Hydration Water Dynamics in Tricalcium Silicate Pastes by Time

Mar 18, 2013 - In the case of panel (a) the BNGM(42) has been used to fit the curve, and all other lines are guides for the eye. It must be mentioned ...
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Hydration Water Dynamics in Tricalcium Silicate Pastes by TimeResolved Incoherent Elastic Neutron Scattering Emiliano Fratini,† Antonio Faraone,‡,§ Francesca Ridi,† Sow-Hsin Chen,∥ and Piero Baglioni*,† †

Department of Chemistry “Ugo Schiff” and CSGI, University of Florence, 50019 Sesto Fiorentino (FI), Italy NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-6100, United States § Department of Materials Science and Engineering, University of Maryland, College Park, Maryland 20742, United States ∥ Department of Nuclear Science and Engineering, MIT, Cambridge, Massachusetts 02139, United States ‡

ABSTRACT: The translational dynamics of the hydration water in tricalcium silicate, as well as the curing kinetics of the paste, have been investigated for the first time using neutron elastic backscattering measurements. A detailed analytical model has been formulated to extract the most important features of the calcium silicate curing process. As the curing time passes, water reacts with the tricalcium silicate, forming amorphous calcium silicate hydrate and crystalline calcium hydroxide. Concurrently, the water translational dynamics slows down due to the increased confinement in the developing matrix. The time evolution of the self-diffusion constant for the hydration water shows a decrease of 1 order of magnitude after two days of curing. The presented results agree with recent molecular dynamics simulations and 1H NMR results on similar systems.

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typical time window does not extend beyond ≈10 ns even in the state-of-the-art high-resolution backscattering spectrometers). Therefore, they can be considered as “immobile” and contribute as an elastic component to the final QENS spectra.1,4,5,11−13 On the other hand, water molecules physically confined into the developing C−S−H gel structure are still “mobile” and give a well-defined quasi-elastic contribution with a relaxation dynamics completely different from that of bulk water at the same temperature.5−7,16 According to the Colloidal Model II,24 the microstructure of the C−S−H gel can be described as a complex porous matrix formed by a basic disk-like object having a layered internal structure. The detailed structure of the basic units has been recently investigated by using small-angle neutron scattering on a pure phase of synthetic C−S−H (I) as a function of the water level inside the gel.25 The water inside the unit is located both in the interlamellar spaces and in very small cavities (intraglobular pores, IGP), with dimensions of or below 1 nm. The packing of these objects produces a porous structure, where two other main populations of pores can be recognized: the small gel pores (SGP), with dimensions from 1 to 3 nm, and the large gel pores (LGP), ranging from 3 to 12 nm. Different approaches have been used to include this complex picture in the modeling of QENS data.2,3,13 By applying a double-Lorentzian fitting function,2 the QENS signal from water at a given hydration time and at very high scattering

INTRODUCTION The Quasi-Elastic1−15 and Inelastic Neutron Scattering12,16−18 (QENS and INS, respectively) techniques can be applied, sometimes in conjunction,12,16,19 to study the hydration process in cement pastes. A review on the subject has been recently published.20 Due to the very high incoherent scattering crosssection of hydrogen atoms, QENS is an ideal technique to study the dynamics of highly hydrogenated systems such as water. In an Elastic Neutron Scattering (ENS) experiment only the fraction of neutrons elastically scattered by the sample as a function of the scattering vector is measured, with the result of data sets with high signal-to-noise ratios and usually a reduced counting time as compared to the QENS approach. Ordinary Portland Cement (OPC), the most widely used construction material, is mainly composed of calcium silicates21 where 50%−70% weight fraction is usually tricalcium silicate, C3S.22 C3S reacts with water to form calcium silicate hydrate C−S−H gel, the “glue” responsible for early strength development. Portlandite (i.e., calcium hydroxide, CH) is formed as a byproduct. The hydration process of a cement paste is a quite complex phenomenon that can be modified by the presence of various additives23 allowing a fine-tuning of the final mechanical properties. C3S is usually employed as a model system for the investigation of the hydration kinetics in cement pastes. QENS provides a direct measure of the conversion of the available water to structurally/chemically bound water and to water constrained in the pores of the cement paste. In this regard, relaxation times for hydroxylic groups and water molecules chemically bound in CH particles and C−S−H are too slow to be appreciated by a QENS measurement (the © 2013 American Chemical Society

Received: December 23, 2012 Revised: March 15, 2013 Published: March 18, 2013 7358

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vector, Q (≥1.9 Å−1) can reveal three distinct contributions: bulk water, chemically bound water, and constrained water (i.e., water adsorbed on surfaces and contained in very small ( 0.1 ps, SV is a simple Debye−Waller factor, with no ω dependence ⎡ u 2 Q2 ⎤ HO ⎥ SHV2O = exp⎢ − 2 ⎢⎣ 3 ⎥⎦

(5)

SHT 2O can be modeled as a Lorentzian function with a Qdependent full width at half-maximum (fwhm), ΓT, described by the Random Jump Diffusion model33,38

(2)

SHT2O(Q , ω) =

The fraction p, or the bound water index, is the spectral weight of the SHP phase scattering, whereas the fraction (1 − p), or the free water index, is the weight of the scattering coming from the water still present in the C3S/H2O paste. We first focus our attention to the scattering originating from the solid hydrated phase. The translational and rotational dynamics of such species are too slow to be appreciated even

ΓT/2 1 π ω 2 + [ΓT/2]2

ΓT = 2

DT Q 2 1 + DTQ 2τres

(6)

where DT is the translational diffusion coefficient and τres is the average residence time between jumps. 7360

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As far as the rotational dynamics is concerned, in the diffusion approximation,33,39 the rotational dynamic structure factor can be expressed as an infinite sum of Lorentzian functions each weighted by a Q-dependent factor SHR2O(Q , ω) = j02 (Qb)δ(ω) +

1 π

∞

∑ (2l + 1)jl2 (Qb) l=1

Equation 9 can be further simplified. In fact, the rotational diffusion coefficient of bulk water around room temperature is of the order of 1 ps−1, which gives Γl=1 R ≈ 1 meV. Higher-order rotational terms give even broader quasi-elastic contributions. Neglecting ΓT and considering the resolution function of IN13, l=1 2 l=1 we estimate Yl=1 H2O ≈ 150 and exp{[YH2O] }erfc(YH2O) ≈ 3 × 10−3, at room temperature for bulk water. This contribution is negligible within the accuracy of the present experiment. However, as the curing time increases, water dynamics slows. As it will be discussed in the following of this paper, the translational diffusion coefficient is expected to decrease by about 1 order of magnitude. Assuming that this is the case for the rotational dynamics as well, we get exp{[YHl=12O]2}erfc(YHl=12O) ≈ 3 × 10−2. On the basis of this calculation, within a few percent accuracy, both at short and long curing times, it is safe to neglect all the contributions to the elastic intensity for l > 0, in essence considering only the EISF, j20(Qb), to account for the effect of water rotation. Moreover, also the effect of the vibrational motion of the hydrogen atoms can be neglected. In fact, the mean square displacement as estimated from the work by Teixeira et al. is (⟨uH2 2O⟩)1/2 ≈ 0.4 Å.33 Its effects on the measured elastic intensity can be estimated considering typical values for the random jump diffusion dynamics of water at room and supercooled temperatures (for example D ≈ 10−9 m2/s and τres ≈ 5 ps). Taking into account also the effect of the rotational EISF, it is found that the DWF reduces the measured elastic intensity by less than 5% for Q values less than 1.5 Å−1. This effect is negligible considering the typical accuracy of the measurements. For Q values larger than 1.5 Å−1 the elastic intensity is less than 5% of the intensity at Q ≈ 0 Å−1, a level which is negligible. Also considering the possibility that the dynamics of the water molecules is slowed down in the cement paste during the hardening process, in a similar way, it can be shown that the error involved in neglecting the DWF of the hydrogen atoms in the water molecules can still be estimated to be of the order of 10%. Thus, for the present sample, the effect of the DWF of the water molecules on the measured elastic intensity can be neglected. In summary, eq 9 reduces to

Γ lR /2 ω 2 + [Γ lR /2]2

Γ lR = 2l(l + 1)DR (7)

where jl(x) is the spherical Bessel function of l-th order; b = 0.98 Å is the distance between the hydrogen atom and the center of mass in a water molecule; and DR is the rotational diffusion coefficient. In the present case, Q ≤ 5.0 Å−1, the first six terms of the summation are required for an accurate description of SHR 2O(Q,ω).16 Within this model each Lorentzian term is the Fourier transform of the l-th order rotational correlation function.36 Thus, the fwhm of the l-th Lorentzian, ΓlR, corresponds to the relaxation rate of the exponential decay of the l-th order rotational correlation function. The l = 0 term is a delta function whose spectral weight is j20(Qb). In this case, j20(Qb) represents the Elastic Incoherent Structure Factor (EISF) of the rotational motion. The EISF is an important quantity in incoherent neutron scattering because it represents the spatial Fourier transform of the volume explored by the hydrogen atoms during their motion. In the present case, the volume explored by the hydrogen atoms of the water molecules through their rotational motion around the center-of-mass is a spherical shell of radius b = 0.98 Å. Using eqs 5−7 in eq 4, the expression for the dynamic structure factor of water used by Teixeira et al.33 is derived SHH2O(Q , ω) = ×

⎡ u 2 Q2 ⎤ ∞ 1 HO ⎥ ∑ (2l + 1)j 2 (Qb) exp⎢ − 2 l ⎢⎣ π 3 ⎥⎦ l = 0

(ΓT + Γ lR )/2 ω 2 + [(ΓT + Γ lR )/2]2

(8)

SHH2O(Q , ω ≈ 0) = j02 (Qb)exp{[YH2O]2 }erfc(YH2O)

To obtain an analytical expression for the elastic scattering intensity from the model outlined in eqs 4−7, we assume a Gaussian resolution function which does not depend on the scattering angle: Res(ω) = (1/2σ)exp((−πω2)/(4σ2)), where the half-width at half-maximum of the resolution (HWHMRes) is Q-independent and can be expressed as HWHMRes = 2σ(ln 2/π)1/2. In the case of IN13, HWHMRes ≈ 4.5 μeV and σ ≈ 2 4.79 μeV.38 Considering that (1/2πσ)∫ +∞ −∞(Z/2/(ω′ + (Z/ 2)2))exp(−(πω′2/4σ2))dω′ = (1/2σ)exp[(π/4σ2)(Z/2)2]erfc((√π/2σ)(Z/2))40 we substitute eq 8 in eq 1, and after normalization of the zero Q intensity, S(Q = 0,ω ≈ 0) = 1,41 we get

YH2O =

(10)

Under the assumptions described above, the total fitting function for the measured elastic intensity results ⎧ ⎡ u 2 Q2 ⎤ I(Q , ω ≈ 0) = A ⎨p × exp⎢ − SHP ⎥ + (1 − p)j02 (Qb) 3 ⎦ ⎣ ⎩ ⎫ exp[YH2 2O]erfc(YH2O)⎬ ⎭ ⎪

⎪

⎪

⎪

⎡ u 2 Q2 ⎤ ∞ HO ⎥ ∑ (2l + 1)j 2 (Qb) SHH2O(Q , ω ≈ 0) = exp⎢ − 2 l ⎢⎣ 3 ⎥⎦ l = 0 exp{[Y Hl 2O]2 }erfc(Y Hl 2O) Y Hl 2O =

π ΓT 2σ 2

YH2O =

⎞ DT Q 2 π ΓT π⎛ ⎟ ⎜ = 2 2σ 2 2σ ⎝ 1 + DTQ τres ⎠ (11)

Equation 11 contains five fitting parameters. However, within the approximation that the coherent scattering can be neglected, the amplitude factor, A, is independent of the curing time. Therefore, its value was determined from a preliminary

l π ΓT + Γ R 2σ 2

(9) 7361

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the initial decay of the elastic intensity as a function of Q. The value of the elastic fraction, p, determines the height of the elastic intensity at high Q. Finally, τres mainly affects how the transition from the low to the high Q regimes, determined by DT and p, respectively, is attained. Because of these characteristics, DT and p are inherently determined more accurately with the ENS technique compared to τres. Especially for low curing time, when the dynamics of water is fast and the decrease of the elastic intensity with Q takes place for Q ≤ 1 Å−1, an analysis of the data where water translational dynamics is described by a simple Fick law could be envisioned. It must be mentioned that eq 11 is based on a simplified model. In particular, it is likely that the water dynamics has a broad distribution of relaxation times originating from the different local environments experienced by the molecules as well as from the “glassy” behavior induced by the interaction with the CH and C−S−H.5 However, more complex models would not be justified for the analysis of ENS data. Therefore, DT and τres have to be considered averaged quantities. Moreover, it has to be kept in mind that the ENS technique, in comparison with QENS, allows for faster measurements and a simplified analysis but gives less accurate results. However, as will be shown in the following, the simplified picture adopted in this work is still able to capture the most important features of the curing process: the development of a solid matrix and the slowing down of the water dynamics. Figure 4 panel (a) shows the time dependence of p, which is proportional to the amount of hydrated phases formed. This is the main quantity used for the determination of the hydration reaction kinetics and is fundamental in predicting the evolution of the hydrated paste’s properties. In particular, the typical stages of the cement hydration process (nucleation and growth and diffusion) can be easily recognized from the evolution of p (see Figure 4, panel a). A marked increase of p signals the beginning of the acceleration period for the nucleation and growth of C−S−H and CH phases. A second sudden change in the slope of p vs tc marks the beginning of the diffusion period, where the reaction is dominated by the diffusion of water molecules through the C−S−H gel that builds around the C3S grains. The evolution of p can be analytically described by using the Boundary Nucleation and Growth Model (BNGM) as derived by Thomas42 where the rate at which the nucleated boundary area transforms, kB, and the rate at which the non-nucleated grains between the boundaries transform, kG, are the only two variables needed for the description of the hydration kinetic up to the diffusional period. At the beginning, the hydration extent is limited (p value remains close to 0) because few nuclei are present.42 kB and kG are obtained by applying the BNGM to the bound water index as extracted from ENS data 0.152 h−1 ± 0.04 h−1 and 0.135 h−1 ± 0.005 h−1, respectively. The value of kB/kG obtained of 1.14 ± 0.34 compares well with results reported for similar batches of C3S hydrated at similar w/c ratio and temperatures (i.e., 1.1−1.3), measured either by isothermal calorimetry,42 DSC,43 or QENS.15 The agreement between the present and previous findings confirms the validity of the assumption employed to obtain eq 11. The behavior of DT and τres, reported in Figure 4 panels (b) and (c), respectively, is consistent with the trend of p. At short tc, DT and τres approach values similar to those reported by Teixeira33 for bulk water at room temperature, although the diffusion coefficient is about 50% overestimated and the residence time is significantly lower. The relative large error

analysis of the high curing time data when its value (which corresponds to the elastic intensity extrapolated for Q = 0) can be obtained more accurately. Similarly, also u2SHP should not depend on tc. Its value was determined to be (u2SHP)1/2 ≈ 0.3 Å, again from the high tc data, where it determines the slope of the elastic intensity at high Q. Once these two parameters have been determined from a preliminary analysis of the data, a more accurate fitting was performed with A and u2SHP fixed. Figure 3 shows, as an example, the fit for three different curing times according to eq 11.

Figure 3. Elastic scan spectra for the C3S/H2O paste at three curing times. The dashed lines are the fits according to eq 11. Error bars represent one standard deviation.

The extracted parameters, bound water index, diffusion coefficient, residence time, and the average jump distance, are reported in Figure 4 as a function of the curing time. As mentioned before, the ENS data have been fitted effectively in terms of three parameters. DT mainly determines the slope of

Figure 4. Evolution of extracted parameters, according to eq 11: (a) bound water index, p, (b) diffusion coefficient, DT, (c) residence time, τres, (d) average jump distance, l. Error bars represent one standard deviation. In the case of panel (a) the BNGM42 has been used to fit the curve, and all other lines are guides for the eye. 7362

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CONCLUSION In this paper, we report an ENS experiment on a curing C3S/ H2O paste showing that the applied technique allows the description of the cement hydration reaction in terms of solid hydrated phases produced and dynamics behavior of the unreacted water. A detailed analytical model has been applied and validated to describe the elastic scattering signal from calcium silicate pastes during the curing process. The obtained results have been discussed in terms of current physicochemical description of the calcium silicate hydration. Water reacts with the C3S, forming amorphous C−S−H and crystalline CH. Concurrently, the water translational dynamics slows due to the increased confinement in the developing matrix (i.e., the selfdiffusion constant for the mobile water decreases by 1 order of magnitude after 2 days of curing). In particular, the water diffusion coefficient obtained from the data agrees with recent MD simulations and 1H NMR field cycling relaxation experiments, evidencing the possibility to directly access the degree of confinement in the C−S−H nanopores. The investigation of water dynamics in cement pastes using ENS cannot be as detailed as that using QENS; however, the present work shows that this method represents a valid alternative able to furnish valuable insight into the diffusive dynamics of the unreacted water molecules with faster measurements and a simplified analytical approach.

of DT at small curing times is due to the fact that water dynamics are very fast compared to the time scale corresponding to the instrumental resolution (≈250 ps). In the present case, DT decreases from about 400 ± 140 Å2/ns (4.0 × 10−9 m2/s) to 40 ± 10 Å2/ns (4.0 × 10−10 m2/s) after 2 days of curing. These results and discrepancies can be explained by considering that the mobile fraction investigated contains both the bulk water and the constrained water component evidenced by Thomas et al.2 It should be noted that this is the first time that the values of p and DT have been determined using the elastic scan method that employs an energy resolution at least 1 order of magnitude higher than what has been used in previous QENS experiments. To study the dynamics of water in C−S−H nanopores, detailed MD simulations for water (simple point charge approach) on the surface of tobermorite have been conducted by the group of Kirkpatrick.44 Although the C−S−H structure is much more disordered and complicated, tobermorite and jennite are well-accepted molecular scale models for C−S−H in the hydrated cement paste. Interestingly, the average diffusion coefficient for all surface-associated H2O molecules in such a system is about 1.0 × 10−10 m2/s, while the value of 2.3 × 10−9 m2/s is generally found in simulations of bulk water using the same force field.44 These data have been experimentally confirmed by 1H NMR field cycling relaxation experiments.45 DT values from Figure 4(b) are in good agreement with both MD44 and 1H NMR results. This agreement strongly reinforces the validity of our approach and legitimates the approximations introduced. As quantitatively shown by DSC30 and by QENS,2 water reacts in a cement paste, and the bulk-like component eventually disappears in favor of constrained water (i.e., strongly interacting with the surface and confined mainly in SGP and IGP). The evidence of an increasing surface area and the relative interacting water in the 1 month old C3S paste has been also evidenced using near-infrared spectroscopy46 by deconvoluting the 7000 cm−1 overtone band. It is important to note that DT after 2 days is 4 times greater than that reported using MD simulations for surface-associated molecules but almost 1 order of magnitude lower than for bulk water. This is not surprising since the ENS experiment probes all the hydrogen scatterings that are missing from the elastic signal, corresponding to the scattering of the mobile species, without distinguishing between water associated with the C−S−H and water confined in the nano-/micropores. An ENS experiment on a 1 month old C3S/ H2O paste is foreseen to validate the MD data. From the combination of the random jump diffusion parameters an average jump length can be also extracted: l2 = 6DTτres (see Figure 4(d)). A subtle decrease from 6 Å, at short tc, to about 4 Å, after 2 days of curing is shown. This further confirms the increase in the confinement imposed by the developing hydrate phases and porosity. The values obtained here are about four times larger than those reported by Teixeira33 for bulk water at room temperature. It cannot be excluded that this result is affected by the intrinsic limitations of the experimental method which have been discussed above. On the other hand, the higher values of the jump length obtained here could be due to the confinement imposed on the water molecules. In fact, it is known that interfacial water has a behavior similar to that of water in the supercooled state,47 and the random jump length in bulk water has been shown to increase up to a value of 2.4 Å upon supercooling water down to 253 K.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: piero.baglioni@unifi.it. Phone: +39 (055) 4573033. Fax: +39 (055) 4573032. 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 The authors thank the Institut Laue-Langevin for allocating beam-time on IN13. CTG-Italcementi is kindly acknowledged for providing the synthetic C3S batches. EF, FR, and PB acknowledge financial support from MIUR and CSGI. Research at MIT is supported by DE-FG02-90ER45429 and 2113-MITDOE-591. We also would like to acknowledge the reviewers for the very helpful revision that allowed a consistent improvement of our manuscript.

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REFERENCES

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dx.doi.org/10.1021/jp312684p | J. Phys. Chem. C 2013, 117, 7358−7364