Charge density surface potential, relation

The charge density, Volta potential, etc., are calculated for the diffuse double layer formed by adsorption of a strong 1 1 electrolyte from aqueous solution onto solid particles. The experimental isotherm can be resolved into individual isotherms without the common monolayer assumption. That for the electrolyte permits relating Guggenheim-Adam surface excess, double layer properties, and equilibrium concentrations. The ratio u0/T2N declines from two at zero potential toward unity with rising potential. Unity is closely reached near kT/e = 10 for spheres of 1000 A. radius but is still about 1.3 for plates. In dispersions of Sterling FTG in aqueous sodium ff-naphthalene sulfonate a maximum potential of kT/e = 7 (170 mv.) is reached at 4 X 10 3M electrolyte. The results are useful in interpretation of the stability of the dispersions. 

The surface tension depends on the potential (the excess charge on the surface) and the composition (chemical potentials of the species) of the contacting phases. For the relation between y and the potential see - Lipp-mann equation. For the composition dependence see -> Gibbs adsorption equation. Since in these equations y is considered being independent of A, they can be used only for fluids, e.g., liquid liquid such as liquid mercury electrolyte, interfaces. By measuring the surface tension of a mercury drop in contact with an electrolyte solution as a function of potential important quantities, such as surface charge density, surface excess of ions, differential capacitance (subentry of... 

We introduce the unperturbed surface potential j/o, that is, the surface potential j/(0) in the absence of interaction ath oo. The surface charge density cr is related... 

When treating the small Debye length case, we shall frequently use surface charge density and potential interchangeably, relating them through Eq. (7.1.12). 

If E, and 2 are assumed to be constant. Eqs. [32[ and [33] predict a linear potential drop within each part of the inner double layer, as shown in Fig. (10b). The dependence of the electric potential with distance, in the region from x = d to the bulk solution, i.e, in the diffuse part of the double layer, will be exponential if the surface potential is moderate, as predicted by Eq. 124). In the case of higher surface potentials, the dependence is that shown in Eq. [26], substituting tpn by yj at X = ti. Similarly, the surface charge density, O is related to y by an equation of the type [28]. 

As noted above, we find that this kinetics formulation is applicable to cases where the salt concentration is low, and deposition extensive, so that the "smeared charge approximation holds. Assuming that depositing DNA-SWCNTs form a homogenous layer on the surface implies that the surface charge will increase with deposited density Ps (in p.m of nanotubes per p.m of surface). As surface charge increases, surface potential relative to bulk solution will also increase. Within the linearized Debye-Hiickel approximation, the surface potential is related to surface charge as ... 

Nakagaki1U) has given a theoretical treatment of the electrostatic interactions by using the Gouy-Chapman equation for the relation between the surface charge density oe and surface potential /. The experimental data for (Lys)n agrees very well with the theoretical curve obtained. 

In order to describe the effects of the double layer on the particle motion, the Poisson equation is used. The Poisson equation relates the electrostatic potential field to the charge density in the double layer, and this gives rise to the concepts of zeta-potential and surface of shear. Using extensions of the double-layer theory, Debye and Huckel, Smoluchowski,... 

The charge within the metal is confined to an extremely thin layer < 1 A) at the surface. There is no charge separation within the metal since if there were there would be an associated potential difference and this would cause a current to flow. Potential V and charge density p (coulomb [C] m 3) are related by the Poisson equation ... 

This relates the change in surface tension with the applied potential at constant electrolyte composition to the surface charge density on the metal, [Pg.44]

Since the sorbing surface holds a charge, its electrical potential differs from that of the solution. The potential difference between surface and fluid is known as the surface potential T and can be expressed in volts. The product e 4 is the work required to bring an elementary charge e from the bulk solution to the sorbing surface. According to one of the main results of double layer theory, the surface potential is related to the surface charge density by,... 

The electrosorption valence can be related to the dipole moment of an adsorbed species introduced in Chapter 4. For this purpose consider an electrode surface that is initially at the pzc and free of adsorbate. When a small excess charge density o is placed on the metal, its potential changes by an amount A given by ... 

The description of the sorption of charged molecules at a charged interface includes an electrostatic term, which is dependent upon the interfacial potential difference, Ai//(V). This term is in turn related to the surface charge density, electric double layer model. The surface charge density is calculated from the concentrations of charged molecules at the interface under the assumption that the membrane itself has a net zero charge, as is the case, for example, for membranes constructed from the zwitterionic lecithin. Moreover,... 

According to the Gouy-Chapman theory the surface charge density gp [C nr2] is related to the potential at the surface y [volt] (Eq. (vi) in Fig. 3.2)... 

The magnitude of charge on a particle can be expressed in any one of several ways total charge (Jp), surface charge density (i pj), specific particle surface gradient or field (Sps charge-to-mass ratio (J c), or specific particle potential (Eps). These are related by the following identities ... 

For our work, expressions of Ohshlma et. al. (37) obtained from an approximate form of the Poisson-Boltzmann equation were used. These analytical expressions agree with the exact solution for xRp 2. (All of our calculations meet this criterion.) The relation between the surface potential and the surface charge density Is (37)... 

This is the fundamental equation for the thermodynamic treatment of polarizable interfaces. It is a relation among interfacial tension y, surface excess 1 -, applied potential V, charge density qM, and solution composition. It shows that interfacial tension varies with the applied potential and with the solution composition. This is in fact the relation that was desired. Its implications will now be analyzed. 

EXAMPLE 11.2 Relation Between Surface Charge Density and Surface Potential. Show that for a 1 1 electrolyte in water at 25°C, Equation (69) can be rearranged to give... 

What is the relation between the surface charge density and the potential in a double layer ... 

---