Mechanisms of cement hydration

Jeffrey Bullard

A little bit of history " There is […] a kind of powder which from natural causes produces astonishing results. It is found in the neighborhood of Baiae and in the country belonging to the towns round about Mount Vesuvius. This substance , when mixed with lime and rubble, not only lends strength to buildings of other kinds, but even when piers of it are constructed in the sea, they set hard under water. " (Marcus Vitruvius Pollio, Liber II, De Architectura, ~25 BC). In these words the Roman engineer Vitruvius firstly described the properties of a material with surprising properties: a mixture of lime and crushed volcanic ashes was able to set under water, the resistance being increased along the time, in a way completely different to any other material. This " magic " material was called pozzolanic from Poz-zuoli, the place near Vesuvio where the ashes were taken from. The reason of the success of the Roman concrete was the substitution of the usual crushed stones (as Greeks, British people and the Romans themselves at the beginning were used to do) with volcanic ashes. According to the modern knowledge, a siliceous and aluminous material in itself does not possess cementitious value, unless it is calcinated and converted in an amorphous form. This calcination process, artificially produced in the modern times, was naturally made by the volcano for the Romans. Nowadays, concrete is the synthetic material with the largest production on Earth: more than 11 billion metric tons are consumed every year all over the world. It is also one of the most complex inorganic systems. After more than a century of systematic studies, basic questions are still unsolved regarding its internal structure over the nanometer to macro-scopic scale range, on its effects on concrete behavior, on the chemical and the physico-chemical mechanisms involved in the hydration reaction, especially in the presence of organic polymers. Most of these questions pertain to the primary hydration product and binding phase of Portland cement paste, the calcium silicate hydrate (C–S–H) gel [1]. Despite the millenary history of the cement, several open questions still arise on the physico-chemical mechanisms underlying its hydration process. This short review addresses some of the most interesting open issues, indicating the main developing strategies for the investigation of this process.

A model is developed to explain why the C-S-H phase that grows during the hydration of Portland Cements initially requires a high water content, much of which is lost by gentle drying. It is proposed that the rapid growth of C-S-H during the hydration of alite (C 3 S) in Portland cements initially occurs by adsorption of fully hydrated aqueous calcium cations onto anhydrous anionic basal sheets of a silicate-deficient (dimeric) tobermorite-like composition. Both divalent (Ca 2+) and univalent (CaOH +) solvated cations are incorporated to balance the negative charge of the basal sheet, leading to significant structural disorder, explaining the poorly-crystalline nature of the C-S-H formed. Some of the solvation water is lost irreversibly on first drying due to the formation of Si-O-Ca-O-Si bridges, explaining irreversible shrinkage. The initially-formed C-S-H is metastable relative to a form with longer silicate chains, towards which it may slowly evolve with separation of water and CH.

Phase transformation in cement during hydration is studied by XRD, FTIR and Mössbauer. The hydration process was monitored by self consistent analysis of the XRD results. Alite and belite phases control the early setting time of cement. Mössbauer spectroscopy results suggest that brownmillerite prolongs setting time. a b s t r a c t We report the phase transformations in Portland cement before and after hydration. The hydration mechanism was studied in detail by using a full Rietveld refinement of the X-ray diffraction (XRD) patterns, Fourier Transformed Infra-Red (FTIR) spectroscopy, Thermogravimetric Analysis (TGA) and Mössbauer spectroscopy at room temperature. From the Rietveld refinement of XRD data, alite, belite, celite, brown-millerite and low quartz phases were detected and quantified as major phases in dry cement powder. After hydration, calcium carbonate, portlandite and ettringite phases were found to form. A large reduction in the amounts of alite and belite phases were observed suggesting the formation of amorphous C–S–H phase and emphasizing the role of alite phase in flash setting of cement, as justified by the XRD and FTIR spectroscopy. Mössbauer spectra of all the unset samples showed quadrupole split doublets corresponding to the brownmillerite phase which remains unchanged even after about one week of hydration, suggesting that brownmillerite did not transform to other phases during initial stage of hydration process.

Cement and Concrete Research 41 (2011) 1208–1223 Contents lists available at ScienceDirect Cement and Concrete Research j o u r n a l h o m e p a g e : h t t p : / / e e s. e l s ev i e r. c o m / C E M C O N / d e f a u l t . a s p Mechanisms of cement hydration Jeffrey W. Bullard a,⁎, Hamlin M. Jennings b, Richard A. Livingston c, Andre Nonat d, George W. Scherer e, Jeffrey S. Schweitzer f, Karen L. Scrivener g, Jeffrey J. Thomas h a Materials and Construction Research Division, National Institute of Standards and Technology, Gaithersburg, MD, USA Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA Department of Materials Science and Engineering, University of Maryland, College Park, MD, USA d Laboratoire Interdisciplinaire Carnot de Bourgogne (ICB), UMR 5209 CNRS-Université de Bourgogne, Dijon, France e Department of Civil and Environmental Engineering/PRISM, Princeton University, Princeton, NJ, USA f Department of Physics, University of Connecticut, Storrs, CT, USA g Institute of Materials, Construction Materials Laboratory, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland h Schlumberger-Doll Research, Cambridge, MA, USA b c a r t i c l e i n f o Article history: Received 21 July 2010 Accepted 22 September 2010 Keywords: Hydration (A) Kinetics (A) Microstructure (B) a b s t r a c t The current state of knowledge of cement hydration mechanisms is reviewed, including the origin of the period of slow reaction in alite and cement, the nature of the acceleration period, the role of calcium sulfate in modifying the reaction rate of tricalcium aluminate, the interactions of silicates and aluminates, and the kinetics of the deceleration period. In addition, several remaining controversies or gaps in understanding are identiﬁed, such as the nature and inﬂuence on kinetics of an early surface hydrate, the mechanistic origin of the beginning of the acceleration period, the manner in which microscopic growth processes lead to the characteristic morphologies of hydration products at larger length scales, and the role played by diffusion in the deceleration period. The review concludes with some perspectives on research needs for the future. Published by Elsevier Ltd. Contents 1. 2. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Scope of this review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Mechanisms of C3S or alite hydration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Initial reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1. Metastable barrier hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2. Slow dissolution step hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Acceleration period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1. Timing of C–S–H nucleation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2. C–S–H growth mechanism and morphology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3. What triggers the onset of N + G? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Deceleration period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. C3A, aluminate phase and portland cements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Interaction between silicates and aluminates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Perspectives for future research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Speciﬁc research needs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1. What are the correct rate-controlling steps and corresponding rate parameters that characterize hydration? 5.2.2. Can chemical kinetics be linked more rigorously to the structure and distribution of hydration products? . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1209 1209 1209 1210 1210 1211 1212 1213 1214 1214 1215 1216 1217 1218 1219 1219 1220 1220 1221 1221 1221 ⁎ Corresponding author. National Institute of Standards and Technology, 100 Bureau Drive, Stop 8615, Gaithersburg, MD 20899, USA. Tel.: + 1 301 975 5725; fax: + 1 301 990 6891. E-mail address: jeffrey.bullard@nist.gov (J.W. Bullard). 0008-8846/$ – see front matter. Published by Elsevier Ltd. doi:10.1016/j.cemconres.2010.09.011 J.W. Bullard et al. / Cement and Concrete Research 41 (2011) 1208–1223 1. Introduction Understanding the kinetic mechanisms of cement hydration intersects both academic and practical interests. From an academic standpoint, the chemical and microstructural phenomena that characterize cement hydration are quite complex and interdependent, making it difﬁcult to resolve the individual mechanisms or the parameters that determine their rates. Fundamental study of hydration therefore offers signiﬁcant scientiﬁc challenges in experimental techniques and multi-scale theoretical modeling methods. From a more practical standpoint, the drive to produce more sustainable concrete materials is leading to more complex mix designs that include increased amounts of secondary mineral additions, often originating as by-products of other industrial processes, and a wide variety of chemical admixtures that can enhance concrete performance. More complete knowledge of basic kinetic mechanisms of hydration is needed to provide a rational basis for mixture proportioning as well as the design and selection of chemical admixtures. Several detailed reviews have been written about the mechanisms that are thought to govern the kinetics of hydration [1–4]. At the time they were published, several important issues – the mechanistic origin of the induction period, the rate-controlling mechanisms during the acceleration period, the most important factors responsible for the subsequent deceleration of hydration, etc. – were addressed but left unresolved due to either lack of data or seemingly equivocal evidence for different viewpoints. But signiﬁcant strides have been made both in experimental techniques and in theoretical models in the intervening years. Our intention is to focus on these more recent developments, thereby providing an updated picture of the current state of knowledge and identifying the remaining controversies or gaps in understanding. Finally, we then propose a road map for future cement hydration research that targets the remaining gaps and could have the greatest impact toward supporting the development of more sustainable concrete materials. 2. Background Models of chemical kinetics that are based on fundamental chemistry and physics at the molecular scale have been feasible for gas-phase systems [5], for nucleation of crystals from a melt or aqueous solution [6], and even for dissolution and growth at crystal surfaces [7–11] by analyzing and modeling the individual kinetic steps in detail. Similarly, a fundamental approach to understanding cement hydration would involve breaking the problem down to the study of the kinetics of the individual mechanistic steps. This approach is desirable because it would provide a foundation for understanding the interactions among the coupled processes, and for establishing how the microscopic kinetics lead to the development of the microstructure at higher length and time scales. Furthermore, mechanistic understanding at the molecular scale would provide knowledge of the dependence of rates of reaction and diffusion on temperature and the state of saturation, that is, the effect of curing conditions. Cement hydration involves a collection of coupled chemical processes, each of which occurs at a rate that is determined both by the nature of the process and by the state of the system at that instant. These processes fall into one of the following categories: 1. Dissolution/dissociation involves detachment of molecular units from the surface of a solid in contact with water. A good comprehensive review of dissolution kinetics was performed by Dove et al. [12,13]. 2. Diffusion describes the transport of solution components through the pore volume of cement paste [5,14] or along the surfaces of solids in the adsorption layer [15,16]. 1209 3. Growth involves surface attachment, the incorporation of molecular units into the structure of a crystalline or amorphous solid within its self-adsorption layer [17]. 4. Nucleation initiates the precipitation of solids heterogeneously on solid surfaces or homogeneously in solution, when the bulk free energy driving force for forming the solid outweighs the energetic penalty of forming the new solid–liquid interface [6]. 5. Complexation, reactions between simple ions to form ion complexes or adsorbed molecular complexes on solid surfaces [18,19]. 6. Adsorption, the accumulation of ions or other molecular units at an interface, such as the surface of a solid particle in a liquid [15,16,19]. These processes may operate in series, in parallel, or in some more complex combination. For example, even simple crystal growth from solution involves diffusion of solute to the proximity of an existing solid surface, adsorption of the solute onto the surface, complexation of several solute species into a molecular unit that can be incorporated into the crystal structure and, ﬁnally, attachment and equilibration of that molecular unit into the structure [9,19]. When in series, these steps are coupled in the sense that the products of one step are the reactants of the next step, and so on. Often, but not always, one step has a signiﬁcantly lower rate than any of the other steps in the sequence. In that case, all but the slowest step, the ratecontrolling step, can reach equilibrium conditions and will determine the activities of the reactants and products of the rate-controlling step [19]. In this simple case where one step is rate-controlling, that step alone is responsible for the observed kinetic rate equation, the rate constant, and their temperature dependences. When the rates of two or more fundamental steps are comparable, then the rate equations and their dependence on system variables can be signiﬁcantly more complicated and difﬁcult to determine experimentally [19]. Unfortunately, the rigorous application of these concepts to cement hydration continues to be elusive because of the difﬁculty of isolating the individual chemical processes for detailed study. Even a task as seemingly simple as determining a fundamental rate law for the dissolution of Ca3SiO5, consistent with thermodynamics and the principle of mass action, is quite challenging because of the competing effects of rapid precipitation of less soluble phases from solution, the difﬁculty of adequately characterizing the surface at which dissolution is occurring and, even more basically, because rate data are usually acquired on polydispere particle suspensions without a complete characterization of the particle size distribution or absolute reactive surface area. The problem becomes exponentially more difﬁcult to analyze when more complex systems like portland cement are contemplated. Therefore, for cement one has been forced to accept only partial knowledge about the net kinetic effects of multiple interacting processes. The key to eventually building more mechanistic, less empirical models of hydration, capable of embracing its full range of chemical and structural complexity, is to develop strategies to isolate and study the individual rate processes that govern cement hydration. Such strategies will inevitably involve a close collaboration among a wide variety of experimental techniques, along with mathematical models and numerical simulation methods that can provide an intellectual framework for interpreting the data. This kind of collaboration has born fruit for unravelling the kinetics of certain processes in environmental geochemistry [10,20,21] and other branches of materials science [22–25]. 2.1. Scope of this review Nearly every review of portland cement (PC) hydration kinetics [1,2,4] spends the majority of its attention on the hydration characteristics tricalcium silicate, Ca3SiO5, or C3S according to conventional 1210 J.W. Bullard et al. / Cement and Concrete Research 41 (2011) 1208–1223 cement chemistry notation.1 One reason is that the impure monoclinic polymorph of C3S, referred to as alite, constitutes about 50% to 70% of PC by mass. Progress in basic understanding of kinetics is made more feasible by restricting attention to this simpler chemical subsystem because the analysis of chemical kinetics becomes increasingly complex with increasing number of components and phases. In addition, alite tends to dominate the early hydration period that comprises setting and early strength development because it is the component most responsible for formation of the calcium silicate hydrate gel (C–S–H), the principle product of hydration. In keeping with this trend, much of the new progress in cement hydration research has been made either on pure C3S or on alite itself. Recent research shows that triclinic C3S has signiﬁcantly different microstructure and hydration kinetics than impure, monoclinic alite [26]. Pure C3S powders tend to be much ﬁner grained than alite powders prepared and ground under similar conditions [26] because impurities in alite, mostly Mg and Al, promote grain growth during cooling from clinkering temperatures. In addition, some have speculated that the different crystal structure or impurity levels in alite alter the density of reactive sites at the surface, (e.g. screw dislocations or stacking faults) which can modify dissolution rates. Finally, there is some evidence that the growth morphology of C–S–H hydration products may be less porous, and therefore more resistant to mass transport, in C3S pastes than in alite pastes [26]. This may be related to the experimental observation that hydration of C3S often slows down markedly at lower degrees of hydration [27] than does hydration of alite [26]. Recent research on hydration of the C3A + gypsum subsystem of PC will also be reviewed because of its importance in determining the calcium sulfate requirements of PC with and without replacement by mineral admixtures. This will include a discussion of the interactions among the silicate and aluminate subsystems that are important for understanding the inﬂuence of sulfate levels on the hydration kinetics of PC with partial replacement by ﬂy ash or blast furnace slag. In closing this section, it is helpful to mention the experimental techniques that have been used to monitor hydration kinetics, because these techniques will be referenced repeatedly in the remainder of the paper. Most of the techniques used to date monitor the net rate of hydration, that is the overall progress of hydration without regard to the action of individual chemical reactions. Such methods include isothermal calorimetry, continuous monitoring of chemical shrinkage, in situ quantitative X-ray diffraction, semicontinuous analysis of pore solution composition, nuclear magnetic resonance spectroscopy (NMR), quasi-elastic neutron scattering (QENS) and small angle neutron scattering (SANS). The relative merits and weaknesses of such methods have been thoroughly assessed elsewhere; being outside the scope of this review, the interested reader is referred to [28] for more details. For now, we note that none of these techniques resolves the details of any particular mechanism, but they have proven useful for comparing the hydration of different cements, for characterizing the inﬂuence of variables such as cement ﬁneness, water-to-solids mass ratio (w/s), cement composition, temperature, and the type and dosage of admixtures. More importantly, comparison of different methods, such as calorimetry and SANS data [29,30], calorimetry and QENS data [31,32], or calorimetry and chemical shrinkage on parallel specimens can provide insights into the hydration process that cannot be obtained by any one method alone. For example, the SANS surface area tracks closely with the cumulative heat measured by calorimetry at very early times, up to about the peak hydration rate, but then diverges as the morphology of the C–S–H phase is not constant with time. The same is true of the constrained water component of the QENS signal. 1 In this shorthand notation, single capital letters are used to denote oxide units, e.g. C = CaO, S = SiO2, A = Al2O3, F = Fe2O3. We will use this convention frequently throughout the paper. 3. Mechanisms of C3S or alite hydration The rates of hydration of (triclinic) C3S, alite, and even PC have long been observed to vary with time by orders of magnitude in a complicated, nonmonotonic fashion. Historically, this fact has led to the division of the overall progress of hydration into four or ﬁve stages, deﬁned by somewhat arbitrary points on a plot of hydration rate versus time [4]. For our purposes in discussing kinetic mechanisms, we ﬁnd it helpful to consider the four periods indicated in the calorimetry plot of hydration rate versus time shown in Fig. 1: (1) initial reaction, (2) period of slow reaction, (3) acceleration period, and (4) deceleration period. The beginning and ending of these stages are still difﬁcult to pinpoint precisely, but they provide a more accurate picture of the current state of knowledge. In this section we undertake a review of recent progress in experimental and theoretical research on cement hydration in terms of its mechanism(s) and implications for microstructure development. Attention is focused on results that have come to light in the last decade, with limited review of earlier work only where necessary for historical context. The interested reader may refer to [4] and references therein for a more comprehensive review of earlier work. 3.1. Initial reaction The initial period is characterized by rapid reactions between C3S and water that begin immediately upon wetting, characterized by a large exothermic signal in isothermal calorimetry experiments [26]. The heat released by wetting the cement powder contri butes to this early exothermic signal, but signiﬁcant heat is also released by dissolution of C3S. The enthalpy of congruent C3S dissolution is − 138 kJ/mol, based on the reaction [33,34]: 2þ C3 S þ 3H2 O→3Ca 2− − þ H2 SiO4 þ 4OH ð1Þ Chemical analyses of the solution phases [35–39] have furnished persuasive evidence that C3S dissolves congruently and quite rapidly in the ﬁrst seconds after wetting. In dilute suspensions of C3S, for example, the increase in silicate concentration over the ﬁrst 30 s suggests that the dissolution rate may be at least 10 μmol m− 2 s− 1 [27]. Stein [40] calculated a theoretical solubility product for C3S of Ksp ≈ 3, when referenced to Eq. (1), which would imply that C3S should continue to dissolve until reaching equilibrium calcium and silicate concentrations in solution of several hundred mmol/L. In fact, it is well known that C3S dissolution rates decelerate very quickly while the solution is still undersaturated, by about 17 orders of magnitude with respect to the ion activity product of Reaction (1) Fig. 1. Rate of alite hydration as a function of time given by isothermal calorimetry measurements. J.W. Bullard et al. / Cement and Concrete Research 41 (2011) 1208–1223 compared to the equilibrium calculation, by the end of this period [27,40,41]. The mechanism of this early deceleration of C3S has been a subject of considerable debate over the years, and many hypotheses have been proposed. The reader is referred to [4] and references therein for a description of the proposed mechanisms. Here we will focus on three mechanistic explanations that continue to have the greatest plausibility in light of recent experimental and theoretical research. 3.1.1. Metastable barrier hypothesis Stein [42] and others [43] have argued that the deceleration is caused by the rapid formation of a continuous but thin metastable layer of a calcium silicate hydrate phase, which Gartner [2] has called C–S–H(m), that effectively passivates the surface by restricting its access to water, or restricts diffusion of detaching ions away from the surface. This thin layer is proposed to reach equilibrium with the solution at the end of the intial reaction period. Jennings [44] reviewed solution composition data from several decades of literature and showed that they tend to lie along one of two curves on a plot of calcium concentration versus silicate concentration, as shown in Fig. 2. The curve with higher Ca and Si concentrations was interpreted as reﬂecting equilibrium of the solution with a metastable hydrate layer having a variable Ca:Si molar ratio, and Gartner and Jennings [41] subsequently used the Gibbs–Duhem relation to estimate the Ca:Si molar ratio of this metastable hydrate as a function of calcium concentration in solution. The metastable barrier hypothesis implies that the metastable hydrate isolates the underlying alite from the solution, which then comes into equilibrium with the hydrate. However, the mechanism for the end of the delay period is not evident. The fact that the time of the end of the slow reaction period has such a precise and repeatable value indicates that there must be some critical process acting during Fig. 2. Concentrations of silica (y-axis in μmol/L) and calcium (x-axis in mmol/L) reported for cement paste pore solution, collected from an extensive literature search in [44], and interpreted as indicating that either of two types of C–S–H can establish equilibrium with the solution. 1211 that period. This must take the form of some continuing chemical reaction or reactions that eventually destabilize the metastable layer in some way [2,4]. Indeed, calorimetry measurements show that the rate of heat output never decreases all the way to zero during the period of slow reaction. Bullard [45] recently simulated the metastable barrier hypothesis for C3S hydration, using a kinetic cellular automaton model of coupled reactions and diffusion phenomena using the principles of mass action and detailed balances. Simulations using the metastable barrier hypothesis adopted assumptions about the composition variability both of the passivating layer and of the more stable forms of C–S–H, based on limited and indirect experimental evidence. Even so, the simulations quantitatively reproduced a number of experimental observations of the evolution of the solution composition, the composition variablity of C–S–H, and the hydration rate of C3S at two different water–cement mass ratios and initial conditions of the solution [27,46,47]. One difﬁculty with the metastable barrier hypothesis has been the scant direct experimental evidence of the existence of such a layer. However, the last several years have witnessed signiﬁcant progress in this area. Nuclear resonance reaction analysis (NRRA), based on the 1H (15N, α, γ)12 resonance, has been used to measure the hydrogen depth proﬁle at and below the surface of a specimen, with a depth resolution of a few nm and a sensitivity to hydrogen of a few μg/g [48,49]. By probing below surfaces of cementitious phases immersed in aqueous solution for different times, they have observed changes in the hydrogen depth proﬁle as a function of time. Some typical depth proﬁles for hydrating triclinic C3S are presented in Fig. 3. The proﬁle is characterized by a Gaussian peak at the surface and a diffusion-like curve into the depth of the sample. The Gaussian peak has been interpreted as a thin but continuous hydrated layer [49]. Based on ideas from the glass corrosion literature, the overall hydrogen depth proﬁle measured by NRRA has been interpreted as a set of layers with differing degrees of calcium/hydrogen exchange, as shown in Fig. 4. Although the Gaussian peak remains essentially ﬁxed at later times (Fig. 3), the proﬁle extends progressively deeper into the solid, reaching appreciable hydrogen concentrations as deep as 0.4 μm after 45 min at 30 °C. This increasing average penetration depth of hydrogen indicates that signiﬁcant hydration reactions are still occurring during the slow reaction period. These conclusions are not too different from the mechanisms proposed in earlier publications [1,2,4,50]. Fig. 3. Progression of hydrogen concentrations with depth and time during the initial and slow reaction periods for triclinic C3S hydrated at 30 °C [49]. 1212 J.W. Bullard et al. / Cement and Concrete Research 41 (2011) 1208–1223 Fig. 4. Schematic diagram of the arrangement of surface layers on a C3S grain during the slow reaction period based on the hydrogen depth proﬁle measured by nuclear resonance reaction analysis (NRRA). More recently, Bellmann et al. [51] have examined pastes and very dilute suspensions of C3S nanoparticles in water. Using 29Si NMR, they observed that an intermediate calcium silicate phase containing hydrated silicate monomers forms very early during hydration, a result that is consistent with earlier research on C3S [50,52–54]. Their data demonstrate that, at least for nanoparticulate C3S, hydration proceeds in two stages: formation of an intermediate silicate hydrate phase followed by conversion of this phase into C–S–H once the solution becomes sufﬁciently concentrated with calcium. With greater direct evidence of the existence of an early hydrate phase, the challenge still remains to demonstrate that the phase has the necessary passivating inﬂuence on C3S to explain the transition to the slow reaction period. NRRA data have been interpreted as indicating a thin surface hydrate that is permeable to calcium and water but not to silicates, although this latter idea is a conjecture because NRRA does not measure either calcium or silicate species. Moreover, the length of the slow reaction period has been correlated with the time required to achieve a critical hydrogen depth in NRRA experiments. For example, increasing temperature both shortens the slow reaction period and increases the rate of penetration of hydrogen below the surface (Fig. 3). And when sucrose, known to be a strong retarder, is added to the solution, the penetration rate of hydrogen below the surface occurs much more slowly than without sucrose [49]. All of these studies therefore provide strong evidence of a direct correlation between the length of the slow reaction period and the rate of development of the surface hydrate. A remaining challenge is to determine if the development of that surface hydrate controls the rate of hydration or if the rate of hydration controls the development of the surface hydrate. If the metastable barrier hypothesis is correct, the layer must cover the great majority of the C3S surfaces and be fairly dense if it is to effectively block the diffusion of one or more dissolved components. There are examples of nanoscale metal oxides such as alumina being able to passivate aluminum surfaces and limit further oxidation, but in those instances the layer is extremely stable thermodynamically and mechanically and has a close crystallographic relationship with the underlying metal, in contrast with the metastable C–S–H phase. Both atomic force microscopy conducted on ﬂat C3S surfaces under water [55] and high-resolution electron microscopy on dried samples [56] have been used to search for evidence of a continuous ﬁlm of this kind. However, although patches of some kind of precipitate are often observed on the surfaces at very early times, evidence for a continuous layer has not been found using these direct methods of surface examination. 3.1.2. Slow dissolution step hypothesis The metastable barrier hypothesis discussed in the last section assumes either explicitly or implicitly that the rate of C3S dissolution in the period of intial reaction would continue to be rapid up to much higher solution concentrations of calcium and silicates if not for the formation of the passivating hydrate layer. However, other researchers have assumed that C3S dissolution rates decrease rapidly for some other reason. Barret et al. [35,36] originally proposed that a “superﬁcially hydroxylated layer” forms on C3S surfaces in contact with water, and that the dissociation of ions from this layer occurs much more slowly than would be otherwise expected for a mineral in highly undersaturated solutions. Nonat et al. [27,39,47,55,57] have adopted this explanation for slow dissolution of C3S and subsequently developed an alternative mechanistic explanation for the initial reactions that is based on a steady state balance between slow dissolution of C3S and initially slow growth of C–S–H. According to these authors, the apparent solubility of the superﬁcially hydroxylated C3S is much lower than the one calculated for C3S, and the dissolution rate decreases very rapidly when the calcium hydroxide concentration increases due to dissolution. When the solution exceeds a maximum supersaturation with respect to C–S–H, C–S–H nucleates very rapidly on C3S surfaces and begins to grow slowly because of its initially low surface area. Growth of C–S–H causes the silicate concentration in solution to decrease and the Ca:Si molar ratio in solution to increase. Within minutes, a steady state condition is set up in which the solution is supersaturated with respect to C–S–H but undersaturated with respect to C3S. Fig. 5 shows this behavior by superimposing the changes in solution concentration on a crosssection of a solubilty diagram in the system CaO–SiO2–H2O, with curves for both C3S and C–S–H indicated in the ﬁgure. The dashed arrow in the ﬁgure indicates the trajectory of the solution concentration for pure congruent dissolution, which continues until a maximum supersaturation is reached with respect to C–S–H (point A in the ﬁgure). Nucleation of C–S–H causes the silicate concentration to decrease (bold arrow in the ﬁgure) as the solution composition approaches the solubility curve for C–S–H. Evidence supporting this view comes from studies of dissolution rates of C3S in stirred suspensions [58]. Increases in Ca and Si concentrations in solution were monitored continuously in suspensions of C3S so dilute (w/s = 50,000) that, theoretically, the solution should never become supersaturated with respect to C–S–H. Without the complicating factor of C–S–H nucleation and growth, congruent dissolution caused the concentrations of Ca and Si to increase continuously in a 3:1 ratio. With this technique, initial C3S dissolution Fig. 5. Cross-section of a solubility diagram in the system CaO–SiO2–H2O. The arrow shows the path followed by the concentrations in solution during the congruent dissolution of C3S. The concentration increases beyond the solubility of C–S–H until the maximum supersaturation from which C–S–H precipitates immediately is reached (point A). From [35,126]. J.W. Bullard et al. / Cement and Concrete Research 41 (2011) 1208–1223 rates were measured as approximately 10 μmol m− 2 s− 1 and the steady-state ion activity product (IAP) was estimated to be log IAP = −17 when referenced to Reaction (1), nearly 17 orders of magnitude less than the solubility product calculated from the Gibbs free energy of the reaction. Along the same lines, the dissolution rates of many natural minerals in aqueous solutions do not follow a smooth relationship with respect to the saturation state of the solution [10,11,20]. Brieﬂy, different mechanisms of dissolution are rate controlling depending on the saturation state of the solution. Far from equilibrium, high rates of dissolution are enabled by etch pit opening at surface defects, whereas closer to equilibrium but still signiﬁcantly undersaturated, the driving force is insufﬁcient to activate the etch pit opening and dissolution occurs primarily by a retreating step mechanism that is much slower. This approach for low-solubility minerals has been applied to alite. Many experimental observations have shown that the rate of C3S and alite dissolution is affected by the initial concentration of the solution [27,39,47,57]. Scanning electron microscope (SEM) observations of unground alite surfaces hydrated in different dilute solutions have further conﬁrmed the importance of the initial saturation state. Samples hydrated in deionised water showed signiﬁcant corrosion of the surface with the presence of small pits (hundreds of nanometers in diameter) whereas samples hydrated in saturated lime solution preserved a smooth planar surface [56]. Other studies performed on alite or cement pastes have also revealed the presence of pits at early times of hydration [59–61]. This mechanism of etch pit activation or deactivation, depending on driving force, implies that dissolution is a rate controlling mechanism and provides a satisfying way to make low dissolution rates of alite consistent with the considerable undersaturations at the end of the intial reaction period. The slow dissolution step hypothesis for the onset of the period of slow reaction is supported by the observed roles of crystallographic defects in the early hydration processes of cementitious material, which have been studied by several researchers [62–64]. Maycock et al. [64] as well as Odler and Schüppstuhl [63] studied the effect of quenching rate on the reactions of alite and found that faster quenching, likely to induce more crystal defects, resulted in shorter induction periods. Fierens and Verhaegen [62] cooled C3S at different rates from 1600 °C to 1300 °C before quenching, and similarly found that the duration of the induction period was related to the length of the thermal treatment. More recently, Juilland et al. [61]. performed a post-thermal annealing treatment at 650 °C on alite of narrow particle size distribution as a way to decrease the defect density. A change of polymorphism from monoclinic M3 to triclinic T1 occurred without any signiﬁcant change of the particle size distribution. Isothermal calorimetry data for the annealed samples show the presence of a very long induction period for the thermally treated samples (Fig. 6), supporting the hypothesis that surface defects control the rate of dissolution and thereby inﬂuence the length of the induction period. A difﬁculty with this slow dissolution step hypothesis is in reconciling the dissolution rates with the observed time dependence of silicate concentrations in the ﬁrst minutes of hydration. Most experiments show a sharp peak in silicate concentration in the ﬁrst minutes after wetting, which decreases almost as rapidly and is followed by a longer period of very slowly decreasing concentrations during the period of slow reaction. Before the peak, increases in silicate concentration can be interpreted as pure C3S dissolution. The sharp decrease has been interpreted as the consumption of silicates due to nucleation of C–S–H [27]. Within 20 min, the silicate concentration decreases to about half its original value and continues to decrease much more slowly for the next 20 min. Therefore, one should expect the C3S dissolution rates after 20 min to be comparable to the rates on the left side of the peak at the same silicate concentration in experiments where the calcium concentration is held ﬁxed at 11 mmol/L, because at both those times the solution has basically the same composition and, therefore, the same driving force for 1213 Fig. 6. Heat evolution of alite untreated (reference, dashed line) and treated at 650 °C for 6 h (plain lines) of narrow particle size distribution. All measurements were performed at 20 °C and the w/s ratio was kept at 0.4. dissolution [27,47]. However, such rapid C3S dissolution rates are not experimentally observed after the initially sharp decrease in silicate concentration until the acceleration period begins. One possible explanation is that the C3S surfaces on the right side of the silicate peak are already signiﬁcantly covered with C–S–H precipitates, so that the dissolution rate per unit area may be rapid but the overall dissolution rate low. 3.2. Acceleration period In unretarded, unannealed C3S and alite systems, the delay period is just the minimum in the hydration rate that is reached after the initial reaction but before the beginning of accelerated growth of hydration products [4]. A true induction period appears to exist as a distinct stage only when chemical retarders are added or materials have been annealed. Furthermore, this delay seems to be just the consequence of the slow reaction (due to one of the mechanisms described previously) until a critical point is reached when the rate of nucleation and growth starts to accelerate. Therefore, we have made the unconventional choice of omitting a separate section for the period of slow reaction, preferring instead to consider its aspects only in terms of the consequences for the onset of the acceleration period, which is generally agreed to be related to a nucleation and growth (N + G) mechanism. Throughout this N + G period of hydration of C3S and alite, the hydration rate, expressed as the time derivative of the degree of hydration,2 dα/dt, increases as αr, where 2/3 b r b 1 [4]. By analogy to autocatalytic chemical reactions, this behavior implies that the rate of hydration in this stage depends on the amount of some hydration product, presumably C–S–H. Supporting this idea, a large and growing body of experimental and modeling evidence [4,27,30,35,37,55,65– 68] indicates that the rate-controlling step of hydration during this period is related to the heterogeneous nucleation and growth of C–S–H on alite and perhaps on other mineral surfaces as well. The evidence for this comes from a number of sources. C–S–H is observed to be formed primarily on surfaces of C3S or alite [4,69,70] when observed by scanning, atomic force, or transmission electron microscopy. In addition, Zajac [71] has reported experimental measurements showing that the hydration rate of C3S is proportional to the surface area of C–S–H as measured by nuclear magnetic 2 We deﬁne the degree of hydration as the mass of C3S consumed divided by its initial mass. 1214 J.W. Bullard et al. / Cement and Concrete Research 41 (2011) 1208–1223 resonance (NMR) spectroscopy. If growth of C–S–H is rate-controlling, the hydration rate is expected to be proportional to the number of active growth sites for C–S–H (i.e., its surface area). Another paper in this issue [72] describes the application of various modeling and simulation methods that strongly support the underlying mechanism as being one of nucleation and growth and discusses in detail various hypotheses regarding the nucleation process (initial or ongoing); growth (isotropic, anisotropic or diffuse) and other mechanisms. 3.2.1. Timing of C–S–H nucleation As already discussed, earlier reviews of cement hydration have concluded that the nucleation of a stable form of C–S–H occurs some time after the formation of a metastable hydrate layer on alite surfaces, and that the growth of the stable C–S–H precipitates happens by conversion of the metastable layer, whether directly or by a throughsolution mechanism. Experimental and modeling studies over the past 10 years, described in Section 3.1, have cast some doubt on the necessity of this conclusion and indicate that nucleation and growth of C–S–H can occur at very early times and may not require a pre-existing hydrate phase. Direct observations of the ﬁrst C–S–H nucleation events in C3S or alite systems are difﬁcult to make. Conclusions drawn in the recent literature are mostly based on inferences from model interpretations of experimental data. For example, Garrault and Nonat [27] use the slow dissolution hypothesis and interpret the decrease in silicate concentrations in the opening seconds or minutes of hydration as the result of C–S–H nucleation, setting up the subsequent balance between C3S dissolution and C–S–H growth. Application of the Avrami model to isothermal calorimetry or QENS data requires assuming an induction period of at least 1 h prior to any C–S–H nucleation to obtain good ﬁts [73,74]. But both Thomas' application of a boundary nucleation and growth (BNG) model to ﬁt isothermal calorimetry data [65] and its application by Scherer et al. to ﬁt chemical shrinkage data [75,76] indicate that initial C–S–H nucleation occurs close to the time of mixing. The interested reader is referred to the companion paper [72] for more detail on the use of the BNG model for ﬁtting these kinds of experimental data. Bullard [45,48] used a kinetic cellular automaton model to simulate the microstructural development and solution chemistry during C3S hydration using either the metastable layer hypothesis or the slow dissolution step hypothesis for the initial reaction and delay period, and found that only heterogeneous nucleation of C–S–H on C3S surfaces could account for experimental observations of the evolution of the solution composition and degree of hydration. Those simulations also differentiated between heterogeneous nucleation and growth of C–S–H, and indicated that nucleation occurs in a fairly short burst over only a few minutes, either at the end of the initial reaction when assuming the slow dissolution step hypothesis or near the onset of the N + G period when assuming the metastable layer hypothesis. The narrow window of C–S–H nucleation occurs in the simulations because nucleation consumes calcium and especially silicates from solution, thus lowering the saturation index of C–S–H enough that the thermodynamic driving force for growth of existing precipitates is less than the energetic barrier to nucleation. The importance of (stable) C–S–H nucleation as a controlling factor in early-age hydration of C3S is underscored by experiments reported by Thomas et al. [67] in which C3S pastes were seeded by adding a reactive form of C–S–H at the time of mixing. In those experiments, the induction period was essentially eliminated and hydration progressed to N + G kinetics immediately and at a higher rate than in an unseeded paste. Earlier, Wu and Young [77] attributed the accelerated rates of hydration of C3S by colloidal silica to C–S–H nucleating on the surface of the silica particles. These results show that the timing of the onset of accelerated rates characterized by the N + G period depends primarily on having enough growing regions of C–S–H to give an appreciable hydration rate. Without seeding, more time is needed for the natural nucleation and growth process to provide enough C–S–H surface area for appreciable growth rates to be observed. Since the deﬁnition of an induction period is a time prior to initial nucleation, the slow early hydration period of unretarded paste should not be so labeled if slow growth of stable C–S–H is indeed occurring during that time. NMR data earlier from Clayden et al. [52] and more recently from Bellmann et al. [51] suggest that dimeric species of silicate only start to be detected at the end of the slow reaction period. This suggests that the polymerization of silicate may be an important mechanism in the transition to nucleation and growth kinetics. 3.2.2. C–S–H growth mechanism and morphology It seems well established that growth of C–S–H controls hydration kinetics from the delay period until some time after the rate maximum. The growth mechanism must be closely related to the observed development of C–S–H structure either as the aggregation of nanoscale particles [78–82], or as large but defective sheets of silicate layers [83]. Gartner [83] proposed a mechanism of growth for branching sheets, which would be consistent with observed kinetics of hydration. This mechanism involves the attachment of silicate tetrahedra at growing silicate chains all along the perimeter of 2D silicate sheets and the incorporation of calcium and hydroxyls in the layers between these sheets to form a tobermorite-like or jennite-like structure. Each existing embryo after nucleation grows in this fashion, and as growth continues the layers form regions of well-ordered, crystalline structure on a length scale of about 5 nm. However, as the sheets grow in 2D, the probability of building a defect into the layer increases with the number of growth sites. The lattice strain caused by a growth defect can cause the sheets to buckle and diverge away from each other, thus causing a disordering of the crystalline structure. This mechanism is generally compatible with the observed kinetics, and the concept that nanograins of C–S–H may actually be domains of bonded but defective calcium silicate layers could explain the high cohesive strength of C–S–H and the observation that the nanograins do not coarsen appreciably despite having exceedingly high surface area. An alternative theory of C–S–H growth is based on the aggregation of C–S–H nanoparticles to form an interpenetrating fractal structure. In this scenario, C–S–H solid particles grow only to a certain characteristic size, on the order of a few nanometers, at which point they stop growing and remain stable for extended periods of time. However, existing C–S–H nanoparticles either can stimulate the heterogenous nucleation of new particles on their surfaces or the aggregation of previously nucleated C–S–H nanoparticles from the solution [67]. A difﬁculty with this idea is that both heterogeneous nucleation on existing surfaces and homogeneous nucleation of nanoparticles in solution requires a higher driving force (i.e. supersaturation of the solution) than continued growth on the existing C–S–H surfaces. However, chemical models and experimental observations indicate that the supersaturation is high enough to cause C–S–H nucleation from solution only in the ﬁrst minutes of hydration [27,54,68]. Unless C–S–H formation is controlled by nucleation of a stable C–S–H by inplace transformation of a metastable C–S–H [2], nucleation is likely conﬁned to very early times. For mature pastes, the Jennings colloid model [79,81,82] envisions two stable morphologies of C–S–H with different packing densities, known as high density (HD) and low density (LD) C–S–H, which is supported by experimental observations such as nanoindentation [84,85]. Moreover, the packing density might be signﬁcantly lower during the early hydration period and then increase with time. Since the observed hydration kinetics during the N + G period depend in part on the rate at which the available space is ﬁlled, this becomes an important kinetic variable, which was considered in the mechanisms proposed by Bishnoi and Scrivener [86] to explain the effect of particle size on the early kinetics, and by Thomas et al. [30] to explain J.W. Bullard et al. / Cement and Concrete Research 41 (2011) 1208–1223 the greater amount of early hydration of C3S observed with CaCl2 acceleration. 3.2.3. What triggers the onset of N + G? Gartner et al. [4] list four proposed mechanisms for the beginning of noticeably accelerating hydration rate after the delay period, shown in Table 1. Each hypothesis has received substantial support in the literature, and experimental data have been produced that argue for or against each one. The topic is still controversial, and we will try only to bring the debate up to the present day with the most recent experiments and models. It should be noted that N + G models assume that both the rate of growth of individual regions of product in any linear direction are constant with time, as are the rate of nucleation of new product regions (per unit of untransformed volume or boundary area) Thus these models imply that the variation in the overall hydration rate with time occurs only due to changes in the total amount of interface between product regions and the solution. This assumption also requires that the driving force for nucleation and for growth be relatively constant with time, at least during the period around the main hydration peak when the nucleation and growth models ﬁt the data closely. It further implies that the rate of C3S dissolution is controlled by the rate of nucleation and growth, and not the other way around. Both the metastable barrier hypothesis and the slow dissolution step hypothesis can explain this dependence of dissolution rates on C–S–H nucleation and growth. The metastable barrier hypothesis proposes that the metastable layer around the C3S particles has a higher solubility than stable C–S–H and controls the solution concentrations of calcium and silicate ions. As stable hydration product precipitates from the pore solution, the metastable layer continuously dissolves at its outer surface to replenish ions to the solution, while simultaneously reforming at its inner surface by C3S dissolution, a process that continues at least until all of the particle surfaces are covered with hydration product (i.e. after the main rate peak). According to the slow dissolution step hypothesis, the delay period is caused by low dissolution rates when the solution composition is not sufﬁciently undersaturated with respect to C3S. During the acceleration period, both C–S–H and CH are present and their increasing rates of growth continuously remove ions from solution which must be replenished by further dissolution of C3S. As already described, a preponderance of experimental evidence indicates that some form of C–S–H exists prior to the end of the slow reaction period, likely being formed near the beginning of that period. Therefore, it is difﬁcult to see how nucleation of C–S–H, by itself, could be the trigger for the acceleration period. In this connection, it is worthwhile recalling that 29Si NMR detects silicate dimers only at the end of the slow reaction period [51]. Although the Table 1 Possible causes of the onset of the N + G period, reproduced from [4]. Hypothesis/mechanism Brief description Nucleation and growth of C–S–H Nucleation and growth of a stable C–S–H happen at the end of the slow reaction period and are ratecontrolling during the acceleration period as a metastable protective layer of hydrate becomes chemically unstable and exposes the high-solubility C3S. Nuclei of stable C–S–H, already formed during initial reaction, grow at a nearly exponential rate. C–S–H growth is rate controlling. No metastable hydrate barrier layer is invoked. Metastable C–S–H barrier layer is semipermeable. Solution inside is close to saturation with respect to C3S. Osmotic pressure leads to its rupture Nucleation and growth of portlandite become ratecontrolling (and thus indirectly control the rate of growth of C–S–H) Growth of stable C–S–H Rupture of initial barrier Nucleation of portlandite (CH) 1215 technique is not very sensitive to small quantities, the dimerization of silicates indicates a possible change in the structure of C–S–H at the end of the slow reaction period. Therefore, the view that continuous nucleation and growth of C–S–H alone causes the transition from slow reaction to acceleration should be revisited to see if a change in the structure of existing C–S–H embryos could further enhance accelerated growth beyond that caused by the increase in surface area of the product. Of the four mechanisms listed in Table 1, mechanical rupture of a surface barrier has been argued to be most consistent with the NRRA results described in Section 3.1.1 [48]. If the barrier layer is permeable to Ca2+ and water but impermeable to silicate ions, the accumulation of a silicate-rich gel, less dense than C3S, could exert a swelling pressure against the surface barrier. By this hypothesis, a critical volume of gel is eventually reached at which the barrier ruptures, allowing the trapped silicate ions to react with the calcium-rich solution. This enables the rapid development of outer product C–S–H throughout the N + G period. If a protective surface layer is indeed ruptured due to pressure exerted by an underlying silica gel, the critical volume of the gel needed for rupture has not yet been determined. However, the critical volume should depend only on the physico-chemical properties of the surface layer and the substrate, and therefore in particular should be independent of the w/s ratio of the paste. A fourth proposed mechanism for the end of the induction period, the delayed nucleation and precipitation of CH, was suggested by Young et al. [87]. This hypothesis does not invoke a surface barrier layer, but instead is based on the observation that during the induction period the solution is supersaturated with respect to CH, and after the induction period the Ca2+ concentration drops rapidly. The maximum supersaturation of the solution with respect to CH (i.e. ratio of the ion activity product to the solubility product of CH) at the onset of the N + G period is often observed to be about 4.5 to 5 for pastes with w/s ~ 1 when proper care is taken to calculate the activities corresponding to the measured concentrations of Ca2+ and OH− and to account for the presence of the CaOH+ complex. Since 1989, the CH nucleation hypothesis has become less popular in light of experimental data that were thought to contradict it. For example, seeding a C3S paste with small particles of CH produced no accelerating effect [88] and may even retard C3S hydration [89]. Similarly, hydration of C3S in lime water is retarded at early ages relative to hydration in initially pure water [90]. Furthermore, when dilute suspensions of C3S are hydrated in an aqueous solution in which the calcium concentration is maintained just below the saturation point of CH [27,47], the hydration kinetics followed the typical trends shown in Fig. 1 despite the fact that portlandite could not nucleate in the suspensions. The same is true of the NRRA experiments discussed earlier [48,49] in which the specimens were in contact with a lime water solution from the beginning. More recent experimental research [56] and modeling studies [68] have shown how the CH nucleation hypothesis can be reconciled to these seemingly contradictory experimental results. If slow C3S hydration during the delay period is due to the slow dissolution step hypothesis, instead of the metastable barrier hypothesis, then the higher concentration of calcium and hydroxyl ions, caused by the presence of CH seeds or by the use of lime water, will lower the driving force for dissolution of C3S. This will slow the dissolution rate of C3S and consequently increase the delay time. However, if very high supersaturations with respect to portlandite could be produced initially, then portlandite nucleation and C–S–H nucleation and growth can occur without the need to dissolve as much C3S. The greater quantity of C–S–H could lead to acceleration at these higher lime concentrations even though retardation is observed at lower lime concentrations. In fact, this phenomenon has been observed experimentally [91]. 1216 J.W. Bullard et al. / Cement and Concrete Research 41 (2011) 1208–1223 In closing this section, we note that almost ten years ago, Gartner et al. [4] stated that the four hypotheses listed in Table 1 have “coexisted somewhat uneasily” in the literature, awaiting more deﬁnitive experimental tests. In the intervening years the experimental investigations and advances in modeling we have described have allowed much more quantitative and detailed analysis of the phenomena occurring in the periods of slow reaction and acceleration. Unfortunately, even this more advanced scrutiny has not settled the issue decisively. Aspects of more than one have been demonstrated to be plausibly consistent with observed changes in rate and chemical composition of the pore solution. This is an area where progress will depend on continued advances in the characterization of the structural and kinetic properties, both in terms of new experimental methods and more sophisticated multi-scale computer modeling techniques. 3.3. Deceleration period Even though the period of “post-peak” decelerating hydration progress (Fig. 1) is important in concrete technology because of the slower strength development, there have been comparatively few quantitative studies of this later period. It is widely considered that at later ages the rate of hydration is controlled by a diffusion process. However, several other factors may also be important, namely: 1. consumption of small particles, leaving only large particles to react; 2. lack of space, or 3. lack of water. The third factor is particularly important in practice. The total volume of hydrates is slightly less than the combined volume of the reacting cement plus water (by about 5% to 10%). This decrease in total volume, known as chemical or le Chatelier shrinkage, leads to the formation of gas-ﬁlled porosity after setting and a decrease in internal relative humidity, which will decrease the hydration rate. Therefore, the analysis of kinetic data in this period must consider whether the system was in contact with a water reservoir or was sealed from external sources of water. The effect of particle size distribution is not only important during the main hydration peak, but after it as well. In a typical cement, the size of the initial particles ranges from around 50 μm to 60 μm down to smaller than 1 μm. Particles less than about 3 μm are completely consumed by about 10 h and particles below 7 μm by 24 h [92]. Knudsen argued in 1980 [93] that the simultaneous hydration of different particle sizes obscures the rate controlling mechanism. His argument is probably applicable only at later times, because the mechanisms of nucleation and unobstructed growth of C–S–H depend only on the total surface area and are therefore not obscured by a range of particle sizes. Nevertheless, to eliminate complications due to broad particle size distributions, Costoya [26] and Bishnoi and Scrivener [86] adopted the practice of studying alite divided into different particle size fractions. The time dependence of the cumulative amount of reaction sometimes has a distinct “knee”, as shown by a plot of the bound water index (BWI) inferred from QENS measurements in Fig. 7. This knee, when observed, is often assumed to correspond to the onset of diffusion. Supporting this idea, mathematical ﬁts of BWI versus time often indicate a transition to a parabolic time dependence at the knee. On the other hand, the transition is not always as obvious as in Fig. 7. Even in QENS studies, the knee is not as exaggerated as in Fig. 7 when three populations of bound water are considered [74,82,94] when calculating BWI instead of only two [31]. The transition is even less evident from cumulative data. In fact, neutron scattering data track calorimetry data closely until shortly after the main peak, but the two curves sometimes diverge afterward [29,31,74]. One reason may be that calorimetry primarily measures the exothermic dissolution of C3S, while neutron scattering tracks microstructural features of Fig. 7. Plots of bound water index (BWI) versus time for C3S hydration measured by quasi-elastic neutron scattering [31]. the hydration products (e.g. states of water) as a proxy for reaction progress. This difference in the way changes are measured may mean that the knee observed in QENS data may reﬂect the onset of some change in the hydrated microstructure rather than a transition in the rate of reaction. But it is important to note that the knee does not coincide with the maximum observed rate of hydration, dα/dt. The dα/dt maximum is in fact the inﬂexion point in the cumulative curve, where there is no indication of a change in rate controlling mechanism. From this and other evidence, it now seems very unlikely that a transition to diffusion rate control is responsible for the ﬁrst period of deceleration immediately after the main peak, although diffusion may becom rate controlling at later ages. The inevitable impingement of different domains of the growing hydration product, which is a fundamental feature of nucleation and growth transformations, reduces the surface available for growth and readily explains the shift from accelerating to decelerating hydration rate (see full discussion in [72]). Based on hydration simulations conducted according to boundary nucleation and growth conditions [65], Bishnoi and Scrivener [85] recently proposed that the shape of the main hydration peak results from the fast outward growth of a diffuse, highly porous C–S–H product. The transition to diffusion controlled kinetics, if it occurs at all, likely happens well after this period of initial impingement and when heat release rates decrease to nearly zero. Such a transition in rate control would occur due to the formation of thick product layers that hinder the transport of reactants. Because this is a microstructural effect, it is useful to look at the overall development of micro- and nanostructure for clues. Allen et al. [30,95,96] have shown using SANS that there are surface fractal and volume fractal length scale regimes associated with the deposition of nanoscale C–S–H onto the hydrating particles, and Mori et al. [97] have inferred a gradual change in fractal dimension of C–S–H gel from a surface fractal at early ages to a volume fractal at the transition point, which they associate with thickening of the layer of hydration products around the hydrating C3S. In addition, examination of microstructures by scanning electron or scanningtransmission electron microscopy often indicate either gaps or regions of low-density product adjacent to the reacting grain surfaces [98–100], while hydration products evidently deposit further away from the grains. These kinds of microstructural features imply that there may not always be a signiﬁcant barrier to the transport of chemical species to and from the reacting grains. Other indirect evidence against the hypothesis of pure diffusion control can be found in the work of Peterson and Juenger [74], who used QENS to examine the hydration of C3S in water and in solutions of CaCl2 or sucrose. They analyzed the cumulative progress of reaction characterized by the bound water index (BWI) and ﬁt the curves with an empirical model, J.W. Bullard et al. / Cement and Concrete Research 41 (2011) 1208–1223 in the spirit of the Avrami model, that divided hydration kinetics into three stages: (1) an induction period at early times, (2) a nucleation and growth period at intermediate times, and (3) a diffusioncontrolled period at later times. In this case, the later time period extended only to about 48 h after mixing, which is still relatively early in the hydration process. Their ﬁts indicated that the diffusion coefﬁcient for C–S–H must vary by more than an order of magnitude depending only on whether triclinic or monoclinic C3S is used as the starting powder. A similar point was made by Bishnoi and Scrivener [86]. They found that, to model the kinetic data for alite powder with different particle sizes, it was necessary to assume that the diffusion constant varied considerably with particle size. Since C–S–H grows by a through-solution process, it is difﬁcult to explain how the source of the solute species or the particle size distribution could inﬂuence the properties of C–S–H so strongly. This suggests instead that the pure diffusion model used to ﬁt the data is incorrect. Other QENS data seem to indicate that ﬁlling of the capillary pore space cannot entirely account for the later age kinetics of C3S hydration. The available pore space in cement paste is essentially deﬁned by the initial amount of water in the mix [50]. The reaction progress variable β(t) described by Livingston et al. [101] is the ratio of water consumed to the initial water in the mix, so this variable should reach unity when the pores are ﬁnally all ﬁlled, assuming that the cement mix has the ideal molar H/C3S ratio of 3.1 which provides just enough capillary pore volume to accommodate the hydration products at complete hydration. However, the experimental evidence contradicts this; for example, the value of β(tD) for the curves presented in Fig. 7 never exceeds about 0.51. Thus the asymptotic kinetic behavior apparently cannot be explained by complete ﬁlling of the capillary pore space with hydration product. Livingston et al. used QENS to further investigate the effect on the asymptotic behavior of varying the w/s ratio. They found that the transition time, tD, was independent of the w/s ratio and, in fact, that the individual curves could be collapsed into a single master curve by a simple vertical scaling that has a linear correlation with the w/s ratio. They concluded that the pore-ﬁlling mechanism could not be solely responsible for the transition to parabolic kinetics at later times. These same authors went on to propose an alternative mechanism for the transition point based on the hypothesis of rapid surface layer development that is complete at the end of the initial reaction period. If this interpretation were correct, the degree of reaction progress achieved at later times would be largely determined by the extent of the reaction during the delay period. 4. C3A, aluminate phase and portland cements In portland cements, which are the basis of well over 99% of cement used, the phase other than alite that most affects the hydration kinetics in the ﬁrst few days is C3A. The reaction of C3A in the absence of calcium sulfate is very fast. Unlike alite, there is no period of slow reaction and setting is almost instantaneous. The ﬁrst hydrates formed have been reported to be poorly crystallized aluminum hydroxide or AFm3 phases, generally described as C2AH8 and C4AH13 [50,102–104], although solid solutions or intercalated mixtures of these phases probably occur. With time, these metastable phases transform to the stable product — hydrogarnet, C3AH6. This transformation begins within 25 min near room temperature [102] and the rate of transformation increases with temperature. This quick setting behavior is undesirable in concrete, where a period of workability is needed before setting to allow the concrete to be placed. For this reason a source of calcium sulfate is added to cements to control the reaction of the aluminate phase, and this latter system 3 AFm phases (Al2O3–Fe2O3-mono) have the general formula [Ca2(Al,Fe)(OH)6] ⨁ X−xH2O, where X represents a formula unit of a singly charged anion or a half unit of a doubly charged anion [100]. 1217 will be the main focus in this section. The calcium sulfate added is generally in the form of gypsum (CaSO4·2H2O), but anhydrite (CaSO4) is often also present in most natural sources of gypsum. The hemihydrate form (CaSO4·0.5H2O, mineral name bassanite) may also be present due to partial dehydration of gypsum during grinding. In the presence of a source of calcium sulfate the pattern of reaction of C3A is dramatically changed, as shown in Fig. 8 [105]. There is an initial period of rapid reaction, after which the rate decreases rapidly within a few minutes. During the intital reaction, ettringite (C3A·3CaSO4·32H2O) is the main hydrate phase formed. This initial period of rapid reaction quickly gives way to a period of low heat output, the length of which depends on the quantity of calcium sulfate in the system. When the added calcium sulfate has all been consumed, the rate of reaction rapidly increases again, with calcium monosulfoaluminate as the main product phase. In cements, the period of slow reaction of C3A should persist until well after the main rate peak of alite to ensure correct setting and hardening. The main question regarding the hydration mechanisms of C3A in the presence of calcium sulfate is the reason for the rapid slow down of the intitial reaction. There are three possible explanations: 1. The product phase ettringite slows the reaction by forming a diffusion barrier at the C3A surfaces 2. Some other phases, for example AFm, slows the reaction in the same way 3. The reaction is slowed down directly by adsorption of some solute species provided by dissolution of calcium sulfate. Most textbooks, following the early literature [3,50,106], attribute the decelerating rate to the formation and thickening of a barrier of ettringite crystals. However, as pointed out by Scrivener and Pratt [107], the morphology of ettringite as hexagonal rods is unlikely to provide a substantial barrier to ion transport. Direct observation of the early reaction of C3A with sulfate in a transmission electron microscope wet cell shows a few scattered rods in the solution (Fig. 9). When samples are dried for examination in the SEM, the rods collapse onto the surface, but even in this conﬁguration, the packing of rods is highly porous. Scrivener and Pratt [107] earlier observed a disorganized layer directly on the surface of the reacting C3A grain; they conjectured that this “gel like” layer could be responsible for slowing down the reaction. However the study of Minard et al. [105] clearly showed that this product is an AFm type phase, which also forms when C3A is hydrated in the absence of calcium sulfate, where there is no retardation of C3A dissolution. Furthermore, they found that there was more formation of this AFm phase when C3A was hydrated with gypsum, compared to hydration with hemihydrate, where hardly any Fig. 8. Heat evolution rate curves during the hydration of C3A (L1) in solutions saturated with respect to portlandite (liquid-to-solid mass ratio = 25) carried out with increasing quantities of gypsum, from [105]. 1218 J.W. Bullard et al. / Cement and Concrete Research 41 (2011) 1208–1223 having an almost vertical acceleration part followed by an exponentially decaying shoulder. Interestingly, the shape of this peak is similar to that observed in the hydration of calcium aluminate (CA) cements, which is another system where crystalline hydration products form. 4.1. Interaction between silicates and aluminates Fig. 9. Grain of C3A in the presence of calium sulfate after 10 min hydration in environmental cell at high accelerating voltage [92]. AFm phase was formed. In contrast, the deceleration in reaction was more rapid with hemihydrate than with gypsum. By process of elimination – the ﬁrst two possibilities having been discredited – Minard et al. [105] attributed the early deceleration of C3A reaction to the adsorption of sulfate ions on the surface of C3A. This can also explain why the reaction slows down more quickly with rapidly soluble hemihydrate than with more slowly dissolving gypsum. For the reaction of C3S, the slowing down of the reaction due to the build up of ions in solution has been discussed already in Section 3, and the important role of defects has been indicated there as well. A similar process could occur in the reaction of C3A with calcium sulfate, whereby sulfate ions adsorb at defect sites and inhibit the formation of etch pits, so slowing down the rate of dissolution. The length of the slow reaction period for the C3A + sulfate system has been reported to increase approximately as the square of the initial sulfate/aluminate ratio of the system [3,106]. In contrast, Minard et al. [105] showed that the length of the period of slow reaction varies roughly linearly with the amount of calcium sulfate, although the situation is complicated by the dispersion of particle sizes. A linear relationship implies that ettringite formation and sulfate consumption during this period occur at a roughly constant rate that is controlled by dissolution of C3A. A linear dependence would further support the conclusion that the reduction in rate is due to a change in dissolution rate and not to a barrier layer in which case the rate would be expected to decrease as the amount of hydration products increase. When all the added calcium sulfate is consumed, the depletion of sulfate ions in solution causes a net desorption of the sulfate ions from the C3A surface in an attempt to re-establish dynamic equilibrium between the adsorbed species and the solution. Therefore, a rapid increase in the dissolution rate is observed. This explanation also is more logical than the hypothesis that a barrier layer of ettringite is responsible for slow C3A reaction because experiments show that the reaction rate increases before the ettringite starts to be consumed by the ongoing reaction. Furthermore, the amount of ettringite declines quite gradually in favor of the more stable monosulfate phase after sulfates are consumed from solution, whereas the large increase in reaction rate of C3A happens over a much narrower time interval. The period of renewed dissolution of C3A, following the consumption of sulfates, leads to the formation of calcium alumino monosulfate according to the reaction: In a properly sulfated portland cement, the second aluminate peak in a calorimetry scan should occur after the main alite hydration peak (at around 10 h). This was discussed by Lerch as early as 1946 [108] (Fig. 10). It is important to note that he studied a cement with a high C3A content (around 14% by Bogue). With a low SO3 addition of 1.3% by mass, a large and sharp peak, corresponding to the reaction of the aluminate phase to form calcium monosulfoaluminate, occurs early and the reaction of alite is both delayed and suppressed. With 2.4% SO3 addition, which he claimed corresponds to proper sulfation, the typical alite reaction peak occurred ﬁrst and was followed shortly thereafter by a large and sharp peak corresponding to the C3A → monsulfoaluminate reaction. However, for a cement with 3.5% SO3, which is a C3A to sulfate ratio more typical of modern cements, calcium monosulfoaluminate was not detected until 50 h. (We note, however, that Blaine ﬁnenesses of modern cements are also often signiﬁcantly higher than in Lerch's time, and ﬁner cements tend to have higher “optimum” SO3 requirements.) The large and sharp calorimetry peak associated with monosulfoaluminate formation in the cement with 2.4% SO3 addition is often confused with a shoulder peak seen after the main silicate peak (Fig. 11). Although this shoulder peak corresponds to the point of exhaustion of solid gypsum, at which point aluminate phase hydration accelerates signiﬁcantly, the main aluminate hydration product at this time still appears to be ettringite, perhaps formed from sulfate previously absorbed in the C–S–H phase [100]. In Fig. 11 a subsequent low broad peak can be seen between about 20 h and 30 h, which appears to correlate with the formation of AFm phase(s). The mineral chemistry can become quite complex at this stage because any of several AFm phases can form, depending on temperature and the availability of carbonate ions or other anions such as chlorides. Even with only sulfate present, one assumes that monosulfoaluminate forms ﬁrst but this can ultimately convert to a solid solution with hydroxyaluminate. These observations indicate the apparent complexity of the interactions between the alite and aluminate phases during hydration. Such complexity highlights the need for simulation tools that can deal with the interactions among phases through the ions in the pore solution and the occupation of space by the hydrated phases. 2C3 A þ C3 Ad 3CaSO4 d 32H2 O þ 4H2 O→3ðC3 Ad CaSO4 d 12H2 OÞ The shape of the calorimetry peak for this reaction is quite different from that of the main hydration peak for alite, the former Fig. 10. Calorimetry of portland cement with different addition of gypsum. Reprinted, with permission, from theASTM Proceedings (1946), copyright ASTM International, 100 Barr Harbor Drive, West Conshohocken, PA 19428 [108]. J.W. Bullard et al. / Cement and Concrete Research 41 (2011) 1208–1223 Fig. 11. Calorimetry curve of modern portland cement, showing typical shoulder peak where a secondary formation of ettringite occurs and subsequent broad peak corresponding to the formation of AFm phase. 5. Perspectives for future research 5.1. Motivation As discussed in this review, cement hydration kinetics has been the subject of extensive investigation and yet the controlling mechanisms remain controversial. It is worth reviewing a couple of reasons for the importance of studying and understanding kinetics, apart from simple intellectual curiosity, as this helps motivate speciﬁc questions and research directions. Because the study of kinetics is a tool for elucidating mechanisms, it complements microstructure analysis by indicating which processes are predominant when structural changes occur. There are at least two broad areas of practical impact: 1) deﬁning ways of controlling the rate of reaction, and therefore the rates of hardening and heat generation, and 2) ﬁnding ways of controlling and monitoring the structure and distribution of products; in short, controlling the microstructure and therefore all the material properties as a function of time. The ﬁrst impact is related to controlling the length of time concrete remains ﬂuid before it begins to gain strength and then the rate of subsequent strength development. The second has a more subtle, and potentially equally important, impact in the quest to control properties by manipulation of the micro- and nanostructure of concrete. As for the rate of reaction, it is often stated that an ideal concrete should stay ﬂuid during transport and placing and then very rapidly gain strength and other engineering properties. Both the mineralogy of cement and the addition of admixtures are used to control the kinetics of setting and hardening, but there is little consensus on the mechanisms, and chemicals are tested largely by trial and error. A mechanistic understanding would provide a powerful tool in the quest for new chemicals that are inexpensive, effective, noncorrosive toward steel reinforcing bars, and able to control equally the length of time before hardening starts and the rate of property development afterward. Control of the microstructure of concrete has advanced remarkably in recent years, with the development of ultra-high strength products, such as Ductal®,4 where the particle size distribution has been optimized on the basis of theoretical models. In contrast, the ability to control the microstructure of C–S–H has received relatively 4 Certain commercial equipment and/or materials are identiﬁed in this report in order to adequately specify the experimental procedure. In no case does such identiﬁcation imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the equipment and/or materials used are necessarily the best available for the purpose. 1219 little direct attention, with a few exceptions [67,109]. Thus the morphology and spatial distribution of the products formed during the hardening of cement paste cannot yet be controlled with the same precision as for metals and other materials, but a mechanistic understanding should provide new strategies for predicting the evolution of microstructure and properties, and ultimately designing microstructure and properties. While the control of microstructure has not been investigated very much, a few studies have correlated morphology with time of formation, i.e. the stage during which the product seems to form. During the 1980s, several papers [110–115] reported that speciﬁc morphological features seem to form during each stage of reaction. The C–S–H needle morphology that typically forms preferentially during the early stages was once seen as a clue to the reaction mechanism [110,113], but this has not stood the test of time. Gartner [83] and others [69,100] have analyzed morphology and established plausible relationships between kinetics and atomic structure. An important aspect of recent progress on hydration kinetics is that the proposed mechanisms have been described in increasingly quantitative terms, which enables better comparisons to data. However, some very important questions remain almost completely unanswered. For example, with a few isolated exceptions [30], knowledge of the mechanisms that control the rate of reaction have not been applied to explain the sometimes dramatically altered rate of reaction, as well as altered microstructure and properties, which often accompany the use of admixtures. This includes accelerators and retarders, mineral admixtures of all kinds and variation in cement composition. This review has identiﬁed several rate phenomena that can control hydration kinetics at different times: 1. 2. 3. 4. Dissolution of cement Diffusion of reactants to site of chemical reaction Nucleation of ﬁrst product Growth of product, perhaps by “autocatalytic” formation of grains of product and which may be limited by chemical reaction or by diffusion of reactants to reaction site The fact that more than one step can control the rate of reaction, depending on the stage of the reaction and perhaps on the presence of admixtures, in itself makes the mapping of the overall hydration process more complex than it would be if the rate were controlled by one step with a single activation energy. This suggests that the reaction kinetics might be best analyzed using a ﬂow chart type of approach, an example of which is shown in Fig. 12, where the rate controlling step can be identiﬁed from among several candidates by evaluating several “if–then” type of statements. For example, the presence of seed clearly removes the nucleation step as being rate controlling, and also stimulates growth of product in the volume of water ﬁlled as opposed to just on the surface (at least this is one interpretation of the kinetic data). Neither dissolution of cement nor diffusion of reactants appears to be rate controlling throughout most of hydration, but rather the rate of product growth appears to control the rate at least until the product becomes congested in the capillary pore space at later ages. As the modern drive for more sustainable concrete pushes the formulation of cement toward increased use of supplementary cementitious materials (SCMs) like ﬂy ash and slag, concrete producers are faced with an ever more complex chemical and structural design space within which to formulate binders. Responding to the demand to replace greater volumes of portland cement with SCMs, producers are increasingly faced with “incompatibility” in the mixes, that is, unexpected and unexplained acceleration or retardation in the kinetics, combined with undesirable strength gain, shrinkage, and cracking. The impact of SCMs on hydration and kinetics is considered in more detail in another paper in this issue [116]. However, it is worth noting that scientiﬁc understanding of the 1220 J.W. Bullard et al. / Cement and Concrete Research 41 (2011) 1208–1223 Fig. 12. Flowchart for organizing thinking about hydration kinetics and mechanisms. inﬂuence of SCMs on cement hydration is still in its infancy, even though some general engineering principles, such as the importance of sulfate balance, are developing. Even so, with concrete technology steadily moving toward these more complex mix designs, it is critical that an engineering/scientiﬁc basis be established for understanding and ameliorating compatibility issues. 5.2. Speciﬁc research needs We close this review by enumerating speciﬁc research that is needed to make progress in fundamental understanding of, and improved capability to predict, cement hydration kinetics and corresponding development of properties that dictate performance and service life of concrete. These research needs are primarily focused on securing a better understanding of the chemistry and physics of hydration kinetics. However, this kind of scientiﬁc progress will not, by itself, translate to real-world impact unless it can be translated into research tools that can be used by cement manufacturers, readymixed concrete suppliers, and admixture developers to improve the quality, delivery, and sustainability of their product. Ideally, such tools must enable the materials engineer to predict concrete properties from characteristics of the starting materials that are readily available, such as a “mill sheet” of the composition and the cement particle size distribution. 5.2.1. What are the correct rate-controlling steps and corresponding rate parameters that characterize hydration? We have tried to conduct this review in terms of basic mechanisms to the extent possible. Nevertheless, it is obvious that a precise, quantitative description of the chemical kinetics is still lacking. As in the introduction of this review, we contend that major progress in understanding hydration kinetics will be best enabled by placing it on the same fundamental ground that gas-phase reactions and certain geochemical processes now enjoy. Perhaps the biggest obstacle preventing this is that the individual reactions have not been isolated to analyze their mechanisms and rates. Signiﬁcant progress has been made in measuring the kinetics of alite dissolution [27,47,56], C–S–H nucleation [27,47] and, to a lesser extent, of C3A + gypsum hydration [105]. Further knowledge is needed of the actual or apparent equilibrium constants and absolute rate constants (i.e., moles per unit time per unit surface area) of the rate-controlling step in the dissolution of each clinker phase and the nucleation and growth of each hydration product phase. A complete description would also include the temperature dependence of these parameters and, especially for applications such as oil-well cementing, the pressure dependence. This kind of information will likely require the use of novel experimental techniques, such as the use of ﬂow-through reactors for controlling solution chemistry combined with in situ vertical-scanning interferometry [21], and will likely require J.W. Bullard et al. / Cement and Concrete Research 41 (2011) 1208–1223 integration with ab initio modeling [117], molecular modeling methods such as molecular dynamics [118], or kinetic Monte Carlo approaches [10,21,119]. When an SCM like ﬂy ash or blast furnace slag is included, this same kind of information for the SCM will be required. Knowledge of these admixtures is still in its infancy, and to make progress, it will ﬁrst be necessary to adequately characterize SCMs to improve our understanding of the important chemical factors (aluminate content, heavy metal and other impurities) and structural factors (glassy versus crystalline phases, particle size distribution) that govern the intrinsic reactivity of an SCM. With this characterization, the reaction mechanisms and corresponding rate constants of glassy phases in aqueous solutions – leaching of ions and dissociation of the silicate network – also will be required. To further complicate the problem, modern concrete formulations invariably contain numerous chemical admixtures (e.g., polycarboxylates and amines) to control workability, setting time, air void content, and shrinkage behavior. More progress likely can be made by systematically examining how hydration rates, and particularly the rates of formation of different hydration products, is inﬂuenced by the addition of chemical admixtures. Examples of this approach have already been given in this review [67,68], but much more can be done to characterize the mechanistic inﬂuences of admixtures. Interactions of organic molecules with ions in solution (e.g., chelation) and with the inorganic surfaces of cement particles (e.g., adsorption) are not well understood. In some cases it may be permissible to assume that these kinds of interactions occur at rates that are fast compared to other cement hydration reactions, thereby allowing one to assume equilibrium conditions for them. Even so, quantitative modeling will require the knowledge of the equilibrium constants or adsorption isotherms for each important kind of interaction. Needless to say, obtaining these kinds of fundamental, comprehensive kinetic data is a challenging long-term research proposition that will undoubtedly involve advances in measurement science and technology, including the introduction of new experimental methods and greater integration with fundamental multi-scale computational modeling. But the understanding it will generate might be considered to be the cement equivalent of mapping the human genome. It will allow the understanding and avoidance of compatibility problems that often plague blended cements, as well as the rational control of setting and strength development in the ﬁeld. Ideally, we envision the development of a shared database containing this kind of information, that could be accessed by researchers worldwide and even updated with more accurate information as it becomes available. 5.2.2. Can chemical kinetics be linked more rigorously to the structure and distribution of hydration products? Early hydration rates can be modiﬁed with temperature or the addition of nucleating agents [67] or other chemical additives [74,90,110,120]. Increased rates of hydration, however, do not necessarily lead to improvements in strength or transport properties at later ages. Controlling both the kinetics and the engineering properties of concrete is a great challenge and will require an understanding of how the amount, spatial distribution, and morphology of hydration products are inﬂuenced by curing conditions and chemical additives (see Ref. [70] for a thorough visual tour of how morphology of hydration products are inﬂuenced by temperature and chemical composition). Progress will undoubtedly be made by combining relevant experimental techniques, such as QENS, SANS, and electron microscopy with advanced multi-scale simulation methods that couple molecular dynamics, Kinetic Monte Carlo, and microstructural models of the rate processes. Another area of incomplete understanding is the way in which C–S–H growth at the nanoscale, either by aggregation of nanocrystals or frustrated growth of sheets, can result in the wide variety 1221 of C–S–H morphologies observed at the microstructural scale [26,49,70,109,121–123], which range from “lamellar” or “ﬁbrillar” to “crumpled foil” to the “Williamson” morphology ﬁrst reported in Ref. [124], which is a spherulitic type resembling a sheaf of wheat. Recent progress in understanding similar ranges of growth morphologies of solids from polymer melts in terms of fundamental growth mechanisms and the roles of impurities and defects [125], are likely to shed light on larger-scale morphological development of C–S–H. Acknowledgments This paper is an outcome of the International Summit on Cement Hydration Kinetics and Modeling. The authors acknowledge ﬁnancial support from the National Science Foundation (NSF) through Grant Award Nos. OISE-0757284 and CMS-0510854, the Federal Highway Administration (FHWA), Mapei, W. R. Grace, BASF, the Tennessee Technological University (TTU) Center for Manufacturing Research (CMR), the Canadian Research Center on Concrete Infrastructure (CRIB) and the Natural Science and Engineering Research Council of Canada (NSERCC). The authors would also like to acknowledge the organizers of the Summit including Joseph J. Biernacki (TTU), Will Hansen (University of Michigan), and Jacques Marchand (Laval University). 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