Browsing by Author "Lützenkirchen, J"

Now showing 1 - 3 of 3
  • Thumbnail Image
    Item
    Consistent treatment of "denticity" in surface complexation models
    (Elsevier; Cambridge Publications, 2010-06) Kulik, DA; Lützenkirchen, J; Payne, TE
    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.
  • No Thumbnail Available
    Item
    Guidelines for thermodynamic sorption modelling in the context of radioactive waste disposal
    (Elsevier, 2013-01-01) Payne, TE; Brendler, V; Ochs, M; Baeyens, B; Brown, PL; Davis, JA; Ekberg, C; Kulik, DA; Lützenkirchen, J; Missana, T; Tachi, Y; Van Loon, LR; Altmann, S
    Thermodynamic sorption models (TSMs) offer the potential to improve the incorporation of sorption in environmental modelling of contaminant migration. One specific application is safety cases for radioactive waste repositories, in which radionuclide sorption on mineral surfaces is usually described using distribution coefficients (K-d values). TSMs can be utilised to provide a scientific basis for the range of K-d values included in the repository safety case, and for assessing the response of K-d to changes in chemical conditions. The development of a TSM involves a series of decisions on model features such as numbers and types of surface sites, sorption reactions and electrostatic correction factors. There has been a lack of consensus on the best ways to develop such models, and on the methods of determination of associated parameter values. The present paper therefore presents recommendations on a number of aspects of model development, which are applicable both to radioactive waste disposal and broader environmental applications. The TSM should be calibrated using a comprehensive sorption data set for the contaminant of interest, showing the impact of major geochemical parameters including pH, ionic strength, contaminant concentration, the effect of ligands, and major competing ions. Complex natural materials should be thoroughly characterised in terms of mineralogy, surface area, cation exchange capacity, and presence of impurities. During the application of numerical optimisation programs to simulate sorption data, it is often preferable that the TSM should be fitted to the experimentally determined K-d parameter, rather than to the frequently used percentage sorbed. Two different modelling approaches, the component additivity and generalised composite, can be used for modelling sorption data for complex materials such as soils. Both approaches may be coupled to the same critically reviewed aqueous thermodynamic data sets, and may incorporate the same, or similar, surface reactions and surface species. The quality of the final sorption model can be assessed against the following characteristics: an appropriate level of complexity, documented and traceable decisions, internal consistency, limitations on the number of adjustable parameter values, an adequate fit to a comprehensive calibration data set, and capability of simulating independent data sets. Key recommendations for the process of TSM development include: definition of modelling objectives, identification of major decision points, a clear decision-making rationale with reference to experimental or theoretical evidence, utilisation of a suitable consultative and iterative model development process, testing to the maximum practicable extent, and thorough documentation of key decisions. These recommendations are consistent with international benchmarks for environmental modelling. Copyright © 2013, Elsevier
  • No Thumbnail Available
    Item
    Treatment of multi-dentate surface complexes and diffuse layer implementation in various speciation codes
    (Elsevier, 2015-04) Lützenkirchen, J; Marsac, R; Kulik, DA; Payne, TE; Xue, ZG; Orsetti, S; Haderlein, SB
    Spectroscopic studies and atomistic simulations of (hydr)oxide surfaces show that ionic aqueous adsorbates can bind to one, two, three, or four surface oxygen atoms (sites), forming multi-dentate species in surface complexation reactions. The law of mass action (LMA) for such reactions can be expressed in several alternative scales of surface concentration (activity). Unlike for mono-dentate surface complexes, the numerical value of the equilibrium constant is not independent of the choice of the surface concentration scale. Here, we show in a number of examples that the different formalisms implemented in popular speciation codes (MINEQL, MINTEQ, PHREEQC, and ECOSAT) yield different results for the same systems when the same parameters are used. We conclude that it is very important to generate general equations to easily transfer stability constants between the different concentration scales. It is of utmost importance for application of these models to reactive transport that the implementation in both the model fitting and speciation codes, and in the transport codes, is transparent to users. We also point to the problem that the implementation of the diffuse layer formalism in the various codes is not necessarily generally applicable. Thus, codes like VisualMinteq or MINEQL involve the Gouy–Chapman equation, which is limited to symmetrical (z:z) electrolytes, while PHREEQC and ECOSAT use general equations. Application of the former two to environmental problems with mixed electrolytes will therefore involve an inconsistency. © 2014 Elsevier Ltd.