Impact of Mg²⁺ and pH on amorphous calcium carbonate nanoparticle formation: Implications for biomineralization and ocean acidification

Significance

Calcium carbonate biomineralization, crucial for many marine organisms, often proceeds via amorphous calcium carbonate (ACC) as an intermediate. Using a stopped-flow in situ small-angle X-ray scattering setup with $\approx$10 ms resolution, we reveal how magnesium and pH work together to shift ACC nanoparticle formation to the spinodal line, resulting in an exceptionally narrow size distribution. This narrow distribution is essential for forming well-ordered crystals from ACC particles, critical in biomineralization. We also show that small pH changes, such as those from ocean acidification, dramatically impact particle size distribution. These findings highlight the roles of magnesium and pH in controlling ACC formation and underscore the vulnerability of marine calcifiers to environmental changes.

Abstract

Crystallization by amorphous calcium carbonate (ACC) particle attachment (CPA) is a prevalent biomineralization mechanism among calcifying organisms. A narrow, controlled size distribution of ACC nanoparticles is essential for macroscopic crystal formation via CPA. Using in situ synchrotron small-angle X-ray scattering, we demonstrate that synthetic magnesium-stabilized ACC (Mg-ACC) nanoparticles form with an exceptionally narrow size distribution near the spinodal line during liquid–liquid phase separation. We monitored ACC formation kinetics at pH 8.4 to 8.9 and Mg²⁺ contents of 50 to 80%, observing a 2-order magnitude rise in nucleation kinetics for a 0.1 pH increase and a 6-order magnitude rise for a 10% Mg²⁺ decrease. Within the binodal region, faster nucleation kinetics result in more monodisperse particles, narrowing the particle size distribution by factors of 2 for a pH increase of merely 0.1 and by a factor of 3 for a 10% Mg²⁺ decrease. While the influence of Mg²⁺ on calcite biomineralization is well studied, its effect on Mg-ACC formation and particle size distribution-an essential parameter in CPA-based biomineralization pathways-remained unexplored. These findings highlight the delicate interplay of pH and Mg²⁺ in controlling the kinetics and thermodynamics of Mg-ACC formation, significantly impacting particle size distribution.

Numerous marine organisms, such as algae, sponges, and mollusks, produce hard, mineralized tissues made of calcium carbonate through the process of biomineralization (1). These calcifying organisms play a crucial role in the global carbon cycle by sequestering significant amounts of atmospheric carbon dioxide. The significance of this carbon dioxide sink becomes evident when considering the extensive coral reefs and vast fields of blooming algae, visible even from space. With ocean acidification likely impeding this cycle, there is a threat of a negative feedback loop, where reduced carbon capture leads to increased ocean acidification, further disrupting CO₂ sequestration (2). Understanding biomineralization mechanisms, and more specifically, the impact of external factors on organisms’ ability to form biogenic calcite, is critical for assessing their impact on these complex mineral formation pathways.

Biogenic calcite often comprises intricate, complex crystals that serve as skeletons and protection against predation. Additionally, these crystals can function as materials for locomotion, buoyancy, and even light detection (3). To form such multifunctionality from just a few available building blocks, organisms must exert meticulous control over the nucleation and growth of the biomineral by regulating the physicochemical boundary conditions under which the mineral forms (4). Although synthetic efforts, especially under standard conditions, have yet to succeed in creating similarly sophisticated materials, understanding biomineralization pathways may pave the way for new approaches in forming synthetic, bioinspired materials (5, 6).

A commonly recognized pathway that plays a significant role in shaping biominerals involves using a transient, amorphous intermediate called amorphous calcium carbonate (ACC). This intermediate can be molded into various forms, shapes, and textures (7, 8). While classical physicochemical parameters, such as supersaturation-dependent on concentration and pH in the case of ACC-determine nucleation pathways, it is also recognized that specific additives, both organic and inorganic, play a crucial role in the mineral’s nucleation and growth. Organic additives, particularly acidic macromolecules, have been shown to decrease ACC nanoparticle size by locally increasing supersaturation (9). They can also stabilize ACC and influence polymorph selection during crystallization, such as forming calcite or vaterite (9, 10). Additionally, these additives may become incorporated into the host crystal during crystallization, inducing anisotropic lattice distortions (11–13).

Inorganic additives, especially magnesium and strontium ions (14), are found in biogenic calcite with concentrations of up to 45 mol% (in the case of magnesium) often incorporated into the crystal structure (15). Magnesium incorporation into ACC, producing magnesium-stabilized ACC (Mg-ACC), can alter biomineral formation mechanism and control their mechanical properties (16) and significantly enhance the stability of the amorphous intermediate against crystallization for several months, ultimately influencing the final polymorph (17). While this has significant implications for Mg-ACC biomineralization, the exact mechanism remains debated. While pure ACC transitions to its more stable polymorphs via water-mediated dissolution-reprecipitation mechanisms, the incorporation of Mg²⁺ into ACC (Mg-ACC) introduces a different stabilization and transformation dynamic (18), it has been proposed that the relatively higher dehydration energy of Mg²⁺ than Ca²⁺ limits water diffusion, which is responsible for the amorphous to crystalline transformation; however, studies have shown that water diffusion in pure ACC is slower than in Mg-ACC, challenging this hypothesis (19). Additionally, the increased incorporation of hydroxyl groups along with Mg²⁺ ions may contribute to the enhanced stability of Mg-ACC (19). While the stabilizing effect of magnesium has been extensively studied, its influence on the initial formation of Mg-ACC, which often precipitates as nanoparticles, remains unclear. Specifically, magnesium’s effect on particle size and size distribution-crucial for determining ACC stability and polymorph control-has not been thoroughly investigated (18).

Numerous biomineralization pathways can be rationalized within the concept of nonclassical nucleation theory. Unlike classical ion-by-ion nucleation, it describes the formation of crystals from metastable intermediates that can assemble via different pathways to produce the final solid (20, 21). One of these pathways is crystallization via particle attachment (CPA) of transient nanoparticles forming a mesocrystalline intermediate that macroscopically mimics classical ion-by-ion growth (22, 23). CPA is widespread and is observed in calcite-forming species such as corals (24, 25), sea urchins (21), and nacre-forming mollusks (3, 22, 26, 27), but even across phyla in mammalian teeth and plants (28, 29). The formation of intermediate mesocrystals requires a very narrow nanoparticle size distribution. Considering the process as the assembly of a colloidal crystal, successful mesocrystal formation necessitates relative size distributions below 5 to 10% (30). Since CPA is widespread and depends on a controlled and narrow nanoparticle size distribution, we aim to understand how various biomineralization-relevant parameters influence ACC nanoparticles’ size and size distribution.

While the role of Mg²⁺ in biomineralization has been extensively discussed in numerous publications over the past decades, this study presents the influence of Mg²⁺ ions on the nucleation and growth of Mg-ACC nanoparticles with exceptionally low size distributions below 5% under mildly alkaline conditions. We utilized synchrotron-based small-angle X-ray scattering (SAXS, ID02, ESRF) (31) coupled with a stopped-flow device to observe the in situ precipitation of CaCl₂ and Na₂CO₃ in the presence of MgCl₂. This approach allows us to gather information about changes in electron density relative to water (the solvent), enabling the determination of particle shape, size, size distribution, and concentration with an unprecedented $\approx$10 ms time resolution. In situ SAXS has proven to be exceptionally valuable for monitoring nucleation processes, as it is one of the few real bulk, in situ structural characterization methods with inherent statistical significance. This technique has resulted in numerous publications on ACC formation (32–36) and bioinspired nanoparticle growth in general (37–39). Remarkably, we found that nucleation kinetics accelerate dramatically with a slight increase in pH or a reduction in Mg²⁺ concentration. We delineate three distinct nucleation or phase separation regions: i) no phase separation at low pH, ii) phase separation through nucleation and growth (binodal region) at intermediate pH, yielding dispersed Mg-ACC nanoparticles with a narrow size distribution, and iii) quasi-spontaneous phase separation at higher pH, leading to large, polydisperse aggregates (spinodal region).

Results

Mg-ACC nanoparticles were synthesized by coprecipitating CaCl₂ and MgCl₂ at molar ratios of 50:50, 70:30, and 80:20 at a total concentration of 0.1 M with equivalent amounts of Na₂CO₃. Triplicate precipitation reactions were performed at different pH values near the point of no phase separation. Accordingly, Mg-ACC nanoparticles were synthesized at pH values of 8.4, 8.5, and 8.7 for a 50:50 Mg ratio; pH values of 8.6, 8.7, 8.8, and 8.9 for a 70:30 Mg ratio; and pH values of 8.7, 8.8, and 8.9 for an 80:20 Mg:Ca ratio. Fig. 1 shows Scanning Electron Microscopy (SEM) images of ACC nanoparticles rapidly dried with acetone after the synthesis at different pH and a constant 70:30 Mg:Ca ratio. For low pH (8.7 and 8.8), we observe the formation of monodisperse, spherical ACC nanoparticles with average particle diameters of 75 $\pm$ 12 and 20 $\pm$ 7 nm, respectively, whereas at pH 8.9, less particulate and more continuous ACC structures are formed.

Fig. 1.

SEM images of ACC nanoparticles prepared at a constant Mg:Ca ratio of 70:30 at pH 8.7, 8.8, and 8.9 (A–C). Fitted SAXS curves of the last time-point of Mg-ACC nanoparticle formation for Mg:Ca molar ratios of (D) 50:50, (E) 70:30, and (F) 80:20 at different pH. For better visibility, an intensity scaling factor was used, as indicated for each SAXS curve. The obtained particle size probabilities, shown on the Right of each SAXS plot, were fitted with a Gaussian distribution.

To elucidate the formation mechanism and the effect of pH and Mg²⁺ concentration on the nucleation and growth of ACC-NP we employed in situ SAXS, recording data at a fixed sample-to-detector distance for each parameter but varied according to the necessary spatial windows of observation for a given particle size. Thus, we present data from two sample-to-detector distances (10 m and 30 m), covering q-ranges of 0.003 to 0.15 nm^-1 and 0.01 to 0.6 nm^-1. Time series were collected at logarithmic time intervals (highest time resolution achievable: 12.3 ms) to enhance temporal resolution during the early stages of particle formation while avoiding beam damage effects at later time points. The reaction was monitored for not more than 120 s to prevent artifacts from the gravitational precipitation of dense, large particles. For each new set of parameters, the capillary was cleaned with a low-concentration citric acid solution followed by a water rinse. Before each dataset, a fresh water background was taken to ensure no fouling of the capillary, enabling accurate background subtraction. Time-resolved and absolutely scaled complete datasets for all pH values and Mg ratios are presented in SI Appendix, Figs. S2–S4.

All SAXS time series exhibit a rapid increase in intensity within the first milliseconds to seconds, reaching an intensity plateau at low q-values and an intensity decay toward high q-values with a power-law slope between 2.0 and 3.5. This pattern suggests the presence of sparse, transient aggregates of calcium and carbonate, exhibiting iso-structural scattering similar to that of a densely coiled polymer. Consecutively, their density and size consistently increase until distinct form-factor oscillations become visible with a q^-4 intensity power-law decay. This indicates the formation of well-defined Mg-ACC nanoparticles with a sharp solvent–particle interface. We further observe a shift in form factor minimum toward lower q-values with time, indicative of nanoparticle growth.

To retrieve quantitative structural information such as Mg-ACC nanoparticle size and size distribution, we employed an analytical scattering model (SI Appendix, section 2.2) to fit the time-dependent SAXS data. In brief, to model the scattering of the Mg-ACC nanoparticles, we used a fractal form factor model with an exponential size cut-off, which can reproduce the scattering behavior of a solid sphere for a fractal dimension approaching 3. This allows for an analytical description of early, transient structures of low-density and solid ACC nanoparticles within the same analytical model by varying the fractal dimension. To describe the distribution in Mg-ACC nanoparticle sizes, we use a Gaussian distribution. The intensity modulation in the mid-q regime originating from particle interaction is modeled using a hard sphere repulsion structure factor accounting for noninterpenetrability, paired with a square well potential structure factor to account for attraction between Mg-ACC nanoparticles (40). The increase at very low q where hard sphere and square well potentials do not exhibit substantial effects on the scattering behavior, was described with a simple power law scattering model using the scattering behavior of a critical density fluctuation described by Ornstein and Zernicke (41). Using this description, we model the time-dependent scattering behavior of the growth of Mg-ACC nanoparticles for all parameters tested (SI Appendix, Figs. S10–S14). Consequently, we can determine the fractal dimension of the emerging precursors to be between 2.2 and 2.6. Their size ranges from 10 to 50 nm, increasing with higher Mg²⁺ concentration and the acidity of the precipitation solution. We show the SAXS curve at the final time point, where the synthesis was complete, in Fig. 1D–F for all Mg:Ca ratios and tested pH values. To obtain the size and size distribution, we use the probability density of size distributions, obtained from fitting each SAXS curve using the calculated scattering behavior of an ensemble of polydisperse spheres in a Monte Carlo simulation-based approach (42). The resulting probability density function was then fitted with a Gaussian size distribution, as shown in Fig. 1D–F (Right panel). We obtain the mean particle size and relative size distribution (RSD), from the full width at half maximum (FWHM) of the Gaussian distribution as follows RSD $=\frac{0.5·\text{FWHM}·\sqrt{2ln2}}{⟨R⟩}·100\%$, where $0.5·\text{FWHM}·\sqrt{2ln2}=1\sigma$, with $\sigma$ being the SD of the Gaussian distribution. We observe a general trend of decreasing nanoparticle size and size distribution with increased precipitation pH and increasing Mg²⁺ concentration, as summarized in Table 1 which correlates well with size and size distribution obtained from ex situ SEM image analysis (SI Appendix, Table S1).

Table 1.

Relevant parameters for ACC nanoparticle formation at different Ca:Mg ratios and pH values

Ca:Mg	pH	$R$/nm	$k_{\text{Avrami}}$/s−3	$k_{\text{Grow}}$/nm$·$s0.5	$k_{\text{RSD}}$/% s−1 × 10−3
50:50	8.4	$167\pm 28$	$0.09\pm 0.02$	$52.07\pm 16.61$	$5.15\pm 2.02$
	8.5	$87\pm 2$	$(1.76\pm 0.14)\times {10}^2$	$10.31\pm 1.08$	$22.47\pm 3.86$
	8.7	$10\pm 7$	$(4.46\pm 4.80)\times {10}^4$	$0.81\pm 0.80$	$33.18\pm 29.04$
70:30	8.6	$127\pm 30$	$0.15\pm 0.08$	$43.16\pm 4.36$	$45.77\pm 9.43$
	8.7	$110\pm 6$	$24.78\pm 8.55$	$15.71\pm 1.03$	$35.81\pm 8.71$
	8.8	$41\pm 4$	$(4.68\pm 0.63)\times {10}^3$	$1.64\pm 0.18$	$26.96\pm 3.47$
80:20	8.7	$143\pm 40$	$(3.25\pm 1.37)\times {10}^{-6}$	$194.68\pm 52.32$	$3.59\pm 0.91$
	8.8	$157\pm 25$	$0.0028\pm 0.0009$	$106.23\pm 9.34$	$3.59\pm 1.40$
	8.9	$95\pm 10$	$2.26\pm 0.47$	$14.05\pm 0.73$	$0.79\pm 0.19$

The table shows final nanoparticle radius ($R$), Avrami kinetic constant ($k_{\text{Avrami}}$), growth rate constant ($k_{\text{Grow}}$), and radial size distribution change ($k_{\text{RSD}}$). Kinetic values are presented with their SD.

To elucidate the formation mechanism of Mg-ACC nanoparticles, we first determine the kinetics of precursor nucleation and growth. We analytically describe the transformation from phase A, the solution containing all solutes, to phase B, the phase-separated precursor particles. By assuming the presence of only phase A and phase B, we exclude time points at which Mg-ACC nanoparticles are formed. We infer the appearance of condensed Mg-ACC nanoparticles from the time-dependent surface-to-volume ratio (SI Appendix, Figs. S5–S7D) of the formed structures. Initially, less dense, fractal-like precursor particles form, transforming into denser Mg-ACC nanoparticles. This transformation reduces the system’s overall surface-to-volume ratio. The time the S/V ratio approaches a constant value is used as the critical time, $t_c$ marking the appearance of Mg-ACC nanoparticles. The volume fraction ($\mathrm{\Phi }$) of the formed particles was determined following SI Appendix, section 2.3 and normalized to $\mathrm{\Phi }(t=0)=0$ and $\mathrm{\Phi }(t=t_c)=1$ representing the transformed fraction (T). Fig. 2A–C shows the transformed fraction as a function of time for all Mg:Ca ratios for varying pH, showing a clear shift to longer nucleation times with decreasing pH and increasing Mg²⁺ concentrations. The time dependence of the transformed fraction can be analytically described by an Avrami-like equation $T(t)=1-e^{-k_{\text{Avrami}}{t}^n}$, where $k_{\text{Avrami}}$ is a kinetic constant and n is a growth exponent related to the mechanism of nucleation and growth. We obtain the best fits of the kinetic constant $k_{\text{Avrami}}$, summarized in Table 1 for a fixed growth exponent of n=3, observing a general trend of an increase of $k_{\text{Avrami}}$ with increasing pH and decrease Mg²⁺ concentration. In the case of Mg-ACC nanoparticles formed at pH 8.7 with a 50:50 Mg ratio, the phase separation is instantaneous and inadequately described by the employed analytical growth model. This quasi-instantaneous formation of particles is also evident in the SAXS data (SI Appendix, Fig. S2C), where only one intermediate structure could be temporally resolved after $\approx$10 ms, and the reaction was completed within 45 ms.

Fig. 2.

(A–C) Shows the transformed fraction of solutes converted to Mg-ACC precursor particles (proto-ACC) as a function of time. We fit the temporal evolution of the transformed fraction with an Avrami-like kinetics. Mg-ACC nanoparticle radius as a function of time for different Mg:Ca ratios (D–F) and different precipitation pH. The error bars correspond to the nanoparticle size distribution. The plots Below show the growth rate ($\mathrm{\Delta }$R/dt) fitted with $\mathrm{\Delta }R/dt(t)=k·t^{-1.5}$ and the relative nanoparticle size distribution (RSD) as a function of Mg-ACC NP formation time.

To understand the growth kinetics and evolution of nanoparticle morphology, we apply the analytical scattering model to all time points (SI Appendix, Figs. S10–S14). This approach allows us to track the nanoparticles’ radius, relative size distribution (Fig. 2D–F), and fractal dimension over time. By analyzing the change in radius ($\mathrm{\Delta }R$), shown in the Middle of Fig. 2D–F, we determine the growth kinetics of Mg-ACC nanoparticles. Shortly after formation, the initial growth rate is highest and subsequently decreases following a power law. This behavior is well described by the growth equation $dR/dt(t)=k_{\text{Grow}}·t^{-n}$, where $n=1.5$ was globally fitted across all datasets, indicating a congruent growth mechanism.

We observe a systematic decrease in growth kinetics $k_{\text{Grow}}$ with increasing pH, from approximately 200 nms^0.5 to 0.8 nms^0.5, across all Mg ratios. Conversely, growth kinetics increase with rising Mg²⁺ concentration (SI Appendix, Fig. S8A), demonstrating an inverse proportionality between the nucleation constant ($k_{\text{Avrami}}$) and growth kinetics ($k_{\text{Grow}}$). This dependency is expected in a closed system with reactant depletion: Faster nucleation produces more, smaller seed particles, which is reflected in the time-dependent number density (SI Appendix, Figs. S5–S7F). These smaller particles compete for monomers, leading to slower overall growth rates.

Concurrent with nanoparticle growth, we observe a consistent narrowing of the relative size distribution (Fig. 2D–F, Bottom). The kinetics of this narrowing are determined by fitting the time-dependent change in RSD $(-\mathrm{\Delta }RSD/dt)$ with a constant function of the form $-\mathrm{\Delta }RSD/dt(t)=k_{\text{RSD}}$. The obtained kinetic constants ($k_{\text{RSD}}$) are presented in Table 1 and plotted in SI Appendix, Fig. S8B, showing narrowing for all parameters tested at a rate of approximately 0.02% s⁻¹. Such narrowing is expected for a constant width of the particle size distribution relative to particle growth $(\sigma /⟨R⟩)$. This growth process, where the initial seed formation determines the size distribution, is often observed for a monomer addition mechanism of particles growing through the attachment of low-molecular molecules/precursors. In this case, we retrieve a power-law of the radius of gyration (R_G) of 1/6 in dependence of the weigh averaged mass (M_w), which reduces to 1/3 when compared to the molecular weight when ACC-NP grow from precursor particles, which do not significantly contribute to the scattering signal, as seen in SI Appendix, Fig. S1. In the case of Ostwald ripening or particle coagulation, where ACC-NP are mutually consumed, typically different scaling behaviors are observed. This underlines that ACC-NP are formed by a monomer addition mechanism rather than Ostwald ripening or particle coagulation, supported by a constant number density of ACC nanoparticles (SI Appendix, Figs. S5–S7F) and following the scattering model-free analysis by Liu et al. (34) which is described in more detail in SI Appendix, section 2.3.

Discussion

We can thus outline the general formation mechanism of Mg-ACC nanoparticles within the window of spatiotemporal resolution of this experiment as follows: Initially, a nucleation burst forms Ca²⁺/Mg²⁺/CO^2-₃ precursors in the size range of 20 to 40 nm that are characterized by a diffuse particle solvent interface and a lower electron density compared to that of the final Mg-ACC nanoparticles. Earlier studies have identified comparable precursors as a transient, hydrated protostructured ACC, likely originating from a dense liquid phase (43) or prenucleation cluster (PNC) enriched liquid (44) formed through liquid–liquid phase separation (43, 45–49). The protostructured Mg-ACC particles condense with concomitant loss of water (48) to form Mg-ACC nanoparticle seeds with a defined water interface, as indicated by their early stage fractal dimension of the nanoparticles (D_F$\approx$ 3, SI Appendix, Fig. S9), corresponding to that of a sphere with homogeneous electron density distribution. Subsequently, the Mg-ACC nanoparticles grow through a monomer addition mechanism. We summarize our results in Fig. 3, showing an increase of the kinetic constant ($k_{\text{Avrami}}$) with increasing precipitation pH for all tested Mg ratios (Fig. 3A). This directly translates to a decrease in the size of the early precursors formed (Fig. 3B), a decrease in the final mean size of Mg-ACC nanoparticles (Fig. 3C), and a decrease or narrowing in RSD (Fig. 3D). Moreover, regardless of the synthesis parameter, we observed a clear exponential dependence of the kinetic constant on the Mg-ACC nanoparticle and precursor particle size (Fig. 3E), manifesting in smaller sizes for faster kinetics. Additionally, an exponential decrease in relative size distribution with increasing early kinetics is evident from Fig. 3F, showing more monodisperse nanoparticles for faster kinetics. This indicates that the final nanoparticle size, as well as the nanoparticle size distribution, is determined in the early stages of particle formation, where the kinetic constant is determined. We conceptualize these findings following notions of liquid–liquid phase separation and classical nucleation theory. Fig. 4A shows the CaCO₃/H₂O phase diagram in temperature-concentration coordinates proposed elsewhere (50), showing a miscibility gap and a lower critical solution temperature. The green line in Fig. 4A represents an isothermal cut through the stability fields of the solution crossing, with increasing concentration, metastable one-phase, and two-phase (binodal) regions, and an unstable two-phase spinodal region. Their boundaries are defined by the equality of chemical potentials for the binodal lines and by $d^{2}G/d{c}_i^2=0$, the second derivative of the Gibbs free energy with concentration, for the spinodal lines, where $c_i$ is the concentration of ions (anions or cations), shown in the Bottom of Fig. 4A. As a result, the first derivative, $dG/d{c}_i$, as well as the driving force for phase separation, increases progressively between the binodal and spinodal lines. Further, through the classical relation of the volumetric change in Gibbs free energy and the critical energy barrier for nucleation, $\mathrm{\Delta }{G}^{\ast }$, $\mathrm{\Delta }{G}^{\ast }\propto \frac{16\pi }{3}·\frac{{\gamma }^3}{{(\mathrm{\Delta }G)}^2}$, with $\gamma$ being the surface tension, we can state a lowering of the critical energy barrier when going deeper into the binodal region. This translates directly to an increase in the nucleation rate J (and nucleation constant $k_{\text{Avrami}}$ being proportional to J in a thermally activated process through the relation $J\propto e^{-\frac{E_A}{k_{B}T}}·e^{-\frac{\mathrm{\Delta }{G}^{\ast }}{k_{B}T}}$, where $T$ is the temperature and $k_B$ is the Boltzmann constant. The first term corresponds to kinetic barriers (such as ion desolvation and structural rearrangement) with the activation energy $E_A$, while the second term represents the thermodynamic contribution through the Gibbs free energy barrier for nucleation. Concomitant with the lowering of the critical energy and increase in formation kinetics, the size of the earliest experimentally determined precursor decreases as the radius of critical nuclei decreases: $R_C\propto 2\gamma /|\mathrm{\Delta }{G}^{\ast }|$.

Fig. 3.

Effect of Mg:Ca ratio and pH to critical dynamical and structural parameters such as phase separation kinetics (A), proto-ACC radius of gyration (R_G) at emergence of earliest structures (B), mean Mg-ACC nanoparticle radius after completed growth (C), and relative radial size distribution of the Mg-ACC NP (D) as a function of pH. (E and F) show a logarithmic dependence of the mean radius and the size of the first precursor structures (dashed line) and the relative radial size distribution (RSD) with the kinetics of phase separation. Data shaded by green rectangles represent points for nanoparticles formed within the spinodal region, while the rest are formed within the binodal. The rapid kinetics observed within the spinodal region exceeded the resolution limits of our fitting procedure, suggesting the actual values are likely higher than those reported. For completeness, the kinetic fits corresponding to the additional 50:50 Mg ratio at pH 8.8 are provided in SI Appendix, Fig. S15. Increasing magnesium concentrations are marked with a dotted-line arrow.

Fig. 4.

(A) The liquid–liquid miscibility gap (LLMG) is located in the metastable zone of the solid–liquid phase diagram. The green dotted line depicts an isothermal cut through the liquid–liquid stability fields, including metastable one-phase and two-phase (binodal) regions and an unstable (spinodal) two-phase region within the LLMG. While pH increases the concentration of CO^2-₃ inducing precipitation deeper in the binodal/spinodal region (see black arrow), an increase of Mg²⁺ is thought to shift the free energy landscape to the Right (pink arrows) due to the higher solubility of MgCO₃. The Mg²⁺ concentration-dependent change in driving force for phase separation is visualized through the construction decrease of $\mathrm{\Delta }\mathrm{\Delta }$G on the G(c) plot. This shift in the free energy landscape correspondingly shifts the binodal and spinodal lines (pink arrows). While spherical particles are formed via nucleation and growth in the binodal region (B), less particulate continuous Mg-ACC structures form in the spinodal region (C).

Analogously, the exponential dependence of the RSD on the kinetic constant can be rationalized. The probability of a nucleating cluster crossing the critical size and becoming a stable particle, a statistical, thermally activated process, depends exponentially on the height of the energy barrier. Thus, for a low energy barrier, the probability of nucleation is high and all stable nuclei will form over a very confined time interval and grow uniformly to ACC nanoparticles with a narrow size distribution. On the contrary, when the energy barrier is high, the likelihood of nucleation decreases, spreading the nucleation process over a longer period. Consequently, the first nuclei to form will have already grown to a certain size by the time the last stable seeds nucleate, resulting in a broader particle size distribution. This narrowing in size distribution through fast kinetics at high supersaturation was proposed in 1950 by LaMer (51); it is visible in Fig. 3F, where the RSD of particles increases exponentially with decreasing nucleation kinetics. We can thus summarize the thermodynamic driving force variation within the binodal region of phase separation. Following the black arrow on the green line in Fig. 4A, going deeper into the binodal region, we find an increase in formation kinetics concomitant with a lowering in the critical nucleus size (Fig. 3B) and an analogous lowering in the final Mg-ACC nanoparticle size (Fig. 3C). Based on the statistical nature of particle formation, this directly translates to a lower size distribution of the formed nanoparticles.

Following this approach, we consider the effect of pH on the formation of Mg-ACC nanoparticles. Mixing CaCl₂/MgCl₂ and Na₂CO₃ at increased alkalinity shifts the HCO^-₃/CO^2-₃ equilibrium toward the carbonate (HCO^-₃ $\rightleftharpoons {\text{H}}^{+}+$CO^2-₃) through the removal of protons, increasing the carbonate concentration. While LLPS directly from HCO^-₃ has been reported (52, 53), we observe an increase in volume fraction of the formed ACC-NP with increasing pH, indicating that particles are formed directly from the carbonate. Consecutively, an increase in pH corresponds to following the black arrow on the green line in Fig. 4A toward higher ion concentration. There is thus a minimum pH (for all Mg²⁺ concentration) where the CO^2-₃ concentration is too low, and the solutions remain as one metastable liquid phase even after mixing. In the case of Mg-ACC formation at a ratio of 50:50, a 0.1 pH increase to 8.4 moves the system from a one-liquid phase into the two-phase region of liquid–liquid miscibility gap, where thermodynamic equilibrium is then reached by the phase separation into a calcium-rich and calcium-poor phase of equal chemical potentials. Thus, based on the thermodynamic notions introduced above, going deeper into the binodal region reduces the critical energy barrier for nucleation, resulting in faster phase separation kinetics and the formation of smaller, more numerous nanoparticle seeds. As Mg-ACC nanoparticles grow by the uptake of smaller molecular clusters, a larger number of smaller initial particles will lead to a larger number of smaller final particles. This is evident from the reduction in particle size with increasing pH and the increase in nanoparticle number density (SI Appendix, Figs. S5–S7F). Additionally, we find a decrease in RSD from 20% to 5% with a 0.1 pH increment between pH 8.4 and 8.5 in agreement with the above-introduced consideration, proposing a more narrow size distribution for faster kinetics ($k_{\text{Avrami}}$) under more alkaline conditions.

When the pH is further increased to 8.7, we observe only the instantaneous formation of large, nonparticulate structures (SI Appendix, Fig. S2C). The kinetics of this formation are too rapid to be adequately resolved even at a $\approx$10 ms time resolution, making it impossible to describe them using Avrami-like kinetics (Fig. 2A, violet curves) analytically. We have shaded this region of very fast kinetics green in Fig. 3A. Here, ACC nanostructures emerge quasi-instantaneously, forming semicontinuous structures rather than undergoing nucleation and growth, in a spinodal liquid–liquid phase decomposition. While similarly rapid kinetics are observed for the 70:30 ratio at pH 8.8, the results still align with binodal decomposition, as indicated by i) an Avrami constant that remains an order of magnitude lower than the (likely underestimated) spinodal kinetics and ii) the low RSD of Mg-ACC NPs, which is characteristic of binodal phase separation. While previous reports have documented ACC formation in the spinodal region (50, 54), they describe the formation of discrete spherical nanoparticles, differing from the structures presented in this work. This finding is crucial as it highlights the existence of an ideal point in the phase diagram for the formation of highly monodisperse Mg-ACC nanoparticles. This ideal point lies in the binodal region but close to the spinodal line, which marks the boundary between the binodal and spinodal regions.

The effect of Mg²⁺ at constant pH on the phase separation behavior of Mg-ACC nanoparticles is indicated by the dot line arrow in Fig. 3 A and C. A significant decrease in phase separation kinetics is observed with increasing Mg²⁺ concentration. We predict this change to originate from a shift in the Gibbs free energy curve toward higher concentration (pink arrow Fig. 4A) with increasing Mg²⁺ due to lower solubility of MgCO₃ (K_S = 10^-7.8) compared to CaCO₃ (K_S = 10^-9), following the dependency of the free energy of a stable state as a function of solubility product $\mathrm{\Delta }G=-RTln{K}_S$. Consequently, this shift in the free energy landscape of Mg-ACC formation shifts the binodal and spinodal lines to higher concentrations. As a result, at a constant pH, the driving force for phase separation is reduced, resulting in larger particles with a broader size distribution. Additionally, shifting the binodal and spinodal lines to the right with increasing Mg²⁺ concentration can allow a higher pH while remaining in a regime where nanoparticles form by nucleation and growth. In contrast, when CaCl₂ was slowly added to a CO^2-₃ solution, Mg²⁺ had no apparent effect on the final particle size (55). The generally lower concentration of Mg²⁺ ions (10 to 20%) and the difference in the mixing method (slow addition or ultrafast mixing) may explain the origin of this discrepancy.

Whereas we cannot rule out that the formation of Mg-ACC nanoparticles may proceed via a direct nucleation and growth process from solution without prior LLPS, our findings—independent of the formation process—have important implications for particle attachment–based biomineralization processes that require very narrow size distribution. Although nucleation in natural systems is significantly more complex due to confinement effects and the presence of organic molecules, our approach allows us to isolate and examine the impact of specific physicochemical parameters. Adjusting the Mg²⁺ concentration at a given pH makes it possible to fine-tune the phase separation kinetics for nanoparticle formation in close vicinity to the spinodal line but within the binodal region, where the most monodisperse Mg-ACC nanoparticles are formed under the given conditions.

The effect of pH on particle size and size distribution is potentially very relevant in the context of current ocean acidification due to increased CO₂ levels in the atmosphere. This phenomenon has significant implications for biomineralizing organisms that rely on particle assembly pathways for material formation. Classical colloidal chemistry teaches us that particle size distributions above 5% greatly hinder the assembly of colloidal crystals, regardless of the interaction potential (30).

Considering that CPA-based biominerals are formed from transient colloidal crystals through ACC nanoparticle assembly, the importance of maintaining a narrow ACC nanoparticle size distribution becomes evident.

Focusing on Mg-ACC nanoparticles formed at a Mg ratio of 70:30, we observe a drastic slowing of reaction kinetics by four orders of magnitude with a slight acidification from pH 8.8 to 8.7. This change also results in a 100% increase in the RSD (from 10% RSD at pH 8.8 to 20% RSD at pH 8.7). This suggests that even slight ocean acidification could potentially have a tremendous impact on biomineralization pathways that involve ACC nanoparticle-based attachment mechanisms.

While the current ocean pH is 8.2, calcifying organisms can regulate pH in their mineralizing microenvironments. Arctica islandica, a marine bivalve mollusk, maintains an extrapallial pH of 9.2 (56), while stony corals exhibit fluctuations between 7.6 and 8.2 (24, 57). Biomineralizing organisms such as mollusks, corals, and sea urchins generally maintain an elevated pH relative to seawater, even under acidified conditions, where CPA may be relevant (58). Although these organisms can regulate pH, the strong pH dependence of ACC formation in CPA scenarios suggests a significant energetic cost under ocean acidification. Producing ACC nanoparticles with a narrow size distribution at lower pH may require increased proton removal, imposing metabolic demands. Direct pH measurements in the extrapallial space of CPA-reliant organisms, such as mollusks, could clarify the relevance of the pH range observed in our study (22).

However, it is also important to note that calcifying organisms might be able to counteract the effect of ocean acidification by decreasing the concentration of Mg²⁺ present during the formation of ACC nanoparticles. This adjustment could help maintain the desired particle size distribution and ensure the proper assembly of biominerals.

Conclusion

In conclusion, we demonstrate how adding magnesium ions to the precipitation reaction of CaCl₂ and Na₂CO₃ to form Mg-ACC nanoparticles can fine-tune the free energy barrier of nucleation, resulting in Mg-ACC nanoparticles with an extremely narrow size distribution. This was showcased using synchrotron-based SAXS coupled with a stopped-flow device, tracking the formation of Mg-ACC nanoparticles with $\approx$10 ms time resolution.

Our findings are well conceptualized within the framework of liquid–liquid phase separation and clearly show that in the region where particles form via nucleation and growth (binodal region), the kinetics of nucleation increase with increasing pH and decreasing magnesium concentration. This acceleration in kinetics, corresponding to a lowering of the free energy barrier of nucleation, leads to the formation of smaller nanoparticles with a narrower size distribution. However, if the driving force for nucleation becomes too large (too high pH or too low [Mg²⁺]), we enter the spinodal region, where only polydisperse larger structures form quasi-instantaneously, faster than the time resolution of our experiment ($\approx$10 ms). These findings illuminate the potential role of magnesium ions in particle assembly–based biomineralization pathways, prevalent in numerous calcifying species. When considering the particle-based mechanism within the context of classical colloidal crystal formation, there is a size distribution limit of 5% above which the formation of colloidal crystals results in sluggish particle aggregates (30). In our case, such a narrow distribution is achievable only for nanoparticles formed near the spinodal line.

Our research provides a deeper understanding of magnesium’s involvement in biomineralization processes. Traditionally, magnesium is considered to control the stability of Mg-ACC, influence crystallization polymorphs, or improve the mechanical properties of biominerals. We highlight how particle assembly–based biomineralization processes might rely on regulating magnesium content during particle formation to produce nanoparticles with narrow size distributions.

Our results also foreshadow the severe impact that ocean acidification could have on Mg-ACC nanoparticle assembly–based biomineralization mechanisms, showing that a pH decrease of merely 0.1 can double the Mg-ACC nanoparticle size distribution. However, we propose that calcifying species might adapt to such external factors by lowering magnesium content during Mg-ACC nanoparticle formation.

While further experiments at ion concentrations closer to those encountered in biomineralization are necessary, we are confident that our results demonstrate a general trend of the effects of magnesium and pH on the formation of Mg-ACC nanoparticles.

Materials and Methods

Amorphous Calcium Carbonate Synthesis.

All chemicals were used as purchased without further purification. Mg-ACC was synthesized from stock solutions of CaCl₂*2H₂O (Merck, EMSURE) and MgCl₂*6H₂O (Merck, EMSURE) at molar ratios of 50:50, 70:30, and 80:20 at a total concentration of 100 mM, which were rapidly mixed in a stopped-flow device with 100 mM solution of Na₂CO₃ (Merck, EMSURE). Solutions were mixed in a 1:1 volumetric ratio and a total final volume of 0.2 mL. To screen different precipitation pH Na₂CO₃ solutions were prepared at different pH by adjusting with HCl (Merck, EMPLURA). For SEM images, above solutions were mixed at a 1:1 volumetric ratio with a final volume of 20 mL under vigorous stirring with a magnetic stirrer. After 1 min solutions were vacuum-filtered using a Büchner funnel and dried with acetone. To avoid crystallization, samples were rapidly transferred to the SEM and imaged.

In Situ Stopped-Flow SAXS.

In situ SAXS measurements were performed at the high-brilliance beamline ID02 at ESRF - The European Synchrotron in Grenoble, France. The X-ray energy was set to 12.5keV. The Eiger2 4M (Dectris) detector was used for these experiments. To account for different particle sizes, two sample-to-detector distances were used: 10 m and 31 m. This setup allowed coverage of a q-range of 0.003 to 0.15 nm^-1 and 0.01 to 0.6 nm^-1. For the in situ measurements, a stopped-flow rapid mixing device (BioLogic Science Instruments, SFM-400) with a dead-time of 2.3 ms was used. The precise stopped-flow sequence can be found in SI. It featured four syringe reservoirs containing 1) water, 2) Na₂CO₃ solution for the reaction, 3) MgCl₂/CaCl₂, and 4) citric acid solution for cleaning and background acquisition. To ensure reproducibility, triplicates were measured for each parameter. The syringes were connected to a flow-through quartz capillary with a 1.5 mm inner diameter (Hilgenberg open quartz capillaries, 10$\mathrm{\mu }$m wall thickness). To prevent radiation damage that could alter the sample in the illuminated volume and degrade the background due to deposits on the capillary walls, the acquisition time was kept constant and short, even for weakly scattering samples. This sometimes led to suboptimal statistics in the initial stages of measurement. Absolute intensity was calculated from water scattering after subtracting the contribution from the empty capillary. The measured water scattering intensity was compared with the theoretically expected scattering level, derived from water’s isothermal compressibility and electronic density, and a correction factor was applied to all SAXS curves. The experiment, identified as ID CH6826, was allocated three days of beamtime. Time-dependent SAXS data were fitted using the Matlab-based program SASET, with analytical expressions referenced from the SASfit documentation (59, 60).

High-Resolution SEM.

Samples were imaged using the Zeiss Ultra-Plus FEG-SEM at 1-2 keV with 4-4.2 mm working distance without prior carbon coating.

Supplementary Material

Appendix 01 (PDF)

Data, Materials, and Software Availability

Raw scattering data is publicly accessible via DOI: 10.15151/ESRF-ES-1305993932 (61). All study data are included in the article and/or SI Appendix.