Charge density Gouy-Chapman theory

Assume is -25 mV for a certain silica surface in contact with O.OOlAf aqueous NaCl at 25°C. Calculate, assuming simple Gouy-Chapman theory (a) at 200 A from the surface, (b) the concentrations of Na and of Cr ions 10 A from the surface, and (c) the surface charge density in electronic charges per unit area. 

In Fig. 8 density profiles are presented for several values of charge density a on the wall and for the wall potential h = — and h= Fig. 9 contains the corresponding ionic charge density profiles. For the adsorptive wall potential h < 0) the profiles q z) in Fig. 9(a) and j (z) in Fig. 8(a) are monotonic, as in the Gouy-Chapman theory. For a wall which is neutral relative to the adsorption A = 0 the density profiles are monotonic with a maximum at the wall position. This maximum also appears on the charge... 

According to the Gouy-Chapman theory, the surface charge densities on the aqueous and membrane sides, and o , respectively, can be expressed as... 

Figure 2.10 Schematic representation of the variation of the excess, or nett, surface charge density as a function of the distance away from the electrode surface, according to the Gouy-Chapman theory. The distance of nearest approach of the ions, with their associated solvation...

Due to the finite size of the ions and the solvent molecules, the solution shows considerable structure at the interface, which is not accounted for in the simple Gouy-Chapman theory. The occurrence of a decrease of C from the maximum near the pzc is caused by dielectric saturation, which lowers the dielectric constant and hence the capacity for high surface-charge densities. 

The Thomas-Fermi model of a metal is similar to the Gouy-Chapman theory for electrolytes. In this model the surface-charge density o is... 

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)... 

Before we proceed to the Gouy-Chapman theory of electrical double layers, it is worthwhile to note that relations similar to Equations (45) and (47) can also be derived for double layers surrounding spherical particles. The equation for surface charge density takes the form... 

At constant surface potential, the force provided by the new model is smaller than predicted by the Gouy-Chapman theory. In contrast, at constant surface charge density, the dielectric constant and the thickness of region I have effects opposite to those at constant surface potential. 

When the surface charge is generated through dissociation equilibrium, the difference between the forces calculated using the new model and the Gouy-Chapman theory is much larger than for constant charge density or constant surface potential. 

Figure 9.20. Relationship between pH, surface potential, (or Coulombic term, log P, or Coulombic free energy, AGcoui) and surface charge density, o (or surface protonation), for various ionic strengths of a 1 1 electrolyte for a hydrous ferric oxide surface [P = exp(--Fi/ // 7 )]. (a) Dependence of the Coulombic term and surface potential on solution pH note the near-Nemstian behavior at low ionic strength, (b) xp versus or these curves correspond to the Gouy-Chapman theory, (c) o versus pH these are the curves obtained experimentally. (From Dzombak and Morel, 1990.)...

In the DL model, assuming Gouy-Chapman theory for a symmetrical electrolyte of charge z and 25°C, the charge density, tr, at some distance away from the surface, is given by... 

Stem improved the Gouy-Chapman theory of the DDL by assuming that some ions are tightly retained immediately next to colloid surfaces in a layer of specifically adsorbed or Stem- layer cations. The double layer is diffuse beyond this layer. A satisfactory approximation of the Stem model can be made by assuming that the specifically adsorbed ions quantitatively reduce the surface density of the colloid. The diffuse portion of the double layer then is assumed to develop on a colloid surface of correspondingly reduced charge density. Sample Stem-modification calculations for a series of monovalent cations are shown in Fig. 8.10, Relatively few of the... 

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