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Instituto de Ciencias de la Construcción Eduardo Torroja (IETcc-CSIC), c/Serrano Galvache 4, Madrid 28033, Spain. ‡ Instituto de Estructura de la M...
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Combined Effect of Amorphous Nanosilica and Temperature on White Portland Cement Hydration Isabel F. Sáez del Bosque,*,† Sagrario Martínez-Ramírez,†,‡ and MaríaTeresa Blanco-Varela† †

Instituto de Ciencias de la Construcción Eduardo Torroja (IETcc-CSIC), c/Serrano Galvache 4, Madrid 28033, Spain Instituto de Estructura de la Materia (IEM-CSIC), c/Serrano 123, Madrid 28006, Spain



ABSTRACT: White cement pastes were hydrated in the presence or absence of amorphous nanosilica (nSA) and cured at 25 or 65 °C. The findings showed that at the higher curing temperature the initial belite hydration rate rose substantially and that this effect was more accentuated in the pastes containing nSA. The C−S−H gel formed in the presence of nSA was more uniform and had a consistently longer mean chain length (MCL) than in the gels formed in the absence of the addition. Moreover, the C−S−H gel formed in nSA-bearing paste cured at the higher temperature had a longer MCL and a higher Al3+ uptake than the gels in the other pastes studied. Lastly, at 65 °C, the presence of nSA stabilized ettringite formation during the first 28 days of paste hydration; while no calcium hemicarboaluminate, which was the sole crystalline aluminate hydrate identified in the unblended pastes, was detected in the nSA-containing pastes.

1. INTRODUCTION The addition of several types of materials in the various stages of cement manufacture has become an increasingly common practice in light of the benefits accruing: lower natural resource consumption, reuse of waste that would otherwise be sent to the landfill, and the reduction of CO2 emissions are, moreover, measures in line with European sustainable development policies.1 In the wake of intensive research on the additions (such as fly ash, silica fume, and blast furnace slag) that have been in use as cement components for decades, these materials are presently addressed in a Spanish and European standard (UNE EN 197-1 2 ) on cement specifications. Further studies are currently underway to assess the viability of using certain industrial byproducts (including ceramic materials, glass and rice husk, or sugar cane ash) as additions in cement manufacture.3−6 In recent years, attention has focused on TiO2, Al2O3, Cr2O3, and Fe2O3 nanoparticles as cement additions, which have been shown to act as nanofillers, reducing porosity, improving mechanical properties, and giving rise to more compact microstructures. At the same time, they act as a seed for hydration product crystallization, thereby expediting cement hydration.7,8 The use of nanosilica (nSA) as an addition has been the object of a good deal of research activity, although the results have not always concurred. Some studies have reported higher compressive strength in both early (3 days) and longer (28 days) age pastes containing nSA than in pure cement pastes.9 This finding contrasts with the behavior observed in other additions such as silica fume (SF) or fly ash (FA), whose beneficial effect on strength appears at later ages.10,11 Other authors found similarities between nSA and SF or FA performance, observing that the gain in compressive strength induced was not immediate, but delayed (from 28 days onward) and attributable primarily to portlandite (CH) consumption by nSA.12 Yet others13,14 discovered that the compressive strength of nSA-bearing blended cements was © 2013 American Chemical Society

higher than in cements containing additions such as silica fume, whose use has been regulated in standards. Most researchers have reported the absence of a linear relationship between the percentage of nanosilica added and the increase in mechanical strength: i.e., above a given percentage, compressive strength ceases to rise due to a lack of sufficient portlandite to react with the nSA.15,16 The improvements in nSA blended cement performance can be attributed to a number of factors. One is the physical effect of nanofilling the voids between cement particles, resulting in more effective packing (a behavior observed in previously described nanoparticles) and lower hydrated cement porosity and permeability.12 But unlike other nanoparticles, nSA reacts with the portlandite generated in cement silicate phase hydration. This pozzolanic reaction yields additional C−S−H gel, the substance that accounts for 60−70% of the hydrated product and the phase that affords cement pastes their mechanical properties and durability. At the same time, the presence of nanosilica has been observed to hasten silicate phase hydration,16−18 more intensely at smaller particle sizes.19 Temperature also expedites cement phase hydration20 and modifies the nanostructure of C−S−H gel21 as well as the microstructure of cement pastes, inducing an uneven distribution of hydration products and raising paste porosity.22,23 Studies of the effect of temperature and the addition of nanosilica on the nanostructure of the C−S−H gel forming during synthetic tricalcium silicate (C3S) hydration have shown that adding nSA quickens C3S hydration at any age or temperature and modifies the structure of very early age C− S−H gel.24 Nonetheless, little is known about the joint effect of temperature and the presence of nSA on belite and alite Received: Revised: Accepted: Published: 11866

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Table 1. XRF Chemical Analysis of BL I 52.5 R White Cement and nSA b

WPC nSA a

SiO2

Al2O3

Fe2O3

MgO

CaO

Na2O

SO3

K2O

TiO2

P2O5

LOIa

21.71 89.993

4.85 0.68

0.32 0.074

0.88 0.001

65.08 0.282

0.15 0.386

3.82

0.57

0.12 0.059

0.06 0.015

2.387 8.92

LOI: loss on ignition at 1 000 °C. bWPC: white Portland cement.

Figure 1. Deconvolution of the 29Si MAS NMR spectrum for the anhydrous blend of WPC and nSA (90/10 wt %): (a) peaks used to deconvolve alite, belite, and nSA; (b) simulation of the entire spectrum.

SiO2 content, ∼90% (Table 1), and a specific surface area of 371 ± 2 m2/g (the full results are shown elsewhere24). The sample analyses were performed on a BRUKER AVANCE-400 (9.4 T) 29Si MAS NMR spectrometer operating at 79.4 MHz for 29Si. The samples were packed into 7 mm ZrO2 rotors. Free induction decay (FID) signals were acquired via MAS and continuous pulse proton decoupling at a field strength (γB2/2π) of 2.5 kHz. Other conditions were as follows: 7 μs for the π/2 excitation pulse, MAS spinning rate of 4 kHz, and 128 scans. Kaolin (δ = −91.5 ppm), referenced to tetramethylsilane (TMS; δ = 0 ppm), was used as the external control for chemical shift in all of the 29Si MAS NMR experiments. The relaxation delay (d1) was 60 s, a value that met the quantitative criterion, for it was five times greater than the longitudinal relaxation (T1) as calculated with the saturation-comb experiment.27 Longitudinal 29Si relaxation times (T1) were measured for both the anhydrous WPC and the paste hydrated for 62 days at 65 °C (BL62d). The saturation-comb consisted of a train of 25 π/2 saturation pulses of 7 μs duration separated by delays of 30 ms. Spectra were obtained for the anhydrous WPC and BL62d with the following values of variable delay (τ): 1, 2, 4, 6, 10, 20, 40, 60, and 100 s. Each spectrum in the series was acquired with 16 scans at a MAS rate of 6 kHz. A relaxation delay of 60 s was applied to prevent excessive probe and sample heating. The anhydrous WPC findings were as follows: for belite, T1 = 9 ± 2 s. T1 was not calculated for alite, for according to the literature,28 it yields shorter T1 values than belite. The T1 values found in paste BL62d were 6 ± 1 and 7 ± 1 s, respectively, for the Q1 and Q2 units in the C−S−H gel formed. The 27Al MAS NMR experiments were conducted on a BRUKER AVANCE-400 (9.4 T), using 2 μs for the π/2 pulse width, a 5 s recycle delay, 400 scans, and a 10 kHz spinning rate. 27Al cross-polarization spectra were collected with contact

hydration, or their effect on hydrated phase stability and C−S− H gel nanostructure. The present study consequently aimed to explore the effect of curing temperature on the hydration of white cement containing nSA by analyzing the nanostructure of the C−S−H gel formed.

2. EXPERIMENTAL SECTION Two types of paste were prepared with Spanish standard UNE 80305 2 class BL I 52.5 R white cement furnished by CEMEX, which was chemically characterized with X-ray fluorescence (XRF; Table 1). In the first paste, deionized water was mixed with 100 wt % white Portland cement (WPC) at a water to cement (w/c) ratio of 0.425. In the second, the pastes were prepared by mixing 90/ 10 wt % WPC and nSA, likewise with deionized water. The w/c (0.66) used was higher, however, due to the higher water demand of nSA, substantiated in the literature.13,25 While some researchers15 have prepared nSA-containing pastes with admixtures, in the present study this possibility was ruled out to avoid the possible effects of a third variable on the C−S−H gel.26 In lieu of that alternative, the w/c was varied to obtain pastes with the same workability and consistency. Both mixes were hand stirred for 3 min and subsequently stored in closed plastic containers at 25 or 65 °C and 100% relative humidity (RH). The hydration reaction was detained at 1, 28, 62, or 182 days with acetone, followed by vacuum drying for approximately 1.5 h. The Ebrosil PD amorphous nanosilica precipitate used was furnished by EQIL. Its X-ray diffraction (XRD), differential thermal analysis/themogravimetric analysis (DTA/TG) and 29 Si magic angle spinning nuclear magnetic resonance (MAS NMR) characterization showed that it had a high amorphous 11867

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time of 2 ms. AlCl3·6H2O (δ = 0 ppm) solution was used as the references for the 27Al chemical shifts relative to the standard, TMS. Spectrum processing and signal deconvolution-based quantitative integration were performed with MestRe-C v3.9 29 software. Six deconvolutions were performed on each spectrum, varying the initial parameters. The values given here are the means of the six results, for which very small standard deviations, on the order of 0.3, were found. Powder XRD studies were conducted on a Bruker D8 Advance diffractometer, consisting of a high voltage, 3 kW generator, a (1.54 Å Cu Kα) copper anode X-ray tube normally operating at 40 kV and 30 mA, a Lynxeye detector with a 3 mm antiscatter slit, and a (0.5%) Ni K-β filter. It was not fitted with a monochromator (i.e., Kα2 was not eliminated). Readings were taken at 2θ diffraction angles ranging from 5 to 60°, with a step size of 0.019° and a count time per step of 0.5 s. The DTA/TG analyses were conducted on a TA Instruments SATQ600 thermal analyzer in a dynamic nitrogen atmosphere in which the samples were heated at a rate of 4 °C/ min from 25 to 1050 °C.

Figure 3. Deconvolution of 29Si MAS NMR spectra for the 62 day WPC + 10 wt % nSA pastes cured at 25 (left) and 65 °C (right).

composition observed was as follows: 49.81 and 20.75% alite and belite, respectively, and 8.19% amorphous nanosilica (slightly lower than the 9 wt % of SiO2 added). The belite to alite ratio by weight was 0.42. The similarity between this value and the 0.40 found in unblended WPC was an indication of the adequacy of the deconvolution method used. The variations in the nanostructure of the C−S−H gel forming during blended WPC−nSA hydration at different temperatures were tracked with 29Si MAS NMR (Figure 2). The signals in the −67 to −77 ppm range were generated by the silicate phase Q0 units present in the unreacted cement. The signals for the C−S−H gel appeared in a lower field: one around −79 ppm, characteristic of Q1 units (chain end tetrahedra or dimers); another around −81 or −82 ppm attributed to the Q2(1Al) units associated with middle chain groups in which one of the adjacent tetrahedra is occupied by aluminum;35,36 and a third around −85 ppm, characteristic of Q2 units (midchain groups where the two adjacent tetrahedra are occupied by silicon).37,38 The spectrum for the 1 day paste cured at 25 °C contained a wide and scantly intense signal between −100 and −117 ppm (Q4 units), denoting the presence of unreacted nSA. The percentage of each Qn unit was determined by deconvolving the respective spectra (Figure 3). The results are listed in Table 2. Figure 4 shows the variations in the Qn units in the C−S−H gel vs time for the two curing temperatures. The Q2 units were observed to rise with time at both temperatures, while the Q2(1Al) units rose during the first 28 days, after which they remained flat. Q1 unit behavior, in turn, depended on the curing temperature, rising with hydration time at 25 °C but declining from the outset at 65 °C. The degree of cement hydration in unblended pastes is normally calculated from the equation β (%) = 100 − Q0,21,39 which gives a value for joint alite and belite hydration. That equation is inappropriate for comparing the values obtained in blended and unblended pastes, however, for in the former the Q0 signals generated by alite and belite account for only 68.5% of the total Si, while the rest is found in the signals attributed to the Q4 and Q3 in nSA. As a result, the degrees of hydration calculated would be higher than in unblended pastes. Equation 1,16,40 by contrast, can be applied to find the degree of hydration in both blended and unblended pastes:

3. RESULTS AND DISCUSSION The 29Si MAS NMR spectrum for anhydrous white cement + 10 wt % nSA (Figure 1) exhibited a relatively narrow signal

Figure 2. 29Si MAS NMR spectra for WPC + 10 wt % nSA paste cured for different times at 25 or 65 °C.

around −71.3 ppm, characteristic of belite30,31 and a series of wide signals between −66 and −77 ppm attributed to alite.32 In addition, a wide, asymmetric signal around −112 ppm with a shoulder around −103 ppm, were respectively associated with the Q4 and Q3 units in nSA,33 the latter denoting the presence of a small proportion of silanol groups in the nSA structure. Figure 1 shows spectrum deconvolution, in which two peaks were used to simulate alite and one to simulate belite, further to the approach proposed by Rawal et al.34 Two peaks were also used to simulate nSA, one for its Q4 and the other, lower in intensity, for its Q3 units. The molar percentages obtained after deconvolution of the 29Si MAS NMR spectrum for anhydrous white cement + 10 wt % nSA were as follows: 45.93% for alite, 25.37% for belite, and 28.60% for nSA (Q4, 26.26%; Q3, 2.43%). The percentages by weight of these phases were calculated from the total amount of SiO2 obtained with XRF and the molar percentages found with 29Si MAS NMR. The 11868

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Table 2. Qn Unit Percentages Found by Deconvolving 29Si MAS NMR Spectra for 90 wt % WPC + 10 wt % nSA Pastesa amount of Qn unit (%) temp (°C) 25

65

a

time (days) 1 28 62 182 1 28 62 182

0

Q1

Q

37.74 13.02 9.74 6.65 12.16 10.11 7.27 6.59

b

28.56 40.93 41.81 42.65 39.75 33.63 30.53 29.97

Q2 b

17.66 28.09 30.18 31.21 30.22 34.66 39.79 41.76

Q2(1Al) b

6.43 17.96 18.16 18.97 17.86 21.59 22.40 21.68

b

MCL

α (%)

AlIV/Si

3.91 4.69 4.74 4.81 4.87 5.98 6.81 6.96

47.07 80.96 85.94 90.14 82.94 87.44 90.05 90.80

0.061 0.103 0.100 0.102 0.102 0.120 0.115 0.116

The error limits for CL and AlIV/Si are estimated to be ±0.05 and ±0.003, respectively. bThe 9.60% Q4 in nSA brings the total to 100.

hydration degrees of alite or belite 0 0 = {1 − (A[Q alite/belite (t )]/A[Q alite/belite (t = 0)])}

(2)

× 100

where A[Q0alite/belite(t)] is the area of the alite or belite Q0 signal in the hydrated paste at a given hydration time and A[Q0alite/belite (t=0)] is the area for the alite or belite Q0 signal at time zero, i.e., in the anhydrous blended cement. As Figure 5 and Table 2 show, increasing the curing temperature raised the total degree of hydration in the cement in both types of pastes. This effect was more accentuated in the 1 day materials, where values of 47.07 and 82.94% were found at 25 and 65 °C, respectively, in pastes containing nSA. The degree of hydration was also observed to rise in the presence of nSA, primarily at early ages (1 day), for the unblended pastes exhibited degrees of hydration of only 37.76 and 68.64% at 25 and 65 °C, respectively. This increase in silicate phase hydration may be explained by the concurrence of two developments. On the one hand, since the water molecules were not confined by the Ca(OH)2 crystals, they could diffuse more deeply into the silicate phase particles,42 and on the other, the nSA−portlandite reaction yielded additional C−S−H gel that acted as a seed, generating more gel during silicate phase hydration. Furthermore, what some authors describe as the ready adsorption of Ca2+ ions onto the nSA surface would lower their concentration in the pore solution, prompting a decline in the degree of saturation of Ca2+ and a re-dissolution of the silicate phases.43,44

Figure 4. Variation over time in the proportion of Qn units in the C− S−H gel formed during the hydration of WPC + 10 wt % nSA blends at 25 and 65 °C.

total degrees of hydration = α = {1 − (A[(Q0(t )]/A[Q0(t = 0)])} × 100

(1)

where A[Q0(t)] is the sum of the areas of all the Q0 signals on a hydrated blended cement spectrum at a given hydration time and A[Q0 (t=0)] is the sum of the areas of all the Q0 signals at time zero, i.e., in the anhydrous blended cement. Adopting the same approach but for each silicate phase present in the cement yields alite and belite degrees of hydration separately, using the following equation proposed by Poulsen et al.:41

Figure 5. Effect of nSA on the total degree of cement hydration at two temperatures: (a) 25 and (b) 65 °C. 11869

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Figure 6. Effect of nSA on the degree of hydration of alite (a, b) and belite (c, d) at 25 (left) and 65 °C (right).

Figure 7. Effect of nSA on the mean chain length (MCL) of the C−S−H gel forming during WPC hydration vs time at (a) 25 and (b) 65 °C.

Figure 9. Al(IV) to Si ratio in gels forming during WPC hydration in the presence and absence of nSA. Figure 8. Variation in the MCL of C−S−H gel with the degree of WPC hydration in the presence and absence of nSA at 25 and 65 °C.

Given the large specific surface and concomitantly high reactivity of nSA, its characteristic bands were only visible on 11870

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Figure 10. Diffractograms of pastes cured at 65 °C: (a) WPC + 10 wt % nSA; (b) WPC.

Figure 11. (a, b) 27Al MAS NMR and (c, d) 27Al CP/MAS NMR spectra for 62 day pastes in the presence and absence of nSA at 65 °C.

the spectrum for the one day paste cured at 25 °C. Curing temperature hastened the early age pozzolanic reaction very significantly, for none of the spectra for the pastes cured at 65 °C contained signals denoting the presence of unreacted nSA. The degree of belite hydration in 1 day pastes containing nSA and cured at 65 °C was eight times greater than in 1 day nSA pastes cured at 25 °C (73% compared to 9%). In the unblended pastes, at 54%, belite hydration was six times greater in the pastes cured at the higher than in the samples cured at the lower temperature (∼9%). These values are an indication of the intense effect of temperature on early age belite hydration in both types of pastes, but particularly in the materials containing nSA. Temperature had a more moderate effect on alite hydration, which was significantly higher at all curing ages and both temperatures in the presence of nSA (Figure 6). Note that together, nSA and temperature induced nearly total hydration of both phases in the 1 day pastes. This result is

of considerable relevance to the precast industry, in which concrete is cured at temperatures of 60−65 °C. The mean chain length (MCL) of the C−S−H gel formed in the two pastes, in turn, calculated with the equation proposed by Richardson,38 rose with time and curing temperature, and was consistently longer in the nSA-containing pastes (Figure 7). In the C−S−H gel formed by hydrating calcium silicates at ambient temperature (∼25 °C), Q1 units or similar proportions of Q1 and Q2 units are known to prevail.42 Nonetheless, at both curing temperatures, even at 25 °C where reactivity was not enhanced by temperature, the presence of nSA induced more C−S−H gels with a higher degree of linear polymerization, i.e., gels with longer MCLs (higher Q2 to Q1 ratios; Figure 7). Some authors21 have contended that in blended Portland cement a higher Q2 to Q1 ratio is indicative of higher mechanical strength. 11871

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C−S−H gels formed in these pastes had less Al3+ than the gels in the nSA-free samples (containing calcium hemicarboaluminate) but more Al3+ than the C−S−H gels in the samples cured at 25 °C. Figure 11 shows 27Al MAS NMR spectra of both samples (with and without nSA) for 62 days hydrated, confirming the increase in Al3+ (IV and V coordination) incorporated into the C−S−H gel for the samples containing nSA avoiding its possibility of further reaction; and an amorphous THA phase was identified in the nSA sample. Additionally a sharp peak in the Al(VI) zone corresponding to Hc can be seen in the spectra of both pastes and no monosulphate or etringitte phases neither crystallines nor amorphous have been identified. Since AFm it is not present in the samples with nSA hydrated for 62 days and only Hc is formed; thus, the sulfates present in AFm have been replaced by carbonates. The presence of Hc indicates a low carbonation.47,48 According to Damidot et al.,49 this compound is incompatible with calcite. In fact, the amount of portlandite in samples cured at 65 °C increases with time in the presence or absence of nSA (Figure 12). Additionally, the portlandite is lower in samples with nSA due to pozzolanic reaction. This pattern is of technological interest; for the temperature (60−70 °C) generally applied in concrete precasting induces AFt destabilization. That in turn favors the formation of AFm 50 and greater adsorption of sulfate ions on the C−S−H gel nanostructure,51−53 a development with significant implications for durability. According to the present findings, however, in the presence of nSA the sulfate ions in the reaction medium are retained in the AFt structure, greatly hindering their adsorption onto the C−S−H gel nanostructure.

Figure 12. Percentage of portlandite of WPC hydration in the presence and absence of nSA at 65 °C.

The mean chain length for C−S−H gels observed in all of the pastes rose linearly with the degree of silicate hydration, with a better fit in pastes containing nSA (Figure 8), while the slopes for the regression lines rose with the presence of nSA at both test temperatures. The Al(IV) to Si ratio was calculated using the Richardson et al. equation38,45 to determine the effect of temperature and the presence of nSA on Al3+ uptake in the C−S−H gel. Those calculations showed that the Al(IV) to Si ratio in the C−S−H gels formed during WPC + nSA hydration rose steeply over time up to 28 days (Figure 9) and declined slightly thereafter. The Al(IV) to Si ratio also increased sharply during the first 28 days in the gels formed in WPC cured at 25 °C and more moderately afterward, while, in the gels generated in WPC paste cured at 65 °C, the ratio declined with hydration time from the outset. Temperature raised the Al(IV) to Si ratio in the C−S−H gel formed in the pastes containing nSA at all test ages. While the ratio rose in early age nSA-free pastes cured at 65 °C, this parameter declined with hydration time, ultimately to below the value recorded for the gels in the pastes cured at 25 °C. The variations in the Al(IV) to Si ratio in C−S−H gels were attendant upon the variation in the type and content of hydrated aluminate in the pastes. The increase in temperature enhanced aluminate phase solubility and consequently the Al3+ concentration in the hydration water at early ages. At early hydration times, the C−S−H gel precipitates at a very high rate because the mechanisms governing hydration are C−S−H gel nucleation and portlandite precipitation. At later ages, by contrast, silicate phase hydration is governed by diffusion, a much slower process due to the very thick layer of C−S−H gel that surrounds the silicate particles.46 All the samples except the WPC pastes cured at 65 °C contained ettringite at early ages (Figure 10). The presence in these latter pastes of a much more soluble phase, calcium hemicarboaluminate hydrate, induced the early age uptake of large amounts of Al3+ into their gel structure. As hydration progressed, however, the Al 3+ concentration in the hydrating solution declined, reducing the amount of Al3+ available to the gels and, with time, the mean Al(IV) to Si ratio. The presence of nSA in the pastes cured at 65 °C stabilized the highly insoluble early age ettringite and calcium monosulfoaluminate hydrate (AFm). Consequently, the initial

4. CONCLUSIONS The following conclusions can be drawn about the effect of temperature and the presence of nanosilica on C−S−H gel nanostructure in WPC hydration. (a) The mean chain length of C−S−H gel rises with hydration time, particularly in pastes cured at higher temperatures (65 °C). At both curing temperatures studied, the extra silica furnished by amorphous nSA induces the formation of C−S−H gels with a higher degree of linear polymerization than found in the gels formed in the absence of nSA. (b) The presence of nSA raises the Al(IV) to Si ratio slightly in C−S−H gels obtained at 25 °C and considerably in mature gels cured at 65 °C. (c) The addition of nSA to white cement expedites joint alite and belite hydration and reinforces the temperature-induced acceleration of early age belite hydration. (d) Adding nSA stabilizes ettringite in samples cured at 65 °C, while the aluminate phase in the absence of the addition is calcium hemicarboaluminate.



AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] and [email protected] Notes

The authors declare no competing financial interest.



ACKNOWLEDGMENTS This research was funded by the Spanish Ministry of Education and Science (Grants MAT2006-11705 and CONSOLIDER CSD2007-00058), the Agencia Estatal Consejo Superior de ́ Investigaciones Cientificas (Grant PIE: 201160E103), and the 11872

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Regional Government of Madrid (Geomaterials Programme, Grant S2009/MAT-1629). Research fellowship BES-200716686 is gratefully acknowledged. We also thank Dr. Isabel Sobrados for performing the 29Si MAS NMR spectra and Dr. ́ Manuel Martin-Pastor for his assistance in their interpretation.



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