Surface charge density inner-sphere complex

The Poisson-Boltzman (P-B) equation commonly serves as the basis from which electrostatic interactions between suspended clay particles in solution are described ([23], see Sec.II. A. 2). In aqueous environments, both inner and outer-sphere complexes may form, and these complexes along with the intrinsic surface charge density are included in the net particle surface charge density (crp, 4). When clay mineral particles are suspended in water, a diffuse double layer (DDL) of ion charge is structured with an associated volumetric charge density (p ) if av 0. Given that the entire system must remain electrically neutral, ap then must equal — f p dx. In its simplest form, the DDL may be described, with the help of the P-B equation, by the traditional Gouy-Chapman [23-27] model, which describes the inner potential variation as a function of distance from the particle surface [23]. 

For inner sphere complexes with the entire charge at the surface plane Uxi x = Zx and the Boltzmann factor becomes simply exp(—ZxFV s/RT). For outer sphere complexes nx = 0 and both activities are determined by ipd only. Assuming that, except for the electrostatic interactions, the surface phase behaves ideal, the ratios of the surface group activities in Eqs. (46), (51) and (52) can be replaced by ratios of site fractions, 6x = SX/Nj where is the total density of surface sites ... 

Thus, current versions of the model allow sorption of inner-sphere complexes directly to surface hydroxyls whereas outer-sphere complexes are located at the [3-plane. Recent modifications have included an extension to allow parameter estimation of surface site densities, surface acidity constants and site densities using Bom solvation and crystal chemical theory (Sverjensky, 1993, 1994 Sverjensky Sahai, 1996 Sahai Sverjensky, 1997a,b) and to treat electrolyte ions as nonspecific adsorbing species that screen charge in the p-plane (Robertson Leckie, 1997). 

The chemical interpretation of o-in measured by the Schofield method depends sensitively on the type and concentration of probe electrolyte used. If these properties are chosen so that the cation in the reacting electrolyte neutralizes precisely the exposed functional group charge associated with isomorphic substitutions and dissociated hydroxyls and so that the anion neutralizes only the exposed protonated functional groups, then q+ and q. will have optimal magnitude for the chosen pH value and CTjn will be truly an intrinsic surface charge density. On the other hand, if the cation in the probe electrolyte is not able to displace all of the native adsorbed cations in, e.g., inner-sphere surface complexes, or if the anion cannot displace all of the native anions bound to protonated functional groups, or if either ion does not form only neutral surface complexes in the soil clay, then Ojn will differ from its optimal value. 

A detailed model of the interfacial region requires the specification of the position of the plane where the diffuse ion swarm begins, A popular choice in the literature of soil chemistry has been jc = 0, which means that outer-sphere surface complexes are neglected entirely and inner-sphere surface complexes are ignored if they would protrude beyond the plane to which (Tin, the intrinsic surface charge density, refers. (See Secs. 1.5 and 3.1 for a discussion of trjn ) That this choice is not reasonable physically, however, can be seen from a simple calculation involving Eq. 5.16. Consider a 1 1 electrolyte at the concentration Cq == 100 mol m" and suppose that /r(0) = SRT/F, a value that is not unrealistic for a smectite siloxane surface. Then k = = 1.04 x 10 m" at 298 K, a =... 

Oh = net proton charge density due to binding of protons and OH" ions a,s = charge density due to inner-sphere surface complexes Oos = charge density due to outer-sphere surface complexes... 

The coordination of these oxygens at the monomolecular step will, of course, change as the mineral reacts with the aqueous solution because the MnOe octahedra shown with the wireframe (Figure 2) must detach as a surface complex as the step migrates. This detachment causes newly uncovered metals to reestablish their inner-coordination spheres by movement and deprotonation of water molecules. If the reaction proceeds at steady state, these water molecules dissociate to maintain a fixed charge density and a fixed numbers of different metal-ligand coordination numbers (7, 8). 

The goal in applying any SCM is to develop a self-consistent methodology for parameter estimation such that a set of standard parameters to describe surface acidity, site density, and the charge/potential relationships for different minerals can be developed and can be used in conjunction with spectroscopic data to guide the selection of appropriate adsorption reactions for the formation of metal ion surface complexes (i.e., inner vs. outer sphere, mono vs. hidentate, mononuclear vs. 

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