Microstructure Determination of Calcium-Silicate-Hydrate Globules by

The basic building block of calcium-silicate-hydrate (C–S–H) gel, which is the major ... The detailed nanostructure of the globule is so far not g...
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Microstructure Determination of Calcium-Silicate-Hydrate Globules by Small-Angle Neutron Scattering Wei-Shan Chiang,† Emiliano Fratini,‡ Piero Baglioni,‡ Dazhi Liu,§ and Sow-Hsin Chen*,† †

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Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States ‡ Department of Chemistry and CSGI, University of Florence, Florence, I 50019, Italy § Spallation Neutron Source, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States ABSTRACT: The basic building block of calcium-silicate-hydrate (C−S−H) gel, which is the major hydration product of a commercial Portland cement paste, is usually referred as “globule” in the Jennings’ colloidal model-II developed for C−S−H. The detailed nanostructure of the globule is so far not given quantitatively. In this paper, we determine the structural parameters of the building block with good accuracy by small-angle neutron scattering technique probing an extended interval of the scattering vector, Q, from 0.015−1.0 Å−1. In this Q-range an interlamellar peak at 0.65−0.80 Å−1 is present, shifting as a function of the water content present in the C−S−H gel. This additional feature enables us to confirm the presence of a lamellar structure and determine the thicknesses of both the water and the hydrated calcium silicate layers respectively proper of the C−S−H globules. derived from scattering measurements9,10 and sorption isotherms experiments.8 According to Jennings’ colloidal model-II (CM-II),8 C−S−H gel present in a hydrated cement paste can be described schematically as shown in Figure 1a. This gel is consisted of

1. INTRODUCTION Cement is a synthetic material of largest production in modern society. There is more than 11 billion metric tons of cement consumed every year all over the world. However, to manufacture one ton of Portland cement clinker, approximately 0.8 tons of CO2 is emitted into the air, which contributes 5−7% of the total human-made CO2 emissions.1 The requirement of reducing cement usage therefore motivates many studies on properties of cement for the sake of a more efficient use of this material. Hydrated calcium silicate gel (CaO)x(SiO2)(H2O)y or shortly C−S−H is the main binding phase in the commercial cement pastes. Its presence is critical to the development of strength and durability of a cement paste. Studies of the microstructure of C−S−H and its effect on the cement properties are therefore essential to the optimized usage of C−S−H-based cements. In the present study, we synthesized pure C−S−H (I) gel with different equilibrium water contents and successfully characterized the microstructure of its constituent building blocks. To the best of our knowledge the method of analysis reported here is completely original. C−S−H is a gel-like material. Existing C−S−H structural models relay on two different theories. On one side, Feldman and Sereda (FS) and others2,3 considered the C−S−H gel network as formed by irregular C−S−H interconnected layers with adsorbed and interlayered water molecules. On the other side, Power and Brownyard (PB) and others4,5 supposed the existence of basic C−S−H units, which generate the C−S−H gel structure as a colloid made of small bricks and its associate gel pores. Subsequently, Jennings6−8 combined the FS and PB hypothesis and obtained a hybrid model able to give an exhaustive interpretation of several experimental evidence such as those © 2012 American Chemical Society

Figure 1. (a) Jennings’ colloidal model-II, CM-II. The C−S−H gel has a fractal structure with a fractal dimension, D, and a cutoff length, ξ. (b) Structure of the basic building block of the C−S−H gel, i.e. the globule. R is the disk radius, θ is the angle between the wave vector Q⃗ and the rotation axis of the globule, L1 and L2 are the layer thickness of hydration water and hydrated calcium silicate, respectively, and ρ1 and ρ2 are their corresponding scattering length densities (slds). ρs is the solvent sld. t is the total thickness of the globule.

assemblies of hydrated globules immersed in aqueous solvent or air depending on the equilibrium water content. In this context, Received: January 23, 2012 Published: January 31, 2012 5055

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both intra- and inter-C−S−H pores and proposed an alternative microstructure of C−S−H gel without assuming a finite building block. They suggested that the C−S−H intralayer distance is about 15 Å, while the inter-C−S−H porosity is around 41 Å thick. Although all these studies indicate a characteristic intralayer lengthscale of 10−15 Å, a direct link between this length-scale and the globule proposed in CM-II is still missing. In this paper, we assume the globule to be a multilamellar object with unknown total thickness t and radius R as depicted in Figure 1b. The globule has a layered substructure where water and calcium silicate layers are alternatively repeated. The present approach is so general that changing the two descriptive parameters t and R takes into account disks-like objects (t ≪ 2R), spheroidal geometries (t = 2R) and even rod-like symmetries (t ≫ 2R). In the following discussion, we denote L as the interlayer distance of the substructure. L can be decomposed into one layer of water with thickness L1 and one layer of calcium silicate with thickness L2 and therefore L = L1 + L2. The resultant unknown total thickness of the globule can then be calculated as t = n̅L, where n̅ is the average number of layers in one globule derived from our model fitting. To the best of our knowledge, this model is the only one that can successfully describe the internal structure of the globule itself and to justify SANS intensity distributions from low-Q region up to 1 Å−1. Our model differs from the results of Dolado et al.17 and McDonald et al.,18 which do not consider in an explicit way the existence of a primary building block for the C−S−H gel structure.

the globules are multilamellar objects with an average thickness of about 4.2 nm. Inside the globules, water can be located in both the interlayer spaces and the very small cavities, called intraglobular pores (IGP), with dimensions around 1 nm. These building blocks pack together to form a porous structure with two main classes of pores: the small gel pores (SGP) with dimension of 1−3 nm and large gel pores (LGP) with size in the range from 3 to 12 nm. Greater pores are usually referred as capillary pores. Neutron scattering technique has been extensively used on cement pastes to investigate the structure of the developing C−S−H gel9−11 and to access the dynamics of the water confined in the gel porosity.12−14 In particular, Allen and co-workers9 used small angle neutron scattering (SANS) technique to study the developing gel structure during the hydration process in ordinary portland cement (OPC). Their results suggested that C−S−H gel is formed by discrete globules with 5 nm diameter which further aggregate together to give a scale-invariant structure with correlation lengths up to about 40 nm. Based on this scenario, their analytical model comprises an interglobule structure factor, S(Q), describing the fractal nature of clustering with a mass fractal dimension D of about 2.6 and an intraglobule structure factor, P(Q), representing an “effective” spherical shape with a diameter of about 5 nm. This picture turns out to be consistent with their SANS and small angle X-ray scattering (SAXS) results.9,10 However, since they only explored the Q-range up to about 0.2 Å−1, where Q is the magnitude of scattering wave vector, their highest Q was not enough to explore the details of the globule and therefore its internal structure is still uncertain. Very recently, Pellenq and co-workers15 proposed a molecular model of C−S−H based on a bottom-up atomistic simulation. Starting from a dry orthorhombic tobermorite lattice with a 11 Å interlayer spacing and using grand canonical Monte Carlo (GCMC) technique, they obtained a model in which water is present both in the interlayer space and in the intralayer cavities inside the calcium oxide layers. This model with calcium/silicon ratio (C/S) = 1.65 results in an interlayer spacing ranging from 11.3 to 11.9 Å and C−S−H density of 2.56 g/cm3, a value close to the experimental result of 2.6 g/cm3 found by Allen et al.10 for a very similar C/S ratio = 1.7. Dolado et al.16,17 simulated the formation of C−S−H structures through the polymerization of Si(OH)4 species which were allowed to react in the presence of solvated calcium ions. This approach is very general and is not based on any preimposed structural model. Their main results16 show that at low C/S ratios, the simulated C−S−H systems resemble mixtures of 1.1, 1.4-nm tobermorite and jennite structures with pentamers or longer chains, while at high C/S ratios, only short 1.4 nm tobermorite and jennite pieces seem to be formed. Intermediate C/S ratios gradually evolve from long to short chains, and from tobermorite- to jennite-like features. Notably, their recent MD simulations17 suggest that C−S−H gel forms a three-dimensional branched structure as a result of interweaving and restructuring processes of growing C−S−H segmental branches (SB). Moreover, they showed that the scattering and diffraction patterns calculated from SB structures are in good agreement with both SANS data, measured by Allen et al.10 for Q > 0.05 Å−1, and recent X-ray Diffraction (XRD) investigations,1 which give evidence for a peak at Q ∼ 0.5 Å−1 linked to d-spacing in the calcium silicate layers of about 12 Å. Skinner et al.1 used XRD method to show that the synthetic C−S−H is nanocrystalline with a characteristic nanograin size of about 3.5 nm and disclosed a remarkable resemblance of synthetic C−S−H structure with 11 Å tobermorite. McDonald et al.18 analyzed NMR data of white cement pastes considering water in

2. EXPERIMENTAL METHODS Synthetic C−S−H was prepared by hydrating pure C3S in an excess of water. A chemically pure batch of tricalcium silicate was obtained from CTG-Italcementi (Bergamo, Italy) as a gift. The specific surface area detected by N2 sorption isotherms (BET) and mean radius of the C3S used in the present study resulted in 0.65 m2/g and 4.66 μm, respectively. Several C−S− H batches were prepared by mixing 4 g of C3S with 1150 g of distilled water. The water was previously boiled and kept sealed to avoid any subsequent carbonation, taking place during the C3S hydration reaction. The excess of water in respect of C3S was essential to prevent any portlandite (Ca(OH) 2 ) coprecipitation, without altering the C−S−H formation. The resulting C3S/water dispersions were sealed in plastic bottles to avoid carbonation and continuously stirred for at least 40 days. The synthesis was conducted at room temperature (i.e., 25 °C). This synthetic route is known to minimize the Ca(OH)2 content while forming quite polydisperse C−S−H phase, which is usually refereed as C−S−H (I).19 The dispersion was filtered under a N2 atmosphere to avoid carbonation and the obtained solid was dried in an oven at 60 °C for three hours. The resulting C−S−H gel was dried to the desired water content using a vacuum oven operating at temperatures below 100 °C. This maximum working temperature allows water to evaporate without causing structural damages. Energy-dispersive X-ray spectroscopy (EDX) evidenced an average Ca/ Si ratio of 1.5 with a standard deviation of about 0.3 confirming the expected inhomogeneity of the sample. EDX spectra were recorded using a X-sight Oxford-Cambridge microprobe coupled with a SEM microscope. Thermo Gravimetric Analysis was performed both to determine the effective hydration of the so-prepared C−S−H gels and to confirm a low carbonation level. Final water content was obtained considering the weight lost up to 200 °C and was normalized only to the amount of 5056

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The model for the internal structure of the globule having layered substructure is depicted in Figure 1(b). Although Jennings’ model does not assign a specific shape to the globules, we analyze SANS data assuming a general form factor for the basic units constituting the gel, where the aspect ratio can vary from cylinders to disks passing through spheroidal objects. In Figure 1(b), R is the disk radius, θ is the angle between the wave vector ⇀ Q and the globule rotation axis, L1 and L2 are layer thickness of hydration water and hydrated calcium silicate, respectively, and ρ1 and ρ2 are their corresponding scattering length densities (slds). ρs is the solvent sld. For C−S−H gel with 10% and 17% water content, the small gel pores (SGPs) are empty so that ρs should be close to the air sld while for 30% hydrated C−S−H gel, the SGPs are almost filled by water so ρs should be close to the bulk water sld. We therefore use two different fitting sld contrast ratios (ρ1 − ρs)/ (ρ2 − ρs), one for 10% and 17% cases and the other for 30% case, during the fitting process. Finally, n represents the number of repeating layers inside a globule. To reduce the fitting parameters, we assume here that the globule has the same radius R and the hydrated calcium silicate layer has the same thickness L2 for all the three investigated C−S−H gels. The interlayer distance, L, therefore only changes with the water layer thickness, L1. The assumption is reasonable since the C−S−H gels are prepared by drying the same product into different water contents and the calcium silicate dimensions (R and L2) should be fixed while only water contents can be changed. It is important to note that different combinations of R, L, and n can change the overall aspect ratio of the globule from a cylinder-like to disk-like object. In this regard, the presented model of particle structure factor includes both of these cases naturally. We define the normalized particle form factor as F(Q,μ) = (1/ρ̅Vp)∫ Vp ρ̅(r)⃗ exp(iQ⃗ ·r)⃗ d3r, where μ = cos θ, ρ̅ is the average scattering length density of the globule, and Vp is the volume of the globule. Our newly derived normalized particle structure factor P(Q,μ) is given by

C−S−H present in the sample, while Ca(OH)2 and CaCO3 contributes were calculated according to the literature20 and subtracted out from the original weight of the sample. The percentages of Ca(OH)2 and CaCO3 were always in the range 5−10% in respect of the total mass of the samples. Thermogravimetric experiments were carried out with a SDT Q600 apparatus (TA Instruments) heating the sample at 10 °C/min from 25 to 1000 °C under a constant flux of pure N2 (100 mL/min). 10%, 17%, and 30% water content cases were achieved at the end of the drying process. SANS experiments were carried out at the Spallation Neutron Source (SNS) at Oak Ridge National Laboratory (ORNL), using the extended Q-range small-angle neutron scattering (EQ-SANS) diffractometer. We used two neutron wavelength bands simultaneously, 2.20−6.50 Å and 9.14−15.11 Å, and a sample-to-detector distance of 1.2 m to obtain the wild Q-range of 0.015−1.3 Å−1. Scattered neutrons were recorded by a two-dimensional position-sensitive detector. Samples were loaded into titanium demountable cells with quartz windows and a 1 mm spacer (i.e., sample thickness). The experiment was conducted at 25 °C and the temperature was maintained by a control system with an accuracy of about 1 °C. The raw data were then corrected for detector sensitivity, sample absorption, empty cell scattering, and then normalized by the incident beam flux and the sample volume and transmission factor to obtain the absolute intensity I(Q)in cm−1. The dQ/Q in EQSANS is about 0.03 at the peak position Q0 = 0.65−0.80 Å−1,21 so for the first approximation, we do not consider the Q resolution effect in this paper.

3. ANALYTICAL FORM OF THE SANS MODEL The C−S−H gel can be pictured as shown in Figure 1a. The gel is consisted of globules packing into a fractal-like object, which is immersed in an aqueous solution or air depending on the water content. The self-similar fractal structure with a fractal dimension D only extends to a maximum cutoff dimension of ξ. Denoting the number density of the globule in the C−S−H gel as Np and the equivalent spherical radius of the globule as Re, the effective pair correlation function of the fractal structure can be written as22−24 g (r ) =

P(Q , μ) = |F(Q , μ)|2 ⎡ ⎤2 2J1(QR 1 − μ2 ) ⎥ 2 2 ⎢ 2 =⎢ ⎥ C (A + B ) 2 ⎣ QR 1 − μ ⎦

where

⎛ r⎞ D 1 D−3 r exp⎜ − ⎟ D 4πNp R e ⎝ ξ⎠

( Q μL )

⎛ Q μ(nL − L 2) ⎞ sin 2 A = (ρ1 − ρs) cos⎜ ⎟ ⎝ ⎠ 2 Qμ

Therefore, we can derive the interglobule structure factor of the porous C−S−H gel as S(Q ) =1 + Np =1 +

∫0

∞

sin(Qr ) r2

dr 4π

Qr

D

(QR e)

1

( Q μL ) 2

⎛ Q μ(nL + L1) ⎞ sin 2 + (ρ2 − ρs) cos⎜ ⎟ ⎝ ⎠ Qμ 2

g (r )

D Γ(D − 1) sin[(D − 1) tan−1(Q ξ)]

1

(2)

( Q μL )

[1 + (Q ξ)−2 ][(D − 1)/2]

⎛ Q μ(nL − L 2) ⎞ sin 2 B = (ρ1 − ρs) sin⎜ ⎟ ⎝ ⎠ 2 Qμ

⎛ ξ ⎞D sin[(D − 1) tan−1(Q ξ)] =1 + ⎜ ⎟ Γ(D + 1) ⎝ Re ⎠ (D − 1)[1 + (Q ξ)2 ][(D − 1)/2](Q ξ)

1

( Q μL )

⎛ Q μ(nL + L1) ⎞ sin 2 + (ρ2 − ρs) sin⎜ ⎟ ⎝ ⎠ Qμ 2

(1)

In eq 1, Γ(x) is the gamma function. The value of S(Q) at Q = 0 limit is given by limQ→0 S(Q) = 1 + Γ (D + 1)(ξ/Re)D, which becomes Q-independent and flat with the magnitude proportional to the Dth power of ξ/Re. This low-Q limit can be used to determine the magnitude of ξ. In this paper, we use the value of ξ = 670 Å obtained by Allen et al.10 determined from their low-Q data.

2

( Q μnL ) (2)

sin 2 2 C= n[(ρ1 − ρs)L1 + (ρ2 − ρs)L 2] sin Q μL 5057

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The particle structure factor P(Q,μ) of the object shown in Figure 1b must then be averaged over all possible directions of globule axis relative to the scattering vector ⇀ Q , i.e., ⟨P(Q)⟩orientation = ∫ 01 P(Q,μ) dμ. It can be shown that the derived particle structure factor satisfies the normalization condition ⟨P(Q)⟩orientation →1 at Q = 0. The number of layers n, the cylindrical globule radius R, and the interlamellar distance L should in general have their own distributions. These will further smooth the function ⟨P(Q)⟩orientation. Here we only introduce an “effective” distribution for the number of layers to take into account all the possible distributions of n, R, and L. It is straightforward to show that a polydispersity on L has similar effect with the one on n. In this regard, the polydispersity on n is defined to be effective because if polydispersities are present even on R and L these will be included in that of n. We assume the effective polydispersity as a Schultz distribution ⎛ Z + 1⎞ ⎜ ⎟ ⎝ n̅ ⎠ Z > −1

fS (n) =

Figure 2. Absolute intensity I(Q) versus Q for C−S−H at three different water contents: 10% (black square), 17% (red circle), and 30% (blue triangle) at 25 °C. The inset shows the enlargement of the peak arising from the interlamellar distance of the globule. The error bars throughout the text represent one standard deviation.

z+1

⎡ ⎛ Z + 1⎞ ⎤ ⎟n / Γ(Z + 1) n z exp⎢ −⎜ ⎥ ⎣ ⎝ n̅ ⎠ ⎦ (3)

plotted in log−log scale, suggesting that the globules pack together to form a fractal object. At high-Q region, there is a diffraction peak associated with the interlayer distance within the globule itself. The inset in Figure 2 displays an enlargement of SANS curves in the peak region. It is clear that on increasing the water content, the high-Q peak shifts to a lower Q position, which corresponds to a larger interlayer distance. The peak width at water contents of 10% and 17% is much broader and less defined than the 30% case. This suggests fewer repeating units (i.e., smaller n)̅ for lower WC cases. The flat incoherent background level reflects the total amount of water confined in the C−S−H gel. Figure 3 shows the fitting results of C−S−H samples at water content of (a) 10%, (b) 17%, and (c) 30% measured at 25 °C. Our model agrees with the data over the entire Q-range from 0.02 to 1.00 Å−1 (see the upper left panel). The fitted parameters for all the investigated samples are listed in Table 1. When conducting the fitting process, the parameter ξ was taken from result of Allen et al.10 and kept fixed to ξ = 670 Å. This approximation is reasonable for two reasons. First, the Q range we covered in the present experiment is not small enough (i.e., lowest Q measured is only 0.01 Å−1) to allow us for a precise estimation of ξ. Second, slightly changing ξ during the fitting process does not affect the fitting results of other parameters significantly. An ultra SANS experiment is required to unambiguously determine ξ. Re in our S(Q) is not a fitting parameter but is mathematically calculated by 2 1/3 Re = (3nR ̅ L/4) , taking into account the parameters extracted from the globule geometry. Our results show that as the water content passes from 10% to 30%, the interlayer distance increases as clearly shown by the shift of the peak positions in the inset of Figure 2. Interestingly, Yu and Kirkpatrick25 showed by thermal analysis and XRD experiments that upon heating, water could be lost by tobermorite in steps that corresponded to decreases in layer spacing from 14 to 12, 11, and 9.6 Å. Only two of these cases can be compared with the present results (L ≈ 9 Å for 10% and 17% and L ≈ 11 Å for 30%). It is worth to note that an interlayer spacing of 12 Å is a value typical of the basal spacing for semicrystalline C−S−H often observed in many synthetic C−S−H preparations1 and in particular when C−S−H (I) is the prominent phase.26 Our globally fitted calcium silicate thickness L2 is 3.5 Å, which is close to GCMC simulation results as reported by Pellenq et al. Their molecular model was shown to be

where n̅ is the mean of the distribution,Z is a width parameter, and Γ(x) is the gamma function. The standard deviation of the distribution can be calculated by σn = (n2 − n2)1/2 = n/(Z + 1)1/2. ̅ Therefore, the orientationally averaged globule particle structure factor is then further averaged over the effective number of layer distribution, i.e., ⟨P(Q)⟩ orientation,n = ∫ 0∞ ⟨P(Q,n)⟩orientation fs(n) dn As a result, the measured SANS intensity distribution in the unit of cm−1 can be expressed as I(Q ) = Np{n πR2[(ρ1 − ρs)L1 + (ρ2 − ρs)L 2]}2 ⟨P(Q )⟩orientation, n S(Q ) + bg

[1/cm]

(4)

From the discussion above, in principle we have unknown fitting parameters in the final form of SANS intensity distribution listed as: an overall prefactor which accounts for the number density of the scattering objects; six parameters contained in ⟨P(Q)⟩orientation,n: interlamellar distance L, calcium silicate layer thickness L2 (assume to be the same for all three investigated cases), average number of layers n̅ in the globule, the width parameter Z of Schultz distribution, sld contrast ratio parameter (ρ1 − ρs)/(ρ2 − ρs) (assume that 10% and 17% cases have the same value which is different from the value of 30% case), disk radius of the globule R; two additional parameters coming from S(Q): the cutoff length ξ and the fractal dimension D. A flat background bg due to the incoherent scattering of hydrogen atoms in the sample is also added. The 2 1/3 equivalent radius Re can be calculated as Re = (3nR ̅ L/4) .

4. RESULTS AND DISCUSSION Our goal in this paper is to determine the effect of the equilibrium water content (WC) on the geometrical parameters (interlayer distance L, average number of layers n̅, and radiusR of the basic unit, i.e. globule) of the C−S−H gel with good accuracy using eq 1-4 derived above. While reducing the water content, the gel passes from a situation where the small gel pores are partially filled (30%) to a situation where only one monolayer of water is present on the C−S−H gel (10%). Figure 2 shows the absolute intensity of C−S−H with three distinct water contents of 10%, 17%, and 30% at 25 °C. The low-Q region in all the three cases is a straight line when 5058

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Figure 3. Model fitting results of C−S−H gel at water content (a) 10% (b) 17% and (c) 30% at 25 °C. The upper left panel shows the absolute intensity of the data (green circle) and its corresponding fitted curve (red line), the upper right panel shows the effective Schultz distribution of the number of layers in the globules, the lower left panel shows the structure factor S(Q) of the fractal structure, and the lower right panel shows the particle structure factor of the globule ⟨P(Q)⟩orientation,n. The error bars of the experimental data in upper left panels represent one standard deviation and are smaller than the circle. The fitted parameters used here are listed in Table 1.

The interlayer distance L and the average number of layers n̅ in 10% and 17% cases do not change too much. However, when increasing the water content from 17% to 30%, the globule geometrical parameters L, n,̅ and σn (standard deviation of the number of layers) all increase significantly and the corresponding “equivalent” radius, Re, increases from 67 to

mechanically stable during the course of long molecular dynamics (MD) simulations performed by Youssef et al.,27 where the calcium silicate layer thickness resulted in the range 3.3−3.9 Å.15,27 With L2 being 3.5 Å, the associated water thickness can be calculated by L1 = L − L2, and results in 5.5, 5.8, and 7.9 Å for 10%, 17%, and 30% cases, respectively. 5059

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Table 1. Parameters Extracted from the Model Fitting for Samples Measured at 25 °Ca water content

interlayer distance, L (Å)

water layer thickness, L1 (Å)b

fractal dimension, D

average number of layers, n̅

standard deviation, σnc

equivalent globule radius, Re (Å)d

10% 17% 30%

8.98 ± 0.01 9.29 ± 0.01 11.33 ± 0.01

5.51 ± 0.04 5.82 ± 0.04 7.86 ± 0.04

2.75 ± 0.003 2.69 ± 0.004 2.58 ± 0.01

4.53 ± 0.02 4.73 ± 0.02 10.86 ± 0.25

2.2 2.1 10.2

65.7 ± 0.1 67.4 ± 0.1 95.0 ± 0.7

a During the fitting process, ξ is fixed as 670 Å .10Scattering length density (sld) contrast ratio (ρ1 − ρs)/(ρ2 − ρs) is fitted as −0.170 ± 0.004 for 10% and 17% hydrated C−S−H gel, assuming the small gel pores (SGPs) are filled by air and as −0.043 ± 0.003 for 30% hydrated C−S−H gel, assuming the SGPs are filled by water. The error bars shown in the table is one standard deviation from the nonlinear least-squares fitting process. bL1 is calculated by L1 = L − L2, where calcium silicate thickness L2 is globally fitted as 3.47 ± 0.04 Å cσn is calculate by σn = (n2 − n2)1/2 = n̅/(Z + 1)1/2, 2 1/3 where Z is an individually fitted width parameter of Schultz distribution. dRe is calculated by Re = (3nR ̅ L/4) , where disk radius R is globally fitted as 96.3 ± 0.1 Å

water layer with thickness of 7.9 Å and calcium silicate layer with thickness of 3.5 Å. The lamellar “face” has a dimension of 2R = 190 Å. The globules have an effective size dispersion described by the Schultz distribution shown in the upper right panel in Figure 3c. When decreasing the water content from 30% to 17%, interlayer distance of the globules becomes smaller (see Table 1) because of the decrease of the water layer thickness. Using the globally fitted calcium silicate thickness for all three cases (3.5 Å), the water layer thickness decreases significantly from 7.9 Å for 30% case to 5.8 Å for 17% case. In addition, the average number of layers of the globule n̅ and its standard deviation σn decrease substantially when changing from 30% to 17% case. This suggests that during drying, the globules tend to decompose or agglomerate (corresponding to those highly populated small n ≈ 2 globules in 30% case, see upper right panel of Figure 3c) themselves into a more uniform size from the initially prepared higher WC gel, which has large size dispersion. The more uniform size of the globules in low water contents, i.e., 10% and 17%, enables the globules to pack into a more compact structure, indicated by their larger fractal dimensions (D = 2.75 for 10% and 2.69 for 17%) compared with the 30% case (D = 2.58). Further drying from 17% to 10% would not change too much the shape parameters of globules since the size becomes rather uniform at low WC. Although the globular sizes obtained here differ from what found in other references,6−9 it should be pointed out that the globule morphologies are very likely depending on the ways of preparing samples. In this regard, we decided to prepare C−S−H gel using a high w/c ratio to minimize and possibly avoid Portlandite formation, whose presence could result in a misleading interpretation of the SANS curves. In addition, as far as we know, this is the first time in the literature that synthetic C−S−H (I) instead of C−S−H embedded in cement is studied by SANS. Therefore, variations could be expected. The proposed approach provides a direct way, other than indirect methods such as N2 sorption isotherms8 and NMR,18 to evaluate the C−S−H globule geometrical parameters. To the best of our knowledge this is also the first time that so many parameters L, L2, R, n,̅ and σn of the C−S−H globule have been obtained from SANS data analysis. It is of fundamental importance to stress that the present results do not preclude the possibility for the real C−S−H to be a continuous extension of branched and interconnected multilamellar sheets where the basic units would be the smallest inhomogeneity (with a disk-like symmetry) present in the sample and the fractal dimension along with the correlation length would describe how these inhomogeneities are arranged in the volume. This assessment would reconcile the present model (and consequently the CM-II) with what has been

95 Å. Even for the low water content cases of 10% and 17%, the equivalent globule radius (about 65 Å) is more than twice of the sphere radius (about 25 Å) given by Allen et al.,9 where their SANS analysis was simply based on a spherical form factor of the C−S−H globule. The total thickness of the basic unit (t = nL) ̅ results in 40.7, 43.9, and 123.0 Å for 10%, 17%, and 30% cases, respectively. The 10% and 17% samples have globule thickness t close to what was expected in the CM-II (= 42 Å)8 while 30% case has t far from 42 Å. However, considering more closely the f S(n) distribution shown in the upper right panel of Figure 3c, we find that its maximum is located at n ≈ 2. This clearly indicates that 30% hydrated C−S−H gel is dominated by globules with thickness nL ≈ 22.7 Å. Our fitting results also show that decreasing the water content from 30% to 10% will cause an increase in the mass fractal dimension D from 2.58 to 2.75. Therefore, low WC C−S−H gel presents less open structure than high WC C−S−H gel as a result of the shrinking imposed by the dehydration process. Similar values of D were reported by Allen et al.10 in 28-days cured cements and also by some of the authors of the present paper even in younger C3S pastes.11 Based on our fitting results, the microstructure of the 30% case can be described as in Figure 4. C−S−H globules are

Figure 4. Illustration of C−S−H globule microstructure at water content of 30%. The average number of layers n̅ = 10.9, the standard deviation σn = 10.2, the disk radius R = 95.0 Å, and the interlayer distance L = 11.3 Å with water layer thickness L1 = 7.9 Å and calcium silicate layer thickness L2 = 3.5 Å. The number of layers follows a Schultz distribution as shown in the upper right panel in Figure 3c. The globules are indeed disk-like objects.

indeed disk-like objects made up of repeating lamellae with thickness of about 11 Å. The lamellar structure is composed of 5060

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recently proposed by McDonald et al.18 and Dolado et al.16,17 without decreasing the importance of the present approach which actually allows us to disclose in a direct way the intralayer spacing, inhomogeneity dimension, and related polydispersity and moreover to characterize how these entities and the overall C−S−H fractal structure would respond to different environmental stimuli (hydration degree, temperature, concentration of additive, etc.). Dolado et al.17 have demonstrated that the simulated SANS curve corresponding to their branched structure also shows a mass fractal regime in low-Q part and their simulated XRD result shows a well-defined peak at 0.55 Å−1 corresponding to a d-spacing of about 12 Å. These features are both present in our extended Q-range SANS curves and therefore we do not exclude a three-dimensional branched structure. In addition, their MD simulation results17 indicate Segmental Branches (SB) with size of 30*30*60 Å3 while our results indicate a larger building block with averaged size of about 200 (diameter)*200 (diameter)*40 (total thickness) Å3 for 10% and 17% cases and of 200*200*120 Å3 for 30% sample. Our much larger sized building blocks suggest that a more continuous C−S−H structure with planar pores as proposed by McDonald et al.18 can also explains the whole picture. However, we chose the Jennings’ description to model our SANS intensity distributions due to its “feasibility” to write down an analytical form factor where we could explicitly include the interlayer spacing. Calcium silicate layer is assumed to have the same thickness L2 for all the investigated samples. Further experiments such as contrast variation by SANS and SAXS measurements are necessary to highlight possible changes of L2 with water content and to confirm this assumption. In addition, by extending the measurement down to 0.001 Å−1, where P(Q) approaches to unity (see lower-right panel in Figure 3), we should be able to accurately determine the parameter ξ.

ACKNOWLEDGMENTS We greatly appreciate the technical assistant of the instrument scientists, J. K. Zhao and W. Heller and the scientific associate, Dr. C. Y. Gao of EQ-SANS at Spallation Neutron Source, Oak Ridge National Laboratory during the measurements. This research is supported by DOE grant number DE-FG0290ER45429. E.F. and P.B. gratefully acknowledge Ministero dell’Istruzione, Università e della Ricerca Scientifica (MIUR, grant PRIN-2008, prot. 20087K9A2J), Consorzio Interuniversitario per lo Sviluppo dei Sistemi a Grande Interfase (CSGI). CTG-Italcementi is kindly acknowledged for providing the synthetic C3S batch.

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REFERENCES

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5. CONCLUSIONS We have synthesized a series of pure C−S−H (I) gels with three different water contents. Small-angle neutron scattering analysis indicates that C−S−H gel is more likely to be consisted of globules, whose dimensions are dependent on the total water content. We are able to determine that the globules are basically disk-like objects with alternating water (thickness L1, strongly affected by the water content) and calcium silicate (thickness L2) layers. The globules are packed in a fractal structure with a cutoff size of 670 Å given by Allen et al.10 and a fractal dimension of D from 2.75 for 10% WC case to 2.58 for 30% WC case. Our main contribution in this paper is to derive explicitly an analytical model for the intraglobule structure factor ⟨P(Q)⟩orientation,n and determine all the parameters in the model experimentally. We expect that in the near future this formalism can be used for analyzing SANS and SAXS data for different preparation of C−S−H gels and cement pastes to correlate the microstructure with the gel property changes. This study thus helps to fine-tune this ubiquitous construction material using a bottom-up approach.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest. 5061

dx.doi.org/10.1021/jp300745g | J. Phys. Chem. C 2012, 116, 5055−5061