29Si NMR in Cement: A Theoretical Study on ... - ACS Publications

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Si NMR in Cement: A Theoretical Study on Calcium Silicate Hydrates

Pawel Rejmak,†,* Jorge S. Dolado,‡ Malcolm J. Stott,§ and Andrés Ayuela†,∥ †

Donostia International Physics Center (DIPC), p. Manuel de Lardizabal 4, p. Manuel de Lardizabal 4, Donostia-San Sebastián, Spain Tecnalia Research and Innovation, Geldo Edificio 700, 48160 Derio, Spain § Queen's University, Kingston, ON K7L 3N6, Canada ∥ Centro de Física de Materiales CFM-MPC, Centro Mixto CSIC-UPV/EHU, p. Manuel de Lardizabal 5, Donostia-San Sebastián, Spain ‡

S Supporting Information *

ABSTRACT: The NMR spectra of 29Si in cement-based materials are studied through calculations of the isotropic shielding of silicon atoms within the density functional theory. We focus on the main component of cement, the calcium-silicate-hydrate gel, using widely accepted models based on the observed structures of jennite and tobermorite minerals. The results show that the 29Si chemical shifts are dependent not only on the degree of condensation of the (SiO4) units, as commonly assumed, but also on the local arrangement of the charge compensating H and Ca cations. We find that the NMR spectra for models of the calcium-silicate-hydrate gel based on tobermorite are in better agreement with experiment than those for jennite-based models.

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INTRODUCTION Despite the ubiquitous application of cement-based materials, our knowledge of these construction materials, particularly on the atomic scale, is still lacking. The product resulting from the hydration of common Portland cement clinker is a porous matrix consisting of several crystallites embedded in a poorly crystallized phase, the so-called calcium−silicate−hydrate (C− S−H) gel.1 This C−S−H gel is the most important hydration product. It constitutes about 50−70% of the fully hydrated cement paste and is responsible for most of the engineering properties of cement-based materials. The structure of C−S−H gel is complex and not fully understood. Various atomistic models of the gel have been proposed, which have Ca−O layers ribbed with silicate chains.2 The most accepted models are based on the crystal structures of jennite3 and tobermorite 14 Å4 minerals, as seen in Figure 1. The silicate chains in these minerals follow the so-called dreierkette structure, wherein each pair of silica pairing tetrahedra sharing O−O edges with CaO octahedra, is followed by a silica bridging tetrahedron, the latter sharing only O vertices with CaO octahedra. The Ca−O layers in tobermorite have bare Ca cations, whereas in jennite they are monohydroxylated. In addition, the bridging tetrahedra in tobermorite are protonated forming silanol groups. Much information on the atomic characteristics of cementitious materials is provided by nuclear magnetic resonance spectroscopy (NMR) of 29Si (ref 5 for a recent review and references). The assignment of observed NMR peaks is based on the assumption that 29Si chemical shifts decrease with the degree of condensation of (SiO4) units, structures which range from isolated monomers to tetrahedrally coordinated networks. This assignment led to the conclusion © 2012 American Chemical Society

Figure 1. Structures of (a) jennite and (b) tobermorite 14 Å minerals. The pairing Si tetrahedra are denoted as Q2; bridging ones, as Q2b (jennite), or Q2bOH (tobermorite) when having a SiOH group. Note that there are two types of charge compensating Ca cations, given with light blue balls, in the layered (L) and interlayer (I) positions.

that the C−S−H gel contains silicate chains with finite lengths of (3n − 1) tetrahedra, n = 1, 2, ..., and the C−S−H structure may be seen as jennite or tobermorite with a number of bridging tetrahedra removed as shown in Figure 2.6 This finite chain model was also supported by the chromatographic analysis of trimethylsilyl derivatives of C−S−H gel.1 The theoretical justification of this model came recently from calculations within the DFT.7 Atomistic simulations of C−S−H Received: March 7, 2012 Published: April 5, 2012 9755

dx.doi.org/10.1021/jp302218j | J. Phys. Chem. C 2012, 116, 9755−9761

The Journal of Physical Chemistry C

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Supporting Information. We will refer to a particular model as An−Bm, where (i) A is T or J denoting tobermorite- or jennitebased models, (ii) n is the length of silicate chains, namely ∞ for minerals and 5 or 2 for C−S−H gel models, (iii) B denotes the charge compensation scheme, either H for protons or Ca for Ca2+/Ca(OH)+ ions, and (iv) m is the serial number of the given model. We also looked at β-belite and α-quartz, as reference systems, with input structures taken from the experimental data.13,14 In addition to the periodic lattice models, we performed some auxiliary calculations on finite cluster models extracted from the optimized periodic structures of β-belite and α-quartz. The clusters for belite and quartz host 21 and 29 Si atoms, respectively (Figure S2 of the Supporting Information). The VESTA code was used for the processing of structures and figures.15 For the description of various types of silica units, we used a common NMR notation, according to which Qn denotes Si atoms in a (SiO4) tetrahedron coordinated to n other tetrahedra. The Si atoms in the tetrahedra terminating dimers or pentamers will be referred to as the Q1 sites. In doubly coordinated tetrahedra, they will be denoted as Q2 and Q2b for the pairing and bridging positions, respectively (see Figure 2). If a Q1 or Q2b tetrahedron hosts a hydroxyl group, it would be denoted by an additional OH index. We will discuss five types of distinguishable Si sites in our models, namely Q1, Q1OH, Q2b, Q2bOH, and Q2. Note that higher coordinated sites Q3 and Q4 are not normally present in C−S−H gels. Computational Methods. For all the periodic models, both the atomic positions and the parameters of the unit cells were optimized using interatomic potentials of the polarizable core−shell type,16 as implemented in the GULP code.17 We employed a potential parametrization slightly refined with respect to ref 10 (Figure S3 of the Supporting Information for details).18 The electronic calculations for these structures were subsequently performed within DFT with the Quantum Espresso code.19 The gradient corrected exchange-correlation functional of Perdew-Burke-Ernzerhof (PBE)20 and the norm conserving pseudopotentials of Troullier−Martins21 were employed. Because of the large size of our models, particularly the ones based on the structure of tobermorite, structural optimization was performed with GULP. The reference models based on β-belite and α-quartz were treated in the same way for internal consistency. The isotropic magnetic shieldings were obtained with the Gauge Including Projector Augmented Waves (GIPAW) method.22 Within this approach, the induced magnetic field and the shielding tensor are calculated from the electric current induced by the external magnetic field using the first order linear response. The all-electron wave functions are used for the calculations of isotropic shielding. These are obtained from the self-consistent pseudowave functions using a linear operator dependent on the field, which ensures the translational invariance of wave functions in the external magnetic field. The GIPAW method has been successfully applied to study 43 Ca and 17O NMR in several Ca silicates, including jennite and tobermorite.23 The plane wave basis had an energy cutoff of 80 Ry. The k-points sampling for tobermorite models was 2 × 1 × 1 (i.e., 2 points along the shortest a lattice constant, being about 6.7 Å). Because jennite lattice constants (about 10 Å) are longer than the shortest dimensions of the tobermorite unit cell, we found that Γ point calculations were sufficient for the jennite based models. A k-point mesh of 4 × 4 × 4 was applied

Figure 2. Optimized structures of the selected models of C−S−H gel: (a) tobermorite-based dimeric model (T2−H1), (b) tobermoritebased pentameric model (T5−H2), and (c) jennite-based pentameric model (J5−1). According to the different local environment of Si tetrahedra, five types of Si atoms are distinguished, namely Q1, Q1OH, Q2, Q2b, and Q2bOH. The charge compensating Ca cations are given as in the previous figure.

gel are still quite scarce,7−12 in particular quantum calculations of the NMR spectra are still missing. The aim of this work is to fulfill this need through the DFT investigation of the 29Si NMR spectra of models of C−S−H gels derived from jennite and tobermorite 14 Å.

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MODELS AND METHODS Geometric models. Our models for C−S−H gel, like those used previously,10 are based on the observed structures of jennite and tobermorite 14 Å. Apart from the mineral structures with infinite silicate chains, we focused on models consisting of dimeric and pentameric silicate species, proposed for C−S−H gel. In agreement with previous suggestions from experimental work,2 we found in preliminary calculations that the structures with pairing tetrahedra removed are less stable than the ones with bridging sites removed (by at least 100 kJ/mol); therefore only the latter are discussed below. The dimeric/pentameric models were obtained by removing each/every second bridging tetrahedra from the infinite chains in the initial unit cell of the mineral doubled along the b direction. The finite chains were obtained by removing either neutral SiO2 units from jennite structure or charged SiO(OH)+ units from tobermorite structure (Figure 2). The excess negative charge can be neutralized with protons, Ca2+ or Ca(OH)+ ions. All of these charge compensating schemes were applied with several possible distributions of cations. The detailed descriptions of the models used along with their structures are attached in the 9756



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reference systems. Because the observed chemical shifts of atoms in a given chemical environment are averaged due to motional effects, we also calculated average values of chemical shifts for a given type of Qn site in M model, replacing the n δi,M GIPAW in formula 1 by the arithmetic average of Q shieldings. More sophisticated methods to include atomic motions within first principles are beyond our current computational facilities, due to the large size of our cells (about 200 atoms).

for belite and quartz models. Checks of the convergence of these computational details are reported in Figure S5 of the Supporting Information. We also performed DFT/PBE calculations for the cluster models with the Amsterdam Density Functional (ADF) program.24 These calculations employed Slater type triple-ζ basis sets augmented with polarization functions.25 The 29Si shieldings were calculated within the Gauge Including Atomic Orbitals approach26 using the NMR package,27 distributed with the ADF code. Computation of 29Si Chemical Shifts. We wish to compare our calculated values with observed NMR chemical shifts. The dispersion of all the computed isotropic shieldings is shown in Figure 3. The quantities measured experimentally are

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RESULTS Structural and Elastic Properties. For selected mineral silicates, the structural and elastic properties from GULP computations were compared with observed values (Figure S6 of the Supporting Information). In all of the cases, the comparison between the theoretical and available experimental data of the minerals is very good. The structural data and elastic constants of C−S−H gel models, with finite chains, are summarized in Table 1. These Table 1. GULP Calculated Properties of C−S−H Gel Models: Density (ρ), Elastic Properties (K − Bulk Modulus, G − Shear Modulus, Y − Young’s Modulus), and the Energy Difference Calculated between Models with the Same Composition in the Unit Cell

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Figure 3. Dispersion of Si GIPAW isotropic magnetic shieldings (in ppm) for various types of Si sites in the finite chain models based on jennite (green) and 14 Å tobermorite (red) structures.

not the magnetic shieldings themselves, but the chemical shifts, taken with respect to the signal of a suitable reference system, typically tetramethylsilane for 29Si. The accurate reproduction of experimental chemical shifts at the DFT level can be difficult because the common functionals account differently for exchange and correlation in the reference and studied systems. This is the case for the reference tetramethylsilane with covalent Si−C bonds and our silicates in which the Si−O bonds have more ionic character. In order to compute chemical shifts with experimental accuracy, it is recommended to use some secondary reference compounds or interpolation procedure.28 We calibrated our results with respect to two silicates with a well-defined single NMR signal, namely β-belite and α-quartz. The observed values of chemical shifts for these species are −71.3 ppm for Q0 in belite29 and −107.4 ppm for Q4 in quartz,30 with a difference of 36.3 ppm. The GIPAW difference between Q0 and Q4 shieldings is only 25.9 ppm, and in the ADF/GIAO cluster calculations, a similar value of 23.4 ppm was obtained. This indicates that the possible inaccuracies in our calculations stem rather from the exchange-correlation functional, not from the particular way of computing NMR shieldings. The chemical shift of i-th 29Si nuclei in M model (δi,M GIPAW) was calculated according to the formula ref, p i,M δGIPAW = δexp +

ρ (g/cm3)

K (GPa)

G (GPa)

Y (GPa)a

T∞ T5−Ca1 T5−Ca2 T5−Ca3 T5−H1 T5−H2 T5−H3 T2−Ca T2−H1 T2−H2 J∞ J5−1 J5−2 J5-H J2 J2-H

2.22 2.26 2.38 2.31 2.20 2.15 2.11 2.32 2.25 2.11 2.35 2.27 2.33 2.23 2.18 2.18

38.6 34.3 45.1 41.6 32.9 32.3 25.8 46.0 42.3 22.8 32.0 24.1 27.9 31.7 29.5 31.4

22.5 23.1 23.1 23.1 21.6 20.3 16.7 25.5 20.9 12.1 19.9 16.5 16.9 14.8 13.6 14.0

56.5 56.6 59.2 58.5 53.2 50.4 41.2 50.1 64.6 30.8 49.5 40.3 42.2 38.4 35.4 36.6

ΔEb (kJ/mol)

105.1 (63.8) 145.0 (83.9) 0.0 (0.0) 0.0 (35.5) 11.3 (0.0) 25.9 (7.2) 0.0 (0.0)

a

K and G according to the Hill definition; Y = (9G)/(3 + (G/K)). bIn parentheses, the DFT/PBE values calculated with the code Quantum Espresso for the GULP relaxed structures.

calculated elastic quantities have larger values than the experimental ones for C−S−H gel31 because of the effects of porosity in the cement materials. The elastic properties depended strongly on the model, although, not surprisingly, they usually increased with density. The biggest discrepancy between our calculated elastic properties and those presented in ref 10 is for the bulk modulus predicted for the T2−Ca model and especially the T2−H1 one. It should be noted that, in the present work, a wider systematic search of structures was made. In these cases, the bulk moduli and densities are even higher than for tobermorite. As a consequence of the optimization, these T2 models have a densely packed structure due to the significant shrinkage of the unit cell in the c direction by about 3 Å after removing the Q2b tetrahedra. The pentameric models of tobermorite, T5−Ca2 and T5−Ca3, also show higher densities and elastic constants than in the basic T∞ structure, because the selected protons were replaced with Ca(OH)+ ions.

ref, p ref, q (δexp − δexp ) ref, q ref, p (σGIPAW − σGIPAW )

ref, p i,M × (σGIPAW − σGIPAW )

model

(1)

where δ and σ denote chemical shifts and isotropic shieldings, respectively, and the p and q letters denote the belite and quartz 9757



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presented in Table 2. Although the predicted values for various types of 29Si sites lie in partially overlapping ranges (Table 2), some general trends are clear: (i) the Q1OH sites are usually less shielded than the Q1 sites saturated only by Ca because of the smaller electron transfer from hydrogens than from Ca cations, (ii) the Q1 sites in tobermorite models are more strongly shielded than those in jennite models, due to the bonding of additional Ca cations in the interlayer position, (iii) the Q2 sites are more strongly shielded than the Q1 sites, (iv) the chemical shifts of the Q2 sites show a smaller dispersion than those of Q1 and Q2b sites. The small dispersion of the Q2 signals is due to the similarity of the neighborhoods of Q2 tetrahedra consisting of two other SiO4 units and four Ca cations in all the models. The mean 29Si chemical shifts of Q2 species lie typically in the range from −82 to −85 ppm, in good agreement with the experimental data. Among the Q2b sites, the ones in the J5 models are the least shielded. This is attributed to the lack of coordination between Q2b tetrahedra and interlayer Ca ions in J models. The tetrahedra in tobermorite models are linked to one (T5−H3) or two (T5−Ca3) interlayer Ca cations and are thus strongly shielded. The Q2bOH sites in tobermorite models are slightly less shielded than the Q2b ones though the effect is not as prominent as in the case of the Q1 and Q1OH species. We next simulated the NMR spectra by broadening and summing the chemical shifts calculated for each 29Si atom. However, the chemical shifts were calculated for static structures at 0 K, and their dispersion is much larger than the experimental ones because atomic motions are neglected. A magnetic nucleus changing its chemical environments sufficiently fast contributes to a single NMR signal at the mean value of the chemical shifts for the various configurations. Because the thermal motions are the fastest for the light nuclei, these dynamical effects should be indeed important at room temperature for our systems due to the presence of mobile hydroxyl groups and water molecules. To average dynamically the NMR spectra, we then assumed that all 29Si nuclei within a certain Qn site for a given model contribute to an average signal (also Table 2). The spectra following both assumptions are presented in Figure 4. Dotted lines are obtained by summing the chemical shifts from individual Si atoms; solid lines, by summing the average chemical shifts for Qn sites in a particular model. Each plot includes one dimeric and three pentameric models, corresponding to a sample of C−S−H gel with a mean chain length of 4.25 tetrahedra. The dotted lines sum 76 and 38 peaks for the T and J models, respectively. For solid curves, there are 10 (T5−Ca plot) or 11 (T5−H and J plots) peaks. The spectra with both dotted and solid lines present a few maxima at similar values. Since solid lines take some account of dynamical effects we will focus on these lines in the discussion which follows.

The densities of jennite based models are slightly smaller in comparison to that of the J∞ structure because the removal of SiO2 units does not lead to much contraction of the unit cell. We calculated the relative energy stability of the models with the same unit cell composition in Table 1. The trends are the same for both J and T5−H models, but the GULP values are significantly larger than the DFT ones. The opposite is found for the T2−H models, though, in these cases, the energy differences are small. 29 Si Chemical Shifts for Minerals. Table 2 shows the chemical shifts calculated according to the formula 1. The Q2 Table 2. Mean Values of Scaled 29Si Chemical Shifts, Obtained from the GIPAW Isotropic Shieldings According to Formula 1 Experimental Chemical Shifts and Its Assignment CaO:SiO2:H2O Tobermorite 14 Å Jennite C−S−H gel

Q1

Q2b or Q2(1Al)

0.8:1.0:1.3 ≈ −80 1.5:1.0:1.83 ≈ −81c 1.7:1.0:1.2−1.8 ≈ −79d ≈ −82d Computed chemical shifts

Model

CaO:SiO2:H2O

T∞ T5−Ca1 T5−Ca2 T5−Ca3 T5−H1 T5−H2 T5−H3 T2−Ca T2−H1 T2−H2 J∞ J5−1 J5−2 J5−H J2 J2−H

0.8:1.0:1.3 1.1:1.0:1.6 1.3:1.0:1.3 1.4:1.0:1.2 1.0:1.0:1.5

1.5:1.0:1.75 1.2:1.0:2.0 1.5:1.0:1.83 1.8:1.0:2.2 1.7:1.0:2.3 2.3:1.0:2.8 2.1:1:2.9

a

Q1 −80.3 −79.0 −76.6 −79.0 −80.0 −78.3 −75.9 −81.5 −74.1 −73.4 −71.9 −75.9 −77.5

Q1OH

Q2b

≈ −85a,b ≈ −85b,c ≈ −85d

Q2bOH

Q2

−81.7 −79.4

−85.9 −83.5 −83.5 −82.8 −84.6 −85.3 −80.5

−78.3 −82.4 −70.5 −75.4 −75.1

Q2

−78.7 −79.6 −81.2

−74.7 −74.0 −77.0 −79.0 −76.3 −71.4

−80.8

−85.1 −86.0 −83.8 −79.7

−74.1

Ref 33. bRef 32. cRef 34, signal at −81 ppm assigned to Q1 defects. d See for example ref 5 and 35. a

values predicted for T∞ and J∞ models agree well with the experimental data for tobermorite 14 Å and jennite.32−34 Our calculations predict Q2b units less shielded than the Q2 ones. Some contradictions exist in the experimental literature. Cong and Kirkpatrick reported a single peak around −85 ppm for synthetic tobermorite and jennite.32 Maeshima et al. reported another deshielded peak for natural tobermorite,33 assigned to Q2b or Q2 sites connected to Al substituted bridging tetrahedral (i.e., Q2(1Al)). Komarneni et al. observed a strong signal at −81 ppm, which they assigned to Q1 sites in the defective structure of jennite.34 It was observed that the Q2b sites were less shielded than the Q2 sites in C−S−H gel,35 thus one could expect a similar trend in all the dreierekette minerals. In our opinion, these discrepancies can be settled only if the 29Si NMR experiments can be performed on a well characterized mineral sample with resolved crystal structure. The simulated spectra of T∞ and J∞ models are attached in Figure S8 of the Supporting Information. 29 Si Chemical Shifts for C−S−H Gel Models. The chemical shifts computed for C−S−H gel models are also

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DISCUSSION Si NMR experimental results for C−S−H gel show two distinct peaks: the first about −79 ppm assigned to Q1 sites, and the second about −85 ppm assigned to Q2 sites. The third peak, about −82 ppm, is often resolved and assigned to Q2(1Al) sites.5 However, cross-polarization and 2D NMR experiments showed the presence of middle peaks in pure silica C−S−H gels, which were assigned to Q2b sites.35 The observed Q2/Q1 ratio evolves with the age of the C−S−H sample indicating that the mean chain length of silicate chains increases with the age of C−S−H gel, with dimers prevailing in fresh 29

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models supports the presence of tobermorite-like phases in C− S−H gel. The calculated NMR spectra of both tobermorite- and jennite-based models are affected by the charge compensation scheme. Most of the Q1OH peaks lie in the range usually assigned to Q0 sites. Weak Q0 signals are observed in some work on mature cement pastes, and are attributed largely to unreacted orthosilicates. Our results indicate that those Q0 peaks can be partially ascribed to Q1OH sites. Note that at high Ca/Si ratio, the Q1OH sites should be scarce, if present at all. We also suggest that the Q2b sites, less shielded than the Q2 ones, may partially contribute to the NMR signals traditionally assigned to the Q2(1Al) or even the Q1 sites. The exact position of Q2b peak may depend on the local Ca concentration and the presence or lack of hydroxyl groups. The assignment of the peak between the Q1 and Q2 signals to the Q2b sites is in qualitative agreement with experimental results obtained with correlated NMR techniques.35 To further differentiate between the jennite and tobermorite models of C−S−H gels it is useful to assess other properties as well as the NMR spectra. First of all, we discuss the stoichiometry. The typical composition of C−S−H gel is (CaO)1.7·(SiO2)·(H2O)1.2−1.8. This measured value for the Ca/ Si ratio is fully realized by the pentameric jennite models. Although the Ca load in tobermorite models is lower, the correct Ca content is attained because Ca(OH)2 domains are known to grow in solid solution with the silicate phase.36 Further experimental studies showed that Ca(OH)2 leaching decreases the Ca/Si ratio of C−S−H gels from 1.7 to about 1.137 If our jennite-like structures model C−S−H gel, the Ca/Si ratio should remain near the initial value of 1.7, as given typically for J5 models. Whereas the Ca/Si ratio after Ca(OH)2 leaching is in the perfect agreement with the corresponding value in our T5 models. Recently, neutron scattering experiments showed that once porosity is excluded, the density of C−S−H gel particles is in the range 2.5−2.9 g/cm3.38 Both jennite and tobermorite models have lower densities than this observed range (see Table 1), although the density of T5-Ca2 models (2.4 g/cm3) is close to the values observed for C−S−H gel. Moreover, higher densities are obtained in tobermorite models by including densely packed water molecules in the interlayer space or at the silicate grain boundaries.11,12 The issue of low density cannot be solved in jennite models by increasing the water content because the degree of hydration in the jennite models regularly exceeds the observed value for C−S−H gel. It is noteworthy that neutron scattering experiments also show the presence of Ca−OH bonds,37 which was attributed to jennite-like species. However, the tobermorite-like structures with finite chains can host Ca(OH)+ ions in the interlayer positions. The latter was suggested by Taylor1 and was realized in our T5−Ca2 and T5−Ca3 models. These tobermorite derived models with interlayer Ca(OH)+ ions could be considered as intermediate structures between normal tobermorite and jennite. C−S−H structure combining tobermorite and jennite features was already suggested in molecular dynamics study.9 Therefore, the models based on tobermorite explain not only the stoichiometry and mass density of C−S−H gel but also its 29Si NMR spectra.

Figure 4. Simulated 29Si NMR spectra of C−S−H gel. The NMR signals correspond to the following models: (a) tobermorite-based with the charge compensation of Ca (T5−Ca and T2−Ca, top) and of protons (T5−H and T2−H2, bottom), and (b) jennite-based (J5 and J2). The spectra show the chemical shifts of individual Si atoms (dotted line) and the average on the site types of Table 2 (solid line). The peaks are broadened with gaussians with a half-maximum width of 2.0 ppm. Vertical solid lines indicate the experimental positions of Q1 (−79 ppm) and Q2 peaks (−85 ppm).

samples, whereas pentameric and longer species are most abundant in aged pastes.1 When discussing the models of mature C−S−H gel, we shall therefore focus on the results obtained for the structures with large pentameric chains. The experimental spectrum closely resembles those simulated for the tobermorite models saturated by Ca ions (part a of Figure 4), with two dominant peaks visible, Q1 and Q2, and the Q2b sites contributing partially to both main peaks.5,35 However, the spectrum obtained for H saturated tobermorite models has three peaks, with the least shielded peak due to the Q1OH sites. For jennite model (part b of Figure 4), there is a spectrum with multiple peaks, shifted too much toward higher values, and quite different from the data reported for C−S−H gel. Although the Q2 signals agree with measured values, the Q1 chemical shifts computed for jennite models are higher than experimental ones. In conclusion, the good agreement of 29Si chemical shifts between experiments and calculations for the T5

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CONCLUSIONS Simulations of various periodic C−S−H gel models have been performed in order to calculate the 29Si chemical shifts. The 9759



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models were derived from observed structures of tobermorite 14 Å and jennite minerals, which are regarded in cement science as canonical models of C−S−H gel. The calculated Q2 chemical shifts were found to be almost model independent, and the Q1 and Q2b signals showed large dispersions. Typically, the shielding of these sites was weaker for hydroxylated species and increased with the number of Ca cations in its nearest neighborhood. We found good agreement between the calculated and experimental chemical shifts for models based on tobermorite 14 Å structure, while jennite-like models showed too high Q1 values. Our calculations support the presence of tobermorite-like domains in C−S−H gel, where they frequently coexist with domains of Ca(OH)2 and water molecules in pore volumes. Note that tobermorite models with interlayer Ca(OH)+ ions agree well with experiment. The poorer agreement between the computed chemical shifts and experiment, along with other structural considerations seem to exclude jennite-like phases as the main components of C−S−H gel.

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ASSOCIATED CONTENT

S Supporting Information *

The detailed description of the models and their geometries, GULP parametrization, complete ref 19, structural and elastic properties computed for mineral phases, the convergence of test SCF results, simulated 29Si NMR spectra of T∞ and J∞ models. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected], [email protected]. Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge the support of the Basque Departamento de Educación and the UPV/EHU (Grant No. IT-366-07), the Spanish Ministerio de Innovación, Ciencia y Tecnologiá (Grant Nos. TEC2007-68065-C03-03 and FIS2010-19609-C02-02), and the ETORTEK research program (NANO-IKER Grant No. IE11-304) funded by the Basque Departamento de Industria and the Diputación Foral de Guipuzcoa. P.R. and M. S. gratefully acknowledge a grant and the hospitality of the Donostia International Physics Center, respectively.

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REFERENCES

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