Plaster Hydration at Different Plaster-to-Water Ratios: Acoustic

Article pubs.acs.org/JPCC

Plaster Hydration at Different Plaster-to-Water Ratios: Acoustic Emission and 3-Dimensional Submicrometric Simulations Annie Lemarchand,*,†,‡ Florent Boudoire,†,‡,§ Elodie Boucard,†,‡,§ Thierry Chotard,§,⊥ and Agnès Smith§ †

Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), Université Pierre et Marie Curie - Paris 6, UMR 7600, 4 place Jussieu, case courrier 121, 75252 Paris Cedex 05, France ‡ CNRS, LPTMC UMR 7600, France § Groupe d’Etude des Matériaux Hétérogènes, E. A. 3178, Centre Européen de la Céramique, Ecole Nationale Supérieure de Céramique Industrielle, ESTER Technopole, 12, rue Atlantis, 87068 Limoges Cedex, France ⊥ Département Génie Mécanique et Productique, Institut Universitaire de Technologie du Limousin, 2 Allée André Maurois, 87065 Limoges Cedex, France ABSTRACT: To relate the dynamics of the reaction to the structure and properties of the resulting material, we develop a three-dimensional submicrometric simulation model for plaster hydration, valid in the entire range of plaster-to-water ratios. Stochastic rules govern the growth without overlap of gypsum needles. The precipitation process is assumed to drive the dissolution of plaster grains. The comparison of the simulation results with optical microscopy images at different times and acoustic emission monitoring during the reaction enable us to assign physical values to the length and time scales and to the main parameters of the model. In agreement with X-ray microtomography images of plaster available online (http://visiblecement.nist.gov/plaster.html), the simulation model predicts that hydration of plaster of Paris is incomplete for the usual values of plaster-to-water ratios used in industry.

1. INTRODUCTION When put into water, calcium sulfate hemihydrate (or plaster) hydrates into calcium sulfate dihydrate (or gypsum) according to 1 3 CaSO4 , H2O + H2O → CaSO4 , 2H2O (1) 2 2 Plaster is widely used as an inexpensive building material with good insulating, fireproofing, and recycling properties,1 but also as a mold in industry, a biocompatible material in medicine and dentistry, or a set retarder and strength enhancer in cements.2 Recently, the control of gypsum crystallization found another application in the problem of water desalination, due to mineral scale formation on the reverse osmosis membrane, leading first to flux decline and eventually shortening of the membrane life.3−5 Whereas conductimetry can be used to follow the kinetics of the reaction at low plaster-to-water ratios, noninvasive experiments are more difficult to perform at the higher values used in industry. Some information can be retrieved from nuclear magnetic resonance (NMR), which follows the proportions of water in different types of pores.6,7 Several works of the last two decades on the measurement of ultrasonic activity during cement setting and monitoring of drying8−11 have shown that passive acoustic techniques can be used to characterize the evolution of physical and chemical processes. In this work, we have chosen to monitor acoustic emission during dissolution of plaster and precipitation of gypsum to reveal the dynamics of the reaction. © 2012 American Chemical Society

However, a predictive tool, able to relate the dynamics of plaster hydration with the structure and properties of the resulting material is still missing. To this goal, we recently developed a two-dimensional submicrometer-scale simulation model of plaster hydration based on a dissolution−precipitation mechanism.12,13 In this model, the growth without overlap of gypsum needles is assumed to drive the dissolution of plaster grains, which therefore follows adiabatically the crystallization process. Needles are supposed to reach local equilibrium and grow with a nearly constant aspect ratio, which minimizes their surface energy. Early needle growth is assumed to be autocatalytic, with a probability proportional to the needle surface. In the present paper, we start from the same model to implement three-dimensional (3D) simulations. The paper is organized as follows. We describe the acoustic emission experiments and the simulation model and algorithm in section 2. Results and discussion are given in section 3. Using a comparison between different experiments and simulations, we assign physical values to the simulation parameters. First, the experimental granulometry is used to fix the length scale and the distribution of plaster grain diameters in the simulations. Then time-resolved optical microscopy images are used to choose the aspect ratio value and the growth probability of the Received: November 4, 2011 Revised: January 17, 2012 Published: January 23, 2012 4671

dx.doi.org/10.1021/jp210601a | J. Phys. Chem. C 2012, 116, 4671−4678

The Journal of Physical Chemistry C

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gypsum needles. Finally, acoustic emission experiments are used to fix the simulation time scale. The results of the acoustic emission experiments for different plaster-to-water ratios are compared with the dynamics of plaster hydration predicted by the simulations. The morphology of the resulting material is analyzed, and the robustness of the simulation predictions is checked by varying the parameter values and some hypotheses of the model. The main result is that hydration of plaster of Paris is an incomplete reaction for the commonly used plasterto-water ratios. Section 4 is devoted to conclusions.

2. EXPERIMENTAL METHODS AND SIMULATION ALGORITHM 2.1. Acoustic Emission. Acoustic emission corresponds to the generation of transient elastic waves associated with the rapid release of energy from localized sources within a material. The measurement of ultrasonic activity is a well-known, nondestructive evaluation technique to monitor flaw formation; failures in structural materials; or, more generally, displacements in multiphase media. This method has been used mainly to monitor the onset of cracking processes in components submitted to external loading. When a material is submitted to stresses, acoustic emission can be generated by a variety of sources, including crack nucleation and propagation, multiple dislocation slip, twinning, grain boundary sliding, realignment or growth of magnetic domains known as the Barkhausen effect, phase transformations in alloys, debonding of fibres in composite materials, or fracture of inclusions in metals.14−17 In the present work, we will record the elastic waves spontaneously emitted during the physical and chemical changes that occur during the precipitation of gypsum. The experimental setup consists of an AEDSP 32/16 MISTRAS digital system from Physical Acoustics Corporation. This system makes it possible to record the waveform and the main usual parameters of acoustic emission, such as count, hit, rise time, duration of hit, count to peak, and amplitude (in dB) versus time. The sampling rate was 8 MHz. Two sensors (PAC microphone R15), one test sensor, and one reference sensor were connected through 40 dB preamplifiers (EPA 1220 A). The reference sensor was used to record noise due to the electromagnetic environment so that these parasite signals could be eventually subtracted from the ones recorded on the test sensor. A coupling fluid (Dough 428 Rhodorsil Silicone) was used to have an airless and flawless contact between the transducer and the specimen. The acoustic emission experimental setup used in this work is presented in Figure 1. 2.2. A Three-Dimensional Simulation Model at a Submicrometric Scale. The simulation model deals with particles of size ranging from 10 nm to 50 μm and relies on probabilistic rules for particle growth or shrinking. In this work, we extend the 2D model developed in references 12 and 13 to a 3D space. Plaster grains are modeled by spheres of variable diameter d that are randomly spread in a cubic box of side L. The choice of the granulometry is discussed in subsection 3.1. At the beginning of the simulation, nuclei are randomly placed on the surface of 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. The direction of the embryonic needles are randomly chosen and remain unchanged during an entire simulation without needle breaking. At any time, the solution is supposed to be supersaturated with respect to dihydrate.18

Figure 1. Experimental setup for acoustic emission measurements. T is temperature, P is pressure, and G is the typical gain (in dB) of the preamplifiers.

During the time step Δt, the growth of each needle is considered. We assume that, during a time step, each needle reaches a state of local equilibrium, so that the growth follows thermodynamic rules and obeys the Wulff theorem:19,20 A needle reaches the parallelepipedic shape, which is supposed to minimize its surface energy. The ratio of length and width or aspect ratio of the needles is allowed to vary in a small interval around the mean value, α. In the initial autocatalytic growth regime, possible needle growth is accepted with surfacedependent probability pS/Sc, where Sc is a critical surface, from which growth is controlled by the diffusion of the reactants in the liquid phase and occurs with constant probability p. Nevertheless, before accepting the actual growth of a needle, it is necessary to check if its faces are blocked by steric hindrance, that is, by contact with other solids, such as plaster grains and other needles. If growth is allowed, the same volume, α w(t)2 Δw0, of dihydrate is deposited on each free face, where Δw0 is constant and w(t) is the needle width at time t. Purely homothetic growth, that is, with strict conservation of the aspect ratio, occurs if none of the pairs of opposite faces is blocked. Even in the case of blocked opposite faces, the growth of a free face is accepted if the aspect ratio of the needle is in the allowed small interval around α. On the simulation time scale, the growth process is irreversible: in the absence of breaking, the needles never shrink. After needle growth, grain shrinking is considered. Taking into account the different values of density and molar masses for plaster or hemihydrate HH (ρHH = 2.32 × 103 kg m−3 and mHH = 0.1452 kg) and gypsum or dihydrate DH (ρDH = 2.63 × 103 kg m−3 and mDH = 0.1722 kg), we deduce the volume of hemihydrate that has to be dissolved from the total volume of dihydrate VDH(t + Δt) − VDH(t) that precipitated during the time step Δt. Each hemihydrate grain k of diameter dk(t) at time t loses an external shell of width ΔR(t ) =

VDH(t + Δt ) − VDH(t ) ρDH mHH ρ HH mDH π ∑k dk(t )2

(2)

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. In the absence of needle-breaking, the number of needles and their orientation are fixed. In particular, needles and grains are 4672



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diameters in the experiments and simulations compare satisfactorily. In addition, using granulometry as a fitting quantity, we are able to define the length scale in the simulation. 3.2. Aspect Ratio and Growth Probabilities for Gypsum Needles. We give in Figure 3 optical microscopy images of a dilute solution of plaster in water at different times. The ratio of plaster mass to water mass is fixed at P/W = 0.05. The aspect ratio of gypsum needle is evaluated to α = 19 ± 1. The dynamics possesses the characteristics of autocatalysis, that is, an induction period with nearly no needle in Figure 2b at time t = 18 min, followed by a sudden acceleration: The grains have nearly the same size in Figure 3c at time t = 38 min as in Figure 3a and have completely disappeared in Figure 3d at time t = 50 min. Figure 3 shows some needles that appear early, rather far from big grains, and lead to long, isolated needles at the end of the reaction. In parallel, the right bottom plaster grain is replaced by a radial distribution of needles with lengths close to the average value. Figure 4 gives the final configurations of needles obtained in the simulations for the optimized granulometry, the same plaster-to-water ratio as in Figure 3, but different values of the critical surface, Sc, after which needle growth occurs with a constant probability. As shown in Figure 4a, a small value of Sc exclusively leads to a sea urchin-like structure, with small variation around the average needle length. In contrast, the large value of Sc used in Figure 4c favors the duration of the autocatalytic growth regime and the formation of big, isolated needles, which appear early and crystallize the main part of the dihydrate. In the following, we choose an intermediate value of the critical surface, Sc = 10 (Figure 4b), which leads mainly to the formation of sea urchin-like structures but does not preclude a certain variability in needle length, as observed in the microscopy images in Figure 3. A cut of the obtained final structure for a plaster-to-water ratio equal to P/W = 1 is given in Figure 5. The results compare well with the X-ray microtomography images found in the literature for plaster of Paris without additives at the same plaster-to-water ratio.21 3.3. Time Step. We have monitored acoustic emission during the hydration of plaster for different plaster-to-water ratios and the same volume of solution. The number of hits emitted during 5 h is recorded when acoustic intensity is >35 dB. The frequency of the ultrasound waves is on the order of 300 kHz. Many phenomena may generate acoustic waves in this range of frequencies. The response of a solid to mechanical constraints such as crack propagation22 is usually considered as the main source of acoustic emission at these frequencies. However, phase transitions,23 liquid transfer in a porous material,10,24 electrochemical reactions,25 and heterogeneous reactions26,27 with gas bubble emission,28,11 dissolution29,30 or precipitation31,32 are also known to be acoustically active. Here, the movement of domain boundaries due to dissolution of plaster grains and the collisions of solid particles with the beaker or with other particles due to gypsum needle growth are suspected to induce acoustic hits.33−35 It is therefore assumed that the time evolution of the cumulative number of acoustic emission hits provides information on the kinetics of the heterogeneous reaction of interest. Figure 6 compares the acoustic emission data for small plaster-to-water ratios, P/W = 0.05 and P/W = 0.5, with simulation results for the time evolution of the scaled volume VDH/V of precipitated dihydrate, where V is a given volume of solution. The beginning of the evolution of acoustic emission

immobile. Table 1 lists the parameters associated with needles and grains. Table 1. Parameters of the Simulation Characterizing a Gypsum Needle and a Plaster Grain needle initially

at time t

during Δt

w0, initial width α, aspect ratio Sc, critical surface controlling growth rate g, surface density of nuclei ρDH, density mDH, molar mass w(t), width S, surface pS/Sc, growth probability for S < Sc p, growth probability for S ≥ Sc α w(t)2 Δw0, volume increase per free face

grain k d, initial diameter

ρHH, density mHH, molar mass dk(t), diameter

ΔR(t), radius decrease (eq 2)

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.

3. RESULTS AND DISCUSSION The comparison between acoustic emission, optical microscopy images, and simulation results allows us to allocate physical values to the parameters of the simulation. 3.1. Length Scale and Distribution for Plaster Grains. To reproduce the volume-weighted distribution for plaster grain diameter used in the experiments, the corresponding distributions in the simulations are built from the weighted sum of two Gaussian distributions of mean value 18 μm and standard deviation 24 μm with weight 0.3 for the small grains and mean value 60 μm and standard deviation 42 μm with weight 0.7 for the big grains, respectively. First, the big grains are randomly placed without overlap until 70% of the total desired plaster volume is reached. Then, the small grains are placed without overlap in the holes between the big grains. Due to the nonoverlapping constraint, the resulting distribution for sphere diameters differs from the pure sum of two Gaussian distributions. As seen in Figure 2, the distributions of grain

Figure 2. Volume-weighted distributions PV(log10 d) of the logarithm of plaster grain diameter log10 d for the plaster of Paris used in the experiments (solid line) and the spheres in a 3D simulation (dashed line) for a plaster-to-water ratio P/W = 2 in a cubic box of side 250 μm containing 226 big grains (sampled from a Gaussian distribution of mean value 60 μm and standard deviation 42 μm, with weight 0.7) and 5126 small grains (sampled from a Gaussian distribution with mean value 18 μm and standard deviation 24 μm, with weight 0.3). 4673



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Figure 4. Final needle configurations deduced from the simulation for different values of the critical surface Sc, after which needle growth occurs with a constant probability, p = 0.1: Sc = (a) 1, (b) 10, (c) 100. Side of the simulation box, L = 300 μm; plaster-to-water ratio, P/W = 0.05. The other parameters take the following values: same granulometry as in Figure 2; number of germs per unit surface area, g = 1/(4π) μm−2; needle aspect ratio, α = 19 ± 1; initial width of the embryonic needles, w0 = 0.01 μm; elementary width increase during a time step, Δw0 = 0.01 μm. Simulation stops when plaster is entirely consumed. Figure 3. Optical microscopy images of a solution of plaster of Paris in water at different times: t = (a) 11, (b) 18, (c) 38, and (d) 50 min for the granulometry given in Figure 2 and a plaster-to-water ratio of P/W = 0.05. Plaster grains and gypsum needles look gray, and water is white. The white arrow indicates a needle that appears early.

of the final number of hits in the case of the acoustic emission experiments. In both cases, a smaller induction period is observed for a larger value of P/W. The two results quantitatively agree, with an induction period 1.45 times smaller for P/W = 0.5 than for P/W = 0.05 in the case of acoustic emission and 1.35 times smaller in the simulations. Hence, we can use the results of acoustic emission for small values of P/W to define the time scale in the simulation. In the following, 20 000 time steps (for the values of the parameters

(before 1 h) is very similar to the early dynamics predicted by the simulation (before 20 000 time steps). We define the induction period as the time necessary to reach 15% of the final value of VDH/V in the case of the simulations and 15% 4674



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Experiments and simulations agree for the times at which qualitative changes in the kinetics occur when P/W is changed, but the number of hits and the volume of precipitated dihydrate show opposite variation. As expected, the simulations predict that the final volume of formed gypsum increases as P/W increases, whereas the cumulative number of hits is smaller for P/W = 0.5 than for P/W = 0.05. As can be seen in Figure 7, a

Figure 5. Cut of the final configuration deduced from the simulation for L = 250 μm, P/W = 1, Sc = 10, p = 0.1, and the other parameters the same as in Figure 4. The needles and the plaster grains appear in white, water in black. Depth effect is rendered by gray gradation. Simulation stops due to steric hindrance.

Figure 7. Comparison between simulation and experimental results at high plaster-to-water ratios: (a) Time evolution of the ratio VDH/V of a formed dihydrate volume and a simulation box volume for L = 250 μm, P/W = 1 (short-dashed line); L = 225 μm, P/W = 1.5 (longdashed line); L = 200 μm, P/W = 2 (solid line), Sc = 10, p = 0.1, and the other parameters the same as in Figure 4. (b) Time evolution of the cumulative number of acoustic emission (CAE) hits during hydration of plaster of Paris for the same granulometry as in Figure 2, P/W = 1 (short-dashed line), P/W = 1.5 (long-dashed line), P/W = 2 (solid line). Plaster is contained in a silicone rubber mold placed on the sensor.

more dramatic decrease of the number of detected hits is observed for P/W = 1 and higher values. If the hits were due to crystal rearrangement and an answer to stresses, the increase of P/W should lead to an increase in the hit number as the P/W ratio increases. Similarly, if hits were due to collisions of particles with the beaker or between particles, an increase in the particle concentration should increase the number of hits, at least for dilute solutions, when increasing the P/W from 0.05 to 0.5. However, due to steric hindrance, movements may become more difficult at higher plaster concentrations, and particle blocking can be argued for P/W > 1. It is more likely that the change in the properties of the medium explains the decrease in the number of detected hits as P/W increases. Solids and liquids are known to have different acoustic impedances, Z = ρc, where ρ is the density and c is the longitudinal wave speed. Impedance of water and air are equal to Zw = 1.48 × 106 Pa s m−1 and Zα = 3.43 × 105 Pa s m−1, respectively. We have performed ultrasonic echography experiments

Figure 6. Comparison between simulation and experimental results at low plaster-to-water ratios: (a) Time evolution of the ratio VDH/V of formed dihydrate volume and simulation box volume for L = 500 μm, P/W = 0.05 (dotted line), L = 300 μm, P/W = 0.5 (dotted−dashed line), Sc = 10, p = 0.1, and the other parameters the same as in Figure 4; (b) time evolution of the cumulative number of acoustic emission (CAE) hits during hydration of plaster of Paris for the same granulometry as in Figure 2, P/W = 0.05 (dotted line), P/W = 0.5 (dotted−dashed line). Plaster is contained in a beaker placed on the sensor.

Sc, p, w0, and Δw0 given in the caption of Figure 4) are considered to be equivalent to 1 h. 4675



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and measures of porosity on the samples of dried plaster resulting from the acoustic emission experiments for the three plaster-towater ratios, P/W = 1, 1.5, and 2. Using these results, we can evaluate the ultrasonic speed and the impedance of plaster. According to Figure 8, the evolution

Figure 8. Ultrasonic speed versus porosity percentage in plaster of Paris for the samples of dried plaster resulting from the acoustic emission experiments for the three plaster-to-water ratios P/W = 1, 1.5, and 2 completed by the sound speed in air.

of ultrasonic speed versus porosity is linear, and the speed in nonporous plaster can be evaluated to cHH = 3150 m s−1. Because of the increase in both the density and ultrasonic speed in plaster with respect to water, the acoustic impedance of plaster, ZHH = ρHHcHH = 7.3 × 106 Pa s m−1, is found to be 5 times larger than the acoustic impedance of water. When an acoustic wave encounters a material of size larger than the wavelength and with a different acoustic impedance, part of the sound wave is reflected, and the wave may not reach the sensor. However, 300 kHz waves are not perturbed by objects less than 5 mm and do not see the 60 μm-diameter plaster grains. The ultrasonic waves travel in an effective biphasic medium, partly liquid, partly solid, at least at the beginning of the reaction, before the formation of large needle aggregates. The resulting impedance is then the weighted sum of water and plaster impedances and therefore increases as the ratio of plaster to water, P/W, increases. For P/W = 0.05, the mean value of acoustic intensity was found equal to 38.7 dB. We assume that acoustic pressure is independent of P/W, since the same physical phenomena are at the origin of the hits. The increase in acoustic impedance due to the larger fraction of solids in the medium is sufficient to explain the decrease in the acoustic intensity at the level of the sensor above the detection threshold of 35 dB for P/W > 0.5. The main part of the hits is not detected for large values of the plaster-to-water ratio, and acoustic emission cannot be used to study the dynamics of pure plaster hydration for P/W ≥ 1. The situation favorably changes in the presence of tartric or citric acid, certainly as a result of the change in crystal morphology induced by such additives.36 3.4. Hydration of Plaster of Paris: An Incomplete Reaction. In contrast to acoustic emission, whose intensity decreases as the plaster-to-water ratio increases, simulations can be carried out for variable P/W values and identical other conditions. In Figure 9a, we give the simulation results for the time evolution of the extent of the reaction for different values of the plaster-to-water ratio. For the values of P/W studied, only P/W = 0.05 leads to a complete reaction. For all the other considered values of P/W, steric hindrance blocks the reaction, and more than 99.5% of the needles belong to a percolating

Figure 9. Extent of reaction, ξ(t), versus time, t, deduced from the simulation for different plaster-to-water ratios: L = 500 μm, P/W = 0.05 (dotted line); L = 300 μm, P/W = 0.5 (dotted−dashed line); L = 250 μm, P/W = 1 (short-dashed line); L = 225 μm, P/W = 1.5 (longdashed line); L = 200 μm, P/W = 2 (solid line); Sc = 10, p = 0.1, and the other parameters the same as in Figure 4. (a) Without needle breaking, (b) with needle breaking when at least three contacts, two of them on opposite faces, and aspect ratio greater than αmin = 18.

cluster at time t = 5 h. Hence, simulation predicts that a reaction is incomplete as soon as P/W reaches 0.5. In particular, for the usual values, P/W ≃ 1.5, used in industry and in the absence of additives, grains of undissolved plaster are expected to remain in the final material. This prediction agrees with the presence of such plaster grains in freely accessible images obtained by X-ray microtomography21 in analogous conditions, that is, for plaster of Paris, P/W = 1 and at times t = 4, 7, 15.5 h. Image processing of the X-ray microtomography pictures reveals that the composition of the material does not evolve among the three different times and leads to an extent of the reaction of 66% ± 8%.21 These experimental results confirm the predictions of the simulation about the morphology of the final material and the dynamics of the reaction: The reaction is incomplete, and blocking occurs after 4 or 5 h for plaster of Paris without additives. In addition, the X-ray microtomography images at different times validate the choice of the time scale that we deduced from the comparison of simulations with acoustic emission results for low P/W values. To check the robustness of the prediction, we consider the influence of different parameters on the extent of the reaction. First, we introduce the possibility of needle breaking in the simulation algorithm. A needle with three contacts, two of them on opposite faces, and an aspect ratio larger than the minimum accepted value is susceptible to breaking in two pieces of half length. One piece remains at its initial place, and the second 4676



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one is placed in the vicinity. One of the vertices of the second piece is randomly placed in the smallest parallelepiped which contains the initial needle. The direction of the second piece is randomly chosen with the condition of nonoverlapping: To mimic the force exerted by the environment at the time of rupture, the second piece moves and takes an orientation different from the initial needle but then remains immobile for the rest of the simulation. Figure 10 gives a schematic representation of the chosen model for needle breaking. The evolution of the extent of the

Figure 11. Extent of the reaction versus time deduced from the simulation for L = 250 μm, P/W = 1, Sc = 10, and p = 0.1. The solid line gives the results for the parameter values of Figure 4 (α = 19 ± 1, same granulometry as in Figure 2). The long-dashed line gives the results for the aspect ratio α = 15 ± 0.79, w0 = 0.0112 μm to have the same initial surface for the embryonic needle as for α = 19, Δw0 = 0.0127 μm so as to precipitate the same volume per time step. The other parameter values are also the same as in Figure 4. The shortdashed line gives the results for the parameter values of Figure 4 except the granulometry: The big grains are sampled from the same distribution as in Figure 2 but with weight 0.3, and the small grains, with weight 0.7. The dotted line gives the results for the parameter values of Figure 4 with possible needle breaking.

4. CONCLUSION We have developed a three-dimensional simulation model of plaster dissolution and gypsum needle precipitation at a submicrometer scale. The comparison of the simulation results with different experiments, including time-resolved optical microscopy and acoustic emission monitoring during the reaction, enables us to assign physical values to the length and time scales and to dynamical and structural parameters introduced in the simulation model. We have investigated the behavior of the time evolution of the extent of the reaction for different plaster-to-water ratios, P/W. As P/W increases, the acoustic impedance of the medium increases due to the larger fraction of solids, and acoustic activity decreases, which prevents us from comparing the experimental results at different P/W values. The main prediction of the simulation is that the hydration of plaster is an incomplete reaction for commonly used values of the plaster-to-water ratio: In the absence of additives, undissolved plaster grains remain in the final material for P/W ≥ 1. This result is confirmed by processing of X-ray microtomography images of plaster that are available in the literature.21

Figure 10. Schematic diagram of needle-breaking process in the simulation: (a) In dark gray, a needle with three contacts, two of them on opposite faces, and the smallest parallelepiped that contains it. (b) The dark gray needle is broken in two pieces of half length, one remains at its initial place, the other one is placed in the neighborhood. One of its vertices is randomly placed in the parallelepiped, and its direction is randomly chosen with the condition of nonoverlapping.

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reaction deduced from the simulation with needle breaking and for different values of P/W is given in Figure 9b. The results are qualitatively different from without breaking for P/W = 0.5, for which the reaction is now complete. However, incomplete dissolution of plaster is again obtained for P/W = 1. Then, without needle breaking, we consider the effects on dynamics of a smaller aspect ratio value or a different granulometry in favor of smaller grains, always for P/W = 1. The results are given in Figure 11. Neither the decrease in the aspect ratio from α = 19 to α = 15 nor the decrease in the plaster grain diameter is sufficient to change the prediction: The simulation always leads to an incomplete reaction for P/W = 1.

AUTHOR INFORMATION

Corresponding Author

*Phone: +33 (0)1 44 27 44 55. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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Plaster Hydration at Different Plaster-to-Water Ratios: Acoustic

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