Colloid coating poly electrolytes

Consider a dilute suspension of polyelectrolyte-coated spherical colloidal particles (soft particles) in a salt-free medium containing counterions only. We assume that the particle core of radius a (which is uncharged) is coated with an ion-penetrable layer of polyelectrolytes of thickness d. The polyelectrolyte-coated particle has thus an inner radius a and an outer radius b = a + d (Fig. 6.4). We also assume that ionized groups of valence Z are distributed at a uniform density N in the poly electrolyte... 

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