Models diffuse-layer sorption

Substantial efforts have been made to develop physicochemical models for ion exchange based on the Gouy-Chapman diffuse-layer theory (e.g., 9, 10). This work not only has provided insight into the role of diffuse-layer sorption in the ion-exchange process but also has pointed to the need to consider other factors, especially specific sorption at the surface. Consideration of specific sorption enables description of the different tendencies of ions to... 

Several physicochemical models of ion exchange that link diffuse-layer theory and various models of surface adsorption exist (9, 10, 14, 15). The difficulty in calculating the diffuse-layer sorption in the presence of mixed electrolytes by using analytical methods, and the sometimes over simplified representation of surface sorption have hindered the development and application of these models. The advances in numerical solution techniques and representations of surface chemical reactions embodied in modem surface complexation mod-... 

Sorption Modeling-Diffuse-Layer Model Parameters... 

To be useful in modeling electrolyte sorption, a theory needs to describe hydrolysis and the mineral surface, account for electrical charge there, and provide for mass balance on the sorbing sites. In addition, an internally consistent and sufficiently broad database of sorption reactions should accompany the theory. Of the approaches available, a class known as surface complexation models (e.g., Adamson, 1976 Stumm, 1992) reflect such an ideal most closely. This class includes the double layer model (also known as the diffuse layer model) and the triple layer model (e.g., Westall and Hohl, 1980 Sverjensky, 1993). 

Macroscopic experiments allow determination of the capacitances, potentials, and binding constants by fitting titration data to a particular model of the surface complexation reaction [105,106,110-121] however, this approach does not allow direct microscopic determination of the inter-layer spacing or the dielectric constant in the inter-layer region. While discrimination between inner-sphere and outer-sphere sorption complexes may be presumed from macroscopic experiments [122,123], direct determination of the structure and nature of surface complexes and the structure of the diffuse layer is not possible by these methods alone [40,124]. Nor is it clear that ideas from the chemistry of isolated species in solution (e.g., outer-vs. inner-sphere complexes) are directly transferable to the surface layer or if additional short- to mid-range structural ordering is important. Instead, in situ (in the presence of bulk water) molecular-scale probes such as X-ray absorption fine structure spectroscopy (XAFS) and X-ray standing wave (XSW) methods are needed to provide this information (see Section 3.4). To date, however, there have been very few molecular-scale experimental studies of the EDL at the metal oxide-aqueous solution interface (see, e.g., [125,126]). 

Current surface complexation models were developed with a focus on minor and trace ions and hence do not consider sorption in the diffuse layer. Even the triple-layer model (34), which can include electrolyte sorption as outer-sphere complexes, does not consider sorption in the diffuse layer. To... 

Surface complexation models can be extended to account explicitly for electrostatic sorption by calculating excess counterion concentrations in the diffuse layer in addition to specific sorption. Counterions in the diffuse layer (e.g., Ca ) can then be treated as distinct from those in bulk solution (e.g., Ca2+) and those that are specifically sorbed (e.g., =Sp-Caf). The total sorption is given by the sum of the concentrations of specifically sorbed and electrostatically sorbed species ... 

The Common Thermodynamic Database Project, CTDP (van der Lee and Lomenech, 2004), is another thermodynamic database that includes sorption equilibrium constants for the constant capacitance model, the diffuse layer model, and... 

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