Charge volume density

Space charge arises because the character of cation distribution differs from that of anion distribution (the signs of Zj are different). The volume charge density depends on the ion distribution,... 

The volume charge density depends on the ion distribution, which obeys the Boltzmann equation ... 

The quantity (symbolized by p) of electrical charge per unit volume, equal to Q/V, with SI units of coulombs per cubic meter. More technically, this definition refers to the volume charge density. See Surface Charge Density... 

The net volume charge density p at points where the potential is tft is, therefore, given by... 

It must be stressed here that for a hard sphere, is related to the surface charge density a (Chapter 1), while for a soft sphere, is related to the volume charge density ZeN. For other types of electrolytes, expressions for Y are given in Chapter 1. 

FIGURE 5.1 A hard particle of surface area A in an electrolyte solution of volume V. Pei(r) is the volume charge density at position r resulting from electrol3de ions and cr(s) is the charge density at position s on the particle surface. 

We derive an alternative expression for Fei, which corresponds to Eq. (5.70) for a hard particle, by considering a discharging process in which all the charges (both the volume charge density pfi (r) and the charge of electrolyte ions) in the system are decreased at the same rate. From Eq. (5.72), we obtain... 

Note that j/(r, v, X) is related to the volume charge density p iir, v, X) resulting from electrolyte ions at position r at stage X in the discharging process starting from the stage V by the following Poisson-Boltzmann equation ... 

We set the electric potential j/ r) to zero at points where the volume charge density p(r) resulting from counterions equals its average value (—zen). We assume that the distribution of counterions obeys a Boltzmann distribution, namely. 

We assume that the equilibrium distribution of ions obeys a Boltzmann distribution so that volume charge density p r) at position r, r being the distance from the particle center (r > a), is given by... 

We assume that charged groups of valence Z are distributed in the surface charge layers at a uniform density N. Since end effects are neglected, the fluid velocity is in the y-direction, depending only on x, and the present system can be considered to be at thermodynamic equilibrium with respect to the x-direction. We define m(x) as the fluid velocity in the y-drrection and Pei(- ) as the volume charge density of electrolyte ions, both independent of y. 

For gel type or precipitated silicas that may be (partially) penetrable for protons the shape of the crs(pH) curves is comparable, but the magnitude of the charge densities may be quite different [42]. Results obtained for Stober silica in the presence of simple 1-1 electrolytes suggest that in this ca.se a Donnan model (volume charge densities) is more appropriate as double layer model than a SGC model. 

The relationship between volume charge density, pv, and the distribution of potential is described by the Poisson equation ... 

If the probe wire is charged, then the centerline potential indicated by the probe is not simply related to the volume charge density in the bed pq (C/m3) but also depends on the charge acquired by the probe 0q (surface charge density C/m2) according to the relation... 

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