Introduction

Mineral formation from solution is a widespread phenomenon with far-reaching implications for both natural and industrial environments. Since ancient times, humans have strived to control this process to our benefit. A critical factor in controlling mineral formation is the role of additives—small quantities of organic and inorganic molecules—which can significantly influence the different stages of mineral formation1. Nature itself provides numerous examples of additive-mediated mineralisation, where organisms, including humans, regulate bone mineralisation through the introduction of specific additives2,3. Overall, additives play a pivotal role in shaping the outcomes of biomineralisation processes4.

Similarly, numerous crystallisation-based industrial processes heavily rely on additives—for example, to enhance the workability of cement pastes for advanced constructions5 or to control the properties of inorganic materials used in catalysis and energy storage6. Even the manufacturing of low-tech materials like gypsum wallboard is orchestrated through the addition of different types of additives7, while in water treatment, crystallisation inhibitors are essential for preventing scale formation8.

Industries are continuously searching for novel additives to boost productivity and product quality9, often inspired by biomineralisation processes. In response to increasing environmental concerns and regulations, there is an urgent need to replace traditional additives, such as phosphorous-based formulations10, with more eco-friendly alternatives. To continue progressing in this area, a comprehensive understanding of how additives influence mineral formation at the nanoscale is essential for the targeted development of more sustainable additives.

Although detailed models explain the influence of additives on crystal growth, their impact on the initial stages of mineral formation, such as supersaturation and nucleation, remains a black box. This gap in understanding is further accentuated by the mounting evidence that nucleation pathways might involve multiple steps, challenging the classical view of single-step nucleation. For example, multistep nucleation pathways have been identified for important natural and industrial minerals like gypsum11,12,13,14, calcium carbonate15,16,17, calcium silicate hydrate, the main binding phase of cement18,19,20, and portlandite21,22.

These multistep pathways involve supra-ionic clusters, larger than simple ion pairs, during the prenucleation stage15. These precursor species, commonly referred to as primary particles or prenucleation clusters (PNCs), have structures that differ from the final crystalline phase15,23. The concentration of the prenucleation species, rather than the supersaturation with respect to the stable phase, appears to be the critical parameter controlling the onset of nucleation16. Identifying the relevant species for nucleation constitutes a first layer of complexity in defining the role of additives during multistep nucleation pathways. A second layer of complexity arises from the presence of intermediate disordered phases that form through the aggregation of the prenucleation species. These (liquid) amorphous phases transform into the final crystalline phase via a solid-state transition, dissolution-precipitation mechanisms, or a combination of both21,24,25,26.

The ongoing debate about the steps involved in mineral nucleation underscores the need to revisit the role of additives in controlling the process, as most current additive models are based on the classical view of nucleation. Recent studies suggest that incorporating non-classical nucleation concepts could fundamentally change our understanding of how additives influence mineral formation27,28, and contribute to the development of advanced mineral-additive-based materials e.g. refs. 13,29. However, a key challenge in the field has been the difficulty of observing the effects of an additive across all stages of the non-classical pathway simultaneously. Most investigations focus on a single step of the process, leaving the overall mechanism incomplete or ambiguous.

In this study, we address this limitation by employing a multi-technique approach that provides a continuous and holistic view of the entire nucleation process, enabling us to monitor the influence of additives on pre-nucleation clusters, amorphous intermediates, and their transformations within a single experimental framework. Specifically, employed high-energy X-ray scattering (HEXS) and multiple potentiometric probes simultaneously to monitor the nucleation process in situ of two important industrial minerals, portlandite and gypsum, which are well-known examples of systems that follow a non-classical pathway. A co-titration routine was used to gradually increase the saturation degree of the system, enabling us to resolve the different stages of the nucleation process. Moreover, we developed a method to correct the detector response during the scattering measurements, improving the signal quality of highly diluted solutions. The potentiometric data provided a macroscopic characterisation of the chemical speciation evolution, while pair distribution function (PDF) analyses of the HEXS data allowed us to track the structural evolution of the different soluble and phase-separated clusters emerging along the nucleation pathway. Small-angle X-ray scattering (SAXS) data provide insights into the size evolution of the phase-separated particles. In addition to these experimental techniques, we performed molecular dynamics (MD) simulations to complete the understanding at the pre-nucleation stage. The studied additives included trisodium trimetaphosphate (STMP), poly(acrylic acid) (PAA) and phytic acid. These were selected based on a combination of industrial relevance (PAA and STMP), functional group diversity (carboxylate and phosphate groups) and green chemistry principles (phytic acid).

Results and discussion

The multistep nucleation pathway

We conducted co-titration experiments to gradually increase the saturation of the system and induce the precipitation of gypsum and portlandite while monitoring the physicochemical properties of the solution using Ca-ISE, conductivity, pH and turbidity (transmittance) probes (Fig. 1). Typical LaMer curves were observed, initially showing an increase in free calcium concentration due to calcium addition. However, this concentration deviated from the added amount, consistent with previous findings for portlandite22 and gypsum14. This deviation indicates the formation of bound Ca-species within the undersaturated concentration range for both minerals ([Ca] = 23 mM and 15 mM for portlandite and gypsum, respectively), referred to as prenucleation species14,15,22.

Fig. 1: Nucleation dynamics of portlandite and gypsum.
Fig. 1: Nucleation dynamics of portlandite and gypsum.
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Co-titration data of the nucleation of portlandite (a) and gypsum (b), in absence and presence of different types of additives. The drop in the transmittance (pink) and calcium signal (dark blue) are denoted by the letters a and b, respectively (see also Table 1). The dark blue thin solid curve represents the concentration of added calcium during the experiment. All curves represent the average of three repetitions, except for portlandite + PAA, gypsum + phytic acid and gypsum + PAA, as these experiments showed too much variance between repetitions. To maintain clarity, this figure presents only the Ca-ISE and transmittance data, while the conductivity and pH data are provided in Supplementary Fig. S2. Source data are provided as a Source Data file.

Subsequently, a drop in transmittance marked the onset of bulk nucleation, indicating the formation of particles with an interface. While the sensitivity of turbidity measurements to nascent particles is theoretically wavelength-dependent, practical factors such as solvent absorption and minimal impact on the measured induction time limit the benefit of using shorter wavelengths in this system. Thus, we define the onset of bulk nucleation as the distinct drop in transmittance measured at 610 nm, which provides a consistent and valid point of comparison for the processes studied. No significant change in the free calcium concentration slope accompanied this drop, implying nucleation proceeded via the consumption of multi-ionic entities (“bound species”) such as calcium-hydroxide or calcium-sulfate ion pairs/complexes, rather than free calcium ions. This conclusion was further supported by the absence of significant anion consumption detected by the conductivity probe (Supplementary Fig. S2). Therefore, the species formed during the initial stages of the transmittance drop represent the formation of a new phase, either liquid or solid, composed of aggregated prenucleation species. Similar observations have been reported for calcium carbonate30 and strontium sulfate31. Finally, a decrease in the free calcium concentration occurred, along with a decrease in conductivity and, in the case of portlandite, also a decrease in pH. Further analysis, discussed later on, links this to the onset of crystallinity in the system, coinciding with a rapid consumption of free calcium ions as they are incorporated into the growing crystal structure. Thus, the free calcium concentration drop marks the onset of widespread crystallisation, consuming free calcium until an (apparent) equilibrium between the aqueous phase and solid phase is established.

Thus, based on the potentiometric probe data collected during the co-titration experiments, the precipitation pathways of portlandite and gypsum can be delineated into three distinct stages (Fig. 2): (i) the prenucleation stage, which involves association processes of ions into prenucleation species taking place prior to nucleation, even in the undersaturated regime, (ii) the (bulk) nucleation stage, which denotes the moment interfaces of a new liquid or solid phase are formed in the bulk of the solution due to cluster aggregation, and (iii) the crystallisation stage, which corresponds to the concurrent development of crystalline order (evidenced by sharp diffraction peaks) and particle growth (indicated by a rapid decrease in free ion concentration). Stage (i) is primarily characterised by the output signal of an ion-selective probe compared to the amount of the dosed ions and can also be recognised by following the signal of a conductivity probe. The onset of stage (ii) is marked by a decrease in the transmittance signal, while stage (iii) is characterised by a decrease in the ion-selective signal (and a decrease in the conductivity signal), eventually reaching a plateau, which indicates equilibrium between the new and the old phase. We will continue to refer to these three stages throughout the manuscript.

Fig. 2: A schematic summary of the output of a typical potentiometric co-titration experiment of portlandite or gypsum precipitation.
Fig. 2: A schematic summary of the output of a typical potentiometric co-titration experiment of portlandite or gypsum precipitation.
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Based on the signal of ion selective electrode, the dosing rate and a turbidity probe, three distinct stages can be identified: (i) the prenucleation stage, which is dominated by ion association and the formation of prenucleation species, characterised by the output signal of an ion-selective probe compared to the amount of the dosed ions. (ii) the nucleation stage—the formation of new interfaces defining a liquid or solid phase—is marked by a drop in transmittance, and (iii) the crystallisation stage, characterised by a decrease in free ions until an equilibrium is reached.

When repeating the co-titration experiments in the presence of additives, the three characteristic nucleation stages observed in the pure systems of portlandite and gypsum, as described in Fig. 2, were still present. However, each additive impacted one or more steps of the nucleation pathway, leading to notable differences, as summarised in Table 1, and discussed in detail below. For instance, in the case of portlandite, PAA and STMP significantly delayed the final transmittance drop (the drop that is associated with a subsequent decrease in free calcium concentration), effectively slowing down precipitation. Both STMP and phytic acid induced a two-step drop in the transmittance (for phytic acid see Supplementary Fig. S3a), whereas the presence of PAA resulted in a more gradually decreasing transmittance signal (Fig. 1a). In the gypsum system, PAA and phytic acid greatly delayed the drop in the transmittance and free calcium concentration, while the shape of the transmittance signal remained largely unchanged with respect to the pure gypsum experiment (Table 1 and Fig. 1b). In contrast, the presence of STMP produced a transmittance and free calcium curve similar to that observed in the pure gypsum case.

Table 1 Overview of the different characteristics of the potentiometric measurements of portlandite (port) and gypsum (gyp) precipitation in the absence and presence of 50 ppm of additive
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The varying transmittance curves suggest different mechanistic impacts of each additive on the nucleation pathway of portlandite and gypsum. PAA, STMP, and phytic acid each induced gradual or two-step drops in transmittance within the portlandite system, while these effects were absent in the gypsum system. This suggests that the species that formed during the prenucleation stage in the portlandite systems are not the result of interactions between calcium and additives, as such species and their accompanying transmittance decreases would be expected in the gypsum systems as well. These species therefore comprise at least the additive and hydroxide ions, with calcium ions as essential components, as shown by control experiments in which NaOH alone failed to reproduce the observed transmittance decrease (Supplementary Fig. S4). Titrations of a CaCl2 solution into the different additive solutions showed only slight transmittance decreases, comparable to a titration of CaCl2 into water, providing additional support for this hypothesis (Supplementary Fig. S4). Additionally, the turbidity probe is sensitive to species near its wavelength (610 nm), implying that the transmittance decreases in the portlandite-additive systems likely correspond to the formation of species significantly larger than ion pairs or single-ion-additive complexes. We will regard these species as prenucleation species.

In the portlandite-phytic acid system, a slight, almost immediate transmittance decrease was observed, stabilising at 99% transmittance after adding 0.5 mM of calcium (Supplementary Fig. S3 for detailed view). A co-titration experiment performed at a higher phytic acid concentration (500 ppm) revealed a more pronounced immediate decrease in transmittance, down to 78% (Supplementary Fig. S5). This implies that large ion-phytate complexes are forming during the prenucleation stage of portlandite, with their number (or size) increasing as the phytate concentration is enhanced. Despite the strong association between calcium ions and phytate in solution32, the slope of the free calcium concentration remains unaltered with respect to the pure system. This can be attributed to the low concentration of phytic acid in the system (50 ppm), implying it has no significant effect on the concentration of bound calcium species during portlandite nucleation (Table 1). Thus, the combined analysis of the transmittance and free calcium concentration curves indicates that phytic acid induces the formation of species larger than ion-additive complexes, but does not alter the overall nucleation kinetics.

In the portlandite-STMP system, the transmittance experiences a first decrease, reaching 69% transmittance, after the addition of 16 mM of calcium (SI = −0.34) (Fig. 1a). During this initial decline, both the slope of the free calcium concentration and the conductivity signal (Supplementary Fig. S2) remain unchanged, suggesting that the species detected by the turbidity probe are formed by aggregation of already present prenucleation clusters. This is supported by complementary SAXS experiments of (Supplementary Note 4 and Fig. S6), which directly reveal the formation of an intermediate phase via the aggregation of prenucleation clusters. Comparison of infra-red (IR) spectra from phosphate and STMP solutions at varying pH levels suggests that STMP does not form phosphate species at either high or low pH (Supplementary Fig. S7). Consequently, the observed decrease in transmittance cannot be attributed to the formation of calcium-phosphate species. When a higher concentration of STMP (500 ppm) was used, a similar two-step decline was also observed, starting at a lower calcium concentration (8 mM) and reaching a lower transmittance (10%, Supplementary Fig. S5). This indicates that an increased concentration of STMP both accelerates the aggregation of prenucleation clusters into intermediate species (as evidenced by the earlier transmittance drop and the SAXS experiments) and promotes their formation (as shown by the more significant transmittance drop). Eventually, a second and final decline in the transmittance occurs at a slightly higher added calcium concentration than in the pure system (50.5 mM Ca). Importantly, there is no observable time lag between the second drop in transmittance and the drop in free calcium concentration (for both 50 and 500 ppm STMP) (Table 1), thus implying that nucleation and crystallisation occur concomitantly, in contrast to the other portlandite systems. These observations suggest that STMP facilitates an initial association step but hinders further association of the prenucleation species, leading to a slight delay of nucleation (requiring an additional 4.1 mM calcium compared to the pure system). This behaviour indicates that STMP stabilises prenucleation species of a specific size, which must reorganise before nucleation and crystallisation can initiate and further growth can proceed. This reorganisation occurs at a supersaturation level higher than that required in the pure portlandite system (Table 1).

In the presence of PAA, the slope of the increasing free calcium concentration during portlandite nucleation is significantly decreased (Table 1), implying enhanced binding of calcium either through complexation with PAA or by promoting the formation of prenucleation species. Considering that 50 ppm of PAA (Mw~5100 Da) contains 0.61 mM carboxyl groups, and assuming each calcium ion binds to two carboxyl groups33, this would result in 0.31 mM of free calcium being bound. Using the slope of the free calcium concentration (Table 1), it can be calculated that after adding e.g. 20 mM of calcium (towards the end of the undersaturated regime), 10.0 mM calcium would be bound in the pure portlandite system. In contrast, 12.2 mM calcium would be bound in the portlandite-PAA system, resulting in a difference significantly larger than 0.31 mM. This disagrees with the scenario of enhanced binding of calcium through complexation with PAA. The decreased slope of the increasing free calcium concentration observed in the portlandite-PAA system is, therefore, more likely related to the promotion of prenucleation species formation containing more than one calcium ion per two PAA carboxyl groups. Furthermore, the gradual decline in the transmittance signal of the portlandite-PAA system suggests the continuous formation of phase-separated particles, possibly derived from these bound species. Following the initial drop in free calcium concentration, both the free calcium concentration and the transmittance signal decrease more gradually in the portlandite-PAA system than in other portlandite systems (Fig. 1a). Additionally, the lag between the drop in transmittance and the free calcium concentration is considerably larger than in the pure case (Table 1). These findings suggest that PAA promotes the formation of a liquid-like intermediate amorphous phase—commonly referred to as a polymer-induced liquid precursor (PILP22)—by locally concentrating ions and stabilising the resulting phase. This stabilisation delays its transformation into the final crystalline product. Furthermore, PAA also inhibits crystal growth, as indicated by the slower decline in free Ca²⁺ concentration.

In contrast to the varying transmittance curves observed in the portlandite-additive systems, the gypsum system exhibits similar shapes of transmittance curves across all tested additives (Fig. 1), highlighting a distinct mineral-specific effect of these additives. Specifically, phytic acid delayed gypsum nucleation while failing to inhibit portlandite nucleation. This difference may stem from the varying pH levels of the two systems (~12 for portlandite vs. ~5.5 for gypsum). In the highly alkaline portlandite system, the slope of the free calcium concentration remains unchanged in the presence of phytic acid compared to the pure system. As discussed above, this indicates that phytic acid does not significantly promote the formation of additional PNCs; however, as indicated by the transmittance and HEXS data (see section “Molecular dynamics simulations”), the formation of an intermediate amorphous phase is promoted. For the gypsum system, phytic acid causes a significant decrease in the slope of the free calcium curve. This reveals a strong interaction at the prenucleation stage, leading to an enhanced formation of bound calcium species. PHREEQC modelling confirms that simple Ca-phytate complexation is negligible (8.25 × 10−5 mM, Supplementary Fig. S8) and cannot account for this pronounced effect. Instead, this evidence seems to suggest that the partially deprotonated phytic acid plays a dual role: it first acts as an anionic template to promote local PNC formation, but the bulky structure of phytic acid then sterically inhibits the aggregation of the PNCs into larger particles. This mechanism effectively traps the mineral precursors as stable, nanoscale clusters, a state consistent with both the enhanced calcium uptake and the significantly delayed nucleation, thereby shifting the overall equilibrium towards these non-crystalline bound states.

On the other hand, the relationship between pH and protonation state of STMP does not account for the differences observed between the gypsum—STMP and portlandite—STMP systems, given that the pK3 of TMP−3 is ~0.6534. This indicates that calcium-additive associations alone cannot fully explain the observed effects on nucleation, suggesting that the influence of additives extends beyond simple cation binding, as discussed above.

The delay in nucleation, as indicated by the delay in the transmittance drop, induced by PAA is similar for both gypsum and portlandite nucleation compared to the pure systems (Table 1). However, the gradual decrease in transmittance observed in the portlandite system is not found in the gypsum system, suggesting that PAA does not induce the formation of phase-separated particles during gypsum nucleation and does not significantly promote association processes in the prenucleation stage. In the gypsum system, PAA acts solely as an effective nucleation retarder by impeding the association of prenucleation species. The \(p{K}_{a}\) value of PAA ranges between 4.5 and 6, depending on the ionic strength and background electrolyte33 and the additive was found to be close to fully deprotonated at pH values larger than 1135. This suggests that the protonation state of PAA may be related to its mineral-specific effect, with the more deprotonated state during portlandite nucleation being more susceptible to bind prenucleation species and be involved in association processes.

Bulk structural evolution

In the pure portlandite system, plotting the relative change of the centre of mass against the added calcium concentration revealed a shift to higher reciprocal space values (Fig. 3 and Supplementary Fig. S9), while the centre of mass value remains constant for the water reference. To determine if this shift is due to a displacement of the water signal to higher q values (indicating densification of the water network) or to the emergence of a new diffuse scattering contribution at higher q values (suggesting a structure denser than water), we calculated the variance of the water reflections (related to the width) across increasing calcium concentrations (q range from 1.3 to 3.7 Å−1).

Fig. 3: Changes in scattering of the sample during nucleation.
Fig. 3: Changes in scattering of the sample during nucleation.
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Development of the centre of mass and variance (which is related to the width of the water reflections) of \(I\left(q\right)\) data (\(1.3\le q\le 3.7\) Å−1) for the portlandite systems (a, b) and gypsum systems (c, d). For each system, the shaded region in the same colour as the curve represents the interval between the start of the drop of the transmittance and the start of the drop of the free calcium concentration. In addition, centre of mass and variance developments of single titrations of CaCl2, NaOH and Na2SO4 are shown. See also Supplementary Fig. S9. Source data are provided as a Source Data file.

The results indicate that during the prenucleation stage for both portlandite and gypsum, the shift in the centre of mass is due to the emergence of additional diffuse scattering, which originates from a disordered phase. Given that the co-titration experiments suggest the presence of bound species, these amorphous precursors are most likely prenucleation entities, such as ion pairs, or aqueous complexes. However, beyond the prenucleation stage a plateau in the portlandite system is observed, which is absent in the gypsum system (Fig. 3). This plateau appears during the crystallisation stage (Fig. 2). This difference between portlandite and gypsum nucleation can be ascribed to differences in the evolution of the amount of diffuse scattering present in the systems at increasing added calcium concentrations. The plateau in the centre of mass development indicates that the bulk formation of prenucleation species and/or disordered associated species has ceased or is being directly transformed into Bragg scattering from newly formed portlandite particles. The corresponding plateau in variance further supports the idea of halted prenucleation species development and the onset of bulk reorganisation into an ordered phase (Fig. 3 and Supplementary Fig. S9).

In the gypsum system, diffuse scattering continues to increase (indicated by a continuous shift of the centre of mass), even at the onset of crystallisation, where a sudden decrease of the variance evolution occurs. This suggests a more abrupt transition from disordered species to a crystalline state, representing a bulk crystallisation step that is nonetheless incomplete, as diffuse scattering still contributes to the water reflection. Thus, while crystallinity develops quickly, a significant amount of disorder remains in the aggregates. This observation aligns well with the non-negligible degree of disorder observed in mature gypsum crystals formed from supersaturated solutions12.

A shift in the centre of mass during the prenucleation stage is also observed in the presence of additives for both portlandite and gypsum. Since this shift is consistent across all additives in both systems, the differing effects observed during the prenucleation stage in the co-titration experiments cannot be attributed to changes in solution densification or the emergence of a denser component in solution (cf. scenarios i and ii in Supplementary Fig. S9).

In the portlandite-additive systems, the plateau in the centre of mass development occurs shortly after the free calcium concentration begins to decrease. This behaviour differs from that observed in the pure portlandite system, where a decrease in free calcium concentration is first observed at 55 mM of added calcium, and the plateau in the centre of mass development appears only after the addition of 59 mM calcium. This seems to suggest that the presence of additives accelerates structural reorganisation relative to the pure case. Closer examination of the diffraction data reveals that, in the pure system, all diffraction peaks appear simultaneously, while in the presence of additives, the (011) reflection emerges earlier than the others. This may indicate that additives promote anisotropic growth by selectively inhibiting certain crystallographic directions, leading to earlier development along uninhibited planes such as (011). However, this interpretation remains tentative, as the system retains a predominantly amorphous character at this stage, as evidenced by the limited structural features in the PDF analysis (see section “Molecular dynamics simulations”). Therefore, while the data point to an accelerated and potentially anisotropic reorganisation pathway in the presence of additives, further study is needed to confirm this mechanism.

The presence of PAA leads to a considerably wider centre of mass plateau compared to other additives, suggesting that PAA extends the bulk reorganisation phase, which corresponds with the slight decrease in transmittance. This implies that, during portlandite nucleation, the tested additives are able to extend the prenucleation stage and/or delay nucleation, but they appear to accelerate the onset of widespread reorganisation after the drop in the free calcium concentration, compared to the pure system.

In the case of gypsum, additives delay the observed decrease in variance to varying extents, depending on the additive used. However, these additives do not alter the timing of this decrease in relation to the drop in transmittance or free calcium concentration drop. This observation suggests that the primary effect of the additives on the bulk structural evolution is their ability to delay the processes leading to the abrupt crystallisation step observed in the gypsum system. Therefore, in the gypsum system, the tested additives are able to extend the prenucleation stage and nucleation stage, but do not manage to extend the crystallisation stage, which is always concomitant with the drop in the free calcium concentration.

Nanoscale structural evolution

Comparing the PDF patterns of the prenucleation stage of portlandite (from 0 to 14 mM of added calcium) with the PDF derived from a titration of a CaCl2 solution into water reveals comparable shapes (Fig. 4a), most clearly a peak at 3.2 Å, related to the chlorine-oxygen interatomic distance36. The similarity between the PDFs during the prenucleation stage of portlandite and the CaCl2 titration suggest that the species present during the portlandite prenucleation stage are primarily solutes, akin to those found in a simple CaCl2 solution.

Fig. 4: Prenucleation stages in portlandite and gypsum nucleation.
Fig. 4: Prenucleation stages in portlandite and gypsum nucleation.
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PDF patterns of the prenucleation stages from co-titrations in the portlandite (a) and gypsum (b) system. These are compared to the PDF of a single titration of CaCl2 and the PDFs of different interatomic distances computed from cif files of the crystalline phases of portlandite37 and gypsum55. The vertical dashed grey lines compare the interatomic distances computed from the cif files to the experimental PDFs. Source data are provided as a Source Data file.

Nevertheless, a closer examination reveals subtle yet significant differences between the PDFs of the portlandite prenucleation stage and dissolved CaCl2. Specifically, the PDF of dissolved CaCl2 shows less order beyond 6 Å, suggesting that the portlandite prenucleation stage possesses a more extended short-range order and is structurally more developed. Additionally, the relative intensities of the first two peaks differ; the second peak is more pronounced in the CaCl2 PDF, indicating a higher contribution of Cl-O distances. In contrast, the portlandite systems appear to contain relatively fewer Cl-O than Ca-O distances. This suggests that the species present during the portlandite prenucleation stage are likely larger than single ions or ion pairs, aligning with observations of prenucleation species during the nucleation of portlandite using small-angle X-ray scattering22.

To gain further insight into the structure of these prenucleation species, we performed MD simulations using ions and molecules at a concentration based on previous calculations of the density of portlandite prenucleation species22. The PDF generated from the simulated structure aligns with the experimental PDF, indicating a low level of short-range order during the prenucleation stage (Supplementary Fig. S10). However, the simulated structure appears even less developed than the experimental PDF, with correlation being lost after the first interatomic distance (Ca-O at r ~ 2.4 Å). The partial PDF of Ca-Ca distances shows a peak slightly above 3.6 Å, but this peak does not reappear in the total PDF (Supplementary Fig. S10), implying that the Ca-Ca signal is overshadowed by other interatomic distances and few Ca-Ca distances are found. Additionally, the Ca-O partial PDF shows a large bump around 4.3 Å rather than a distinct peak, further confirming the poor short-range order of the prenucleation species.

During the gypsum prenucleation stage, defined from the start of the experiment until 23 mM added calcium, there was minimal order beyond 6 Å (Fig. 4b). The closest Ca-O distance at 2.4 Å is observed, and a Ca-S distance at 3.2 Å appears as a peak comparable to that observed in the crystalline PDF, implying calcium is bound to sulfate. However, similar to the portlandite systems, the initial Ca-Ca interatomic distance at 4.02 Å is barely discernible. Furthermore, the peak corresponding to the second Ca-O interatomic distance at 4.3 Å is not clearly visible, suggesting that the prenucleation species are solute-like with very limited long-range structure. A previous MD study on gypsum prenucleation clusters12 identified a single Ca-Ca distance and two or three calcium ions per cluster unit. The clusters observed in this study are thus more evolved than the prenucleation clusters detected in our experimental PDFs. This difference can likely be attributed to the direct mixing experiments that formed the basis of the MD simulations12, which reached higher supersaturations compared to our co-titration experiments and do not include data from the undersaturated regime.

Comparison of the PDFs from the prenucleation stages for the portlandite-additive systems with those of pure portlandite reveals no discernable differences (Fig. 4a). For instance, although the peak at 3.6 Å, corresponding to the shortest Ca-Ca distance in crystalline portlandite, shows varying levels of contribution across the different portlandite-additive systems (Fig. 4a), the peak is barely observable and might originate from unreal features in the structure factor. This suggests that the calcium ion from the first coordination shell is either hydroxylated or associated with H2O, rather than being part of a structure including another calcium ion37. Furthermore, the Ca-O peak from the second coordination shell located at 4.3 Å, is barely discernible during the prenucleation stage for all additives. This observation indicates a shorter short-range order than typically expected in crystalline portlandite.

Similarly, in the gypsum-additive systems, only minor contributions are observed to the peak corresponding to the shortest Ca-Ca distance in crystalline gypsum (4.02 Å, Fig. 4b). Additionally, minor shifts are observed in the peaks around 6 Å, associated with higher-order water coordination shells around the solute-like compound38,39. This suggests that the additives have no significant impact on the bulk structure of the prenucleation species and that the poor short-range structure observed during the prenucleation stage of gypsum is not significantly altered by the additives.

The PDFs of the nucleation stage in both the portlandite and gypsum systems, in the absence or the presence of additives, do not show significant differences compared to the PDFs of the prenucleation stages (Supplementary Fig. S12). The negligible difference between these PDF signals indicates that, during the initial drop in transmittance, aggregation occurs without a concurrent ordering step. Thus, for the tested conditions, nucleation in both systems proceeds as a densification step, marked by the clustering of primary species, that continues until crystallisation begins, but does not initially involve the formation of a crystal structure40,41. Consequently, in these systems, additives that delay the transmittance drop delay the aggregation step, rather than delaying the development of crystallinity. It should be noted that under different experimental conditions nucleation and crystallisation could occur concurrently, in which case the behaviour and mode of action of the same additives might differ.

A notable difference between the portlandite and gypsum systems is the significantly larger time lag, both absolute and relative (Table 1), between the decrease in the transmittance signal and the drop in free calcium concentration during gypsum formation (Fig. 5). This delay is observed not only in the pure system but also in systems with additives. It suggests that (i) gypsum nucleation occurs via the consumption of bound prenucleation species, and (ii) these species have a relatively long lifetime, likely contributing to the substantial delay in crystallisation.

Fig. 5: Temporal offset between nucleation and crystallisation.
Fig. 5: Temporal offset between nucleation and crystallisation.
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Time lag between the decrease in transmittance and free calcium concentration observed in the co-titration experiments, for the portlandite systems (a) and gypsum systems (b). Source data are provided as a Source Data file.

PAA is the only additive that effectively increases the time lag, both in the portlandite and gypsum systems. However, the corresponding PDF patterns do not exhibit a significant change with respect to the prenucleation stage (Supplementary Fig. S12), suggesting that the influence of PAA during the nucleation stage is not observable on the bulk structure. This indicates that PAA is the only additive that effectively slows down aggregation processes during gypsum and portlandite nucleation.

In contrast, STMP is the only additive that shortens the time lag in the case of portlandite (Fig. 5a). This effect can be directly related to the ability of STMP to promote the formation of an intermediate amorphous phase, likely similar to the one observed in the additive-free system. Once the driving force for crystallisation becomes sufficiently high, this amorphous phase begins to reorganise and grow, leading to a simultaneous decrease in turbidity and free calcium concentration.

In order to be able to further quantify the results from HEXS measurements in terms of the development of crystallinity, we defined a fitting routine of the scattering data.

In both the pure portlandite and pure gypsum system, crystallinity started to develop concomitantly with the drop in the free calcium concentration (as seen at the right end of the dark blue shaded regions in Fig. 6a, b). This confirms that no reorganisation leading to crystallinity occurs before the crystallisation step, indicating that during the prenucleation stage and nucleation stage, only poorly ordered species are present. This finding is consistent with previous reports, including electron microscopy imaging and in situ scattering data for portlandite22 and gypsum14. In addition to these findings, our results reveal that while crystallinity developed relatively gradually in the portlandite system, the gypsum system exhibited a much more abrupt crystallisation step. This contrast highlights that, despite both systems following a similar multistep pathway, intrinsic differences exist—likely due to the incorporation of structural water in gypsum. This requirement for greater structural reorganisation introduces a higher kinetic barrier, resulting in a pronounced lag phase followed by a rapid, near-instantaneous crystallisation and growth.

Fig. 6: Evolution of the structure factor during nucleation.
Fig. 6: Evolution of the structure factor during nucleation.
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Results of fitting the structure factor \(S\left(q\right)\) to the start of the prenucleation stage and crystalline stage of each portlandite (a) and gypsum (b) system. The structure factor was fitted at increasing intervals of added calcium concentration. For each system, the shaded region in the same colour as the curve represents the interval between the start of the drop of the transmittance and the start of the drop of the free calcium concentration, corresponding to the nucleation stage shown in Fig. 2. Source data are provided as a Source Data file.

By applying a scaling factor in our analysis (see Methods), we quantified the amount of crystalline material formed during the co-titration experiments. The fits to the \(S\left(q\right)\) data indicated that the fraction of crystalline phase remained consistently low across all systems, never exceeding 10% relative to fully crystalline powder references. This low crystallinity reflects not only a limited amount of solid material but also the disordered structural nature of the precipitates. This interpretation is supported by the PDFs, which reveal a marked lack of long-range order. Specifically, the precipitates formed during titration show no significant correlations at interatomic distances beyond r >8 Å, which is contrasting sharply with the well-defined peaks observed in the crystalline reference samples (see Supplementary Fig. S11). These results directly indicate that the crystalline structure of the nascent solids is not fully developed.

To verify that this observation was not an artefact of measuring in the aqueous phase, we conducted control experiments using high-concentration suspensions of mature portlandite and gypsum, analysed under identical HEXS conditions. The resulting \(S\left(q\right)\) and PDF profiles matched those of their respective crystalline powder references (Supplementary Fig. S11), confirming that high crystallinity is indeed detectable in solution. Taken together, these findings demonstrate that the low crystallinity observed in our co-titration experiments is an intrinsic property of the precipitates. A fully developed, long-range ordered crystalline phase does not form within the timescale of the experiment, which aligns with previous reports of structural disorder during the early stages of mineral formation from solution, e.g. refs. 42,43,44.

Figure 6 shows that while phytic acid and STMP induce a crystallinity development similar to pure portlandite, PAA triggers crystallinity formation early on in the prenucleation stage, after 15 mM of added calcium (which is below the theoretical solubility limit of portlandite). The PDF data of the portlandite-PAA system revealed limited order beyond 6 Å, suggesting that the crystalline domains are either very small or present in minimal quantities. However, PAA also delayed the drop in transmittance and significantly increased the time lag between the drop in transmittance and the drop in free calcium during portlandite nucleation, effectively extending the processes leading to macroscale crystallisation. Thus, counterintuitively, PAA induces the development of nanoscale crystalline phases while simultaneously delaying the formation of macroscale particles and macroscale crystallinity.

In the gypsum system, both PAA and phytic acid delayed the appearance of crystallinity, as evidenced by the increased time lag between the drop in transmittance and free calcium concentration (Fig. 5b), as well as the overall delay of the decrease in free calcium concentration. Comparing the effects on the processes leading to crystallisation (time lag) and nucleation (drop in transmittance) relative to the pure gypsum system (Table 1), phytic acid predominantly delays nucleation by retarding the drop in transmittance. In contrast, PAA primarily slows down the processes leading to crystallisation by extending the time lag. STMP has a minimal effect on both crystallisation and nucleation.

The effect of additives on the gypsum system clearly differs from their impact on the portlandite system, which can be attributed in part to the distinct intrinsic nucleation pathways of portlandite and gypsum. The centre of mass analysis revealed that the gypsum system is characterised by an abrupt crystallisation event, whereas the portlandite system undergoes a more gradual transition from prenucleation species to crystalline domains. This suggests that, in the portlandite nucleation pathway, the formation and association of prenucleation species during the nucleation stage represent the “fast step” which is the most challenging step to influence. In contrast, the abrupt crystallisation event of the gypsum system resembles a sudden process (akin to “falling off a cliff”), making it difficult to halt once initiated. Therefore, additives that target the intermediate steps in the gypsum nucleation pathway have a more pronounced effect, as these stages are easier to influence compared to a crystallisation event. In the case of portlandite, effective additives should interact with the phase-separated species to extend the reorganisation event, which occurs more gradually. Alternatively, additives can delay the association of prenucleation species during the prenucleation stage.

The different additive mechanisms observed during gypsum and portlandite nucleation are also partially linked to their respective pH conditions. PAA interacts differently with calcium-based precursor species depending on the pH of the system and on the nature of the clusters. In the high-pH portlandite system, fully deprotonated PAA chains template charged prenucleation clusters, which are then bridged by free Ca²⁺ to yield a (liquid) amorphous Ca-OH phase. Similar behaviour was observed in our previous work using a slightly higher molecular weight PAA (Mw ~6100 Da)22 and aligns with the generally accepted role of PAA in stabilising PILPs in CaCO₃ systems, e.g. refs. 45. These amorphous domains may create localised regions of high supersaturation, promoting the nucleation of small crystalline domains—an effect also suggested for calcium carbonate in the presence of another polymer, polystyrene sulfonate46. As nucleation proceeds, PAA may inhibit the association of these domains either through steric hindrance or by forming stable complexes that resist further organisation into ordered structures47. Conversely, in the CaSO₄ system at pH ~6, PAA exhibits a distinct dual-function behaviour. It primarily templates the formation of neutral CaSO₄⁰ clusters, as evidenced by the markedly reduced Ca-ISE slope. However, because these neutral clusters cannot engage in charge-mediated bridging, PAA stabilises them through steric and electrostatic interactions. This stabilisation hinders further aggregation, extends the induction time, and delays the transition to a macroscopic crystalline phase.

For phytic acid, its protonation state appears to govern its contrasting behaviour in the portlandite and gypsum systems. In the high-pH environment of portlandite (pH 12), fully deprotonated phytic acid forms an amorphous Ca–(OH)–phytate complex, as evidenced by an initial turbidity drop and in situ HEXS data. It directly binds Ca²⁺ and OH⁻, delaying the rise in Ca-ISE and OH⁻ signals until binding sites are saturated (cf. Supplementary Fig. S2c), consistent with theoretical calcium-binding capacities (~0.5 mM Ca at 50 ppm and ~4 mM at 500 ppm of phytic acid). The resulting complexes appear kinetically stable (as indicated by the turbidity plateau) and off-pathway, sequestering reactants without significantly affecting the induction time for portlandite nucleation. Conversely, at pH ~5 in the gypsum system, the partially deprotonated phytic acid32 exhibits a dual role. It first acts as an anionic template to promote the local formation of CaSO₄ prenucleation clusters, which is indicated by the reduced Ca-ISE slope (Table 1). However, its bulky molecular structure then sterically inhibits the aggregation of these newly formed clusters. This two-step mechanism of templating followed by inhibition is what ultimately prolongs the induction time for gypsum precipitation.

The behaviour of STMP cannot be attributed to differences in its protonation state (pk3 = 0.65), which remains similar across both systems. Rather, at high pH, a cooperative mechanism emerges involving charged precursor species, TMP³⁻ and Ca²⁺ ions, leading to the formation of an extended amorphous network (cf. SAXS data, Supplementary Fig. S6). This model is further supported by control experiments showing that aggregation is suppressed when Ca²⁺ is replaced by Na⁺ (Supplementary Fig. S4). Additionally, no aggregation is observed in the neutral CaSO₄ system, where uncharged CaSO₄⁰ complexes lack the electrostatic interactions necessary to initiate bridging with TMP³⁻.

Finally, looking toward future work, it is important to consider the dominant nucleation mechanism when evaluating the effect of additives, as the nucleation pathway may differ between homogeneous and heterogeneous nucleation. In the case of gypsum, a recent study48 suggests that heterogeneous nucleation may follow a pathway consistent with the classical nucleation model, involving the direct formation of a nucleus with properties closely resembling those of the final gypsum phase. If this is indeed the case, the effect of additives could be substantially different.

Overall, these findings demonstrate that the function of an additive is not inherent but is determined by the chemical environment of the crystallising system and its intrinsic nucleation kinetics. By comparing portlandite and gypsum, we show that while pH affects the protonation state of the additive, the key chemical factor is the presence of charged prenucleation clusters. These clusters enable electrostatic bridging, promoting amorphous (liquid) phase formation, whereas neutral precursors are sterically inhibited by the same additives. Moreover, the gradual pathway of portlandite versus the abrupt nucleation of gypsum dictates where additives can most effectively intervene. Together, these insights provide a rationale for moving beyond generic inhibitors toward the design of system-specific additives for industrial applications.

Methods

Co-titration experiments

The following chemicals (≥99% pure) were purchased from Roth and used without further purification to prepare stock solutions using ultrapure water: CaCl2⋅2H2O, NaOH and Na2SO4. The following organic compounds were purchased from Sigma-Aldrich and used in specific experiments: trisodium trimetaphosphate (≥95% pure), phytic acid sodium salt hydrate, poly(acrylic acid sodium salt) (MW~5100 Da by GPC) and dissolved into ultrapure water. Additive and stock solutions specific to each experiment (Table 2) were freshly prepared before each experimental run. As the nucleation of portlandite from solution is sensitive to carbonation, the solutions were freshly prepared with degassed ultrapure water (resistivity: 18.2 MΩ). To investigate the nucleation process of gypsum and portlandite, we employed a titration setup consisting of a 905 Titrando system by Metrohm, two dosing units (Dosino 800) and an 856 Conductivity Module (Fig. 7). To induce nucleation, two stock solutions were slowly titrated at equal rates into a reactor vessel containing an initial solution of 50 mL of ultrapure water (Table 2).

Fig. 7: Schematic view of the experimental setup employed to monitor the evolution of nucleation by combining a potentiometric setup with synchrotron-based high-energy X-ray scattering (HEXS).
Fig. 7: Schematic view of the experimental setup employed to monitor the evolution of nucleation by combining a potentiometric setup with synchrotron-based high-energy X-ray scattering (HEXS).
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The solution from the reaction vessel continuously flows through a capillary aligned with the X-ray beam. A water reference cell (marked in yellow) is used to correct for the detector response.

Table 2 The co-titration experiments carried out in this study, with their addition rates \(v\), the concentration of the additive \({c}_{{additive}}\) if present and the concentrations of stock solution 1 and stock solution 2
Full size table

To investigate the effect of various organic molecules on the nucleation of gypsum and portlandite, the initial solution contained 50 ppm of the specified organic compound. The chemical speciation of the solution was monitored using a pH probe (Metrohm No. 6.0262.100), a conductivity probe (Metrohm No. 6.0915.100), and a combined calcium ion selective electrode (Ca ISE, Metrohm No. 6.0510.100) to measure the free calcium concentration. The moment of phase separation was detected with a turbidity probe (Metrohm No. 6.1115.000, set at 610 nm), which tracked the transmittance of the solution. Before each nucleation experiment, the calcium electrode was calibrated by titrating a 0.5 M CaCl2 solution into 50 mL ultrapure water. The resulting calibration curve was fitted by applying the Nernst equation, upon which the measured voltage could be related to the free calcium concentration, [\({{{{\rm{Ca}}}}}_{{free}}\)], in the solution. This approach assumes that the activity coefficients for Ca2+ are comparable between the calibration and the co-titration, despite a small but unavoidable difference in ionic strength between the two. While this introduces some uncertainty—particularly given the potential formation of unknown prenucleation species that affect ionic speciation—it falls within the experimental error of the titration data. Given these limitations, the assumption is considered acceptable, especially since our primary goal is to compare trends in calcium concentration across experiments rather than to determine absolute values. A calibration protocol to obtain absolute concentrations from Ca-ISE data can be found in the work by Kellermeier et al.14.

A constant stirring rate of 500 rpm was applied to ensure a well-mixed solution. The titration was ceased when a constant signal of the calcium electrode was reached, which corresponds to the presence of the final stable phase. All titration experiments were repeated at least three times to obtain validated results. For the portlandite experiments, the reactor vessel was sealed and a continuous stream of N2 gas was purged over the solution to prevent the in- or out-diffusion of atmospheric CO2.

High-energy X-ray scattering experiments

Experimental setup

After defining the appropriate conditions for portlandite and gypsum nucleation using the titration setup, the experiments were conducted at the ID15A beamline at the ESRF and the precipitation reaction was monitored from start to finish, simultaneously using potentiometric probes and HEXS. Using tubing and a peristaltic pump (pumping rate: 100 mL h−1), the solution of the reactor vessel was continuously pumped through a flow cell containing a polyimide capillary (inner radius: 1.5 mm) where a monochromatic beam of X-rays (63.40 keV) was directed onto the sample (Fig. 7). The scattered X-rays were collected by a DECTRIS PILATUS3X CdTe 2 M detector. Prior to the experiment, two background samples were measured, i.e. an empty polyimide capillary and a polyimide capillary filled with ultrapure water, in addition to a calibration measurement of CeO2 powder.

Data quality improvement and data analysis

Due to the highly diluted solutions of CaSO4 and Ca(OH)2, particularly during the prenucleation stage, the scattering from the nucleating material was minimal, posing a challenge in distinguishing this signal after subtraction of the water background. For example, the integrated intensity pattern \(I\left(q\right)\) of the initial stage of the gypsum nucleation reaction (after adding 23 mM Ca) showed a difference with pure water which was at maximum 0.51 % (Supplementary Fig. S1). Furthermore, we found that the detector response varied during the experiment due to charge accumulation in defects of the CdTe crystals. This posed a problem when comparing signals. To overcome this limitation, we developed a method to measure the detector response variation as a function of time. This enabled us to correct the data and obtain an improved sample signal. Our method consisted of placing a second cell, containing a 1.5 mm sealed polyimide capillary filled with ultrapure water, next to the sample flow cell to serve as a reference cell (Fig. 7). During the experiment, the water reference cell was measured after each 10 sample measurements of 2 s each.

After azimuthally integrating the 2D images resulting from our measurements, we used an extensive data treatment method to pre-process the integrated one-dimensional datasets \(I\left(q\right)\). The datasets were renormalised by the incoming beam intensity to correct for potential fluctuations in beam intensity. Occasionally, bubbles appeared in the reactor vessel or tubing, generating a distorted signal. To address this issue, an intensity correction was applied by applying a moving median filter to the development of the sum of intensities with time. Following this, the data was corrected for the detector response by utilising the integrated intensity data from the water reference cell. For each point in reciprocal space \(q\), a second-order polynomial was fitted to visualise the development of the intensity of the water reference over time. Assuming the intensity values of the water reference stay constant over time, we were able to quantify the detector response. By dividing the integrated dataset of the sample by the fitted polynomial, we could correct for the detector response and improve the data quality.

Further data-analysis utilised the Diffpy package49 to calculate the structure factor \(S\left(q\right)\) and the PDF from the pre-treated integrated intensity data \(I\left(q\right)\). Our analysis also included a method to select the appropriate background scale for each \(I\left(q\right)\) sample dataset, ensuring that the water background was not significantly over- or under-subtracted from the sample. To achieve this, we computed the integral of the squared PDF and selected the background scale where the resulting integral, after background subtraction, was closest to zero50. This approach allowed us to obtain a PDF with minimal contribution from the (water) background.

Upon the correct subtraction of the water background, we defined a method to fit the structure factor. We chose to fit the structure factor \(S\left(q\right)\) rather than the PDF, as the appearance of crystalline peaks was most clearly displayed in the structure factor datasets. Two parameters \({c}_{1}\) and \({c}_{2}\) were fitted to track the similarity of the structure factor at each added calcium concentration to both the structure factor of the prenucleation stage (\(S{\left(q\right)}_{{prenucleation}}\)) and the structure factor of a crystalline, powder phase (\(S{\left(q\right)}_{{crystalline}}\)). Fitting both the contribution of the broad peaks (prenucleation stage) and the sharp peaks (crystalline stage) aids in preventing overfitting of one of these contributions.

$$S{\left(q\right)}_{{fit}}={c}_{1}\cdot S{\left(q\right)}_{{prenucleation}}+{c}_{2}\cdot S{\left(q\right)}_{{crystalline}}$$
(1)

While the structure factor of the prenucleation stage was obtained from the first part of each experiment, the structure factor of the crystalline phase was obtained through filtering the solution after each experiment and measuring the dried powder. Before applying the fit, we formulated a correction factor in the form of the concentration of calcium corresponding to the specific structure factor. By assuming that this method would scale the structure factors to the amount of calcium in the sample, we were able to quantify the result of our fits.

Molecular dynamics simulations

In order to interpret the experimental PDFs and understand the interactions between water molecules, calcium and hydroxide ions during the initial stages of the portlandite nucleation pathway, MD simulations were performed. The MD simulations were carried out using the LAMMPS code51 and the ReaxFF force field52. We employed the Ca/O/H parameters from ref. 53, which were previously validated to accurately reproduce the structural and elastic properties of crystalline portlandite. To model the prenucleation stage, the system composition was based on the species density reported by Madeja et al.22. Three replicate simulations were prepared using Packmol54, each containing 24 Ca²⁺ ions, 48 OH⁻ ions, and 680 H₂O molecules in a 32 Å side box. The three initial configurations were simulated individually and the results analysed together for better statistical sampling.

An NPT ensemble was used, where temperature was maintained at 10 K and then increased to 298 K in 200 steps during 200 ps. Subsequently, the system was allowed for density equilibration for 100 ps, with a Nosé-Hoover thermostat and barostat set with temperature and pressure damping parameters of 20 fs and 200 fs, respectively. Finally, the simulations ran for 50 ns in an NVT ensemble at 298 K with a 0.2 fs time step, utilising the Verlet integration algorithm and a Nosé-Hoover thermostat with a 20 fs temperature damping parameter to maintain constant temperature without pressure control. A sample input file for the LAMMPS code is provided with this paper. Prior to the calculation of the (partial) PDFs with Diffpy49, the bulk water was removed so that the O-O interatomic distances of water molecules would not contribute to the PDF, allowing for a direct comparison with the experimental PDF.