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Analysis of C-S-H growth rates in supersaturated conditions
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Analysis of C-S-H growth rates in supersaturated conditions Frank Bellmanna,⁎, George W. Schererb a b
Bauhaus University Weimar, Germany Princeton University, USA
A R T I C L E I N F O
A B S T R A C T
Keywords: C-S-H Kinetics Growth rate
The growth rate of calcium-silicate-hydrate (C-S-H) was analyzed by following the evolution of calcium and silicon concentrations in supersaturated solutions. In these experiments, the supersaturated solution was produced by mixing a saturated calcium hydroxide solution and a solution obtained from the hydration of tricalcium silicate. A continuous decrease of the silicon concentration over time was observed during the experiments and the C-S-H formation rate was calculated from the amount of silicon that was precipitated between two consecutive analyses. The data obtained in this study demonstrate that the interfacial growth rate of C-S-H depends mainly on the supersaturation with respect to this phase, the availability of calcite as a substrate for heterogeneous nucleation and the calcium concentration in solution. A mean value of approximately 10 nmol of C-S-H per m2 per second was obtained for the interfacial growth rate of C-S-H in conditions that are relevant for the hydration of tricalcium silicate.
1. Introduction There is continuing interest in the kinetics of tricalcium silicate hydration, because the impure form of this phase (alite) is the major component of Portland cement clinker [1]. Starting from a qualitative discussion of experimentally observed trends and effects, the discussion shifts now to a quantitative description of the individual reaction steps of the hydration. It was recognized long ago that the hydration of tricalcium silicate is a dissolution-precipitation process. The kinetics of such a process can be analyzed by describing the rates of the individual reaction steps, including dissolution, nucleation and growth [2]. It is commonly assumed that the rate of the slowest step dictates the rate of the global process. Dissolution rates for tricalcium silicate were analyzed recently in a number of studies [3–9] using different experimental techniques. These studies demonstrate that the interfacial dissolution rate is very fast in pure water, but decreases to approximately 0.1–1.0 μmol/(s·m2) for tricalcium silicate undersaturations relevant for the hydration process. The induction time for the onset of precipitation of calcium-silicatehydrate (C-S-H)1 in supersaturated solutions was analyzed for homogeneous and heterogeneous nucleation [10–11]. It was concluded that heterogeneous nucleation on calcite and dicalcium silicate occurs before homogeneous nucleation. It can be expected that this is also
⁎
1
valid for tricalcium silicate but it was not possible to analyze induction times in the presence of this phase [10]. In contrast to dissolution rates and induction times preceding nucleation, there are no experimental kinetic data reported for the growth of C-S-H complementing theoretical calculations [12,13]. A detailed knowledge of kinetic parameters for the three reaction steps of tricalcium silicate hydration would allow a quantitative simulation of the global process by boundary nucleation and growth models [14]. C-S-H is the main hydration product of tricalcium silicate. Its properties were reviewed in detail by Taylor [1] and a review of recent studies was published in 2008 by Richardson [15]. The stoichiometry of C-S-H is variable depending on the conditions (particularly, the calcium concentration) during formation. At room temperature, a molar Ca/Si of approximately 1.7 is expected during hydration of tricalcium silicate leading to the co-precipitation of calcium hydroxide. The water content is 20–44% depending on the drying conditions [1]. A number of studies were devoted to analyzing the solubility of C-S-H, which is affected by a number of parameters including preparation method and structural details [16–19]. In this study, the precipitation rate of C-S-H was analyzed by following the evolution of calcium and silicon concentration in solutions supersaturated with respect to this phase. These supersaturated solutions were produced by adding a solution with a relatively high silicon concentration to a saturated calcium hydroxide solution in the
Corresponding author. E-mail address: [email protected] (F. Bellmann). We use standard cement chemistry notation: C = CaO, S = SiO2, H = H2O, and the dashes in C-S-H indicate that it is a nonstoichiometric compound.
http://dx.doi.org/10.1016/j.cemconres.2017.05.007 Received 21 February 2016; Received in revised form 5 May 2017; Accepted 8 May 2017 0008-8846/ © 2017 Elsevier Ltd. All rights reserved.
Please cite this article as: Bellmann, F., Cement and Concrete Research (2017), http://dx.doi.org/10.1016/j.cemconres.2017.05.007
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tested using commercial standard solutions and carefully measured test solutions. The 1σ-standard deviation of the silicon line at 251.611 nm was 2.2% and that of the calcium line at 373.690 nm was 1.9%. These values were used to calculate the standard deviation of the supersaturation and the precipitation rate (see below). In some experiments, the amount of solution with high [Si], the titration velocity or the substrate addition were varied to investigate the impact of these parameters on the C-S-H growth rate. If not stated otherwise, the last sampling of the solution was conducted after 245 min and the solid was instantly separated by a pressure filtration device with 0.45 μm filters. The material was dried at 60 °C for further analysis by BET and Scanning Electron Microscopy (SEM). The dry powders were applied on an adhesive carbon film and the samples were examined without application of a conductive metal or carbon layer. Charge build-up was minimized during image acquisition by reducing the acceleration voltage (2 kV) and the probe current (< 100 pA) in the electron microscope (FEI Nova nano SEM 230) when the samples were examined at high vacuum. The resolution of the instrument under these conditions is 5 nm. The nucleation density of CS-H at the substrate surface was determined by counting the C-S-H particles on four different micrographs taken from each sample. Considering the low number of micrographs used for the estimation of the mean nucleation density, the values obtained by this method are a rather rough approximation.
presence of calcite as a substrate for heterogeneous nucleation. The salient features of the growth kinetics and morphology are reported here, and a detailed analysis of the kinetics is presented in ref. 20. 2. Materials and methods A saturated calcium hydroxide (CH) solution was obtained by stirring solid calcium hydroxide (Merck, p.a.) in twice deionized water. Remains of undissolved CH were separated from the saturated solution after equilibration using a pressure filtration device and filters with a pore size of 0.45 μm. The contact with carbon dioxide from the atmosphere was avoided by directly filtering the solution into a closed glass bottle having a volume of 1 L. Solutions obtained in this way had a calcium concentration [Ca], between 20 and 23 mmol/L and a silicon concentration, [Si], between 2 and 8 μmol/L. These trace concentrations of Si are due to the presence of minor amounts of SiO2 in the CH used to prepare the solutions. The variation in [Ca] was attributed to small differences in temperature (21 ± 2 °C). In some additional experiments, undersaturated or supersaturated CH solutions were used to test the impact of [Ca] on the growth rate. The solutions were always freshly produced before the growth experiment, which results in minor variations of the starting conditions. The solution with a relatively high silicon concentration was obtained by hydration of tricalcium silicate (C3S) at a high water/ solids ratio. Twice deionized water (450 g) and C3S (0.45 g) were vigorously stirred while monitoring the conductivity of the solution. The sample of C3S used in this study was produced from calcium carbonate and SiO2 by three times burning at 1600 °C. It was phasepure (triclinic polymorph), contained no foreign oxides and had a BET surface area of 0.41 m2/g. After approximately 2 min hydration, when the conductivity exceeded a value of 0.95 mS/cm, the hydration of C3S was terminated by filtration. A pressure filtration device and filters with a pore size of 0.45 μm were used for this purpose. The solutions produced in this way had [Ca] between 3.0 and 3.3 mmol/L and [Si] between 1060 and 1230 μmol/L, depending on the time required to filter the solution (approx. 2 min). This routine allows the production of solutions with a relatively high silicon concentration in the absence of foreign ions such as sodium or potassium. In the precipitation rate experiments, 0.7 L saturated CH solution was stirred with 5.00 g calcium carbonate (calcite, Merck, reag. ph. eur., BET = 0.54 m2/g). In some of the C-S-H precipitation experiments, the amount of calcite was modified to test the impact of the substrate/solution ratio on the growth rate. A small volume of the solution (10 mL) was removed before adding the second solution to test the initial calcium and silicon concentrations. The solution with high [Si] was added to the saturated CH solution by means of a titrator in 4 steps each having a volume of 20 mL using a titration velocity of 10 mL/min. It was realized at a later stage of the study that the added volume was often below the specified value of 20 mL due to a build-up of pressure in the closed bottle during titration. Consequently, it was not possible to calculate the amount of silicon added during titration from the silicon concentration of this solution and the dosed volume. Homogenization of the two solutions was achieved by fast stirring during the experiment. There was a time lapse of ~30 s between the four additions for the automatic refilling of the titration device. The solution composition was tested after each addition and in distinct time intervals after the last addition. For each sampling, ~ 10 mL of the suspension were removed by a syringe and filtered through a syringe filter head (0.20 μm). The filtered solutions were acidified to prevent precipitation and carbonation during storage and analysis by adding ~ 0.2 g 5 M HNO3. The exact dilution factors were recorded by weighing each sample before and after the addition of the acid. Calcium and silicon concentrations of the samples were analyzed by Inductively Coupled Plasma-Optical Emission Spectroscopy (ICP-OES) using a Horiba Jobin Yvon, active M with the following parameters: radial observation, 1000 W, λCa = 373.690, λSi = 251.611 nm). Accuracy and precision of the instrument were
2.1. Data evaluation The analysis of the solution provides the evolution of [Ca] and [Si] in the supersaturated solutions during the course of the experiments. In a first step, the original concentrations were calculated by accounting for the dilution with HNO3. These concentrations can then be plotted as a function of time. A further evaluation of the data requires the calculation of the supersaturation for the individual data points. The hydroxide ion concentration is obtained from the electrochemical balance assuming that silicon is present in the form of H3SiO4− ions:
[OH−] = 2⋅[Ca2+] + [CaOH+]–[H3SiO4−]
(1)
Together with the other ionic concentrations, the results can be used to estimate the ionic strength of the solution,
I S = 0.5⋅Σ mi⋅z i 2
(2)
compute activity coefficients using the extended Debye-Hückel equation,
⎛ −A⋅z2⋅ I S ⎞ i ⎟ + bi⋅I S log γi = ⎜ ⎝ 1 + B⋅a i⋅ I S ⎠
(3)
and therefrom the activity of the individual ionic species:
{ai} = [mi ]⋅γi
(4)
The following values were used in Eq. (3): A = 0.5094, B = 0.3289, a = 4.86 for Ca2+, a = 10.65 for OH−, a = 4 for CaOH+, H3SiO4− and H2SiO42-, b = 0.15 for Ca2+, b = 0 for OH−, CaOH+, H3SiO4− and H2SiO42- [21]. Complex formation of Ca2+ ions with hydroxide ions is considered in Eq. (5):
0.0602 = {Ca2+}⋅{OH−} {CaOH+}
(5)
The presence of this complex reduces the concentration of calcium ions in the form of Ca2+. Deprotonation of silicic acid is calculated by using log K = −13.33 for the second dissociation constant. The activities for Ca2+, OH− and H3SiO4− allow the computation of the supersaturation (βk, k = 1, 2, 3) with respect to end-members for the CS-H solid solution series, Eqs. (6)–(8), assuming calcium/silicon-ratios of 0.8, 1.0 and 1.8 [16].
β1 = {Ca2+}0.80 ⋅{H3SiO4−}⋅{OH−}0.60 1.26⋅10−7 2
(6)
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β2 = {Ca2+}1.00 ⋅{H3SiO4−}⋅{OH−}1.00 1.68⋅10−9
(7)
β3 = {Ca2+}1.81⋅{H3SiO4−}⋅{OH−}2.62 2.76⋅10−14
(8)
According to the ideal solid solution model [22], which is applied to C-S-H in ref. [16], the total supersaturation (βtot) is the sum of the supersaturation for the individual end-members:
βtot =β1 +β2 +β3
(9)
Details related to the speciation model and the derivation of the solubility products are provided in ref. [16], which also includes references for dissociation constants and complex formation constants. It was assumed in the computation of the C-S-H precipitation rate that the silicon removed from the solution between two subsequent analyses does not produce new nuclei, but is consumed during the growth of the existing nuclei. Nuclei are only formed in the first 5 min after the last addition of the solution with the high silicon concentration. This hypothesis is supported by arguments presented below. The silicon concentration analyzed by ICP-OES is given in units of μmol/L and the absolute amount of silicon in the solution is calculated from the volume of the solution that is known from the original volume of the saturated calcium hydroxide solution modified by titration and sampling. The C-S-H formation rate in units of nmol C-S-H/s is obtained by dividing the difference in silicon content of the solution between two consecutive analyses by the time between the two samplings. The interfacial growth rate in nmol C-S-H/(m2·s) is calculated by dividing the formation rate by the surface area of the growing phase. This surface area can be analyzed by BET or computed from the number and size of the C-S-H particles. The standard deviation reported for the measured [Ca] and [Si] was used to calculate the 1σ-standard deviation of the supersaturation obtaining a value of 7.5%. The standard deviation of [Si] can affect the calculation of the growth rate, which is calculated from the reduction of Si between the samplings. The mean value of 1σ-standard deviation of the growth rate obtained assuming the maximum deviation in these analyses is 20.3%. These values are added as error bars in the following plots.
Fig. 1. Evolution of the silicon concentration in saturated calcium hydroxide solution in the presence of 5 g calcium carbonate after addition of 80 mL of a solution with a high silicon concentration by titration (2 experiments). The 1σ-standard variation of the values for the concentrations has the same size or is smaller than triangles and squares used to indicate the data points.
Fig. 2. Evolution of the calcium concentration in saturated calcium hydroxide solution in the presence of 5 g calcium carbonate after addition of 80 mL of a solution with a high silicon concentration by titration (2 experiments). The error bars give the 1σ-standard deviation.
3. Results It can be assumed that the growth rate of C-S-H depends on the following parameters: supersaturation, surface area available for nucleation and growth, nuclei concentration, substrate material, duration of mixing and calcium concentration. These parameters and additional factors related to the experimental set-up were varied independently to determine their impact on the growth rate.
strongly increased silicon concentration as the particles passing the filter would be later dissolved during acid addition for solution stabilization before analysis by ICP-OES. Most of the nuclei appear within 5 min after the last addition in the period of the highest supersaturation, based on comparison of the nucleation densities after 5 min and at the end of the experiment (see below). The C-S-H formation rate was calculated for each sampling and the results of the computation are provided in Fig. 3. A plot of formation rates in units of nmol C-S-H/s versus the supersaturation with respect to C-S-H indicates an almost linear correlation between formation rate and supersaturation at the conditions used in this experiment. This is misleading, however, because the surface area on which C-S-H is precipitating increases as β decreases; when that factor is taken into account, we will see that the actual growth rate of C-S-H depends nonlinearly on supersaturation. The highest formation rate observed in the experiments is 32 nmol C-S-H/s at high supersaturation (βtot = 38). A slope of formation rate versus supersaturation of ~1 nmol C-S-H/s is found at lower supersaturations. The data in Fig. 3 indicate that the formation rate cannot be resolved at supersaturations below βtot = 5 that are reached at the end of the experiment. This value depends on the speciation model and solubility data used in this study, which affect βtot. Slightly different numbers can be expected if other models are applied. Similar results were obtained when the experiment was repeated at
3.1. Supersaturation The impact of supersaturation on the C-S-H formation rate in the presence of 5 g of calcite was measured two times to test the precision of the analysis. Figs. 1 and 2 present the evolution of the ionic concentrations during the precipitation experiment. The initial CH solution had [Ca] ≈ 23 mmol/L that continuously decreased during titration, because the solution with the high silicon concentration had [Ca] = 3.3 mmol/L. The reduction to ~21 mmol/L results from the dilution of the initial solution during titration and [Ca] remains approximately constant after the last addition, owing to the small amount of C-S-H produced. Fig. 1 shows the evolution of [Si] during the experiment. The initial CH solution has [Si] = 2 μmol/L that rises to 100 μmol/L during titration. When the titration process is terminated, [Si] falls again reaching a value of 7 μmol/L after 255 min. This decrease is attributed to the growth of C-S-H that nucleates on calcium carbonate. There is no increase in the silicon concentration when using a coarser filter for the last sampling which ensures that all C-S-H particles are retained by the filter. Inefficient filtering would result in a 3
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Fig. 3. C-S-H formation rates in units of nmol/s calculated from the data in Figs. 1 and 2 as a function of supersaturation βtot. The error bars give the 1σ-standard deviation.
a slightly lower calcium concentration (red triangles in Figs. 1 and 2). Higher formation rates than would be expected based on a linear dependency on the supersaturation were obtained for the first data points at high supersaturation in this second experiment (Fig. 3). Higher formation rates at lower calcium concentrations are also observed during a systematic variation of [Ca] that is reported below.
Fig. 5. Surface of calcite particle after C-S-H growth experiment (5 g calcite).
3.2. Substrate surface available for nucleation and growth In the current section, the impact of the substrate surface area available for nucleation and growth is investigated by repeating the experiment with different amounts of calcite to derive information on the growth mode. The following calcite amounts were used in the experiments: 0.5, 1.0, 3.0, and 10.0 g. Although there are minor differences in the concentrations of the starting solutions, broadly the same features can be recognized in these experiments. There is an increase in [Si] (Fig. 4) accompanied by a decrease in [Ca] during titration; the maximum in [Si] and its decrease after titration are much alike. A higher silicon concentration in the solution used for titration in the experiment with 1 g calcite resulted in a somewhat higher [Si] after addition. There is a tendency towards a faster reduction of silicon due to C-S-H precipitation when the amount of calcite is increased owing to the larger number of nucleation sites. The calcium concentration after titration stays almost constant and the evolution is similar to the one reported in Fig. 2. The exact values are provided as Supplementary Material. The evolution of the concentrations was used to calculate the supersaturation with respect to C-S-H for each data point and the C-S-H formation rate (Fig. S1). These data are in agreement with precipitation of C-S-H starting on isolated nucleation
Fig. 6. Calcite particle from Fig. 5 at lower magnification.
sites also observed by SEM. Figs. 5 and 6 present micrographs that were acquired after the reference experiment (5 g calcite, titration 4 × 20 mL, 10 mL/min, starting in saturated calcium hydroxide solution). It can be seen that small C-S-H particles are formed by heterogeneous nucleation at the surface of the calcite substrate. The C-S-H particles have a flake-like shape. Most of the individual particles have a length between 5 and 40 nm and a thickness between 2 and 15 nm. It can be seen that the calcite surface is not completely covered and the contact between the C-S-H particles is rather limited initially (Fig. 5). Although the nucleation density and the size of the C-S-H particles can be highly different in the individual micrographs, virtually all calcite surfaces are covered to some extent (Fig. 6). For the replicate runs in Figs. 1 and 2, the nucleation density was ~380 μm−2 in the first test and ~640 μm−2 in the second. The nucleation density was also counted in a similar experiment that was terminated 5 min after the end of the titration (Fig. 7). A nucleation density of 420 μm−2 was estimated for this sample indicating that most of the nuclei form at the highest supersaturation at the end of the titration process or shortly thereafter. Fig. 8 provides information about the identification of nuclei in the counting procedure. Figs. 9 and 10 show micrographs from the experiments with 0.5 g calcite and 10 g calcite, respectively. The nucleation density is only affected to a minor extent, but the size of the C-S-H particles is significantly higher in the experiment with 0.5 g calcite (Fig. 9). The particle densities are difficult to count and the values show standard
Fig. 4. Evolution of the silicon concentration in saturated calcium hydroxide solution containing different amounts of calcite after addition of 80 mL of a solution with a high silicon concentration.
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Fig. 7. Substrate surface 5 min after titration with very small C-S-H particles (approximately 20 nm).
Fig. 10. Surface of calcite particle after C-S-H growth experiment (10 g calcite).
density on the calculated interfacial growth rates is relatively low [20]. 3.3. Impact of maximum supersaturation The amount of silicon solution added during titration affects the maximum supersaturation at the end of the addition process, so the effect of the maximum supersaturation on the formation rate was tested. Additional experiments with a systematic variation of the amount of solution added by the titration device (60 mL, 91 mL, 100 mL) were conducted and the results compared to the run with 80 mL used in the reference experiment. A constant titration velocity of 10 mL/min and a constant amount of substrate (5 g calcite) were used. The evolution of [Si] in these experiments is presented in Fig. 11. The highest concentration after addition of 60 mL solution is [Si] = 74 μmol/L, whereas [Si] = 119 μmol/L after the addition of 100 mL of a solution with a high silicon concentration. Despite the different peak concentrations, the descending part of the curves is similar, indicating comparable growth mechanisms and rates. The calcium concentration in the solutions is similar to that in Fig. 2. It decreases during titration due to dilution and remains constant thereafter within experimental uncertainty. The values are included in the Supplementary Material. Two experiments were stopped at a later time to test whether the growth of C-S-H still continues after the normal experiment duration (4 h 5 min). The experiments with the addition of 60 mL and 91 mL, respectively were terminated 22 h 10 min after titration and [Si]
Fig. 8. Detail from Fig. 10 with markers (■) demonstrating the counting procedure.
deviations up to 40%. It is expected that the results are also affected by systematic errors associated with the counting procedure (viz., difficulty in resolving very small or conjoined particles). However, a numerical simulation has shown that the impact of the nucleation
Fig. 11. Evolution of the silicon concentration in saturated calcium hydroxide solution in the presence of 5 g calcite after addition of different amounts of a solution with a high silicon concentration.
Fig. 9. Surface of calcite particle after C-S-H growth experiment (0.5 g calcite).
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decreased from 14 to 9 μmol/L (60 mL) and from 15 to 11 μmol/L (91 mL) within that time. The solution was still supersaturated (βtot = 4.8 and 5.2, respectively) at the end of the experiment, but the C-S-H formation rate was lower than 0.05 nmol/s within the final period (Fig. S2). 3.4. Duration of mixing The addition of the solution with a high silicon concentration by titration is a rather slow process. Each titration step with a velocity of 10 mL/min takes 2 min and there is also a time interval of 0.5 min between two consecutive titrations related to filling the titration device, so the addition of 80 mL solution in four steps extends over almost 10 min. To test the impact of duration of the mixing process, complementary experiments with a lower titration velocity (5 mL/min) and with a very fast addition of the solution (7 s) were conducted. The solution with the high silicon concentration was added by a large syringe in the experiment with very rapid mixing. The evolution of [Si] in these experiments is reported in Fig. 12 and [Ca] is included in the Supplementary material as it follows the trend in Fig. 2. Although the curves in Fig. 12 are offset due to a variation in the duration of the addition, almost the same slopes can be recognized in the decrease of [Si] over time. This indicates that the C-S-H formation rate is hardly dependent on the duration of the addition. This conclusion is supported by Fig. S3 and the detailed analysis in ref. 20.
Fig. 13. Evolution of the silicon concentration in saturated, supersaturated and undersaturated calcium hydroxide solution in the presence of 5 g calcium carbonate after addition of a solution with a high silicon concentration.
concentration after addition of 80 mL solution is strongly affected by the calcium concentration of the starting solution. The decrease of [Si] at [Ca] = 15 mmol/L is much slower than at [Ca] = 23 mmol/L, but this effect is influenced by a modification of the supersaturation, which is lower in this experiment. The C-S-H formation rates are almost identical in these two experiments (Fig. S4). In contrast to this, the addition of 160 mL solution leads to a much higher formation rate. It will be shown in the discussion section that this results from a change in the number of nuclei of C-S-H formed during the experiments. The experiment in a solution supersaturated with respect to CH shows a reduced maximum [Si] that indicates strong nucleation and growth already during titration.
3.5. Impact of calcium concentration on C-S-H growth rate The calcium concentration is known to affect the calcium/silicon ratio of C-S-H and it might also affect the kinetics of nucleation and growth of this material during hydration of C3S, so this parameter was analyzed in additional experiments. Although most of the growth of CS-H takes place in a solution that is saturated with respect to CH, when working at low water/binder ratios, undersaturated conditions (for portlandite) can play an important role in suspension experiments. The impact of the calcium concentration was investigated by comparing the C-S-H formation rate at [Ca] = 15 mmol/L and [Ca] = 32 mmol/L to the data obtained at [Ca] = 21–23 mmol/L. A higher amount of silicon is required at low calcium concentrations to obtain the same supersaturation with respect to C-S-H as in experiments in saturated CH solution. Beside the addition of 80 mL of a solution with a high [Si], the titration was extended to 160 mL in an additional experiment. Other parameters, such as titration velocity (10 mL/min) and amount of substrate (5 g calcium carbonate), were kept constant. The results of these experiments are presented in Fig. 13 and in the Supplementary Material. It is observed that the slope of the silicon
3.6. Growth of C-S-H after homogeneous nucleation Most of the experiments in this study were conducted in the presence of calcite that is known to have a surface favorable for C-SH nucleation [10]. The impact of calcite on the formation rate was investigated in an additional experiment in the absence of substrate material. The solution with a high silicon concentration was added in four titrations steps with a velocity of 10 mL/min to a saturated CH solution. The evolution of [Si] is reported in Fig. 14; [Ca] follows the trend in Fig. 2 and the data is available in the Supplementary material (Table S1). The silicon concentration stays more or less constant for a period of 15 min after the titration when calcite is absent from the system. It is expected that this period is the nucleation time lag at this supersaturation for the homogeneous nucleation of C-S-H in the
Fig. 12. Evolution of the silicon concentration in saturated calcium hydroxide solution in the presence of 5 g calcium carbonate after addition of 80 mL of a solution with a high silicon concentration using different addition velocities.
Fig. 14. Evolution of the silicon concentration in saturated calcium hydroxide solution in the presence or absence of 5 g calcium carbonate after addition of 80 mL of a solution with a high silicon concentration.
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particles. A more rigorous analysis, taking account of growth rate anisotropy and particle impingement, is presented in ref. 20. Calculation of the average growth rate requires knowledge of the molar volume and surface area of the growing particles. The calculation is complicated by the fact that the surface area of C-S-H is difficult to analyze and changes during the growth experiment. Two different methods were used to estimate the surface area of the hydrates: gas adsorption and numerical calculation using particle shapes and nucleation densities based on SEM data. The surface area of the C-S-H particles at the end of the experiment can be analyzed by gas adsorption (BET) after subtraction of the uncovered part of the surface area of the substrate. However, the specific surface area of the samples in this study is relatively small and thus the surface area of the precipitates contains significant uncertainties. The results are also affected by assumptions made for the calcite/CS-H ratio in the samples analyzed by BET. Table 1 provides BET data for samples with a mass exceeding 2 g after the experiment. These values are the specific surface areas of the calcite powders used as a substrate with a small amount of C-S-H deposited on the surface. The second method to estimate the surface of C-S-H, which is a simplification of the approach used in ref. 20, relies on the calculation of the surface area of the hydrate particles during the growth process. Input parameters for this computation are the volume of precipitated CS-H, number of particles, and particle shape. The volume of precipitated C-S-H is obtained from the amount of silicon precipitated during the experiment and the molar volume of C-S-H (7.6·10− 5 m3/mol); this value is based on the data in ref. [23], assuming 2 mol of water per formula unit of C-S-H. The titration device was affected by a build-up of pressure in the closed bottle, so the amount of dosed silicon had to be extrapolated. It is found from this extrapolation that the added silicon is slightly higher (5–8%) than indicated by the first sampling after addition. The total number of C-S-H particles can be calculated from the mass and specific surface area of the substrate, together with the CS-H particle density on the substrate obtained by SEM. The particle
solution, or for heterogeneous nucleation on less favorable surfaces. Once nucleation has occurred, the decrease in [Si] over time is slower than in the presence of calcium carbonate. The rate of C-S-H formation is presented in Fig. S5. The solid residue obtained after filtration of the sample without calcite was analyzed by SEM. Figs. S6 and S7 indicate the formation of aggregates consisting of flake-like particles with a length between 50 and 500 nm. The particles formed in this case are much larger than in the presence of a calcite substrate. It was not possible to estimate the nucleation density of this sample as there was no surface available for heterogeneous nucleation. This sample was also analyzed by energydispersive X-ray spectroscopy (EDS). The spectra, shown in the Supplemental material, confirm the presence of calcium, silicon and oxygen in the analyzed material (Fig. S8). It was not possible to extract reliable information about the Ca/Si-ratio in the C-S-H particles. 4. Discussion The experimental investigations in this study provide formation rates in nmol/s for the precipitation of C-S-H on a calcite substrate surface. These rates strongly depend on the supersaturation during the growth process and the calcium concentration in the solution. Compared to these two factors, other parameters such as maximum supersaturation, amount of substrate and duration of the mixing process have a much lower impact on the formation kinetics expressed in the units of nmol/s. SEM micrographs taken after the experiments demonstrate that the C-S-H particles grow from distinct sites on the substrate surface after heterogeneous nucleation. To relate the data from these experiments to the growth rate of C-SH, the formation rates in nmol/s need to be expressed as interfacial growth rates in nmol/(s·m2) or as linear growth rates in nm/h. From the shape of the particles in the SEM images, it is clear that the growth rate is anisotropic, but we will estimate the average rate of growth by dividing the volume of C-S-H precipitated by the surface area of the Table 1 Summary of the growth rate experiments. Starting solution
Added solution
Substrate
Nuclei density [μm− 2]
Growth rate at βtot = 20 [nmol C-S-H/(s·m2)]
BET [m2/g]
0.7 L saturated calcium hydroxide solution (Ca = 23.3 mmol/L, Si = 2 μmol/L) 0.7 L saturated calcium hydroxide solution (Ca = 21.8 mmol/L, Si = 6 μmol/L) 0.7 L saturated calcium hydroxide solution (Ca = 23.1 mmol/L, Si = 3 μmol/L) 0.7 L saturated calcium hydroxide solution (Ca = 22.7 mmol/L, Si = 4 μmol/L) 0.7 L saturated calcium hydroxide solution (Ca = 22.6 mmol/L, Si = 5 μmol/L) 0.7 L saturated calcium hydroxide solution (Ca = 22.3 mmol/L, Si = 8 μmol/L) 0.7 L saturated calcium hydroxide solution (Ca = 21.0 mmol/L, Si = 4 μmol/L) 0.7 L saturated calcium hydroxide solution (Ca = 22.2 mmol/L, Si = 7 μmol/L) 0.7 L saturated calcium hydroxide solution (Ca = 22.8 mmol/L, Si = 4 μmol/L) 0.7 L saturated calcium hydroxide solution (Ca = 20.8 mmol/L, Si = 6 μmol/L) 0.7 L saturated calcium hydroxide solution (Ca = 22.0 mmol/L, Si = 4 μmol/L) 0.7 L undersaturated calcium hydroxide solution (Ca = 14.8 mmol/L, Si = 3 μmol/L) 0.7 L undersaturated calcium hydroxide solution (Ca = 15.3 mmol/L, Si = 6 μmol/L) 0.7 L supersaturated calcium hydroxide solution (Ca = 31.6 mmol/L, Si = 8 μmol/L) 0.7 L saturated calcium hydroxide solution (Ca = 21.7 mmol/L, Si = 6 μmol/L)
4 × 20 mL, 10 mL/min 4 × 20 mL, 10 mL/min 4 × 20 mL, 10 mL/min 4 × 20 mL, 10 mL/min 4 × 20 mL, 10 mL/min 4 × 20 mL, 10 mL/min 3 × 20 mL, 10 mL/min 4.5 × 20 mL, 10 mL/min 5 × 20 mL, 10 mL/min 4 × 20 mL, 5 mL/min 80 mL, rapid mixing 4 × 20 mL, 10 mL/min 8 × 20 mL, 10 mL/min 4 × 20 mL, 10 mL/min 4 × 20 mL, 10 mL/min
5.0 g calcite
380
10.3
0.77
5.0 g calcite
640
10.5
0.78
0.5 g calcite
255
15.2
Not analyzed
1.0 g calcite
274
6.6
Not analyzed
3.0 g calcite
461
5.8
1.08
10.0 g calcite
323
10.3
0.51
5.0 g calcite
202
10.6
0.64
5.0 g calcite
318
12.4
0.84
5.0 g calcite
358
11.1
0.86
5.0 g calcite
292
14.1
0.67
5.0 g calcite
309
11.8
0.69
5.0 g calcite
123
35.8
0.54
5.0 g calcite
213
38.0
0.91
5.0 g calcite
231
6.1
0.69
no substrate
–
not available
Not analyzed
7
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Fig. 16. Interfacial growth rates for C-S-H calculated from data in Fig. 3 and Fig. 15 as a function of supersaturation. The error bars give the 1σ-standard deviation for the data based on ICP-OES data and does not include uncertainties related to the surface area estimation (see text).
Fig. 15. Evolution of the surface area of C-S-H for two experiments calculated from the silicon concentrations in Fig. 1, particle density from Table 1 and assumptions for the particle shape.
(0.7 m2). The other two experiments with a higher interfacial growth rate were performed in undersaturated CH solution. This indicates that the mean interfacial growth rate of ~10 nmol/(s·m2) is valid in a saturated CH solution whereas higher growth rates are expected for lower calcium concentrations at the same supersaturation. Also not included in the mean value is the experiment in supersaturated CH solution. The detailed analysis in ref. 20 indicates higher growth rates of G2 ≈ 20–24 nmol/(s·m2) at βtot = 20, but this refers to growth perpendicular to the substrate; in the plane of the substrate, the ellipsoidal particles are estimated to have growth rates of G3 ≈ G2 and G1 ≈ G2/5. The difference to the aforementioned mean value of ~10 nmol/(s·m2) is related to the geometric assumptions used in the definition of the growth rate. It is here assumed that growth takes place perpendicular to the surface of C-S-H particles; for an ellipsoidal particle, the average rate normal to the surface is smaller than G2, owing to the lower value of G1 (i.e., the rate of increase in thickness of the flake-like ellipsoid). The perpendicular growth rates reported here are lower by a factor of 2.7 than the values of G2 reported in ref. 20. A quantitative analysis of this point is presented in Appendix 3 of that paper. It is possible that the C-S-H growth rates also depend on other parameters that were not investigated in this study. For example, the transport of ions that can be affected by the rate of stirring and the water/solids ratio in the experiments; however, the growth rates are so slow that those factors are probably negligible. On the other hand, there is clearly an effect of [Ca] at a given supersaturation and significant effects are likely to be found in the presence of other ions, such as sulfates and aluminates. The latter factors are beyond the scope of the present work, but they could be explored using the present experimental procedure. The results of the experimental investigations in this study are fitted to a boundary nucleation and growth model to obtain additional information for parameters such as calcium/silicon ratio of the growing phase, particle shape, nucleation density and calcium concentration in solution in ref. [20].
shape found in the SEM micrographs is approximated as identical semiellipsoidal particles with axes a3 = a2 = 5 a1 where a3 is the length in contact with the substrate, a2 is the height perpendicular to the substrate, and a1 is the thickness of the particle. The same particle shape was used for all calculations independent from the Ca-concentration in solution as it was not possible to see differences in particle shapes of the nano-sized C-S-H particles by SEM. Again, the growth rate is found by dividing the volume of C-S-H by the area of the semiellipsoids, so that the anisotropic rates are averaged out. The surface areas obtained by these calculations are shown in Fig. 15 for two experiments. Most of the silicon is precipitated in the first 50 min of the experiment and the total surface area of the C-S-H particles has reached approximately 90% of the final value within this period. Values between 100 and 150 m2/g for the specific surface area of C-S-H are computed for the end of the experiment. The calculation is sensitive to the shape assumed for the C-S-H particles and the nucleation density. Both parameters were obtained from SEM micrographs and it is expected that the accuracy of the C-S-H surface is not better than 1.0 m2. The final values for the total C-S-H surface area precipitated on the calcite, estimated from the particle shape and amount of C-S-H, are higher (2.0 and 2.4 m2, respectively) than the surface area re-calculated from the BET results in Table 1 (1.5 and 1.6 m2, respectively). The over-estimate is to be expected, because overlap of the particles is neglected in the calculation; extensive overlap results in the total surface area being less than the sum of the areas of nonoverlapping ellipsoids. The gap of about 30% between these values indicates the importance of accurate estimation of the surface area for the analysis of growth rates. Therefore, a more rigorous treatment for the analysis of C-S-H growth rates is provided in ref. 20. Fig. 16 shows the interfacial growth rates versus supersaturation for two experiments. Supplementary data for the other experiments are summarized in Table 1 and provided in more detail in ref. [20]. This plot indicates that the growth rate of C-S-H depends nonlinearly on the supersaturation. Whereas this curve is roughly parabolic, the analysis in ref. 20 (taking account of particle impingement) shows that it is cubic. The estimated interfacial growth rate at a supersaturation βtot = 20 that is relevant for the hydration of tricalcum silicate is presented in Table 1. Most of the values are in the range between 5 and 15 nmol/ (s·m2) with a mean value of 10.4 nmol/(s·m2) and a standard deviation of 2.5 nmol/(s·m2). A higher growth rate is observed in some experiments which are not included in the calculation of the mean value. The run with a very low amount of substrate (0.5 g calcite) gave a slightly higher value for the interfacial growth rate although the formation rates in μmol/s were almost identical to the other experiments (Fig. S1). This is due to the much lower C-S-H surface area calculated for this sample
5. Conclusions The following conclusions can be drawn from this study:
• The • 8
growth kinetics of calcium silicate hydrate (C-S-H) can be analyzed by monitoring the evolution of the silicon concentration in solutions supersaturated with respect to this phase. Application of the results of the growth experiments to the hydration of tricalcium silicate is facilitated when the supersaturation is in
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•
•
• • • •
DTFH61-12- H-00003 and ARRA Grant 611-473300-60026039 PROJ0002228. The information in this paper does not necessarily reflect the opinion or policy of the federal government and no official endorsement should be inferred.
the same range as observed during hydration, the solution is nearly saturated with respect to calcium hydroxide, foreign ions are absent from the system and the solution is undersaturated with respect to other silicate phases. These conditions can be met when the supersaturated solution is prepared by mixing saturated calcium hydroxide solution with a solution obtained from the early hydration of tricalcium silicate in a ratio that is approximately 10:1. If calcite is added to the supersaturated solutions as a substrate, the decrease of the silicon concentration resulting from nucleation and growth of C-S-H starts much sooner than in the absence of calcite. This confirms other studies that have shown that calcite is a favorable substrate for heterogeneous nucleation of C-S-H, resulting in a lower critical supersaturation and induction time than for homogeneous nucleation. Rapid formation of nuclei on calcite allows measurement of the growth rate of C-S-H without complications from concurrent nucleation. The decrease of the silicon concentration between two consecutive analyses of the solution and the time between the samplings can be used to calculate a formation rate in units of nmol/s for the growth of C-S-H. This formation rate is strongly affected by the supersaturation in the solution, the availability of calcite as a substrate for heterogeneous nucleation, and the calcium concentration in solution. Other parameters such as amount of substrate material, duration of mixing, and the ratio of the starting solutions have only a minor effect on the C-S-H formation rate. A calculation of interfacial growth rates in nmol/(s·m2) or linear growth rates in nm/h from the formation rates requires knowledge of the surface area of the growing phase. Values for the surface area were derived from BET data and from particle concentration and shape as determined by SEM. The average growth rate of C-S-H depends nonlinearly on the supersaturation. It is shown in ref. 20 that this dependence is roughly cubic. The average interfacial growth rate of C-S-H after heterogeneous nucleation on a calcite substrate in solutions nearly saturated with respect to calcium hydroxide at a supersaturation β = 20 is approximately 10 nmol/(s·m2). Higher growth rates are observed for lower calcium concentrations. The technique used in this study can be used to analyze the impact of foreign ions or organic additives on the C-S-H growth rate.
References [1] H.F.W. Taylor, Cement Chemistry, Thomas-Telford, London, 1997. [2] A.C. Lasaga, Kinetic Theory in the Earth Sciences, Princeton University Press, Princeton (New Jersey, USA), 1998. [3] L. Nicoleau, Interactions physico-chimiques entre le latex et les phases minérales constituent le ciment au cours de l' hydratation (PhD thesis), Université de Bourgogne, 2004. [4] L. Nicoleau, A. Nonat, D. Perrey, The di- and tricalcium silicate dissolutions, Cem. Concr. Res. 47 (5) (2013) 14–30. [5] L. Nicoleau, E. Schreiner, A. Nonat, Ion specific effects influencing the dissolution of tricalcium silicate, Cem. Concr. Res. 59 (5) (2014) 118–138. [6] P. Juilland, E. Gallucci, Morpho-topological investigation of the mechanisms and kinetic regimes of alite dissolution, Cem. Concr. Res. 76 (2015) 180–191. [7] J. Bisschop, A. Kurlov, A flow-through method for measuring the dissolution rate of alite and Portland cement clinker, Cem. Concr. Res. 51 (2013) 47–56. [8] F. Bellmann, T. Sowoidnich, B. Möser, Formation of an intermediate phase and influence of crystallographic defects on dissolution of C3S, in: Á. Palomo, A. Zaragoza, J.C. López Agüí (Eds.), Proceedings of the XIII. International Congress on the Chemistry of Cement, 2011, p. 320 (3.-8.7, Madrid (Spain)). [9] F. Bellmann, Th. Sowoidnich, H.-M. Ludwig, D. Damidot, Dissolution rates during the early hydration of tricalcium silicate, Cem. Concr. Res. 72 (2015) 108–116. [10] S. Garrault-Gauffinet, A. Nonat, Experimental investigation of calcium silicate hydrate (C-S-H) nucleation, J. Cryst. Growth 200 (3–4) (1999) 565–574. [11] E. Ntafalias, P.G. Koutsoukos, Spontaneous precipitation of calcium silicate hydrate in aqueous solutions, Cryst. Res. Technol. 45 (1) (2010) 39–47. [12] C. Labbez, B. Jönsson, C.E. Woodward, A. Nonat, M. Delhorme, The growth of charged platelets, Phys. Chem. Chem. Phys. 16 (2014) 23800–23808. [13] M. Delhorme, C. Labbez, M. Turesson, E. Lesniewska, C.E. Woodward, B. Jönsson, Aggregation of calcium silicate hydrate nanoplatelets, Langmuir 32 (2016) 2058–2066. [14] G.W. Scherer, J. Zhang, J.J. Thomas, Nucleation and growth models for hydration of cement, Cem. Concr. Res. 42 (7) (2012) 982–993. [15] I.G. Richardson, The calcium silicate hydrates, Cem. Concr. Res. 38 (2008) 137–158. [16] J.W. Bullard, G.W. Scherer, An ideal solid solution model for C-S-H, J. Am. Ceram. Soc. 99 (12) (2016) 4137–4145. [17] H.M. Jennings, Aqueous solubility relationships for two types of calcium silicate hydrate, J. Am. Ceram. Soc. 69 (8) (1986) 614–618. [18] J.J. Chen, J.J. Thomas, H.F.W. Taylor, H.M. Jennings, Solubility and structure of calcium silicate hydrate, Cem. Concr. Res. 34 (2004) 1499–1519. [19] B. Lothenbach, A. Nonat, Calcium silicate hydrates: solid and liquid phase composition, Cem. Concr. Res. 78 (2015) 57–70. [20] G.W. Scherer, F. Bellmann, Kinetic analysis of C-S-H growth, Cem. Concr. Res. (2017), http://dx.doi.org/10.1016/j.cemconres.2016.07.017 (in this issue). [21] W. Hummel, U. Berner, E. Curti, F.J. Pearson, T. Thoenen, Nagra/PSI Chemical Thermodynamic Data Base 01/01, Universal-Publishers, USA, 2002 (uPUBLISH. com ). [22] E. Nourtier-Mazauric, B. Guy, B. Fritz, E. Brosse, D. Garcia, A. Clement, Modelling the dissolution/precipitation of ideal solid solutions, Oil & Gas Sci. Tech. Rev. IFP 60 (2) (2005) 401–415. [23] J.J. Thomas, H.M. Jennings, A.J. Allen, Relationships between composition and density of tobermorite, jennite, and nanoscale CaO-SiO2-H2O, J. Phys. Chem. C 114 (2010) 7594–7601.
Supplementary data to this article can be found online at http://dx. doi.org/10.1016/j.cemconres.2017.05.007. Acknowledgements GWS was supported by Federal Highway Administration Grant
9
Contents lists available at ScienceDirect
Cement and Concrete Research journal homepage: www.elsevier.com/locate/cemconres
Analysis of C-S-H growth rates in supersaturated conditions Frank Bellmanna,⁎, George W. Schererb a b
Bauhaus University Weimar, Germany Princeton University, USA
A R T I C L E I N F O
A B S T R A C T
Keywords: C-S-H Kinetics Growth rate
The growth rate of calcium-silicate-hydrate (C-S-H) was analyzed by following the evolution of calcium and silicon concentrations in supersaturated solutions. In these experiments, the supersaturated solution was produced by mixing a saturated calcium hydroxide solution and a solution obtained from the hydration of tricalcium silicate. A continuous decrease of the silicon concentration over time was observed during the experiments and the C-S-H formation rate was calculated from the amount of silicon that was precipitated between two consecutive analyses. The data obtained in this study demonstrate that the interfacial growth rate of C-S-H depends mainly on the supersaturation with respect to this phase, the availability of calcite as a substrate for heterogeneous nucleation and the calcium concentration in solution. A mean value of approximately 10 nmol of C-S-H per m2 per second was obtained for the interfacial growth rate of C-S-H in conditions that are relevant for the hydration of tricalcium silicate.
1. Introduction There is continuing interest in the kinetics of tricalcium silicate hydration, because the impure form of this phase (alite) is the major component of Portland cement clinker [1]. Starting from a qualitative discussion of experimentally observed trends and effects, the discussion shifts now to a quantitative description of the individual reaction steps of the hydration. It was recognized long ago that the hydration of tricalcium silicate is a dissolution-precipitation process. The kinetics of such a process can be analyzed by describing the rates of the individual reaction steps, including dissolution, nucleation and growth [2]. It is commonly assumed that the rate of the slowest step dictates the rate of the global process. Dissolution rates for tricalcium silicate were analyzed recently in a number of studies [3–9] using different experimental techniques. These studies demonstrate that the interfacial dissolution rate is very fast in pure water, but decreases to approximately 0.1–1.0 μmol/(s·m2) for tricalcium silicate undersaturations relevant for the hydration process. The induction time for the onset of precipitation of calcium-silicatehydrate (C-S-H)1 in supersaturated solutions was analyzed for homogeneous and heterogeneous nucleation [10–11]. It was concluded that heterogeneous nucleation on calcite and dicalcium silicate occurs before homogeneous nucleation. It can be expected that this is also
⁎
1
valid for tricalcium silicate but it was not possible to analyze induction times in the presence of this phase [10]. In contrast to dissolution rates and induction times preceding nucleation, there are no experimental kinetic data reported for the growth of C-S-H complementing theoretical calculations [12,13]. A detailed knowledge of kinetic parameters for the three reaction steps of tricalcium silicate hydration would allow a quantitative simulation of the global process by boundary nucleation and growth models [14]. C-S-H is the main hydration product of tricalcium silicate. Its properties were reviewed in detail by Taylor [1] and a review of recent studies was published in 2008 by Richardson [15]. The stoichiometry of C-S-H is variable depending on the conditions (particularly, the calcium concentration) during formation. At room temperature, a molar Ca/Si of approximately 1.7 is expected during hydration of tricalcium silicate leading to the co-precipitation of calcium hydroxide. The water content is 20–44% depending on the drying conditions [1]. A number of studies were devoted to analyzing the solubility of C-S-H, which is affected by a number of parameters including preparation method and structural details [16–19]. In this study, the precipitation rate of C-S-H was analyzed by following the evolution of calcium and silicon concentration in solutions supersaturated with respect to this phase. These supersaturated solutions were produced by adding a solution with a relatively high silicon concentration to a saturated calcium hydroxide solution in the
Corresponding author. E-mail address: [email protected] (F. Bellmann). We use standard cement chemistry notation: C = CaO, S = SiO2, H = H2O, and the dashes in C-S-H indicate that it is a nonstoichiometric compound.
http://dx.doi.org/10.1016/j.cemconres.2017.05.007 Received 21 February 2016; Received in revised form 5 May 2017; Accepted 8 May 2017 0008-8846/ © 2017 Elsevier Ltd. All rights reserved.
Please cite this article as: Bellmann, F., Cement and Concrete Research (2017), http://dx.doi.org/10.1016/j.cemconres.2017.05.007
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tested using commercial standard solutions and carefully measured test solutions. The 1σ-standard deviation of the silicon line at 251.611 nm was 2.2% and that of the calcium line at 373.690 nm was 1.9%. These values were used to calculate the standard deviation of the supersaturation and the precipitation rate (see below). In some experiments, the amount of solution with high [Si], the titration velocity or the substrate addition were varied to investigate the impact of these parameters on the C-S-H growth rate. If not stated otherwise, the last sampling of the solution was conducted after 245 min and the solid was instantly separated by a pressure filtration device with 0.45 μm filters. The material was dried at 60 °C for further analysis by BET and Scanning Electron Microscopy (SEM). The dry powders were applied on an adhesive carbon film and the samples were examined without application of a conductive metal or carbon layer. Charge build-up was minimized during image acquisition by reducing the acceleration voltage (2 kV) and the probe current (< 100 pA) in the electron microscope (FEI Nova nano SEM 230) when the samples were examined at high vacuum. The resolution of the instrument under these conditions is 5 nm. The nucleation density of CS-H at the substrate surface was determined by counting the C-S-H particles on four different micrographs taken from each sample. Considering the low number of micrographs used for the estimation of the mean nucleation density, the values obtained by this method are a rather rough approximation.
presence of calcite as a substrate for heterogeneous nucleation. The salient features of the growth kinetics and morphology are reported here, and a detailed analysis of the kinetics is presented in ref. 20. 2. Materials and methods A saturated calcium hydroxide (CH) solution was obtained by stirring solid calcium hydroxide (Merck, p.a.) in twice deionized water. Remains of undissolved CH were separated from the saturated solution after equilibration using a pressure filtration device and filters with a pore size of 0.45 μm. The contact with carbon dioxide from the atmosphere was avoided by directly filtering the solution into a closed glass bottle having a volume of 1 L. Solutions obtained in this way had a calcium concentration [Ca], between 20 and 23 mmol/L and a silicon concentration, [Si], between 2 and 8 μmol/L. These trace concentrations of Si are due to the presence of minor amounts of SiO2 in the CH used to prepare the solutions. The variation in [Ca] was attributed to small differences in temperature (21 ± 2 °C). In some additional experiments, undersaturated or supersaturated CH solutions were used to test the impact of [Ca] on the growth rate. The solutions were always freshly produced before the growth experiment, which results in minor variations of the starting conditions. The solution with a relatively high silicon concentration was obtained by hydration of tricalcium silicate (C3S) at a high water/ solids ratio. Twice deionized water (450 g) and C3S (0.45 g) were vigorously stirred while monitoring the conductivity of the solution. The sample of C3S used in this study was produced from calcium carbonate and SiO2 by three times burning at 1600 °C. It was phasepure (triclinic polymorph), contained no foreign oxides and had a BET surface area of 0.41 m2/g. After approximately 2 min hydration, when the conductivity exceeded a value of 0.95 mS/cm, the hydration of C3S was terminated by filtration. A pressure filtration device and filters with a pore size of 0.45 μm were used for this purpose. The solutions produced in this way had [Ca] between 3.0 and 3.3 mmol/L and [Si] between 1060 and 1230 μmol/L, depending on the time required to filter the solution (approx. 2 min). This routine allows the production of solutions with a relatively high silicon concentration in the absence of foreign ions such as sodium or potassium. In the precipitation rate experiments, 0.7 L saturated CH solution was stirred with 5.00 g calcium carbonate (calcite, Merck, reag. ph. eur., BET = 0.54 m2/g). In some of the C-S-H precipitation experiments, the amount of calcite was modified to test the impact of the substrate/solution ratio on the growth rate. A small volume of the solution (10 mL) was removed before adding the second solution to test the initial calcium and silicon concentrations. The solution with high [Si] was added to the saturated CH solution by means of a titrator in 4 steps each having a volume of 20 mL using a titration velocity of 10 mL/min. It was realized at a later stage of the study that the added volume was often below the specified value of 20 mL due to a build-up of pressure in the closed bottle during titration. Consequently, it was not possible to calculate the amount of silicon added during titration from the silicon concentration of this solution and the dosed volume. Homogenization of the two solutions was achieved by fast stirring during the experiment. There was a time lapse of ~30 s between the four additions for the automatic refilling of the titration device. The solution composition was tested after each addition and in distinct time intervals after the last addition. For each sampling, ~ 10 mL of the suspension were removed by a syringe and filtered through a syringe filter head (0.20 μm). The filtered solutions were acidified to prevent precipitation and carbonation during storage and analysis by adding ~ 0.2 g 5 M HNO3. The exact dilution factors were recorded by weighing each sample before and after the addition of the acid. Calcium and silicon concentrations of the samples were analyzed by Inductively Coupled Plasma-Optical Emission Spectroscopy (ICP-OES) using a Horiba Jobin Yvon, active M with the following parameters: radial observation, 1000 W, λCa = 373.690, λSi = 251.611 nm). Accuracy and precision of the instrument were
2.1. Data evaluation The analysis of the solution provides the evolution of [Ca] and [Si] in the supersaturated solutions during the course of the experiments. In a first step, the original concentrations were calculated by accounting for the dilution with HNO3. These concentrations can then be plotted as a function of time. A further evaluation of the data requires the calculation of the supersaturation for the individual data points. The hydroxide ion concentration is obtained from the electrochemical balance assuming that silicon is present in the form of H3SiO4− ions:
[OH−] = 2⋅[Ca2+] + [CaOH+]–[H3SiO4−]
(1)
Together with the other ionic concentrations, the results can be used to estimate the ionic strength of the solution,
I S = 0.5⋅Σ mi⋅z i 2
(2)
compute activity coefficients using the extended Debye-Hückel equation,
⎛ −A⋅z2⋅ I S ⎞ i ⎟ + bi⋅I S log γi = ⎜ ⎝ 1 + B⋅a i⋅ I S ⎠
(3)
and therefrom the activity of the individual ionic species:
{ai} = [mi ]⋅γi
(4)
The following values were used in Eq. (3): A = 0.5094, B = 0.3289, a = 4.86 for Ca2+, a = 10.65 for OH−, a = 4 for CaOH+, H3SiO4− and H2SiO42-, b = 0.15 for Ca2+, b = 0 for OH−, CaOH+, H3SiO4− and H2SiO42- [21]. Complex formation of Ca2+ ions with hydroxide ions is considered in Eq. (5):
0.0602 = {Ca2+}⋅{OH−} {CaOH+}
(5)
The presence of this complex reduces the concentration of calcium ions in the form of Ca2+. Deprotonation of silicic acid is calculated by using log K = −13.33 for the second dissociation constant. The activities for Ca2+, OH− and H3SiO4− allow the computation of the supersaturation (βk, k = 1, 2, 3) with respect to end-members for the CS-H solid solution series, Eqs. (6)–(8), assuming calcium/silicon-ratios of 0.8, 1.0 and 1.8 [16].
β1 = {Ca2+}0.80 ⋅{H3SiO4−}⋅{OH−}0.60 1.26⋅10−7 2
(6)
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β2 = {Ca2+}1.00 ⋅{H3SiO4−}⋅{OH−}1.00 1.68⋅10−9
(7)
β3 = {Ca2+}1.81⋅{H3SiO4−}⋅{OH−}2.62 2.76⋅10−14
(8)
According to the ideal solid solution model [22], which is applied to C-S-H in ref. [16], the total supersaturation (βtot) is the sum of the supersaturation for the individual end-members:
βtot =β1 +β2 +β3
(9)
Details related to the speciation model and the derivation of the solubility products are provided in ref. [16], which also includes references for dissociation constants and complex formation constants. It was assumed in the computation of the C-S-H precipitation rate that the silicon removed from the solution between two subsequent analyses does not produce new nuclei, but is consumed during the growth of the existing nuclei. Nuclei are only formed in the first 5 min after the last addition of the solution with the high silicon concentration. This hypothesis is supported by arguments presented below. The silicon concentration analyzed by ICP-OES is given in units of μmol/L and the absolute amount of silicon in the solution is calculated from the volume of the solution that is known from the original volume of the saturated calcium hydroxide solution modified by titration and sampling. The C-S-H formation rate in units of nmol C-S-H/s is obtained by dividing the difference in silicon content of the solution between two consecutive analyses by the time between the two samplings. The interfacial growth rate in nmol C-S-H/(m2·s) is calculated by dividing the formation rate by the surface area of the growing phase. This surface area can be analyzed by BET or computed from the number and size of the C-S-H particles. The standard deviation reported for the measured [Ca] and [Si] was used to calculate the 1σ-standard deviation of the supersaturation obtaining a value of 7.5%. The standard deviation of [Si] can affect the calculation of the growth rate, which is calculated from the reduction of Si between the samplings. The mean value of 1σ-standard deviation of the growth rate obtained assuming the maximum deviation in these analyses is 20.3%. These values are added as error bars in the following plots.
Fig. 1. Evolution of the silicon concentration in saturated calcium hydroxide solution in the presence of 5 g calcium carbonate after addition of 80 mL of a solution with a high silicon concentration by titration (2 experiments). The 1σ-standard variation of the values for the concentrations has the same size or is smaller than triangles and squares used to indicate the data points.
Fig. 2. Evolution of the calcium concentration in saturated calcium hydroxide solution in the presence of 5 g calcium carbonate after addition of 80 mL of a solution with a high silicon concentration by titration (2 experiments). The error bars give the 1σ-standard deviation.
3. Results It can be assumed that the growth rate of C-S-H depends on the following parameters: supersaturation, surface area available for nucleation and growth, nuclei concentration, substrate material, duration of mixing and calcium concentration. These parameters and additional factors related to the experimental set-up were varied independently to determine their impact on the growth rate.
strongly increased silicon concentration as the particles passing the filter would be later dissolved during acid addition for solution stabilization before analysis by ICP-OES. Most of the nuclei appear within 5 min after the last addition in the period of the highest supersaturation, based on comparison of the nucleation densities after 5 min and at the end of the experiment (see below). The C-S-H formation rate was calculated for each sampling and the results of the computation are provided in Fig. 3. A plot of formation rates in units of nmol C-S-H/s versus the supersaturation with respect to C-S-H indicates an almost linear correlation between formation rate and supersaturation at the conditions used in this experiment. This is misleading, however, because the surface area on which C-S-H is precipitating increases as β decreases; when that factor is taken into account, we will see that the actual growth rate of C-S-H depends nonlinearly on supersaturation. The highest formation rate observed in the experiments is 32 nmol C-S-H/s at high supersaturation (βtot = 38). A slope of formation rate versus supersaturation of ~1 nmol C-S-H/s is found at lower supersaturations. The data in Fig. 3 indicate that the formation rate cannot be resolved at supersaturations below βtot = 5 that are reached at the end of the experiment. This value depends on the speciation model and solubility data used in this study, which affect βtot. Slightly different numbers can be expected if other models are applied. Similar results were obtained when the experiment was repeated at
3.1. Supersaturation The impact of supersaturation on the C-S-H formation rate in the presence of 5 g of calcite was measured two times to test the precision of the analysis. Figs. 1 and 2 present the evolution of the ionic concentrations during the precipitation experiment. The initial CH solution had [Ca] ≈ 23 mmol/L that continuously decreased during titration, because the solution with the high silicon concentration had [Ca] = 3.3 mmol/L. The reduction to ~21 mmol/L results from the dilution of the initial solution during titration and [Ca] remains approximately constant after the last addition, owing to the small amount of C-S-H produced. Fig. 1 shows the evolution of [Si] during the experiment. The initial CH solution has [Si] = 2 μmol/L that rises to 100 μmol/L during titration. When the titration process is terminated, [Si] falls again reaching a value of 7 μmol/L after 255 min. This decrease is attributed to the growth of C-S-H that nucleates on calcium carbonate. There is no increase in the silicon concentration when using a coarser filter for the last sampling which ensures that all C-S-H particles are retained by the filter. Inefficient filtering would result in a 3
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Fig. 3. C-S-H formation rates in units of nmol/s calculated from the data in Figs. 1 and 2 as a function of supersaturation βtot. The error bars give the 1σ-standard deviation.
a slightly lower calcium concentration (red triangles in Figs. 1 and 2). Higher formation rates than would be expected based on a linear dependency on the supersaturation were obtained for the first data points at high supersaturation in this second experiment (Fig. 3). Higher formation rates at lower calcium concentrations are also observed during a systematic variation of [Ca] that is reported below.
Fig. 5. Surface of calcite particle after C-S-H growth experiment (5 g calcite).
3.2. Substrate surface available for nucleation and growth In the current section, the impact of the substrate surface area available for nucleation and growth is investigated by repeating the experiment with different amounts of calcite to derive information on the growth mode. The following calcite amounts were used in the experiments: 0.5, 1.0, 3.0, and 10.0 g. Although there are minor differences in the concentrations of the starting solutions, broadly the same features can be recognized in these experiments. There is an increase in [Si] (Fig. 4) accompanied by a decrease in [Ca] during titration; the maximum in [Si] and its decrease after titration are much alike. A higher silicon concentration in the solution used for titration in the experiment with 1 g calcite resulted in a somewhat higher [Si] after addition. There is a tendency towards a faster reduction of silicon due to C-S-H precipitation when the amount of calcite is increased owing to the larger number of nucleation sites. The calcium concentration after titration stays almost constant and the evolution is similar to the one reported in Fig. 2. The exact values are provided as Supplementary Material. The evolution of the concentrations was used to calculate the supersaturation with respect to C-S-H for each data point and the C-S-H formation rate (Fig. S1). These data are in agreement with precipitation of C-S-H starting on isolated nucleation
Fig. 6. Calcite particle from Fig. 5 at lower magnification.
sites also observed by SEM. Figs. 5 and 6 present micrographs that were acquired after the reference experiment (5 g calcite, titration 4 × 20 mL, 10 mL/min, starting in saturated calcium hydroxide solution). It can be seen that small C-S-H particles are formed by heterogeneous nucleation at the surface of the calcite substrate. The C-S-H particles have a flake-like shape. Most of the individual particles have a length between 5 and 40 nm and a thickness between 2 and 15 nm. It can be seen that the calcite surface is not completely covered and the contact between the C-S-H particles is rather limited initially (Fig. 5). Although the nucleation density and the size of the C-S-H particles can be highly different in the individual micrographs, virtually all calcite surfaces are covered to some extent (Fig. 6). For the replicate runs in Figs. 1 and 2, the nucleation density was ~380 μm−2 in the first test and ~640 μm−2 in the second. The nucleation density was also counted in a similar experiment that was terminated 5 min after the end of the titration (Fig. 7). A nucleation density of 420 μm−2 was estimated for this sample indicating that most of the nuclei form at the highest supersaturation at the end of the titration process or shortly thereafter. Fig. 8 provides information about the identification of nuclei in the counting procedure. Figs. 9 and 10 show micrographs from the experiments with 0.5 g calcite and 10 g calcite, respectively. The nucleation density is only affected to a minor extent, but the size of the C-S-H particles is significantly higher in the experiment with 0.5 g calcite (Fig. 9). The particle densities are difficult to count and the values show standard
Fig. 4. Evolution of the silicon concentration in saturated calcium hydroxide solution containing different amounts of calcite after addition of 80 mL of a solution with a high silicon concentration.
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Fig. 7. Substrate surface 5 min after titration with very small C-S-H particles (approximately 20 nm).
Fig. 10. Surface of calcite particle after C-S-H growth experiment (10 g calcite).
density on the calculated interfacial growth rates is relatively low [20]. 3.3. Impact of maximum supersaturation The amount of silicon solution added during titration affects the maximum supersaturation at the end of the addition process, so the effect of the maximum supersaturation on the formation rate was tested. Additional experiments with a systematic variation of the amount of solution added by the titration device (60 mL, 91 mL, 100 mL) were conducted and the results compared to the run with 80 mL used in the reference experiment. A constant titration velocity of 10 mL/min and a constant amount of substrate (5 g calcite) were used. The evolution of [Si] in these experiments is presented in Fig. 11. The highest concentration after addition of 60 mL solution is [Si] = 74 μmol/L, whereas [Si] = 119 μmol/L after the addition of 100 mL of a solution with a high silicon concentration. Despite the different peak concentrations, the descending part of the curves is similar, indicating comparable growth mechanisms and rates. The calcium concentration in the solutions is similar to that in Fig. 2. It decreases during titration due to dilution and remains constant thereafter within experimental uncertainty. The values are included in the Supplementary Material. Two experiments were stopped at a later time to test whether the growth of C-S-H still continues after the normal experiment duration (4 h 5 min). The experiments with the addition of 60 mL and 91 mL, respectively were terminated 22 h 10 min after titration and [Si]
Fig. 8. Detail from Fig. 10 with markers (■) demonstrating the counting procedure.
deviations up to 40%. It is expected that the results are also affected by systematic errors associated with the counting procedure (viz., difficulty in resolving very small or conjoined particles). However, a numerical simulation has shown that the impact of the nucleation
Fig. 11. Evolution of the silicon concentration in saturated calcium hydroxide solution in the presence of 5 g calcite after addition of different amounts of a solution with a high silicon concentration.
Fig. 9. Surface of calcite particle after C-S-H growth experiment (0.5 g calcite).
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decreased from 14 to 9 μmol/L (60 mL) and from 15 to 11 μmol/L (91 mL) within that time. The solution was still supersaturated (βtot = 4.8 and 5.2, respectively) at the end of the experiment, but the C-S-H formation rate was lower than 0.05 nmol/s within the final period (Fig. S2). 3.4. Duration of mixing The addition of the solution with a high silicon concentration by titration is a rather slow process. Each titration step with a velocity of 10 mL/min takes 2 min and there is also a time interval of 0.5 min between two consecutive titrations related to filling the titration device, so the addition of 80 mL solution in four steps extends over almost 10 min. To test the impact of duration of the mixing process, complementary experiments with a lower titration velocity (5 mL/min) and with a very fast addition of the solution (7 s) were conducted. The solution with the high silicon concentration was added by a large syringe in the experiment with very rapid mixing. The evolution of [Si] in these experiments is reported in Fig. 12 and [Ca] is included in the Supplementary material as it follows the trend in Fig. 2. Although the curves in Fig. 12 are offset due to a variation in the duration of the addition, almost the same slopes can be recognized in the decrease of [Si] over time. This indicates that the C-S-H formation rate is hardly dependent on the duration of the addition. This conclusion is supported by Fig. S3 and the detailed analysis in ref. 20.
Fig. 13. Evolution of the silicon concentration in saturated, supersaturated and undersaturated calcium hydroxide solution in the presence of 5 g calcium carbonate after addition of a solution with a high silicon concentration.
concentration after addition of 80 mL solution is strongly affected by the calcium concentration of the starting solution. The decrease of [Si] at [Ca] = 15 mmol/L is much slower than at [Ca] = 23 mmol/L, but this effect is influenced by a modification of the supersaturation, which is lower in this experiment. The C-S-H formation rates are almost identical in these two experiments (Fig. S4). In contrast to this, the addition of 160 mL solution leads to a much higher formation rate. It will be shown in the discussion section that this results from a change in the number of nuclei of C-S-H formed during the experiments. The experiment in a solution supersaturated with respect to CH shows a reduced maximum [Si] that indicates strong nucleation and growth already during titration.
3.5. Impact of calcium concentration on C-S-H growth rate The calcium concentration is known to affect the calcium/silicon ratio of C-S-H and it might also affect the kinetics of nucleation and growth of this material during hydration of C3S, so this parameter was analyzed in additional experiments. Although most of the growth of CS-H takes place in a solution that is saturated with respect to CH, when working at low water/binder ratios, undersaturated conditions (for portlandite) can play an important role in suspension experiments. The impact of the calcium concentration was investigated by comparing the C-S-H formation rate at [Ca] = 15 mmol/L and [Ca] = 32 mmol/L to the data obtained at [Ca] = 21–23 mmol/L. A higher amount of silicon is required at low calcium concentrations to obtain the same supersaturation with respect to C-S-H as in experiments in saturated CH solution. Beside the addition of 80 mL of a solution with a high [Si], the titration was extended to 160 mL in an additional experiment. Other parameters, such as titration velocity (10 mL/min) and amount of substrate (5 g calcium carbonate), were kept constant. The results of these experiments are presented in Fig. 13 and in the Supplementary Material. It is observed that the slope of the silicon
3.6. Growth of C-S-H after homogeneous nucleation Most of the experiments in this study were conducted in the presence of calcite that is known to have a surface favorable for C-SH nucleation [10]. The impact of calcite on the formation rate was investigated in an additional experiment in the absence of substrate material. The solution with a high silicon concentration was added in four titrations steps with a velocity of 10 mL/min to a saturated CH solution. The evolution of [Si] is reported in Fig. 14; [Ca] follows the trend in Fig. 2 and the data is available in the Supplementary material (Table S1). The silicon concentration stays more or less constant for a period of 15 min after the titration when calcite is absent from the system. It is expected that this period is the nucleation time lag at this supersaturation for the homogeneous nucleation of C-S-H in the
Fig. 12. Evolution of the silicon concentration in saturated calcium hydroxide solution in the presence of 5 g calcium carbonate after addition of 80 mL of a solution with a high silicon concentration using different addition velocities.
Fig. 14. Evolution of the silicon concentration in saturated calcium hydroxide solution in the presence or absence of 5 g calcium carbonate after addition of 80 mL of a solution with a high silicon concentration.
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particles. A more rigorous analysis, taking account of growth rate anisotropy and particle impingement, is presented in ref. 20. Calculation of the average growth rate requires knowledge of the molar volume and surface area of the growing particles. The calculation is complicated by the fact that the surface area of C-S-H is difficult to analyze and changes during the growth experiment. Two different methods were used to estimate the surface area of the hydrates: gas adsorption and numerical calculation using particle shapes and nucleation densities based on SEM data. The surface area of the C-S-H particles at the end of the experiment can be analyzed by gas adsorption (BET) after subtraction of the uncovered part of the surface area of the substrate. However, the specific surface area of the samples in this study is relatively small and thus the surface area of the precipitates contains significant uncertainties. The results are also affected by assumptions made for the calcite/CS-H ratio in the samples analyzed by BET. Table 1 provides BET data for samples with a mass exceeding 2 g after the experiment. These values are the specific surface areas of the calcite powders used as a substrate with a small amount of C-S-H deposited on the surface. The second method to estimate the surface of C-S-H, which is a simplification of the approach used in ref. 20, relies on the calculation of the surface area of the hydrate particles during the growth process. Input parameters for this computation are the volume of precipitated CS-H, number of particles, and particle shape. The volume of precipitated C-S-H is obtained from the amount of silicon precipitated during the experiment and the molar volume of C-S-H (7.6·10− 5 m3/mol); this value is based on the data in ref. [23], assuming 2 mol of water per formula unit of C-S-H. The titration device was affected by a build-up of pressure in the closed bottle, so the amount of dosed silicon had to be extrapolated. It is found from this extrapolation that the added silicon is slightly higher (5–8%) than indicated by the first sampling after addition. The total number of C-S-H particles can be calculated from the mass and specific surface area of the substrate, together with the CS-H particle density on the substrate obtained by SEM. The particle
solution, or for heterogeneous nucleation on less favorable surfaces. Once nucleation has occurred, the decrease in [Si] over time is slower than in the presence of calcium carbonate. The rate of C-S-H formation is presented in Fig. S5. The solid residue obtained after filtration of the sample without calcite was analyzed by SEM. Figs. S6 and S7 indicate the formation of aggregates consisting of flake-like particles with a length between 50 and 500 nm. The particles formed in this case are much larger than in the presence of a calcite substrate. It was not possible to estimate the nucleation density of this sample as there was no surface available for heterogeneous nucleation. This sample was also analyzed by energydispersive X-ray spectroscopy (EDS). The spectra, shown in the Supplemental material, confirm the presence of calcium, silicon and oxygen in the analyzed material (Fig. S8). It was not possible to extract reliable information about the Ca/Si-ratio in the C-S-H particles. 4. Discussion The experimental investigations in this study provide formation rates in nmol/s for the precipitation of C-S-H on a calcite substrate surface. These rates strongly depend on the supersaturation during the growth process and the calcium concentration in the solution. Compared to these two factors, other parameters such as maximum supersaturation, amount of substrate and duration of the mixing process have a much lower impact on the formation kinetics expressed in the units of nmol/s. SEM micrographs taken after the experiments demonstrate that the C-S-H particles grow from distinct sites on the substrate surface after heterogeneous nucleation. To relate the data from these experiments to the growth rate of C-SH, the formation rates in nmol/s need to be expressed as interfacial growth rates in nmol/(s·m2) or as linear growth rates in nm/h. From the shape of the particles in the SEM images, it is clear that the growth rate is anisotropic, but we will estimate the average rate of growth by dividing the volume of C-S-H precipitated by the surface area of the Table 1 Summary of the growth rate experiments. Starting solution
Added solution
Substrate
Nuclei density [μm− 2]
Growth rate at βtot = 20 [nmol C-S-H/(s·m2)]
BET [m2/g]
0.7 L saturated calcium hydroxide solution (Ca = 23.3 mmol/L, Si = 2 μmol/L) 0.7 L saturated calcium hydroxide solution (Ca = 21.8 mmol/L, Si = 6 μmol/L) 0.7 L saturated calcium hydroxide solution (Ca = 23.1 mmol/L, Si = 3 μmol/L) 0.7 L saturated calcium hydroxide solution (Ca = 22.7 mmol/L, Si = 4 μmol/L) 0.7 L saturated calcium hydroxide solution (Ca = 22.6 mmol/L, Si = 5 μmol/L) 0.7 L saturated calcium hydroxide solution (Ca = 22.3 mmol/L, Si = 8 μmol/L) 0.7 L saturated calcium hydroxide solution (Ca = 21.0 mmol/L, Si = 4 μmol/L) 0.7 L saturated calcium hydroxide solution (Ca = 22.2 mmol/L, Si = 7 μmol/L) 0.7 L saturated calcium hydroxide solution (Ca = 22.8 mmol/L, Si = 4 μmol/L) 0.7 L saturated calcium hydroxide solution (Ca = 20.8 mmol/L, Si = 6 μmol/L) 0.7 L saturated calcium hydroxide solution (Ca = 22.0 mmol/L, Si = 4 μmol/L) 0.7 L undersaturated calcium hydroxide solution (Ca = 14.8 mmol/L, Si = 3 μmol/L) 0.7 L undersaturated calcium hydroxide solution (Ca = 15.3 mmol/L, Si = 6 μmol/L) 0.7 L supersaturated calcium hydroxide solution (Ca = 31.6 mmol/L, Si = 8 μmol/L) 0.7 L saturated calcium hydroxide solution (Ca = 21.7 mmol/L, Si = 6 μmol/L)
4 × 20 mL, 10 mL/min 4 × 20 mL, 10 mL/min 4 × 20 mL, 10 mL/min 4 × 20 mL, 10 mL/min 4 × 20 mL, 10 mL/min 4 × 20 mL, 10 mL/min 3 × 20 mL, 10 mL/min 4.5 × 20 mL, 10 mL/min 5 × 20 mL, 10 mL/min 4 × 20 mL, 5 mL/min 80 mL, rapid mixing 4 × 20 mL, 10 mL/min 8 × 20 mL, 10 mL/min 4 × 20 mL, 10 mL/min 4 × 20 mL, 10 mL/min
5.0 g calcite
380
10.3
0.77
5.0 g calcite
640
10.5
0.78
0.5 g calcite
255
15.2
Not analyzed
1.0 g calcite
274
6.6
Not analyzed
3.0 g calcite
461
5.8
1.08
10.0 g calcite
323
10.3
0.51
5.0 g calcite
202
10.6
0.64
5.0 g calcite
318
12.4
0.84
5.0 g calcite
358
11.1
0.86
5.0 g calcite
292
14.1
0.67
5.0 g calcite
309
11.8
0.69
5.0 g calcite
123
35.8
0.54
5.0 g calcite
213
38.0
0.91
5.0 g calcite
231
6.1
0.69
no substrate
–
not available
Not analyzed
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Fig. 16. Interfacial growth rates for C-S-H calculated from data in Fig. 3 and Fig. 15 as a function of supersaturation. The error bars give the 1σ-standard deviation for the data based on ICP-OES data and does not include uncertainties related to the surface area estimation (see text).
Fig. 15. Evolution of the surface area of C-S-H for two experiments calculated from the silicon concentrations in Fig. 1, particle density from Table 1 and assumptions for the particle shape.
(0.7 m2). The other two experiments with a higher interfacial growth rate were performed in undersaturated CH solution. This indicates that the mean interfacial growth rate of ~10 nmol/(s·m2) is valid in a saturated CH solution whereas higher growth rates are expected for lower calcium concentrations at the same supersaturation. Also not included in the mean value is the experiment in supersaturated CH solution. The detailed analysis in ref. 20 indicates higher growth rates of G2 ≈ 20–24 nmol/(s·m2) at βtot = 20, but this refers to growth perpendicular to the substrate; in the plane of the substrate, the ellipsoidal particles are estimated to have growth rates of G3 ≈ G2 and G1 ≈ G2/5. The difference to the aforementioned mean value of ~10 nmol/(s·m2) is related to the geometric assumptions used in the definition of the growth rate. It is here assumed that growth takes place perpendicular to the surface of C-S-H particles; for an ellipsoidal particle, the average rate normal to the surface is smaller than G2, owing to the lower value of G1 (i.e., the rate of increase in thickness of the flake-like ellipsoid). The perpendicular growth rates reported here are lower by a factor of 2.7 than the values of G2 reported in ref. 20. A quantitative analysis of this point is presented in Appendix 3 of that paper. It is possible that the C-S-H growth rates also depend on other parameters that were not investigated in this study. For example, the transport of ions that can be affected by the rate of stirring and the water/solids ratio in the experiments; however, the growth rates are so slow that those factors are probably negligible. On the other hand, there is clearly an effect of [Ca] at a given supersaturation and significant effects are likely to be found in the presence of other ions, such as sulfates and aluminates. The latter factors are beyond the scope of the present work, but they could be explored using the present experimental procedure. The results of the experimental investigations in this study are fitted to a boundary nucleation and growth model to obtain additional information for parameters such as calcium/silicon ratio of the growing phase, particle shape, nucleation density and calcium concentration in solution in ref. [20].
shape found in the SEM micrographs is approximated as identical semiellipsoidal particles with axes a3 = a2 = 5 a1 where a3 is the length in contact with the substrate, a2 is the height perpendicular to the substrate, and a1 is the thickness of the particle. The same particle shape was used for all calculations independent from the Ca-concentration in solution as it was not possible to see differences in particle shapes of the nano-sized C-S-H particles by SEM. Again, the growth rate is found by dividing the volume of C-S-H by the area of the semiellipsoids, so that the anisotropic rates are averaged out. The surface areas obtained by these calculations are shown in Fig. 15 for two experiments. Most of the silicon is precipitated in the first 50 min of the experiment and the total surface area of the C-S-H particles has reached approximately 90% of the final value within this period. Values between 100 and 150 m2/g for the specific surface area of C-S-H are computed for the end of the experiment. The calculation is sensitive to the shape assumed for the C-S-H particles and the nucleation density. Both parameters were obtained from SEM micrographs and it is expected that the accuracy of the C-S-H surface is not better than 1.0 m2. The final values for the total C-S-H surface area precipitated on the calcite, estimated from the particle shape and amount of C-S-H, are higher (2.0 and 2.4 m2, respectively) than the surface area re-calculated from the BET results in Table 1 (1.5 and 1.6 m2, respectively). The over-estimate is to be expected, because overlap of the particles is neglected in the calculation; extensive overlap results in the total surface area being less than the sum of the areas of nonoverlapping ellipsoids. The gap of about 30% between these values indicates the importance of accurate estimation of the surface area for the analysis of growth rates. Therefore, a more rigorous treatment for the analysis of C-S-H growth rates is provided in ref. 20. Fig. 16 shows the interfacial growth rates versus supersaturation for two experiments. Supplementary data for the other experiments are summarized in Table 1 and provided in more detail in ref. [20]. This plot indicates that the growth rate of C-S-H depends nonlinearly on the supersaturation. Whereas this curve is roughly parabolic, the analysis in ref. 20 (taking account of particle impingement) shows that it is cubic. The estimated interfacial growth rate at a supersaturation βtot = 20 that is relevant for the hydration of tricalcum silicate is presented in Table 1. Most of the values are in the range between 5 and 15 nmol/ (s·m2) with a mean value of 10.4 nmol/(s·m2) and a standard deviation of 2.5 nmol/(s·m2). A higher growth rate is observed in some experiments which are not included in the calculation of the mean value. The run with a very low amount of substrate (0.5 g calcite) gave a slightly higher value for the interfacial growth rate although the formation rates in μmol/s were almost identical to the other experiments (Fig. S1). This is due to the much lower C-S-H surface area calculated for this sample
5. Conclusions The following conclusions can be drawn from this study:
• The • 8
growth kinetics of calcium silicate hydrate (C-S-H) can be analyzed by monitoring the evolution of the silicon concentration in solutions supersaturated with respect to this phase. Application of the results of the growth experiments to the hydration of tricalcium silicate is facilitated when the supersaturation is in
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•
•
• • • •
DTFH61-12- H-00003 and ARRA Grant 611-473300-60026039 PROJ0002228. The information in this paper does not necessarily reflect the opinion or policy of the federal government and no official endorsement should be inferred.
the same range as observed during hydration, the solution is nearly saturated with respect to calcium hydroxide, foreign ions are absent from the system and the solution is undersaturated with respect to other silicate phases. These conditions can be met when the supersaturated solution is prepared by mixing saturated calcium hydroxide solution with a solution obtained from the early hydration of tricalcium silicate in a ratio that is approximately 10:1. If calcite is added to the supersaturated solutions as a substrate, the decrease of the silicon concentration resulting from nucleation and growth of C-S-H starts much sooner than in the absence of calcite. This confirms other studies that have shown that calcite is a favorable substrate for heterogeneous nucleation of C-S-H, resulting in a lower critical supersaturation and induction time than for homogeneous nucleation. Rapid formation of nuclei on calcite allows measurement of the growth rate of C-S-H without complications from concurrent nucleation. The decrease of the silicon concentration between two consecutive analyses of the solution and the time between the samplings can be used to calculate a formation rate in units of nmol/s for the growth of C-S-H. This formation rate is strongly affected by the supersaturation in the solution, the availability of calcite as a substrate for heterogeneous nucleation, and the calcium concentration in solution. Other parameters such as amount of substrate material, duration of mixing, and the ratio of the starting solutions have only a minor effect on the C-S-H formation rate. A calculation of interfacial growth rates in nmol/(s·m2) or linear growth rates in nm/h from the formation rates requires knowledge of the surface area of the growing phase. Values for the surface area were derived from BET data and from particle concentration and shape as determined by SEM. The average growth rate of C-S-H depends nonlinearly on the supersaturation. It is shown in ref. 20 that this dependence is roughly cubic. The average interfacial growth rate of C-S-H after heterogeneous nucleation on a calcite substrate in solutions nearly saturated with respect to calcium hydroxide at a supersaturation β = 20 is approximately 10 nmol/(s·m2). Higher growth rates are observed for lower calcium concentrations. The technique used in this study can be used to analyze the impact of foreign ions or organic additives on the C-S-H growth rate.
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Supplementary data to this article can be found online at http://dx. doi.org/10.1016/j.cemconres.2017.05.007. Acknowledgements GWS was supported by Federal Highway Administration Grant
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