Diffuse double layer adsorption

Some emphasis is given in the first two chapters to show that complex formation equilibria permit to predict quantitatively the extent of adsorption of H+, OH , of metal ions and ligands as a function of pH, solution variables and of surface characteristics. Although the surface chemistry of hydrous oxides is somewhat similar to that of reversible electrodes the charge development and sorption mechanism for oxides and other mineral surfaces are different. Charge development on hydrous oxides often results from coordinative interactions at the oxide surface. The surface coordinative model describes quantitatively how surface charge develops, and permits to incorporate the central features of the Electric Double Layer theory, above all the Gouy-Chapman diffuse double layer model. 

The main, currently used, surface complexation models (SCMs) are the constant capacitance, the diffuse double layer (DDL) or two layer, the triple layer, the four layer and the CD-MUSIC models. These models differ mainly in their descriptions of the electrical double layer at the oxide/solution interface and, in particular, in the locations of the various adsorbing species. As a result, the electrostatic equations which are used to relate surface potential to surface charge, i. e. the way the free energy of adsorption is divided into its chemical and electrostatic components, are different for each model. A further difference is the method by which the weakly bound (non specifically adsorbing see below) ions are treated. The CD-MUSIC model differs from all the others in that it attempts to take into account the nature and arrangement of the surface functional groups of the adsorbent. These models, which are fully described in a number of reviews (Westall and Hohl, 1980 Westall, 1986, 1987 James and Parks, 1982 Sparks, 1986 Schindler and Stumm, 1987 Davis and Kent, 1990 Hiemstra and Van Riemsdijk, 1996 Venema et al., 1996) are summarised here. 

It is the outer portion of the double layer that interests us most as far as colloidal stability is concerned. The existence of a Stern layer does not invalidate the expressions for the diffuse part of the double layer. As a matter of fact, by lowering the potential at the inner boundary of the diffuse double layer, we enhance the validity of low-potential approximations. The only problem is that specific adsorption effects make it difficult to decide what value to use for J/6. 

In subsequent chapters it will be the potential in the diffuse double layer that concerns us. It can be described relative to its value at the inner limit of the diffuse double layer, which may be either the actual surface or the Stern surface. We continue to use the symbol p0 for the potential at this inner limit. It should be remembered, however, that specific adsorption may make this quantity lower than the concentration of potential-determining ions in the solution would indicate. We see in Chapter 12 how the potential at some (unknown) location close to this inner limit can be measured. It is called the zeta potential. 

The possible usefulness of this relationship — which is known as the Hiickel equation — should not be overlooked. Throughout Chapter 11 we were concerned with the potential surrounding a charged particle. Equation (11.1) provides a way of evaluating the potential at the surface, i/ o, in terms of the concentration of potential-determining ions. Owing to ion adsorption in the Stern layer, this may not be the appropriate value to use for the potential at the inner limit of the diffuse double layer. Although f is not necessarily identical to i/ o, it is nevertheless a quantity of considerable interest. 

Fig. 2.2 Structure of the electric double layer under different conditions of electrode polarization (a) metal positively charged, anions present at the inner Helmholtz plane (chemically interacting with metal) and in the diffuse double layer beyond the outer Helmholtz plane (b) metal negatively charged, inner Helmholtz plane empty, cations in diffuse layer (c) metal positively charged, strong adsorption of anions in inner Helmholtz plane, balancing cations in the diffuse layer...

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. 

Figure 1. Schematic Diffuse double layer formed as a result of anion adsorption, showing the effect of negative adsorption of similions on the bulk concentration. A. Initial electrolyte concentration. B. Final electrolyte concentration. C. Final concentration if there were no negative adsorption of similions...

It is postulated that one of the ions of the adsorbed 1 1 electrolyte is surface active and that it forms an ionized monolayer at the solid/liquid interface. All counterions are assumed located in the diffuse double layer (no specific adsorption). Similions are negatively adsorbed in the diffuse double layer. Since the surface-containing region must be electrically neutral, the total moles of electrolyte adsorbed, n2a, equals the total moles of counterions in the diffuse double layer which must be equal to the sum of the moles of similions in the diffuse double layer and the charged surface, A[Pg.158]

While the linear adsorption isotherms of Figure 4 are illustrative only, they are not inconsistent with reality. The simplest theory of the electrical double layer, the Gouy-Chapman approximation, predicts that if the pH is not far from the isoelectric point, the charge represented by counter ions in the diffuse double layer is related to the surface potential as follows (4, 52, 86) ... 

HFOa Adsorption isotherms for arsenite and arsenate over free concentration range from 10-7 to 10-3 M (pH 4-10). Fitted to Langmuir isotherm at low concentrations and linear isotherm at higher concentrations. Dzombakand Morel (1990) fitted this data to their diffuse double layer model Pierce and Moore (1982)... 

Clays are generally considered to be effective barriers for flow of water and solutes due to their low permeability and high ion adsorption capacity. However, as environmental criteria for the emission of contaminants and water from clay barriers become increasingly stringent, it is crucial to be aware of all relevant driving forces and fluxes and to take them into account in model assessments. In this respect the processes of chemical and electro-osmosis may not be neglected in clayey materials of hydraulic conductivity < 10-9 m/s [7], At these low conductivities the surface charge of the clay particles and the counter-ion accumulation in diffuse double layers enable explanation and quantification of osmotic processes and semi-permeability in clays [1],... 

The same procedure has been applied to the data shown in Fig. 3.40 (solid line 3) though Eq. (3.87) strictly holds only for neutral chains in good solvent [248], It this case all points that cannot be accounted for by the DLVO-theory have been included. The resulting h = 186 A is larger than the thickness h of the adsorption layer. It may be speculated that this ensues from the diffuse double layer interactions omitted in this treatment. 

A more mechanistic and robust depiction of reversible metal adsorption is provided by SCMs that account explicitly for competitive speciation reactions using an equilibrium thermodynamic framework. Examples of SCMs in current use include the constant capacitance model (CCM), the diffuse double-layer model (DDLM), and the triple-layer model (TLM) (Stumm Morgan, 1996 Koretsky, 2000). Each of these models envisages... 

The surface after adsorption will be chained with a potential, as in Figure 9.14, so that primary adsorption can be treated in terms of a capacitor model called the Stem model [43]. The other type of adsorption that can occur involves an exchange of ions in the diffuse layer with those of the surface. In the case of ion exchange, the primary ions are chemically bound to the structure of the solid and exchanged between ions in the diffuse double layer. 

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