Gibbs energy minimization approach to modeling sorption equilibria at the mineral-water interface: Thermodynamic relations for multi-site-surface complexation

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ID: 294717
2002
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Abstract
A Gibbs energy minimization (GEM) approach to calculate chemical equilibria involving surface complexation at the mineral-water interfaces is presented, permitting the whole continuum “aqueous speciation - heterogeneous adsorption - surface (co)precipitation - solid solution” to be modeled only in elemental stoichiometry, without additional material balance constraints for the total number of surface sites. The thermodynamic stability of surface-bound species is considered in a way similar to that of the solid-solution endmembers, gases, and aqueous species. This consideration is made possible by introducing: (1) the standard and reference states of surface species involving a single value of reference site density Γo; (2) an expression of (electro)chemical potential linking quantities of the surface species with the amount and specific surface area of the sorbent; (3) activity/concentration relationships between aqueous sorbates and surface species, based on the surface activity terms (SAT) as functions of the maximum site densities Γmax; (4) the surface type area fractions φα,t for describing faces or patches on heterogeneous surface of multi-site-surface sorption mineral phases; (5) an elemental stoichiometry and standard partial molal properties of the amphoteric neutral surface functional group ≡OH and derived surface complexes at ambient conditions, comparable between all (hydr)oxide mineral surfaces. For the ;OH group (in 2pKA surface complexation models), a O0.5Ho stoichiometry is conventionally defined from a reaction 0.5H2Oaq = >O0.5Ho, with logKn = 1.74436 (at Γo = 20 μmol · m−2) which is independent of temperature, pressure, pH, fO2, amount and specific surface area of the sorbent, aqueous speciation, and surface speciation. It follows that all the non-reacted >O0.5Ho groups have constant activity in the presence of liquid H2O and are thus macroscopically indistinguishable. The surface heterogeneity is described via standard thermodynamic properties of the surface complexes (reacted groups), such as “surface hydronium” >O0.5H2+, “surface hydroxyl” >O0.5−, adsorbed cations or anions, as well as through φα,t and the common or individual Γt,max parameters. Theoretical findings, implemented in the GEM-Selektor code, are illustrated by modeling the literature potentiometric titration and adsorption data for silica and rutile in NaCl solutions with the triple-layer (TLM), the generalized double-layer (DLM), and the non-electrostatic (NEM) surface complexation models (SCM). Some examples were also calculated with the FITEQL3.2 code to check for compatibility. It is shown: (1) how approximate conversions between partial molal properties of surface species and intrinsic adsorption constants can be performed for different total site densities ΓC ≠ Γo; (2) what are the regions of “geometrically ideal” and “non-ideal” adsorption behavior for the chosen SCM and how they are controlled by the SAT = f(Γmax) on heterogeneous surfaces; and (3) why different sets of TLM parameters are not thermodynamically equivalent, and how a meaningful “optimal” set can be determined from titration data. Due to the separation of Γmax parameters from Γo and, hence, from thermodynamic constants, the thermodynamic SCMs (in GEM implementation) can provide more insight into the relationships between surface types, complexes, bulk mineral sorbent, and aqueous sorbates, therefore permitting a more thorough use of microscopic/spectroscopic data in sorption modeling than has ever been possible.
Reference Key
openalex_W1964417493 Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Dmitrii A. Kulik
Journal american journal of science
Year 2002
DOI
10.2475/ajs.302.3.227
URL
https://doi.org/10.2475/ajs.302.3.227
Keywords Keywords not found

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