DFT Study on the Effect of Water on the Carbonation of Portlandite

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DFT Study on the Effect of Water on the Carbonation of Portlandite Andreas Funk* and H. F. Reinhard Trettin Universität Siegen, Institut für Bau- und Werkstoffchemie, Paul-Bonatz-Strasse 9-11, D-57076 Siegen, Germany ABSTRACT: Hardening of lime-based binders is a process where carbonation of portlandite plays an important role. Additionally, carbonation of hydrated lime is of general technical interest, e.g., for carbon dioxide capture. The mechanisms responsible for this reaction are not well-known. In this work, we study the carbonation of portlandite without water and with one water molecule at atomistic scale. Density functional theory (DFT) is used to simulate the reaction path and to accurately calculate minima and transition states on the potential-energy surface. We find that water significantly lowers reaction barriers and stabilizes the partially carbonated reaction product, which gives atomistic proof to experimental results. From our atomistic point of view, we explain the reasons for this effect of water on the carbonation of portlandite.

1. INTRODUCTION Portlandite (calcium hydroxide) is an important reactant of lime-based binders in building chemistry. The carbonation of portlandite hardens the binders, a process necessary for the performance as building materials. In addition, the carbonation of hydrated lime is also an unwanted reaction in flue gas desulphurization and a possible candidate for carbon dioxide capture in technical processes. To understand the carbonation reaction of calcium hydroxide, kinetic studies have been carried out.1−3 In these studies, the effects of temperature and air moisture on the carbonation reaction have been revealed. As these studies were not performed at an atomistic level, the initial steps of the carbonation reaction and the influence of water onto those could not be understood. The carbonation of brucite (magnesium hydroxide) has been studied using density functional theory. The authors suggested a mechanism of dehydroxylation with subsequent carbonation of the resulting oxide, but the effect of water has not been inspected.4 A most recent study dealt with the adsorption of CO2 on transition metal hydroxides and developed a model based upon atomistic calculations, but did not give any insight to the reaction path of carbonation.5 Much more effort has been taken to understand the mechanisms of formation and reactivity of carbonic acid from quantum mechanical simulations.6−11 These include mechanisms of direct reactions of carbon dioxide with water7,10,11 as well as those of a combination of catalytic water molecules and microsolvation of the species10,11 or of the mechanism in solution.6,8 It can be concluded that a reaction is possible with only one water molecule,6,7,10,11 although it is more favorable to have three or four water molecules interacting with carbon dioxide.6,10,11 Reactions of carbon dioxide with oxide surfaces have recently been studied with quantum chemical methods12 to get more detailed information on the carbon dioxide adsorption and how it is influenced by water. As a result, water is shown to make adsorption of carbon dioxide more favorable for oxide surfaces. We have simulated the carbonation reaction of portlandite on the (001) surface, which is the most hydroxide-rich surface © 2013 American Chemical Society

of portlandite, using density functional theory. We show reaction products, transition states, and the effect of water.

2. COMPUTATIONAL SETUP Density functional theory (DFT)13 has been applied within the Gaussian and plane waves (GPW) method14 to optimize the structures into minima on the potential-energy surfaces (PES) of portlandite interacting with carbon dioxide, hydrogen carbonate anions and carbonic acid, respectively. For all calculations, the program CP2K15,14 has been used. The generalized gradient approximation (GGA) density functional of Perdew, Burke and Ernzerhof16 with the modifications proposed by Zhang and Yang17 (revPBE) has been applied for the solution of the Kohn−Sham equations. Energy and gradients have been corrected for dispersion effects using the D3 set of parameters of Grimme et al.18 A large cutoff value of 700 Ry (350 Eh) has been applied for the auxiliary basis set of plane waves (PW) to ensure convergence of the electron charge density. The double-ζ Gaussian-type basis set for valence bonds with additional polarization functions optimized for condensed phases developed by VandeVondele and Hutter19 was used for the discretization of the Kohn−Sham orbitals. The dual-space norm-conserving pseudopotentials of Goedecker et al.20 were used to avoid explicit treatment of core electrons. A convergence threshold of 10−8 Eh has been applied for the self-consistent field (SCF) evaluations, while the standard criteria have been applied for geometry optimizations of minima on the PES. This means residual mean square (RMS) values of 0.30 mEh/a0 for gradients and 0.0015 a0 for displacements, respectively, and of a convergence within 0.45 mEh/a0 for maximum gradients and within 0.0030 a0 for maximum displacements. This gave better accuracy than 1 meV (0.036749 mEh) for all optimizations. Transition states have been approximated using the climbing image nudged elastic band method (CI-NEB).21 In this method, a series of images (structures) of the system between the initial state and the final Received: Revised: Accepted: Published: 2168

October 30, 2012 January 10, 2013 January 10, 2013 January 10, 2013 dx.doi.org/10.1021/ie302972k | Ind. Eng. Chem. Res. 2013, 52, 2168−2173

Industrial & Engineering Chemistry Research

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state are constructed and connected using a spring interaction between the images. This creates an elastic band. The optimization of the band gives the minimum energy path between initial state and final state including any transition states in a very reliable way.21 Transition states have been converged within RMS values of 0.50 mEh/a0 for gradients and 10−4 a0 for displacements, respectively. Geometry optimizations of the minima have been performed in three steps. In the first step, the conjugate gradient method with two-point extrapolation was used to achieve convergence within an order of magnitude of the required final convergence. Then the structure was optimized using the Broyden-Fletcher-GoldfarbShanno (BFGS) Hessian update in the quasi-Newton framework to achieve all required convergence criteria. The structure of portlandite obtained by neutron scattering22 has been taken as initial guess for the calculations. An orthogonal unit cell has been constructed with the angles α = β = γ = 90° and side lengths of a = 3.58900 Å, b = 6.21635 Å, and c = 4.9110 Å, respectively, in a way that the structure terminates with hydroxide anions at both ends in c direction (cf. Figure 1). The supercell was constructed with four unit

Figure 2. Orthogonal supercell used for the computations (Ca: gray spheres, O: red spheres, H: white spheres). Periodicity is in x (a) and y (b) directions. The trigonal unit cell is displayed blue. Figure 1. Orthogonal unit cell of portlandite used for the computations (Ca: gray spheres, O: red spheres, H: white spheres, structural data taken from ref 22).

starting with the reactant being 10 Å, 1 Å and −1 Å above the surface. Being 10 Å above the surface the interactions of surface and reactant are below 0.01 kJ/mol and thus negligible as our desired accuracy for the reaction path calculations is 0.1 kJ/mol. It can be concluded that the placement of the reactant 10 Å above the surface represents the situation before any reaction takes place in a sufficient approximation. At a distance of 1 Å adsorption at the surface should be most probable, but a chemical reaction may also occur. At −1 Å, the reactant is forced into the hydroxide layer, enforcing a chemical reaction if possible. There is more than one possible pathway for those chemical reactions and several reaction paths have been taken into consideration ranging from a placement directly above a hydroxide site to a placement in the center of a thought triangle formed of three hydroxide sites. The best results were obtained if the reactant was placed in vicinity to a hydroxide site, yet not in the center of the triangle. This places the reactant within the collision cross section of the hydroxide ion, but does not place the hydroxide’s hydrogen atom between the hydroxide’s oxide and the reactant. The latter produces the need for a large geometrical rearrangement and can even lead to a repulsion of the reactant. The geometry optimizations are unconstrained except for the constant angles and side lengths of the simulation cell and periodicity. Nonchemical bonds were considered hydrogen bonds if the bond length was below 3.0 Å and the angle between the bond and the donating O−H chemical bond was between 120° and 240°.

cells in a direction, two unit cells in b direction, and six unit cells in c direction, respectively (cf. Figure 2). This gives a surface of 4 × 4 Ca(OH)2 units with OH subunit termination. Having a surface of this size enables the placement of the reactant without spurious interaction with its periodic images. The depth of six layers is sufficient to provide a crystal environment. Optimizations of the unit cell under the constraint that all angles are kept constant showed negligible effects (less than 0.5% deviation between crystallographic data and optimized cell data) in a and b directions and a change of geometry of less than one percent in c direction, which is equal to the deviation between DFT and X-ray data found by Laugesen.23 Thus, an optimization of the supercell has not been conducted. For all calculations presented in this work, two-dimensional periodic boundary conditions have been applied with periodicity in a and b directions. The analytic Poisson solver as implemented in CP2K has been used for the treatment of the periodic charges. The simulation cell had side lengths of a = x = 14.3560 Å, b = y = 12.4327 Å and c = z = 55.0000 Å. This provides enough space for the insertion of reactants (CO2 and H2CO3) and reordering of the lattice planes in the c direction while keeping the wave function completely inside the simulation cell in the nonperiodic c direction. A series of geometry optimizations were conducted for each reactant, 2169

dx.doi.org/10.1021/ie302972k | Ind. Eng. Chem. Res. 2013, 52, 2168−2173


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Figure 3. Water-free reaction path of the carbonation of portlandite (Ca: large gray spheres, C: medium gray spheres, O: red spheres, H: white spheres). Hydrogen bonds are displayed blue. Transition states are denoted “TS”. All enthalpies are given in kJ/mol.

Figure 4. Reaction path of the carbonation of portlandite with carbonic acid (Ca: large gray spheres, C: medium gray spheres, O: red spheres, H: white spheres). Hydrogen bonds are displayed blue. Transition states are denoted “TS”. All enthalpies are in kJ/mol.

3. RESULTS AND DISCUSSION 3.1. Reactions with Carbon Dioxide. The structure with free CO2 being about 10 Å above the (001) surface of portlandite, shows no interaction between reactant and crystal surface. Even dispersion forces are solely inside the crystal structure. This structure is the energetic reference for all following products of water-free CO2 as reactant. Reducing the distance to the surface to 1 Å does not enforce a chemical reaction. Instead, the distance is optimized to about 2.35 Å, leading to an adsorbed structure held by two weak hydrogen bonds of together −18.2 kJ/mol (cf. Figure 3, structure A). This is a smaller value than the enthalpies of adsorption recently reported for transition metal hydroxides, which range from −26.2 kJ/mol for Fe(OH)2 to −52.0 kJ/mol for Mn(OH)2.4 Further reduction of the distance between CO2 and the surface to −1 Å presses the reactant into the terminal hydroxide layer. This enforces a chemical reaction of CO2 and OH− to HCO3−. The enthalpy of reaction with respect to free CO2 is −44.7 kJ/mol and the structure can be accessed via a transition state of 114.9 kJ/mol. The hydrogen carbonate anion is stabilized by three weak hydrogen bonds donated by neighboring hydroxide ions (cf. Figure 3, structure B). Finally, the carbonate structure is formed by a single proton transfer from HCO3− to OH−. Compared to free CO2, the carbonate is unstable by 44.7 kJ/mol and can be accessed via a

transition state of 85.5 kJ/mol. The carbonate anion is stabilized by two hydrogen bonds, one from a hydroxide anion and one from the water molecule formed during the reaction. The final structure shows a strong distortion of the entire surface layer, including the calcium ions (cf. Figure 3, structure C). The calcium ions in direct vicinity to carbonate are pushed up to 60 pm into the solid, while the hydroxide ions in the layer underneath the calcium layer are pushed up to 30 pm into the slab if they are neighboring the strongly distorted calcium ions mentioned before. The displacement in x (a) and y (b) directions is below 5 pm. From an energetic point of view, it can be guessed that the probability for this final reaction is very low at room temperature and standard pressure, which fits to experimental results that almost no carbonation occurs in the absence of water.2,3 All stable structures and energies are shown in Figure 3. The empirical dispersion corrections to the energies allow characterization of contributions to the binding energy. All structures are held together by chemical bonding and hydrogen bonding enthalpies, while dispersion has a negative effect on the stability of the structures. 3.2. Reactions with Carbonic Acid and Complexes of Carbon Dioxide and Carbonic Acid with Water. H2CO3 is not found in nature as an isolated species. However, using H2CO3 as reactant in the calculations is favorable, as it may dissociate into H+ and HCO3− as well as into 2 H+ and CO32−. 2170



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Figure 5. Reaction path of the carbonation of portlandite with four water molecules added (Ca: large gray spheres, C: medium gray spheres, O: red spheres, H: white spheres). Hydrogen bonds are displayed blue. Transition states are denoted “TS”. In structure E, the proton in the dislocation potential is displayed green and marked with an arrow. All enthalpies are in kJ/mol.

Furthermore, the transition states are significantly lowered compared to the reactions with CO2 (section 3.1 of this work). Interestingly, the distortion of the atoms in the surface layer is identical within 3 pm to that mentioned in section 3.1. This indicates that the carbonate structure is stabilized solely by additional hydrogen bonds. If a complex of one carbon dioxide molecule and one water molecule is used instead of carbonic acid, the structures where HCO3− and CO32− are formed are indistinguishable from those observed for reactions of portlandite with carbonic acid. Only the adsorbed species is different. Its enthalpy of adsorption is −8.4 kJ/mol, which is slightly more than half of the value found for carbonic acid. Although already a second water molecule added to the reacting water molecule significantly lowers the reaction barrier for the formation of H2CO310,11 we have chosen a complex of CO2 with four water molecules and a complex of H2CO3 with three water molecules, respectively, for our simulations. This is the maximum amount of water molecules participating in the formation reaction of H2CO3 known from recent quantum chemical studies, e.g., one water molecule reacts and up to three act catalytically.10,11 The free reactant acting as reference has been the complex of CO2 with four water molecules (cf, Figure 5, structure A). It is 37.9 kJ/mol more stable than the free complex of H2CO3 with three water molecules (cf. Figure 5, structure B) which is found as reaction product for carbonic acid formation. As the most stable complex should be used as reference, the [CO2(H2O)4] complex placed 10 Å above the surface was chosen as reference structure. The reduction of the distance between the reactant and the surface to 1 Å allowed for two principle structures to be formed. The first structure is arranged in a way that CO2 is adsorbed on the surface and the water molecules are above CO2 (cf. Figure 5, structure C1), while in the second structure water is adsorbed on the surface and CO2 is adsorbed on the water tetramer (cf. Figure 5, structure C2). The first structure

Of course, no stable dissociation occurs in the absence of water, but an indirect dissociation can be observed in the way that H+ directly reacts with OH− to water. To take the fact into account that H2CO3 is not observed as an isolated species, the reference for the calculations of the heats of reaction is a complex of CO2 and water (being 10 Å above the surface), which should be the stable structure while no adsorption and no reaction takes place. A calculation of H2CO3 being placed 10 Å above the surface showed that carbonic acid is 79.9 kJ/mol less stable than the complex of CO2 and H2O. The reduction of the distance of H2CO3 to 1 Å above the surface leads to strong adsorption. A Zundel-like species is formed with one hydrogen atom of H2CO3 having a bond length of 132 pm to the respective oxygen atom of H2CO3 and 114 pm to the oxygen atom of OH−, respectively. The complex is stabilized by five hydrogen bonds, one intramolecular hydrogen bond of the HCO3−H−OH complex and four from neighboring hydroxide groups (cf. Figure 4, structure A). The enthalpy of the adsorption reaction is −15.4 kJ/mol. Enforcement of a chemical reaction by pressing the reactant 1 Å into the hydroxide layer gives hydrogen carbonate. The resulting products are stabilized by three hydrogen bonds from neighboring hydroxide anions and one hydrogen bond from the water molecule formed in the reaction (cf. figure 4, structure B). The enthalpy of reaction with respect to a free cluster of CO2 and H2O is −49.6 kJ/mol and a transition state of 47.5 kJ/ mol has to be crossed. The carbonate structure is formed by a final proton transfer from HCO3− to OH−. The transition state is at 29.3 kJ/mol compared to the free CO2-water complex. The carbonate anion is stabilized by one hydrogen bond from each water molecule, respectively, and one hydrogen bond from a neighboring hydroxide anion. One water molecule is hydrogen bonded by two neighboring hydroxide anions. Although this product has an enthalpy of reaction of −0.7 kJ/mol with respect to the free CO2−water complex, it is about 45 kJ/mol more stable than the carbonated structure formed in the water-free reaction. 2171



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findings in section 3.1. In the case of one water molecule added to CO2 dispersion energies contribute 77% to the adsorption enthalpy, 44% to the reaction enthalpy released from the formation of hydrogen carbonate, and 73% to the reaction enthalpy of the formation of carbonate. In the case of four water molecules added to CO2 dispersion energies contribute between 60% (water on surface) and 100% (CO2 on surface) to the adsorption enthalpy, 38% to the reaction enthalpy of hydrogen carbonate formation, and 41% to the reaction enthalpy of carbonate formation.

gives an adsorption enthalpy of −10.0 kJ/mol and the second structure gives −44.5 kJ/mol, respectively. This makes the second structure the by far more probable arrangement of adsorbed molecules. In the first case, the structure is stabilized by two weak hydrogen bonds between the surface and CO2, while in the second case four hydrogen bonds are formed between the water molecules and the surface. The reaction of CO2 with portlandite can be enforced by pressing it 10 pm into the surface, as previously shown. The water molecules, however, have to stay adsorbed on the surface. Otherwise, the geometry optimizations need far too many steps to converge. Starting from the structure where water is adsorbed on the surface (Figure 5, structure C2) hydrogen carbonate is formed (cf. Figure 5, structure D). The transition state is at a relative enthalpy of 91.5 kJ/mol. The major part of this energy barrier is due to the diffusion of CO2 through the adsorbed water molecules. The reaction enthalpy of the formation of HCO3− is −72.5 kJ/mol. If a cluster of H2CO3 with three water molecules is used as reactant, then HCO3− is formed in a barrierless reaction. An isolated adsorbed structure of H2CO3 is not found in presence of three water molecules. In this case, the reaction barrier would only be that of carbonic acid formation. Both reaction paths are shown in Figure 5. The resulting structure is stabilized by a total of eight hydrogen bonds, which are four additional hydrogen bonds compared to the free reactant. If compared to structure C2 (cf. figure 5), then the difference is that the hydrogen bonds between reactant and surface layer are much stronger than in the adsorbed structure. If a proton transfer energy barrier of 6.3 kJ/mol (−66.2 kJ/ mol relative to the reference structure) is overcome, then carbonate is formed (cf. Figure 5, structure E), which has an enthalpy of formation of −66.5 kJ/mol. If the error of the method is taken into consideration, then the transition state can be considered inexistent. It should also be noted that the carbonate ion forms a very strong hydrogen bond of 138 pm length to the water molecule formed by the reaction of HCO3− and OH−. This water molecule has a bond length of the donating OH group elongated to 111 pm. At the same time, a strong hydrogen bond of 166 pm length was donated by HCO3− prior to the proton transfer (cf. Figure 5, structure D) with the OH bond of HCO3− being elongated to 103 pm. Thus, a proton dislocation potential-energy path of the form CO32−···H+···OH− can be assumed with a very mobile proton (displayed green in Figure 5, structure E) moving between carbonate, where it forms HCO3− and hydroxide where it forms H2O. This would allow for a fast formation of carbonate from hydrogen carbonate and back transfer to hydrogen carbonate. The minimum structure of this potential is the hydrogen carbonate structure (cf. Figure 5, structure D). Additional water molecules may reshape the proton dislocation potential-energy path in favor of carbonate formation. The dislocation of the surface layer is much lower than in the cases with less water molecules. The maximum dislocation of calcium ions is 30 pm into the slab and of hydroxide ions below the calcium layer are pushed no more than 15 pm into the solid. This effect seems to be produced by the hydrogen bond network that stabilizes the entire reactive complex. The product is stabilized by a total of ten hydrogen bonds, one of which is part of the dislocation minimum and thus very strong. These are six additional hydrogen bonds if compared to the free reactant. It should be noted that in this series of reactions dispersive interactions stabilize the product, which is in contrast to the

4. CONCLUSIONS We have studied the carbonation of portlandite without and with water using density functional theory. The reaction paths from free carbon dioxide to carbonate have been revealed for both, the reaction without water and with one water molecule. The total reaction according to our simulation is as follows: Ca(OH)2 + CO2 → Ca(HCO3)(OH) → CaCO3 + H 2O

If no water is present, then the highest reaction barrier, being the rate-limiting step, is 114.9 kJ/mol and leads to hydrogen carbonate. The total reaction to carbonate is endothermic and needs 44.7 kJ/mol of energy. If water is present, then the ratelimiting transition state is lowered to 47.5 kJ/mol. In this case, hydrogen carbonate is formed as an intermediate reaction product, too. The total carbonation reaction is slightly exothermic, giving a reaction enthalpy of −0.7 kJ/mol. This is about the same amount of energy as the reaction enthalpy of the formation of hydrogen carbonate from carbon dioxide in portlandite. Thus, already a single water molecule per carbon dioxide molecule reduces the first transition state by 67.4 kJ/ mol and the reaction enthalpy from carbon dioxide to carbonate by 45.4 kJ/mol. Furthermore, the second transition state is reduced from 85.5 to 29.3 kJ/mol. Addition of four water molecules per carbon dioxide molecule makes the reaction barrierless if carbonic acid is formed before a reaction takes place or lowers the transition state by 23.4 to 91.5 kJ/mol if CO2 has to diffuse through adsorbed water molecules. The second transition state is reduced by 151.7 kJ/mol to −66.2 kJ/ mol with respect to the water-free reaction if four water molecules are added. This is effectively a removal of the reaction barrier. Addition of four water molecules to the reactant has a minor effect on the formation of hydrogen carbonate, which is 27.8 kJ/mol more exothermic than without water, but a significant effect on the formation of carbonate, which is 111.2 kJ/mol more exothermic than without water. As there is no real reaction barrier between both structures, a carbonate structure seems to be within a proton dislocation potential-energy path, but it is not the minimum of this potential. At the same time, adsorption of the reactant and the intermediate formation of hydrogen carbonate are almost unchanged by addition of one water molecule. Altogether, the addition of water turns the carbonation reaction of portlandite out to be much more favorable, which is in agreement with experimental results2,3 where no carbonation occurred without water. The driving force for this effect seems to be a better arrangement of hydrogen bonds, which stabilizes the product (carbonate) in the surface layer of portlandite. Additionally, these structural arrangements reduce the effect that the sum of all dispersion forces after reaction is lower than that of the free species. This further stabilizes the products and transition states. 2172



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AUTHOR INFORMATION

Corresponding Author

*Tel: +49 (0)271-740-4702 Fax: +49 (0)271-740-2938 E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the Regionales Rechenzentrum der Universität zu Köln (RRZK) for computing time on the HPC cluster CHEOPS and the Zentrum für Informations- und Medientechnologie der Universität Siegen (ZIMT) for computing time on the HPC cluster HorUS. Lars Packschies, Stefan Borowski (both RRZK) and Gerd Pokorra (ZIMT) are appreciated for their help with installation and running of CP2K on the HPC clusters.

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DFT Study on the Effect of Water on the Carbonation of Portlandite

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