Laura M Hamm

Ian C Bourg

Adam F Wallace

Benjamin Rotenberg

Molecular Simulation of CO2-and CO3-Brine-Mineral Systems

and research institutions in France or abroad, or from public or private research centers.

INTRODUCTION

Atomistic simulations-molecular dynamics (MD) and Monte Carlo (MC) simulations, ab initio and density functional theory (DFT) calculations-have proved useful in gaining insight into the molecular basis of fundamental processes in aquatic geochemistry, such as solvation, ion pair formation, adsorption, molecular diffusion, and the energetics of mineral phases [START_REF] Rotenberg | Water and ions in clays: Unraveling the interlayer/micropore exchange using molecular dynamics[END_REF][START_REF] Bickmore | Bond-valence constraints on liquid water structure[END_REF][START_REF] Hamm | Molecular dynamics of ion hydration in the presence of small carboxylated molecules and implications for calcification[END_REF][START_REF] Kerisit | Molecular simulation of the diffusion of uranyl carbonate species in aqueous solution[END_REF][START_REF] Hofmann | Ion desolvation as a mechanism for kinetic isotope fractionation in aqueous systems[END_REF][START_REF] Stack | Accurate rates of the complex mechanisms for growth and dissolution of minerals using a combination of rare-event theories[END_REF][START_REF] Wallace | Microscopic evidence for liquidliquid separation in supersaturated CaCO 3 solutions[END_REF]. Key strengths of these simulations are their ability to examine the behavior of individual atoms (where spectroscopic and other experimental methods would probe the average behavior of large numbers of molecules) and to allow constraints that would be difficult or impossible to impose in the laboratory. These features make atomistic simulations powerful tools for elucidating the manner in which collective phenomena arise from molecular scale properties in geochemical systems. The range of length and time scales probed by atomistic simulations (from angstroms to tens of nanometers and from femtoseconds to microseconds, continuously expanding with advances in the availability and sophistication of computational resources) makes them ideally suited to complement several spectroscopic techniques, including x-ray, neutron, and nuclear magnetic resonance methods.

A major limitation of the methods described in the present chapter, particularly in the case of classical mechanical (MD and MC) simulations, is the approximate nature of the models that are used to describe interatomic forces. In the simplest of these simulations, bond lengths and angles are fixed; inter-atomic interactions are modeled as the sum of two-body interactions that depend only on the identity of the interacting atoms and the distance between them; and chemical bonds are not allowed to break or form during a simulation [START_REF] Allen | Computer simulation of liquids[END_REF][START_REF] Frenkel | Understanding molecular simulation: From algorithms to applications[END_REF]. The choice of force fields (i.e., interatomic potential models) can strongly influence predicted properties such as the structure of liquid water [START_REF] Hura | Water structure as a function of temperature from X-ray scattering experiments and ab initio molecular dynamics[END_REF][START_REF] Bickmore | Bond-valence constraints on liquid water structure[END_REF], the solubility of CO 2 in water [START_REF] Lísal | Analysis of Henry's constant for carbon dioxide in water via Monte Carlo simulation[END_REF], CO 2 -water interfacial tension [START_REF] Nielsen | Predicting CO 2 -water interfacial tension under pressure and temperature conditions of geologic CO 2 storage[END_REF], and the structure of calcite-water interfaces [START_REF] Fenter | Is the calcite-water interface understood? direct comparisons of molecular dynamics simulations with specular X-ray reflectivity data[END_REF]. In this chapter, we describe how, despite these limitations, carefully designed atomistic simulations can generate useful fundamental insight into the geochemical properties of mineral-water-CO 2 and -CO 3 systems at conditions relevant to geologic carbon sequestration (GCS).

CO 3 -BRINE-MINERAL SYSTEMS CO 3 -brine speciation

The aqueous speciation of carbonate-bearing solutions has been extensively studied due to its importance as the primary buffer system in natural waters and in many engineered settings. Thermodynamic solution speciation models account for the equilibria between gaseous and solvated CO 2(aq) as well as the step wise decomposition of carbonic acid, H 2 CO 3 , into bicarbonate and carbonate ions, HCO 3 -and CO 3 2-. As aqueous carbon dioxide and carbonic acid are not easily distinguishable by analytical titration and carbonic acid is far less abundant in solution than aqueous carbon dioxide, it has become commonplace to represent the concentrations of both species collectively as the hypothetical species H 2 CO 3 * . In addition to these basic relations, speciation models also include mineral solubility products (i.e. K sp = {M(II)}{CO 3 2-}) and equilibrium constants for ion hydrolysis (i.e. K hyd = {M(II)OH + }{H + }/{M(II)}) and ion pair formation (i.e. K ip = {M(II)}{HCO 3 -} / {M(II)HCO 3 + }), such that the solubility of a given M(II)-carbonate mineral phase is equal to the sum over the activities of all the M(II)-containing species in solution under a given set of environmental conditions (temperature, pressure, CO 2 fugacity, ionic strength). Although evermore sophisticated activity coefficient corrections must be applied to account for non-ideal interactions between species at higher concentrations (Debye and Hückel 1923;[START_REF] Davies | Ion Association[END_REF][START_REF] Pitzer | Thermodynamics of electrolytes. I. Theoretical basis and general equations[END_REF], ion activity models remain the preeminent means by which dilute solutions and brines are modeled.

Recent experimental work on the early stages of homogeneous CaCO 3 crystallization, however, has challenged the standard treatment of electrolyte solutions as presented above. Titration experiments [START_REF] Gebauer | Stable prenucleation calcium carbonate clusters[END_REF] show that the calcium ion activity of a sodium bicarbonate buffer solution deviates from the amount of calcium dosed into the solution. On its own, this result is completely consistent with traditional speciation models that predict non-ideal solution behavior (i.e., ion pairing). However, analytical ultracentrifugation [START_REF] Gebauer | Stable prenucleation calcium carbonate clusters[END_REF][START_REF] Gebauer | Prenucleation clusters and non-classical nucleation[END_REF] and cryo-TEM [START_REF] Pouget | The initial stages of template-controlled CaCO 3 formation revealed by cryo-TEM[END_REF]) also suggest that ions are concentrated in subnanometer clusters that are not accounted for by ion activity models. While the presence of clusters is expected in supersaturated solutions such as those employed in these experiments, the apparently monodisperse cluster size distribution has been interpreted as evidence that the species are stable or metastable "prenucleation" clusters (PNC), although there are alternative mechanisms that can also produce similar distributions [START_REF] Faatz | Amorphous calcium carbonate: synthesis and potential intermediate in biomineralization[END_REF][START_REF] Binder | Spinodal decomposition[END_REF]. If indeed ions more favorably reside in cluster species than as ion pairs and free ions, perhaps even at equilibrium [START_REF] Gebauer | Stable prenucleation calcium carbonate clusters[END_REF][START_REF] Gebauer | Proto-valcite and proto-vaterite in amorphous calcium carbonates[END_REF][START_REF] Gebauer | Prenucleation clusters and non-classical nucleation[END_REF], then presumably the formation of calcium carbonate from solution follows a non-classical nucleation pathway dominated by cluster-cluster aggregation (PNC theory) rather than ion-by-ion addition as assumed by classical theory. Moreover, if ions are concentrated in cluster phases rather than distributed throughout solution, theoretical treatments of mass transport may need to be modified or adjusted to make more accurate predictions of real system behavior.

The possible existence of additional stable calcium carbonate/bicarbonate ion species in solution that are larger than ion pairs is not necessarily inconsistent with the tenants of standard ion activity models. Indeed the presence of triple and quadruple ion species has been suspected previously in a number of systems including iron bicarbonate solutions [START_REF] Marcus | Ion pairing[END_REF][START_REF] Fosbøl | Review and recommended thermodynamic properties of FeCO 3[END_REF]. However, in order to reconcile the existence of additional ion species with the demonstrated predictive capabilities of existing speciation models, the abundance of the additional species must be negligible near equilibrium such that their omission from standard thermodynamic databases has little effect on model predictions. Since the assertion of PNC theory [START_REF] Gebauer | Stable prenucleation calcium carbonate clusters[END_REF][START_REF] Gebauer | Proto-valcite and proto-vaterite in amorphous calcium carbonates[END_REF][START_REF] Gebauer | Prenucleation clusters and non-classical nucleation[END_REF][START_REF] Bewernitz | A metastable liquid precursor phase of calcium carbonate and its interactions with polyaspartate[END_REF], numerous MD simulation based investigations have probed the onset of CaCO 3 formation from supersaturated solutions in search of stable prenucleation clusters. To date, these studies have been unable to attribute special thermodynamic significance to a cluster of any size, which is the hallmark of PNC theory (Tribello et al. 2009;Raiteri and Gale 2010;[START_REF] Demichelis | Stable prenucleation mineral clusters are liquid-like ionic polymers[END_REF][START_REF] Wallace | Microscopic evidence for liquidliquid separation in supersaturated CaCO 3 solutions[END_REF]). In the high pH limit, it has been demonstrated, by inference (Tribello et al. 2009;Raiteri and Gale 2010) and by direct quantification of the free energy landscape [START_REF] Demichelis | Stable prenucleation mineral clusters are liquid-like ionic polymers[END_REF][START_REF] Wallace | Microscopic evidence for liquidliquid separation in supersaturated CaCO 3 solutions[END_REF], that there is no thermodynamic barrier opposing cluster formation in concentrated solutions (>15 mmol dm -3 as CaCO 3 °). This is most consistent with spinodal decomposition as a phaseseparation mechanism [START_REF] Markov | Crystal Growth for Beginners: Fundamentals of Nucleation, Crystal Growth and Epitaxy[END_REF][START_REF] Binder | Spinodal decomposition[END_REF] and implies that there is a binodal in the system that describes the coexistence of an ion-rich dense liquid phase, and an ion-poor dilute solution phase (Figure 1) [START_REF] Faatz | Amorphous calcium carbonate: synthesis and potential intermediate in biomineralization[END_REF][START_REF] Rieger | Precursor structures in the crystallization/precipitation processes of CaCO 3 and control of particle formation by polyelectrolytes[END_REF][START_REF] Wolf | Early homogenous amorphous precursor stages of calcium carbonate and subsequent crystal growth in levitated droplets[END_REF][START_REF] Wolf | Carbonate-coordinated metal complexes precede the formation of liquid amorphous mineral emulsions of divalent metal carbonates[END_REF][START_REF] Wallace | Microscopic evidence for liquidliquid separation in supersaturated CaCO 3 solutions[END_REF]. However, where bicarbonate ions persist at lower pH, the cluster size distribution is exponential [START_REF] Demichelis | Stable prenucleation mineral clusters are liquid-like ionic polymers[END_REF], which is in line with the expectations of classical nucleation theory [START_REF] Markov | Crystal Growth for Beginners: Fundamentals of Nucleation, Crystal Growth and Epitaxy[END_REF]. [START_REF] Wallace | Microscopic evidence for liquidliquid separation in supersaturated CaCO 3 solutions[END_REF]. The gray horizontal line represents a constant temperature slice through the stability fields as the solution ion activity product is increased. The solubility of all polymorphs is represented by a single solubility line (SL), which bounds the undersaturated solution field (dark gray region in the lower left corner). This simplification highlights that the solid phases of CaCO 3 (calcite, aragonite, vaterite, presumably ACC) all display the same general retrograde solubility behavior. Indirect nucleation of the solid phases proceeds to the high concentration side of the dashed black liquid-liquid coexistence line (L-L). The phase field bounded by the L-L line and the dashed gray spinodal line (SP) and labeled "Nucleation of liquid CaCO 3 " indicates the conditions where nucleation of the dense liquid phase (DLP) is possible. In the region bounded by the spinodal line the solution is unstable to fluctuations and liquid-liquid separation proceeds spontaneously. The retrograde solubility of the DLP (i.e. concave up orientation of the system binodal) is assumed based on the behavior of the MgSO 4 -H 2 O system at high temperature [START_REF] Wallace | Microscopic evidence for liquidliquid separation in supersaturated CaCO 3 solutions[END_REF]) and the arguments in support of a lower critical point temperature presented by [START_REF] Faatz | Amorphous calcium carbonate: synthesis and potential intermediate in biomineralization[END_REF]. [From Wallace AF et al. (2013) Science 341:885-889. Reprinted with permission from AAAS]

Recent molecular dynamics studies have also posited that liquid-like or bona fide liquid phases of calcium carbonate may form in solution [START_REF] Demichelis | Stable prenucleation mineral clusters are liquid-like ionic polymers[END_REF][START_REF] Wallace | Microscopic evidence for liquidliquid separation in supersaturated CaCO 3 solutions[END_REF]. [START_REF] Demichelis | Stable prenucleation mineral clusters are liquid-like ionic polymers[END_REF] first noted that at high concentrations (> 50 mmol dm -3 ) hydrated Ca-carbonate and Ca-bicarbonate cluster phases adopt linear and branched configurations that are highly dynamic and reorder quickly. From these results they coined the term DOLLOP, which stands for "dynamically ordered liquid-like oxyanion polymer." [START_REF] Wallace | Microscopic evidence for liquidliquid separation in supersaturated CaCO 3 solutions[END_REF] later showed that in the high pH limit DOLLOP evolves quickly into a dense liquid phase (DLP) that is stable at lower concentrations (~15 mmol dm -3 or less) and that first coalesces and, then, partially dehydrates to form a material whose structure is consistent with hydrated amorphous calcium carbonate. Several experimental studies have also suggested the presence of liquid calcium carbonate based on the interpretation of light scattering [START_REF] Faatz | Amorphous calcium carbonate: synthesis and potential intermediate in biomineralization[END_REF]) and cryo-electron microscopy data [START_REF] Rieger | Precursor structures in the crystallization/precipitation processes of CaCO 3 and control of particle formation by polyelectrolytes[END_REF][START_REF] Wolf | Early homogenous amorphous precursor stages of calcium carbonate and subsequent crystal growth in levitated droplets[END_REF]. These studies were unable to convincingly demonstrate that the observed particles were indeed liquid rather than amorphous and solid. However, from the biomineralization literature it is well known that organic molecules can stabilize a metastable liquid form of calcium carbonate called PILP (Polymer Induced Liquid Precursor) (Gower and Odom 2000;[START_REF] Jee | Oriented hydroxyapatite in turkey tendon mineralized via the polymer-induced liquid-precursor (PILP) process[END_REF][START_REF] Jiang | The existence region and composition of a polymer-induced liquid precursor phase for DL-glutamic acid crystals[END_REF]. It therefore seems plausible that a dense liquid phase may also form in the absence of organics, with the inorganic liquid state being presumably less stable than PILP. The possible coexistence of such a phase with a more dilute liquid suggests that under certain conditions the carbonate system could be buffered by the metastable equilibrium between the two liquid states rather than by the solubility limit of solid CaCO 3 (Figure 1). The case for liquid-liquid separation is also supported in part by the recent experimental documentation of liquid-liquid coexistence in the MgSO 4 -water system [START_REF] Wang | In situ observations of liquid-liquid phase separation in aqueous MgSO 4 solutions: Geological and geochemical implications[END_REF]), albeit at substantially higher temperatures than suggested for CaCO 3 , and by a nuclear magnetic resonance (NMR) study that supports the notion that liquid calcium carbonate phases can form in the absence of organic polymers [START_REF] Bewernitz | A metastable liquid precursor phase of calcium carbonate and its interactions with polyaspartate[END_REF].

Amorphous M (II) CO 3 phases

Amorphous phases of Ca, Mg, and Fe(II) carbonate have been characterized to varying degrees experimentally [START_REF] Michel | Structural characteristics of synthetic amorphous calcium carbonate[END_REF][START_REF] Radha | Energetic and structural studies of amorphous Ca 1-x Mg x CO 3 •nH 2 O (0 ≤ x ≤ 1)[END_REF][START_REF] Radha | Transformation and crystallization energetics of synthetic and biogenic amorphous calcium carbonate[END_REF][START_REF] Sel | Amorphous iron (II) carbonate: Crystallization energetics and comparison to other minerals related to CO 2 sequestration[END_REF]. While amorphous calcium carbonate is an important precursor phase in the formation of biogenic carbonates, the extent to which such amorphous phases may persist in abiotic environments is unknown. Modeling efforts to date have focused primarily on the structure of the calcium bearing end member, amorphous calcium carbonate (ACC). As synthesized in the laboratory, ACC contains approximately one mole of water per formula unit of CaCO 3 , though "anhydrous" biogenic forms have been observed with reduced water contents [START_REF] Radha | Transformation and crystallization energetics of synthetic and biogenic amorphous calcium carbonate[END_REF][START_REF] Gong | Phase transitions in biogenic amorphous calcium carbonate[END_REF]. Molecular dynamics simulations have demonstrated that dehydrated ACC is more dense and ordered than hydrous ACC [START_REF] Saharay | Dehydration-induced amorphous phases of calcium carbonate[END_REF]. Despite the apparent polyamorphism of ACC, the aforementioned synthetic variety remains the only non-biogenic form that has been successfully stabilized in the laboratory at ambient temperature and pressure conditions. However, the presence of a transient anhydrous phase has been inferred at high temperatures from the interpretation of Differential Scanning Calorimetry profiles [START_REF] Radha | Transformation and crystallization energetics of synthetic and biogenic amorphous calcium carbonate[END_REF]). 1 H and 13 C nuclear magnetic resonance spectroscopy has provided some insights into the structural and compositional characteristics of synthetic hydrated ACC [START_REF] Michel | Structural characteristics of synthetic amorphous calcium carbonate[END_REF][START_REF] Nebel | On the structure of amorphous calcium carbonate--a detailed study by solid-state NMR spectroscopy[END_REF]. These studies suggested a low abundance of hydroxyl moieties in the structure, as well as the presence of two populations of water molecules that are present in roughly equal proportions. On the millisecond timescale, one of these populations was immobile and the other had a somewhat restricted mobility. Additionally, two distinct populations of carbonate ions were identified that are distinguished by their proximity to immobile water molecules (~25% close to immobile H 2 O at room temperature). Another study combining NMR with X-ray diffraction (XRD) reported 13 C spectra for amorphous "proto-calcite" and "proto-vaterite" phases [START_REF] Gebauer | Proto-valcite and proto-vaterite in amorphous calcium carbonates[END_REF]; however, the alternative and more traditional interpretation of these data maintains that the observed line broadening in the NMR spectra (and XRD patterns) arises from the presence of nanocrystalline rather than amorphous material in the samples [START_REF] Jäger | A solid-state NMR investigation of the structure of nanocrystalline hydroxyapatite[END_REF].

The initial theoretical study of the ACC structure [START_REF] Goodwin | Nanoporous structure and medium-range order in synthetic amorphous calcium carbonate. Chem Mater Gower LB, Odom DJ[END_REF]) utilized the Reverse Monte Carlo (RMC) approach [START_REF] Mcgreevy | RMC : modeling disordered structures[END_REF][START_REF] Mcgreevy | Reverse Monte Carlo modelling[END_REF], which refines the atomic positions against experimental data using Metropolis-type Monte Carlo moves to minimize the numerical differences between the observed and model data. In the case of ACC, the RMC procedure was applied to the pair distribution function (PDF) of synthetic hydrated ACC as obtained from total X-ray scattering (Figure 2b). Recent work has shown that the PDF of stable biogenic ACC is essentially identical to that obtained from synthetic ACC [START_REF] Reeder | Characterization of structure in biogenic amorphous calcium carbonate: pair distribution function and nuclear magnetic resonance studies of lobster gastrolith[END_REF]. The RMC-derived structure suggested that ACC is nanoporous and chemically heterogeneous, expressing both waterpoor Ca-rich regions and Ca-deficient regions that are relatively enriched in water and carbonate ions. Although this structure model has also been shown to be consistent with the results of calcium K-edge EXAFS and NMR spectroscopy [START_REF] Michel | Structural characteristics of synthetic amorphous calcium carbonate[END_REF][START_REF] Goodwin | Nanoporous structure and medium-range order in synthetic amorphous calcium carbonate. Chem Mater Gower LB, Odom DJ[END_REF], subsequent molecular dynamics simulations have shown that the RMC-derived structure corresponds to an unstable state, and that the system tends to become more homogeneous over time [START_REF] Singer | Structure and transformation of amorphous calcium carbonate: A solid-state 43 Ca NMR and computational molecular dynamics investigation[END_REF]. The observed instability of the RMC structure highlights the main drawbacks of the RMC approach. While RMC modeling generally produces well-converged PDFs, the solution is not necessarily unique and a large number of candidate structures may fit the experimental data equally well; moreover, because the structure refinement is not based upon an underlying energy model, there is no guarantee that the solution will correspond to a locally stable state on the energy landscape. Despite these limitations, RMC is a valuable technique that can provide insights into the local structure of disordered materials.

As an alternative to RMC, [START_REF] Wallace | Microscopic evidence for liquidliquid separation in supersaturated CaCO 3 solutions[END_REF] constructed a model of hydrated ACC based on the results of MD simulations of calcium carbonate nanoparticle aggregation, coalescence, and dehydration (Figure 2c). This approach utilized replicaexchange molecular dynamics (REMD) (Sugita and Okamoto 1999;[START_REF] Okur | Improved efficiency of replica exchange simulations through use of a hybrid explicit/implicit solvation model[END_REF]Chaudhury et al. 2012) to first grow hydrated carbonate clusters into a size regime comparable to the coherent X-ray scattering length in synthetic ACC (~1.5 nm) as well as to the so-called prenucleation clusters, which have an average diameter somewhat less than 1 nm according to cryo-TEM measurements [START_REF] Pouget | The initial stages of template-controlled CaCO 3 formation revealed by cryo-TEM[END_REF]). The initial aggregate structure was obtained by randomly packing copies of a single 1.5 -2 nm diameter CaCO 3 (nH 2 O) cluster into a solvent-filled cell. Subsequently, the calcium to water ratio was slowly adjusted to match that of synthetic ACC (Ca/H 2 O ~1.0) over a series of constant pressure molecular dynamics simulations. At each iteration, a few solvent molecules were removed from the solvent rich volumes between the clusters. The net effect of this procedure is that the clusters were driven to coalesce without disturbing the structural water molecules that are intrinsic to their character. The model ACC structure obtained by this approach, though not as exact a match to the experimental PDF as the RMC results, is locally stable and faithfully reproduces the most salient aspects of the experimental PDF (Figure 2). Future studies of amorphous carbonate structures may benefit from a hybrid approach that integrates the beneficial aspects of the MD based approach with those of RMC. Rather than modeling the experimental ACC structure, other workers have focused their efforts on characterizing the free energy landscape underlying structural transitions in anhydrous CaCO 3 nanoparticles using the metadynamics approach [START_REF] Laio | Metadynamics: a method to simulate rare events and reconstruct the free energy in biophysics, chemistry and material science[END_REF]Quigley andRodger 2008, 2009;Quigley et al. 2009[START_REF] Quigley | Sampling the structure of calcium carbonate nanoparticles with metadynamics[END_REF]. The common objective of almost all of these studies has been to determine which phase of CaCO 3 is thermodynamically preferred at a given nanoparticle size. The initial results of [START_REF] Quigley | Free energy and structure of calcium carbonate nanoparticles during early stages of crystallization[END_REF], performed at constant density for a ~2 nm diameter particle (75 CaCO 3 units), displayed two free energy minima corresponding to separate disordered and semi-ordered states, with the disordered state being overwhelmingly preferred. Later work by the same group showed that for larger particles (192 and 300 formula units) the landscape is possibly reversed, with the amorphous state being metastable with respect to both vaterite and calcite-like states [START_REF] Freeman | Structural control of crystal nuclei by an eggshell protein[END_REF]. The thermodynamic barriers associated with transforming between the disordered and semi-ordered states were predicted to be on the order of several hundred times k B T , suggesting that reordering of the particles in the solid state is unlikely. However, in their most recent work, Quigley et al. (2011) showed that in constant pressure rather than constant density simulations (i.e. in the NPT versus the NVT ensemble) this trend reverses for the 75 formula unit cluster and the disordered state was predicted to be metastable with respect to a partially ordered state where more than 25% of the ions occupied calcite-like environments. Additionally, in the NPT simulations the barrier between the disordered and semi-ordered states was substantially reduced to a few tens of times k B T, which suggests that some degree of ordering in the particles may be possible without partial dissolution. It was suggested that the enhanced stability of the amorphous phase at constant density arises from spatial confinement of the particle and solvent, as observed experimentally [START_REF] Stephens | Early stages of crystallization of calcium carbonate revealed in picoliter droplets[END_REF]). However, it is well known that synthetic and biogenic amorphous calcium carbonate contains a certain amount of water that may influence the stability of these phases; to date only anhydrous CaCO 3 particles have been investigated with the metadynamics simulation technique.

Crystalline carbonate phases

Bulk Properties. Although it has been estimated that calcite and dolomite represent upwards of 90% of all naturally-formed carbonate minerals, according to [START_REF] Railsback | Patterns in the compositions, properties, and geochemistry of carbonate minerals[END_REF] there are at least 277 minerals that contain carbonate in their structure; these comprise a diverse class of materials that can contain multiple anion species including carbonate, bicarbonate, hydroxide, chloride, fluoride, sulfate, phosphate, and silicate among others. Many of these phases may yet prove to be consequential for carbon capture, storage, and utilization efforts, particularly if impurities from the injection stream are present in significant quantities (Chialvo et al., 2013a) and if the pH of the brine is too low to support nucleation and growth of pure carbonate phases. This exposes a gap in the theoretical literature, at least as it pertains to mineral trapping of CO 2 , in which the vast majority of calculations and simulations continue to be performed on phases that are naturally abundant but not necessarily very important for carbon sequestration. However, this also presents an opportunity for theoretical efforts to provide insights in the phase stability of less abundant carbonate minerals for which thermodynamic data are limited. A relatively recent report [START_REF] Krupka | Thermodynamic data for geochemical modeling of carbonate reactions associated with CO 2 sequestration -literature review[END_REF] attempted for the first time to consolidate all of the available data for the whole suite of carbonate-containing phases into a single thermodynamic database.

Ab initio and DFT calculations are widely used to determine the structure and properties of crystalline carbonate phases at high pressures where experimental measurements are arduous or impossible [START_REF] Skorodumova | Stability of the MgCO 3 structures under lower mantle conditions[END_REF]. These methods also are valuable tools for refining and testing structure solutions for difficult phases such as vaterite, for which there is still much disagreement [START_REF] Demichelis | A new structural model for disorder in vaterite from first-principles calculations[END_REF][START_REF] Mugnaioli | Ab Initio structure determination of vaterite by automated electron diffraction[END_REF][START_REF] Wang | Energetics and kinetics of carbonate orientational ordering in vaterite calcium carbonate[END_REF]. Primarily, these simulation studies have aimed to determine the elastic properties (i.e. bulk moduli) [START_REF] Elstnerová | Ab initio study of thermodynamic, structural, and elastic properties of Mg-substituted crystalline calcite[END_REF][START_REF] Brik | First-principles calculations of structural, electronic, optical and elastic properties of magnesite MgCO 3 and calcite CaCO 3[END_REF]Ungureanu et al. 2012;Carteret et al. 2013), vibrational spectra [START_REF] Medeiros | Firstprinciples calculations of structural, electronic, and optical absorption properties of CaCO 3 vaterite[END_REF][START_REF] Kupka | Experimental and theoretical studies on corals. I. Toward understanding the origin of color in precious red corals from Raman and IR spectroscopies and DFT calculations[END_REF], and thermochemical properties such as heat capacity (Ungureanu et al. 2010) that are critical for predicting phase stability. Where comparison with experimental data is possible, good agreement is generally achievable. These data are often useful for constraining empirical potential models that can be used in MD and MC simulations. Several studies have also used quantum and classical methods to investigate the substitution of M(II) cations in the calcite and dolomite structures (de [START_REF] De Leeuw | Modeling absorption and segregation of magnesium and cadmium ions to calcite surfaces: introducing MgCO 3 and CdCO 3 potential models[END_REF]de Leeuw et al., 2002;[START_REF] Austen | The interaction of dolomite surfaces with metal impurities: a computer simulation study[END_REF][START_REF] Elstnerová | Ab initio study of thermodynamic, structural, and elastic properties of Mg-substituted crystalline calcite[END_REF][START_REF] Stashans | A new insight on the role of Mg in calcite[END_REF] and to characterize cation disorder in dolomite [START_REF] Zucchini | Ab initio study of cation disorder in dolomite[END_REF]. Additionally, the thermodynamics of mixing [described in more detail in Radha and Navrostky (2013)] have been investigated using classical approaches for the (Ca,Mg)CO 3 [START_REF] Vinograd | Activity-composition in the system CaCO 3 -MgCO 3 predicted from static structure energy calculations and Monte Carlo simulations[END_REF]), (Ca,Mn)CO 3 [START_REF] Wang | Mixing thermodynamics of the calcitestructured (Mn,Ca)CO 3 solid solution: a computer simulation study[END_REF], and (Ca,Sr)CO 3 [START_REF] Kulik | Ca,Sr)CO 3 aqueous-solid solution systems: From atomistic simulations to thermodynamic modelling[END_REF]) solid solutions (Figure 3). Density functional theory calculations on transition metal carbonates, particularly iron(II) carbonate (siderite) and manganese(II) carbonate (rhodochrocite) have focused primarily on understanding the electronic band structures of these phases [START_REF] Sherman | Electronic structures of siderite (FeCO 3 ) and rhodochrosite (MnCO 3 ): Oxygen K-edge spectroscopy and hybrid density functional theory[END_REF][START_REF] Badaut | Influence of exchange correlation on the symmetry and properties of siderite according to density-functional theory[END_REF]). In the case of siderite, DFT calculations have also been applied to the analysis of the pressure induced magnetic transition from high spin to low spin iron at 40-50 GPa [START_REF] Shi | First-principles calculations of the electronic structure and pressure-induced magnetic transition in siderite FeCO 3[END_REF][START_REF] Ming | First-principles study of pressure-induced magnetic transition in siderite FeCO 3[END_REF]. Interface with water. Compared to the number of high-precision experimental methods available to characterize the bulk structure of materials, there are relatively few scattering and spectroscopic approaches that can provide high fidelity information about interfacial structure. The only available data concerning the interfacial structure of carbonate mineral surfaces with water comes from specular and non-specular X-ray reflectivity (XR) studies of the calcite-water interface. Specular XR provides a laterally averaged view of the interfacial structure (i.e. only information about the vertical positions of atoms relative to the interface). Non-specular XR is a complimentary technique that can provide information about both the vertical and lateral positions of atoms across the interface, but it is only sensitive to atoms that reside in well defined sites, and much more time is required to make high quality measurements relative to specular XR. On its face it appears that non-specular XR might be generally preferable because of its ability to provide three-dimensional information about the interfacial structure. However, in their recent reexamination of the calcite-water interface, [START_REF] Fenter | Calcite (104)-water interface structure, revisited[END_REF] strongly suggested that the uncertainties associated with previous studies [START_REF] Geissbühler | Threedimensional structure of the calcite-water interface by surface X-ray scattering[END_REF][START_REF] Heberling | Structure and reactivity of the calcite-water interface[END_REF] are substantially larger than the uncertainties in their present specular XR results due to the likely quantitative instability of the calcite surface during the course of the measurements. While [START_REF] Fenter | Calcite (104)-water interface structure, revisited[END_REF] observed that their data were inconsistent with previous combined non-specular and specular XR model fits, they reported consistency across the board with respect to the specular XR components of earlier studies [START_REF] Geissbühler | Threedimensional structure of the calcite-water interface by surface X-ray scattering[END_REF][START_REF] Heberling | Structure and reactivity of the calcite-water interface[END_REF]. These specular XR results show the presence of at least two structured water layers adjacent to the {10-14} surface, and indicate that the calcite surface is relaxed (to a depth of up to 4 to 6 unit cells) relative to the bulk structure of calcite [START_REF] Fenter | Calcite (104)-water interface structure, revisited[END_REF].

The structure of the calcite-water interface has been studied by molecular orbital calculations [START_REF] Lardge | Investigation of the interaction of water with the calcite (10.4) surface using ab initio aimulation[END_REF]Villegas-Jiménez et al. 2009) and classical molecular dynamics [START_REF] Spagnoli | Atomistic simulation of the free energies of dissolution of ions from flat and stepped calcite surfaces[END_REF]Cooke and Elliott 2007;[START_REF] Aschauer | Growth modification of seeded calcite using carboxylic acids: atomistic simulations[END_REF]Cooke et al. 2010;[START_REF] Miyake | High-temperature molecular dynamics simulation of aragonite[END_REF]Doudou et al. 2012;[START_REF] Wolthers | Calcite surface structure and reactivity: molecular dynamics simulations and macroscopic surface modelling of the calcite-water interface[END_REF]. While ab initio and DFT approaches are appealing due to the robust treatment of interatomic forces, their applicability to the calcite-water interface is challenging because the interfacial region is thick, spanning several unit cell depths of the calcite surface and extending a nanometer or more into the bulk solution. Handling such a large system is not readily tractable for electronic structure methods; therefore, investigations of this kind have been limited to the study of small portions of the calcite surface in contact with very few water molecules; these system sizes may or may not be sufficient to constitute an adequate representation of the interfacial region. Conversely, MD simulations can easily handle large systems due to their more empirical treatment of interatomic forces, but their results can be very sensitive to the parameterization of the forcefield. In a recent study, [START_REF] Fenter | Is the calcite-water interface understood? direct comparisons of molecular dynamics simulations with specular X-ray reflectivity data[END_REF] compared experimental specular XR model fits to the results of four different MD simulations that used empirical potentials with different functional forms (nonpolarizable, polarizable, reactive). Quantitative agreement between the measured and predicted XR spectra was found to be poor in each case, primarily because the MD models did not correctly predict the relaxation of the calcite structure in the vicinity of the interface (Figure 4). Remarkably, the two most simple force fields (non-polarizable, non-reactive empirical pair potentials) tested by [START_REF] Fenter | Is the calcite-water interface understood? direct comparisons of molecular dynamics simulations with specular X-ray reflectivity data[END_REF] predicted interfacial water structures that were consistent with the XR data, whereas the more complex (polarizable or reactive) force fields did not. Molecular dynamics simulations and ab initio calculations have also been used to assess the acidity of various sites on the {10-14} surface (defects, terraces, acute and obtuse ledges, kinks, and corner sites). On defect-free terraces, water is favored to adsorb associatively [START_REF] Kerisit | Atomistic simulation of the dissociative adsorption of water on calcite surfaces[END_REF][START_REF] Lardge | Investigation of the interaction of water with the calcite (10.4) surface using ab initio aimulation[END_REF]). However, defect and edge sites can promote water dissociation [START_REF] Kerisit | Atomistic simulation of the dissociative adsorption of water on calcite surfaces[END_REF]. From X-ray photoelectron spectroscopy (XPS) there is evidence of H-CO 3 and Ca-OH type bonding environments being present on the calcite surface [START_REF] Stipp | Structure and bonding environments at the calcite surface as observed with X-ray photoelectron spectroscopy (XPS) and low energy electron diffraction (LEED)[END_REF]. Two recent studies [START_REF] Andersson | How acidic is water on calcite?[END_REF][START_REF] Wolthers | Calcite surface structure and reactivity: molecular dynamics simulations and macroscopic surface modelling of the calcite-water interface[END_REF]) concluded also that the acidity of surface sites depends strongly on the nature of the local water structure and that dissociative adsorption is promoted to varying degrees at edge, kink, and corner sites, with dissociation being generally most favored at kink and corner sites and along acute step edges. These findings reinforce the experimental observation that obtuse and acute steps behave differently, particularly with respect to their interactions with impurities [START_REF] Davis | The role of Mg 2+ as an impurity in calcite growth[END_REF][START_REF] Davis | Morphological consequences of differential M g2+ incorporation at structurally distinct steps on calcite[END_REF]Wasylenki et al. 2005aWasylenki et al. , 2005c)). Additional insights into the behavior of impurity ions at the calcite-water interface may be gained by revisiting previous studies (de [START_REF] De Leeuw | Modeling absorption and segregation of magnesium and cadmium ions to calcite surfaces: introducing MgCO 3 and CdCO 3 potential models[END_REF][START_REF] De Leeuw | Molecular dynamics simulations of the growth inhibiting effect of Fe 2+ , Mg 2+ , Cd 2+ , and Sr 2+ on calcite crystal growth[END_REF]de Leeuw et al. 2002;[START_REF] De Leeuw | A computer modeling study of the inhibiting effect of organic adsorbates on calcite crystal growth[END_REF] with reactive empirical potentials that can account for variations in surface speciation.

Geochemical kinetics at M (II) CO 3 -water interfaces

Formation of carbonate minerals. To date, modeling studies of carbonate mineral formation from solution have focused predominantly on the calcite-water system. Typically it is assumed that mineral precipitation occurs by nucleation, which is a specific mechanism of phase-separation by which the free energy of a metastable system is reduced by overcoming a free energy barrier opposing the formation of a new phase [START_REF] Yoreo | In situ investigations of carbonate nucleation on mineral and organic surfaces. this volume Debye P, Hückel E[END_REF][START_REF] Radha | A new approach for studying nucleation phenomena using molecular simulations: Application to CO 2 hydrate clathrates[END_REF]. Physically, nucleation occurs as thermally driven fluctuations induce the assembly of unstable clusters, which grow ionby-ion against a free energy barrier until a critical size threshold is surpassed. Beyond the critical size the clusters are stable with respect to dissolution, and unstable with respect to continued growth of the new phase. However, because the height of the free energy barrier opposing nucleation is inversely proportional to supersaturation, the free energy barrier opposing nucleation vanishes if the chemical driving force for precipitation becomes large enough. When the free energy barrier disappears, the phase-separation mechanism changes from nucleation to spinodal decomposition. At the spinodal line, the same fluctuations that in the case of nucleation form clusters that are unstable with respect to dissolution instead produce clusters that are unstable with respect to growth. Furthermore, once the system enters the spinodal regime, the assumption of ion-by-ion growth that is implicit in the classical kinetic treatment of nucleation (Nielsen 1964) no longer applies in a strict sense and phase separation may proceed by cluster coalescence as well as by single ion addition.

The mechanism of phase-separation in CaCO 3 -water systems is challenging to discern largely because the many varied observations concerning the early stages of mineral formation are difficult to reconcile within a single theoretical framework. It is likely, especially given recent suggestion that there may be a liquid-liquid binodal in the system [START_REF] Wallace | Microscopic evidence for liquidliquid separation in supersaturated CaCO 3 solutions[END_REF], that much of the observed variability may arise from the particular relationship of a given set of experimental conditions to the supposed liquidliquid coexistence line. At low driving force, direct nucleation of the solid phases may be the only accessible mechanism. If the system approaches the binodal (and, beyond that, the spinodal) it may also become possible to form a dense liquid phase by nucleation and spinodal decomposition.

Theorists have the potential to quantify free energy landscapes of early stage carbonate mineral formation, although the rarity of nucleation events makes the simulation of systems comparable to experimental conditions difficult for suitably long timescales. Additionally, the ability of potential-based simulation methods to elucidate phase separation processes depends on the development of force fields that accurately describe both solid and aqueous phases. The force field for the CaCO 3 -water system developed by Raiteri et al. (2010) is a promising step towards the goal of simulating CaCO 3 precipitation events as it accurately reproduces free energies of component ions in solution as well as the energy difference for the calcite to aragonite phase transition. The use of non-reactive potentials, however, prevents direct description of carbonate speciation and limits its applicability for studying nucleation events because carbonatebicarbonate conversion occurs during CaCO 3 nucleation at pH levels relevant to natural systems. Development of reactive carbonate models, like the one recently proposed by [START_REF] Gale | A reactive force field for aqueous-calcium carbonate systems[END_REF] for the aqueous calcium carbonate system, will help future simulation efforts better study carbonate formation processes.

At present, most simulations pertinent to CaCO 3 nucleation have utilized MD simulations [START_REF] Martin | Application of molecular dynamics DL_POLY codes to interfaces of inorganic materials[END_REF]Raiteri and Gale 2010;[START_REF] Demichelis | Stable prenucleation mineral clusters are liquid-like ionic polymers[END_REF][START_REF] Finney | Probing the structure and stability of calcium carbonate pre-nucleation clusters[END_REF] and enhanced sampling methods including umbrella sampling (Tribello et al. 2009;[START_REF] Demichelis | Stable prenucleation mineral clusters are liquid-like ionic polymers[END_REF]) and metadynamics [START_REF] Quigley | Free energy and structure of calcium carbonate nanoparticles during early stages of crystallization[END_REF] in an attempt to identify CaCO 3 species that act as intermediates between ions in solution and post-nucleation amorphous or crystalline CaCO 3 phases. Di Tommaso and de Leeuw (2008[START_REF] Tommaso | Theoretical study of the dimerization of calcium carbonate in aqueous solution under natural water conditions[END_REF] have examined Ca-CO 3 ion pair formation as a first step towards modeling homogeneous nucleation from solution. Such simulations have repeatedly shown that cluster aggregation and ion or cluster addition to amorphous nanoparticles in solution is essentially barrier-less (Figure 5), unlike ion or cluster addition to ordered CaCO 3 phases [START_REF] Martin | Application of molecular dynamics DL_POLY codes to interfaces of inorganic materials[END_REF]Tribello et al. 2009;Raiteri and Gale 2010). An interplay between calcium -carbonate coordination number and ion hydration has been invoked to explain differences in cluster stability based on size [START_REF] Finney | Probing the structure and stability of calcium carbonate pre-nucleation clusters[END_REF], although no specific cluster size or makeup has been identified as a likely candidate for the stable prenucleation clusters. Hydration effects also are influential in modulating the energetic barriers to cluster aggregation and growth -the disorder of water layers at unstructured CaCO 3 nanoparticles may explain the low energy barrier to forming and growing these species compared to crystalline particles, which exert stronger ordering on the surrounding water molecules (Tribello et al. 2009;Raiteri and Gale 2010). Additional simulations of heterogeneous nucleation on self-assembled monolayers have examined the roles of monolayer ionization, epitaxial matching, and headgroup orientation on nucleating CaCO 3 [START_REF] Freeman | Simulations of calcite crystallization on selfassembled monolayers[END_REF], and successfully predicted the orientations of calcite crystallization on carboxylic-acid terminated surfaces (Quigley et al. 2009).

It should be noted that the majority of these simulations describe high pH and high supersaturation regimes, where CO 3 2-is the dominant carbonate species and cluster growth and aggregation can be observed on time scales accessible by simulation. Both of these limitations are problematic because the dominant species in most natural systems is HCO 3 -and because the mechanism of phase separation depends upon supersaturation. Thus, high concentration simulations may only probe those mechanisms, such as spinodal decomposition, that are active at high driving forces.

Ion attachment and detachment at carbonate step edges.

The flat {10-14} surface of calcite is by far the most stable face and dominates the morphology of the mineral. From atomic force microscopy (AFM) experiments, growth and dissolution on these surfaces is known to occur at steps [START_REF] Gratz | Step dynamics and spiral growth on calcite[END_REF]) and spiral dislocations (Hillner et al. 1993). Early simulations of ion detachment at steps include a kinetic Monte Carlo model that reproduces AFM data for calcite dissolution [START_REF] Mccoy | Kinetic Monte Carlo investigation of pit formation at the CaCO 3 (1014) surface-water interface[END_REF] and MD simulations that predicted CaCO 3 unit removal to be more energetically favorable from the obtuse step compared to the acute step (de [START_REF] De Leeuw | Molecular dynamics simulation of crystal dissolution from calcite steps[END_REF], as seen experimentally. Subsequent MD calculations of free energy profiles [START_REF] Spagnoli | Atomistic simulation of the free energies of dissolution of ions from flat and stepped calcite surfaces[END_REF]) and energy minimizations [START_REF] Kerisit | Atomistic simulation of the dissociative adsorption of water on calcite surfaces[END_REF]) concluded that ion detachment occurs preferentially at step edges compared to the flat surface, and identified the reaction of water with edge CO 3 groups as the first step in the detachment process. In the case of BaSO 4 , a potential analog for CaCO 3 , metadynamics and umbrella sampling calculations showed that metal detachment from step edges is a multi-step process as described in Figure 6 [START_REF] Stack | Accurate rates of the complex mechanisms for growth and dissolution of minerals using a combination of rare-event theories[END_REF]. Metal detachment from calcite step edges may be equally complex.

Simulations of ion attachment at carbonate step edges have been carried out for MCO 3 (where M = Ca 2+ , Mg 2+ , Fe 2+ , Sr 2+ , or Cd 2+ ) growth on the calcite {10-14} surface (de Leeuw 2002). As for attachment of Ca 2+ ions, the initial incorporation of impurity ions is more exothermic at the obtuse step, with free energies of attachment 44 to 86 kJ mol -1 more negative than at the acute step, depending on the cation. The calculated free energies indicate that impurity incorporation competes effectively with calcite formation for a single row of growth, but becomes increasingly endothermic for subsequent rows due to the mismatch with the underlying calcite lattice. Thus, subsequent growth becomes unfavorable [START_REF] Davis | The role of Mg 2+ as an impurity in calcite growth[END_REF] and growth is poisoned, as seen experimentally (Wasylenki et al. 2005b;[START_REF] Nielsen | General model for calcite growth kinetics in the presence of impurity ions[END_REF]. The development of a new force field for MD simulations of hydrated calcium carbonate (Raiteri et al. 2010) highlights a few differences from previous models [START_REF] Jackson | A transferable interatomic potential for calcium carbonate[END_REF][START_REF] Pavese | Interatomic potentials for CaCO 3 polymorphs (calcite and aragonite), fitted to elastic and vibrational data[END_REF][START_REF] Pavese | Modelling of the thermal dependence of structural and elastic properties of calcite, CaCO 3[END_REF] with implications for step growth. Namely, inner-sphere complexation of Ca 2+ at the flat {10-14} surface is unfavorable and CO 3 2-is only weakly attracted to the interface. Thus, the traditional view of growth wherein ions adsorb to the surface and, then, diffuse to growth sites may be unrealistic for the calcite {10-14} surface, as ions prefer to diffuse via solution. Continued development of force field parameters that accurately describe the energetics of both aqueous and solid phases will aid in future simulations of carbonate growth mechanisms. Influence of organic species on carbonate formation and growth. Organic additives have long been known to modify calcium carbonate growth rate [START_REF] Addadi | Interactions between acidic proteins and crystals: stereochemical requirements in biomineralization[END_REF], morphology [START_REF] Wada | Effects of carboxylic acids on calcite formation in the presence of Mg 2+ ions[END_REF], and nucleating phase [START_REF] Falini | Control of aragonite or calcite polymorphism by mollusk shell macromolecules[END_REF]. With recent developments in understanding the early stages of CaCO 3 crystallization, more attention is being paid to how organic molecules affect the formation, evolution, and stability of amorphous CaCO 3 phases and prenucleation species. While the motivation for these studies often lies in understanding biomineralization, organic species are ubiquitous in most environments and are likely to also influence non-biogenic carbonate formation. The specific functions of organic additives and the mechanisms by which they act, however, remain difficult to discern because of their chemical complexity and the fact that a single organic molecule can have multiple roles, and these roles can change depending on concentration and other conditions. Titration work in the presence of organic molecules by [START_REF] Gebauer | The multiple roles of additives in CaCO 3 crystallization: A quantitative case study[END_REF] constitutes a first effort at developing a framework to categorize additives based on their effects on all stages of CaCO 3 formation. Organic species are divided into classes based on their interaction with calcium ions, soluble clusters, nanoparticles, amorphous intermediates, and nucleated crystals.

In an attempt to examine how acetate, aspartate and citrate influence prenucleation clusters of CaCO 3 within the context of these categories, the MD simulation study by [START_REF] Raiteri | Exploring the influence of organic species on pre-and postnucleation calcium carbonate[END_REF] highlights the complexity of organic-CaCO 3 interactions and the difficulty in identifying individual roles and mechanisms. Both aspartate and citrate are classified as nucleation inhibitors from titration data, yet only citrate binds strongly enough to Ca 2+ in solution to inhibit nucleation through the lowering of supersaturation. The simulations indicate that aspartate, which is also classified as a stabilizer of amorphous intermediates, has a moderate binding affinity for both clusters and amorphous nanoparticles (a weaker affinity than citrate, which is classified as a stabilizer of prenucleation clusters but not of amorphous intermediates). This moderate affinity of aspartate for amorphous nanoparticles presumably allows stabilization of the intermediate phase, as seen in the experimental formation of polymerinduced liquid precursor (PILP) in the presence of polyaspartate (Gower and Odom 2000) and in agreement with other MD simulation work [START_REF] Finney | Probing the structure and stability of calcium carbonate pre-nucleation clusters[END_REF]. Additionally, the strong interaction of citrate with all CaCO 3 species except basal calcite surfaces may help explain the experimentally observed bias towards calcite in systems containing citrate. Results from the metadynamics work of [START_REF] Freeman | Structural control of crystal nuclei by an eggshell protein[END_REF] suggest a similar mechanism at work in the case of eggshell protein OC-17; the protein is proposed to bind to ACC nanoparticles, facilitate the transformation to calcite and, then, desorb from the crystal surface as the mineral begins to grow.

Other computational studies have focused on understanding the mechanisms that underlie experimentally observed effects of organics on CaCO 3 step growth kinetics. Atomistic energy minimizations of phosphonates indicate that these molecules bind more strongly to steps than to the flat {10-14} surface, confirming results of AFM growth experiments [START_REF] Nancollas | A controlled composition study of calcium carbonate crystal growth: The influence of scale inhibitors[END_REF][START_REF] Gratz | Step dynamics and spiral growth on calcite[END_REF]). More recent MD simulation work again confirms the preference of organic species (in this case polyaspartate and polyacrylic acid) for steps over flat surfaces, and further speculates that the inhibitory ability depends on an interplay between surface/step binding affinity and affinity for ions in solution [START_REF] Aschauer | Growth modification of seeded calcite using carboxylic acids: atomistic simulations[END_REF]. Experimental studies demonstrate that impurities, including organic molecules (peptides and peptoids), influence calcite growth differently depending on their concentration: at low concentrations they accelerate calcite step velocities and growth rates, whereas at high concentrations they inhibit calcite growth (Elhadj et al. 2006a;[START_REF] Bai | Microsecond molecular dynamics simulations of the kinetic pathways of gas hydrate formation from solid surfaces[END_REF]). The organic concentration at which growth is inhibited is related to the effectiveness of the organic as a growth accelerator (more effective growth promotion corresponds to a lower inhibitory concentration). Elhadj et al. (2006b) modeled polyaspartate (Asp n ) attachment at calcite steps with a quantum mechanics method and determined that binding strength increases with Asp chain length, reducing the Asp n concentration required to block step growth. Results from molecular simulations have also suggested that enhancements in step growth rate may be explained by the ability of organic molecules to lower dehydration barriers, either of ions [START_REF] Hamm | Molecular dynamics of ion hydration in the presence of small carboxylated molecules and implications for calcification[END_REF][START_REF] Piana | Aspartic acid as a crystal growth catalyst[END_REF] or of the mineral surface [START_REF] Piana | Assisted desolvation as a key kinetic step for crystal growth[END_REF], both of which represent significant barriers to step growth. Lastly, organic self-assembled monolayers, commonly used experimentally as templates for heterogeneous CaCO 3 nucleation [START_REF] Aizenberg | Control of crystal nucleation by patterned self-assembled monolayers[END_REF][START_REF] Yoreo | In situ investigations of carbonate nucleation on mineral and organic surfaces. this volume Debye P, Hückel E[END_REF], also have been studied computationally to understand their interaction with nucleating CaCO 3 minerals. This work (Quigley et al., 2009) demonstrated that the formation of oriented crystals on self-assembled monolayers does not arise as a consequence of epitaxy, but rather by the cooperative reorganization of both the mineral phase and the organic layer.

Equation of state.

In order to predict the fate of CO 2 in geologic carbon sequestration, it is essential to consider the phase behavior of CO 2 when placed in contact with the geological medium [START_REF] Depaolo | The onset of calcium carbonate nucleation: a density functional theory molecular dynamics and hybrid microsolvation/continuum study[END_REF]. A molecular model used for that purpose should correctly describe the thermodynamic properties of mixtures of CO 2 with brine as a function of thermodynamic conditions: pressure (P) or density (ρ), temperature (T), and composition (nature of the ions and their concentrations) in the aqueous phase. Several force fields have been proposed in the literature to investigate, using various approaches [the most common being the Grand Canonical Monte Carlo (GCMC) simulation technique], the phase behavior of pure CO 2 and its mixture with pure and salty water.

The most popular force field for CO 2 , the EPM2 model, was introduced by [START_REF] Harris | Carbon dioxide's liquid-vapor coexistence curve and critical properties as predicted by a simple molecular model[END_REF]. This simple 3-site model, in which C and O atoms interact via pairwise additive Lennard-Jones (LJ) and Coulomb (with point charges) potentials, is able to correctly capture the Liquid-Vapor equilibrium (LVE) and the critical properties of pure CO 2 in the (ρ,T) plane. Accounting for flexibility in this model does not appreciably change the phase boundaries, and simulations with the EPM2 model usually treat the CO 2 molecule as a rigid entity. The similar Exp-6 and TraPPE (Transferable Potential for Phase Equilibria) models are also able to describe the LVE of pure CO 2 [START_REF] Potoff | Molecular simulation of phase equilibria for mixtures of polar and non-polar components[END_REF][START_REF] Potoff | Vapor-liquid equilibria of mixtures containing alkanes, carbon dioxide, and nitrogen[END_REF]. [START_REF] Zhang | An optimized molecular potential for carbon dioxide[END_REF] optimized parameters of a similar force field for the prediction of the LVE and critical properties. Other force fields have been proposed, either with increased complexity to refine the prediction of CO 2 properties (such as the composition of the coexisting phases or the critical behavior) or with simplified interactions to increase computational efficiency. Examples of the latter type include several 1-site models that differ according to their treatment of electrostatic [point quadrupole [START_REF] Vrabec | A set of molecular models for symmetric quadrupolar fluids[END_REF], thermally averaged quadrupole [START_REF] Mognetti | Efficient prediction of thermodynamic properties of quadrupolar fluids from simulation of a coarse-grained model: The case of carbon dioxide[END_REF] or without explicit electrostatics (Avendano et al. 2011)] and non-electrostatic interactions [isotropic [START_REF] Mognetti | Efficient prediction of thermodynamic properties of quadrupolar fluids from simulation of a coarse-grained model: The case of carbon dioxide[END_REF][START_REF] Vrabec | A set of molecular models for symmetric quadrupolar fluids[END_REF] or anisotropic LJ [START_REF] Persson | Simple one-center model for linear molecules: application to carbon dioxide[END_REF], with Lorentz-Berthelot combining rules for interactions between atoms of different type or more elaborate ones [START_REF] Schacht | Using an analytic equation of state to obtain quantitative solubilities of CO 2 by molecular simulation[END_REF]]. A 3-site model with LJ interactions and a point quadrupole, optimized for LVE, has also been proposed [START_REF] Merker | Molecular model for carbon dioxide optimized to vapor-liquid equilibria[END_REF]. These simpler models are usually parameterized to reproduce the experimental LVE and/or critical properties or analytical equations of state such as the Statistical Associating Fluid Theory (SAFT) model (Avendano et al. 2011;[START_REF] Schacht | Using an analytic equation of state to obtain quantitative solubilities of CO 2 by molecular simulation[END_REF]). In the opposite direction, refined models have been proposed that introduce flexibility [START_REF] Zhu | A fully flexible potential model for carbon dioxide[END_REF][START_REF] Cygan | Molecular simulation of carbon dioxide capture by montmorillonite using an accurate and flexible force field[END_REF] or polarization effects using distributed point polarizabilities (Wang et al. 2012a). Finally, ab initio calculations have enabled the direct investigation of the effect of dispersion on the properties of supercritical CO 2 (scCO 2 ) [START_REF] Balasubramanian | Ab initio molecular dynamics study of supercritical dioxide including dispersion corrections[END_REF]) and the development of improved force fields accounting for non-additive interactions [START_REF] Oakley | Additive and nonadditive models of vapor-liquid equilibrium in CO2 from first principles[END_REF] or based on a rigorous energy decomposition and Symmetry Adapted Perturbation Theory (Yu et al. 2011).

Some studies have been devoted to the properties of a single phase, such as the effect of density on the structure of scCO 2 along an isotherm (Ishii et al. 1996), the structure of liquid CO 2 [START_REF] Neuefeind | The structure of liquid carbon dioxide and carbon disulfide[END_REF] or more rarely dynamical properties (In Het [START_REF] Panhuis | A molecular dynamics study of carbon dioxide in water: diffusion, structure and thermodynamics[END_REF][START_REF] Nieto-Draghi | Thermodynamic and transport properties of carbon dioxide from molecular simulation[END_REF][START_REF] Garcia-Ratés | Molecular modeling of diffusion coefficient and ionic conductivity of CO 2 in aqueous ionic solutions[END_REF]. In all cases, comparison with experimental data provides a critical test of the accuracy of the force fields. For example, Nieto-Draghi et al. (2007) found that the EPM2 model reasonably describes the shear viscosity and thermal conductivity under sub-critical conditions, except for the thermal conductivity at low density. Such a good prediction of dynamical properties by EPM2 is remarkable, since this force field was calibrated to reproduce only thermodynamic properties, and suggests that the interactions between CO 2 molecules are relatively well described on the microscopic level.

The phase equilibria of pure CO 2 have been investigated in many simulation studies, not only for their interest per se and their relevance for practical applications, but also as a critical test of molecular models, in particular as a first step towards predicting the phase behavior of mixtures containing CO 2 . For example, Errington et al. (1998) used GCMC simulations to predict the LVE of pure CO 2 with the EPM2 model and its binary mixture with water. The same model was investigated by [START_REF] Vorholz | Vapor+liquid equilibrium of water, carbon dioxide, and the binary system, water+carbon dioxide, from molecular simulation[END_REF] using GCMC simulations in the NVT and NPT ensembles (Figure 8a). These studies, together with the above-mentioned ones, confirm the ability of EPM2 to correctly describe the LVE and critical properties of pure CO 2 . The Fluid-Solid equilibria (FSE) have attracted less attention, but have also provided interesting insights. [START_REF] Albo | On the calculation of supercritical fluid-solid equilibria by molecular simulation[END_REF] discussed the relevance of simulation methods and the choice of force field for the prediction of these equilibria. More recently, Péréz-Sanchez et al. ( 2013) analyzed the role of the quadrupole moment on the melting curve of dry ice up to 1000 MPa by comparing several popular force fields. They found that, firstly, while the models were all able to reproduce the experimental LVE, their prediction of the melting curve differed significantly; secondly, of all the models tested, the TraPPE force field yielded the best predictions for melting curve and triple point properties and; thirdly, a large quadrupole moment is required to correctly describe the properties of the solid phase. From the dynamical point of view, molecular simulations have been used by [START_REF] Leyssale | Molecular simulation of the homogeneous crystal nucleation of carbon dioxide[END_REF] to investigate homogeneous crystal nucleation in supercooled CO 2 .

Several groups have built upon the promising results on the thermodynamic properties of pure CO 2 by combining the EPM2 or TraPPE models with popular force fields for water to predict the phase behavior of their binary mixtures. For example, Errington et al. (1998) and [START_REF] Vorholz | Vapor+liquid equilibrium of water, carbon dioxide, and the binary system, water+carbon dioxide, from molecular simulation[END_REF] investigated the SPC and TIP4P water models. They found that the use of standard combining rules for the LJ parameters of the pure components yielded very good results for the LVE between EPM2 and both SPC or TIP4P, for temperatures of 348 to 393 K and pressures up to 20 MPa. Among several combinations of force fields for the solubility of CO 2 in water over a wide range of thermodynamic conditions, the Exp-6 model of Errington and Panagiotopoulos (Errington and Panagiotopoulos, 1998;[START_REF] Potoff | Molecular simulation of phase equilibria for mixtures of polar and non-polar components[END_REF] gives the best agreement with experimental data [START_REF] Lísal | Analysis of Henry's constant for carbon dioxide in water via Monte Carlo simulation[END_REF]. The most comprehensive comparison of force fields for mixtures of water and CO 2 , over a wide range of P (0 to 1000 bar) and T (323 to 623 K) was carried out by [START_REF] Liu | Monte Carlo simulations of highpressure phase equilibria of CO 2 -H 2 O mixtures[END_REF]. While none of the models could reproduce the experimental data over the whole range of thermodynamic conditions, it was found that, firstly, below 523 K, i.e. away from the critical region of water, the Exp-6 model gives the best predictions for the CO 2 -rich phase, whereas the TraPPE/TIP4P2005 combination is more accurate for the H 2 O-rich phase (Figure 8b); secondly, near the critical region (523 to 623 K) none of the models correctly predicts the critical behavior, even though the Exp-6 model gives the correct qualitative features and; thirdly, modified Lorentz-Berthelot combining rules provide only minor improvements. This extensive study highlights the need for improving the force fields for the prediction of binary mixture properties. To achieve this goal, it might be useful to consider in the parameterization process the dynamical properties, which have been only rarely investigated for mixtures [START_REF] Fernández | Self-diffusion and binary Maxwell-Stefan diffusion coefficients of quadrupolar real fluids from molecular simulation[END_REF][START_REF] Nieto-Draghi | Thermodynamic and transport properties of carbon dioxide from molecular simulation[END_REF][START_REF] Garcia-Ratés | Molecular modeling of diffusion coefficient and ionic conductivity of CO 2 in aqueous ionic solutions[END_REF]). An alternative approach consists in designing modified Lorentz-Berthelot combining rules for the CO 2water interaction that are fitted to the mutual solubility of water and CO 2 , but with the mole fraction of water in CO 2 corrected to account for the polarization change associated with water evaporation [START_REF] Vlcek | Optimized unlike-pair interactions for watercarbon dioxide mixtures described by the SPC/E and EPM2 models[END_REF]Chialvo et al. 2013a). This approach follows naturally from the fact that non-polarizable water models will necessarily underestimate the enthalpy of vaporization of water because they inherently cannot account for the different dipole moments of water in scCO 2 and in liquid water.

Finally, a few studies have considered the more complex mixtures of CO 2 with brine. [START_REF] Vorholz | Molecular simulation of the solubility of carbon dioxide in aqueous solutions of sodium chloride[END_REF] tested the ability of the SPC and TIP4P (for water) and EPM2 (for CO 2 ) models, with various potentials for sodium and chloride ions, to reproduce the solubility of CO 2 in NaCl aqueous solutions, for temperatures of 373 to 433 K and pressures up to 10 MPa. Several salt molalities, including above the solubility limit, were simulated. While the "salting-out" effect observed in experiments was qualitatively reproduced, the decrease in CO 2 solubility in the presence of salt was overestimated. Improvements can be obtained by introducing modified combining rules for the interactions between unlike species. Molecular dynamics simulations further provided data on the diffusion and electric conductivity of CO 2 -brine mixtures, for which few experimental results are available, as well as molecular scale information, such as rotational relaxation times. Garcia-Ratés et al. ( 2012) investigated these properties with the SPC/E and EPM2 models for water and CO 2 and two models for the ions. Finally, the solvation of cations in scCO 2 -water mixtures at 300 K was studied by Criscenti and Cygan (2013). This study investigated the partitioning of alkali and alkaline-earth metals between the liquid aqueous and supercritical CO 2 -rich phases. Although ions consistently prefer the aqueous phase, the partitioning of cations into CO 2 increases with ion size, because of the inverse relation between ion size and solvation energy. When both phases are in contact, cations can be found in the CO 2 phase as partially (e.g., K + or Cs + ) or fully (Sr 2+ ) hydrated complexes. Interfacial tension. Once the composition of the co-existing fluid phases is known under given thermodynamic conditions, molecular simulations allow computing another important property in the context of CO 2 sequestration, namely the interfacial tension between the two phases, and interpreting its microscopic origin. Such simulations usually involve slabs of fluids and the determination of the normal and tangential components of the local pressure tensor: the interfacial tension (IFT) is then given by the integral of the difference between these components across the interface. In fact, these interfacial components are also related to the bulk phase stability. [START_REF] Kraska | The relation of interface properties and bulk phase stability: molecular dynamics simulations of carbon dioxide[END_REF] exploited this connection to the LVE of CO 2 in order to predict the spinodal (limit of metastability) and the equation of state in the unstable region. The interface between pure water and scCO 2 was investigated with the SPC and EPM2 models by [START_REF] Zhao | Molecular dynamics investigation of the various atomic force contributions to the interfacial tension at the supercritical CO 2 -water interface[END_REF]. By analyzing the relative contribution of the water-water, CO 2 -CO 2 and water-CO 2 interactions to the IFT, they showed that the overall IFT is dominated by the water "self" contribution (consistently with the very large IFT for the water liquid-vapor interface) and that the CO 2 -water interactions contribute negatively, i.e., they lower the IFT. The decomposition of the IFT according to the various terms of the force field (electrostatic, bond stretching, angle bending, LJ) indicated that only the LJ interactions contribute favorably to the surface tension. Nevertheless, one should keep in mind that such a decomposition in the design of a force field is not without its ambiguities and, therefore, the last point should be considered with caution. Finally, the authors considered the orientation of interfacial molecules and found that both water and CO 2 are aligned nearly parallel to the Gibbs Dividing Surface. The brine-water interface was also investigated by [START_REF] Zhao | Molecular dynamics investigation of the various atomic force contributions to the interfacial tension at the supercritical CO 2 -water interface[END_REF] who considered a 2.7 M CaCl 2 aqueous solution. They predicted that IFT increases with salinity, as observed experimentally, and they suggested that this salinity-dependence results from a change in the orientation of interfacial water caused by the ions.

The most comprehensive molecular simulation study of the water-CO 2 IFT was performed by [START_REF] Nielsen | Predicting CO 2 -water interfacial tension under pressure and temperature conditions of geologic CO 2 storage[END_REF]. They assessed the ability of several force fields to predict the IFT at pressure and temperature conditions relevant to GCS (Figure 9). The combinations of three CO 2 models and two water models all predicted the same qualitative trends: at fixed T, the IFT decreases strongly with increasing P below the critical CO 2 pressure, then levels off, while it depends only slightly on T at fixed P, as observed experimentally. Quantitative differences were observed between the different force fields, mainly due to variations in the description of short-range interactions that dominate the overall value of the IFT. The PPL CO 2 model (In Het [START_REF] Panhuis | A molecular dynamics study of carbon dioxide in water: diffusion, structure and thermodynamics[END_REF] combined with the TIP4P/2005 CO 2 model [START_REF] Abascal | A general purpose model for the condensed phases of water: TIP4P/2005[END_REF] provided the best agreement with experimental data over the whole 5-45 MPa range at 383 K. The PPL model combined with the SPC/E water model underestimated the IFT by ~10mN/m, i.e. the amount by which SPC/E underestimates the IFT of pure liquid water. The simulation results of [START_REF] Nielsen | Predicting CO 2 -water interfacial tension under pressure and temperature conditions of geologic CO 2 storage[END_REF] showed that the P-dependence of IFT is consistent with the Gibbs adsorption equation [dγ wg = -Γ CO2 (H2O) dµ CO2 , where γ wg is the CO 2 -water IFT, µ CO2 is the chemical potential of CO 2 , and Γ CO2 (H2O) is the surface excess of CO 2 at the interface (calculated using water as a reference phase)]. The difference between the IFT values predicted with different CO 2 models was shown to result from differences in the CO 2 -water LJ interaction predicted by different models: the PPL model predicts a stronger short-range CO 2 -water attraction, hence more CO 2 adsorption on the water surface and a larger P-dependence of IFT, in agreement with experimental data. As mentioned above, IFT results from various contributions, whose subtle balance depends on the arrangement of the interfacial molecules. [START_REF] Willard | Instantaneous liquid interfaces[END_REF] demonstrated that the interfacial structure cannot be understood properly by considering only the Gibbs Dividing Surface (GDS), which is smeared out by capillary fluctuations. Rather, they introduced the notion of an instantaneous interface that fluctuates in time and showed that when the structure of molecules is analyzed with respect to this interface one recovers a layered structure that is progressively damped over a few molecular layers, as in the vicinity of a solid object. [START_REF] Zhang | Analysis of the subcritical carbon dioxide-water interface[END_REF] re-examined the structure of the interface between water and sub-critical CO 2 using this concept. Under these conditions, they observed, as in experiments, the adsorption of a CO 2 layer on the water surface (which is at the origin of the decrease in IFT compared to pure water, as noted above). In addition, the density profile decays almost exponentially from the interface, with a characteristic length that diverges with increasing pressure according to an inverse power law. No effect of CO 2 adsorption on the orientation of interfacial water molecules was observed.

CO 2 -brine-mineral systems with a single fluid phase

Clay interlayer nanopores. Much of the atomistic simulation research on CO 2 near mineral surfaces has used clay minerals, a well-characterized nanoporous medium [START_REF] Rotenberg | Water and ions in clays: Unraveling the interlayer/micropore exchange using molecular dynamics[END_REF][START_REF] Bourg | Connecting the molecular scale to the continuum scale for diffusion processes in smectite-rich porous media[END_REF][START_REF] Ferrage | Hydration properties and interlayer organization of and ions in synthetic Na-smectite with tetrahedral layer charge. Part 2. Toward a precise coupling between molecular simulations and diffraction data[END_REF][START_REF] Marry | Water dynamics in hectorite clays: influence of temperature studied by coupling neutron spin echo and molecular dynamics[END_REF] of relevance to the geochemistry of clayshale and mudstone caprocks of GCS sites [START_REF] Carey | Molecular models for the intercalation of methane hydrate complexes in montmorillonite clay[END_REF][START_REF] Kaszuba | Experimental perspectives of mineral dissolution and precipitation due to carbon dioxide-water-rock interactions. this volume Kendall TA, Martin ST[END_REF]. The adsorption of CO 2 in clay nanopores has been mainly considered in the absence of water. Experimentally, the incorporation of CO 2 in pyrophyllite during dehydroxylation has been observed by infrared spectroscopy [START_REF] Wang | Infrared study of CO 2 incorporation into pyrophyllite [Al 2 Si 4 O 10 (OH) 2 ] during dehydroxylation[END_REF]) and X-ray diffraction has allowed following the intercalation of CO 2 in Nafluorohectorite near ambient conditions: the expansion in basal spacing is similar to that obtained during intercalation with water, but it occurs at a rate that is several orders of magnitude slower [START_REF] Hemmen | X-ray studies of carbon dioxide intercalation in Na-fluorohectorite clay at near-ambient conditions[END_REF]. The density of CO 2 confined in Namontmorillonite with a sub-single hydration layer depends on the bulk scCO 2 density [START_REF] Rother | CO 2 sorption to subsingle hydration layer montmorillonite clay studied by excess sorption and neutron diffraction measurements[END_REF]. [START_REF] Yang | Structure and diffusion behavior of dense carbon dioxide fluid in clay-like slit pores by molecular dynamics simulation[END_REF] used MD simulations to investigate the structure and diffusion of CO 2 in clay-like slit pores, finding in particular a decrease in the diffusion coefficient under confinement. Cole et al. (2010) carried out MD simulations of dry scCO 2 in mica interlayers and observed, in line with the behavior of water, a layering of the fluid and a decrease in mobility compared to bulk scCO 2 . It would be interesting to investigate how some of the observed features, such as the formation of hydrogen bonds between CO 2 oxygens and surface hydroxyl groups, are affected by the presence of water. The swelling of Na-montmorillonite in contact with CO 2 was studied by [START_REF] Yang | Molecular simulation of swelling and structure for Na-Wyoming montmorillonite in supercritical CO 2[END_REF] using GCMC simulations. Whereas swelling is thermodynamically favorable under supercritical conditions (10 MPa and 318.15 K), it is unfavorable at lower CO 2 pressure (0.1 MPa). In the former case, it was found that Na + counterions were not well solvated by CO 2 and remained close to the surface. The swelling of organoclays, where inorganic counterions are replaced by alkylammonium chains, by scCO 2 has also been simulated by [START_REF] Yu | Molecular simulation of swelling and interlayer structure for organoclay in supercritical CO 2[END_REF].

More relevant in the context of geological sequestration is the case where clay is in contact with both CO 2 and water. Recent experiments have shown that the uptake of CO 2 depends on the initial water content -hence also on the nature of the counterion [START_REF] Giesting | Interaction of carbon dioxide with Na-exchanged montmorillonite at pressures to 640 bars: Implications for CO 2 sequestration[END_REF][START_REF] Schaef | In situ XRD study of Ca 2+ saturated montmorillonite (STX-1) exposed to anhydrous and wet supercritical carbon dioxide[END_REF]. [START_REF] Botan | Carbon dioxide in montmorillonite clay hydrates: thermodynamics, structure, and transport from molecular simulation[END_REF] used molecular simulations to investigate the thermodynamics, structure and transport in Na-montmorillonite in contact with water and CO 2 (Figure 10). They considered clay interlayer nanopores in equilibrium with a reservoir at 348 K and two pressures in which two bulk phases coexist: an H 2 O-rich liquid phase and a CO 2 -rich gas (at 25 bars) or supercritical fluid (at 125 bar). This bulk phase coexistence determines the chemical potentials of water and CO 2 used in GCMC simulations, with the rigid SPC and EPM2 models, to determine the swelling free energy curves and composition of the metastable states. The bihydrated state, which is the most stable in the absence of CO 2 under the investigated conditions, remains the most stable in the presence of CO 2 , i.e., no swelling (by CO 2 uptake) or shrinkage (by water removal) was predicted if the clay remains in contact with the water reservoir. The CO 2 uptake is limited to its dissolution in interlayer water without dramatic changes in the overall fluid density and the water structure. The CO 2 molecules tend to stay close to the clay surface, oriented so as to partially enter the hexagonal cavities. The diffusion coefficient of CO 2 is reduced compared to its value in bulk liquid water by a factor 50 and 5 in the mono-and bihydrated states, respectively. The presence of CO 2 also slows down the diffusion of interlayer water and cations. 2012) recently developed a fully flexible CO 2 model for the simulation of CO 2 and water in clays. This model better reproduces the vibrational properties of bulk CO 2 than earlier flexible force fields and, when used in conjunction with the flexible SPC or TIP4P water models, more accurately predicts the diffusion coefficient of CO 2 in bulk water at 0.1 MPa compared to its rigid counterparts (which overestimate it). In simulations of a hydrated Na-montmorillonite clay, the addition of two CO 2 molecules per unit cell in the interlayer space was predicted to cause an increase in the interlayer distance (i.e., swelling) for all considered water contents. This finding does not contradict the results of [START_REF] Botan | Carbon dioxide in montmorillonite clay hydrates: thermodynamics, structure, and transport from molecular simulation[END_REF], because [START_REF] Cygan | Molecular simulation of carbon dioxide capture by montmorillonite using an accurate and flexible force field[END_REF] simulated systems with a fixed number of interlayer water and CO 2 molecules, whereas [START_REF] Botan | Carbon dioxide in montmorillonite clay hydrates: thermodynamics, structure, and transport from molecular simulation[END_REF] simulated systems with fixed chemical potential. Flexibility of water and CO 2 does not have a large impact on the structure of the interlayer fluid but is obviously essential for the prediction of vibrational properties. In particular, [START_REF] Cygan | Molecular simulation of carbon dioxide capture by montmorillonite using an accurate and flexible force field[END_REF] predicted that the bending motion of CO 2 is blue-shifted by 10 to 15 cm -1 in the clay interlayer while the asymmetric stretch mode is virtually unaffected by confinement, in qualitative agreement with their diffuse-reflectance infrared spectroscopy results.

Nanoporous silica and zeolites. A significant body of atomistic simulation research exists on the adsorption of CO 2 in nanoporous silica and zeolites at relatively low pressures and in the absence of water, because of the potential utility of these materials in carbon capture. These studies show that CO 2 has a significant affinity for silica surfaces that is strongly dependent on the details of the pore structure and the presence of surface charge sites [START_REF] Kim | Predicting large CO 2 adsorption in aluminosilicate zeolites for postcombustion carbon dioxide capture[END_REF]. At conditions more relevant to GCS (high P and T, presence of water), few atomistic simulation studies have been carried out. Gravimetric and neutron scattering data show that confinement in silica nanopores can promote the formation of a dense adsorbed phase even in pores as large as 35 nm [START_REF] Melnichenko | Monitoring phase behavior of sub-and supercritical CO 2 confined in porous fractal silica with 85% porosity[END_REF]Cole et al., 2010;[START_REF] Rother | Pore size effects on the sorption of supercritical CO 2 in mesoporous CPG-10 silica[END_REF] but this has never been tested by atomistic simulation, to our knowledge. Molecular dynamics simulations described elsewhere in this volume show that the solubility of CO 2 in water-filled silica nanopores is highly sensivity to nanopore size and the hydrophilicity of the silica surface (Chialvo et al. 2013a,b).

CO 2 -brine-mineral systems with two fluid phases

Thin films of adsorbed water at CO 2 -mineral interfaces. Hydrophilic mineral surfaces (such as silica, mica, and carbonates), when exposed to humid air, are well known to adsorb thin films of liquid water (up to hundreds of nanometers thick) with a chemical potential lower than that of bulk liquid water [START_REF] Pashley | Surface forces in adsorbed multilayers of water on quartz[END_REF][START_REF] Balmer | The effect of surface ions on water adsorption to mica[END_REF][START_REF] Asay | Effects of surface chemistry on structure and thermodynamics of water layers at solid-vapor interfaces[END_REF][START_REF] Salmeron | Water growth on metals and oxides: binding, dissociation and role of hydroxyl groups[END_REF]Tokunaga 2009[START_REF] Kim | Thickness measurements of nanoscale brine films on silica surfaces under geologic CO 2 sequestration conditions using synchrotron X-ray fluorescence[END_REF][START_REF] Bohr | Thickness and structure of the water film deposited from vapour on calcite surfaces[END_REF][START_REF] Rubasinghege | Role(s) of adsorbed water in the surface chemistry of environmental interfaces[END_REF]. These adsorbed water films influence the hydrogeology of unsaturated porous media (Tokunaga 2009;[START_REF] Diaz | Hysteresis during contact angles measurement[END_REF]) and the geochemistry of mineral-air interfaces (Kendall and Martin 2005; Rubasinghege and Grassian 2013). On quartz and silica surfaces at low relative vapor pressures (p/p sat ≤ 0.8), the thickness of these films ranges from zero to about two statistical water monolayers [START_REF] Asay | Effects of surface chemistry on structure and thermodynamics of water layers at solid-vapor interfaces[END_REF]Tokunaga 2009[START_REF] Kim | Thickness measurements of nanoscale brine films on silica surfaces under geologic CO 2 sequestration conditions using synchrotron X-ray fluorescence[END_REF]. These two water monolayers are strongly adsorbed as measured by their isosteric heat of adsorption [START_REF] Asay | Effects of surface chemistry on structure and thermodynamics of water layers at solid-vapor interfaces[END_REF]. Beyond the first two water monolayers, water is much more weakly adsorbed [START_REF] Pashley | Multilayer adsorption of water on silica: An analysis of experimental results[END_REF][START_REF] Asay | Effects of surface chemistry on structure and thermodynamics of water layers at solid-vapor interfaces[END_REF]); nevertheless, water film thickness continues to increase with relative vapor pressure and reaches tens to hundreds of nanometers at p/p sat > 0.975 [START_REF] Pashley | Surface forces in adsorbed multilayers of water on quartz[END_REF][START_REF] Kim | Thickness measurements of nanoscale brine films on silica surfaces under geologic CO 2 sequestration conditions using synchrotron X-ray fluorescence[END_REF]. Mica surfaces are somewhat less hydrophilic than silica and they carry only one water monolayer at p/p sat ≈ 0.65 [START_REF] Balmer | The effect of surface ions on water adsorption to mica[END_REF].

In geological CO 2 storage formations, adsorbed water films may play important roles by mediating the interaction of humid scCO 2 with mineral surfaces [START_REF] Mcgrail | Water reactivity in the liquid and supercritical CO 2 phase: Has half the story been neglected?[END_REF][START_REF] Kwak | The role of H 2 O in the carbonation of forsterite in supercritical CO 2[END_REF][START_REF] Loring | In situ infrared spectroscopic study of forsterite carbonation in wet supercritical CO 2[END_REF][START_REF] Shao | Effects of salinity and the extent of water on supercritical CO 2 -induced phlogopite dissolution and secondary mineral formation[END_REF]Tokunaga and Wan 2013). At present, however, the properties of adsorbed water films at mineral-CO 2 interfaces remain poorly understood. [START_REF] Loring | In situ infrared spectroscopic study of forsterite carbonation in wet supercritical CO 2[END_REF] roughly estimated the thickness of water films at forsterite-scCO 2 interfaces by infrared spectroscopy as 0.1, 0.2, 1.0 and 2.0 nm at p/p sat = 0.47, 0.81, 0.95 and 1.36, respectively (for comparison, a single water monolayer has a thickness of about 0.3 nm). [START_REF] Kim | Thickness measurements of nanoscale brine films on silica surfaces under geologic CO 2 sequestration conditions using synchrotron X-ray fluorescence[END_REF] probed water films at silica-scCO 2 interfaces at low capillary pressures (P c = 0.18 to 3.7 kPa, equivalent to p/p sat ~0.99999) using X-ray synchrotron fluorescence. At the conditions of their study, water film thickness was less than 2 nm, but a more precise quantification of adsorbed film thickness was prevented by capillary condensation on surface roughness features.

Molecular dynamics and Monte Carlo simulations have been used to study adsorbed water films in the absence of CO 2 , for example on silica [START_REF] Wensink | Properties of adsorbed water layers and the effect of adsorbed layers on interparticle forces by liquid[END_REF][START_REF] Romero-Vargas Castrillón | Structure and energetics of thin film water[END_REF], calcite [START_REF] Stöckelmann | Adsorption isotherms of water vapor on calcite: A molecular dynamics-Monte Carlo hybrid simulation using a polarizable water model[END_REF][START_REF] Rahaman | Dynamics of water adsorption onto a calcite surface as a function of relative humidity[END_REF], mica [START_REF] Malani | Adsorption isotherms of water on mica: redistribution and film growth[END_REF], and talc surfaces [START_REF] Rotenberg | Molecular explanation for why talc surfaces can be both hydrophilic and hydrophobic[END_REF]. In these studies, plots of the average water density as a function of distance from the surface showed that up to two water monolayers are structured by the surface. In the presence of CO 2 , to our knowledge, only two atomistic simulations have probed adsorbed water films, on forsterite [START_REF] Kerisit | Structure and dynamics of forsterite-scCO 2 /H 2 O interfaces as a function of water content[END_REF]) and quartz [START_REF] Bagherzadeh | Influence of hydrated silica surfaces on interfacial water in the presence of clathrate hydrate forming gases[END_REF]. In atomistic simulations, film thickness can be controlled by imposing the vapor pressure of water in the gas phase [START_REF] Stöckelmann | Adsorption isotherms of water vapor on calcite: A molecular dynamics-Monte Carlo hybrid simulation using a polarizable water model[END_REF][START_REF] Rahaman | Dynamics of water adsorption onto a calcite surface as a function of relative humidity[END_REF][START_REF] Malani | Adsorption isotherms of water on mica: redistribution and film growth[END_REF], the total number of water molecules in the simulation cell [START_REF] Romero-Vargas Castrillón | Structure and energetics of thin film water[END_REF][START_REF] Kerisit | Structure and dynamics of forsterite-scCO 2 /H 2 O interfaces as a function of water content[END_REF], or the radius of curvature r m of a water vapor or CO 2 bubble in the simulated system [START_REF] Wensink | Properties of adsorbed water layers and the effect of adsorbed layers on interparticle forces by liquid[END_REF][START_REF] Bagherzadeh | Influence of hydrated silica surfaces on interfacial water in the presence of clathrate hydrate forming gases[END_REF]. This last property is related to the relative vapor pressure p/p sat through the Kelvin equation [START_REF] Wensink | Properties of adsorbed water layers and the effect of adsorbed layers on interparticle forces by liquid[END_REF]:

where γ wg is the interfacial tension between liquid water and the non-wetting phase (CO 2 or water vapor) and ν m is the molar volume of water. Overall, atomistic simulations show that, in both mineral-water-air and mineral-water-CO 2 systems, water molecules located in the first one or two monolayers on hydrophilic mineral surfaces have a large isosteric heat of adsorption (in agreement with experimental results) and a low diffusivity relative to bulk liquid water [START_REF] Wensink | Properties of adsorbed water layers and the effect of adsorbed layers on interparticle forces by liquid[END_REF][START_REF] Rahaman | Dynamics of water adsorption onto a calcite surface as a function of relative humidity[END_REF][START_REF] Malani | Adsorption isotherms of water on mica: redistribution and film growth[END_REF][START_REF] Kerisit | Structure and dynamics of forsterite-scCO 2 /H 2 O interfaces as a function of water content[END_REF]). These distinct properties of the first one or two water monolayers result from the participation of interfacial water in the solvation of adsorbed [START_REF] Malani | Adsorption isotherms of water on mica: redistribution and film growth[END_REF] or structural [START_REF] Rahaman | Dynamics of water adsorption onto a calcite surface as a function of relative humidity[END_REF][START_REF] Kerisit | Structure and dynamics of forsterite-scCO 2 /H 2 O interfaces as a function of water content[END_REF]) surface metal cations (Figure 11a) and in hydrogen bonding with surface O atoms and OH groups [START_REF] Rahaman | Dynamics of water adsorption onto a calcite surface as a function of relative humidity[END_REF][START_REF] Romero-Vargas Castrillón | Structure and energetics of thin film water[END_REF]. Water molecules located beyond the first two monolayers behave essentially as bulk water [START_REF] Kerisit | Structure and dynamics of forsterite-scCO 2 /H 2 O interfaces as a function of water content[END_REF].

Grand Canonical Monte Carlo simulation predictions of water film thickness vs. p/p sat on silica [START_REF] Leroch | Simulation of forces between humid amorphous silica surfaces: A comparison of empirical atomistic force fields[END_REF], mica [START_REF] Malani | Adsorption isotherms of water on mica: redistribution and film growth[END_REF], and calcite surfaces [START_REF] Rahaman | Dynamics of water adsorption onto a calcite surface as a function of relative humidity[END_REF]) in mineral-water-vapor systems predict that these surfaces have similar hydration properties at p/p sat values up to 0.7, where they carry a single statistical water monolayer (Figure 11b). The apparent discrepancy between the monolayer coverage of silica at p/p sat ~0.7 predicted by GCMC simulation [START_REF] Leroch | Simulation of forces between humid amorphous silica surfaces: A comparison of empirical atomistic force fields[END_REF] and the bilayer coverage observed experimentally at the same relative vapor pressure [START_REF] Asay | Effects of surface chemistry on structure and thermodynamics of water layers at solid-vapor interfaces[END_REF]) may arise from the pH-dependence of silica surface charge: at near-neutral pH values, silica has a negative surface charge density because of the deprotonation of silanol groups [>Si-OH = >Si-O -+ H + , with pK a = 7.0 ± 0.6 [START_REF] Sonnefeld | Determination of electric double layer parameters for spherical silica particles under application of the triple layer model using surface charge density data and results of electrokinetic sonic amplitude measurements[END_REF]Carroll et al. 2002;[START_REF] Dove | Surface charge density on silica in alkali and alkaline earth chloride electrolyte solutions Geochim[END_REF]]. The uncharged silica surface (with fully protonated silanol groups) simulated by [START_REF] Leroch | Simulation of forces between humid amorphous silica surfaces: A comparison of empirical atomistic force fields[END_REF] is of acidic conditions, the point of zero net charge of silica being located near pH 3 (Wang et al. 2012b). Figure 11b includes data obtained in systems where p/p sat < 1 was imposed by placing a bubble of water vapor [START_REF] Wensink | Properties of adsorbed water layers and the effect of adsorbed layers on interparticle forces by liquid[END_REF][START_REF] Bagherzadeh | Influence of hydrated silica surfaces on interfacial water in the presence of clathrate hydrate forming gases[END_REF] or CO 2 [START_REF] Bagherzadeh | Influence of hydrated silica surfaces on interfacial water in the presence of clathrate hydrate forming gases[END_REF] in contact with the adsorbed water film. Experimental and simulation results show that at p/p sat ~ 0.7, pristine (negatively charged) silica surfaces carry two water monolayers [START_REF] Asay | Effects of surface chemistry on structure and thermodynamics of water layers at solid-vapor interfaces[END_REF], uncharged silica surfaces (representative of pH ~ 3) carry one water monolayer [START_REF] Leroch | Simulation of forces between humid amorphous silica surfaces: A comparison of empirical atomistic force fields[END_REF], and uncharged silica surfaces exposed to a bulk CO 2 fluid carry zero water monolayers [START_REF] Bagherzadeh | Influence of hydrated silica surfaces on interfacial water in the presence of clathrate hydrate forming gases[END_REF]. [START_REF] Bagherzadeh | Influence of hydrated silica surfaces on interfacial water in the presence of clathrate hydrate forming gases[END_REF][START_REF] Leroch | Simulation of forces between humid amorphous silica surfaces: A comparison of empirical atomistic force fields[END_REF][START_REF] Wensink | Properties of adsorbed water layers and the effect of adsorbed layers on interparticle forces by liquid[END_REF], calcite [START_REF] Rahaman | Dynamics of water adsorption onto a calcite surface as a function of relative humidity[END_REF], and mica [START_REF] Malani | Adsorption isotherms of water on mica: redistribution and film growth[END_REF]. Values of film thickness and p/p sat in the simulations of [START_REF] Wensink | Properties of adsorbed water layers and the effect of adsorbed layers on interparticle forces by liquid[END_REF] and [START_REF] Bagherzadeh | Influence of hydrated silica surfaces on interfacial water in the presence of clathrate hydrate forming gases[END_REF] were estimated by visual inspection of MD simulation snapshots and by applying Eq. 1 with γ gw = 54.7 mN m -1 and r m = 1.1 ± 0.2 nm [START_REF] Wensink | Properties of adsorbed water layers and the effect of adsorbed layers on interparticle forces by liquid[END_REF] or with γ gw = 80.1 or 70.1 mN m -1 (in the absence or presence of CO 2 , respectively) and r m = 1.93 ± 0.4 nm [START_REF] Bagherzadeh | Influence of hydrated silica surfaces on interfacial water in the presence of clathrate hydrate forming gases[END_REF] [γ gw values were roughly estimated from the results of Vega and deMiguel (2007) and [START_REF] Nielsen | Predicting CO 2 -water interfacial tension under pressure and temperature conditions of geologic CO 2 storage[END_REF]]. [Figure 11a reprinted from Geochim Cosmochim Acta 84, Kerisit S, Weare JH, Felmy AR, Structure and dynamics of forsterite-scCO 2 /H 2 O interfaces as a function of water content, p 137-151, 2012, with permission from Elsevier.] CO 2 -brine-mineral wetting angles. The wettability of mineral surfaces by brine vs. CO 2 -characterized by the mineral-brine-CO 2 wetting angle θ-is an important property of rock formations used in GCS (Tokunaga and Wan 2013). Knowledge of θ is required to convert mercury intrusion porosimetry data into a CO 2 -brine capillary pressuresaturation relation [START_REF] Espinoza | Water-CO 2 -mineral systems: Interfacial tension, contact angle, and diffusion-Implications to CO 2 geological storage[END_REF][START_REF] Pini | Capillary pressure and heterogeneity for the CO2/water system in sandstone rocks at reservoir conditions[END_REF], to predict the maximum column height of CO 2 that can be immobilized under a seal formation (Chiquet et al. 2007b;Chalbaud et al. 2009;Iglauer et al. 2012b), and to derive correlations for the residual CO 2 saturation S g,r [START_REF] Spiteri | A new model of trapping and relative permeability hysteresis for all wettability characteristics[END_REF]Iglauer et al. 2012a). These relationships arise from the well-known Young-Laplace equation (P c = γ wg /r m ), where r m is the radius of curvature of the CO 2 -brine interface. If r m is expressed as a function of the wetting angle and pore aperture, this yields for a cylindrical pore of radius r p :

Despite their importance, the θ values of mineral surfaces in GCS-relevant conditions are poorly characterized. Experimental results obtained at the most widely studied conditions (silica surfaces, T ~ 298 K, low salinity) show significant discrepancies in both the magnitude of θ and its pressure dependence (Figure 12a). Experimental studies also disagree on the influence of salinity [θ either increases [START_REF] Espinoza | Water-CO 2 -mineral systems: Interfacial tension, contact angle, and diffusion-Implications to CO 2 geological storage[END_REF][START_REF] Jung | Supercritical CO 2 and ionic strength effects on wettability of silica surfaces: equilibrium contact angle measurements[END_REF][START_REF] Farokhpoor | Wettability behaviour of CO 2 at storage conditions[END_REF] or decreases with NaCl concentration (Chiquet et al. 2007b;Wang et al. 2012b)] and on the hysteresis of measured θ values [reported as either negligible [START_REF] Bikkina | Contact angle measurements of CO2-water-quartz/calcite systems in the perspective of carbon sequestration[END_REF][START_REF] Jung | Supercritical CO 2 and ionic strength effects on wettability of silica surfaces: equilibrium contact angle measurements[END_REF] or up to ~20° [START_REF] Dickson | Wetting phenomena at the CO2/water/glass interface[END_REF]Chiquet et al. 2007b;[START_REF] Broseta | Are rocks still water-wet in the presence of dense CO2 or H2S?[END_REF]]. The influence of pH is almost entirely unexamined (Wang et al. 2012) and few studies have measured the θ values of minerals other than silica, with the exception of calcite [START_REF] Espinoza | Water-CO 2 -mineral systems: Interfacial tension, contact angle, and diffusion-Implications to CO 2 geological storage[END_REF][START_REF] Bikkina | Contact angle measurements of CO2-water-quartz/calcite systems in the perspective of carbon sequestration[END_REF]Wang et al. 2012b;[START_REF] Farokhpoor | Wettability behaviour of CO 2 at storage conditions[END_REF] and phyllosilicates (Chiquet et al. 2007b;Wang et al. 2012b;[START_REF] Farokhpoor | Wettability behaviour of CO 2 at storage conditions[END_REF]. Figure 12 shows that θ = 21 ± 11° in silica-water-CO 2 systems at low P (Chiquet et al. 2007b;[START_REF] Espinoza | Water-CO 2 -mineral systems: Interfacial tension, contact angle, and diffusion-Implications to CO 2 geological storage[END_REF][START_REF] Bikkina | Contact angle measurements of CO2-water-quartz/calcite systems in the perspective of carbon sequestration[END_REF][START_REF] Jung | Supercritical CO 2 and ionic strength effects on wettability of silica surfaces: equilibrium contact angle measurements[END_REF]Wang et al. 2012b;[START_REF] Farokhpoor | Wettability behaviour of CO 2 at storage conditions[END_REF]. For comparison, θ = 0° in silica-water-air systems [START_REF] Lamb | Controlled wettability of quartz surfaces[END_REF]. This difference suggests that the presence of CO 2 decreases the hydrophilicity of silica, perhaps because it causes the pH to approach the point of zero net charge of silica (Chiquet et al. 2007b;Wang et al. 2012b).

The range of behaviors shown in Figure 12a illustrates the difficulty of accurately characterizing θ. Experimental measurements of θ are highly sensitive to trace levels of impurities that can accumulate at interfaces [START_REF] Pashley | Surface forces in adsorbed multilayers of water on quartz[END_REF][START_REF] Lamb | Controlled wettability of quartz surfaces[END_REF][START_REF] Stipp | Structure and bonding environments at the calcite surface as observed with X-ray photoelectron spectroscopy (XPS) and low energy electron diffraction (LEED)[END_REF]. Another experimental difficulty is the hysteresis between wetting angles measured during imbibition (θ i ) and drainage (θ d < θ i ). This hysteresis may be enhanced by surface roughness [START_REF] Dickson | Wetting phenomena at the CO2/water/glass interface[END_REF]Chiquet et al. 2007b;[START_REF] Broseta | Are rocks still water-wet in the presence of dense CO2 or H2S?[END_REF]), but it can also occur on atomically smooth surfaces [START_REF] Diaz | Hysteresis during contact angles measurement[END_REF]. The few studies that measured a wetting angle hysteresis reported drainage wetting angles θ d [START_REF] Dickson | Wetting phenomena at the CO2/water/glass interface[END_REF]Chiquet et al. 2007b;[START_REF] Farokhpoor | Wettability behaviour of CO 2 at storage conditions[END_REF]), but some studies may have reported θ values that are intermediate between θ d and θ i . Finally, the θ-values themselves may be influenced by surface roughness, a poorly controlled parameter that may evolve upon exposure to CO 2 [START_REF] Espinoza | Water-CO 2 -mineral systems: Interfacial tension, contact angle, and diffusion-Implications to CO 2 geological storage[END_REF]. The inset images show a photograph of a CO 2 droplet on a quartz surface in water during a goniometric contact angle experiment (Wang et al. 2012) and a MD simulation cell containing a CO 2 bubble confined in an otherwise water-filled pore between quartz surfaces [START_REF] Bagherzadeh | Influence of hydrated silica surfaces on interfacial water in the presence of clathrate hydrate forming gases[END_REF]. All studies used pristine quartz surfaces and T = 293 to 309 K unless otherwise noted. [START_REF] Dickson | Wetting phenomena at the CO2/water/glass interface[END_REF] 2012) simulated a surface with only silanol functional groups. The first two types of surfaces should be quite different from the pristine silica surfaces probed experimentally, because the formation of silanol sites on silica surfaces is highly favorable [START_REF] Lamb | Controlled wettability of quartz surfaces[END_REF][START_REF] Du | Molecular dynamics simulations of hydration, dissolution and nucleation processes at the alpha-quartz (0001) surface in liquid water[END_REF][START_REF] Salmeron | Water growth on metals and oxides: binding, dissociation and role of hydroxyl groups[END_REF]), but they may be analogous to the synthetically dehydroxylated silica surface studied by [START_REF] Dickson | Wetting phenomena at the CO2/water/glass interface[END_REF].

A notable difficulty in predicting θ from atomistic simulations is the lack of a set of inter-atomic potential parameters known to accurately predict the solid-water (γ sw ), solid-CO 2 (γ sg ), and water-CO 2 (γ wg ) interfacial tensions. These interfacial tensions determine the wetting angle through the well-known Young equation:

In the absence of a well-tested set of force fields for CO 2 -water-mineral wettability studies, Iglauer et al. (2012b) used CO 2 and water models (EPM2, TIP4P/2005) that predicts γ wg within ~10 mN m -1 [START_REF] Nielsen | Predicting CO 2 -water interfacial tension under pressure and temperature conditions of geologic CO 2 storage[END_REF], but they selected a silica-water interaction model (van Beest et al., 1990) that overestimates the strength of the silicawater interaction [in the absence of CO 2 , they predicted θ = 0° for water on a silica surface that carries only siloxane functional groups, whereas the experimental value for a fully dehydroxylated silica surface is about 42° [START_REF] Lamb | Controlled wettability of quartz surfaces[END_REF]]. [START_REF] Bagherzadeh | Influence of hydrated silica surfaces on interfacial water in the presence of clathrate hydrate forming gases[END_REF] used a water model (TIP4P/Ice) that significantly overestimates the surface tension of liquid water (Vega and de Miguel 2007) and a silica-water interaction model [START_REF] Lopes | Development of an empirical force field for silica. Application to the quartz-water interface[END_REF]) that was not designed for use with the TIP4P/Ice water model and that performs less than optimally when used with at least one other water model [START_REF] Skelton | Simulations of the quartz(101̅ 1)/water interface: A comparison of classical force fields, ab initio molecular dynamics, and X-ray reflectivity experiments[END_REF]. In recent years, the CLAYFF model (Cygan et al. 2004b) has emerged as a remarkably accurate model of the interaction between silicate minerals and liquid water [START_REF] Bourg | Connecting the molecular scale to the continuum scale for diffusion processes in smectite-rich porous media[END_REF][START_REF] Ferrage | Hydration properties and interlayer organization of and ions in synthetic Na-smectite with tetrahedral layer charge. Part 2. Toward a precise coupling between molecular simulations and diffraction data[END_REF][START_REF] Marry | Water dynamics in hectorite clays: influence of temperature studied by coupling neutron spin echo and molecular dynamics[END_REF][START_REF] Skelton | Simulations of the quartz(101̅ 1)/water interface: A comparison of classical force fields, ab initio molecular dynamics, and X-ray reflectivity experiments[END_REF][START_REF] Bourg | Molecular dynamics simulations of water structure and diffusion in silica nanopores[END_REF][START_REF] Leroch | Simulation of forces between humid amorphous silica surfaces: A comparison of empirical atomistic force fields[END_REF], but this model has been exclusively used with two water models [the SPC and SPC/E water models [START_REF] Berendsen | Interaction models for water in relation to protein hydration[END_REF][START_REF] Berendsen | The missing term in effective pair potentials[END_REF]] that underestimate the surface tension of liquid water (Vega and de Miguel 2007; [START_REF] Nielsen | Predicting CO 2 -water interfacial tension under pressure and temperature conditions of geologic CO 2 storage[END_REF]). When used with the SPC water model, the CLAYFF model underestimates the adhesive energy caused by a water meniscus between silica surfaces in humid air (p/p sat = 0.3 to 0.8) by 5 to 22 % [START_REF] Leroch | Simulation of forces between humid amorphous silica surfaces: A comparison of empirical atomistic force fields[END_REF].

Another notable difficulty associated with atomistic simulation predictions of θ is that systems larger than ~10 5 atoms are difficult to model at a reasonable computational cost for the durations (tens of nanoseconds) required to probe wetting angles. Therefore, atomistic simulations of wetting phenomena necessarily probe very small CO 2 bubbles or water droplets (with diameters on the order of 5 nm) that may have distinct properties from those of macroscopic bubbles and drops. For example, pressure may be difficult to define in nanoscale bubbles that too small to contain a bulk-fluid-like region (Cosden and Lukes 2011). Furthermore, interfacial energies are sensitive to long-range interactions; therefore, they may be influenced by interfacial curvature (Cosden and Lukes 2011;[START_REF] Nejad | A molecular dynamics study of nano-bubble surface tension[END_REF] and by the choice of approximations used in evaluating long-range van der Waals interactions [START_REF] Wensink | Properties of adsorbed water layers and the effect of adsorbed layers on interparticle forces by liquid[END_REF][START_REF] Biscay | Monte Carlo simulations of the pressure dependence of the water-acid gas interfacial tensions[END_REF]Cosden and Lukes 2011).

The θ values of Si oxide surfaces reported in Figure 12 can be grouped into two distinct datasets. The first set includes all studies of partly or completely de-hydroxylated silica surfaces [START_REF] Dickson | Wetting phenomena at the CO2/water/glass interface[END_REF][START_REF] Liu | Molecular dynamics simulation of wetting behavior at CO 2 /water/solid interfaces[END_REF]Iglauer et al. 2012b). These surfaces are weakly hydrophilic in the absence of CO 2 and they show a strong wettability alteration with increasing CO 2 pressure. The second set includes all studies of pristine silica surfaces (Chiquet et al. 2007b;[START_REF] Espinoza | Water-CO 2 -mineral systems: Interfacial tension, contact angle, and diffusion-Implications to CO 2 geological storage[END_REF][START_REF] Bikkina | Contact angle measurements of CO2-water-quartz/calcite systems in the perspective of carbon sequestration[END_REF][START_REF] Jung | Supercritical CO 2 and ionic strength effects on wettability of silica surfaces: equilibrium contact angle measurements[END_REF]Wang et al. 2012b). The density of silanol functional groups determines whether a silica surface belongs to one or the other group. Within the second dataset, the MD simulation results of [START_REF] Bagherzadeh | Influence of hydrated silica surfaces on interfacial water in the presence of clathrate hydrate forming gases[END_REF] are most closely consistent with the experimental results of Chiquet et al. (2007b). The origin of the difference between studies that show a P-dependence of θ (Chiquet et al. 2007b;[START_REF] Bagherzadeh | Influence of hydrated silica surfaces on interfacial water in the presence of clathrate hydrate forming gases[END_REF][START_REF] Jung | Supercritical CO 2 and ionic strength effects on wettability of silica surfaces: equilibrium contact angle measurements[END_REF] and those that do not [START_REF] Espinoza | Water-CO 2 -mineral systems: Interfacial tension, contact angle, and diffusion-Implications to CO 2 geological storage[END_REF][START_REF] Bikkina | Contact angle measurements of CO2-water-quartz/calcite systems in the perspective of carbon sequestration[END_REF]Wang et al. 2012b) is not known. This question should lend itself readily to an atomistic scale analysis of the P-dependence of the interfacial energies γ gs , γ gw , and γ ws (Iglauer et al. 2012b).

CO 2 clathrate hydrates

Gas clathrate hydrates (Figure 13a) play important roles in certain GCS concepts, such as carbon sequestration in deep ocean sediments [START_REF] House | Permanent carbon dioxide storage in deep-sea sediments[END_REF]Tohidi et al. 2010) and CO 2 -CH 4 substitution in natural methane hydrate formations (Ota et al. 2005;[START_REF] Park | Sequestering carbon dioxide into complex structures of naturally occurring gas hydrates[END_REF][START_REF] Espinoza | P-wave monitoring of hydrate-bearing sand during CH 4 -CO 2 replacement[END_REF]. The potential usefulness of gas hydrates as a CO 2 storage medium is illustrated by the fact that the molecular CO 2 :H 2 O ratio in these hydrates can be as high as 1:5.75, about 300 times the solubility of CO 2 in water at ambient conditions. A substantial fraction of the molecular modeling research on CO 2 -H 2 O systems has focused on CO 2 hydrates [their bulk properties (Chialvo et al. 2002;[START_REF] Ota | Monte Carlo approach to structure and thermodynamic property of CO 2 hydrate[END_REF][START_REF] Geng | Molecular simulation of the potential of methane reoccupation during the replacement of methane hydrate by CO 2[END_REF][START_REF] Jiang | Comparison of the properties of xenon, methane, and carbon dioxide hydrates from equilibrium and nonequilibrium molecular dynamics simulations[END_REF], their nucleation (Radhakrishnan andTrout 2002), growth (Tung et al. 2011a), and dissolution [START_REF] Sarupria | Molecular dynamics study of carbon dioxide hydrate dissociation[END_REF], their stability near mineral surfaces [START_REF] Bai | Microsecond molecular dynamics simulations of the kinetic pathways of gas hydrate formation from solid surfaces[END_REF], and the conversion from CH 4 to CO 2 hydrates [START_REF] Geng | Molecular simulation of the potential of methane reoccupation during the replacement of methane hydrate by CO 2[END_REF]Tung et al. 2011b)].

From a technical point of view, atomistic simulations of CO 2 hydrates benefit from the existence of well-tested force fields that are known to predict the properties of these crystals with reasonable accuracy [START_REF] Jiang | Comparison of the properties of xenon, methane, and carbon dioxide hydrates from equilibrium and nonequilibrium molecular dynamics simulations[END_REF][START_REF] Sarupria | Molecular dynamics study of carbon dioxide hydrate dissociation[END_REF]Tung et al. 2011a). In particular, the combination of the TIP4P/Ew water model [START_REF] Horn | Development of an improved four-site water model for biomolecular simulations: TIP4P-Ew[END_REF]), the EPM2 CO 2 model [START_REF] Harris | Carbon dioxide's liquid-vapor coexistence curve and critical properties as predicted by a simple molecular model[END_REF], and the CO 2 -water interaction parameters of Sun and Duan (2005) [parameterized to fit the quantum mechanical calculations of [START_REF] Sadlej | Ab initio study of energy, structure and dynamics of the water-carbon dioxide complex[END_REF]] yields a remarkably good prediction of CO 2 hydrate melting temperature (Figure 13b; Tung et al. 2011a). One complicating aspect of the atomistic modeling of CO 2 hydrates that the cage occupancy of real CO 2 hydrates is lower than one CO 2 molecule per cage: it ranges from 0.8 to 1.0 and depends on cage size [the large cages of the gas hydrate sI structure are almost fully occupied, the small cages are partly occupied (Circone et al. 2003;Sun and Duan 2005;Takeya et al. 2010)]. Molecular simulation studies have almost always probed the condition of full cage occupancy [START_REF] Jiang | Comparison of the properties of xenon, methane, and carbon dioxide hydrates from equilibrium and nonequilibrium molecular dynamics simulations[END_REF]Tung et al. 2011a). In a rare study of CO 2 hydrates with partial cage occupancy, [START_REF] Sarupria | Molecular dynamics study of carbon dioxide hydrate dissociation[END_REF] showed that the melting temperature of CO 2 clathrate hydrate decreases by 2 to 4 K as cage occupancy decreases from 1.0 to 0.87 and that this destabilization is greater if CO 2 is removed from the larger cages of the clathrate structure.

Atomistic simulations of bulk CO 2 hydrates and their interfaces with liquid water have yielded several insights into the nano-scale properties of CO 2 hydrates. For example, simulations of bulk CO 2 hydrates revealed that their thermal conductivity is ~20 % smaller than that of CH 4 hydrates (Jiang and Jordan 2010), a difference that could have important implications for the process of storing CO 2 in CH 4 hydrate formations. Simulations of CO 2 hydrate growth showed that the growth rate is on the order of 0.10 to 0.16 m s -1 , with little pressure-dependence, and that growth proceeds through the formation of a transient amorphous phase that contains more large cages and fewer small cages than the bulk CO 2 hydrate (Tung et al. 2011a), a finding consistent with simulations showing that the binding energy of CO 2 is about 4.0 kJ mol -1 greater in the large cages than in the small cages [START_REF] Jiang | Comparison of the properties of xenon, methane, and carbon dioxide hydrates from equilibrium and nonequilibrium molecular dynamics simulations[END_REF]. Simulations of the dissolution of CO 2 hydrates show that dissolution is a collective phenomenon with an activation energy of 62 to 70 kJ mol -1 (consistent with the breaking of 3-5 hydrogen bonds) and a rate that increases as cage occupancy decreases [START_REF] Sarupria | Molecular dynamics study of carbon dioxide hydrate dissociation[END_REF]. Simulations of CO 2 hydrate dissolution and growth (Figure 13c) have not detected the formation of transient ice-like structures [START_REF] Sarupria | Molecular dynamics study of carbon dioxide hydrate dissociation[END_REF]Tung et al. 2011a). Finally, simulations show that the replacement of CH 4 by CO 2 in clathrate hydrate crystals can occur in the absence of clathrate melting (Tung et al. 2011b) and that the CH 4 -CO 2 mixed hydrate, with CH 4 occupying the small clathrate cages, is more stable than either the CH 4 or the CO 2 hydrates [START_REF] Geng | Molecular simulation of the potential of methane reoccupation during the replacement of methane hydrate by CO 2[END_REF], in agreement with experimental evidence that CO 2 displaces CH 4 much more readily from large cages than from small cages (Ota et al. 2005).

An emerging research area in the simulation of gas hydrates is the influence of mineral surfaces on hydrate nucleation, growth, and dissolution. Experimental studies suggest that mineral surfaces influence the kinetics and thermodynamics of methane hydrate growth in porous media (Cha et al. 1988;Uchida et al. 2004;[START_REF] Koster Van Groos | The stability of methane hydrate intercalates of montmorillonite and nontronite: Implications for carbon storage in ocean-floor environments[END_REF], but the details of this effect are not well established [START_REF] Park | Do montmorillonite surfaces promote methane hydrate formation? Monte Carlo and molecular dynamics simulations[END_REF]Cygan et al. 2004a) and its existence in the case of CO 2 hydrates is unknown. To our knowledge, only two atomistic-scale simulation studies have studied CO 2 or CH 4 hydrate crystals near mineral surfaces [START_REF] Bai | Microsecond molecular dynamics simulations of the kinetic pathways of gas hydrate formation from solid surfaces[END_REF][START_REF] Liang | Crystal growth simulations of methane hydrates in the presence of silica surfaces[END_REF]. Both studies simulated uncharged silica surfaces and found that a thin water film (0.5 to 1.0 nm thick) separates the gas hydrate from the mineral surface [START_REF] Bai | Microsecond molecular dynamics simulations of the kinetic pathways of gas hydrate formation from solid surfaces[END_REF][START_REF] Liang | Crystal growth simulations of methane hydrates in the presence of silica surfaces[END_REF]). This finding is consistent with the well-established observation that a 0.4 to 0.6 nm thick layer of surface water in silica nanopores freezes at a much lower temperature than bulk liquid water does not form a crystalline ice phase [START_REF] Hansen | Low-temperature phase transition of water confined in mesopores probed by NMR. Influence on pore size distribution[END_REF][START_REF] Schreiber | Melting and freezing of water in ordered mesoporous silica materials[END_REF]) and with the strong adsorption of one or two water monolayers on flat silica surfaces (discussed in the section on adsorbed water films). The simulation study by [START_REF] Liang | Crystal growth simulations of methane hydrates in the presence of silica surfaces[END_REF] provides tantalizing evidence that MD simulations may allow evaluating the silica-water-gas hydrate wetting angle.

FUTURE RESEARCH OPPORTUNITIES

Atomistic simulations can play an important role in helping to improve thermodynamic models of mineral-brine-CO 2 systems, one of the poorly constrained inputs of current GCS models [START_REF] Xu | Numerical modeling of injection and mineral trapping of CO 2 with H 2 S and SO 2 in a sandstone formation[END_REF]. In particular, MD simulation techniques can probe the stability of metal carbonate/bicarbonate ion species in solution that are larger than ion pairs [START_REF] Fosbøl | Review and recommended thermodynamic properties of FeCO 3[END_REF][START_REF] Marcus | Ion pairing[END_REF] and the thermodynamics of CO 2 impurities such as H 2 S and SO 2 (Chialvo et al., 2013a). Classical or quantum mechanical calculations also could be used to inform thermodynamic models of aqueous Al species [START_REF] Gaus | Reactive transport modeling of the impact of CO 2 injection on the clayey cap rock at Sleipner (North Sea)[END_REF].

Continued development of force field parameters that accurately describe the energetics of both aqueous and solid phases will aid in future simulations of carbonate growth mechanisms. Comparisons of experimental and atomistic simulation results will continue to play a central role in this effort as shown by recent XR data on the structure of the calcite-water interface [START_REF] Fenter | Is the calcite-water interface understood? direct comparisons of molecular dynamics simulations with specular X-ray reflectivity data[END_REF]. Ab initio and DFT predictions of calcite-water interfaces can play an important role in constraining new force fields. Development of reactive carbonate models, like the one proposed by [START_REF] Gale | A reactive force field for aqueous-calcium carbonate systems[END_REF] for the aqueous-calcium carbonate system, could also play an important role in this effort because of the possible importance of water dissociation at calcite kink sites.

Investigations of synthetic and biogenic ACC should elucidate the water content of these phases and its influence on their stability. For example, the metadynamics technique (so far been applied only to anhydrous CaCO 3 particles) should be applied to hydrated ACC.

Simulations of the interplay between organic and inorganic species in solution during mineralization remain challenging because the mechanisms of CaCO 3 crystallization are still not fully understood. In a simpler crystallization system like urea, for which MD and kinetic Monte Carlo modeling has successfully described the mechanisms of crystal growth and dissolution [START_REF] Piana | Understanding the barriers to crystal growth: dynamical simulation of the dissolution and growth of urea from aqueous solution[END_REF], simulation is able to predicts growth rates and morphologies in the presence of organic species in good agreement with experiment [START_REF] Salvalaglio | Uncovering molecular details of urea crystal growth in the presence of additives[END_REF]. For carbonates, the information gained from simulations of additive effects during the early stages of crystallization will be much less complicated to interpret once the pathways to mineral formation are known.

Atomistic simulations are barely beginning to be applied to the study of wetting properties (behavior of adsorbed water, wetting angles) in mineral-brine-CO 2 systems. Carefully designed simulations can provide information on the dependence of these properties on the type of mineral surface, and the influence of solutes such as electrolyte ions, dissolved organic molecules, or CO 2 impurities (H 2 S, SO 2 ). Advances in this area will require the identification of a set of force fields that can accurately predict the interfacial energies of mineral-water, mineral-CO 2 , and water-CO 2 interfaces. Future simulations should determine the origin of the difference between studies that show a dependence of θ in silica-water-CO 2 systems (Chiquet et al. 2007b;[START_REF] Bagherzadeh | Influence of hydrated silica surfaces on interfacial water in the presence of clathrate hydrate forming gases[END_REF][START_REF] Jung | Supercritical CO 2 and ionic strength effects on wettability of silica surfaces: equilibrium contact angle measurements[END_REF] and those that do not [START_REF] Espinoza | Water-CO 2 -mineral systems: Interfacial tension, contact angle, and diffusion-Implications to CO 2 geological storage[END_REF][START_REF] Bikkina | Contact angle measurements of CO2-water-quartz/calcite systems in the perspective of carbon sequestration[END_REF]Wang et al. 2012b

Figure 1 :

 1 Figure1: Schematic representation of the presumptive phase relationships in the CaCO 3 -H 2 O system at ambient pressure[START_REF] Wallace | Microscopic evidence for liquidliquid separation in supersaturated CaCO 3 solutions[END_REF]. The gray horizontal line represents a constant temperature slice through the stability fields as the solution ion activity product is increased. The solubility of all polymorphs is represented by a single solubility line (SL), which bounds the undersaturated solution field (dark gray region in the lower left corner). This simplification highlights that the solid phases of CaCO 3 (calcite, aragonite, vaterite, presumably ACC) all display the same general retrograde solubility behavior. Indirect nucleation of the solid phases proceeds to the high concentration side of the dashed black liquid-liquid coexistence line (L-L). The phase field bounded by the L-L line and the dashed gray spinodal line (SP) and labeled "Nucleation of liquid CaCO 3 " indicates the conditions where nucleation of the dense liquid phase (DLP) is possible. In the region bounded by the spinodal line the solution is unstable to fluctuations and liquid-liquid separation proceeds spontaneously. The retrograde solubility of the DLP (i.e. concave up orientation of the system binodal) is assumed based on the behavior of the MgSO 4 -H 2 O system at high temperature[START_REF] Wallace | Microscopic evidence for liquidliquid separation in supersaturated CaCO 3 solutions[END_REF]) and the arguments in support of a lower critical point temperature presented by[START_REF] Faatz | Amorphous calcium carbonate: synthesis and potential intermediate in biomineralization[END_REF].[From Wallace AF et al. (2013) Science 341:885-889. Reprinted with permission from AAAS]

Figure 2 :

 2 Figure 2: (a) Comparison of the experimental X-ray pair distribution function with the molecular dynamics-derived model structure of amorphous calcium carbonate (Wallace et al. 2013). (b) Snapshot of the RMC fit to the experimental PDF (Goodwin et al. 2010). (c) Model structure of amorphous calcium carbonate obtained from MD simulations of CaCO 3 (nH 2 O) cluster aggregation and dehydration (Wallace et al. 2013). [Figures 2a and 2c from Wallace AF et al (2013) Science 341:885-889. Reprinted with permission from AAAS. Figure 2b adapted with permission from Goodwin AL et al. (2010) Chem Mater 22:3197-3205. Copyright 2010 American Chemical Society.]

Figure 3 .

 3 Figure 3. Prediction of the thermodynamics of mixing of the rhombohedral carbonate system Ca 1-x Mg x CO 3 based on atomistic simulations (Vinograd et al. 2007). (a) Excess static structure energies of 700 Ca 1-x Mg x CO 3 structures (4 × 4 × 1 supercell with x = 0.125 to 0.875 and different distributions of Ca and Mg atoms) predicted with an empirical model of interatomic interactions; the dashed line connects the minimum energy structures. (b) Comparison of predicted and experimental calcite-magnesite phase diagrams. The symbols and solid lines are experimental results (Goldsmith 1983); the gray and white regions indicate predictions of phase stablility and instability (or metastability). The model predictions were obtained using a coarse-grained Monte Carlo simulation (12 × 12 × 4 supercell) where interactions between metal sites were described with an effective pair potential parameterized to fit the all-atom simulation results in (a). [Reprinted from Geochim Cosmochim Acta 71, Vinograd VL, Burton BP, Gale JD, Allan NL, Winkler B, Activity-composition relations in the system CaCO 3 -MgCO 3 predicted from static structure energy calculations and Monte Carlo simulations, p 974-983, Copyright 2007, with permission from Elsevier.]

Figure 4 .

 4 Figure 4. Examination of the structure of water and calcite on terraces of the {10-14} calcite surface using a combination of X-ray reflectivity (XR) data and MD simulation results (Fenter et al. 2013). (a) MD simulation prediction of water structure on the calcite surface. The lower part of the figure shows the average position of the calcite atoms during the simulation (spheres: Ca atoms; sticks: C and O atoms). The upper part of the figure shows the range of positions of water O atoms during the simulation (O atoms shown as points, with coordinates taken from 500 frames sampled at regular intervals during the simulation). The planes of O atoms coordinated to surface Ca and CO 3 groups are labeled 1 and 2. (b) Comparison of the normalized XR data (circles) with four different fitting schemes (lines):(1) direct fit to the XR data, (2) direct comparison of the full MD data with the XR data, (3) hybrid scheme in which only the interfacial calcite structure was taken from the MD results, and (4) hybrid scheme in which only the interfacial water structure was taken from the MD results. (c) Total electron density profile in the direction normal to the interface (z = 0 at the location of the plane of surface Ca atoms) calculated by direct fit to the XR data (fit 1) or by using a fitting procedure that was informed by two different MD models (fits 2 and 3). All three fits described the XR data equally well. [Adapted with permission from[START_REF] Fenter | Is the calcite-water interface understood? direct comparisons of molecular dynamics simulations with specular X-ray reflectivity data[END_REF]) J Phys Chem C 117:5028-5042. Copyright 2013 American Chemical Society.]

Figure 5 :

 5 Figure 5: Atomistic scale calculations with model ACC clusters demonstrate that calcium ion and CaCO 3 ion pair addition to ACC are energetically favorable processes. (a) Illustration of a CaCO 3 ion pair (visible on the left with water molecules in its first solvation shell) being added to a model ACC cluster (the large structure on the right, also shown with its neighboring water molecules) and free energy profiles for the addition of a CaCO 3 ion pair to ACC clusters of varying size (formula units, fu) and hydration state (Raiteri and Gale 2010). The equivalent profile for addition to the (10-14) surface of calcite (light gray line with an overall minimum at ~5 Å instead of ~3 Å) is shown for comparison. (b) Model ACC cluster with potential calcium ion addition sites (shown as large spheres) and free energy profiles for the addition of Ca 2+ at the different sites (Tribello et al. 2009). [Adapted with permission from Raiteri P and Gale JD (2013) J Am Chem Soc 132:17623-17634, Copyright 2010 American Chemical Society, and Tribello GA et al. (2009) J Phys Chem B 113:11680-11687, Copyright 2009 American Chemical Society.]

Figure 6 :

 6 Figure6: Metadynamics and umbrella sampling calculations reveal that the attachment of Ba 2+ on a BaSO 4 step edge involves several stable states: (1) Ba at the step edge, (2) Ba slightly detached from the step edge, (3) Ba forming an inner-sphere surface complex above the step edge, and (4) Ba in solution[START_REF] Stack | Accurate rates of the complex mechanisms for growth and dissolution of minerals using a combination of rare-event theories[END_REF]). The different stable states are shown in (a) a twodimensional map of the potential energy landscape calculated with the metadynamics method, and (b) a plot of the free energy profile along the minimum free energy path as calculated with the umbrella sampling technique (this technique shows a fifth stable state at ξ ≈ 7.5 Å where Ba forms an outer-sphere surface complex). The potential energy landscape associated with Ca 2+ attachment to a CaCO 3 kink site is likely to be similarly complex. [Adapted with permission from[START_REF] Stack | Accurate rates of the complex mechanisms for growth and dissolution of minerals using a combination of rare-event theories[END_REF]) J Am Chem Soc 134:11-14. Copyright 2012 American Chemical Society.]

Figure 7 :

 7 Figure 7: Organic acids may influence calcite growth rates either by (a) interacting with Ca 2+ in solution, of (b) interacting with growth (kink) sites on the calcite surface. (a) Molecular dynamics simulations show that Asp binding to Ca 2+ in bulk liquid water strongly disrupts the solvation shell of calcium; in particular, the number of water molecules coordinating Ca decreases from 8 to 5 as Asp approaches Ca (Hamm et al. 2010). (b) Molecular dynamics simulations show that n-Asp spontaneously adsorbs on negatively charged kink sites, but not on the uncharged flat surface of calcite (Aschauer et al. 2010). [Figure 7a adapted with permission from Hamm LM et al. (2010) J Phys Chem B 114:10488-10495, Copyright 2010 American Chemical Society; Figure 7b reprinted from J Colloid Interface Sci 346, Aschauer U, Spagnoli D, Bowen P, Parker SC, Growth modification of seeded calcite using carboxylic acids: atomistic simulations, p 226-231, Copyright 2010, with permission from Elsevier.]

Figure 8 :

 8 Figure 8: Model predictions of the phase properties of pure CO 2 (left) and CO 2 -water mixtures (right). (a) Pressure-density relation of pure CO 2 calculated with the equation of state of Bender (1970) (solid line) or predicted using GCMC simulation with the EPM2 CO 2 model (open symbols) at T = 290 to 520 K (Vorholz et al. 2000). (b) Pressure-composition relation of CO 2water two-phase mixtures predicted using GCMC simulation (Liu et al. 2011) with different models of water and CO 2 [Exp-6 water and CO 2 (Δ), EPM2+TIP4P/2005 (+), TraPPE+TIP4P2005 (×), EPM2+SPC (ο), EPM2+TIP4P (∇)]. The filled symbols are experimental data from Wiebe and Gaddy (1939) (circles), Wiebe (1941) (stars), and Takenouchi and Kennedy (1964) (diamonds). [Figure 8a reprinted from Fluid Phase Equil 226, Vorholz J, Harismiadis VI, Panagiotopoulos AZ, Rumpf B, Maurer G, Molecular simulation of the solubility of carbon dioxide in aqueous solutions of sodium chloride, p 237-250, Copyright 2004, with permission from Elsevier; Figure 8b reproduced with permission from Liu Y et al. (2011) J Phys Chem B 115:6629-6635, Copyright 2011 American Chemical Society.]

Figure 9 :

 9 Figure 9: Molecular dynamics simulation prediction of CO 2 -water IFT and CO 2 adsorption on the surface of liquid water (Nielsen et al. 2012). (a) Snapshot of a single CO 2 molecule and the water molecules in its first solvation shell. (b) Snapshot of a MD simulation cell containing two coexisting fluid phases (liquid water and scCO 2 ) and two parallel interfaces; the graph shows the density profile of water and CO 2 molecules in the direction normal to the CO 2 -water interfaces; adsorption of CO 2 on the water surface is evidenced by the small enhancement in CO 2 density near the interface. (c) Experimental data on IFT vs. P at 383 K [black triangles and dashed line (Chiquet et al. 2007a)] compared with MD simulation predictions obtained with different combinations of water (SPC/E, TIP4P/2005) and CO 2 (EPM2, PPL) models (gray symbols and lines). Simulation results with the SPC/E water model were renormalized to the surface tension of TIP4P2005 water by adding 8.4 mN m -1 to the predicted IFT values. (d) Experimental data and MD simulation predictions of CO 2 surface excess Γ CO2 (H2O) vs. P. The experimental values were calculated from the experimental data on IFT vs. P in (c) using the Gibbs adsorption equation. [Figure modified from Geochim Cosmochim Acta 81, Nielsen LC, Bourg IC, Sposito G, Predicting CO 2 -water interfacial tension under pressure and temperature conditions of geologic CO 2 storage, p 28-38, Copyright 2012, with permission from Elsevier.]

Figure 10 :

 10 Figure 10: Grand Canonical Monte Carlo prediction of the solubility of CO 2 in water-filled smectite clay interlayer nanopores at 348 K and 25 or 125 bar as a function of clay basal spacing (Botan et al. 2010). (a) Schematic view of the simulated system containing stacked smectite lamellae and interlayer nanopores filled with water, Na + , and CO 2(aq) . (b) Predictions of the solubility of CO 2 in nanopore water as a function of clay basal spacing (black and gray squares at 25 and 125 bar, respectively). The solubility of CO 2 in bulk liquid water at 25 and 125 bar is shown by the horizontal black and gray lines. The vertical shaded bars indicate the stable swelling states of the clay mineral (the one-and two-layer hydrates). The results show that CO 2 is more soluble in clay interlayer water than in bulk liquid water. [Figure modified with permission from Botan A et al. (2010) J Phys Chem C 114:14962-14969. Copyright 2010 American Chemical Society.]

Figure 11 :

 11 Figure 11: (a) Molecular dynamics simulation snapshot of a sub-monolayer adsorbed water film at the forsterite-scCO 2 interface (Kerisit et al. 2012). The figure shows that adsorbed water molecules are attracted to the forsterite surface because of their affinity for structural Mg 2+ ions (light gray spheres). (b) Compilation of MD and GCMC simulation predictions of the thickness of adsorbed water films on flat mineral surfaces at T = 298 to 300 K on silica[START_REF] Bagherzadeh | Influence of hydrated silica surfaces on interfacial water in the presence of clathrate hydrate forming gases[END_REF][START_REF] Leroch | Simulation of forces between humid amorphous silica surfaces: A comparison of empirical atomistic force fields[END_REF][START_REF] Wensink | Properties of adsorbed water layers and the effect of adsorbed layers on interparticle forces by liquid[END_REF], calcite[START_REF] Rahaman | Dynamics of water adsorption onto a calcite surface as a function of relative humidity[END_REF], and mica[START_REF] Malani | Adsorption isotherms of water on mica: redistribution and film growth[END_REF]. Values of film thickness and p/p sat in the simulations of[START_REF] Wensink | Properties of adsorbed water layers and the effect of adsorbed layers on interparticle forces by liquid[END_REF] and[START_REF] Bagherzadeh | Influence of hydrated silica surfaces on interfacial water in the presence of clathrate hydrate forming gases[END_REF] were estimated by visual inspection of MD simulation snapshots and by applying Eq. 1 with γ gw = 54.7 mN m -1 and r m = 1.1 ± 0.2 nm[START_REF] Wensink | Properties of adsorbed water layers and the effect of adsorbed layers on interparticle forces by liquid[END_REF] or with γ gw = 80.1 or 70.1 mN m -1 (in the absence or presence of CO 2 , respectively) and r m = 1.93 ± 0.4 nm[START_REF] Bagherzadeh | Influence of hydrated silica surfaces on interfacial water in the presence of clathrate hydrate forming gases[END_REF] [γ gw values were roughly estimated from the results of

Figure 12 :

 12 Figure 12: Compilation of (a) measurements and (b) MD simulations of the mineral-water-CO 2 wetting angle θ on silica surfaces at low ionic strengths (I ≤ 0.2 M NaCl) as a function of pressure.The inset images show a photograph of a CO 2 droplet on a quartz surface in water during a goniometric contact angle experiment(Wang et al. 2012) and a MD simulation cell containing a CO 2 bubble confined in an otherwise water-filled pore between quartz surfaces[START_REF] Bagherzadeh | Influence of hydrated silica surfaces on interfacial water in the presence of clathrate hydrate forming gases[END_REF]. All studies used pristine quartz surfaces and T = 293 to 309 K unless otherwise noted.[START_REF] Dickson | Wetting phenomena at the CO2/water/glass interface[END_REF] used a reduced-hydrophilicity silica surface treated by silanization to remove 63 % of silanol groups. Wang et al. (2012b) used T = 303 K at 7 MPa, 323 K at 20 MPa. Jung and Wan (2012) used T = 318 K and an amorphous silica surface. Liu et al. (2010) used T = 318 K and a crystobalite surface with ~35 % of the hydroxyl site density of a pristine silica surface. Iglauer et al. (2012b) used a dehydroxylated quartz surface with no silanol surface functional groups. Pressure in the simulations of Liu et al. (2010) was estimated from the reported CO 2 densities using National Institute of Standards and Technology (NIST) data on the pressuredensity relation of pure CO 2 at 318 K. Pressure in the simulations of Bagherzadeh et al. (2012) was roughly estimated as the average value of the diagonal pressure tensor components in directions parallel to the silica surfaces (calculated by the authors for the entire simulation cell), renormalized such that P = 0 in the absence of CO 2 . [Figure 12a inset reproduced with permission from Wang S et al. (2012) Environ Sci Technol 47:234-241. Copyright 2012 American Chemical Society. Figure 12b inset reproduced with permission from Bagherzadeh SA et al (2012) J Phys Chem C 116:24907-24915. Copyright 2012 American Chemical Society.]

  Figure 12: Compilation of (a) measurements and (b) MD simulations of the mineral-water-CO 2 wetting angle θ on silica surfaces at low ionic strengths (I ≤ 0.2 M NaCl) as a function of pressure.The inset images show a photograph of a CO 2 droplet on a quartz surface in water during a goniometric contact angle experiment(Wang et al. 2012) and a MD simulation cell containing a CO 2 bubble confined in an otherwise water-filled pore between quartz surfaces[START_REF] Bagherzadeh | Influence of hydrated silica surfaces on interfacial water in the presence of clathrate hydrate forming gases[END_REF]. All studies used pristine quartz surfaces and T = 293 to 309 K unless otherwise noted.[START_REF] Dickson | Wetting phenomena at the CO2/water/glass interface[END_REF] used a reduced-hydrophilicity silica surface treated by silanization to remove 63 % of silanol groups. Wang et al. (2012b) used T = 303 K at 7 MPa, 323 K at 20 MPa. Jung and Wan (2012) used T = 318 K and an amorphous silica surface. Liu et al. (2010) used T = 318 K and a crystobalite surface with ~35 % of the hydroxyl site density of a pristine silica surface. Iglauer et al. (2012b) used a dehydroxylated quartz surface with no silanol surface functional groups. Pressure in the simulations of Liu et al. (2010) was estimated from the reported CO 2 densities using National Institute of Standards and Technology (NIST) data on the pressuredensity relation of pure CO 2 at 318 K. Pressure in the simulations of Bagherzadeh et al. (2012) was roughly estimated as the average value of the diagonal pressure tensor components in directions parallel to the silica surfaces (calculated by the authors for the entire simulation cell), renormalized such that P = 0 in the absence of CO 2 . [Figure 12a inset reproduced with permission from Wang S et al. (2012) Environ Sci Technol 47:234-241. Copyright 2012 American Chemical Society. Figure 12b inset reproduced with permission from Bagherzadeh SA et al (2012) J Phys Chem C 116:24907-24915. Copyright 2012 American Chemical Society.]

Figure 13 :

 13 Figure 13: Prediction of the properties of CO 2 hydrates in contact with bulk liquid water. (a) Structure of the host lattice in the sI clathrate hydrate; the large and small cages are shown in light and dark gray, respectively (Hoshikawa et al. 2006). (b) Comparison of experimental measurements [open symbols (Takenouchi and Kennedy 1965; Jager and Sloan 2001; Yang et al. 2001)] and MD simulation predictions [filled symbols (Tung et al. 2010, 2011a)] of the threephase coexistence conditions of CO 2 and CH 4 hydrates (triangles and circles, respectively) (Tung et al. 2011b). (c) Interface between CO 2 hydrate and bulk liquid water during a simulation of CO 2 hydrate dissociation; water molecules are displayed in lighter or darker gray depending on whether their local coordination is more clathrate-like or liquid-like (Sarupria and Debenedetti 2011). [Figure 13a reprinted with permission from Hoshikawa A et al (2006) J Chem Phys

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ACKNOWLEDGMENTS

This material was prepared by LMH, AFW, and ICB with support from the Center for Nanoscale Control of Geologic CO 2 (NCGC), an Energy Frontiers Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DE-AC02-05CH11231.