Kinetic Model of Calcium-Silicate Hydrate Nucleation and Growth in

Article pubs.acs.org/crystal

Kinetic Model of Calcium-Silicate Hydrate Nucleation and Growth in the Presence of PCE Superplasticizers Luca Valentini,*,† Marco Favero,† Maria C. Dalconi,† Vincenzo Russo,‡ Giorgio Ferrari,‡ and Gilberto Artioli† †

Department of Geosciences and CIRCe Center, University of Padua, Padua 35131, Italy Research and Development Department, Mapei SpA, Milan 20158, Italy

‡

S Supporting Information *

ABSTRACT: Calcium-silicate hydrate (commonly referred to as C−S−H in cement chemistry) is the main phase and the “glue” of hydrated cement, the binding matrix of building materials such as concrete, which is an essential commodity for modern infrastructures and housing. The basic mechanisms that control cement hydration and the modes of C−S−H formation are not fully understood and the picture becomes even more complicated when organic polycarboxylate-based additives (PCE) are added with the aim of controlling the rheology of the fresh paste and the strength of the final product. Here, a kinetic model of nucleation and growth, with unconstrained nucleation mechanism (homogeneous/heterogeneous) and time-dependent growth rate, is described and used to fit the rate of C−S−H precipitation obtained by in situ X-ray powder diffraction. The kinetic model predicts a switch from heterogeneous to homogeneous nucleation and an overall inhibition of C−S−H precipitation in the presence of PCE. This mechanism exerts a fundamental role in controlling the experimentally observed decrease in the early age rate of cement hydration in the presence of PCE.

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INTRODUCTION Currently, the proportion of people living in urban areas amounts to more than 50% of the world population, a figure that is expected to increase up to 66% by 2050.1 From this perspective, building materials represent a key commodity for modern societies, especially for the developing countries, where the majority of urban growth is occurring, in need of infrastructures and modern housing.2 In this context, cementbased materials are widely used due to high performance at low cost, with a broad worldwide availability of raw materials, as well as relatively low environmental footprint per unit mass produced.3 On the other hand, the massive annual production of cement, amounting to approximately 4 Gt in 2014,4 results in a significant contribution to the annual worldwide CO2 emissions (approximately 5−7% of the total anthropogenic CO23). The rising demand of cement-based materials must, therefore, take into account the need to drastically cut greenhouse gas emissions in order to meet the expected goal of reducing the carbon footprint for cement production of 30% by 2050.5 Meeting such ambitious goals requires an extensive knowledge-based approach to the development of sustainable cement-based materials, hence the fundamental importance of understanding the details of the basic processes controlling the physical chemistry of cement. Cement hydration consists of a series of chemical reactions by which anhydrous phases dissolve into a set of ionic species in aqueous solution that, upon © XXXX American Chemical Society

reaching supersaturation, precipitate into hydrated phases, resulting in the formation of a viscous slurry of particles that eventually evolves into an elastic solid. The time interval during which stiffening of the viscous slurry occurs is defined as “setting”. Microscopically, setting occurs when percolation of the isolated particles is achieved.6 As hydration proceeds beyond the setting point, mechanical strength is developed. The main hydration product of ordinary Portland cement is a calcium-silicate hydrate, commonly referred to as C−S−H (in cement chemistry notation C = CaO; S = SiO2; H = H2O). C− S−H is characterized by a pseudotobermoritic defective crystal structure7,8 that forms branching nanoscale colloidal-like particles,9 conveying cohesive properties to the hydrating cement paste.10 In normal hydration conditions, C−S−H forms at the interface between anhydrous cement particles and water by heterogeneous nucleation.11 Recent studies12,13 have shown that a change in the C−S−H nucleation mechanism is observed when cement is hydrated in the presence of polycarboxylate ether (PCE) superplasticizers, which are a fundamental class of admixtures added to the mix water in order to control the rheology of the slurry and enhance workability of high performance cement. Received: August 5, 2015 Revised: December 18, 2015

A

DOI: 10.1021/acs.cgd.5b01127 Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design

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repeat units n is 20 and 13, respectively, for PCE−17−3 and PCE− 17−4. Additional information on the characterization of the used PCEs can be found in the Supporting Information. For each sample, in situ XRD coupled with Rietveld refinement provided the timedependent fraction of each crystalline phase present in the system (detailed procedures can be found in the Supporting Information). The time-dependent C−S−H content was determined from the XRD results using a mass-balance algorithm, as implemented in the software RieCalc.18

In this paper, a kinetic model that combines generalized forms of the Johnson−Mehl−Avrami−Kolmogorov (JMAK) and “boundary nucleation and growth” (BNG) models is presented and applied to the study of C−S−H nucleation and growth kinetics. The kinetic model includes a parametrization of the time-dependent nucleation and growth rates. The model is used to fit the time-dependent C−S−H volume fraction present in model cement pastes, as measured by in situ X-ray powder diffraction (XRD) combined with Rietveld refinement and mass balance calculations. The kinetic model provides quantitative information about the rates of C−S−H nucleation and growth and their variation in the presence of PCE superplasticizers.

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KINETIC MODEL The time-dependent C−S−H volume fraction obtained by XRD for the different systems is fitted by implementing a model that provides quantitative information on the kinetics of C−S−H nucleation and growth. The kinetic model combines generalized forms of the Johnson−Mehl−Avrami−Kolmogorov19−22 (JMAK) and “boundary nucleation and growth”23 (BNG) models. The JMAK model has previously been implemented in numerical codes for the simulation of cement hydration kinetics and microstructural development.24−26 In its basic form, this model assumes that (a) nuclei of a new phase are formed at a constant rate at random locations throughout the available space; (b) the volume of the newly formed nuclei is negligible; (c) the nuclei grow at constant rate. The actual mechanisms of C−S−H nucleation and growth violate some of the above assumptions. Specifically, it has been shown experimentally that, in normal hydration conditions, C− S−H nucleate at the surface of anhydrous cement particles11 rather then randomly throughout the available space. Moreover, and perhaps more importantly, the rates of nucleation and growth are not constant, but strongly depend on the degree of C−S−H supersaturation, which is in turn related to the ionic concentration of Ca and Si in the pore solution. The former issue has been addressed, in previous studies, by adapting a kinetic model, originally conceived for the study of recrystallization of metals at grain boundaries,27 to the kinetics of cement hydration (“boundary nucleation and growth” or BNG model). The BNG model assumes that nucleation is restricted to the surface of anhydrous cement phases and has been extensively used to fit calorimetric data.23,28,29 In those studies, the BNG model provided overall better fits compared to the JMAK model, although it still has some limitations. First, it has been shown that when cement is hydrated in the presence of nucleation seeds or PCE superplasticizers, the assumption that nucleation is restricted to pre-existing interfaces becomes invalid, as nucleation may occur throughout the pore solution.12,13,30 Moreover, in its standard formulation, the BNG model assumes constant nucleation and growth rates. It has been shown that, as a consequence of such an assumption, the BNG model predicts an unrealistically large volume fraction of hydration products when the rate of hydration reaches its maximum.31 A first attempt of addressing this issue has recently been carried out by implementing time-dependent growth rates obtained by fitting the results of cellular-automaton simulations of C3S hydration.32 An additional issue is related to the application of such kinetic models, which predict the time-dependent phase fraction of a newly forming phase, to indirect experimental data, such as those based on calorimetry.23,28,29 Although calorimetry can provide important information on the overall rate of cement hydration kinetics, the output of calorimetry measurements represents an integration of the rates of dissolution−precipitation relative to the single phases present

MATERIALS AND EXPERIMENTAL METHODS

Monoclinic Ca3SiO5 (C3S in cement chemistry notation) provided by Mineral Research Processing (Meyzieu, France)14 was used as a model cement. C3S is the most abundant phase (about 70% by mass) in unhydrated ordinary Portland cement and its reaction is responsible for setting and initial strengthening of the paste. Pastes were prepared by mixing C3S with deionized water at 0.5 water/solid mass ratio (details of C3S properties and sample preparation can be found in the Supporting Information). Samples containing PCE superplasticizers were prepared with the aim of quantitatively investigating the effect of such admixtures on the hydration kinetics. Two different PCEs were used, each at a dosage of 0.05% and 0.10% by mass of C3S. Such dosages are somewhat lower compared to those commonly used in field applications. The choice of adopting a low dosage was motivated both by the lack of aluminate phases, which are those that preferentially interact with PCE molecules,15,16 and by the need of inducing a delay in the hydration kinetics that is measurable by in situ XRD in a reasonable time. Two different sets of C3S pastes were prepared, in which PCEs were added: (a) directly in the mix water; (b) in delayed mode, after the first 4 min of mixing. The used PCEs consist of comb copolymers of methacrylic acid and polyoxiethylene methacrylate, synthesized from methacrylic acid and methoxypolyethylene glycol-methacrylate, formed by the repetition of n segments, each containing N backbone repeating units and a side chain formed by P units. A generic nomenclature PCE−P−N, based on the description of Gay and Raphael,17 is used to define each of the used PCEs (Figure1). Based on this scheme, the two PCEs used in the experiments are named PCE−17−3 and PCE−17−4. The number of

Figure 1. General structure of the PCEs used. Each of the n segments is composed of N backbone units, with one grafted side-chain consisting of P monomeric units. B



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in the system. Therefore, fitting calorimetry curves by BNG or JMAK models requires the use of a conversion factor that has not an immediate physical meaning. In this study, the above issues are addressed by adopting a kinetic model, based on the combination of generalized versions of the JMAK and BNG models, with time-dependent rates. The model, which provides the time-dependent volume of a generic phase forming by a process of nucleation and growth, is used to fit the time-dependent volume fraction of C− S−H as obtained by in situ XRD. Therefore, the fit parameters of the model are obtained by a more direct comparison with experimental data, rather than those obtained by fitting the data to calorimetry23,28,33 and chemical shrinkage29,33 measurements, or computer simulations.32 The generic form of the kinetic equation is X(t ) = A{1 − exp[−X(t )ehom − X(t )ehet ]}

ment in directions parallel to the substrate and integrating over y, after using the convenient change of variable u = y/Γy(t) Ve(t ) =

4 π 3

∫0

OvB =

∫τ

(2)

G (t ) =

∫0

t − yτ / Γy(t )

∫0

1

Γ̅ (t ){1 − exp[−πNs Γ̅ 2(t )(1 − u 2)]} du

1 Gmax [f1 (t ) + nf2 (t )] 1+n

f1 (t ) = exp[−B(t − t0)2 ]

f2 (t ) =

(9)

1 1 + erf[C(t − t0)] 2 2

(10) (11)

where t0 is the time at which G achieves its maximum and B and C are empirical parameters controlling the shape of the curve. The generic functional form of eq 9 is displayed in Figure 2. The choice of such a functional form is justified by the fact that supersaturation represents the driving force for growth, and supersaturation curves for C3S hydration, such as those obtained by electrical conductivity,35 possess a similar shape, characterized by an initial increase, followed by a gradual decrease after reaching a maximum. The curve obtained by the kinetic model is fitted to the experimental data by using a gradient descent algorithm, which evaluates the physical parameters OBV (substrate surface per unit volume), NS (number of heterogeneous nuclei per unit surface of substrate), NV (number of homogeneous nuclei per unit volume), as well as the parameters that control the shape of the growth-rate function. By using this method, the nucleation mechanism (homogeneous or heterogeneous) is not enforced a

(4)

{I(t )[Γx(t )Γz(t ) − y 2 ]} dτ

(7)

where Gmax is the maximum growth rate, n is a scaling parameter, and the functions f1 and f 2 are defined as follows

with NV being the initial number of nuclei per unit volume. The extendend phase volume Xhet e formed by heterogeneous nucleation is obtained by taking into account a semiellipsoid nucleating and growing on a flat surface perpendicular to the y direction. The extended surface Se of a set of particles nucleating at time τ and intersecting a plane at distance y from the substrate is given by Se(t , y) = π

(6)

where NS is the number of nuclei per unit surface of substrate initially present. In this study, the time-dependent rate of C−S−H formation, as obtained by in situ XRD and mass balance, is fitted by the use of eq 1 combined with eqs 4 and 8. The use of site saturation conditions is justified by the fact that, during C3S hydration, the degree of supersaturation necessary for inducing nucleation is only reached after the first few minutes.34 The assumption of an initial fixed number of nuclei is an acceptable approximation considering the fact that the first XRD data point is obtained after about 20 min. The time-dependent growth rate G is parametrized by the following equations

(3)

4 πNv Γ̅ 3(t ) 3

[−πI(t )Γx(t )Γz(t )(1 − u 2)]

(8)

where G is the time-dependent growth rate along a given direction. Equation 2 can be simplified if nucleation occurs only during a short period of time at the beginning of the reaction (“site saturation” regime) such that it can be assumed that a fixed number of nuclei are initially present. Also, if the nuclei are randomly oriented, an averaged isotropic growth rate G can be used and eq 2 becomes X(t )ehom =

t − uτ

SBET R wc/ρw + 1/ρc

X(t )ehet = OvB

t

Gi(t ) dt

∫0

where Rwc is the water to C3S mass ratio, ρw and ρc are the density of water and C3S, respectively. For site saturation and nuclei randomly oriented on the substrate, the extended volume becomes

(1)

in which I is the time-dependent nucleation rate and Γ(t) is the length at time t, along a given direction, of the semiaxis of an ideal ellipsoidal particle nucleated at time τ, expressed as Γi(t ) =

Γy{1 − exp

The extended volume of particles heterogeneously nucleated in the whole volume is then given by OBV Ve with OBV being the amount of substrate per unit volume in the system, related to the BET surface area SBET of the C3S particles by the following relation29

t

I(t )[Γx(t )Γy(t )Γz(t )] dτ

1

dτ } du

where X is the volume fraction of the generic phase at a given time, A is a scaling factor corresponding to the phase fraction at completion of the reaction, and Xhom and Xhet e e are the extended volume fractions of the phase formed, respectively, by homogeneous and heterogeneous nucleation. The extended volume represents the theoretical volume that would form if there was no overlap among particles and is related to the actual volume fraction by the equation X = 1 − exp(−Xe) . The extended phase volume formed by homogeneous nucleation is expressed by a JMAK equation written in the following form X(t )ehom =

∫0

(5)

The contribution to the extended surface at y vanishes for particles nucleating at τ → t and when Γy ≪ y, i.e., if the growth rate Gy perpendicular to the substrate is very small. The extended volume Ve of particles nucleating at a single substrate is obtained by taking into account particle impingeC



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the hydration rate (except in the presence of PCE 17−3 at a dosage of 0.05%), followed by a faster deceleration is observed in the presence of the PCEs. The delay in the onset of acceleration, in the presence of PCE superplasticizers, is wellknown in the literature.36 The increase in the peak of the hydration rate has been previously observed, by means of isothermal calorimetry, in ordinary Portland cement pastes hydrated in the presence of PCEs,37 although this does not seem to be the rule. On the other hand, minor variations in the hydration kinetics are observed when PCEs are added in delayed mode. Data from the literature show that, in the presence of PCE added in delayed mode to ordinary Portland cement, a delay in the hydration kinetics is observed,38,39 whose extent can in some cases be even larger than that observed for direct PCE addition. However, to the best of our knowledge, no data on delayed PCE addition to C3S pastes are present in the published literature. A quantitative analysis of the kinetics of C3S hydration is performed using the kinetic model described in the previous section to fit the experimental curves describing the rate of C− S−H precipitation (Figures 5 and 6). The amount of substrate per unit volume OBV used in eq 8 was obtained by using eq 7 with a value of the BET specific surface area of 423.6 m2/kg as measured by gas adsorption and a density of 3.12 × 103 kg/m3 for C3S.40 The obtained value OBV = 5.17 × 105 m−1 was kept constant in the model. Although the BET surface area does not necessarily correspond to the actual reactive surface41 and changes in the initial specific surface may occur due to the presence of PCE superplasticizers and early dissolution, the decision to keep the value of OBV constant was motivated by the need to minimize the number of variables used in the fit. Moreover, in order to prove the validity of the model with a further reduced number of fitting parameters, the values of NS and NV were kept constant when fitting the XRD data relative to the C3S paste hydrated in the presence of PCE added in

Figure 2. Generic functional form for the time-dependent growth rate as expressed by eqs 9−11.

priori, but is automatically adapted by the kinetic model, based on the shape of the experimental curves.

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RESULTS The variation of C3S hydration kinetics in pure water and in the presence of different types and amounts of PCE superplasticizers, as obtained by the XRD analyses, is displayed in Figures 3 and 4, for PCE addition in the mix water and delayed mode, respectively. The advancement of the reaction is displayed as the time variation of the degree of hydration, which is expressed as the cumulative amount of C3S consumed at a given time. Figures 3 and 4 also display the rate of hydration, which is the differential C3S consumed during a given XRD time interval of 20 min. Significant changes in the hydration kinetics are observed when PCEs are added in the mix water, in particular: the beginning of the acceleration period is delayed in the presence of the PCEs; a higher peak in

Figure 3. Degree and rate of C3S hydration in pure water and in the presence of different amounts of PCE 17−4 and PCE 17−3 added in the mix water. One in two data points are plotted to facilitate visualization. The dashed lines in the bottom row were added as a visualization aid. D



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Figure 4. Degree and rate of C3S hydration in pure water and in the presence of different amounts of PCE 17−4 and PCE 17−3 added in delayed mode. One in two data points are plotted to facilitate visualization. The dashed lines in the bottom row were added as a visualization aid.

model, are displayed in Figure 7. In the presence of PCEs added in the mix water, a significant reduction of the growth rate, up to its peak, is observed, with the occurrence of the peak being delayed proportionally to the amount of PCE added. Qualitatively similar trends are observed for delayed PCE addition, although the reduction of the growth rate is significantly smaller.

delayed mode. The addition of PCE after 4 min since the beginning of hydration should ensure that C−S−H nucleation has occurred without the perturbing action of PCE. Previous experiments and simulations suggest that C−S−H nucleation occurs within a few minutes after mixing.11,34 Therefore, the number of nuclei formed when PCE is added in delayed mode does not change with respect to those forming when C3S is hydrated without PCE. A summary of the fitting parameters for the different systems is reported in Table 1. The results of the kinetic model predict a switch from heterogeneous to homogeneous nucleation, when PCEs are added in the mix water. In the absence of PCE, the amount of homogeneous nuclei is negligible and the number of heterogeneous nuclei per unit surface of substrate is 4.55 × 1011 (previous models from the literature had obtained values between 1.16 × 1011 and 1.47 × 1013).29,32 In the presence of PCEs added directly in the mix water, the number of homogeneous nuclei, at each dosage and for both PCEs, is approximately an order of magnitude larger compared to the number of heterogeneous nuclei per unit volume (the number of heterogeneous nuclei per unit volume is obtained by multiplying NS by OBV). The total number of nuclei is nearly halved in the presence of PCE. The maximum value for the growth rate of C−S−H in the absence of PCE, as predicted by the kinetic model, is 3.50 × 10−11 m/s (a previous model with constant growth rate, for C3S hydration at 20 °C in pure water at Rwc = 0.4, gave a growth rate of 1.94 × 10−11 m/s).28 The value of the maximum growth rate decreases by about 30% to 40% in the presence of PCE added in the mix water. In the case of PCEs added in delayed mode, the number of nuclei forming remains unchanged with respect to the number of those forming in the absence of PCE, since complete nucleation is expected to occur before the addition. It follows that in this case no change in nucleation mechanism occurs and the PCEs can only affect the growth rate. Curves of the time-dependent growth rate for the different systems, as obtained by the kinetic

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DISCUSSION The kinetic model described in this paper reproduces the kinetics of C−S−H nucleation and growth, in pure water and in the presence of PCE superplasticizers, with excellent accuracy (R2 coefficients vary between 0.984 and 0.996). The model predicts that in the absence of PCE, C−S−H nuclei essentially form heterogeneously at the surface of C3S. This behavior is well documented in the literature; however, it should be noted that heterogeneous nucleation has not been constrained a priori into the model, since the relative abundance of heterogeneous and homogeneous nuclei is automatically adjusted by the fitting algorithm. The predicted switch toward homogeneous nucleation, in the presence of PCE added in the mix water, is in agreement with recent experimental observations based on nondestructive phase-resolved imaging13 as well as on ultracentrifugation measurements.12 Such a change in nucleation mechanism could be induced either by inhibition of hetrogeneous nucleation due to interference of the PCE sidechains in proximity to the substrate, or by a templating action of the backbone of unadsorbed PCE molecules. In the latter case, it would be more correct to use a more generic term such as through-solution nucleation. Independent of the actual mechanism that perturbs the nucleation process, the model also predicts that the total number of C−S−H nuclei formed is smaller in the presence of PCE added to the mix water. Additionally, the results of the kinetic model predict a significant decrease in the rate of C−S− H growth. In the presence of PCE added in delayed mode, the E



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Figure 5. Results of data fitting by means of the kinetic model for C3S without additives (blank) and with PCE added in the mix water. The data relative to the blank sample are plotted in both columns in order to aid the comparison with the experiments in which PCE is added. The symbols are experimental data points representing the rate of C−S−H precipitation (one in two data points are displayed with the aim of facilitating visualization). Solid lines are fitting curves obtained by combining eq 1 with eqs 4 and 8. Rates are obtained by differentiating the phase fractions with respect to time.

number of fit parameters is reduced, since the initial number of nuclei NS and NV is kept constant, but the kinetic model fits the data equally well. The effect of PCEs added in delayed mode is much smaller and the hydration kinetics are similar to those relative to C3S hydration in the absence of PCE. Nevertheless, a slight decrease of the growth rate is observed. Inhibition of nucleation and growth in the presence of organic additives is well documented42 and can provide a possible explanation to the commonly observed delay in the beginning of the accelerating kinetic stage induced by PCE superplasticizers. According to a different school of thought, delay is mainly controlled by inhibition of the active sites of C3S dissolution by the adsorbed PCE molecules.43−45 Differentiating the effects ralated to precipitation of hydrates and dissolution of the anhydrous phases is not straightforward. Indeed, the reduction in C−S−H growth rate predicted by the kinetic model may in principle be a consequence of a slower C3S dissolution induced by adsorbed PCE molecules, having the effect of hindering the supply of ions necessary for C−S−H to precipitate. Although inhibition of dissolution induced by adsorbed PCE may play a role, we favor the hypothesis that the slower kinetics are mainly controlled by the inhibition of C−S−H precipitation, since experimental observations show that retardation is increased proportionally to the dosage of PCE, even at dosages above the

saturation plateau.46 Therefore, it is likely that the PCE molecules added in excess exert their action directly on the precipitating C−S−H. Formation of etch pits on the surface of C3S may lead to an increase of reactive surface with time47 that may potentially adsorb the excess PCE molecules present in the pore solution. However, such an increase in PCE adsorption with time has to be demonstrated. Again, we stress the difficulty of separating the effects of precipitation and dissolution. However, independent of the mechanism controlling the retardation induced by PCE superplasticizers, the results show that C−S−H nucleation switches from heterogeneous to mainly homogeneous when PCE is added in the mix water. Such a change in nucleation mechanism must have a fundamental role in controlling the observed change in hydration kinetics, since the retardation is much smaller when PCE is added in delayed mode, in which case the heterogeneous nucleation mechanism remains unchanged. The fact that, contrary to what observed for C3S, delayed PCE addition induces a significant retardation in Portland cement systems, suggests that the interaction of PCE molecules with aluminate phases exerts a strong kinetic control. F



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Figure 6. Results of data fitting by means of the kinetic model for C3S without additives (blank) and with PCE added in delayed mode. The data relative to the blank sample are plotted in both columns in order to aid the comparison with the experiments in which PCE is added. The symbols are experimental data points representing the rate of C−S−H precipitation (one in two data points are displayed with the aim of facilitating visualization). Solid lines are fitting curves obtained by combining eq 1 with eqs 4 and 8. Rates are obtained by differentiating the phase fractions with respect to time.

Table 1. Output of the Kinetic Model SAMPLE

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BLANK 0.05% PCE 0.05% PCE 0.10% PCE 0.10% PCE 0.05% PCE 0.05% PCE 0.10% PCE 0.10% PCE

17−4 17−3 17−4 17−3 17−4 17−3 17−4 17−3

delay

NSHET (m−2)

NVHET (m−3)

NVHOM (m−3)

NVTOT (m−3)

Gmax (10−11 m/s)

N/A N N N N Y Y Y Y

× × × × × × × × ×

× × × × × × × × ×

× × × × × × × × ×

× × × × × × × × ×

3.50 2.37 2.10 2.14 2.16 3.31 3.15 3.08 3.16

4.55 2.98 2.40 1.38 5.00 4.55 4.55 4.55 4.55

11

10 1010 1010 1010 109 1011 1011 1011 1011

2.35 1.54 1.24 7.13 2.59 2.35 2.35 2.35 2.35

17

10 1016 1016 1015 1016 1017 1017 1017 1017

CONCLUSIONS

1.50 1.32 1.22 1.33 1.26 1.50 1.50 1.50 1.50

12

10 1017 1017 1017 1017 1012 1012 1012 1012

2.35 1.47 1.34 1.40 1.52 2.35 2.35 2.35 2.35

17

10 1017 1017 1017 1017 1017 1017 1017 1017

3. The model predicts a switch to homogeneous nucleation (or nucleation in the pore solution induced by the templating effect of the PCE molecules) when PCE is added directly in the mix water. 4. Both the number of nuclei per unit volume and the growth rate decrease in the presence of PCE. 5. Delayed PCE addition does not affect C−S−H nucleation and the effect on C−S−H growth rate is smaller compared to that induced by direct PCE addition in the mix water. 6. Inhibition of C−S−H nucleation and growth plays a fundamental role in the delay of the transition from the period

In this paper, a kinetic model for the nucleation and growth of C−S−H, the main phase of hydrated cement, has been described and used to fit data obtained by in situ X-ray powder diffraction, combined with Rietveld analysis and mass balance calculations. The following points can be summarized: 1. Time-dependent growth rate is implemented in the kinetic model and the nucleation mechanism is not constrained a priori. 2. The kinetic model fits the experimental data points with excellent accuracy. G



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Figure 7. Time-dependent rate of C−S−H growth in pure water and in the presence of PCE (added in the mix water or in delayed mode) resulting from the kinetic model.

of slow reaction to acceleration, when PCE superplasticizers are added in the system. Further research may refine the kinetic model in order to explore the role of unconventional nucleation mechanisms (e.g., formation of prenuclaetion clusters48) and different modes of growth and aggregation, which may lead to the formation of scale-invariant structures.49,50

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.cgd.5b01127. Details of sample preparation, in situ X-ray powder diffraction analysis and polymer characterization (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Mapei S.p.A. supported the research through the MapeiUNIPD research agreement. Two anonymous reviewers are thanked for their constructuve comments that contributed to improving the overall quality of the manuscript. Allan Myerson is thanked for editorial handling.

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REFERENCES

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Kinetic Model of Calcium-Silicate Hydrate Nucleation and Growth in

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