Submicrometric Picture of Plaster Hydration: Dynamic and Space

Article pubs.acs.org/JPCC

Submicrometric Picture of Plaster Hydration: Dynamic and SpaceResolved Raman Spectroscopy versus Kinetic Monte Carlo Simulations Suzanne Joiret,†,‡ Francoise Pillier,†,‡ and Annie Lemarchand*,§,∥ †

Sorbonne Universités, UPMC Univ Paris 06, Laboratoire Interfaces et Systèmes Electrochimiques (LISE, UMR 8235), 4 place Jussieu, case courrier 133, 75252 Paris Cedex 05, France ‡ CNRS (LISE, UMR 8235), 3 Rue Michel-Ange, 75016 Paris, France § Sorbonne Universités, UPMC Univ Paris 06, Laboratoire de Physique Théorique de la Matière Condensée (LPTMC, UMR 7600), 4 place Jussieu, case courrier 121, 75252 Paris Cedex 05, France ∥ CNRS (LPTMC, UMR 7600), 3 Rue Michel-Ange, 75016 Paris, France ABSTRACT: To propose a picture of plaster hydration at a submicrometric scale, we have developed a kinetic Monte Carlo simulation model of gypsum crystal growth. Raman spectroscopy is used to check the model and to assign physical values to the parameters. Special focus is put on the effects of increasing plaster-to-water ratio and using citric acid as an additive. The hypothesis about the autocatalytic growth of gypsum needles during the first stage of the reaction is confirmed by the correct simulation of the induction period preceding the fast growth regime. The aspect ratio of gypsum needles, defined as the ratio of needle length and width, emerges as a relevant parameter to control both dynamics and material structure. Addition of citric acid is known to produce compact gypsum crystals instead of long needles. The choice of a small aspect ratio is sufficient for the simulations to reproduce the effects of citric acid, including the slowing down of the reaction without recourse to fitting parameters. The kinetic Monte Carlo simulation model proved to be a predictive tool that could assist the rational development of novel additives and reagent treatments with the aim of producing materials with predefined properties.

1. INTRODUCTION For thousands of years, gypsum or calcium sulfate dihydrate, CaSO4·2H2O, has been empirically produced from the hydration of plaster of Paris (bassanite) or β-calcium sulfate hemihydrate, CaSO4·1/2H2O, without the phenomenon being subject to intense efforts of modeling. Gypsum is widely used for many purposes as, for example, plaster board for the building industry, casting molds for ceramics production, highquality stone for dental prosthesis, bone grafting, and local drug delivery in biomedical applications.1,2 The effects of many different additives on the structure of the resulting crystal have been reported.3−16 Different uses require the optimization of different properties, which has been essentially attempted by a trial-and-error approach, which, despite the low cost of the raw material, results in a repetitive, ineffective, and eventually expensive procedure. To build a comprehensive picture of plaster hydration at a mesoscopic scale and to rationalize the search for an additive designed to produce a material with the desired properties, we recently proposed a model and a kinetic Monte Carlo simulation algorithm.17 The chosen submicrometric description scale is original in the framework of crystal growth and lies between the molecular level18,19 and the macroscopic scale.20−24 The model relies on a few basic ingredients so that it is easy to relate the variation of a parameter to the resulting dynamics and structure. Up to now, the chosen © 2014 American Chemical Society

experimental techniques, such as measurements of electrical conductivity,4,21,25 acoustic emission,26,15,17 and cryogenic transmission electron microscopy,27,28 proved to be badly suited to follow dynamics at the relatively high plaster-to-water ratios typically used to synthesize gypsum materials. Nuclear magnetic resonance (NMR) offers a nice technique to follow the structural changes occurring during plaster setting,29 but as for previously used techniques such as calorimetry, 30 information is not straightforwardly related to the instantaneous value of the extent of the reaction. One of our aims is to show that Raman spectroscopy is a well-adapted tool to investigate the dynamics of plaster hydration in the entire range of the plaster-to-water ratios and to study some structural properties of the obtained material. The essential point is that the stretching vibration of the tetrahedral sulfate group is affected by the change of environment in the crystals of hemihydrate and dihydrate,31,32 so that the progress of the hydration reaction can be followed. We will compare the results of dynamic Raman spectroscopy with the extent of the reaction predicted by the simulation results, in order to test the model and assign physical values to the parameters. Special focus will be put on the influence of Received: October 7, 2014 Revised: November 18, 2014 Published: November 19, 2014 28730

dx.doi.org/10.1021/jp510114j | J. Phys. Chem. C 2014, 118, 28730−28738

The Journal of Physical Chemistry C

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increasing plaster-to-water ratio on dynamics and on dynamical and morphological consequences of using citric acid as an additive. Rather than looking for best fits to reach excellent quantitative agreement between the simulation results and specific experimental situations, our goal is to check the hypotheses of the model and to develop a predictive simulation tool valid in a general context. The paper is organized as follows. The experimental methods and the simulation algorithm are detailed in the next section. Section 3 contains results and discussion. The conclusion is given in section 4.

2. EXPERIMENTAL METHODS AND SIMULATION ALGORITHM 2.1. Experimental Methods. Surface analyses of the samples were performed with a LEICA STEROSCAN 440 scanning electron microscope (SEM). Raman microspectroscopy was performed with a Labram (Horiba) spectrometer. The samples were irradiated with a He−Ne laser at λ = 632.8 nm with an Olympus BX 41 microscope. The laser power was set at 1 mW to avoid any thermal effect on the sample during the analyses. The investigated area is limited to 5 μm2 using a 50 ultra-long working distance (ULWD) objective lens. The confocal hole was set at maximum to record the spectrum from the entire layer thickness (150 μm). A specially designed cell was used for Raman experiments. It consists of a parallelepiped with a volume of 104 × 104 × 150 μm3 made from two microscope coverslips with a Scotch tape spacer, ensuring that the experiment is reproducible at the microscopic scale. The amounts of hemihydrate and water have been adjusted to take into account the volume expansion of the resulting material. Hemihydrate and citric acid were purchased from SigmaAldrich. Deionized water was used. Hemihydrate has been dried at 130 °C for 1 week and then kept under Argon atmosphere. For each experiment, Raman light was collected for 30 s during each 31 s until the end of hydration. Then, a 140 μm × 90 μm cartography was recorded with a 2 μm step to examine if the reaction was complete and evaluate the final value of the extent of the reaction. 2.2. Simulation Algorithm. The simulation procedure relies on a kinetic Monte Carlo algorithm.17 An initial configuration of plaster grains with germination sites is defined, and random processes of gypsum needle growth and plaster grain dissolution are sequentially performed. The speed of plaster hydration is supposed to be imposed by gypsum precipitation, so that the fast dissolution process adiabatically follows the growth process. This hypothesis should be reconsidered in the case of α-hemihydrate, known to have a lower specific surface than the one of β-hemihydrate. The real shape of β-hemihydrate grains is not taken into account and they are modeled by spheres of variable diameter d that are randomly spread in a cubic box of side L with periodic boundary conditions. According to Figure 1, the diameter of the big grains may reach 30 μm and the diameter of the small grains is of the order of 1 μm. The typical size of hemihydrate grains is used to choose the length scale in the simulation. Big grains are first placed and smaller grains are then added to sample the desired diameter distribution function PV given in Figure 1 and defined by volume-weighted mean value ⟨d⟩V and standard deviation σd. More precisely, the grain diameters are sampled from the weighted sum of two Gaussian distributions. The distribution of the bigger grains is characterized by a mean value of 40 μm, a standard deviation of 42 μm, and a weight of

Figure 1. Scanning electron microscope image of β-hemihydrate grains of the plaster used in the experiments and volume-weighted distribution PV of the logarithm of plaster grain diameter log10 d used in the simulations (d in μm).

0.3. The distribution of the smaller grains is characterized by a mean value of 18 μm, a standard deviation of 24 μm, and a weight of 0.7. However, it is to be noted that, due to the nonoverlapping constraint, the resulting distribution differs from the sum of two Gaussians: big grains are less and less easily inserted into the simulation box whereas small grains are more systematically accepted. Consequently, the shape of the obtained distribution and its consistency with the experimental data have to be checked a posteriori. A given plaster-to-water ratio, mp/mw, is imposed, where mp and mw are the masses of plaster and water, respectively. We admit that all the nuclei preexist on the surface of the hemihydrate grains when the reaction of hydration begins. At the beginning of the simulation, nuclei are randomly placed on the grains with a surface density g. The nuclei are supposed to already have the shape of embryonic gypsum needles. They are rectangular parallelepipeds with a square base of side w0, of the order of a few nanometers, and an aspect ratio α0 = l0/w0, where l0 is the initial length. The direction of the embryonic needles is randomly chosen. The number and direction of needles remain unchanged during simulation. At any time, the solution is supposed to be supersaturated with respect to dihydrate.21 During the simulation time step Δt, the growth of each needle is considered. Local equilibrium, which would imply that, at each time step, a needle reaches the shape that minimizes its surface energy, is not strictly obeyed. A needle is supposed to keep a parallelepiped shape but with a variable aspect ratio α = l/w, where l and w are needle length and width, respectively. The kinetic Monte Carlo procedure requires the definition of the rates of particle growth and shrinking. Two different needle-growth regimes are considered. First, an autocalytic, surface-dependent growth is accepted with probability pS/Sc until needle total surface S reaches a critical value Sc. Then, growth is supposed to be controlled by the diffusion of the reactants in the liquid phase and occurs with constant probability p. Actual needle growth is accepted if the faces are not blocked by steric hindrance, i.e., by the contact with other solids, such as plaster grains and other needles. If growth is allowed, the same volume, αw2Δw0, of gypsum is deposited on each free face, where Δw0 is constant. Purely homothetic growth, i.e., with strict conservation of the aspect ratio, occurs if none of the pairs of opposite faces is blocked. Even in the case 28731



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of blocked opposite faces, the growth of a free face is accepted if the aspect ratio of the needle is in the allowed interval. On the simulation time scale, the growth process is irreversible and the needles never shrink. After needle growth, grain shrinking is systematically performed. During time t and t + Δt, the increase ΔVDH(t) = VDH(t + Δt) − VDH(t) of the total volume of gypsum or dihydrate (DH) is equal to the sum of the volumes precipitated during Δt on the needles for which growth has been accepted. Consequently, the number of moles of dihydrate that precipitated is equal to nDH(t) = ΔVDH(t)(ρDH/mDH), where ρDH = 2.32 × 103 kg·m−3 is the density of dihydrate and mDH = 0.1722 kg is the molar mass of dihydrate. The same number of moles of plaster or hemihydrate (HH) has to be dissolved. Consequently, the total volume of hemihydrate to be dissolved is ρ m ΔVHH(t ) = ΔVDH(t ) DH HH ρHH mDH (1) where ρHH = 2.63 × 103 kg·m−3 and mHH = 0.1452 kg are the density and molar mass of hemihydrate, respectively. We assume that all the hemihydrate grains lose an external shell of the same width ΔR, so that ΔVHH(t ) = ΔRπ ∑ dk 2 k

Figure 2. Initial (a, c) and final (b, d) configurations obtained in a simulation for an aspect ratio of needles α = 12 ± 7 and a plaster-towater ratio mp/mw = 0.6 for (a, b) and mp/mw = 3 for (c, d). The other parameter values are given in Table 1. The simulation box is a cube of 80 μm sides. Plaster grains (blue spheres) of diameter d < 0.6 μm in (a) and d < 4 μm in (c) are omitted; gypsum needles are represented in orange. Simulation stops when all plaster grains have been dissolved in (b) and due to blocking of all the needles in (d).

(2)

where dk is the diameter of the hemihydrate grain k and where the summation is performed over all the grains existing at time t. Using eqs 1 and 2, we find that the external shell lost by each hemihydrate grain has a width equal to ΔR =

ΔVDH(t ) ρDH mHH π ∑k dk 2 ρHH mDH

Table 1. Parameters Characterizing a Gypsum Needle and a Plaster Grain and Values Used in the Simulations; The Side of the Simulation Box Is Fixed at L = 80 μm

(3)

To summarize, the algorithm consists of a sequence of two steps. First, growth of each needle is considered with the appropriate probability and performed if steric hindrance and aspect ratio conservation permit it. Second, shrinking of each grain is completed, according to conservation of matter. The number of needles and their orientation are fixed. Needles and grains are immobile. After a succession of growth and dissolution steps, the simulation ends either when the total amount of hemihydrate has dissolved or when all the needles are blocked by steric hindrance. Typically, the simulation algorithm allows us to follow the reaction, from an initial configuration of plaster grains to a final configuration of gypsum needles, as shown in Figure 2 (left), for mp/mw = 0.6. Table 1 lists the parameters introduced in the simulations and gives the values that are used in all the simulations. Different plaster-to-water ratios, 0.6 ≤ mp/mw ≤ 3, are considered. Instead of kinetic Monte Carlo simulations, a stochastic description relying on a master equation for the probability of needle lengths has been established for the same model of plaster hydration in order to derive analytical expressions for the mean reaction time and its standard deviation.33

gypsum needle initially

initial width: w0 = 0.008 μm, initial aspect ratio: α0, in pure water: α0 = 12,

at time t

3. RESULTS AND DISCUSSION 3.1. Without Additives. To reproduce the needle shape observed in Figures 3 and 4 from plaster in pure water without additives, we allow the aspect ratio α of needles to fluctuate around 12. One of the goals of this work is to show that dynamics of plaster hydration may be followed by dynamic Raman

during Δt = 1 s

with citric acid: α0 = 2, aspect ratio: α, in pure water: α = 12 ± 7, with citric acid: α = 2 ± 0.2, critical surface controlling growth rate: Sc = 0.1 μm2, surface density of embryonic needle: g = 1/π μm−2 if d > 1 μm, 1 embryonic needle per grain if d ≤ 1 μm, density: ρDH = 2.63 × 103 kg· m−3, molar mass: mDH = 0.1722 kg width: w, surface: S, growth probability: pS/Sc if S < Sc (Sc = 0.1 μm2), p = 0.1 if S ≥ Sc, volume increase per free face: αw2Δw0,

plaster grain volume-weighted mean diameter: ⟨d⟩V = 13.3 μm volume-weighted standard deviation of diameter: σd = 3.7 μm plaster-to-water ratio: mp/mw,

density: ρHH = 2.32 × 103 kg· m−3, molar mass: mHH = 0.1452 kg diameter of grain k: dk,

radius decrease: ΔR

with Δw0 = 0.005 μm

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Figure 3. Scanning electron microscope image of gypsum needles obtained without additives and for a plaster-to-water ratio mp/mw = 0.6. Typical values of needle width w and length l are indicated.

Figure 5. (Top) Raman spectra of pure plaster of Paris (bassanite) or β-calcium sulfate hemihydrate (dashed blue line) and pure gypsum or calcium sulfate dihydrate (solid red line). The vertical lines define the range of wave numbers used to evaluate the presence of hemihydrate in a sample. (Bottom) Dynamic Raman spectroscopy of a sample of βhemihydrate and pure water without additives for mp/mw = 2. Time decay of the peak around νHH = 1015 cm−1 due to consumption of hemihydrate and simultaneous time increase of the peak around νDH = 1007 cm−1 due to precipitation of dihydrate. Figure 4. Scanning electron microscope image of gypsum needles obtained without additives and for a plaster-to-water ratio mp/mw = 2. Needles are thinner and smaller than in Figure 3, obtained for mp/mw = 0.6.

spectroscopy. As shown in Figure 5 (top), the stretching vibration of sulfate ions SO2− 4 is affected by the difference of environment in the hemihydrated and dihydrated calcium sulfate crystals, leading to two separated bands in the Raman spectrum of a reactive mixture of plaster and water. Qualitatively, the consumption of hemihydrate (HH) and simultaneous formation of dihydrate (DH) are deduced from the decreasing amplitude of the band around νHH = 1015 cm−1 and the increasing amplitude of the band around νDH = 1007 cm−1, as shown in Figure 5 (bottom). However, Figure 5 (top) reveals that the spectrum of pure hemihydrate possesses a small bump around 1007 cm −1 that pollutes the band of dihydrate.31,32 Consequently, time-dependent relative values of the extent of the reaction are deduced from the evolution of the area of the characteristic band associated with hemihydrate in the range 1017−1023 cm−1. When the extent of the reaction is no longer evolving, space-resolved Raman spectra are acquired to determine if the reaction is complete or to evaluate a spatial average of the fraction of remaining hemihydrate in the obtained material. Then, the fraction of formed dihydrate is computed and used to normalize the extent of the reaction. For sufficiently low values of plaster-to-water ratio, mp/mw = 0.6 and 2, space-resolved Raman spectroscopy of the obtained materials does not evidence a residual peak around νHH = 1015 cm−1 in any local spectrum, proving that the reaction is complete in the entire sample. On the contrary, for mp/mw = 3, the cartography given in Figure 6 reveals that hemihydrate is still present in the form of grains after the end of the reaction.

Figure 6. Space-resolved Raman spectroscopy of the material obtained 24 h after mixing of β-hemihydrate and pure water without additives for mp/mw = 3. A 140 μm by 90 μm sample is analyzed with a resolution of 2 μm. The grayscale represents the area (in arbitrary units) of the hemihydrate band in the range 1017−1023 cm−1, white pixels correspond to pure hemihydrate, and black pixels correspond to pure dihydrate.

Quantitative results are given in Figure 7 for three different plaster-to-water ratios, mp/mw = 0.6, 2, and 3, including high values, for which the previously employed techniques, such as conductimetry21,25 and acoustic emission,17 failed. Indeed, as the proportion of solid compared to liquid increases, the ultrasonic waves are screened and do not reach the sensor: The cumulative number of acoustic emission hits detected during the reaction becomes too low to allow for the detection of the inflection point of the curve.17 The value mp/mw = 0.6 corresponds to dilute conditions under which setting of the material is not easily obtained. The value mp/mw = 2 is typically used in the building industry and to obtain reusable, porous gypsum molds, for example, to produce ceramics, whereas the 28733



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in the case of incomplete reaction, where VHH(t = 0) is the initial volume of hemihydrate. The appropriate balance between the initial surface-dependent growth and the later growth at constant rate is crucial to reproduce that the reaction is faster for a larger value of the plaster-to-water ratio. The relevant parameter is the ratio p/Sc. With the width increase Δw0 = 0.005 μm during the growth process, the choice of the constant growth probability rate p = 0.1 simply fixes the time scale. A physical value of the time step Δt = 1 s is attributed by comparing simulation results and dynamic Raman spectroscopy for mp/mw = 3 in Figure 7. Close simulation results would be obtained by dividing Δw0 by a given factor and multiplying p by the same factor with the constraint p ≤ 1. However, the model is clearly not valid at the atomic scale, and the choice of smaller values of Δw0 would be unphysical. Too big values of Δw0 would favor the formation of very big needles, which would drain most of the matter, generate a high level of steric hindrance, and eventually lead to an incomplete reaction for values of mp/mw < 3. If the critical surface Sc is increased at constant p, in order to lengthen the initial induction period with respect to the abrupt transition, the behaviors at different mp/mw are initially identical and differ at longer time only due to steric hindrance, which leads to a slowing down of the reaction instead of an acceleration as mp/mw increases. Therefore, the critical surface Sc cannot be chosen as too large. The best qualitative agreement with the experimental results is obtained for p/Sc = 1, for which the induction period is less pronounced than in the experimental results. To slow down the reaction at short time, the initial width w0 = 0.008 μm of the embryonic needles is chosen small, but this parameter can clearly not sufficiently influence the slopes at short times of the curves given in Figure 7, which remain larger than in the experimental curves. Hence, the results of the simulation model qualitatively agree with the results of Raman spectroscopy: an increase of the plaster-to-water ratio speeds up the reaction, but for mp/mw = 3, the extent of the reaction does not reach 1, revealing that the reaction is incomplete. Whereas for mp/mw = 0.6 and 2, the simulation ends when all the hemihydrate has been dissolved, the simulation stops for mp/mw = 3 because of the blocking of all the gypsum needles. The further growth of each needle is hindered, either because each face is in contact with another solid or because the growth of some remaining free faces would move away the aspect ratio α from the acceptable range. The comparison between the initial and final configurations given in Figure 3 for mp/mw = 3 clearly shows that some plaster grains are still present at the end of the simulation at the places where big plaster grains were initially present. This result suggests that, in Figure 6, the white clusters associated with the detection of the typical hemihydrate band around 1015 cm−1 in the space-resolved Raman spectra are located at the initial places of big plaster grains. The simulations also give access to the structure of the material from a few tens of nanometers to a hundred micrometers. In particular, a quantitative analysis of needle length can be easily deduced from the configurations. The time variation of the volume-weighted mean needle length ⟨l⟩V is given in Figure 8. After a short induction time identical for the different plaster-to-water ratios mp/mw in the range 0.6 and 3, the mean length increases linearly for mp/mw = 0.6 whereas ⟨l⟩V saturates and tends to a limit for mp/mw = 3. Length variation shows that needle growth is not perturbed by steric hindrance at a low plaster-to-water ratio mp/mw = 0.6, contrary to what is

Figure 7. (Top) Extent of the reaction, ξRaman, deduced from dynamic Raman spectroscopy for mp/mw = 3 (solid green line), mp/mw = 2 (dashed blue line), and mp/mw = 0.6 (dotted red line). The data are normalized from the analysis of the obtained material by spaceresolved Raman spectroscopy. (Bottom) Extent of reaction, ξ, versus time, t, deduced from the simulations for an aspect ratio of needles α = 12 ± 7 and different plaster-to-water ratios: mp/mw = 3 (solid green line), mp/mw = 2 (dashed blue line), and mp/mw = 0.6 (dotted red line). The other parameters are given in Table 1.

value mp/mw = 3 leads to hard, scratch-resistant materials, employed, for example, in dental prosthesis. For sufficiently small values of plaster-to-water ratio, mp/mw ≤ 2, the evolution can be decomposed into three stages, an induction period followed by a rapid increase and a relaxation toward the final state, which confirms the results of conductimetry obtained in dilute conditions.21,25 For mp/mw = 3, no induction period is detectable and growth dynamics is fast from the beginning of the reaction. In the entire range of explored plaster-to-water ratios, hydration of plaster is found to be faster for larger values of mp/mw. However, for mp/mw = 3, the reaction slows down during the final relaxation stage, which suggests that crystal growth is hindered in such a medium. The absolute value of the extent of the reaction, deduced from the results of spaceresolved Raman spectroscopy of the final material, is 1 μm and create a single embryonic needle per grain of smaller diameter. We obtain typical volume-weighted mean needle lengths ⟨l⟩V = 10 μm for mp/mw = 0.6 and ⟨l⟩V = 6 μm for mp/ mw = 3. 3.2. With Citric Acid. By exploiting the same properties of the Raman spectra as during hydration of plaster in pure water, we follow the formation of dihydrate when an aqueous solution of 0.005 M citric acid is employed. As clearly shown in Figure 9, the addition of citric acid retards the reaction. According to the experimental results obtained for mp/mw = 2, the inflection point in the evolution of the progress of the reaction is observed at t ≈ 8200 s with citric acid whereas it is seen at t ≈ 1150 s without additives: the explosive regime is reached about 7 times later in the presence of citric acid. Figure 10 shows that an important effect of the addition of citric acid is to change the shape of gypsum needles.12,15,29 Instead of the long needles observed when using pure water, compact crystals are obtained when a small amount of citric acid is added. We choose to model the effect of citric acid by only changing the value of the

Figure 9. (Top) Extent of reaction, ξRaman, deduced from dynamic Raman spectroscopy when a dilute solution of citric acid (5 mM) is used for mp/mw = 2 (dashed blue line). The result obtained in pure water for mp/mw = 2 (thin dashed blue line) is given for comparison. (Bottom) Extent of reaction, ξ, versus time, t, deduced from the simulations for an aspect ratio of needles α = 2 ± 0.2 (bold lines), simulating the addition of citric acid, and different plaster-to-water ratios: mp/mw = 3 (solid green line), mp/mw = 2 (dashed blue line), and mp/mw = 0.6 (dotted red line). The results of Figure 7 (bottom), obtained for α = 12 ± 7 (thin lines), are given for comparison. The other parameters are given in Table 1.

Figure 10. Scanning electron microscope image of gypsum needles when a dilute solution of citric acid (5 mM) is used for mp/mw = 0.6.

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α prove that needle aspect ratio is the relevant parameter capturing the main effects of citric acid on dynamics. The simulation results confirm that the formation of more compact crystals slows down the reaction. This result is not in contradiction with common use of citric acid as setting retarder. It is, however, worth noting that setting is not directly related to the extent of the reaction but to the moment where needles form percolating clusters. The change in the mechanical properties of the material is attributed to the formation of a skeleton of contacting needles, with local dissolution− precipitation phenomena leading to stiffening of the structure. For a total number n of needles, Figure 12 gives the time

aspect ratio of the needles, with all the other parameters taking the same values as for the case of pure water. According to Figure 10, we choose α = 2 ± 0.2. The consequences of the decrease of the aspect ratio on the simulation results are now discussed. The initial and final configurations for mp/mw = 2 and α = 2 ± 0.2 are given in Figure 11. Fifty percent of the different random initial

Figure 12. Ratio nperco/n of needles belonging to a percolating cluster, nperco, to the total number, n, of needles versus time, t, for an aspect ratio of needles α = 2 ± 0.2 (bold lines), simulating the addition of citric acid, and different plaster-to-water ratios: mp/mw = 3 (solid green line), mp/mw = 2 (dashed blue line), and mp/mw = 0.6 (dotted red line). The corresponding curves obtained for α = 12 ± 7, simulating the use of pure water, are drawn with thin lines.

Figure 11. Initial (top) and final (bottom) configurations obtained in a simulation for an aspect ratio of needles α = 2 ± 0.2, simulating the addition of citric acid, and a plaster-to-water ratio mp/mw = 2. The simulation box is a cube of 80 μm sides. Plaster grains (blue spheres) of diameter d < 4 μm are omitted; gypsum needles are represented in orange. Simulation stops due to steric hindrance.

evolution of the ratio nperco/n of needles belonging to a percolating cluster for the aspect ratios α = 2 ± 0.2 and α = 12 ± 7, simulating the use of water with and without citric acid, respectively. The moment at which nperco/n suddenly increases provides a prediction of the beginning of setting. For the plaster-to-water ratio mp/mw = 2, the simulation results evaluate that the beginning of setting starts about 6 times later for α = 2 ± 0.2 than for α = 12 ± 7. Dividing the aspect ratio by a factor of 6 delays setting by the same factor. The influence of the aspect ratio on the percolation threshold of an assembly of particles has been largely demonstrated34 and already studied in the case of gypsum setting.35 In addition to the consequences on kinetics, the more intuitive effect of crystal shape on the properties of the final material have also been pointed out.36 To summarize, the extent of the reaction and the ratio of needles belonging to a percolating cluster behave similarly as plaster-to-water ratio mp/mw is increased for small and high values of the aspect ratio α. According to the predictions of the simulations, the reaction is found to be faster and setting begins earlier for higher values of mp/mw, and citric acid, responsible for the formation of more compact needles, slows down the reaction and delays setting.

conditions generated led to an incomplete reaction as obtained in the case given in Figure 11. As shown in Figure 9, the variations of the extent of the reaction versus plaster-to-water ratio mp/mw remain qualitatively the same when the aspect ratio α is changed. The reaction is faster as mp/mw increases, for small and high values of α. The most striking result is that the sole change of the aspect ratio from α = 12 ± 7 to α = 2 ± 0.2 is able to reproduce the slowing down of the reaction observed in the experiments when using citric acid as an additive. Without recourse to any fitting parameter, we find that, for mp/ mw = 2, the decrease of the aspect ratio from 12 to 2 on average slows down the reaction by a factor of 5, which compares well with the factor 7 found using Raman spectroscopy and replacing pure water by a dilute solution of citric acid. Dividing the aspect ratio by a factor of 6 divides the needle surface, i.e., initial surface-dependent growth rate, by 6; roughly speaking, it results in a slowing down of the beginning of the reaction by approximately the same factor. Assuming that the addition of citric acid has several consequences and playing with other parameters, such as the surface density of germs g on plaster grains, could marginally improve the agreement. Nevertheless, the correct quantitative predictions obtained when varying only 28736



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4. CONCLUSION In this paper, we have compared the prediction of kinetic Monte Carlo simulations of gypsum crystal growth with Raman spectroscopy results. Dynamic Raman spectroscopy proves to be well-suited to follow plaster hydration in the entire range of plaster-to-water ratios relevant for the various applications of gypsum materials. In line with the well-known use of citric acid as setting retarder, the slowing down of the reaction is observed when citric acid is added to water. The hypotheses on which the model relies are supported by the experimental results. In particular, the induction period preceding the abrupt precipitation of gypsum is correctly reproduced by assuming that, at the beginning of the reaction, needle growth is an autocatalytic process, whose rate is proportional to the needle surface. The retarding effect induced by citric acid is correlated with the formation of more compact needles, i.e., to a decrease of needle aspect ratio. The essential role played by the needle surface during the first stage of the reaction is confirmed by the fact that the simulations properly account for an increase of the induction period, when only the needle aspect ratio is decreased, with all the other parameters being kept constant. Despite the immediate increase and stabilization of conductivity observed as plaster is introduced in the solution,21,15 slow dissolution of hemihydrate37 is sometimes invoked in the literature to explain the origin of the induction period. An hypothetic slower dissolution of hemihydrate in the presence of citric acid15 does not need to be incorporated into the model to mimic the increase of the induction period. In the presence of an additive that reduces the needle surface, the sole decrease of needle aspect ratio by a given factor is sufficient to quantitatively reproduce the slowing down of the reaction by the same factor. The simulation results found for citric acid are immediately generalizable to other additives such as malic acid15 and tartaric acid,12 known to sensitively modify needle aspect ratio. Investigations of the composition of the obtained material using space-resolved Raman spectroscopy combined with the analysis of the simulation results have pointed out the crucial role played by the initial granulometry of the plaster powder: For a high value of the plaster-to-water ratio, mp/mw = 3, initially big plaster grains do not entirely dissolve and reaction is incomplete. Even if there are still pores in the obtained material, needle growth stops due to steric hindrance. These results suggest the possibility to replace a part of the plaster by other components and to control the impact on the mechanical properties of the resulting material.38 Plaster granulometry, surface density of nucleation sites on big plaster grains, and aspect ratio of gypsum needle emerge as relevant parameters that should certainly be determined to select an additive or a treatment of the initial powder in view of obtaining dynamical and structural properties of interest. The kinetic Monte Carlo simulation model that we have developed appears as a predictive tool that offers promising prospects for a rational development of novel additives and avoids the recourse to blind, repetitive experiments.

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Submicrometric Picture of Plaster Hydration: Dynamic and Space

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