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Feb 3, 2017 - ABSTRACT: Quantitative description of thermodynamic and molecular mechanism of Al incorporation into calcium-silicate hydrates (C-S-H), ...
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Thermodynamics and Molecular Mechanism of Al Incorporation in Calcium Silicate Hydrates Sergey V. Churakov*,†,‡ and Christophe Labbez§ †

Institute of Geological Sciences, University of Bern, CH-3012, Bern, Switzerland Laboratory for Waste Management, Paul Scherrer Institute, CH-5232, Villigen-PSI, Switzerland § Laboratoire Interdisciplinaire Carnot de Bourgogne, UMR 6303 CNRS, Université Bourgogne Franche-Comté, FR-21078 Dijon, France ‡

S Supporting Information *

ABSTRACT: Quantitative description of thermodynamic and molecular mechanism of Al incorporation into calcium-silicate hydrates (C-S-H), the main binder in hydrated cement paste, is essential for development of novel cementitious materials with a lower CO2 footprint. Thermodynamics integration based on ab initio molecular dynamic simulations was applied to estimate the Gibbs free energy of the Al exchange between different silica tetrahedral sites forming the dreierketten-chains at the C-S-H surface and aqueous Al(OH)4− anions. The calculations confirm that the Al substitute for Si into bridging tetrahedral sites with an estimated equilibrium constant KAl/Si ∼ 1. Al for Si substitution is further found to favor the crosslinking between adjacent chains of the same C-S-H layer. This result is in a good agreement with recent conclusions made from 27 Al MAS NMR spectroscopy results. Mesoscale Monte Carlo simulations were performed with the calculated KAl/Si to interpret experimental observations of Al incorporation into C-S-H. The simulation results suggest that the chemical affinity of Al to C-SH is controlled by electrostatic interactions and the Al(OH)4−/Si(OH)3O− aqueous molar ratio.

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INTRODUCTION Concrete is the most common material used worldwide on the basis of its low cost, high availability, ease of casting, and versatility to various environments. It is produced by mixing cement (clinker composed of ∼70% tricalcium silicates), aggregates (gravels, sand), and water. The current concrete production exceeds 1010 tons/year.1 However, this success comes at a big price: the production of cement, the key binding element in concrete, is responsible for 5−8% of global human CO2 emissions. Cement is produced from mixtures of limestones and clays which are heated at high temperatures (∼1500 °C) to chemically react into clinker. About 40% of this CO2 comes from fuel to heat the kilns but, as a highly optimized process, is very unlikely to be reduced any further, and ∼60% results from the calcination of limestones (CaCO3) to produce lime (Ca(OH)2) and its subsequent clinkering reaction with clay.2 Various routes for CO2 footprint reduction due to cement production have been envisaged.3−6 Up to date, the most employed and pragmatic solution is the partial replacement of clinker by natural and artificial pozzolanic materials (e.g., metakaolin, fly ash, silica fume, etc.) which are referred to as supplementary cementitious materials (SCM). The obtained low-CO2 cementitious materials have inevitably different chemistry. As a result, solids forming during hydration chemically differ from ordinary Portland cements and therefore © 2017 American Chemical Society

perform and behave differently in concrete. However, despite recent efforts, the knowledge about the long-term stability and composition of the hydrates formed from the hydration of these new low-CO2 cementitious materials remains fragmentary. This lack of knowledge is a barrier to further development of this approach aimed at reducing CO2 emission during cement manufacturing. In this letter, we focus our attention on the stability and composition of calcium silicate hydrate, C-S-H, the single most important binding phase in most hydrated cements. C-S-H has a foillike structure with very small coherent diffraction domains (∼5 nm).7−9 It is generally accepted that the structure of a single C-S-H foil is similar to that of tobermorite, a naturally occurring mineral.10,11 The basic structural unit of tobermorite consists of a calcium oxide layer flanked on both sides by a wollastonite-like dreierketten chain, a repeating motif alternating two pairing tetrahedra (Sip), bound to the calcium oxide layer, and one bridging tetrahedra (Sib), linking the pairing tetrahedra; see Figure 1. The composition of C-S-H varies with the activity of its constitutive species in solution, i.e., silicate, calcium, and hydronium ions. It is conventionally described by the nonstoichiometric calcium to Received: December 21, 2016 Revised: February 2, 2017 Published: February 3, 2017 4412

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signal (in addition to Al in Q2p and Q3p sites). It has been supposed to be the result of Al in pairing position (Q2p) or in Q2b position charge balance by Ca2+ ions.25 Although the chemical shift of the third signal Al(IV) and its quadrupolar constant seems to favor the first hypothesis (e.g., incorporation of Al in pairing position (Q2p), it contradicts recent theoretical calculations ranging from classical molecular to first-principles simulations.26−28 However, in none of these works has a proper evaluation of the Gibbs free energy of the Al−Si substitution reaction been performed. At best, groundstate energy differences between relative positions were estimated. The lack of systematic evaluation of reaction Gibbs free energy hinders the development of predictive thermodynamic models for the incorporation of aluminum in C-S-H and, thus, the long-term stability of C-(A)-S-H. In this work we apply full scale ab initio molecular dynamic simulations to calculate the Gibbs free energy of the Al−Si substitution in C-S-H:

Figure 1. Left: A snapshot from the ab initio molecular dynamics simulations of Helmholtz free energy for the Al−Si exchange reaction (eq 1). The surface tetrahedra involved in the exchange reaction are shown in green. Oxygen atoms are red. Hydrogen atoms are indicated by empty circles. Calcium atoms are gray. Silica atoms are light brown. Right: Schematic view on the Si tetrahedra chain on the C-S-H surface. Bridging and pairing tetrahedra are shown in blue and orange, respectively. Structurally different types of tetrahedra studied in this work are indicated by green tetrahedra. Acronym used in the text is indicated next to the site. Surface OH groups are shown as white circles. Orientation of OH sites and hydrogen bonding is explicitly indicated for neighboring Q1P1 and Q1P2 sites, for the sake of clarity.

0 ≡Si CSH + Al(OH)−4,aq ↔ ≡Al −C − S − H + Si(OH)04,aq

(1)

Combining ab initio molecular dynamics simulations and thermodynamic integration technique, we were able to evaluate for the first time the free energy of the reaction in eq 1 for different surface sites (Q1, Q2b, Q2p, Q3b) (Figure 1). With these free energies of reaction at hand, the various scenarios proposed in the literature to interpret the 29Si and 27Al MAS NMR studies are discussed. The Gibbs free energy is further used in a mesoscale grand canonical Monte Carlo (GCMC) simulation to discuss and interpret the observed substitution of Si by Al under various conditions. In particular, we tackle the following questions: (i) Can the Al/Si substitution in the Q3b position be compatible with the cross-linking of two adjacent silicate chains of the same C-A-S-H layer? (ii) Is the Al/Si substitution in the Q2p thermodynamically possible? If it is not, how then can the third Al(IV) signal be interpreted? (iii) What are the main factors limiting the incorporation of Al in C-S-H?

silicon ratio (Ca/Si) which can vary between 0.7 and 1.7. The Ca/Si ratio increases with the increase in Ca(OH)2 bulk concentration and is controlled by two mechanisms: (1) depolymerization of the Si chains through the removal of bridging tetrahedra (i.e., formation of point defects); (2) adsorption of Ca2+ ions. In the second mechanism, Ca2+ ions compensate for the deprotonated silanol groups whose proportion notably increases at high pH (≡Si−OH → ≡Si− O− + H+) . The correlation between activities of silicate, calcium, and hydronium ions and the Ca/Si ratio in the C-S-H phase is well-demonstrated by experimental data10,12 and explained by classical geochemical modeling13,14 as far as no other ions than Ca2+, OH−, and silicate participate in the precipitation of C-S-H. In cements blended with silica-rich SCM, typically slag, fly ash, or metakaolin, the composition and structure of C-S-H is much less well-defined; obviously the thermodynamic modeling of phase equilibria is still in its infancy. Typically, such SCM leads to a lower Ca/Si ratio down to ∼0.9 and to incorporation of aluminum. The Al/Si ratio in such systems was found to increase up to about 0.25.15−18 29Si and 27Al MAS NMR studies revealed that Al incorporation predominantly proceeds by chemical substitution of the silicate group in the tetrahedrally coordinated environment by the Al(IV)O4− group. At low Ca/ Si ratio (low Ca(OH)2 concentration), Al substitutes for the bridging Si in both Q2p (bound to two other Si) and Q3p (bound to three other Si) structural positions.19−23 In 11 Å tobermorite, a crystalline prototype for C-S-H, the Q3 position corresponds to the cross-linking of two chains of independent tobermorite sheets. In the case of Al-substituted C-S-H (C-A-S-H), the occurrence of such cross-linking is incompatible with the large basal spacing between the layers observed by X-ray diffraction.24,25 Instead, it has been hypothesized that the cross-linking occurs between two adjacent chains of the same C-A-S-H layer. As the Ca/Si ratio increases, the Al in Q3 positions disappears and the fraction of Al in Q2b decreases in favor of a third Al(IV) NMR

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COMPUTATIONAL METHOD System Setup. The simulation setup used in this work (Figure 1) is similar to one applied recently in the simulation of the acid−base properties of the C-S-H surface.29 At the early stages of cement hydration, a C-S-H particle comprises only a few tobermorite-like structural layers [Ca4Si6O14(OH)2]2− × 2H2O. In our simulation setup, water was confined by a single 2D periodic C-S-H layer structurally identical to 11 Å tobermorite. At the one surface side of the platelet, the tetrahedral chain was considered to be fully polymerized, while at the other surface side, the silica tetrahedra formed only dimers. These two structurally different surfaces represent limiting cases for the structural order in C-S-H. Fully polymerized chain is built by two pairing and one bridging Si tetrahedra. The C-S-H surface was maintained electroneutral by protonation of the surface sites. The protons were attached to bridging tetrahedra to apical sites and Si-(OH)-Ca linkages. The chain is considered as “fully depolymerized” when it consists of only Si-tetrahedra pairs with protonated terminating oxygen sites. The system chemical composition was 4 × [Ca4Si5O12(OH)4] × 131H2O × [Al(OH)4]. The size of the simulation supercell was 11.26 × 14.56 × 31.02 Å. Use of one and the same simulation setup is essential for consistent calculations and comparison of Si−Al isomorphic substitutions in C-S-H. Aqueous silica and alumina complexes were modeled 4413

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The Journal of Physical Chemistry C as tetrahedral Si(OH)04 and Al(OH)−4 species located in the middle of the simulation cell, respectively. These complexes are also the dominant aqueous species of silica and alumina at neutral pH. Ab Initio Calculations. All ab initio calculations were performed based on the density functional theory using the Gaussian and Plane Waves method (GPW) as implemented in the CP2K simulation package.30,31 The Kohn−Sham orbitals were expanded using a linear combination of atom-centered Gaussian type orbital functions using “short range” double-ζ valence polarized basis set.32 The electron charge density was expanded using an auxiliary basis set of plane waves up to a 320 Ry cutoff. The dual space norm-conserving pseudopotentials33 were applied to avoid explicit consideration of core electrons and BLYP functional34 applied to account for exchange and correlation effects. Dispersion interaction was taken into account by using DFT+D2 method.35 Born−Oppenheimer ab initio MD simulations were performed with a time step of 0.5 fs at 330 K using the Nose−Hoover thermostat.36,37 A slightly elevated temperature was used to prevent the glassy behavior of BLYP water at ambient conditions.38 A detailed description of the system setup and testing is described elsewhere.29 Thermodynamic Integration. The Helmholtz free energy of the reaction (eq 1) was calculated based on thermodynamic integration employing ab initio molecular dynamics simulations of a system described by an λ-dependent Hamiltonian at the DFT level of theory:39 ΔA =

∫0

protonation state of ≡Si(OH)02 can be titrated according to the two subsequent equilibrium de/protonation reactions:

(6)

(7)

The equilibrium constant is calculated from the reaction free energy obtained by the ab initio MD as described above. For the sake of simplicity, the C-S-H surface is assumed to be covered by infinite silicate chains, i.e., their depolymerization reaction is not considered. Within this approximation, the Al incorporation in C-S-H is thus only possible through the direct Al−Si substitution reaction (eq 7). This scenario is the most realistic for C-S-H with low Ca/Si ratios (close to 0.8) where the density of vacancies in bridging sites is small and the direct Al incorporation into those vacant bridging sites can be neglected. Obviously, at higher Ca/Si ratios this assumption becomes less accurate and should be used with care, especially when comparison with the experimental data is made. The Al−Si exchange reaction (eq 7) was modeled using the semigrand ensemble.42 The Boltzmann factors for the forward and backward reactions are calculated as follows:

(2)

exp( − β ΔU ) =

N> Si exp( − β ΔU conf ) N> Al + 1

exp[ − ln(10)(pK Al/Si − pSiaq + pAl aq)]

(3)

where H0 and H1 are the Hamiltonians describing the system of adduct and product in eq 1, respectively. The integral in eq 2 was approximated by the five-point interpolation formula: ΔA ≈ ΔA̅ 7 32 = [ΔE0 + ΔE1] + [ΔE0.25 + ΔE0.75] 90 90 12 + ΔE0.5 90

≡Si(OH)O− + H 2O ↔ ≡SiO22 − + H3O+aq

≡Si(OH)O− + Al(OH)−4,aq ↔ ≡Al(OH)−2 + Si(OH)3 O−aq

where ⟨ΔE⟩λ is the potential energy of reaction (eq 1) sampled in the canonical ensemble defined by an λ-dependent Hamiltonian: Hλ = (1 − λ)H0 + λH1

(5)

The corresponding equilibrium constants are set to pKa,1 = 9.8 (first deprotonation reaction) and pKa,2 = 11.7 (second deprotonation reaction, see below). The bridging silicates can be further substituted by aluminates (and vice versa) through the following equilibrium reaction:

1

dλ⟨ΔE⟩λ

≡Si(OH)02 + H 2O ↔ ≡Si(OH)O− + H3O+aq

exp( − β ΔU ) =

(8)

N> Al exp( − β ΔU conf ) N> Si + 1

exp[+ ln 10(pK Al/Si − pSiaq + pAl aq)]

(9)

where N>Al and N>Si are the instantaneous numbers of ≡Si(OH)O− and ≡Al(OH)−2 sites; pKAl/Si is the negative decimal logarithm of the free energy of the reaction in eq 7. The pSiaq and pAlaq are negative decimal logarithm of activity of Si(OH)3O−aq and Al(OH)−4,aq species in aqueous phase. For the sake of sampling efficiency, the aqueous aluminate and silicate species were not explicitly treated, but instead the activities of Al and Si species in solution (e.g., pSiaq and pAlaq) were imposed in the simulation. Simulation Details. The bridging tetrahedra were distributed on a regular rectangular mesh with 5.65 × 7.38 Å2 cell size according to the structure of tobermorite.43 The surface site density is 2.41 sites nm−2, whereas the density of the surface ≡XOH groups (≡X designates either Al or Si) is 4.82 sites nm −2 , identical to our previous simulations.29,44 Equilibrium distribution of ions and the protonation state of the C-S-H surface were obtained by Monte Carlo simulations in the grand canonical ensemble (i.e., constant chemical potential, volume, and temperature), using the standard Metropolis algorithm. In addition to the conventional GCMC insertion/deletion moves, the surface sites were allowed to titrate according to the eqs 7 and 8 according to the method previously described.40 In the mesoscale model used here, the

(4)

Five independent trajectories are necessary to calculate the free energy. The trajectories are described by a Hamiltonian for adducts, products, and their linear combination, respectively. The length of the sampling trajectory varied from 10 to 15 ps depending on the convergence of the target quantities, followed by at least 10 ps of equilibration. The initial configuration for the ab initio runs was taken from our previous ab initio simulation of the system. Grand Canonical Monte Carlo Simulation. The general concept of a coarse-grained model for the C-S-H surface and the principle of titration for the GCMC method are described in detail in our previous publications.29,40,41 Technical details related to this work are provided in Supporting Information. The C-S-H surface is modeled as an infinite planar wall covered by explicit silicate bridging sites regularly distributed on a rectangular lattice. Each bridging silicate, initially in the 4414

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Al−O and O−H distances in Al(OH)−4 is reported in Table 2. Oxygen atoms of Al(OH)−4 accept on average 1.94 hydrogen bonds from water molecules. Hydrogen atoms of OH groups in Al(OH)−4 complex donate on average 0.92 hydrogen bonds. Several attempts have been made in the past to estimate the acidity of OH groups of complex ions based on bond distances.48 In general, longer OH bonds and short metal− OH bonds are associated with higher acidity of the OH groups. The OH bond geometry and mean values of hydrogen bonds clearly indicate higher acidity of aqueous silicic acid in comparison to alumina aqua complex. ≡Al(OH)−4 complex is a weaker acceptor of hydrogen bonds from water molecules, in consistency with the overall negative charge of the complex and stronger structuring of the surrounding water dipoles. Geometry of Si and Al Tetrahedra on the C-A-S-H Surface. Averaged geometry (Si−OH, Al−OH, and O−H bond lengths) of structurally different tetrahedra at the C-S-H surface is summarized in Table 2. On average, tetrahedral sites on the C-S-H surface expand by 7% when Al substitutes for Si. The statistics of hydrogen bonds accepted by oxygen atoms of the tetrahedral surface sites from water molecules and the hydrogen bonds donated by the protonated surface groups are reported in Supporting Information (Table S1). The data obtained for the tobermorite surface occupied by Si is in agreement with the results obtained in our previous study.29 Substitution of Al for Si in the tetrahedral sites dramatically changes acid−base properties of the surface. The net surface charge changes from neutral to negative, leading to an increase in the number of hydrogen bonds accepted by oxygen sites of tetrahedra occupied by Al by a factor 1.5−2.0. These changes in the surface charge and the surface hydration mechanism would have consequences for the adsorption of the cations at the Alsubstituted tetrahedra. It can be expected that incorporation of Al in the tetrahedral chain will facilitate uptake of cations by CA-S-H at low pH conditions. The grand canonical Monte Carlo simulations described in the next section rely on pKa constants for the ≡SiOH group on C-S-H surface derived from ab initio simulations.29 No such data are available for ≡AlOH groups at the C-A-S-H surface. Recently, the pKa values of ≡AlOH groups in tetrahedral positions at edge sites of clay minerals were evaluated. These simulations predict that the pKa of Al−O bonds at the clay surface is larger than 15.00.49 Using these results as a proxy, we argue that deprotonation of ≡AlOH surface groups and Al(OH)−4 in solution can be neglected at pH < 13. Thermodynamics of Al−Si Exchange. The free energy and the corresponding pK values of the Al−Si exchange reactions between aqueous Al(OH)4− ions and structurally different tetrahedral sites at the surface of C-S-H as well as the simulation conditions and the standard state references are reported in Table 2. The calculations indicate that the substitution of Al for Si is favorable at bridging Q2 and Q3 sites. The values of the Helmholtz free energy for the exchange reactions at bridging sites range between −2.1 kcal/mol for Q3B2 and 4.0 kcal/mol for Q2B2. The obtained variation of the substitution energies is within the range of the uncertainties of the simulations estimated to be ±6 kcal/mol. The main contribution to the uncertainty is related to the sampling statistics controlled by sluggish dynamics of water. Despite the uncertainty of the calculated energies, it is worth mentioning that the substitution energies obtained for cross-linking Q3B1 and Q3B2 sites are systematically lower than those predicted for Q2B1 and Q2B2 sites. This indicates that the presence of Al favors

ionization of the bridging sites corresponds to a change of their charge state, namely going from “0” to “−1” and “−2” for deprotonated ≡Si(OH)O− and doubly deprotonated ≡SiO2− 2 groups (i.e., eqs 5 and 6). Because the second de/protonation reaction in the current model takes place at the same site, the electrostatic repulsive energy between the two neighboring deprotonated oxygen atoms has to be taken into account implicitly. This repulsion energy can be in principle calculated from the structural distance between the oxygen atoms. It remains, however, uncertain whether it is appropriate to use the formal coulomb charge and the bulk dielectric constant for such a short interaction distance (rij < 3 Å). Therefore, in this study the repulsion energy was set to match previous experimental and theoretical data of surface charge titration of C-S-H.44,45 The electrostatic interaction energy of 16.6 kJ mol−1, which corresponds to 1.9 pKa unit difference between the second and the first deprotonation constant, gives a good description of the surface charge formation of C-S-H, see Figure S1 (Supporting Information).

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RESULTS AND DISCUSSION Structure of Aqueous Si(OH)40 and Al(OH)−4 Complexes. The O···Hw and H···Ow radial distribution functions (RDFs) for aqueous Si(OH)04 and Al(OH)−4 complexes in the middle of the simulated macropore are shown in Figure 2.

Figure 2. Oxygen−hydrogen radial distribution functions of aqueous complexes Al(OH)4− and Si(OH)40. Hw and Ow are hydrogen and oxygen atoms of water molecules, respectively.

Calculated average Si−O and O−H distances (Table 1) are consistent with the data reported for simulations of aqueous silicic acid.46,47 Each oxygen atom of aqueous Si(OH)04 accepts on average 1.24 hydrogen bonds from water molecules. The hydrogen atom of a OH− group within Si(OH)04 complex donates on average 1.00 hydrogen bonds. The average length of Table 1. Geometry of {Si}×Si and {Al}Si ′ Tetrahedra on the C(A)-S-H Surface and in Solutiona {Si}×Si] R̅ ij ± 2σ Q0aq(Me−OH) Q0aq(O−H) Q2B(Me−OapH) Q2B(Me−ObH) Q2B(Oap−H) Q2B(Ob−H) Q2P(Me−O) Q1P1(Me−OH) Q1P2(Me−OH) Q1P1(O−H) Q1P2(O−H) a

1.653 1.010 1.633 1.658 1.007 1.007 1.642 1.685 1.678 1.004 1.007

± ± ± ± ± ± ± ± ± ± ±

0.0013 0.0042 0.0078 0.0026 0.0044 0.0081 0.0306 0.0020 0.0031 0.0078 0.0030

{Al}Si′ R̅ ij ± 2σ 1.783 0.989 1.767 1.777 0.994 0.980 1.764 1.810 1.799 0.989 0.999

± ± ± ± ± ± ± ± ± ± ±

0.0020 0.0032 0.0030 0.0054 0.0035 0.0085 0.0305 0.0059 0.0025 0.0034 0.0062

The standard deviations are calculated using block averages. 4415

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Table 2. Calculated Helmholtz Free Energy of Al−Si Exchange Reactions (eq 1) for Different Tetrahedral Sites at the C-S-H Surface Indicated in Figure 1 ΔA [kcal/mol] pKAl/Si

Q2B1

Q2P

Q1P1

Q1P2

Q3B2

Q3B1

Q2B2

1.5 ± 6.1 1.1 ± 4.5

25.7 ± 6.1 18.9 ± 4.5

24.4 ± 6.5 17.2 ± 4.8

26.5 ± 6.2 19.4 ± 4.5

−2.1 ± 6.3 −1.5 ± 4.6

0.3 ± 6.5 0.2 ± 4.8

4.0 ± 6.0 2.9 ± 4.4

Figure 3. Top (setup I) left: Experimental Al/Si ratio in solid C-(A)-S-H versus [Al(OH)4−] [Si(OH)3O−] ratio in solution, obtained at pH > 11 and various Ca/Si ratios (points).50 The black line represents a simplified analytical expression for Al/Si ratio (eq 10). The analytical results are compared with the results of GCMC simulations (colored lines) in 1 mM CaCl2 solution at different pH controlled by NaOH concentration (see text for details). Top (setup I) right: Speciation of C-A-S-H surface as a function of pH obtained by GCMC simulation for [Al(OH)−4 ]aq/ [Si(OH)3O−]aq equal to 0.01, 0.1, and 1 are shown by solid, dashed, and dotted lines, respectively. The results to Al-free system are shown by symbols. Note that at [Al(OH)−4 ]aq/[Si(OH)3O−]aq equal to 0 and 0.01, respectively, the lines representing concentrations of [≡Al(OH)−2 ] and [≡Si(OH)O−] species overlap. Middle left and right (setup II): Same as above but assuming that Al substitution in the neighboring bridging tetrahedral sites is not allowed. Bottom (setup III): Same as above, but Al substitution in the neighboring bridging tetrahedral sites is penalized by 5 kcal/mol.

Recently, Pegado et al.28 compared the internal energy of tobermorite-like structures with Al substitutions in different bridging and pairing tetrahedral sites using DFT simulations in vacuum. The internal energies of the {Al}′2QB1 ⇔ {Al}′1QP and {Al}′2QB1 ⇔ {Al}′2QP exchange reactions were calculated to be 23.0 and 17.9 kcal/mol, respectively. According to our calculations of the free energy differences for these exchange reactions in the presence of water, they were found to be 22.9 and 24.1 kcal/mol, respectively. Notably, both static energy calculation for the surface in vacuum and the free energy

formation of cross-linking Q3B sites between parallel Si-chains as suggested from NMR data. The substitution energy obtained for the Al−Si exchange in the pairing site, Q2P and Q1P1, is consistently higher (24.0−26.0 kcal/mol, respectively). Therefore, the substitution of Al for Si in pairing sites is strongly unfavorable. Indeed, according to this calculated free energy and the corresponding reaction pK = 17 ± 5, an Al/Si substitution reaction would take place in the pairing site when bulk aqueous concentrations of aluminate ion are at least 13 orders of magnitude larger than those in the bridging sites. 4416

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experimental data. The strong overestimation of the experimental data can be explained by the fact that all bridging sites may not be available for the Al−Si substitution. The Figure 3 (middle) demonstrates the predictions of eq 10 assuming that only half of tetrahedral sites Si can be substituted by Al, i.e., the first nearest neighbors of bridging Al are not available for substitution (setup II). Such a model can also be derived from eq 10, setting (p, q) to (6, 5). In this limiting case, the maximum (Al/Si)CASH ratio is equal to 0.2. The experimental data points are found between these two limiting analytical solutions for setups I and II. The effect of the surface speciation on the Al incorporation, neglected in the analytical expression (eq 10), is investigated by mesoscale GCMC simulations. Figure 3 shows the surface speciation of C-S-H varying [Al(OH) 4−]/[Si(OH) 3O −]aq equilibrium concentrations in a 1 mM CaCl2 background electrolyte at different pH. The pH is varied by adding an appropriate amount of NaOH into the simulation cell. GCMC simulations demonstrate that in all three modeling setups considered here, the concentration of surface sites SiO(OH)− initially increases with pH before to peak at pH ∼ 11.5. At higher pH, the site concentration ≡SiO(OH)− decreases in favor of ≡SiO2− 2 surface sites, thus giving the bow-shaped curve for ≡SiO(OH)−. These dependencies are in agreement with experimental data and simulations of surface titration of C-SH.44,45 In the presence of Al, the concentration of ≡SiO(OH)− sites decreases proportionally and the concentration of ≡Al(OH)−2 consistently shows a maxima near pH 11.5. This result is general and suggests that C-S-H has the highest affinity to Al in the pH range 11.0−11.5. In other words, Al is incorporated into the C-S-H structure in the maximal amount and thus results in the largest structural Al/Si ratio in this narrow pH range. Note that the pH value at which the Al incorporation is maximal also depends on the Ca 2+ concentration and, to a smaller extent, on alkali ion concentration. In all simulations setups, the GCMC calculations consistently predict a lower (Al/Si)CASH ratio in comparison to the predictions of the analytical solution (eq 10). Setup I seems to overestimate whereas the setup II seems to underestimate (Al/Si) CASH ratios compared to the experimental data. Setup III is in the best agreement with the experimental trend showing quasi-linear dependence of Al incorporation in C-S-H on a linear-logarithmic scale. Despite a good agreement with the experimental data, setup III neglects one very important structural and chemical parameter of C-S-H, namely the dependence of the tetrahedral chain length on the fluid composition.52 The mean chain length in C-S-H is known to depend strongly on the Ca/Si ratio in solution. The assumption of an infinite chain length is applicable only at low pH and low Ca/Si ratio. One may expect that the depolymerization of the Si-chain will lead to a higher (Al/Si)CASH ratio and can eventually result in even better agreement between the experimental observation and the prediction of the two-KAl/Si model (setup III) for the Al incorporation in C-S-H. Such model extension would require us to consider a de/polymerization reaction for both Si and Al tetrahedra. This goes beyond the scope of this paper and will be addressed in future work. Finally, we evaluated the effect of Al incorporation on the surface charge density and calculated ζ-potential of the C-S-H surface. Results of GCMC simulations with the 2-pKAl/Si model (setup III) are presented in Figure 4. Simulation results for setups I and II are reported in Supporting Information. The

calculation performed with an explicit solvent at room temperature show the same results for the energy of the exchange reaction. A possible explanation could be the canceling of the hydration energy and entropic contributions for the reactants and products with similar molecular topology. Surface Speciation Controls for C-A-S-H. According to the obtained thermodynamics data, Al is incorporated in C-S-H into bridging tetrahedral sites. The Al/Si ratio in C-A-S-H is thus limited by the availability of bridging sites. The relative fraction of these sites from a purely structural point of view is Q2B/Q2P = 0.5. The experimentally observed Al/Si ratios in C-AS-H hardly exceed 0.3 and are partially attributed to secondary phase formation.17,19,50 Large differences in the measured Al/Si ratios are reported depending on the route of synthesis and the equilibrium time. The maximal structurally possible Al/Si ratio (0.5) is not reached in experiments for several reasons. First, it was suggested by the spectroscopic data25 and confirmed by the current simulation results that the presence of Al favors formation of the Q3B tetrahedral cross-linked parallel chains in the same layer. Following Loewenstein’s Al−Al avoidance rule,51 only half of such cross-linked Q3B pairs can be occupied by Al. Second, recent large scale ab initio calculations of lattice energies for Al−Si exchange in C-S-H 28 showed that incorporation of second Al in the first nearest bridging sites (in the same chain or in a parallel chain) is penalized by about 5 kcal/mol. This excess energy is sufficient to hinder their incorporation at typical experimental conditions ([Al]aq/[Si]aq < 1000). Finally, the Al incorporation is limited by the stability of C-A-S-H and the precipitation of secondary phases, e.g., katoite, limiting the range of accessible aluminate concentration in the solution.50 In order to quantify the Al incorporation in C-S-H at equilibrium conditions, we at first formulate a simplified analytical expression relating the (Al/Si)CASH ratio in C-S-H to the [Al(OH)−4 ]/[Si(OH)3O−]aq ratio in solution (eq 7). Taking pKAl/Si ∼ 1, well in agreement with the calculated free energy of the Al/Si exchange (Table 2) and further assuming that all silicate bridging sites are in single deprotonated state ≡SiO− (see SI for more details), it can be shown that (Al/Si)CASH ≈

K Al/Si[Al(OH)−4 ]/[Si(OH)3 O−] p + qK Al/Si[Al(OH)−4 ]/[Si(OH)3 O−] (10)

where (p, q) are two constants equal to (3, 2) when all bridging sites are available for Al−Si substitution. Figure 3 (top) shows the predictions of this simplified model in comparison with experimental data.15,17 Note that the experimental data sets were obtained at different chemical conditions with respect to Ca/Si ratio and slight deviation of pH. Nevertheless, they follow a common trend as a function of Al/Si concentration ratio. Here we consider three models. Setup I: Al can be substituted for Si in any singly deprotonated bridging tetrahedral site. Setup II: formation on the nearest neighbor Al−Al bridging tetrahedral is not permitted. Setup III: the formation of Al−Al neighbors in bridging tetrahedral site is penalized by 5 kcal/mol according to our recent DFT calculations.28 A good agreement between experimental data and analytical model (setup I) (eq 10) was obtained up to [Al(OH)−4 ]/ [Si(OH)3O−]aq ∼ 0.5. At higher [Al(OH)−4 ]/[Si(OH)3O−]aq ratios, the analytical expression predicts too steep an increase of the (Al/Si)CASH curve which levels off at 0.5, well above the 4417

DOI: 10.1021/acs.jpcc.6b12850 J. Phys. Chem. C 2017, 121, 4412−4419

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Article

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b12850. Detailed description of the simulation algorithm, derivation of a simplified analytical expression for Al incorporation in C-A-S-H at low Al concentration, and structural parameters of C-A-S-H and modeling benchmarks (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Tel. ++41(0)56 310 4113. Fax. ++41(0)56 310 2821. E-mail: [email protected]. ORCID

Sergey V. Churakov: 0000-0001-8213-9206 Christophe Labbez: 0000-0001-6652-6329

Figure 4. Surface ionization fraction and ζ-potential at the C-S-H surface for model III (see main text and Figure 3) as a function of pH for different [Al(OH)−4 ]aq/[Si(OH)3O−]aq ratios.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge access to the high performance computing facilities at the Swiss Center of Scientific Computing (Lugano). C.S. acknowledges financial support from the Swiss National Foundation grant number CRSI22_130419/1. C.S. acknowledges partial financial support provided by the National Co-operative for the Disposal of Radioactive Waste (Nagra), Wettingen, Switzerland. C.L. acknowledges partial financial support from the CNRS (NEEDS-MIPOR program) and from the European Consortium NanoCem (http://www.nanocem. org/).

effect of structural incorporation of Al on the surface charge as well as ζ-potential is very moderate. This is because the reaction exchange is coupled to protonation deprotonation and does not change the surface charge. Compared to the Al free system, the charge is increasing at low pH and decreasing at high pH with the crossover point at pH ∼ 11.5, corresponding to maximal concentration of Al(OH)−2 and ≡SiO(OH)− surface species. This is well in agreement with the experimental observations showing that Al incorporation has minor effect on the electrokinetic properties of C-A-S-H.

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SUMMARY Our theoretical calculations provide for the first time the free energies for the Al/Si substitution reactions in C-(A)-S-H at structurally different surface sites in the presence of explicit solvent. In agreement with wet chemical data and Al NMR measurements our calculations predict that the substitutions mainly occur in the Q2b position and can lead to formation of inplane Q3b sites cross-linking parallel chains.23 They further show that the substitution in pairing position is very unfavorable if not impossible, contrary to the hypothesis proposed in recent studies25 to tentatively explain the weak third Qn peak appearing in the Al NMR signal at Ca/Si > 0.8. In other words, our theoretical study seems to give arguments against the tentative scenario put forward to explain the growth of a third Al(IV) peak at the expense of two first peaks corresponding to Al in Q2P and Q3P sites.25 Although further studies are required to clarify this point, a possible explanation for this third peak could be an Al tetrahedron in a bridging position loosely bound to the silicate chain. Mesoscale GCMC simulations of Al adsorption on C-SH based on the ab initio data allowed us to rationalize the dependence of the Al affinity from the bulk equilibrium conditions. The Al affinity is clearly controlled by the protonation state of the Si-tetrahedral sites of the C-S-H surface. In particular, the highest Al affinity was observed at pH ∼ 11.5, corresponding to the maximal concentration of SiO(OH)− surface species. Finally, in agreement with recent estimates of lattice energies,28 our thermodynamic calculations confirm that the formation of Al−Al pairs in the nearest neighbor bridging sites is not favorable.

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