Introduction

Cement is produced worldwide at the astonishing rate of about 150 t s−1. It is indispensable for social and technological development, and yet, there are many aspects of this material that we do not understand. One of the most crucial ones is the nucleation and growth of the C-S-H, the main component of the hardened cement paste. C-S-H is the acronym for hydrated calcium silicate, an X-ray amorphous phase of variable composition (CaO)x(SiO2)y(H2O)z with a layered structure that resembles the tobermorite family of minerals. On the one hand, the nucleation of the C-S-H plays an important role on the hydration kinetics and hence rheology and work-ability of the cement paste. As C-S-H nucleates (and grows) the saturation index of the pore solution decreases, leading to undersaturated conditions that accelerates calcium silicates’ dissolution1,2,3. On the other hand, the nucleation and growth controls the microstructure of the C-S-H gel. The heterogeneous distribution of nuclei3 determines how the C-S-H will fill the space, governing the pore size distribution and tortuosity. Last but not least, the nucleation may define the mesoscale structure4 and composition of the solid C-S-H itself5.

Recent studies indicate that C-S-H nucleation takes place in at least two steps6,7,8,9,10. In contrast to the classical nucleation theory (CNT), multistep nucleation paths involve several (meta)stable states preceding the formation of stable nuclei. The exact number of steps and the nucleation paths are system-dependent, yet there are some common features11,12,13 like the existence of thermodynamically stable pre-nucleation clusters (PNCs) or more generally metastable primary particles (PPs). The PNCs are small, formally do not have a phase interface, and should be considered solutes rather than solids14,15,16. Second, the aggregation of PNCs triggers a phase separation into a solvent and dense-liquid-like or amorphous solid regions, the latter crystallizing over time16,17. The PNC aggregation has been proposed to be driven by a decrease of entropy upon dehydration18, a decrease in the solute dynamics19, a destabilization of clusters due to progressive chemical reactions or speciation20,21, or intracluster conversion22. Direct experimental observation of PNCs and PPs structure and dynamics is extremely challenging due to the time and size scales. For calcium sulfate, the formation and evolution of PNCs up to the final (CaSO4)4 ⋅ xH2O polymorphs has been monitored in situ by X-ray small- and wide-angle scattering14, and rod-like particles have been reconstructed based on the experiments and MD simulations23. For Ca-phosphate and Ca-carbonate, atomistic simulations have also identified the formation of dynamically ordered liquid-like oxyanion polymers (DOLLOPs) formed by ion pairs in solution18,24. In the mentioned cases, the PNCs and DOLLOPs do not have the exact structure of the final crystal phases, and it is suggested that a posterior ordering of larger aggregates is what defines the different crystalline polymorphs. However, for barite (BaSO4)4 compact clusters resembling crystalline motifs have been reported after MD simulations in aqueous environments25.

In the particular case of C-S-H synthesized from sodium silicate and calcium nitrate solutions10,26, dynamic light scattering (DLS), small-angle X-ray scattering (SAXS), and transmission electron microscopy (TEM) have shown two well differentiated steps: the formation of “amorphous solid spheroids" of about 50-60 nm that reorganize into C-S-H platelets with time6,7,8,9,10. In presence of polycarboxylates, the formation of the spheroids is reported to be similar, yet the crystallization is delayed, attributed to a slower diffusion of water from the spheroid7. A higher Ca concentration has shown to accelerate the transformation from the amorphous spheroids to the nanoplatelets9, which was suggested to occur via dissolution-precipitation of C-S-H. Obtaining further microscopic details remains elusive because of the complex characterization of transient species, which are distinguished by their small size and short lifetimes. Missing information includes (1) to determine which are the dominant species and their characteristics, (2) their stability with respect to the species in solution and with respect to the final solid, (3) how they merge/aggregate to form larger structures, and (4) how the platelet structure emerges from the aggregates. Despite the little understanding of the actual nucleation paths in C-S-H, there is enough evidence from related systems showing that if we can understand it, we might be able to control it. For instance, organic additives like polysaccharides, lignosulfonate, and polyacrylate have been shown to (des)stabilize calcium hydroxide PNCs27, and Mg2+ to retard the crystallization by the stabilization of CaCO3 PNCs28.

Very few studies have explored ion complexation and PPs using atomistic simulations. Yang et al.29 used density functional theory (DFT) to compute the formation free energies of Ca-silicate ion pairs, and Li et al. explored the energy landscape of Ca coordination in [Ca(H2O)x(SiO2(OH)2)] complexes by ab-initio metadynamics30. Regarding PPs, Manzano et al. proposed a C-S-H PP after cleaving a “basic building block" from tobermorite and jennite crystals, which was relaxed with ab-initio calculations31. They suggested that these PPs could aggregate differently depending on the Ca2+ content in solution. Finally, a recent study has explored a two-step route for the C-S-H nucleation32. First, portlandite PPs are formed, and second, the reaction of silicate dimers with the portlandite PPs will induce a topochemical phase transition to form C-S-H monolayers.

In this work, we will investigate the structure and stability of C-S-H primary particles using atomistic simulation methods, specifically DFT and evolutionary algorithms (EA). Our goal is to determine the structure of energetically accessible small clusters (with the composition nCaO + nSiO2 + xH2O where n = 1, 2, 4) that might appear during the initial stages of C-S-H nucleation. Then, we compare the structural resemblances of the PPs with the bulk C-S-H and study their aggregation kinetics with MD. Based on our simulations and the available experimental data, we suggest a formation pathway for the C-S-H nucleation.

Results

In the following subsections, we will show the results for C-S-H clusters of different sizes and water contents. The general composition is nCaO+nSiO2 + xH2O with n = 1, 2, 4 and x variable from size to size. Following the contracted nomenclature used in cement chemistry, the clusters will be named as CnSnHx where C stands for CaO, S stands for SiO2 and H stands for H2O. Although the average value of Ca/Si ratio for C-S-H in cement is ~1.7, the Ca/Si ratio for the EA was chosen to be 1 and kept constant for all the clusters, which deserves an explanation. For the smaller clusters, CSHx, there is experimental33,34,35 and computational36 evidence about the existence of Ca/Si = 1 complexes. The general belief is that the prevalent silicate species in the pore solution are CaSiO4H2 complexes (log K = 4.6), and the extra Ca will be in the form of a hydrated Ca2+ ion. For larger clusters, there is no experimental information, so we assume as a working hypothesis that the CSHx complexes will aggregate and form dimeric species (C2S2Hx). We cannot rule out that additional Ca+2 ions will participate in the aggregation, forming dimeric clusters with Ca/Si > 1. However, given the structure of the C2S2Hx that we will present in Discussion (2), we consider that the existence of Ca/Si = 1 dimers is plausible. Then, additional Ca should take part in the C-S-H structure in the aggregation stage. Consequently, for the MD simulations in Discussion (5) we added Ca(OH)2 in the solution to increase the Ca/Si ratio to 1.5, a value closer to the actual C-S-H composition.

CSHx complexes

First we seek for the most stable coordination complex of a silicate monomer with one Ca ion. Following the above criteria we chose CSH10 as initial stoichiometry, which would corresponds to a neutral CaSi(OH)2O2 system plus 7 or 8 water molecules. It must be notice that the EA does not assume any charge state for the different units in the complex, it just keeps the atoms in the system constant. Therefore the EA can explore both complexes with Si-OH + Ca-OH or Si-O-Ca + water.

Figure 1 shows a sketch-map of the clusters found during the global minimization with energy lower than E0 + 150 kJ mol−1, E0 being the energy of the lowest energy cluster. The sketch-map is a graphical representation in which clusters are represented by points, and the similarity between the clusters is depicted by the distance between the points. Closer points indicate a higher degree of structural similarity, while farther points represent a lower level of similarity. In Fig. 1a the color scale represents the energy difference, while in Fig. 1b–g the colors represent a mapping of several structural properties. The sketch-map shows 2 different regions. In region I the low energy complexes all contain a silicate tetrahedron bonded to a 6- or 7-fold coordinated Ca atom [Fig. 1c]. The silicon and calcium atoms are mostly bonded by a single Si-O-Ca bond, and 7 or 8 water molecules are found around the complex, with 4 or 5 filling the Ca hydration shell. In region II, the complexes include 5-fold coordinated silicate groups, with energies at least 1.35 kJ mol−1 higher than those in region I. In this case, the silicon and calcium atoms are mostly bonded by two Si-O-Ca bonds [Fig. 1d]. The appearance of pentacoordinated silica is not a surprise as it is a common transient structure during condensation or hydrolysis reactions, especially in high pH environments37.

Fig. 1: Sketch-map representation of the CSH10 clusters.
figure 1

Each point represents a different primary particle (PP), and the distances between points represent the structural similarity between the PPs. The closer the points are, the more similar their structures are and vice versa. The colormap in (a) represents the energy difference ΔE with respect to the lowest energy PP. The atomic structure of the best PPs are also shown, with Ca atoms represented in green, Si atoms in orange, O atoms in red and H atoms in white. The regions I and II each represent a group of low energy PPs with similar structural properties. b–g Collection of structural properties of the clusters color mapped into the same Sketch-map. nSi−O, nCa−O and nSi−O−Ca represent respectively the number of Si-O, Ca-O and Si-O-Ca bonds. dSi−Ca represents the distance between the Si and Ca atom in the PP. n\({}_{{{{{{{{{\rm{H}}}}}}}}}_{2}{{{{{{{\rm{O}}}}}}}}}\) and nOH represent the number of water molecules and hydroxil groups in the PP. Source data are provided as a Source Data file.

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It is important to notice that many complexes within accessible energies present 7-coordinated atoms [see Fig. 1c]. That is the coordination of Ca atoms in the C-S-H gel intralayer region31,32, and it is common to use such a structural feature to characterize the early formation of C-S-H from Synchrotron X-ray powder diffraction (SXRPD)38,39. Our simulations indicate that the complexes may already display such coordination, and therefore they may interfere with the characterization of the solid phase. The same EA search has been made for stoichiometries with less water, CSH6 and CSH2, and are shown in the supplementary information (SI). Decreasing the water content does not change the formed complexes substantially: the best clusters also contain a silicate tetrahedron linked to the Ca atom, but the coordination of the Ca atoms decreases due to the lack of water molecules.

Overall, the most stable complexes found by EA are similar to those reported before by atomistic simulation methods29,30,36, yet direct comparisons are not possible. For instance, Li et al. studied the energy landscape of Ca-coordination in a CaSiO4H2 neutral cluster, but they did not consider the 7-fold coordination that we find predominant. Galmarini et al. reported the free energy landscape for the aggregation of a SiO2(OH)\({}_{2}^{2-}\) and Ca2+. The complex formation is favorable, with an Ca-Si equilibrium distance of 3.6 Å, in excellent agreement with the distance of the most stable clusters found by EA, [Fig. 1e]. However, their conformation is fixed and the protonation state is not the same as the the predicted by EA.

C2S2Hx clusters

The next step in the C-S-H nucleation would be the formation of primary particles by the interaction (merging) of complexes in solution. Therefore, we have explored the most stable PPs for the stoichiometry C2S2H20. At this stage is clear the potential of EA to unravel the structure of the PPs: the complexes from “CSHx complexes” have a relatively simple structure that can be guessed by chemical intuition, but for larger systems, the task could be more complicated. Thanks to EA, we do not need to assume any initial structure or feature, and the global optimization will lead us to the lowest energy structures.

Two sets of low energy structures can be distinguished in the sketch-map in Fig. 2a for the C2S2H20: region I, where the most stable candidates are found, with silicate dimmers, and region II with isolated silicate monomers [blue and green respectively in Fig. 2d]. The energy difference between the best candidate from region I and the best candidate from region II is just 6.7 kJ mol−1, which suggests that both PPs could cohexist at room temperature. The best structures of region I contain mostly 6-fold coordinated Ca atoms, although some 5- and 7-fold coordinated Ca are also present, and the silicate groups are mainly tetrahedral. In region II, the average Ca-O coordination is slightly larger, ranging from 5.5 to 6.5, and although the silicate groups mostly contain 4-fold coordination, some 5-fold coordinated silicates are present. A constant characteristic for low energy structures from both regions is that the Ca atoms are linked (by oxygen atoms and/or hydroxyl groups) and never separated.

Fig. 2: Sketch-map representation of the C2S2H10 clusters.
figure 2

Each point represents a different primary particle (PP), and the distances between points represent the structural similarity between the PPs. The closer the points are, the more similar their structures are and vice versa. The colormap in (a) represents the energy difference ΔE with respect to the lowest energy PP. The atomic structure of the best PPs are also shown, with Ca atoms represented in green, Si atoms in orange, O atoms in red and H atoms in white. The regions I and II each represent a group of low energy PPs with similar structural properties. b–g Collection of structural properties of the clusters color mapped into the same Sketch-map. nSi−O, nCa−O, nSi−O−Si and nCa−O−Ca represent respectively the number of Si-O, Ca-O, Si-O-Si and Ca-O-Ca bonds. n\({}_{{{{{{{{{\rm{H}}}}}}}}}_{2}{{{{{{{\rm{O}}}}}}}}}\) and nOH represent the number of water molecules and hydroxil groups in the PP. Source data are provided as a Source Data file.

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We performed simulations decreasing the water content of the C2S2Hx cluster from x = 20 to x = 12, 4 (see the SI). As expected, the coordination of the Ca ions decreases, but the main structure of the silicate arrangement remains, with the two Ca atoms linked to each other and to silicate monomers or dimmers. We found that the number of low-energy structures containing monomers increases as the water content decreases, probably to maximize the coordination of Ca atoms.

C4S4Hx clusters

We went one step further simulating clusters with the stoichiometry C4S4Hx, which would correspond to the aggregation of 2 C2S2Hx PPs. For the C4S4H8 PPs we divided the similarity map into two regions. Region I comprises low energy PPs with heterogeneous characteristics in terms of silicate chain network, number of water molecules and OH groups, as shown in Fig. 3b–d. Nevertheless, the lowest energy structures within region I share similar characteristics: they are formed by a silicate monomer and a silicate trimer, and their gyration radius is <0.3 nm, at the lower end of the range for all the structures. Therefore, a more compact structure is energetically favorable. Region II contains clusters with a silicate dimer and two monomers. The energy difference between the best structures in region I and II is 11.1 kJ mol−1, a non-negligible value that points to the higher stability of the longer silicate chains in region I. It is specially interesting the emergence of silicate monomers and trimers within the most favorable clusters. It is usually believed that trimers do not appear at any stage of C-S-H formation, and monomers disappear soon after hydration starts40,41. However, recent works report the presence of Q0,1,2,3 NMR signals for synthetic C-S-H at very early nucleation times that change over time until only Q1,2 remain9. That suggests a wide population of silicate oligomer structures in the amorphous globules that evolve during crystallization to form the linear chains following the well known 2n-1 length rule41.

Fig. 3: Sketch-map representation of the C4S4H8 and C4H4S2 clusters.
figure 3

Each point represents a different primary particle (PP), and the distances between points represent the structural similarity between the PPs. The closer the points are, the more similar their structures are and vice versa. The colormap in (a–f) represents the energy difference ΔE with respect to the lowest energy PP for each stoichiometry. The atomic structure of the best PPs are also shown, with Ca atoms represented in green, Si atoms in orange, O atoms in red and H atoms in white. The regions I and II each represent a group of low energy PPs with similar structural properties. b–d Collection of structural properties of the clusters color mapped into the same Sketch-map for C4S4H8 PPs. e The different silicate arrangements found in the PPs. g–i Collection of structural properties of the clusters color mapped into the same Sketch-map for C4S4H2 PPs. nchain shows the silicate arrangement as shown in (e). n\({}_{{{{{{{{{\rm{H}}}}}}}}}_{2}{{{{{{{\rm{O}}}}}}}}}\) and nOH represent the number of water molecules and hydroxil groups in the PP. Source data are provided as a Source Data file.

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For this size, we also include the less hydrated PPs with C4S4H2 stoichiometry [Fig. 3e], because the most stable cluster structure is of special interest. Due to the lower amount of water molecules, the obtained clusters do not cover a large configurational space, and they are very homogeneous. We only distinguish one region, with clusters made of 2 silicate dimers linked by Ca atoms, and no water. The lowest energy structures are symmetrical, and the Ca atoms form a central layer with the silicate dimers at the top and bottom, which resembles the atomic arrangement in tobermorite. In fact, the clusters have a very similar structure as the one reported by Manzano et al. in 200731. In that study, a common structural feature was found in tobermorite and jennite crystals, which are considered perfect versions of the C-S-H in cement, and was isolated to build a cluster. The cluster was relaxed in vacuum using ab-initio simulations, and it was proposed as the smallest building block of C-S-H. The exact same cluster isolated and relaxed from the crystals is also found by EA as one of the lowest energy structures, with an energy of just 5.1 kJ mol−1 larger than the global minimum obtained by EA. The only structural difference between the lowest energy cluster and the one reported in ref. 31 is the orientation of the silicate dimers, perpendicular in the former and parallel in the latter. The fact that EA predict a low-energy structure with the same atomic arrangement as tobermorite strongly suggests that the C4S4H2 cluster could indeed be the C-S-H basic building block.

Aggregation of the primary particles

After determining the lowest energy clusters for the different sizes, we explored different steps of the possible C-S-H aggregation pathway. First, we computed the sequential enthalpy of formation of the complexes/PPs formed by merging smaller structures. For each size, the lowest energy cluster was relaxed using DFT including an implicit solvent effect.

The first step is the formation of CSHx complexes from the ions in solution. The ions have been selected based on the predominant individual speciation states of Ca and silicic acid in high-pH environments. According to Refs. 42,43, Ca is present mainly as Ca2+ with a minor presence of Ca(OH)+, and silicates mainly as H3SiO\({}_{4}^{-}\) and H2SiO\({}_{4}^{2-}\) (see SI for details). To better reproduce the solvent effect, a variable number of water molecules were explicitly added to the species in solution based on the estimation by Yang and White29. All the enthalpies of formation and reaction stoichiometries for the complex formation are shown in the SI. Figure 4a shows the most favorable ones relevant to our discussion, which corresponds to the pathways starting from the ionic species with the highest charges Ca2+(H2O)6 and H2SiO\({}_{4}^{-2}\)(H2O)6 as reactants. The formation of the CSH10 complex from the species in solution is very exothermic, indicating a considerable stabilization of the ions. It must be noted that despite the initial species in solution being charged, the complex is neutral, with a H3SiO\({}_{4}^{-}\) silicate sharing its deprotonated oxygen atom with the Ca atom, which completes its hydration sphere with five water molecules and a hydroxyl group. To better understand the speciation at high pH, charged complexes and PPs will be considered in future works. Nevertheless, we can suggest that the formation of the CSH10 complex is very favorable and it can be a dominant complex in cement pore solution, in agreement with previous simulations36 and experiments33,34,35

Fig. 4: Aggregation of the C-S-H complexes and primary particles.
figure 4

a Free energies of the primary particles (PP) aggregation for several formation paths. The values are given in kJ mol−1. b Representation of the Plombierite (tobermorite 14 Å) atomic structure. The two highlighted features are comparable to the atomic arrangement of the C2S2Hx -I and the C4S4H2 prymary particles (PP). c Example of an aggregate formed from C2S2H20 clusters in solution after 10ns of MD simulation. d Computed pair distribution functions G(r) for the largest aggregate over the last 5ns of simulation, and its comparison with the computed G(r) of a bulk C-S-H model with Ca/Si = 1.566 and tobermorite 14 Å. e Evolution of the averaged aggregate size < S > over time. The size is defined in terms of number of atoms that for the aggregate normalized by the number of atoms in a primary particle (PP) S0. f Average water loss < H2O > from the aggregates over time. g Asphericity of the aggregates as a function of the gyration radius Rg. Source data are provided as a Source Data file.

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The second step is the formation of the C2S2H20 PPs by merging two complexes. Based on the experimental data, the dimeric PPs could be of key importance in C-S-H nucleation. During the hydration of tricalcium silicate, dimers are formed after ~1 h and are the dominant silicate species at all stages40. According to our simulations, the formation of C2S2H20 from the complexes or from species in solution is also favorable. Based on the energetics and kinetics, we can expect that two complexes would merge into a C2S2H20-II, with two independent silicate monomers. Then, an intra-cluster condensation reaction would take place to form the dimer. The free energy of the dimeric C2S2H20-I cluster is slightly larger than that of the monomeric cluster, and therefore the total free energy gain must be attributed to an increase of the entropy due to the released water molecule, as suggested before16,18,44. The C2S2H20-II structure is noteworthy: the Ca atoms are close to each other and opposite to the siloxane bond between the silicates. As shown in Fig. 4b, such an arrangement can be found in tobermorite crystals, as well as in C-S-H and jennite crystals (see Fig. S17)5. This suggests that the silicate dimerization stage is the critical step that directs the formation of the C-S-H gel towards tobermorite-like lamellar structures.

To analyze the aggregation dynamics of the C2S2H20 PPs we performed four MD simulations with different (and random) initial distribution of eight C2S2H20 PPs in water. To simulate the experimental composition of the amorphous spheroids6 and move closer to the experimental Ca/Si ratio of the C-S-H in cement pastes eight Ca(OH)2 groups were added to the solution. After an equilibration period in the NPT ensemble, the silicate density in the simulation box was 0.38 ± 0.02, nearly 19 times lower than in the C-S-H and matching perfectly with the experimental estimation6. The mass density was ρ = 1.02 ± 0.02 g cm−3, close to the bulk water density, which indicates a liquid-like nature of the amorphous spheroids. We observe that the C2S2H20 PPs do not dissociate, i.e., the calcium atoms remain attached to the silicate dimers, so the dimeric PPs are stable.

The PPs and Ca(OH)2 complexes in solution are highly dynamic and tend to form aggregates that grow over time, even within the limited simulation time (15 ns). The aggregates were defined using a distance cutoff between atoms of 2.7 Å, which accounts for the typical Ca-O distance45. An example of an aggregate structure comprising four PPs and 2 Ca(OH)2 complexes is depicted in Fig. 4c. In Fig. 4e we show the size of the larger aggregate S as a function of time, averaged over four simulations and normalized by the size of one C2S2H20 PPs S0. It can be seen the PPs aggregate very fast in short times, and they are dynamic, with PPs moving back and forward from the cut-off distance. Figure 4e shows the asphericity of the clusters as a function of the gyration radius. Clearly, larger clusters tend to be more elongated, in agreement with the structure of the DOLLOPs and rod-like particles proposed as primary particles for CaCO3 and CaSO4 nucleation14,44. The elongated shapes maximize the Ca-water coordination, which might stabilize these aggregates until they assemble into larger morphologies. A similar mechanism has been proposed for the nucleation of gypsum14, with primary species that form aggregates without any coherent diffraction signal despite their large size, which suggests a disorder arrangement. The solvation water that we observe in this work may be the reason for the misalignment and disorder between the aggregates.

To analyse the internal structure of the aggregates we have computed the pair distribution function G(r) for the last 5ns of simulation, when the aggregate size has stabilized to its maximum value, and compare it with that of tobermorite 14 Å and a bulk C-S-H model. The diffraction peaks were identified by examining their distinct components, as displayed in the SI, and the water contribution was eliminated by subtracting the weighted G(r) of bulk water. Below 3 Å the peaks correspond to the first Ca-O, Si-O and O-O neighbors, and therefore are similar for the aggregates and the bulk systems. Above 3 Å the peaks for the aggregate are dominated by the contribution of the heavy atoms Ca and Si. The Ca-Ca, Si-Si, and Ca-Si signals are considerably stronger than in C-S-H and tobermorite. Conversely, the signals involving O are negligible, and the correlation is lost after 6 Å due to the shape of the particles. The lack of defined peaks for the X-O pairs beyond the bonded atoms suggest a considerable disorder: the short-range coordination of metal cations is the expected one, with SiO4 silicate tetrahedra and CaO6 heptahedra, but the orientation and arrangement of these species does not have any medium-range order. Therefore, we cannot state that the aggregates present a C-S-H-like structure yet.

The last step in the formation path involves the formation of C4S4Hx PPs. Based on the fast aggregation of C2S2H20 in MD simulations, and the fact that EA predict clusters with silicate trimers as the most favorable ones, we suggest that C4S4Hx clusters may not present in solution. However, the C4S4H2 structures can be seen as C-S-H basic building blocks, as shown in Fig. 4b, so we propose that they will be formed by progressive dehydration within the large C2S2H20 aggregates. In fact, dehydration has been suggested to be a key step in CaCO3 nucleation, as releasing water leads to an increase of the entropy, reducing the free energy of the nuclei16,18,44. Our DFT simulations of isolated clusters indicate that dehydration is slightly favorable. More interesting is the evolution of the C2S2H20 aggregates in solution. As can be seen in Fig. 4g, the mean number of water molecules attached to the aggregates decreases with time. The decrease is due to the aggregation itself, since the PPs lose water molecules from their hydration shells, and also due to rearrangements within clusters, including condensation reactions between the C2S2H20 and Ca(OH)2. Despite only observing the initial steps of dehydration, we suggest that C4S4H2 clusters will be progressively formed within the aggregates leading to crystallization.

Discussion

Based on all the obtained results we can propose a possible C-S-H nucleation path. For that we have used as a starting point the three stages observed in turbidity experiments as a function of time6 (see Fig. 5). The suggested nucleation path can be described in 4 steps, the two initial ones within the first stage of nucleation:

  1. 1.

    The main species in the supersaturated solution, Ca2+ and SiO\({}_{4}^{2-}\), form Ca(OH)-O-Si(OH)3 complexes. Energetically, the reaction is very favorable, and previous investigations reported a barrierless aggregation36, so the formation of the complexes is expected to be fast.

  2. 2.

    The complexes merge into C2S2H20 primary particles (PPs). The silicate dimers are formed via condensation reaction within the PP.

  3. 3.

    The C2S2H20 PPs are very dynamic and rapidly aggregate into large clusters. These large aggregates tend to be elongated and they are highly solvated (possibly stabilized) by water. Groups of clusters more or less entangled would form the experimentally observed amorphous globules. If the experimental silicate density is correct6, the density of the globules should be close the bulk water value, ρ ≈ 1.02 g cm−3, so the globules could be seen as liquid-like in nature. In this stage NMR experiments indicate that the silicate oligomers may include species different from dimers8,9 which we have not explored in this work, yet EA predicts favorable clusters with silicate monomers and trimers.

  4. 4.

    The large aggregates slowly dehydrate, and C4S4H2 structures are formed within them. These C4S4H2 structures present a tobermorite-like structure and can be seen as the basic building block for the C-S-H formation. Finally, a slow process of dehydration and rearrangement of the C4S4H2 within the aggregates will result in the C-S-H layers. If present, branched silicate oligomers should de-polimerise during this crystallization stage to form linear chains.

Fig. 5: Schematic representation of the C-S-H nucleation pathways.
figure 5

The shape of the turbidity vs time defines 3 stages stages in the nucleation process (based on ref. 6). The experimental TEM image in step 3 shows an amorphous C-S-H globule, and the TEM image in step 4 the formation of C-S-H layers. The experimental images have been adapted from ref. 26, Pages No. 33-39, Copyright 2018, with permission from Elsevier. The Qn signals in steps (3) and (4) are based on ref. 9, and represent the connectivity of the silicate groups.

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Overall, we have used atomistic simulation methods to investigate the structure and formation of C-S-H complexes and PPs, and then discuss a possible C-S-H nucleation pathway based on the simulations and evidence from the literature. This work is the first computational step in the challenging path toward understanding and controlling C-S-H nucleation, and have significant implications for advancing in the design and optimization of cementitious materials. A deeper understanding of the nucleation mechanisms can aid in tailoring additives to regulate it, modifying the rates and mechanisms, and therefore controling the rehology, the pore structure, the strength, or the durability. Nevertheless, we must keep in mind that the actual nucleation path may be different depending on the C-S-H formation process (synthetic, from C3S dissolution, from cement hydration) and the presence of guest ions, the co-nucleation of other phases, etc. In future work, the role of these variables should be explored, as well as seek for a more detailed and quantitative description of the aggregate formation and the dehydration/crystallization stage.

Methods

The prediction of the most stable clusters was done using evolutionary algorithms as implemented in the USPEX code (v.10.3)46,47,48. For each system, a first generation of 500 clusters were created and relaxed using the ReaxFF force field49 with the Ca/Si/O/H set of parameters from Refs. 45,50,51. From the first generation, the best 25 clusters were selected to start the evolutionary algorithm. In each generation, the clusters were relaxed in two steps to accelerate the calculations, first using empirical potentials (ReaxFF) and then DFT. The energy minimization with empirical potentials was done with GULP(4.2.0)52 using the conjugate gradient and the ReaxFF force field45,50,51. The DFT minimizations were also done with conjugate gradients using the SIESTA code (4.1)53. The electron exchange-correlation has been taken into account at the generalized gradient approximation (GGA) using the Perdew-Burke-Enrzerhof (PBE) functional54. Grimme dispersion correction was used to include van der Walls interactions55. A double-ζ polarized (DZP) basis set was used for the pseudo-atomic orbitals. The best structures were further minimized using the Polarizable Continuum Model (PCM) to simulate the high pH environment, using a dielectric constant of ϵ = 56, which corresponds to NaOH solution with a pH of around 1456. For that, the Gaussian09 code was use57, with the PBE XC functional, a 6-311+G(d) basis set58 and the empirical dispersion by Grimme55.

To compute the structural similarity between the clusters, the smooth overlap of atomic positions (SOAP) was used59. The Ca, Si and O atoms were used as centers of the SOAP descriptor, with a cut-off of 3.5 Å. 16 radial functions and 12 angular functions were used to expand the descriptor and the best-match structural kernel was used to compute the final structural distance between structures60. Then, the Sketch-map method was used to reduce the similarity matrix to a 2D representation of the explored phase space61,62. These 2D representation maps together with the atomic structure of the clusters are included as .json files in the supplementary material, ready for interactive visualization in the chemiscope online tool63 (for more information see SI).

The molecular dynamics (MD) simulations were done using LAMMPS (21-Jan-2020)64 and the ReaxFF force field. Four independent simulations were done starting from different configurations generated by random packing of 8 C2S2H20 clusters and 8 Ca(OH)2 molecules with 700 H2O molecules in a 7 nm side box. After 200 ps for density equilibration in the NPT ensemble, the simulations were run for 15 ns in the NPT ensemble, with a 0.2 fs timestep and using the Verlet integrator.