Consistent treatment of "denticity" in surface complexation models
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Date
2010-06
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Elsevier; Cambridge Publications
Abstract
Spectroscopic studies and atomistic simulations of (hydr)oxide surfaces, which show that some aqueous cations bind to two or four surface oxygen atoms, have increased interest in multi-dentate surface complexation models (SCMs) [1-3]. However, it remains unclear how the (fitted) values of
intrinsic equilibrium constants K int/m (referenced to infinite dilution) for δ-dentate M surface-binding reactions (δ >1) depend on the choice of concentration scale. In existing SCM codes, a surface complex may be treated in scales of either: molarity/molality ([]); site coverage fraction (Θ); surface mole fraction (x); molecular surface density (Γ, in mol•m-2); or relative density Γ/Γo (o, where Γo = 2 •10-5 mol•m-2 is the reference adsorbed density [4]). Our aim was to investigate, for ‘denticities’ 1≤ δ ≤4, how to convert the K int,δ values fitted for a given titration data set (the same solid concentration cS, specific surface area As, and monolayer site density ΓC) between different concentration scales. For single-site monodentate surface binding reactions, K int/m expressed in all concentration scales ([], Θ, x, Γ, o) reduce to the same value K M int,1. For the binding with δ≤2, conversion factors from xKM int,δ to ΘKM int,δ are about δ. From []KM int,δ to any other scale, they involve (csAsΓx)δ-1 which is ca. 10-5 for δ = 2 or 10-15 for δ = 4 at typical cS = 1 g•dm-3, As = 10 m2g-1, and ΓC = 10-6 mol•m-2. Conversions of K/int from [], Θ and x scales into the Γ scale involve (ΓC)1-δ, which has a value ranging from 10/5 to 10/18 at 10-6 < ΓC < 10-5 mol•m-2. The K/int conversions from [], Θ and x to the o scale include (Γo/ΓC)δ-1 which vanishes if ΓC = Γo (then oKM int,δ = xKM int,δ). Our findings show that the use of published KM int,δ (δ ≥ 2) in SCMs may lead to erroneous results, if concentration scales are not precisely defined both in the original fitting and in the subsequent application. At trace ion concentrations, using formally monodentate surface species would be safe especially on ‘strong’ sites, for which the density is typically adjusted to reproduce multi-site isotherms. Our results from comparative fitting of KM/int,δ with SCM codes using different scales show the magnitudes of ‘denticity effects’; we discuss ways to correct for these effects in re-using, comparing or correlating values of KM/int,δ. In a further thermodynamic treatment, e.g. deriving the entropy effect of the adsorption reaction from KM/int,δ fitted for different temperatures, the constants must first be made dimensionless and independent of δ and ΓC by converting them into the (o) scale.
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Keywords
Complexes, Density, Simulation, Cations, Binding energy, Surface area
Citation
Kulik, D. A., Lützenkirchen, J., & Payne, T. E. (2010). Consistent treatment of "denticity" in surface complexation models. 20th Annual V.M. Goldschmidt Conference (Goldschmidt 2010) - "Earth, Energy and the Environment", 13th - 18th June 2010. Knoxville, Tennessee: Knoxville Convention Center. In Geochimica et Cosmochimica Acta, 74(12), A544.