained on the basis of the linear superposition approximation can be applied not only to hard particles but also to soft particles. We now apply Derjaguin s approximation to these results to obtain the sphere-sphere interaction energy, as shown below. 

In this chapter, we give approximate analytic expressions for the force and potential energy of the electrical double-layer interaction two soft particles. As shown in Fig. 15.1, a spherical soft particle becomes a hard sphere without surface structures, while a soft particle tends to a spherical polyelectrolyte when the particle core is absent. Expressions for the interaction force and energy between two soft particles thus cover various limiting cases that include hard particle/hard particle interaction, soft particle/hard particle interaction, soft particle/porous particle interaction, and porous particle/porous particle interaction. 

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). 

However, PDMS-modified silica aggregates seem to coat nearly the entire toner particle. Their topographical diameter is doubled compared to the HMDS-coated particles, but the diameter estimated from the phase image is very similar to the one foimd for the HMDS-modified ones. The maximum phase shift is reduced compared to the samples above. This indicates that the silica aggregates are covered by a soft material - the silylation layer. This soft material covers not only the particles but also the resin surface in between them. This can be seen by the decreased phase shift in between the silica particles compared to the pure resin. As in sample (Fig. 5b), probably the PDMS silylation layer interacts with the toner resin surface, increasing the overall adhesion. 

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