Understanding the mechanism of ion diffusion in hardened cement paste is of great importance for predicting long-term durability of concrete structures. Gel pores in calcium silicate hydrate (CeSeH) phase forms dominant pathway for transport in cement paste with low w/c ratios where the electrical double layer effects play an important role. Experimental results suggest that the effective diffusivity of chloride ions is similar as that of tritiated water (HTO) and higher than the sodium ions. This difference can be attributed to the electrical double layer near the charged CeSeH surfaces. In order to understand species transport processes in CeSeH and to quantify its effective diffusivity, a multiscale modeling technique has been proposed to combine atomic-scale and pore-scale modeling. At the pore scale, the lattice Boltzmann method is used to solve a modified Nernst Planck equation to model transport of ions in gel pores. The modified Nernst Planck equation accounts for steric and ion-ion correlation effects by using correction term for excess chemical potential computed through the results from the grand canonical Monte Carlo scheme at atomic scale and in turn bridges atomic scale model with pore scale model. Quantitative analysis of pore size influence on effective diffusivity carried out by this multiscale model shows that the contribution of the Stern layer to ion transport is not negligible for pores with diameter less than 10 nm. The developed model is able to reproduce qualitatively the trends of the diffusivity of different ions reported in literature.
Atomistic simulations provide insight into the crystal structure of minerals, surfaces, and mineral-fluid interaction mechanisms. Such modelling has been successfully applied to better understand structural, thermodynamic, and transport properties of clay minerals, the thermodynamics of ions adsorption, and clay mineral surface reactivity at an atomic scale. In principle, quantum mechanics- based modelling allows system description without use of any empirical system-dependent parameters. In practice, however, the complete quantum mechanical description of the condensed matter is only feasible for small systems containing few atoms, due to the limitations of currently available computational resources. Therefore, the simulations of complex reactive processes rely on a number of approximations at different levels of theory. These approximations are chosen as a compromise between the computational accuracy and the ability to include the relevant chemical processes.
This chapter starts with a short overview of the methods of quantum chemistry currently applied to the simulations of clay minerals. Theoretical equations are intentionally excluded. The focus is on the physical rationale behind the methods, assumptions applied, and their consequences for the interpretation of the results. For the theoretical details of the methods, the reader is directed to the specialized text books and review articles provided as references. The second part of the chapter deals with the applications. The chapter starts with the description of the bulk crystal structure, continues with the structural properties of the surfaces and surface-fluid interfaces, and concludes with thermodynamic and structural aspects of adsorption.
Clay minerals are important adsorbents in soils and sediments for hazardous contaminants in the environment. A whole variety of adsorption models for clay minerals has been developed over the past few decades. In the first part of this chapter, a brief overview of existing models describing cation exchange and surface complexation is presented. The second part presents for a large number of heavy metals and radionuclides exhibiting oxidation states from + I to + VI experimental adsorption data onto montmorillonite (Mt) and illite. A quasimechanistic nonelectrostatic adsorption model is applied to describe quantitatively the uptake of these elements over a broad pH, background electrolyte, and adsorbate concentration range. In the third part, special focus is put on the adsorption behaviour of iron on Mt. Wherever possible, a multidisciplinary approach is followed, whereby the wet chemistry studies are complemented by modelling and spectroscopic investigations with the aim of validating the underlying assumptions in the adsorption model.
Dissolution of carbonate minerals is a complex multistep process,
characterized by the particular sequence of steps dependent on pH and background
electrolyte concentration. Currently, available dissolution models for carbonates do
not consider dependence of the surface speciation on the local surface topography.
We have developed a new approach combining grand canonical Monte Carlo
(GCMC) and kinetic Monte Carlo (KMC) methods to investigate the influence of
water pH and electrolyte concentration onto processes of surface charging and
dissolution of carbonates. GCMC simulations of the calcite−electrolyte system are
used to calculate populations of protonated sites. We consider two basic speciation
models characterized by different spatial charge distributions at the surface: “ionic”,
where surface >CO32− sites are represented by “−2” charges at the corresponding
lattice positions; and “oxygen”, where surface >CO32− sites are represented by triplets
of “−2/3” charges at the positions of oxygen atoms.
The speciation of carbonate ion
protonation probabilities is found to be controlled by local charge densities and the
presence of electrolyte species.
In all simulation results, protonation affinity of the surface >CO32− sites followed the trend kink (most acidic) > step > terrace (least acidic), with the same trend observed with respect to adsorption probabilities of Cl− ions. The influence of protonated site concentrations obtained in GCMC simulations was investigated in KMC simulations. The direct comparison of simulated and experimental data showed that the oxygen model, with an assumption of congruent dissolution, reproduces both the pH dependence of the calcite dissolution rate and the morphology of the calcite surface. On the basis of the considered model, we could identify four key factors that define pH-dependent dissolution mechanisms of calcite: (1) increase of the kink site propagation rate at pH < 10; (2) increase of kink site generation frequency at pH 4−7; (3) increase of monolayer pit generation frequency at pH = 2−4; and (4) acceleration of kink site propagation and generation at pH 2−4 due to the second protonation step. The combined GCMC + KMC approach shows great potential in resolving surface speciation of carbonates as functions of solvent composition and surface geometry and their influence on the dissolution mechanisms and rates. Generally, this approach could potentially be applied to any other mineral−fluid system.
Reactivity of minerals is controlled by chemical processes at mineral- fluid interfaces acting at different time- and length scales. Various modeling approaches are available to characterize scale-specific aspects of mineral-fluid interface chemistry. Most fundamental aspects of mineral reactivity are provided by atomic scale simulations. Several attempts have been made to interpret macroscopic observation based on atomic scale simulations alone. Many of them have failed however, because of neglecting the pore scale transport phenomena. Pore scale simulation, provide an elegant way to link idealized nanometer scale atomistic description of mineral reactivity with structural and compositional heterogeneities of natural systems. The main challenges are the spatial and temporal coupling of physical models and the upscaling of transport parameters for the macroscopic interpretation of the system behavior. This paper summarizes the current molecular-scale knowledge on mineral-fluid inter- face chemistry, obtained from complementary coarse-grain simulation approaches. Using the most recent developments in this field, we highlight the complexity and challenges of the pore-scale modeling and suggest a roadmap for the process-based description of mineral dissolution/precipitation across different scales.
The diffusion of SO42- in Opalinus Clay: Measurements of effective diffusion coefficients and evaluation of their importance in view of microbial mediated reactions in the near field of radioactive waste repositories
Through-diffusion experiments with 36Cl-, 35SO42− and HTO in Opalinus Clay (OPA) samples from a deep borehole in North-East Switzerland (Benken; BE) have been performed. The effect of burial depth on the experimental results has been investigated. It could be shown that the effective diffusion coefficients decrease with sample depth for all three tracers. Moreover, there was a good correlation with the texture of the samples. The diffusion coefficients for HTO are the largest (De = 5.4–8.8 × 10−12 m2 s−1), followed by those for 36Cl- (De = 0.7–1.9 × 10−12 m2 s−1), and finally 35SO42− (De = 0.2–0.6 × 10−12 m2 s−1). 36Cl- was partially excluded from the total porosity resulting in an accessible porosity smaller than the total porosity (εCl = 0.041–0.064). 35SO42−, on the other hand, showed interaction with OPA resulting in a capacity factor (α) larger than the total porosity (εtot = 0.13–0.16). Using extended Archie's law the accessible porosity for 35SO42− was estimated between 0.013 and 0.030. This enabled to evaluate the sorption coefficient of 35SO42− from the measured capacity factor, resulting in values of Kd between 6 × 10−5 and 9 × 10−5 m3 kg−1.
Through-diffusion experiments with tritiated water (HTO) and 36Cl- as a function of pore water concentration (0.01–5 M) were performed on two Ordovician-age argillaceous rock samples from the Blue Mountain Fm and Queenston Fm shales of the Paleozoic intracratonic Michigan Basin in Canada. This study reveals that the effect of ionic strength on the anion-transport porosity is similar, and only the minimal anion excluded porosity is higher in the Blue Mountain Fm shale. The differences in rock sample mineralogy cannot explain this effect. It is hypothesized that the structure of the Blue Mountain Fm shale samples has led to pore space openings suffi- ciently small that they behave as interlayers. Such pores are defined as interlayer equivalent (ILE) pores. These ILE pores, as in the case of interlayer pores, can act to permanently limit the anion-accessible porosity. Pore-size distribution measurements provide further evidence of increased potential for ILE pores within the Blue Mountain Fm samples. A Donnan model, which includes consideration of both ILE and uncharged pores, is shown to describe the effect of molar concentration on the anion-accessible porosity in the argillaceous rocks investigated.
The pore size distribution of two natural argillaceous rock samples, Opalinus Clay (OPA) and Helvetic Marl (HM) was investigated with five different methods: NMR, NMR cryoporometry, mercury intrusion porosimetry and CO2 adsorption, as well as N2 adsorption. Due to different physical principles of these methods different ranges of pore width could be detected, from micropores (< 2 nm) to mesopores (2–50 nm) and macropores (> 50 nm). The aim was to shed light on the role of small pores on the transport properties of natural ar- gillaceous rocks, in particular to explain the differences of anion diffusion in the two argillaceous rock sam- ples. Knowing that Helvetic Marl exhibits a stronger anion exclusion than Opalinus Clay it was hypothesized that HM (with its smaller phyllosilicate and smectite content compared to OPA) has more interlayer equivalent (ILE) pores than OPA. ILE pores are defined as pores so narrow (< 0.5 nm) that diffuse double layers, formed at negatively charged surfaces, are overlapping. Accordingly, ILE pores behave similarly as interlayer pores and may block the anion diffusion. This study could not confirm the hypothesis that HM has more ILE pores. Similar pores size distributions were determined for both materials, even with a tendency of a larger fraction of small pores in OPA as compared to HM. However, all methods have limitations in the range of very small (nm) pores.
The effect of the pore water composition on the diffusive anion transport was studied for two different argillaceous, low permeability sedimentary rocks, Opalinus Clay (OPA) and Helvetic Marl (HM). The samples were saturated with different solutions with varying molar concentration and different main cations in the solution: NaCl based pore solutions and CaCl2 based pore solutions. The total porosity was measured by through-diffusion experiments with the neutral tracer HTO. Experiments performed in NaCl solutions resulted in a porosity of 0.12 for OPA and 0.03 for HM, and are consistent with results of the experiments in CaCl2 solutions. The total porosity was independent of the molar concentration, in contrast to the measured anion porosity, which increased with increasing molar concentration. It could further be observed that the pore solution based on the bivalent cation calcium shielded the negative surface charge stronger than the monovalent cation sodium, resulting in a larger measureable anion-accessible porosity in the case of CaCl2 solutions.
The data was modelled based on an adapted Donnan approach of Birgersson and Karnland (2009). The model had to be adjusted with a permanent free, uncharged porosity, as well as with structural information on the permanent anion exclusion because of so-called bottleneck pores. Both parameters can only be evaluated from experiments. Nevertheless, taking these two adaptions into account, the effect of varying pore water compositions on the anion-accessible porosity of the investigated argillaceous rocks could be satisfactorily described.
Understanding ion transport through clays and clay membranes is important for many geochemical and environmental applications. Ion transport is affected by electrostatic forces exerted by charged clay surfaces. Anions are partly excluded from pore water near these surfaces, whereas cations are enriched. Such effects can be modeled by the Donnan approach. Here we introduce a new, comparatively simple way to represent Donnan equilibria in transport simulations. We include charged surfaces as immobile ions in the balance equation and calculate coupled transport of all components, including the immobile charges, with the Nernst-Planck equation. This results in an additional diffusion potential that influences ion transport, leading to Donnan ion distributions while maintaining local charge balance. The validity of our new approach was demonstrated by comparing Nernst-Planck simulations using the reactive transport code Flotran with analytical solutions available for simple Donnan systems. Attention has to be paid to the numerical evaluation of the electrochemical migration term in the Nernst-Planck equation to obtain correct results for asymmetric electrolytes. Sensitivity simulations demonstrate the influence of various Donnan model parameters on simulated anion accessible porosities. It is furthermore shown that the salt diffusion coefficient in a Donnan pore depends on local concentrations, in contrast to the aqueous salt diffusion coefficient. Our approach can be easily implemented into other transport codes. It is versatile and facilitates, for instance, assessing the implications of different activity models for the Donnan porosity.
Safety assessment studies of future nuclear waste repositories carried out in many countries predict selenium-79 to be a critical radionuclide due to its presence as anions in three relevant oxidation states (VI, IV, -II) resulting in weak retardation by most common rock minerals. This assumption, however, ignores its potential uptake by AFm phases, positively charged anion exchangers, which are present in significant quantities in the cementitious materials used in artificial barriers. Here we report for the first time wet chemistry and spectroscopic data on the interaction of the most relevant selenium anion species under the expected strongly reducing conditions, i.e. HSe-, with two AFm phases commonly found in cement, monocarbonate (AFm-MC) and hemicarbonate (AFm-HC). Batch sorption experiments showed that HSe- is retained much more strongly by AFm-HC (solid-liquid distribution ratio, Rd, of 100±50 L kg-1) than by AFm-MC (Rd = 4±2 L kg-1) at the equilibrium pH (~12). X-ray absorption fine-structure (XAFS) spectroscopy revealed that the larger d-spacing in AFm-HC (d-spacing = 8.2 Å) provides easy access for HSe- to the AFm interlayer space for sorption, whereas the smaller d-spacing of AFm-MC (d-spacing = 7.55 Å) hinders interlayer access and limits HSe- sorption mostly to the outer planar surfaces and edges of the latter AFm phase. XAFS spectra further demonstrated that Se(-II) prevalently sorbed in the interlayers of AFm-HC, is better protected from oxidation than Se(-II) prevalently sorbed onto the outer surfaces of AFm-MC. The quantitative sorption data along with the molecular-scale process understanding obtained from this study provide crucial insight into the Se retention by the cementitious near-field of a radioactive waste repository under reducing conditions.
14C-containing dissolved organic compounds may significantly contribute to the calculated annual overall dose emanated from a deep geological repository for radioactive waste. To date, there is a general lack of knowledge concerning the transport behaviour of low molecular weight organic compounds in the geosphere. The present work is aiming at a generic approach to measure weak adsorption of such compounds onto selected clay minerals. Percolation experiments were employed to sensitively measure the retardation of low molecular weight carboxylates and alcohols in compacted illite and kaolinite as a function of the ionic strength. Detection limits of ~10-5m3kg-1 for the involved sorption distribution coefficients were attained thereby. The adsorption of alcohols on clays was near the detection limit and assumed to occur predominately via H-bonding. The adsorption of organic anions was influenced by several factors such as molecular structure, type of clay surfaces and the chemical composition of the aqueous phase. It was found that the relative position of neighbouring hydroxyl groups strongly influ- enced the retardation behaviour. Alpha-hydroxylated carboxylates, such as lactate, were found to be most retarded. Ligand exchange at the edge aluminol sites is the most probable explanation for the uptake of the negatively charged organic test compounds by the clay surface. The breakthrough behaviour of organic anions was additionally impacted by anion exclusion in illite. The demonstrated weak retardation of the test compounds can be robustly introduced in transport models, leading thus to a much lower contribution of 14C to the expected long-term overall dose.
An internally consistent thermodynamic dataset for aqueous species in the system Ca-Mg-Na-K-Al-Si-O-H-C-Cl was generated using the thermodynamic database for minerals of Holland and Powell (1998; updated Thermocalc dataset ds55). This dataset makes it possible to perform geochemical and reactive transport modeling with high levels of accuracy and reliability.
The stability of major aqueous complexes at elevated temperatures and pressures was constrained using selected reaction constant data (for example plot A and B). The Gibbs energy of formation of aqueous ions and complexes was simultaneously optimized with GEMSFITS against a large selection of solubility experiments over a wide range of conditions, taking the standard properties of minerals (unmodified) from the Holland and Powell internally consistent database (for example, plot C). The resulting thermodynamic dataset is consistent with the complex formation data, with the mineral solubility experiments, and with the standard properties of minerals from Holland and Powell database. The internally consistent dataset can be used to model natural fluid-rock interaction (for example, plot D).
Comparison of calculated and measured experimental data for: (A) the stability constant of HCO3- as function of pressure at temperatures of 55, 150 and 250 °C; (B) the association constant of CaCl+ as function of temperature at saturated water vapor pressure; (C) calcite solubility in NaCl solutions at 400 °C; (D) log(Ca/Mg) molar ratios from sedimentary fluids in equilibrium with calcite and disordered dolomite, at temperatures of 50 to 150 °C and at saturated water vapor pressure.
Mineral precipitation and dissolution in aqueous solutions has a significant effect on solute transport and structural properties of porous media. The understanding of the involved physical mechanisms,
which cover a large range of spatial and temporal scales, plays a key role in several geochemical and industrial processes.
Here, by coupling pore scale reactive transport simulations with classical
nucleation theory, we demonstrate how the interplay between homogeneous and heterogeneous
precipitation kinetics along with the non-linear dependence on solute concentration affects the
evolution of the system. Such phenomena are usually neglected in pure macroscopic modelling.
Comprehensive parametric analysis and comparison with laboratory experiments confirm that
incorporation of detailed microscale physical processes in the models is compulsory. This sheds light on
the inherent coupling mechanisms and bridges the gap between atomistic processes and macroscopic
Iron occurs in clay minerals in both ferric and ferrous forms. Depending on its oxidation state and the environmental conditions, it can participate in redox reactions and influence the sorption processes at surfaces of clay minerals. Knowing the oxidation state and the preferential structural position of Fe2+ and Fe3+ is essential for the detailed understanding of the mechanism and kinetics of such processes. In this study, molecular dynamics (MD) calculations based on density functional theory (DFT+U) were applied to simulate the incorporated Fe in bulk montmorillonite and to explain the measured Fe K-edge X-ray absorption fine structure (XAFS) spectra. The analysis of the experimental data and simulation results suggested that iron in montmorillonite is preferentially incorporated as Fe3+ into the octahedral layer. The simulations showed that there is no preferential occupation of cis- or trans-sites by Fe2+ and Fe3+ in bulk montmorillonite. A very good agreement between the ab initio simulated and the measured XAFS spectra demonstrate the robustness of the employed simulation approach.
Quantitative description of thermodynamic and molecular mechanism of Al incorporation into calcium-silicate hydrates (C-S-H), the main binder in hydrated cement paste, is essential for development of novel cementitious materials with a lower CO2 footprint. Thermodynamics integration
based on ab initio molecular dynamic simulations was applied to estimate the Gibbs free energy of the Al exchange between different silica tetrahedral sites forming the dreierketten-chains at the C-S-H surface and aqueous Al(OH)4− anions. The calculations confirm that the Al substitute for Si into bridging tetrahedral sites with an estimated equilibrium constant KAl/Si ∼ 1. Al for Si substitution is further found to favor the crosslinking between adjacent chains of the same C-S-H layer. This result is in a good agreement with recent conclusions made from 27Al MAS NMR spectroscopy results. Mesoscale Monte Carlo simulations were performed with the calculated KAl/Si to interpret experimental observations of Al incorporation into C-S-H. The simulation results suggest that the chemical affinity of Al to C-S-H is controlled by electrostatic interactions and the Al(OH)4−/Si(OH)3O− aqueous molar ratio.
The anion exclusion behavior in two different clay stones, Opalinus Clay (OPA) and Helvetic Marl (HM), was studied using a well-established experimental through-diffusion technique. The ionic strength of the pore water was varied between 0.01 and 5 M to evaluate its effect on the diffusion of HTO and 36Cl−. The total porosity determined by HTO-diffusion was independent of the ionic strength, while the anion accessible porosity varies with the ionic strength of the pore water. In the case of Opalinus Clay, the anion accessible porosity increases from 3% at low ionic strength (0.01 M) up to 8.4% at high ionic strength (5 M), whereas the anion accessible porosity of Helvetic Marl increases from 0.6% up to only 1.1%. The anion exclusion effect in HM is thus more pronounced than that in OPA, even at high ionic strength. This observation can be correlated to differences in mineralogy and to the fact that HM has a larger fraction of interlayer equivalent pores. Interlayer equivalent pores are small pores in compressed clay stones that are small enough to have, because of overlapping electric double layers, properties similar to those of interlayers and are therefore rather inaccessible for anions.