Introduction

Portland cement (PC) and concrete are the foremost fabricated and extensively utilized man-made materials due to the swift urbanization of global populace1,2. The anticipated demands of projected urbanization necessitate the consumption of ~30 billion tonnes/year of concrete3, thereby contributing to the substantial production of PC (∼4 billion tonnes/year) accompanied by ∼2.7 billion tonnes/year of carbon dioxide (CO2) emissions1,4,5 and large consumption of natural resources1. To systematically devise strategies for reducing the carbon footprint of cement and optimizing the related performance (gelation, strength and durability), a comprehensive understanding on the early-age hydration reactions of individual cement components is imperative4,6. This holds particularly true for tricalcium aluminate (Ca3Al2O6, also denoted as C3A in cement chemistry notation, where C stands for CaO, A for Al2O3, S for SiO2, and H for H2O) as it exhibits a proclivity for early-stage hydration preceding other cement components, thus playing a pivotal role in structural build-up of cement colloids7,8,9,10. Regrettably, numerous unresolved inquiries persist concerning the intricate dissolution and precipitation processes of C3A and its relevant hydrates, which govern the setting and early hardening of cement11,12,13,14,15.

The C3A hydration manifests distinct stages characterized by the dissolution of surface ions and the precipitation of initial calcium-aluminate-hydrates15. Owing to its exceptionally high reactivity with water, the polycrystalline C3A displays heterogeneous dissolution rates, giving rise to individual pits within a remarkably brief span of <0.1 s. The surface topography subsequently undergoes a coupled transformation marked by the formation of etch pits, point defects and dislocations over a few seconds, ultimately resulting in the development of an Al-rich layer8,15,16,17,18. Controversies persist in elucidating this phenomenon. One perspective proposes incongruent dissolution of Ca and Al ions from the C3A surface, supported by the initial formation of a Ca-depleted outer layer and a continuous decrease in Ca/Al ratio from the C3A bulk towards its surface following contact with water7,15,19. An alternative hypothesis suggests the interface-coupled dissolution-reprecipitation (ICDP) mechanism, positing that the dissolution of Ca and Al ions should be congruent initially or at least minimally enriched in Ca before achieving congruency over time. Dissolved Ca ions elevate the pH, enhancing Al solubility and ultimately stabilizing the Ca/Al ratio in the solution until precipitation occurs. Consequently, the pore solution becomes saturated with Al(OH)4-, and AH3 gel forms on the crystal surface before other Ca-rich hydrates, resulting in high Ca/Al ratios in aqueous solutions (low Ca/Al ratio on the surface)7,15,18. However, this explanation is challenged by recent findings showing that increased pH induced by direct addition of NaOH does not significantly enhance Al ion dissolution20,21. Additionally, hydrous Al layers containing bound water may exhibit similar behavior to AH3 gel, rendering their identification through thermal analysis18. Although nanoscopic X-ray ptychography has offered direct images of “gel-like” areas on C3A particle surfaces with a few hundred nanometers thickness after exposure to a sulfate solution for 30–90 min8, further study is required to confirm this observation7.

The hydration kinetics of C3A can be substantially modulated by soluble sulfates to mitigate the impractical occurrence of “flash set”18. Cubic C3A rapidly reacts with CaSO4 to form ettringite (AFt) within minutes15,22, succeeded by an induction period lasting several hours in isothermal calorimetric curves13,14. This induction period typically concludes with a renewed hydration heat release, converting AFt into sulfate-bearing Al2O3-Fe2O3-mono (AFm) phases13,14,15. Despite extensive studies, questions remain regarding the retarding effect of gypsum, leading to debates centered around two hypotheses: the barrier and adsorption theories. In the barrier theory, AFt or AFm phases formed on the C3A surface act as diffusion barriers, impeding bustling ion-water exchanges in hydration reactions8,14,15. While the barrier theory has elucidated certain aspects of the typical heat release curve during C3A hydration, a growing consensus suggests its limitations. Recent findings indicate that AFt exhibits a porous structure that is not conducive to impeding the diffusion of interfacial ions and water molecules8,23. Instead, the prevailing view posits that ion pairs of Ca2+ and SO42- adsorb onto the Al-rich layer of the C3A surface, effectively obstructing active sites and thereby retarding the hydration kinetics. This inhibition primarily operates through dissolution-controlling mechanisms rather than diffusion-controlling mechanisms8,18,23.

Despite extensive experimental investigations on initial hydration of C3A, a wide array of debates persists regarding its hydration in both pure water and CaSO4-containing solutions15. These debates encompass questions pertained to both the dissolution and participation processes inherent to C3A hydration. As real-time observation of dissolution and participation processes during early-age C3A hydration is experimentally challenging and the underlying mechanisms are often deduced indirectly from micro- or macroscopic experimental phenomena, the comprehensive elucidation and explanation heavily rely on the molecular-level understanding of surface activity and interface reactions occurring at the C3A/water interface through the atomistical simulations. To this end, density functional theory (DFT)-based static calculations were initially employed to probe the reactive sites within C3A crystal24. It’s theoretically demonstrated that O and Ca ions are active sites in C3A bulk and are susceptible to electrophilic and nucleophilic attacks, respectively. This suggests that preliminary reaction steps between C3A and water molecules originate from the surface Ca and O ions24. However, static DFT calculations encounter challenges in providing comprehensive kinetic and thermodynamic descriptions of the interactions between water and C3A surface25,26. Subsequent force-field classical molecular dynamics (MD) simulations partially addressed this limitation and revealed that the non-bridging O atoms in the six-member rings of AlO4 tetrahedra are more prone to protonation than the bridging O sites. Consequently, the surrounded Ca ions can readily accommodate the hydroxide ions (OH-) induced by water dissociation, leading to the formation of calcium hydroxide (CH)27. Nevertheless, these non-reactive classical MD simulations appear insufficient to capture the bond breakage and formation involved in the initial dissolution process of C3A, along with the corresponding free energy landscapes. Importantly, they often lack the requisite accuracy and reliability to fully elucidate the intricate physicochemical reactions occurring at the solid/aqueous solution interfaces28,29.

In response to these challenges, we have undertaken a series of advanced ab-initio (specifically the DFT) calculations to delve deeper insights into the molecular-scale kinetics and thermodynamics of the initial hydration of C3A. Leveraging cutting-edge techniques such as ab-initio molecular dynamics (AIMD) and well-tempered metadynamics (WT-MetaD), we can accurately describe the intricate interfacial reactions and dynamics, thereby addressing the limitations of classical MD and static DFT calculations. We have demonstrated that the initial hydration of C3A commences with significant surface hydroxylation due to the pronounced dissociation of water molecules in the vicinity areas. This phenomenon further facilitates the gradual desorption of Ca ions through a metal-proton exchange reaction (MPER), following the nucleophilic attack by oxygen ions from water molecules (Ow). The dissolution pathways and free energies of these Ca ions are ultimately unveiled to follow the ligand-exchange mechanism with multiple sequential reactions, where the ultimate products are Ca ions adopting fivefold and sixfold coordination, with corresponding free energy barriers of 18.76 kJ/mol and 27.52 kJ/mol, respectively. Finally, these Ca complexes precipitate back on to the remaining Al-rich layer through the interface-coupled dissolution-reprecipitation (ICDP) mechanism, demonstrating dynamically stable inner-sphere adsorption states. Our findings shed the light on the molecular scale understanding the initial hydration process of C3A and the calculated kinetics and thermodynamics can contribute valuable insights for accurately modeling cement hydration and thereby effectively predicting and controlling its macroscopic performance.

Results

Distribution of surface ions and water molecules

We began the calculations on conducting an extensive AIMD simulation on the C3A/water interface to gain a comprehensive and basic understanding on the dynamic behavior of C3A surface in contact with water molecules (Fig. 1). The C3A surface exhibits a strong attraction to water molecules, boosting their rapid dissociation in the assistant of hydrogen bond (HB) networks30,31. Consequently, these dissociated and intact water molecules significantly hydroxylate the exposed C3A surface, leading to the stabilization of their orientation and distribution (Fig. 1a). After further scrutinizing the density distribution of surface ions and water molecules along the z-axis, we can pinpoint the localized areas of water molecules spanning ~14–21 Å, which is subsequently defined as the interface region for calculating the density map and charge distribution. Interestingly, some Ca ions slightly dissolve from the surface during this AIMD simulation, resulting in a relatively flat but broader density profile. This behavior contrasts significantly with the distribution of Al ions on the C3A surface, where the AlO4 six-membered rings serve as the structural framework of C3A unit cell and remain dynamically stable throughout the simulations. By combinedly analyzing the number densities of Hw and Ow, density ratio (\(\rho \left({O}_{w}\right)/\rho \left({H}_{w}\right)\)) and atomic excess (\(\Delta \rho\), see Supplementary Note 3 for details) of water molecules, we can distinguish five distinct layers of water molecules with varying thicknesses, which is also presented on γ-Al2O3 and tricalcium silicate (Ca3SiO5, C3S) surfaces due to their hydrophilic natures31,32. A further analysis shows that the first layer (layer I) locates just below the C3A surface and primarily consists of OH groups (dissociated water molecules). This layer can be defined as the chemisorbed layer of water molecules with a thickness of 4 Å (~14–18 Å), much thicker than those formed on γ-Al2O3 (~2 Å)31 or C3S surfaces (~1.5 Å)33. This indicates that the C3A surface is highly reactive, featuring a greater active site density and a stronger affinity to water molecules. The physisorbed layer (layer II) with a thickness of 3 Å (~18–21 Å) is presented following the first layer where most water molecules are intact but demonstrate reduced movability and higher structural organization. Consequently, the density peak of Ow slightly precedes that of Hw, leading to a small Ow-rich region (positive \(\Delta \rho\) values and \(\rho \left({O}_{w}\right)/\rho \left({H}_{w}\right)\) > 0.5). The third region (~21–24 Å, layer III) occurs with a gentle oscillation both in number density and atomic excess, which is subsequently transferred to the density of 33.33 nm−3 and 66.66 nm−3 for Ow and Hw, respectively (~24–29 Å, layer IV), aligning well with the bulk water density. This indicates that our AIMD simulations accurately reproduced the interfacial properties of the C3A/water system. In this context, atomic excess and density ratio fluctuate around 0 and 0.5, respectively, suggesting negligible effects of the C3A surface on this region. The water/vacuum interface region finally extends from 29 Å to 34 Å (layer V), where the density number and ratio smoothly decrease to 0 as expected. However, unusual negative values of atomic excess in this region are attributed to the ordered water molecules with hydrogen ions orienting towards the vacuum region31,34. These findings are further corroborated by an additional classical MD simulation on a larger system based on the ReaxFF force-filed35,36 (Supplementary Note 4 and Supplementary Fig. 3).

Fig. 1: Distribution of surface ions and water molecules.
figure 1

a Snapshot for the distribution of surface ions and water molecules. b Number density of H2O, Ca and Al projected to z-axis. c Density ratio (\(\rho \left({O}_{w}\right)/\rho \left({H}_{w}\right)\)) and atomic excess (\(\triangle \rho\)) of H2O projected to z-axis. d Radial distribution function (RDF, g(r)) of various ion pairs (the shaded region delineates the low coordination of Ot-Hw, Al-Ow and Ca-Ow, and is magnified in the upper right corner) and (e) the corresponding coordination numbers (CNs). Number density of (f) Hw and (g) Ow within the interface region (~14–21 Å) projected to xy plane. For clarity, we denote Ow (Hw) as the oxygen (hydrogen) ions of water molecules, and Ot represents the oxygen ions on the C3A surface. Notably, Ot can be further categorized into bridging and non-bridging oxygen ions (Ob and Onb) within the AlO4 six-membered rings. The dynamic distribution of surface ions and water molecules are ensemble-averaged during a ~ 20 ps production run following a ~21 ps pre-equilibrium process. The surface line (vertical red dashed line) is determined based on the average positions of the outermost Al ions and used to define the distribution of water molecules in the vicinity regions (layers I – V divided by the vertical bule dashed lines) of the surface in the assistant of density ratio and atomic excess of H2O. The horizontal red dashed line in (c) denotes the zero value of atomic excess and serves to delineate the bulk water region (i.e., layer IV).

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To gain insights into the factors influencing the observed atom distribution, we calculated the radial distribution function (RDF, g(r)) and density maps of Hw and Ow within the interface regions (Fig. 1d–g). The RDF curves reveal clear peaks at ~1 Å and ~2.40 Å for Ot-Hw and Ca-Ow, respectively. These results are in good agreement with experimental and theoretical values for O-H and Ca-O distances37,38,39, indicating a strong coordination between the water molecules and C3A surface. Notably, no distinct coordination is observed between Al and Ow ions. This can be attributed to the fact that the coordination state between Al and Ow cannot be adequately sampled within the limited timescale of AIMD simulations. Meanwhile, the stable coordination structure of AlO4 tetrahedra and these Ot ions within the first coordination shell of Al ions may screen direct interactions between Al and Ow ions, thus causing the illusory relatively high coordination numbers (CNs) than those for Ot-Hw and Ca-Ow (Fig. 1e actually shows the CNs of Al-Ow in the second coordination shell). These results can be supplemented by classical MD simulations on the RDF of C3A/water interface model, where a low Al-Ow coordination at 1.90 Å with number of 0.23 per/Al atom is observed in the large simulation box with long simulation time (Supplementary Note 4 and Supplementary Fig. 3). This bond length slightly deviates from the equilibrium bond length determined by experiments and simulations24,27,40, indicating the weak interactions between Al and Ow. To further clearly interpret this, the number densities of Hw and Ow in the interface region were projected to C3A surface (Fig. 1f, g). It’s interesting to find the Hw ions prefer to clustering around surface Ot ions, thus hydroxylating the exposed surface. This is consistent with the discussions on atom distribution and RDF. Besides, surface Ca ions are predominantly surrounded by Ow ions, whether in the form of OH groups or intact water molecules. When considering the earlier discussions, this coordination environment facilitates the slight dissolution of Ca ions from the surface through MPER, which successfully interprets the leaching of mental ions from mineral/aqueous solution interfaces41,42 although such step (superficial protonation) should be ruled out as being rate-determining16.

Dynamics of surface ions and water molecules

We next analyzed the interfacial dynamics of C3A/water system (Fig. 2). The hydrogen bonds (HBs) are formed between the surface Ot and Ow ions when the C3A surface is attacked by water molecules, thus disrupting the HB network and decreasing HB numbers among water molecules before 21 ps (Fig. 2a). Subsequently, the HB numbers of Ot-Ow are dynamically stable, leading to a slower fluctuation in HBs among water molecules after 21 ps. This indicates that our system has reached an equilibrium state, not only in terms of potential energy and system temperature but also with regard to interfacial properties. Consequently, the results are highly reliable and reproducible. By further checking the ion pairs involved in Ot-Ow HBs, we find that HBs primarily form between Onb and Ow ions, as evidenced by the two curves displaying similar quantities over time. Interestingly, most of Onb ions, despite being hydroxylated and attached to hydrogen ions from adjacent water molecules, only act as HB acceptors upon closer inspection of the coordination details. As a result, we hardly observe any proton hops between the surface Ot and Ow ions, which should be commonly present in mineral/aqueous solution interfaces and facilitated by continuous HB networks30,43. This limited proton hopping is yet attributed to the highly nucleophilic nature of the Ot ions, particularly the Onb ions, which form strong bonds with Hw ions and consequently restrict proton transfers. This behavior is similar with what has been observed on ionic oxygen ions on C3S surfaces24,27,43.

Fig. 2: Dynamics of surface ions and water molecules.
figure 2

a Hydrogen bond (HB) number and b bond number density evolution during the whole simulation. c Comparison of bond number density of various cement components. The raw data for calcium silicates is from references44,45. Time-dependent radial distribution function (TDRDF) of (d) Ot-Hw, (e) Al-Ow and (f) Ca-Ow, respectively. The shaded lines with spikes in (a) and (b) depict the original curves of HB number and bond number density, respectively. For clarity and comparison, these curves have been averaged (illustrated as colored solid lines). To assess the bond number density across various surfaces of cement components, averaging is conducted on their equilibrium values with error bars denoting the standard deviation. The TDRDF profiles are computed by averaging RDF data over 1 ps trajectories sampled every 4 ps.

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We also quantified the bond number density for all possible bonds between C3A surface and water molecules (Fig. 2b). Specifically, the Ow-Hw bond number density represents the number density of OH groups and is equivalent to the numbers of dissociated water molecules. The evolution of bond number densities can be divided into three distinct stages, except for Al-Ow, which remains relatively stable. In the first stage (~0–9 ps), the bond number densities increase rapidly over time, particularly pronounced for Ca-Ow due to the high density of active sites on C3A surface. Subsequently, these active sites are gradually saturated by either hydrogen ions or OH groups, thus slowing down increase rate in bond number density from 9 ps to 21 ps. Finally, the bond number density reaches a steady state as the surface active sites become nearly saturated with water molecules (~21–41 ps). The similar responses are also observed on C3S and dicalcium silicate (Ca2SiO4, C2S) surfaces44,45,46, although they demonstrate lower bond number densities than those of C3A (Fig. 2c), meaning the diffusion of water molecules (including the protons and OH groups) are the main controlling factor for the very early-age hydration process (or strictly defined as the wetting) of C3A14. However, the bond number density of Al-Ow shows no significant increase during the entire simulation, consisting with the RDF results discussed earlier (Fig. 1d). This implies that Al ions are much less prone to dissolution from C3A surface in the assistance of water molecules compared to Ca ions as they demonstrate distinct coordination environments and electronic nature15. Consequently, we can speculate that Ca and Al ions follow incongruent dissolution pathways, leading to the formation of a Ca-leaching layer during the initial hydration process of C3A. This hypothesis can be experimentally verified by the evolutions of surface zeta potentials and compositions during C3A hydration7,8,19,23.

The time-dependent radial distribution function (TDRDF) was also calculated to verify the dynamic evolution of these interfacial properties (Fig. 2d–f). Consistent with the bond number density results, the TDRDF intensities for Ot-Hw (Fig. 2d) and Ca-Ow (Fig. 2f) exhibit an increase with time, eventually reaching stable values after 21 ps. Conversely, the TDRDF intensity for Al-Ow remains almost unchanged with a relatively low value during the whole simulation. We also calculated the time-dependent density (TDD) profiles of surface ions and water molecules (Supplementary Note 5 and Supplementary Fig. 4). The surface Ot and Ca ions are the most active sites in C3A surface, accommodating the protons and water oxygens, respectively, when in contact with water molecules. Thus, a narrow distribution of Hw and Ow ions are finally observed with the time increase, while a broader distribution of Ca ions is presented in the later stage (Supplementary Fig. 4). Compared with the rapid re-arrangement of surface Ot and Ca ions, the surface Al ions remain stable due to the thermodynamic stable six-membered ring structure, thereby resulting in a spatial separation with three layers of distribution (Supplementary Fig. 4c). Consequently, it is plausible that a higher energy barrier may be required for dissolving Al ions from the perfect C3A surface that that of Ca ions.

Electronic properties

Based on the above discussions on distribution and dynamics of surface ions and water molecules involved in C3A/water interface, we next investigated the insightful interaction mechanisms between water molecules and surface active sites, particularly the Ot and Ca ions to reveal their reactivity nature at electron scale (Fig. 3 and Supplementary Note 1). The analysis of charge density difference (\(\Delta q\)) reveals a significant redistribution of charges in the interface region during the binding process (Fig. 3a, b). This redistribution underscores that high affinity of C3A surface to water molecules is primarily driven by electrostatic interactions between the active sites and water. Similar charge redistribution can also be presented on C3S/water interface43. Specifically, the charge accumulates (positive \(\Delta q\)) around the Ow and Ot ions, while delocalizes (negative \(\Delta q\)) predominantly around the Ca and Hw ions, which mirrors the bond formation and dynamic evolution previously described. To gain deeper insights, we also computed the total and local density of states (TDOS and LDOS) for different surface ions and water molecules (Fig. 3c, d). It is evident that the Oa ions (comprising Ob, Onb and Ow ions) dominate the valence-band maximum (VBM), which can be further distinguished with Ow ions exhibiting the closest energy level to Fermi level (Ef) in the valence-band. Conversely, Ca ions primarily contribute to the conduction-band minimum (CBM) with the closest energy level to Ef in the conduction-band. These findings suggest that Ow ions predominantly serve as basic sites in water molecules, susceptible to electrophilic attacks, while Ca ions act as acid sites on C3A surface, subject to nucleophilic attacks24,47. This corresponds well with DFT studies on identifying the active sites of C3A, both with and without interaction with CaSO424,48.

Fig. 3: Electronic properties of C3A/water interface.
figure 3

Charge distribution of interface region projected to (a) z-axis and (b) xy plane (iso-surface value of 2.62 × 10−2  e/Å3). c Local density of states (LDOS) of various surface ions and (d) detailed LDOS of various oxygen ions. The positive \(\triangle q\) value (a) or yellow areas (b) refer charge accumulation regions around these ions, while a negative value or green areas mean charge depletion regions.

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Calcium dissolution with CN (Ca-Ow) from 1 to 3

To date, we have uncovered the insightful interaction process between C3A surface and aqueous solutions at molecular scale and determined the active sites and the underlying electronic nature governing these reactive encounters, which finally induces slight dissolution of surface Ca ions in the assistant of water molecules. Nevertheless, it should be noted that these slightly dissolved Ca ions are still strongly interacted with the surface Ot ions and perform an inner-sphere complex, meaning that the full dissolution of Ca ions from C3A surface is still rare event during the limited AIMD sampling time scale. Here, we revealed the full dissolution pathways and free energy landscapes for two kinds of surface Ca ions with different coordination numbers (CNs) in the assistant of WT-MetaD. This choice is substantiated by the existing literatures, which indicates that the coordination environments of central ions play a pivotal role in controlling their sequential dissolution pathways and free energies32,49. In the following discussions, we primarily focus on the low-coordinated Ca ion, while the high-coordinated state with water molecules can be found in the Supplementary Note 7 and Supplementary Fig. 8.

For such dissolution, we can readily distinguish four distinct free energy minima on the first-stage free energy surface (FES) for Ca dissolution, corresponding to the initial, intermediate and final states involved in this first-stage reaction (Fig. 4a). Specifically, the selected Ca ion initially adopts a metastable state of (3,0) on the freshly cleaved (001) surface due to the disruption of its coordination environment. Subsequently, the surface undergoes significant reconstruction, transforming the (3,0) state into a (4,0) state through the rotation and slight displacement of AlO4 tetrahedra (Supplementary Note 10 and Supplementary Movie 1). The (4,0) state quickly transfers to A (4,1) state when water molecules encounter the C3A surface, indicating the water molecules can stabilize the slightly detached surface Ca ions. Upon crossing a small free energy barrier (ΔA⧧ (A-B) = 1.88 kJ/mol), a lower free energy basin B (4,2) emerges on the FES, representing the most stable sate among all the four minima states (Fig. 4b). Through further inspecting the configuration evolution (Fig. 4c), we can find two additional water molecules (the water molecules include both the intact and dissociated ones as our reaction coordinate cannot well-define the OH groups and intact water molecules) and four surface Ot ions coordinate with the selected Ca ions, forming an octahedral structure. This coordination environment is typically associated with the stability of Ca ions, observed both in aqueous solutions and cement hydrates37,50. The reaction pathways then diverge into two paths at state B and converge at state D (3,3) with a well-defined octahedral coordination environment consisting of three surface Ot ions and three Ow ions (Fig. 4b, c). For path A-B-C-D, it follows a ligand exchange reaction mechanism32,49,51, where the bond breakage between Ca and Ot occurs by crossing two free energy barriers (ΔA⧧ (B-C) = 14.47 kJ/mol and ΔA⧧ (C-D) = 3.07 kJ/mol) and an intermediate state C (4,3) only when additional water molecules or OH groups encounter the Ca ion. This reaction mechanism is also observed in simulating the dissolution of Ca ions from the C2S and C3S surfaces32,52,53, where the seven-coordinated structure is a crucial state for the subsequent reactions between water molecules and Ca ions, despite its severe distortion into a octahedral-like coordination54. For path A-B-D, the bond breakage of Ca-Ot and bond formation of Ca-Ow occur simultaneously, thereby only crossing one free energy barrier (ΔA⧧ (B-D) = 18.05 kJ/mol) to form the stable six-coordinated configuration for Ca ion. The rate-determining step for the later sequential reactions has a relatively higher free energy barrier than the first one, indicating path A-B-C-D is more kinetically favorable with the free energy barrier for rate-determining step of 14.47 kJ/mol.

Fig. 4: Calcium dissolution with coordination numbers to water molecules (CN (Ca-Ow)) ranging from 1 to 3.
figure 4

a Free energy surface, b reaction coordinate and (c) corresponding snapshots of configuration evolution along the reaction pathways. In the above representations, the sates along the dissolution pathways are notated in the form of X (CN (Ca-Ot), CN (Ca-Ow)), where X indicates the state number on the free energy surface or the snapshots (e.g., the A, B, etc.), CN (Ca-Ot) and CN (Ca-Ow) represent coordination numbers of Ca to Ot and Ow, respectively in state X. “TS” denotes the transition state. The upper right corners display the states with Helmholtz free energy values (in kJ/mol) relative to state A. The saffron yellow values above the arrows represent free energy barriers (in kJ/mol), while the black values below the arrows denote the free energy differences between two adjacent states (in kJ/mol). The arrows with varied colors signify the distinct reaction pathways that align with those depicted in (b).

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Calcium dissolution with CN (Ca-Ow) from 4 to 6

In the first-stage dissolution of Ca ions, the FES covers coordination numbers with water molecules <4. Crossing a large free energy barrier is necessary to further dissolve the Ca ions when accommodating more water molecules and breaking the surface interactions with these Ca ions. Therefore, we introduced a “wall” to restrict the collective variables (CVs) from fully exploring the regions of interest (where CN (Ca-Ow) is >3). A more complex FES is then unmasked with six distinguished free energy minima (Fig. 5a). The reaction pathways start from the stable state E (1,4) and easily and quickly transfer to a more stable state F (1,5) with a small free energy barrier of 4.13 kJ/mol (Fig. 5b, c). Although this six-coordinated structure demonstrates similar configuration with those in the first-stage dissolution (B and D), it’s not the most stable state in such FES. Instead, it can further transform to the most stable state I (0,5) with a free energy barrier of 18.76 kJ/mol following the ligand-exchange mechanisms, despite such configuration demonstrates heavily distorted trigonal bipyramid (D3h) structure32,49. Meanwhile, we also note a kinetically unfavorable reaction pathway for transferring state F to state I through two intermediate states G (1,6) and H (0,6) after crossing three free energy barriers (ΔA⧧ (F-G) = 33.52 kJ/mol, ΔA⧧ (G-H) = 27.52 kJ/mol and ΔA⧧ (H-I) = 56.32 kJ/mol). It is interesting to note that sixfold coordination of Ca ion is not the most stable structure on such FES, although it has comparative relative free energies with I (0,5) (Fig. 5c). This indicates that state I and H can transform mutually through liberating or accommodating one water molecule both from the thermodynamic and kinetic views. Such transformation can also occur between state I and state J (0,4). However, the reverse reaction, involving accommodating one more water molecule, is more thermodynamically and kinetically favorable when compared to the forward and backward reaction barriers (ΔA⧧ (I-J) = 33.27 kJ/mol and ΔA⧧ (J-I) = 2.13 kJ/mol). By further inspecting the configuration evolution (Fig. 5c), we finally conclude that one of the surface Onb ions near the dissolved Ca ion has strong electrostatic interactions with the central Ca ion coordinated by five or six water molecules, which can then partially destroy the hydration shell of the central Ca ion by further forming the distorted fivefold coordination for such Ca ion. On the other hand, this interaction can also perturbate the coordination shell of Ca ion with an octahedral configuration and even transform it to sevenfold or sixfold coordination states (i.e., state G (1,6) or F (1,5)), which can be further confirmed by our equilibrium AIMD simulation implemented on the state H (0,6) (Supplementary Note 8 and Supplementary Fig. 9). This unique phenomenon is consistent with the simulation statements that the hydration structure of Ca2+ is highly variable in aqueous solutions with several shallow local minima in the free-energy curves55.

Fig. 5: Calcium dissolution with coordination numbers to water molecules (CN (Ca-Ow)) ranging from 4 to 6.
figure 5

a Free energy surface, b reaction coordinate and c corresponding snapshots of configuration evolution along the reaction pathways. In the above representations, the sates along the dissolution pathways are notated in the form of X (CN (Ca-Ot), CN (Ca-Ow)), where X indicates the state number on the free energy surface or the snapshots (e.g., the A, B, etc.), CN (Ca-Ot) and CN (Ca-Ow) represent coordination numbers of Ca to Ot and Ow, respectively in state X. “TS” denotes the transition state. The upper right corners display the states with Helmholtz free energy values (in kJ/mol) relative to state E. The saffron yellow values above the arrows represent free energy barriers (in kJ/mol), while the black values below the arrows denote the free energy differences between two adjacent states (in kJ/mol). The arrows with varied colors signify the distinct reaction pathways that align with those depicted in (b).

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Discussion

Molecular-level C3A hydration

We can now provide a detailed description of the initial hydration processes of cubic C3A at molecular scale based on the above ab-initio calculations (Fig. 6). The C3A surface exhibits a pronounced chemical affinity to water molecules, leading to a rapid and substantial dissociation of these molecules. The Hw and Ow then strongly coordinate with the surface Onb and Ca ions to initiate the dissolution of surface Ca ions through the MPER41,42. Subsequent reactions of water dissociation and surface hydroxylation heterogeneously and incongruently desorb the surface Ca ions prior to Al ions, promoting the formation of various inner-sphere complexes (Ca ions with different CNs to water). The following full dissolution of the selected Ca ions presents a complex FES and reaction coordinate due to the intricate interactions between ligand water molecules and surface active ions. However, it generally follows ligand-exchange mechanisms32,49,51. When considering state I (0,5) as the final state, the minimum free energy pathway (MFEP) consists of E-F-I with a free energy barrier of 18.76 kJ/mol for the rate-determining step (from F to I). On the other hand, when state H (0,6) is taken as the final state, the MFEP involves E-F-G-H with a higher free energy barrier of 27.52 kJ/mol for the rate-determining step (from G to H). Nevertheless, both states can dynamically convert to surface-bound coordination states (i.e., state G (1,6) or F (1,5)) according to our following equilibrium AIMD simulation, indicating such Ca complexes can adsorb and precipitate on the hydrous Al-rich layers and yielding the positively charged C3A surface (Supplementary Note 9 and Supplementary Fig. 10). This phenomenon indirectly supports the experimentally observed positive zeta potentials of C3A14,19,23,56 and further confirms that Ca ions may inhibit C3A dissolution at high concentrations19,23. Finally, the surface-bound precipitates (CaOnb(OH)x(H2O)y) containing several liberated OH groups will form an amorphous CH layer on the Ca leaching surface. Such amorphous layer is kinetically favored as the local coordination environment is enriched with OH groups and benefits the full hydration of Ca ions, despite the adjacent aqueous solution is significantly undersaturated with respect to even crystalline CH16. Moreover, this amorphous layer can also act as the precursor and finally transform to AFt or various AFm phase induced by the thermodynamic driving force15. The overall reactions recognize the formation of surface alteration layers (SALs) consisting of Al-rich layer and re-participated Ca complexes during the initial hydration processes of C3A induced by the ICDP mechanism57 and emphasize the critical roles of incongruent dissolution-triggered Al-rich layers in determining surface activity and interface reactions18,23. When SO42- ions are also included in the electrical double layer (EDL) of the partially dissolved C3A surface, a pronounced inhibition on C3A dissolution is realized23. This effect is achieved by adsorbing SO42- ions on the surface through electrostatic attraction with the surface-bound Ca complexes, thereby obstructing the coordination sites that would be otherwise occupied by H+ or OH- ions that are known to catalyze the dissolution of alumina58 and C3S32.

Fig. 6: Molecular-level C3A hydration and the associated sequential reactions.
figure 6

For clarity, the Ca-coordinated O ions in water molecules and hydroxy groups are highlighted in green, while the other Ca ions (excluding the selected one for the dissolution reaction) are omitted to clearly illustrate the coordination state of the formed Ca complex from step II to IV.

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Implications for cement hydration

The molecular-level descriptions of the initial hydration of C3A can be seamlessly integrated into real-life cement hydration to optimize its performance through a bottom-up approach, especially when combined with multi-scale simulation and experimental methods. First, we have systematically identified the elementary reaction steps and rate-determining steps for Ca dissolution. The rate equation for such dissolution can be precisely formulated using the transition-state theory59, advancing the power function-based empirical rate equation that describes the overall dissolution process of C3A in the absence of certain knowledge about the reaction sequences and the rate-determining steps60. Second, the ab-initio calculations can serve as a benchmark for force-field parameters specifically designed for investigating the initial hydration of C3A through classical MD simulations. This enables us to explore the hydration process of C3A under conditions closer to actual scenarios, considering factors such as surface defects, solid solution, pH, etc. Finally, the revealed kinetics and thermodynamics can be integrated into the thermodynamic database of cubic C3A. These data are typically experimentally acquired through a dissolution approach, where the water activity and flow rate are specially designed to facilitate in-situ observation of surface topography evolution7,16,17,61 while minimizing the precipitation of secondary or intermediate solids. In this way, the dissolution reaction is proceeded in the forward direction and the rate equation can be written as a power function of reactant concentrations or activities16. By combining these three aspects, we can comprehensively capture the full hydration processes of C3A from the molecular scale to the macro-scale and interpret the early-age hydration of cement in real-life.

In conclusion, we have identified the sequential reactions involved in the C3A/water interface through atomistic simulations and provided a comprehensive description of the molecular-level initial hydration of C3A based on the simulations and pertinent literatures. This study paves the way for understanding and controlling the early-age hydration reactions of cement components, with significant implications for the design and optimization of cement-based materials. A deeper comprehension of the initial hydration of C3A can facilitate the design of admixtures to regulate and modify kinetics and mechanisms, thereby manipulating the rheology, structural build-up and even durability of cement. However, it is essential to acknowledge the complexity of actual cement hydration reactions, particularly in the case of C3A, which involves multi-step and interrelated reactions affected by crystal polymorphs, solution chemistry, surface defects, etc. Future research should consider these variables and strive for a more detailed and quantitative description of Al dissolution and the early precipitation of calcium-aluminate-hydrates.

Methods

Model construction

The cubic crystal (Pa-3 space group) structure of C3A utilized in this study is sourced from reference62, with a sizable unit cell measuring 15.26 × 15.26 × 15.26 Å3. Initially, the bulk C3A structure was optimized using the Vienna ab-initio Software Package (VASP)63,64 (Supplementary Note 1). Subsequently, to create the solid/aqueous solution interface model, the original bulk model was cleaved along the (001) plane (Supplementary Note 2). The stoichiometric lower part of the C3A bulk was then fixed (bulk area) and only the upper part was relaxed (surface area) during the following simulations31,43. A ~ 15 Å layer containing 122 water molecules was then added to this surface to achieve an aqueous environment with a density of 1 g/cm3 and establish the C3A/water interface. The vacuum space between the interface model and its periodic image was ~21 Å. As a result, the final cell dimensions were 15.39 × 15.39 × 52.13 Å3, comprising a total of 630 atoms.

AIMD simulation

The AIMD simulations were conducted using the CP2K/Quickstep package65 by employing density functional theory (DFT) based on a hybrid Gaussian plane wave (GPW) approach66. In this scheme, orbitals are represented using an atom-centered Gaussian-type basis set, while an auxiliary plane wave basis set is used to expand the electron density in reciprocal space. The convergence criteria for energy and self-consistent field (SCF) were set to 10−12 Ha and 10−6 Ha, respectively. To enhance wave function optimization and SCF convergence, an orbital transformation (OT) method67 was employed, along with a wave function extrapolation strategy known as always stable predictor corrector (ASPC). In the calculations, the valence electrons considered were the 1 s electron for H, 2 s and 2p electrons for O, 3 s and 3p electrons for Al, and 3 s, 3p, and 4 s electrons for Ca. The remaining core electrons were described using Goedecker-Teter-Hutter (GTH) pseudopotentials68,69. A double-ζ Valence Polarized (DZVP) Gaussian-type basis set was employed70, and the energy cutoff for the auxiliary plane wave basis set was set to 400 Ry. The exchange-correlation effects were treated with the Perdew-Burke-Ernzerhof (PBE) functional71, including dispersion correction using the Grimme D3 method72. Due to the large size of the supercell, only the Γ point was used for Brillouin-zone integrations in all calculations. To capture the structural evolution of the interface model and bulk solution, Born-Oppenheimer molecular dynamics (BOMD) was utilized under canonical ensemble (NVT) conditions. A Nose-Hoover thermostat maintained the temperature at 300 K. Deuterium masses were used for protons to minimize nuclear vibrational frequencies with a timestep of 1 fs, which is a commonly used value in the literature to prevent energy drifts and maintain computational stability43,73. The AIMD simulation was divided into two stages: an initial ~21 ps equilibrium stage and a final ~20 ps stage for statistical analysis of the distribution and dynamics of surface ions and water molecules (Supplementary Fig. 2). Additionally, the last frame of this AIMD run was specifically extracted for calculations of electronic properties using the DFT-implemented VASP package63,64, along with the VASPKIT plugin74. All atomistic configurations were visualized and analyzed using the VESTA software75.

WT-MetaD simulation

The dissolution process and the associated free energies of Ca ions from the C3A surface cannot be directly observed during the timescale of MD simulations, even though C3A exhibits exceptionally high reactivity and dissolves within 0.1 s15. Such rapid events are still rare in conventional MD sampling. Therefore, to address this limitation, we employed an enhanced sampling method known as metadynamics to sample the dissolution pathways and generate corresponding free energy surfaces within the limited timescale of AIMD simulations. All WT-MetaD simulations concerning Ca dissolution were conducted using the CP2K software65 plugin integrated with the PLUMED package76,77. We employed two CVs characterized by the CNs to construct the two-dimensional free energy surfaces for Ca dissolution. Specifically, the CNs (Ca-Ot/w) represented the coordination numbers of the selected surface Ca ion with all the oxygen ions from the C3A slab (Ot) and from water molecules (Ow), respectively. These CNs were defined according to the rules implemented in PLUMED76,77

$${{{{{\rm{CN}}}}}}({{{{{\rm{Ca}}}}}}-{{{{{{\rm{O}}}}}}}_{{{{{{\rm{t}}}}}}/{{{{{\rm{w}}}}}}})=\mathop{\sum}\limits_{i\in {Ca}}\mathop{\sum}\limits_{j\in {O}_{t/w}}{s}_{{ij}}=\mathop{\sum}\limits_{i\in {Ca}}\mathop{\sum}\limits_{j\in {O}_{t/w}}\frac{1-{(\frac{{r}_{{ij}}-{d}_{0}}{{r}_{0}})}^{n}}{1-{(\frac{{r}_{{ij}}-{d}_{0}}{{r}_{0}})}^{m}}$$
(1)

where \({r}_{{ij}}\) is the distance between atom i and j. \({d}_{0}\) is the function central value. \({s}_{{ij}}\) is a rational type of switching function describing the coordination between atom i and j. \({r}_{0}\) is the acceptance distance of the switching function. n and m are two integer exponents with n < m. Specific parameter values were employed: \({d}_{0}\) and \({r}_{0}\) were set at 2.36 Å and 0.4 Å, respectively, based on the radial distribution function of Ca-Ot/w. The values of n and m were chosen as 4 and 10, respectively. Gaussian hills were added every 20 steps for both CVs with an initial height of 3.5 kJ/mol and a width of 0.15, following established methodology32,76,78. A bias factor of 10 was applied for Ca dissolution. Furthermore, quadratic walls with a force constant of 2000 kJ/mol were intentionally positioned in the WT-MetaD simulations to confine the fluctuations of the CVs within the defined area of interest. Details regarding the time evolution of both CNs, convergence tests for free energy surfaces, and the evaluation of errors between two free energy minima can be found in the Supplementary Note 6.