Hydrated Layer Formation on Tricalcium and Dicalcium Silicate Surfaces

the rate of hydration in controlled conditions and numerical simulation of the growth of C-S-H on a ... control the layer formation during the first k...
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Langmuir 2001, 17, 8131-8138

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Hydrated Layer Formation on Tricalcium and Dicalcium Silicate Surfaces: Experimental Study and Numerical Simulations Sandrine Garrault* and Andre´ Nonat LRRS, UMR CNRS-Universite´ de Bourgogne 5613, Faculte´ des Sciences Mirande, BP 47870, 21078 Dijon Cedex, France Received July 30, 2001. In Final Form: September 28, 2001 In this paper, an original approach is used to study the calcium silicate hydrate (C-S-H) layer formation on the surface of grains of anhydrous silicate during tricalcium and dicalcium silicate hydration from the variation of the rate of hydration with lime concentration. The effects of C-S-H nucleation and growth on the curves for the degree of reaction against time have been separated in both experimental study of the rate of hydration in controlled conditions and numerical simulation of the growth of C-S-H on a surface from a particle aggregation model. The influence of the number of nuclei and of the different growth modes has been quantified.

Introduction Portland cement is a mixture of solid phases which all react with water.1 Tricalcium silicate (Ca3SiO5) and dicalcium silicate (Ca2SiO4) are its main components and are often used in model systems to study cement hydration.2 It is generally recognized that setting and hardening of cement are due to the formation of a calcium silicate hydrate generally known as C-S-H at contact points between cement particles.3-5 C-S-H formation takes place during Ca3SiO5 and Ca2SiO4 hydration by a dissolution-precipitation process.6,7 The aim of this work is to elucidate the kinetics of C-S-H formation during the early stage of hydration. So, to be able to control all the parameters we chose to work with pure calcium silicate phases and in diluted suspensions. Indeed, a perfect continuity of phenomena from the paste to more diluted suspensions has been demonstrated in the case of early hydration of pure calcium silicate phases;8 this is not absolutely true for actual cement containing alkalies. Moreover, during a paste hydration, the Ca(OH)2 (lime) concentration varies due to the difference of stoichiometry (Ca/Si) between anhydrous phases and hydrated ones and due to the simultaneous precipitation of portlandite (Ca(OH)2). We developed an experimental procedure allowing the lime concentration in diluted suspensions to be kept constant. Each experiment is then representative of what happens at a given instant (a given concentration) during the paste hydration. The rate of C-S-H formation follows a dissymmetric sigmoid law (see Figure 1). This is due to the fact that (1) Taylor, H. F. W. Cement Chemistry, 2nd ed.; Thomas Telford: London, 1997. (2) RILEM Committee 68-MMH, Task Group 3 Rev. Mate´ r. Constr. 1977, 102 (17), 457-468. (3) Nonat, A.; Mutin, J. C. Proceedings of the international RILEM Worshop on Hydration and Setting, July 1991; Nonat, A., Mutin, J. C., Eds.; E & FN SPON: London, 1992; pp 171-191. (4) Jiang, S. P.; Mutin, J. C.; Nonat, A. Cem. Concr. Res. 1995, 25 (4), 779. (5) Jiang, S. P.; Mutin, J. C.; Nonat, A. Cem. Concr. Res. 1995, 26 (3), 491-500. (6) Barret, P.; Bertrandie, D. J. Chim. Phys. 1986, 765-775. (7) Barret, P.; Me´ne´trier, D.; Bertrandie, D. Cem. Concr. Res. 1983, 13, 725-738. (8) Damidot, D.; Nonat, A.; Barret, P. J. Am. Ceram. Soc. 1990, 73 (11), 3319-3322.

Figure 1. Variation of the kinetics of hydration of tricalcium silicate against time for two different calcium hydroxide concentrations.

C-S-H grows at the solid-solution interface and gradually forms a diffusion barrier around the anhydrous calcium silicate grains. The significant slowing down of the reaction corresponding to region II (Figure 1, second kinetics stage) is usually attributed to the existence of a continuous hydrated layer which limits the progress of the reaction for reaction degrees less than 50% depending on the size of the initial calcium silicate grains. Nevertheless, the mechanism of hydrate growing at the grainsolution interface is not well understood. In particular, it would be interesting to determine the parameters which control the layer formation during the first kinetics stage. The kinetics of hydration vary with lime concentration in solution as shown in Figure 1.8 For a low lime concentration, the percentage of hydration does not exceed 10% and no initial period is observed in the evolution curve. On the contrary, for a larger lime concentration we observe an initial transient before the increasing formation of C-S-H and a final saturation to a quite large percentage of hydration of the calcium silicate grain. The C-S-H formation occurs via an heterogeneous nucleation process, whose characteristics vary with lime concentration;9the C-S-H precipitation occurs in the 5 (9) Garrault-Gauffinet, S.; Nonat, A. J. Cryst. Growth 1999, 200, 565-574.

10.1021/la011201z CCC: $20.00 © 2001 American Chemical Society Published on Web 11/30/2001

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Figure 2. Variation of the silica concentrations against time during Ca3SiO5 hydration in two different lime solutions. On the right figure are represented the solubility curve of C-S-H and the maximum supersaturation curve of C-S-H on the Ca(OH)2SiO2 diagram. The evolution of the composition of solution is given for Ca3SiO5 hydration at 11 mmol/L in Ca(OH)2.

min after suspending calcium silicate in water (Figure 2). All the curves [SiO2] ) f(t) show a rise corresponding to the pure dissolution of Ca3SiO5 or Ca2SiO4 according to the reactions7,10

Ca3SiO5 + 3H2O f 3Ca2+ + 4OH- + H2SiO42- (1) Ca2SiO4 + 2H2O f 2Ca2+ + 2OH- + H2SiO42- (2) until the system reaches the maximum of supersaturation with respect to C-S-H (Ca3SiO5 solubility is never reached, but in some cases the Ca2SiO4 solubility can be reached6), which precipitates according to

C/S Ca2+ + 2(C/S - 1) OH- + H2SiO42- f CaOC/S-SiO2-H2O (3) where the C/S is the CaO/SiO2 ratio of the C-S-H formed (C/S < 2). The decrease corresponds to the fast precipitation of nuclei. The number of initial C-S-H nuclei depends on the decrease in silicate concentrations. This number of nuclei increases when the lime concentration decreases. The nuclei grow on the anhydrous silicate surface to form the diffusion layer when the different islets of growth coalesce. On the other hand, atomic force microscopy (AFM) observations performed on flat surface of Ca3SiO5 underscored that C-S-H growth proceeds by oriented threedimensional aggregation of nanometric thin elements.11 Unfortunately, it is not practicable to monitor the lime concentration in solution in AFM. The influence of lime concentration on growth rates cannot be resolved using the microscopic technique. However, it appears of a crucial importance in the control of hydration rate. So, the aim of this work is to quantify the growth rate of C-S-H (10) Barret, P.; Bertrandie, D. J. Am. Ceram. Soc. 1990, 73 (11), 3486-3492. (11) Gauffinet, S., Finot, E., Lesniewska, E.; Nonat, A. C. R. Acad. Sci. Ser. IIa: Sci. Terre Plane` tes 1998, 327, 231-236.

parallel and perpendicular to the surface of anhydrous calcium silicates at different lime concentrations in solution. To understand this important issue, we have performed an experimental study of the rate of hydration under controlled conditions. The experimental data have been compared with results obtained by numerical simulations. The numerical approach is based on a particle-aggregation model as suggested by the AFM observations. This comparative study allows assessment of the role of the different parameters such as the initial number of nuclei and the growth mode of these nuclei. Experimental Section Materials. Dicalcium silicate and tricalcium silicate are supplied by Lafarge LCR, and both contained less than 0.2% free lime. The two solids were ground, and their granulometric distributions are centered around 10 and 15 µm, respectively. Hydration Solutions. During the hydration of calcium silicates in normal conditions, the solution is mainly a calcium hydroxide solution: the silica concentration varies between 10-4 and 10-5 mol/L, while the calcium concentration varies between 10-2 and 3.5 × 10-2 mol/L. It may be then under- or supersaturated with respect to portlandite as well (the solubility at 25 °C is 22 mmol/L). In the experiments described here, the lime concentration in solution was maintained constant at a value between 10-2 and 3.5 × 10-2 mol/L. Undersaturated and saturated lime solutions were obtained by mixing freshly decarbonated lime with water. Supersaturated lime solutions were obtained from Ca3SiO5 suspensions in water. Hydration Experiments at Constant Lime Concentration. All the experiments were carried out using thermoregulated cells at 25 °C with a constant water/cement ratio (200 mL of solution and 4 g of calcium silicate) and under a nitrogen atmosphere to avoid calcium carbonate formation. According to eq 1, during hydration, the dissolution of 1 mol of Ca3SiO5 releases 3 mol of Ca2+ ions and 1 mol of silicate ions in solution, while precipitation of 1 mol of C-S-H consumes only C/S mol of calcium ions (C/S < 2) and one mol of silicate ions (eq 3). Thus, the lime concentration increases during the hydration process until maximum supersaturation is reached with respect to Ca(OH)2, which then precipitates. Maintaining the lime concentration in solution constant requires the removal of the solution of the (3 - C/S) mol of Ca(OH)2 produced by the

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Table 1. Variation of the C-S-H Quantity Nucleated at the Beginning of Ca3SiO5 and Ca2SiO4 Hydration for Different Lime Concentrations

tricalcium silicate l/s ) 50

dicalcium silicate l/s ) 20

[Ca(OH)2] mmol/L

[SiO2] µmol/L corresponding to the maximum of supersaturation

[SiO2] µmol/L at the end of pretreatment

C/S of the C-S-H

quantity of precipitated C-S-H for 20 g of product (µmol)

11 19.5 22 33 5 9 11 12 22 28.2

85 50 37 25 390 172 92.5 99 20 11.25

55 30 27 24 330 144 75 81 18.5 11

1.3 1.4 1.8 2.5 1.2 1.25 1.3 1.3 1.8 1.95

50 36 23 6 60 30 20 21 6 1

dissolution of Ca3SiO5, which is not consumed by the precipitation of C-S-H. The lime concentration is monitored by measuring the electrical conductivity which is proportional, in that case, to the calcium hydroxide concentration. At the onset of the experiment, a value of electrical conductivity is fixed. When it increases, that is, the calcium concentration increases, a volume of pure water is added whereas the same volume of solution is sucked up by an air pump through a filter so that the water/ cement (w/c) ratio is maintained constant. The percentage of hydration is then calculated from the number of calcium ions taken from the solution. In the case of Ca2SiO4 hydration, regulation of lime concentration is not necessary since it does not vary more than 2 mmol/L under the conditions used (w/c ) 50). In this case, reaction advancement is deduced from the electrical conductivity variation. Variation of the Number of C-S-H Nuclei: Pretreatments. As it is necessary to vary the quantity of C-S-H nuclei, all samples were pretreated for 30 min at various lime concentrations. Such a process enables control of the quantity of C-S-H precipitated during this time as shown in Table 1. This quantity is deduced from the [SiO2] ) f(t) curves (Figure 2) and is proportional to the number of initial nuclei since it has been shown in previous studies9 that the size of nuclei does not vary so much with the lime concentration in solution (in the concentration range studied here). The silicate concentration is measured in the liquid phase by colorimetry by the phosphomolybdate complex method. The quantity of C-S-H nucleating during the prehydration is deduced from the difference in the silicate concentration between the maximum of supersaturation with respect to C-S-H and the end of the pretreatment, taking into account the mole of SiO2 produced by the initial dissolution.

quantity of precipitated hydrate )

V (∆[SiO2]) 1/3(C/S) - 1 (see Figure 2)

where V is the volume of solution. For 20 g (corresponding to 88 mmol) of tricalcium silicate, the maximum amount of C-S-H precipitated is 50 µmol, corresponding to the hydration of 50 µmol of Ca3SiO5. So, at the end of the preliminary hydration, the degree of hydration is lower than 0.06% for the tricalcium silicate and lower than 0.05% for the dicalcium silicate. After filtration, the prehydrated grains are hydrated in another lime solution where the C-S-H nuclei only grow on the silicate surface. The hypothesis is made that there would not be new sites of nucleation on the surface of the anhydrous silicate when grains of silicates already supporting nuclei of C-S-H are again suspended in solution.

Results and Discussion Experimental Results. Two kinds of experiments were performed to elucidate, on one hand, the role played by the initial quantity of nuclei and to determine, on the other hand, the growth mode of C-S-H on the surface of the anhydrous silicate. In the first one, prehydrated samples under different conditions (i.e., with different

Figure 3. Variation of the percentage of hydration against time during the hydration of Ca3SiO5 grains wearing different quantities of C-S-H nuclei for two different lime concentrations (11 and 22 mmol/L).

Figure 4. Variation of the percentage of reaction against time during the hydration of Ca2SiO4 grains wearing different quantities of C-S-H nuclei for two different lime concentrations (11 and 22 mmol/L).

quantity of nuclei) were hydrated in the same lime solution; in the second one, samples prehydrated under the same conditions (i.e., with the same quantity of nuclei) were hydrated in different lime solutions. This allows one to evaluate the influence of lime concentration on the growth mode. The two sets of experiments were performed for tricalcium and dicalcium silicates. By this way, we were able to check the influence of the solubility and of the calcium silicate surface which provides ions by dissolution. Effect of the Number of Nuclei. Samples of tricalcium silicate were prehydrated for 30 min in two different lime solutions (11 and 22 mmol/L) in order to get two different quantities of C-S-H nuclei on the surface of the Ca3SiO5 grains as indicated in Table 1. After filtration, the two types of pretreated grains were hydrated in lime solutions (11 and 22 mmol/L). The results are presented in Figure 3. In the same way (Figure 4), Ca2SiO4 samples were prehydrated in different lime solutions (5, 9, 12, and 22

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percentage of 25%. This suggests that the mode of growth of C-S-H on the surface of the grains is crucially affected by the lime concentration. At low lime concentration, the grain is covered more rapidly and with a lower amount of hydrate than at high lime concentration. It can be assumed that at a low lime concentration the C-S-H growth parallel to the surface of the grain is faster than at high lime concentration. To account for these various effects, in particular the influence of the growth rate of C-S-H, we have developed a phenomenological model which includes the relevant parameters identified by the experiments. Figure 5. Variation with lime concentration of the percentage of hydration against time during the hydration of Ca3SiO5 grains wearing the same quantity of C-S-H nuclei.

Figure 6. Variation with lime concentration of the percentage of hydration against time during the hydration of Ca2SiO4 grains wearing the same quantity of C-S-H nuclei.

mmol/L) (Table 1) and then hydrated in lime solutions (11 and 22 mmol/L). In all situations, one can conclude that the greater the number of initial nuclei, the shorter the initial period in the curve of percentage reaction against time. It can be also observed that the percentage of hydration at which the rate of hydration becomes controlled by diffusion through the product layer does not change very much when only the quantity of initial nuclei varies. Effect of Lime Concentration on Growth of Nuclei. Several Ca3SiO5 samples were prehydrated under the same experimental conditions ([Ca(OH)2] ) 11 mmol/L) in order to have the same quantity of initial C-S-H nuclei (corresponding to 50 µmol) for each sample. They were then hydrated in different lime solutions (18, 21, 25, and 28 mmol/L), and the results are presented in Figure 5. Ca2SiO4 samples were also preliminarily hydrated in the same conditions ([Ca(OH)2] ) 12 mmol/L) and hydrated in two different lime solutions, as shown in Figure 6. In the case of Ca3SiO5 hydration, the percentage of reaction for which the surface was completely covered by C-S-H, that is, when the reaction drastically decelerates, reached 10% for hydration in solutions in which the lime concentration was below 22 mmol/L (18 and 21 mmol/L). In contrast, the percentage of reaction was near 25% for lime concentrations above 22 mmol/L (25 and 28 mmol/L). For Ca2SiO4, the reaction becomes limited by diffusion near 3% and 8% of hydration when the lime concentrations were 14 and 21 mmol/L, respectively. From the experimental studies, it clearly appears that the percentage of hydration and the characteristic time for which the calcium silicate grain, whatever the calcium silicate, becomes completely covered by the hydrate layer decreases with decreasing lime concentration in solution. For instance, the time needed to reach the end of the first kinetic stage corresponding to 10% of hydration is about 6 h while it increases to 10 h for a final hydration

Model and Numerical Simulations The observations of hydration by AFM11 show that the C-S-H growth proceeds by oriented three-dimensional aggregation of identical units. On the other hand, the observation of a fast initial decrease in silica concentration should coincide with an initial nucleation step followed by the growth of these nuclei. The experimental curves have thus been interpreted by considering that the C-S-H formation process consists of a primary heterogeneous C-S-H nucleation leading to the formation of clusters followed by the growth of these nuclei. As shown experimentally, the cluster grows on the silicate surface with a growth rate depending on the lime concentration in solution. Thanks to the modeling, we will be able to elucidate the mechanisms that control the kinetics of hydration of the silicate, including the influence of lime concentration in solution. We split the growth step into two processes corresponding to the growth of clusters on the surface (here termed parallel growth) and the increase of the cluster thickness (here termed perpendicular growth). Each process is characterized by a distinct growth rate. In the model proposed, the heterogeneous nucleation is described by a random distribution of particles on the surface. The growth is obtained by aggregation of particles identical to the nucleus deposited around it in directions both parallel to the calcium silicate surface and perpendicular to it. The growth model depends on three parameters: the number of initial growth clusters, the parallel growth rate, and the perpendicular growth rate. We chose a numerical model allowing us to get simulated images of the growth of C-S-H in order to make a comparison with AFM observations. Ca3SiO5 and Ca2SiO4 surfaces are simulated by 2.5 × 105 cells represented by the elements of a matrix B(500,500) whose elements are 0 or 1. A C-S-H nucleus occupies a cell and is then assigned a value of 1. The number of nuclei is controlled by applying a threshold value to the elements of an initial random matrix A whose elements are ranged between 0 and 1. As an example, in order to have 10 nuclei on the surface, that is, 10 “1’s” on the B(500,500) matrix, the threshold value is equal to 0.000 04. The parallel growth is obtained by successive convolution products of the “surface matrix B(500,500)” by a “growth matrix C(x,y)”. The matrix obtained after the convolution has a dimension greater than the surface matrix. To reduce the matrix obtained, “D(500+x-1,500+y-1)”, the following matrix E is defined as i+(x-1)/2 E(500,500) with Eij ) Dj+(y-1)/2 } 1 < i < 500

To account for the actual quasi-spherical symmetry of calcium silicate grains, we introduce boundary conditions.

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Figure 7. Algorithm of the calculations.

In other words, when a growing cluster reaches one of the matrix sides, the growth continues on the opposite side to satisfy the limit conditions. Each convolution product is associated with an iteration (I). The number of generated elements per element at each iteration is equal to the dimension of the growth matrix. The perpendicular growth is obtained by superposing (kI) layers identical to those formed by parallel growth under the assumption of identical growth in each point of the surface; this is in accordance with AFM observations of C-S-H growth.11 At each iteration, the number of generated elements is multiplied by k (multiplication factor). Therefore, this is a linear function of the number of iterations. The successive steps of calculation in the numerical simulation are reported in the algorithm detailed in Figure 7.

Figure 8 shows the agreement between a simulated image and an AFM image of C-S-H formation on a calcium silicate surface. Ca3SIO5 Hydration. Numerical Simulations of Experimental Curves. It is only possible to simulate with the model the part of the experimental curves corresponding to the growth process which is not limited by diffusion, that is, before the complete coverage of the calcium silicate grains by hydrates (first kinetic stage). This part is the beginning of the sigmoid curve after the inflection point. The inflection point corresponds to the time at which the growing clusters begin to coalesce. To fit the experimental curves, it is necessary to determine the parameters of the model, the number of initial nuclei (the threshold randomly generated matrix), the parallel growth rate (dimension of the convolution matrix), and the perpendicular growth rate (the value of the multiplication factor). The parameters have been determined by a trial-error procedure in

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Figure 8. Comparison between a simulated image and an AFM image of C-S-H formation on a tricalcium silicate surface obtained by direct observation after 4 h of hydration. The simulated image is obtained for the 15th iteration with a growth matrix with dimensions of (3 × 7), and the value of k is 3. The relative height of the AFM image is 50 nm.

Figure 9. Variation of the percentage of hydration obtained experimentally and by simulation during the hydration in the same lime solution of Ca3SiO5 grains wearing different quantities of C-S-H nuclei.

such a way as to get self-consistent results: On one hand, the curves corresponding to experiments in which the hydration solutions were the same but the prehydrated samples varied must be simulated using the same convolution matrix and multiplication factor and a different initial surface matrix. On the other hand, the experimental curves corresponding to the hydration of the same prehydrated sample in different solutions must be simulated using the same initial matrix with a different convolution matrix and multiplication factors. The agreement between the simulated and experimental curves is excellent in all cases (Figures 9 and 10). The hypothesis of the separation between nucleation and growth of clusters around the initial nuclei without appearance of other growth sites during hydration should be valid. One can notice on Figure 9 that the number of nuclei in the simulation is in the same ratio as the quantities of C-S-H precipitated as nuclei during the initial stage of the experiment. In all cases, the scale factors linking up the number of iterations to the time (time scale factor) on one hand and the number of generated elements to the percentage of reaction (reaction scale factor) on the other hand are the same: they are 13.6 and 3 × 10-7, respectively, for the tricalcium silicate used in these experiments. The dimension of the growth matrix varies from (3 × 3) to (60 × 5), all elements being set to one. The value of the parameter k varies from 3 to 6. Ca2SIO4 Hydration. To test the validity of the model, experimental percentage of reaction evolution curves

Figure 10. Variation of the percentage of hydration obtained experimentally and by simulation during the hydration in different lime solutions of Ca3SiO5 grains wearing the same quantity of C-S-H nuclei.

obtained during hydration of Ca2SiO4 grains in different lime solutions were simulated using the parallel growth and perpendicular growth rates determined to simulate Ca3SiO5 hydration curves in the same lime solutions. It is necessary however to take into account the variation of the reaction scale factor since it depends on the size of the calcium silicate grains. The diameter of the Ca2SiO4 grains was greater than that of the Ca3SiO5 grains (the average diameters of Ca3SiO5 and Ca2SiO4 were 10 and 15 µm, respectively). When the C-S-H covers the Ca3SiO5 grains, the thickness of the hydrate layer is the same whatever the size of the grains (for hydration under the same conditions),12 but the larger the initial grain, the smaller the percentage of reaction reached at that time. If this observation remains true for the dicalcium silicate, to simulate experimental curves for the Ca2SiO4 hydration it is necessary to modify the reaction scale factor. The variation of the degree of reaction according to the initial granularity of Ca3SiO5 grains established by Lecoq12 allows one to determine this new ratio. According to Lecoq, the degree of reaction reached when silicate grains are completely covered by the hydrate layer in this case would be 1.5 times weaker since the diameter of Ca2SiO4 grains is approximately 1.5 times greater than that of the Ca3(12) Lecoq, X.; Nonat, A. Colloque Sciences et Technologie des poudres; Socie´te´ de Chimie Industrielle: Lyon, 1994; Chapter 15.

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Figure 11. Variation of the percentage of hydration obtained experimentally and by simulation during the hydration in two different lime solutions of Ca2SiO4 grains wearing the same quantity of C-S-H nuclei.

Figure 12. Variation against [Ca(OH)2] of the parallel growth matrix dimensions and of the linear function of the iteration number representative of the perpendicular growth rate.

SiO5 grains so the reaction scale factor has been fixed by dividing by 1.5 the one used for Ca3SiO5 hydration. The number of initial nuclei was calculated as follows: dicalcium silicate grains were prehydrated for 30 min at 11 mmol/L; approximately 20 µmol of C-S-H nuclei was precipitated on grains contained in 20 g. The specific surface of Ca2SiO4 grains is 1.2 times smaller than that of Ca3SiO5 grains; then, for the same quantity of nuclei and the same mass of product, the coverage of the surface of the anhydrous grain by nuclei is superior in the case of the Ca2SiO4. For the same quantity of initial nuclei (20 µmol for 20 g), 60 cells were randomly distributed to simulate Ca3SiO5 hydration curves; 70 cells were therefore distributed to simulate those obtained in the case of hydration of Ca2SiO4. The good agreement between the experimental curves and the simulated ones obtained with the above assumptions shows (Figure 11) that the rate of the hydration of tricalcium and dicalcium silicates depends only on the growth of C-S-H. It is not influenced in the conditions studied here, neither by the solubility of the anhydrous silicate nor by the nature of the surface on which C-S-H grows. Variation of the Growth Rates with Lime Concentration. Figure 12 shows variations in the dimensions of the parallel growth matrix and in the linear function of the number of iterations (multiplication factor) used to simulate experimental curves resulting from hydration in solutions of calcium hydroxide in concentrations of 11 to 30 mmol/L. The values found are unique for each concentration. The results obtained agree with hypotheses of variations

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of the growth mode with the concentration of calcium hydroxide in solution. The parallel growth rate decreases with the concentration in calcium hydroxide. On the contrary, the perpendicular growth rate varies very little but these values show a discontinuity around 22 mmol/L. The value corresponding to high concentration is 1.5 times the value obtained at low concentration. This discontinuity according to the concentration in hydroxide of calcium affects many properties of the C-S-H and corresponds to the transition between phases β and γ.13 The model does not yield absolute rates. The perpendicular rate of C-S-H growth represents a rate of C-S-H precipitated which can be expressed in mol/s, which is not a linear rate (nm/s). For these reasons, the discontinuity pointed out in perpendicular growth rate variation could be simply due to a change in the C-S-H density between the phases β and γ. The structure of C-S-H, derived from that of tobermorite, is a layered structure in which each layer is composed of planes of calcium ions coordinated by oxygen atoms from silicate tetrahedrally arranged in parallel linear chains.14,15 In view of this layered structure, it seems probable that the layers are orientated in the way of maximal elongation of nanoparticles. The anisotropy of the C-S-H structure can be at the origin of the difference between parallel and perpendicular rates. The silica concentration varies between 10-4 and 10-5 mol/L, while the calcium concentration varies between 10-2 and 3.5 × 10-2 mol/L during calcium silicate hydration. The silica ions are probably the limiting species in the hydration reaction. If the rate of C-S-H growth decreases as lime concentration increases, this is certainly a consequence of the induced decrease of silica concentration. Origin of the Kinetics Initial Stage. The initial period is very important since in terms of technology it is the period during which concrete may be carried and put in place. This initial stage (Figure 1, labeled IS) has been object of many hypotheses.2,16,17 Some hold that it is controlled by a thin protective layer formed by the first C-S-H precipitated on anhydrous calcium silicate grains. In this case, the rupture or the increase of the permeability of the protective layer would explain the end of the initial period. These explanations seem unlikely. As a fact, previous studies have shown that the more the suspension is diluted, the more the C-S-H quantity precipitated during the nucleation is important and the faster the hydration. All these preliminary results go against a possible initial protective C-S-H layer existence. On the other hand, the good agreement obtained between simulated and experimental curves, presented here, shows that the initial stage may be explained by considering only the nucleation and growth of clusters of C-S-H on the surface. Conclusion The influence of the C-S-H nucleation and growth rate on the hydration kinetics of tricalcium and dicalcium (13) Greenberg, S. A.; Chang, T. N. J. Phys. Chem. 1965, 69 (1), 182-188. (14) Nonat, A.; Lecoq, X. Nuclear Magnetic Resonance Spectroscopy of Cement-based Materials; Colombet, P., Grimmer, A. R., Zanni, H., Eds.; Springer-Verlag: New York, 1997. (15) Hamid, S. A. Z. Kristallogr. 1981, 154, 189-198. (16) Stein, H. N. Cemento 1977, 3-4. (17) Thomas, N. L.; Double, D. D. Cem. Concr. Res. 1981, 11, 675687.

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silicates has been experimentally determined in a detailed manner for the first time. A simple numerical simulation enabled us to show that the number of C-S-H nuclei formed in the first minutes of hydration controls the initial period of the evolution of the percentage of reaction. It also led to quantification of the variation of the growth rates parallel and perpendicular to the calcium silicate grain surface, revealed by AFM experiments, with lime concentration in solution.

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The simulation of the experimental kinetics hydration curves of Ca3SiO5 and Ca2SiO4 has shown that the only dependence of calcium silicate hydrate is on the lime concentration in solution; it is not influenced by the nature of the surface on which it grows. Acknowledgment. The authors express their gratitude to F. Baras (ULB, Bruxelles) for her interest to this work. LA011201Z