The nucleation of C–S–H via prenucleation clusters

With an estimated annual production of 4.4 × 10⁹ tons of cement, the therewith-produced concrete is by far the most used material in the world.¹ The binder in concrete is mostly ordinary Portland cement (OPC) or blends of OPC and supplementary cementitious materials.¹ The hydrated cement is responsible for the outstanding properties of concrete, such as strength and durability. The hydration process involves dissolution reactions of the cement phases and precipitation of hydration products via nucleation and growth.² The most important cement phase is alite (an impure form of tricalcium silicate, C₃S, and cement notation: C=CaO, S=SiO₂, and H=H₂O), which reacts to calcium–silicate–hydrate (C–S–H).³ However, the knowledge on the C–S–H formation is still vague.

In the first experimental work on C–S–H nucleation, it was found that the nucleation of C–S–H obeys the classical nucleation theory, whereby the induction time of the nucleation increases with the increasing saturation degree with respect to C–S–H.⁴ Additionally, it was found in the study that the nucleation at surfaces is dominated against the homogeneous nucleation, which reflects the observations in hydrated types of cement. It was further found that C–S–H nucleation proceeds via a two-step pathway.⁵ The first step is associated with a metastable liquid precursor, which are amorphous C–S–H spheroids poor in calcium and charge-balanced by sodium. In the second step, the formed C–S–H spheroids aggregate to larger structures. However, it was not investigated in detail if the C–S–H spheroids are formed via smaller structures, such as pre-nucleation clusters (PNCs) in accordance with other systems like CaCO₃.⁶ The results gained from nucleation experiments on C–S–H by the means of analytical ultracentrifugation (AUC) showed the formation of pre-nucleation clusters of C–S–H only in the presence of organic polymers.⁷ However, the long acquisition time used in this study may have blurred the event of nucleation in the absence of organic polymers so that the detection of pre-nucleation clusters could have been concealed by the duration of the experiment.

Nucleation of C–S–H is found to be the dominant event because the growth of C–S–H seems to be very limited,⁸ which may be caused by the inclusion of calcium sites that bridge the interlayer structure and lead to stabilization of the structure.⁹ It was investigated by AFM (wet-cell) that the C–S–H forms platelets with a thickness of 5 nm¹⁰—a thickness that is in accordance to Ref. 11. The crystallite size of the initially formed C–S–H was determined by XRD with values between 7.7 and 9.1 nm,¹² which is slightly larger as the AFM observations by¹⁰ that could be the result of the use of different experimental setups and that this value remains unchanged during the hydration process of C₃S was seen as an indication that nucleation occurs predominantly, and the growth of C–S–H is the result of the agglomeration of these crystallites.¹² Similarly, C–S–H globules calculated from SANS studies showed dimensions of 5 nm,¹³ which may flocculate to form larger C–S–H structures. Therefore, some evidence is present that the growth of C–S–H is the result of the agglomeration of smaller particles.

The knowledge about nucleation is enhanced dramatically in the last 20 years. Especially interesting are non-classical nucleation pathways like the prenucleation cluster pathway,^14–17 which were first found for not only CaCO₃⁶ but also a number of other materials like calcium phosphate,¹⁸ CoFe₂O₄,¹⁹ iron oxides,²⁰ InAs,²¹ and organic molecules like amino acids.²² 

Here, it is broadly agreed that ions form the dynamic prenucleation clusters,²³ which are thermodynamically stable with respect to the ions. However, in the case of CaCO₃, it was shown that further up-concentration to the solubility limit of the mineral crosses the binodal and leads to the nucleation of liquid nano droplets.²⁴ Also, the spinodal limit and phase diagram were determined for CaCO₃.²⁵ Since nucleated droplets have an interface with the surrounding solvent, they can coalesce to larger droplets, and further, water elimination can lead to amorphous nanoparticles, in which finally crystallization can occur. The whole prenucleation cluster pathway can be seen in Ref. 26. It is clear that the prenucleation cluster pathway involves a number of species after nucleation, but prior to nucleation, several different prenucleation cluster sizes have been identified.⁶ How many different prenucleation cluster species exist is yet an open question and typically limited by the analytical capabilities to detect them.

The investigation of the properties of C–S–H is very challenging due to, for example, the variable chemical composition (Ca/Si ratio, water content²⁷), the size of C–S–H particles in the range of nanometers,²⁸ the sensitivity of C–S–H against radiation and vacuum,²⁹ and the presence of other phases in the vicinity of C–S–H. This is true for mature C–S–H, but to reveal the early stages of the formation of C–S–H is even more complicated. As a result, little is known about the structure formation process of C–S–H during the early stages of OPC hydration. This gap in knowledge is crucial because it has been realized that e.g., the fresh concrete properties may also be influenced by the early formation of C–S–H.^30–32 Moreover, to design the properties of the mature C–S–H, the formation process of C–S–H from the start of the OPC hydration must be known.

Because the formation of C–S–H during OPC hydration is superimposed by several side reactions, model systems are frequently used instead.³³ Exemplarily, double decomposition experiments,³⁴ reactions of CaO and silica,³⁵ or the hydration of C₃S³⁶ are utilized. Each of these model systems has limitations. Precipitation via double decomposition experiments and reactions between CaO and silica showed that the Ca/Si ratio is limited to values of 1.5 without producing portlandite as a possible secondary reaction product.³⁷ Recent improvements of the protocol of the double decomposition method showed that this ratio can be increased to 2.0 without the formation of portlandite.³⁴ However, with the educts, the crystallization of C–S–H takes place in solutions that additionally contain foreign ions, such as, for example, sodium or chloride. These ions can also influence the crystallization kinetics and the composition of the C–S–H.^5,38 Alternatively, the hydration of C₃S with C–S–H as a reaction product can be studied in the absence of foreign ions.³⁶ In this case, the precipitation of portlandite must be suppressed by titration techniques conducted in stirred C₃S-suspensions, in which the saturated Ca(OH)₂-solution is used as a starting solution.

The aim of the present work is to investigate the early stage of C–S–H formation under conditions that are close to cement pastes. For this purpose, the C₃S hydration will be conducted under controlled conditions using a slightly modified protocol of Ref. 36 that allows the sampling of aliquots during the experimental run with the aim to follow the nucleation of C–S–H without side reactions from hydrating C₃S. The work focuses on the detection of building units of C–S–H in the aqueous phase. For this purpose, the aqueous phase is investigated by the means of analytical ultracentrifugation that allows us to determine the sedimentation properties of solutes down to ions in liquids. Additionally, the aqueous phase was investigated with respect to the chemical composition by means of inductively coupled plasma-optical emission spectroscopy (ICP-OES). With the combination of AUC and ICP-OES, the properties of the aqueous phase are investigated with new precision that allows us to follow the formation of C–S–H from the very early stages on.

A mixture of calcium carbonate (CaCO₃, Merck, p.a.) and amorphous silica (SiO₂, Merck, p.a.) was burned at 1550 °C in order to synthesize triclinic C₃S. After the burning, the material was cooled at room temperature and ground in a disk mill (made of zirconia). This procedure was repeated three times.

The chemical analysis of the C₃S was determined by the chemical wet analysis and is given in Table I.

The N₂-BET specific surface area (SSA) was determined according to DIN ISO 9277 (BET procedure, Beckman Coulter SA3100). The SAA of the C₃S measures 0.392 m²/g.

Calcium hydroxide (Merck, p.A.) was mixed with purified water in order to prepare the starting solution saturated with respect to calcium hydroxide for the suspension experiments (∼2 g/L). After one hour, the Ca(OH)₂-suspension was filtered (Whatman, filter mesh of 0.45 µm, N₂-pressure filtration). The suspension experiments were started by adding C₃S to the aqueous phase. All preparation steps were conducted at 25 °C in N₂ atmosphere to prevent carbonation.

Because the formation of C–S–H during the hydration of C₃S is accompanied by different site reactions, such as the formation of portlandite, and a variation of the properties of C–S–H in dependence of the calcium concentration of the aqueous phase,²⁷ the experiments were designed in the first series to investigate the early formation of C–S–H during hydration of C₃S under controlled conditions in detail. For this purpose, the experiments need to be conducted in diluted suspensions. In the second step, these findings are compared with the practical case of C₃S hydration in pastes (i.e., concentrated suspensions), which cannot be controlled in such detail as in the first step. The paste hydration experiments serve, therefore, as a proof-of-concept of the experiments performed under controlled conditions.

The control of the hydration regarded the calcium concentration of the aqueous phase, which is one of the important parameters for the kinetics of the C₃S hydration and the properties of the C–S–H phases. By means of titration techniques, the calcium concentration was kept at constant values. Moreover, the experimental setup allows us to exclude the formation of portlandite, which would otherwise superimpose the data of C–S–H formation. The principle of the experiment was taken from Nonat et al.³⁶ but was modified in order to be able to withdraw aliquots at different time intervals.

The aliquots were taken by a syringe and subsequently filtered through syringe filters (0.2 µm pore size) in order to get the aqueous phase. Approximately 100 µl of the aqueous phase was filled into the measuring cells of the AUC, whereas ∼5 ml of this sample was stabilized by 5 mM HNO₃ at a dilution between 3% and 5% for the analysis with respect to the chemical composition by the means of ICP-OES. The measured concentrations were corrected by taking this dilution (<2%) into account. This procedure was also applied for the aqueous phase of the C₃S pastes; however, the pastes were precedingly centrifuged to separate the solid and the liquid phases (10 min at centrifugation field of 15 000 g).

All preparational experiments were conducted at 25 °C. Throughout the experiments including filling of the aqueous phase into the cells of the AUC, the contact with CO₂ was excluded by working under N₂ atmosphere. Therefore, the formation of CaCO₃ in the aqueous phase can be excluded.

The aqueous phase extracted from the hydrated C₃S samples (diluted suspensions, concentrated pastes) was filled into 12 mm Ti double sector cells (Nanolytics, Potsdam, Germany) with sapphire windows (preparation time was ∼5 min). MilliQ water was used in the reference sector. These measuring cells were put into an An-60 Ti rotor in an analytical ultracentrifuge (AUC, Beckman-Coulter XL-I), which was operated at 20 °C. The sedimentation of the particles was assessed by the means of advanced Rayleigh interference optics developed by Nanolytics³⁹ at 60 000 rpm. Different time-dependent measurement profiles were used. For the determination of the time-dependent development of the species dispersed in the aqueous phase, at first, short measuring intervals of 20 s for a duration of 49.5 min were applied. Then, the approach to sedimentation equilibrium of the aqueous species was investigated by measuring for 6 h with a time interval between each measurement of 2 min. Each sample was measured in four-plicate. The filled rotor with the cells was tempered to 20 °C for 1 h before the start of the experiment.

For the determination of the time-dependent development of the aqueous species, the AUC measurement data were divided into three packages each of them containing 50 individual scans over a time period of 16.5 min with a time increment of 20 s. These data were evaluated using the two-dimensional spectrum analysis (2DSA) with 50 Monte Carlo (MC) iterations⁴⁰ in UltraScan III version 4.0, revision 6577 for Linux.⁴¹ The 2DSA data evaluation steps were performed using the UltraScan-in-a-Box platform by AUC Solutions, Houston, TX. These evaluations were performed with a determined, averaged density of 1.61 g/ml of the sample in the aqueous phase of C₃S suspension after 22 h hydration time and the density and viscosity values of water at 20 °C. This average density stems from the density distribution determined using the solvent density variation method via sedimentation velocity experiments (see the supplementary material part 1).

The experimentally determined values from the 2DSA-MC method [s, D, and c (the partial concentration)] and the derived values from s and D (d_D, ρ_D, M′ and f/f_sph) for each detected species with a concentration equal to or higher than 1% are presented in Table S1 for the aqueous phase of C₃S suspensions under controlled conditions and Table S5 for the C₃S pastes without control of the aqueous phase. Some of the found species were detected just once (with a standard deviation of 0) from four-plicate in the 2DSA-MC evaluation method. These species were eliminated for further calculations. Next, the species with similar s-values in the range of 0.3 S, which is considered to be the accuracy of AUC-SV experiments, were combined to one species with the respective average values. Therefore, the species in the range of 0.514–0.829, 1.14–1.46, 1.46–1.77, 2.09–2.4, 2.71–3.03, 3.66–3.97, 4.29–4.6, and 7.11–7.43 S were combined to one with the respective average values. Table S2 for suspensions and Table S6 for pastes show the overview of these selected s-averaged values, which are also plotted in Fig. 3. All these determined species plotted over all hydration times and over the three observation time scan packages form the main averaged 10 s-species groups with their average values. These main averaged 10 s-species groups are shown in Fig. 3 as the dashed lines and in Table II for the aqueous phase of C₃S suspensions under controlled conditions and Table S7 for the C₃S pastes without control. For the main averaged 10 s-species groups with their averaged s_av, D_av, and ρ_D,av values, the exact hydrodynamic parameters were calculated according to Eqs. (3)–(6). Table S4 for the suspensions and S9 for the pastes show these calculated values.

From the hydrated volume (V′) and the hydrated frictional ratio (f/f_sph) of each of the hydrated main averaged 10 s-species, the possible geometry was simulated for basic shapes as a hard body with both major (a) and minor (b) axes and the axial ratios (p) for a prolate and oblate ellipsoid of revolution, a cylinder with the aspect ratio p = L/d > 1 as a long rod and with L/d < 1 as a disk, as well as the diameter of the minimal hydrated sphere (d_sph). The exact procedure is described in the supplementary material part 4. Table III shows the geometrical simulation results for the aqueous phase of C₃S suspensions under controlled conditions and Table S10 for the C₃S pastes without control.

Ion concentrations of the aqueous phase of C₃S suspensions and pastes were measured by inductively coupled plasma optical emission spectroscopy (ICP-OES, Horiba ActivaM, Jobin Yvon) at λ = 317.933 and 373.690 nm (Ca) and λ = 251.611 nm (Si). The limit of detection was 0.07 µmol/l for Si, and the limit of quantification was 0.2 µmol/l for Si.

The time-dependent development of the ion concentrations of the aqueous phase during the hydration of C₃S is shown in Fig. 1(a) for two experiments. For the control of the calcium concentration of the aqueous phase, in situ measurements of the electrical conductivity (EC) were conducted. The EC values determined by ex situ measurements with a different probe show only slight variations (9.4 ± 0.6 mS/cm). Consequently, both pH and calcium ion concentrations are nearly constant (pH = 12.58 ± 0.03; [Ca] = 22.8 ± 1.4 mM). In contrast, the silicon concentration in the aqueous phase varies. A first increase to 40–45 µM is observed after 10 min of hydration caused by C₃S dissolution, which is followed by a drop after 1 h of hydration. Thereafter, a slight increase in silicon concentrations is analyzed, which ends with a drop of these values after 3 h of hydration. This decrease continues until 24 h of hydration.

The plot of the ion concentrations of silicate against calcium in Fig. 1(b) underlines that the critical supersaturation with respect to portlandite ([Ca] = 30–36 mM⁴²) has not been reached. Instead, the concentrations start at the curve that is characteristic for hydrating C₃S and associated with metastable C–S–H⁴³ and changes toward the curve of stable C–S–H⁴⁴ with low variations of calcium ion concentrations. Therefore, the aqueous phase composition proves the C–S–H formation from supersaturated solutions (consumption of silicate ion concentration) without the precipitation of portlandite (calcium ion concentrations below the supersaturation with respect to portlandite).

Analytical ultracentrifugation (AUC) proved to be a key technique in the detection of prenucleation clusters.⁶ Since it has Angström resolution in particle size and can detect species well below a nm in size.^46,47 Consequently, the C–S–H formation is analyzed in more detail by AUC in the following. Basically, the sedimentation coefficient and the diffusion coefficient distributions are determined by AUC in the performed sedimentation velocity experiments. From the diffusion coefficient, the frictional ratio f/f₀ is calculated that reflects the friction of the species compared with a sphere. For this, a sample density was determined by using the solvent density variation method via sedimentation velocity experiments, which is 1.61 g/ml in our calculations. The details on this density determination can be found in the supplementary material document (Sec. I). In Fig. 2, the relative concentration of aqueous species in dependence on the sedimentation coefficient as well as the diffusion coefficient is plotted exemplarily for the aqueous phase sampled after 1 h of C₃S hydration for the scans 1–150 (a), 1–50 (b), 50–100 (c), and 100–150 (d).

Figure 2(a) shows the analysis when all scans (1–150) are evaluated. It can be seen that the detected species have a sedimentation coefficient between 0.2 and 2.5 S, whereby the species with a sedimentation coefficient of 0.2 S (ions and/or oligomers) dominate. When only scans 1–50 are examined [Fig. 2(b), 0–16.5 min], the sedimentation coefficient differs from the consideration of all scans in Fig. 2(a). Here, the sedimentation coefficient varies in the range between 1 and 10.5 S, which is caused by different species dispersed within the aqueous phase. At the same time, the diffusion coefficient changes for these individual species indicating that these species have different shapes/hydration properties. Although species with a sedimentation coefficient of s < 1 S dominate the distribution in scans 50–100 (observation range between 16.5 and 33 min) and 100–150 (observation range between 33 and 49.5 min), other species appear in Figs. 2(c) and 2(d). At the observation period between 16.5 and 33 min [Fig. 2(c)], non-dominant species (the partial concentration below 1%) with s = 2.5 S, s = 5 S, and s = 8 S were detected, whereas at the observation range between 33 and 49.5 min, species with 1–2.5 S as well as 5 S are observed [Fig. 2(d)]. Also, the diffusion coefficient is different for the species observed for the different scan times. These results show that we observe larger transient species at the beginning of the experiment in the first 16.5 min (Scans 1–50, Fig. 2(b)), which disappear at longer observation times. Because we observed transient species, we separated the data in three packages as described in the following.

In Fig. 3(a), the results of the AUC investigations of the aqueous phase of C₃S suspensions hydrated under controlled conditions for 0.5, 1.0, 3.0, 4.5, 6.0, 15.0, 18.5, 21.5, and 24.0 h are plotted for the observation periods between 0 and 16.5 min (P1), 16.5–33 min (P2), and 33–49.5 min (P3). The full dataset for all detected species in P1–P3 is available in the supplementary material Tables S1(a)–S1(h). For P1 and all investigated hydration times, a multitude of species can be observed ranging from ions (s = 0.2 S), which are the main constitutes of the aqueous phase [Fig. 3(a)], small ion associates (s = 0.6 S), and species in the range of prenucleation clusters (1.4–2.1 S). In addition to the ions, the investigation of the aqueous phase of hydrating C₃S revealed the presence of larger nanoparticles (2.1 ≤ s ≤ 10.4 S). This result was obtained for all investigated samples within 24 h of hydration, although some particular species were not detected in every sample. The detection of the species is dependent on the observation period. The largest species are observed at the fastest observation time between 0 and 16.5 min after sampling (P1). When the aqueous phase is analyzed 16.5–33 min after the sampling (P2), the large species that were detected at 0–16.5 min are not present in the aqueous phase anymore showing that they are transient and must have reacted, grown, or aggregated further to an extent that they were not detectable anymore by AUC. Two possibilities for this exist, which we cannot distinguish on basis of the AUC data. The first possibility is that some species grow/aggregate/react so fast that they form species with sizes approaching the range of a few hundred nm, which would immediately sediment to the bottom at the here applied high centrifugal fields (280 000 g), being already high enough to sediment ions. The second possibility is that some species grow/aggregate/react slowly but continuously, which would continuously increase their sedimentation velocity so that they smear out in the detection as individual species in the determination of the sedimentation coefficient distribution.

At a later observation period between 33 and 49.5 min (P3), the detected species are even smaller than that in P2. Therefore, the AUC experiments show the dynamic nucleation and growth process of C–S–H. Really large species were not detected at all, and the best chance to observe larger species in the nucleation and growth process is the observation of the early scans (P1). The larger species only observable in P1 are not visible when all experimental scans are taken into account (1–150) because they are suppressed in the evaluation by the majority of smaller species like ions present in all scans. We want to note that the two smaller species s1 and s2 were only rarely detected in P1 because the sedimentation time was not yet sufficient to allow for detectable sedimentation of ions or small ion associates. Despite the dynamic situation with respect to species growth and aggregation, the selected time intervals were sufficient to detect the presented species with statistical confidence.

What also becomes evident from Fig. 3(a) is that regardless of hydration time, the same species were observed (s1–s10) for all hydration times except 4.5 and 6 h for an unknown reason. Since all the shown hydration times were investigated by individual AUC experiments, this shows that the detected species are reproducible in terms of their sedimentation coefficient spanning the range from ions (s1) via ion oligomers (s2), prenucleation clusters, and liquid droplets (s3–s7) to larger species like nanoparticles (s8–s10). We want to note here that in the case of highly dynamic species like prenucleation clusters, average values will be detected by the relatively slow AUC method.

The aqueous phase of C₃S hydrated in the form of a paste (l/C₃S = 0.5) was additionally investigated by the means of AUC. This serves as an indication, if, with respect to the C₃S suspension experiments at l/C₃S = 50 in Fig. 3(a), the same or other species are detected. The experiment was repeated one time. Because of the limited amount of aqueous phase, the samples were extracted after 10, 30, and 60 min of hydration. The results for different observation periods are shown in Fig. 3(b). Comparable results were obtained, and although fewer species were detected in comparison to the suspension experiments, the same ten species were detected.

AUC reveals that the aqueous phase contains the majority of the ions (s = 0.2 S). Additionally, the presence of ion-clusters (0.5 ≤ s ≤ 2.1 S) and larger nanospecies (2.1 ≤ s ≤ 10 S) was detected. This result is observed for all samples and hydration periods. Therefore, the results from suspension experiments are supported by the paste hydration experiments.

When looking at the partial concentrations of the different species shown in Fig. 4, we can clearly see a dominance of the small species (ions and ion aggregates) detected in P2 and P3, which make up mostly >80% partial concentration in that experiment. Only in P1 were larger species detected, but their partial concentration is typically well below 10% showing that the prenucleation species and nanoparticles/droplets are only present at low concentrations but in multiple different species.

However, the larger species have diameters between 4 and 8 nm (Fig. 5), which is typical for prenucleation clusters and small nanodroplets.⁶ We also observe larger species with sizes between 10 and 70 nm. Very likely, also larger species were formed, but they could not be detected due to their transient character.

To determine if the species are dissolved, liquid or solid, we determined their density as plotted in the supplementary material Fig. S3 since density is a good indicator. Although a large number of species was detected even for the paste, the values for each detected species in Fig. S3 do not show an evident trend besides that densities between 1.1 and 1.6 g/ml were found. Much clearer information can be found for the averaged values for each species as is presented in Table II below. The data show that we observe species with a very low density of (1.00–1.06 g/ml, s4, s6, and s7), which is almost equal to that of the solvent (ρ_H2O = 0.99821 g/ml). All other species have considerably higher densities of 1.28–1.45 g/ml for s1–s3 and 1.38–1.61 g/ml for s5, s8, s9, and s10.

The larger species have considerable molar masses ranging from 3 × 10⁴ to 9 × 10⁷ g/mol, whereas those of the small ion or ion oligomer species are small with molar masses only between 200 and 1200 g/mol (Fig. 6). Some species with masses in the range of 1 × 10⁴ g/mol–3 × 10⁴ g/mol typical for prenucleation clusters are also clearly visible. It is important to take into account that the here reported molar masses are the molar masses of the sedimenting species including its associated hydration water. Therefore, these molar masses can be considerably higher than that of the corresponding anhydrous species, especially for liquid droplets, which contain a large majority of water.

The conducted hydration experiments with the control of the aqueous phase have shown that the experimental setup enables the reaction of C₃S at a constant calcium ion concentration. Thus, the aim of the conducted experiments, i.e., to exclude the presence of foreign ions as well as to avoid the formation of portlandite as the second hydration product of C₃S hydration was achieved in accordance with the work of Nonat et al.³⁶ The ion concentration measured by ICP-OES was determined for different hydration periods and showed the formation of C–S–H from supersaturated solutions indicated by the decrease in silicon concentration at constant calcium concentration. Therefore, the data obtained by AUC can clearly be related to C–S–H formation, which leads to the detected decrease of the degree of supersaturation with increasing hydration time of C₃S in accordance with earlier findings.^33,45 It should be noted that the ion concentrations analyzed by ICP-OES are the total concentrations without separation into different species because the aqueous phase was treated after extraction from the suspension with HNO₃ to avoid precipitation reactions in such supersaturated solutions that may interfere the analysis.

The data presented above in the “Results” section clearly show that all detected species belong to one of the ten groups as identified via the sedimentation coefficient in Fig. 3. This enables us to take the average sedimentation and diffusion coefficients s, resp. D as the main experimental data to better recognize the trends in our data. Since we observe the same species independent of the hydration time, the groups of scans P1–P3 and whether we look at the aqueous C₃S suspension or the supernatant of the C₃S paste, we do not take these into account as a variable since, obviously, the species involved in C–S–H nucleation and growth are the same. Therefore, it is possible to average all data with a sedimentation coefficient belonging to the groups s1–s10. These data are presented in Table II.

Before we start to discuss the results in Table II in detail, it is important to consider potential errors, which are made by the calculation of derived quantities from the experimental data. The directly experimentally accessible quantities in Table II are the sedimentation coefficient s and the diffusion coefficient D, which are given as averages from multiple species as already mentioned before. The sedimentation coefficient s is the primary quantity from AUC experiments and can be determined with an accuracy better than 0.3 S, even for very complex mixtures with >20 co-sedimenting species.⁴⁶ We see in Table II that this is met for all species except species s7. Therefore, the error caused by s in further calculations can be considered to be small, and we do not take s further into account here. A parameter, which is more error prone than s is D, since it is, in principle, derived from the broadening of the sedimenting boundary, which is complex to determine in a multiple species mixture, especially if many species are very small as is the case in our investigated samples. We can see in Table II above that the statistical errors for D can be rather high in the range of 1%–32%, the biggest errors being detected for s3 (32%) and s6 (29%). Therefore, we have investigated how these statistical errors translate to all relevant derived quantities by calculating them for the average value as well as those +/− the error limit (Table S3). We can see that the errors in the derived quantities are well visible, but the important point is that even with the given error intervals for the derived quantities, they still differ significantly so that differences between the ten detected species can be discussed, which is a prerequisite for the following discussion.

We can see in Table II that the by far dominant species are hydrated ions with a molar mass of 400 +/− 170 g/mol. This shows that we deal with simple ions like hydroxide ions and hydrated Ca²⁺, which contains 6–8 H₂O in the first hydration shell and 4–10 in the second hydration shell.⁴⁸ corresponding to molar masses of 220–364 g/mol as well as with larger ions like silica oligomers or possibly calcium–silicate complexes.⁴⁹ The size about 1 nm also indicates larger species than simple ions since for CaCO₃ prenucleation clusters (PNCs), the hydrodynamic radius of the free ions was found to be 420 pm.⁶ However, since AUC cannot separate several ions from each other anymore, the species s1 is an average over all ions/oligomers in solution. In a previous study, the diameter of the critical nucleus was determined to measure 1 nm⁴ and is, therefore, in the size range of s1 that we discuss as ions/oligomers. Since diameter of the critical nucleus is dependent on the degree of supersaturation,⁵⁰ we can calculate this value according to the approach in Ref. 4. With this, the diameter of the critical nuclei for our aqueous phase composition (Fig. 1) measures 1.7 nm. This value is still in the range of the ions/oligomers we have detected. However, the values that we have determined are always the species plus the surrounding water molecules. As it was found that hydration water plays a significant role in nucleation¹⁴ and a molecular mass of 400 +/− 170 g/mol is too small for nuclei, we cannot confirm the value of the critical nucleus in Ref. 4.

The next bigger species s2 already has a molar mass of 2100 g/mol, which is in the size range of the 4000 g/mol reported for CaCO₃ prenucleation clusters.⁶ However, since molar mass of the ions/oligomers s1 is already 400 g/mol, species s2 could also be an ion associate or larger oligomer. An indication of this is also the density of 1.44 g/ml, which is almost equal to that of s1 (1.45 g/ml). On the other hand, for CaCO₃ PNCs,⁶ a density of 1.48 g/ml was found also agreeing well with our analysis. The next bigger species s3 can be identified as prenucleation clusters with a molar mass of 1.7 × 10⁴ g/mol. Their density of 1.28 g/ml is considerably lower than that of the ions/oligomers s1.

Species s4, s6, and s7 distinguish themselves drastically with respect to their density of 1.00–1.06 g/ml, which is almost identical to that of the solvent water (0.998 21 g/ml). The interpretation is obvious that these species must be liquid nanodroplets with sizes of 12 nm (s7), 24 nm (s6), and 60 nm (s4). They have huge molar masses of 5.2 × 10⁵ g/mol (s7), 4.9 × 10⁶ g/mol (s6), and 7.0 × 10⁷ g/mol (s4), and with respect to their very low density, these droplets must mainly consist of water. This is different for the dense liquid phase reported for proteins⁵¹ or small organic molecules.⁵² However, the nucleation of liquid droplets from PNCs²⁶ by crossing the bimodal, and thus, reducing water mobility²⁴ was reported for CaCO₃ PNCs, a system that is close to the one under investigation in this study. We appear to observe an analogous phenomenon here and three different average droplet sizes, which are likely species in a coalescence scenario of growing droplets. We can speculate that the three different droplets consist of the known three different types of silicate oligomers (H₄SiO₄, H₃SiO₄⁻, and H₂SiO₄²⁻), whereby at the pH of 12 and above, as in our study, we mainly expect H₃SiO₄⁻. Further studies are needed to evaluate the composition of the droplets. Droplets/spherical structures of C–S–H with sizes around 50 nm were already reported in the literature, but only when stabilizing polymers are added.^7,53 Liquid droplets are well known for organic molecules in the form of the two-step nucleation mechanism, which was first theoretically predicted⁵⁴ and then observed for not only proteins^51,55 but also organic molecules and other substances.⁵² In this mechanism, first, a dense liquid phase with dimensions in the μm range is formed by phase separation in which a crystal grows in a second step. The low molecular weight molecule Ibuprofen was found to also form a dense liquid phase as proven by ¹H-NMR PFG-STE self-diffusion experiments, but with a remarkably small intermolecular distance between the individual molecules (determined by ¹H–¹H NOESY NMR). This distance is almost as small as that in the crystal, and densification in the dense liquid phase was followed by the generation of a structural order.⁵² Visualization of the Ibuprofen liquid droplets by Cryo-TEM revealed their expected spherical shape, which would correspond to f/f₀ = 1, but their size was in the range of hundreds of nm, which is by far larger than the small droplets observed in this study. However, it may well be that due to the low electron contrast of a liquid droplet of a small organic molecule solution, the very small droplets in the range of a few nm could not be observed by TEM.

The first nucleated solid species is s5 as judged by the density, which increased again to 1.38 g/ml. The molar mass is moderate with 2.1 × 10⁵ g/mol, and this species seems to be the first solid species in a growth series.

Species s8, s9, and s10 are most likely C–S–H particles as deduced from their density of 1.53, 1.61, and 1.61 g/ml, respectively. In addition, an increasing molecular mass [40.8 × 10³ g/mol (s8), 50.2 × 10³ g/mol (s9), and 86.0 × 10³ g/mol (s10)] and size [4.44 nm (s8), 4.62 nm (s9), and 5.53 nm (s10)] in this sequence is detected. As reported,⁵⁶ the simulated density of 11 Å-tobermorite units as representative of crystalline C–S–H is 2.40 g/ml and, therefore, greater than the measured density of our C–S–H-particles (s5, s8, s9, and s10). However, this calculated density⁵⁶ reflecting the unit cell of 11 Å-tobermorite does not account for the water trapped inside aggregates of 11 Å-tobermorite or other C–S–H aggregates. According to the model of Jennings¹¹ and recent findings,⁵⁷ it is conclusive that such aggregation of C–S–H occurs. As such, our study gives additional¹³ experimental evidences that such C–S–H aggregates are formed. Moreover, the data indicate that the structures release water molecules during their aggregation/growth, which results in an increase in the density as well as the molecular mass. However, it is very likely that the detected structure is amorphous.

Table III reports the experimental data of the ten species, and simulation results regarding the shape and size of the possible geometries of those species can be derived on that basis. Species s1 (ions, oligomers) can be regarded spherical, same is expected for s2 and s3. The droplets may most probably be spherical (s4, s6, and s7) similar to the observation of the C–S–H clusters formed in the presence of organic polymers.⁷ Vaguer is the discussion of the shape of the hydrated C–S–H (s8, s9, and s10). The morphology of mature C–S–H is dependent on the C–S–H composition (mainly the Ca/Si-ratio).⁵⁸ We may expect needle-like C–S–H for the Ca/Si ratio of 1.7 in our experiments. Such needles/rods may be grown from different sub-crystals such as oblate ellipsoids, prolate ellipsoids, discs, or even spheres or may be grown from rods. All these possibilities are addressed in Table III. Although the sizes of the C–S–H (Ca/Si = 1.7) may differ, the individual rods have a length of ∼100–1000 nm and thicknesses between 50 nm (basis) and 5 nm (top end).⁵⁹ Therefore, all sub-structures could potentially aggregate to those mature C–S–H.

The gathered results of the increasing density of the C–S–H species with hydration time can be seen as stepwise crystallization of the species with lower density to higher density as known as Ostwald’s ripening, which is also observed in Biomineralization.⁶⁰ The transient behavior of C–S–H is already known, which is identified in different Ca/Si ratios as well as stability. Furthermore, the results indicate that the nucleation of solids takes place in a small region of water that contains a critical concentration of nucleating ions. When nucleation occurs in such droplets, the water that is in between the hydrated ions will be released. By this, the density increases with ongoing nucleation. First, amorphous solids can form, which subsequently crystallize increasing their order. All of this is accompanied by a density increase, which we experimentally observe here.

If we take 1 as water and 2 as the solid in the sedimenting species, we can get the amount of water with the reported C–S–H density of 2.6 g/ml (11 Å-tobermorite).⁵⁶ Therefore, the water amounts are 0.988 (s6), 0.961 (s7), 0.668 (s8), and 0.625 (s9 and s10). This means that the majority even of the most dense detected species is still water.

If we assemble our findings in a more global picture of C₃S (cement) hydration, we have to take into account the acquisition time in the AUC as well as the fact that C–S–H nucleates almost exclusively at the surfaces of C₃S (in cement alite, belite).^3,4 The results demonstrated that the detection of the species (except s1, s2, and s3) was only possible when the acquisition time was short. This means that these species are transient, and growth/aggregation processes occur. This is expected because the aqueous phase is supersaturated with respect to C–S–H as shown by Fig. 1(b). However, the observation of heterogeneous crystallization of C–S–H in C₃S (cement) pastes may impact our results in a way that the species beyond s1, s2, and s3 are only present for very short periods before they are approaching the surfaces. Furthermore, the presence of alkalis in the aqueous phase of OPC hydration³ may change either the distribution of clusters or their composition. Additionally, it is unclear how the findings of the present work could be transferred into the case when the aqueous phase is undersaturated with respect to portlandite. In such conditions, it was shown that C–S–H growth is different.²⁷ Nevertheless, the results of our study clearly show that C–S–H crystallization is linked to the formation of pre-nucleation clusters. Therefore, the nucleation of C–S–H follows the non-classical pathway.⁶¹ 

In summary, the mechanism of the C–S–H formation is sketched in Fig. 7.

The present work was aimed at gaining insight into the early stages of C–S–H nucleation and growth, which was investigated by the means of two different series of C₃S-hydration experiments. The first C₃S-hydration experiment was designed to produce C–S–H without the conventionally occurring precipitation of the second hydration product of C₃S, i.e., portlandite. Additionally, the presence of foreign ions was excluded, which may interfere the structure formation of C–S–H. The second series of experiments were designed as proof-of-concept by hydrating C₃S without control under conventional conditions (paste experiments) under additional formation of portlandite. In both cases, the aqueous phase was the subject of the study.

The results show that C–S–H nucleation is characterized by the formation of prenucleation clusters (PNC), of which we found two types. The C–S–H nucleation starts with the formation of droplets having low density due to their high water content. The water in these droplets will be released in different steps so that the density of species increases. By that, C–S–H droplets and amorphous C–S–H will be formed.

The supplementary material contains the experimental data on C3S suspensions and C3S pastes as well as the determination of the density of C–S–H clusters and the simulation background.

The Deutsche Forschungsgemeinschaft (DFG) was acknowledged for financial support of this Project No. 401097244 (CO 194/23-1, LU 1652/35-1). We also thank D. Haffke (University of Konstanz, Germany) for the experimental support, conducting the solvent density variation experiments, and providing us with a LabVIEW program for the calculations of the hydrodynamic and geometrical parameters. The authors also thank L. Dobler (University of Konstanz, Germany) for providing us with a script to export the 3D plot results of the 2DSA evaluation in UltraScan.

The authors have no conflicts to disclose.

T. Sowoidnich: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Supervision (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). D. Damidot: Supervision (supporting); Writing – review & editing (supporting). H.-M. Ludwig: Funding acquisition (equal); Project administration (equal); Resources (equal); Supervision (equal); Writing – review & editing (supporting). J. Germroth: Data curation (supporting); Formal analysis (supporting);Investigation (equal). R. Rosenberg: Data curation (equal); Formal analysis (equal); Methodology (equal); Software (equal); Validation (equal); Visualization (lead); Writing – original draft (equal); Writing – review & editing (equal). H. Cölfen: Conceptualization (equal); Formal analysis (equal); Funding acquisition (lead); Methodology (equal); Project administration (lead); Resources (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available within the article and its supplementary material.