Particle Charges in Nonaqueous Colloidal Dispersions

Abstract

Numerical solutions of the Poisson−Boltzmann equation for potentials in the electrical double layer surrounding a particle are used to derive a new relationship between the particle charge q and the surface potential ζ. Unlike the linear ζ−q relation for a particle in charge-free media, the new relation shows that as the particle charge increases, the initial linear increase of the potential slows down and asymptotes to a finite value. The asymptotic values of the potential at high particle charges are dependent on the Debye length (or the ionic charge density) of the media and are of the order of a few hundred millivolts for particles in typical nonaqueous dispersions, e.g., those used as liquid developers for electrographic images. Thus, with this relationship, the reported values of charge and the electrophoretic mobility determined experimentally for these dispersions correspond to physically reasonable values of ζ potentials, which are smaller than that expected from the linear relation by more than an order of magnitude. In addition, the variations of particle charges with ionic charge densities and particle concentrations are examined.

Numerical Solution of the Poisson–Boltzmann Equation for a Spherical Cavity

“…In this case, the properties of the system only depend on the ionic valences (z 1 , z 2 ), the value of Ka, and the parameter D, Eqs. [9] and [11]. For equal ion mobilities, the parameter D is proportional to the ratio between the volume charge density and the conductivity at the center of the cavity.…”

“…According to Eqs. [9] and [11], the charge density at the origin is proportional to the product D * (Ka) 2 , and does not depend on the ion valences. Figures 7a and 7b show that, for a given charge density at the center of the cavity, the potential drop strongly increases with the valence of those ions that have the same sign as that of the charge density.…”

“…It is tempting to assign to the parameter K , Eq. [9], the meaning of the reciprocal of the Debye screening length κ. However, κ is traditionally defined in terms of the ion concentrations in an electroneutral solution while K , Eq.…”

“…However, κ is traditionally defined in terms of the ion concentrations in an electroneutral solution while K , Eq. [9], is defined at the center of the cavity where the liquid is, in general, charged (Eq. [2]).…”

Controlling the self-assembly of magnetic nanoparticles by competing dipolar and isotropic particle interactions

“…The effective zeta-potential ζ p of a single particle is not accessible experimentally, and is instead estimated from equation 1. 29 The latter depends on the dielectric constant of the medium and the ionic strength, and can thus be 15 assumed to be low in the present system. In correspondence with other weakly charged particulate systems in organic media under virtually salt-free conditions, we assume a value for κR = 0.2, (R = d c /2) thus corresponding to a long-ranged electrostatic repulsion potential as a result of the low ionic strength in organic media 20 (dashed lines in Figure 4).…”