Nanoscale kinetics of amorphous calcium carbonate precipitation in H 2 O and D 2 O †

Calcium carbonate (CaCO 3 ) is one of the most well-studied and abundant natural materials on Earth. Crystallisation of CaCO 3 is often observed to proceed via an amorphous calcium carbonate (ACC) phase, as a precursor to more stable crystalline polymorphs such as vaterite and calcite. Despite its importance, the kinetics of ACC formation have proved diﬃcult to study, in part due to rapid precipitation at moderate supersaturations, and the instability of ACC with respect to all other polymorphs. However, ACC can be stabilised under confinement conditions, such as those provided by a nanopipette. This paper demonstrates electrochemical mixing of a Ca 2+ salt (CaCl 2 ) and a HCO 3 (cid:2) salt (NaHCO 3 ) in a nanopipette to repeatedly and reversibly precipitate nanoparticles of ACC under confined conditions, as confirmed by scanning transmission electron microscopy (STEM). Measuring the current as a function of applied potential across the end of the nanopipette and time provides millisecond-resolved measurements of the induction time for ACC precipitation. We demonstrate that under conditions of electrochemical mixing, ACC precipitation is extremely fast, and highly pH sensitive with an apparent third order dependence on CO 32 (cid:2) concentration. Furthermore, the rate is very similar for the equivalent CO 32 (cid:2) concentrations in D 2 O, suggesting that neither ion dehydration nor HCO 3 (cid:2) deprotonation represent significant energetic barriers to the formation of ACC. Finite element method simulations of the electrochemical mixing process enable the supersaturation to be estimated for all conditions and accurately predict the location of precipitation.


Introduction
The crystallisation of calcium carbonate (CaCO 3 ) is an area of great interest, 1,2 especially in biomineralisation, 3 where CaCO 3 can exist as a variety of structural forms and morphologies. The formation of particular CaCO 3 polymorphs is crucial to many global biogeochemical processes, 4 and carbonate mineral formation has been proposed as a safe long-term method for carbon capture and storage. 5 CaCO 3 is also used in a wide variety of commercial products: it is an extender in paints, pharmaceuticals and adhesives, a filler in cement and plaster, and a mild abrasive in cleaning products. The earliest forming, least stable solid phase of CaCO 3 is amorphous calcium carbonate (ACC), a variably hydrated, poorly ordered metastable precursor to more stable polymorphs such as vaterite, aragonite and calcite. 1 While the ability to study and control the nucleation and growth of ACC may provide insight into how control is achieved in biological systems 6 and how polymorphism can be controlled in synthetic crystals, 7 current theories around the nucleation and growth of ACC and its subsequent crystallisation remain controversial, with various intermediates and pathways being suggested. 8,9 Liquid-like forms have been observed in quenched samples recovered from solutions immediately prior to CaCO 3 precipitation, 10,11 leading to suggestions that under certain conditions precipitation may be aided by a liquid-liquid phase separation, in which a supersaturated solution can decompose into a solute-rich phase consisting of ions, ion pairs or clusters and a solute-poor phase. [12][13][14] Above a certain concentration (marked by the spinodal) the solution becomes unstable with respect to this transformation, leading to the rapid formation of a disordered emulsion-like solution structure. 10 The limit of solution stability has been determined to lie between [Ca 2+ ] = 3-4 mM, 15 in agreement with previous reports of a change in the mechanism of CaCO 3 precipitation in this concentration range. 16 There is also experimental evidence for the association of Ca 2+ and CO 3 2À in stable so-called pre-nucleation clusters in both undersaturated and supersaturated solutions. [17][18][19] The formation of such clusters has been supported by molecular dynamics simulations, although there is ongoing debate in the literature about the existence and role of pre-nucleation clusters in the formation of CaCO 3 . 12,13,17,20 Measurement of the water dynamics using THz spectroscopy during precipitation suggests that aggregation of pre-nucleation clusters may be the origin of the liquid-liquid phase separation. 21 Irrespective of whether ACC forms from a dense liquid phase or directly from the mother solution, desolvation of the constituent ions must occur, with desolvation of the cation conventionally considered to be the rate determining step in crystallisation. 22 Given the apparent significance of the solvent in the precipitation of ACC, it is surprising there are no studies comparing the precipitation rates in H 2 O with that in D 2 O. In general, the stronger H-bonding in D 2 O leads to significant differences in its solvation behaviour when compared to H 2 O. 23,24 In the case of ion pairs or clusters, D 2 O would be expected to favour aggregation, and has previously been suggested to decrease the dissociation constant of the ion pair Pb(NO 3 ) + , 25 as well as favouring the exchange of water for Cl À (i.e. formation of an ion pair) in several transition metal complexes. 26 Isotopic exchange also provides an opportunity to examine the role of HCO 3 À in the kinetics of ACC precipitation. While not directly included in the solubility product, HCO 3 À provides a source of CO 3 2À in solution, and appears in clusters simulated under lower pH conditions (though we note the lack of a dynamic equilibrium of the form CO 3 2À " HCO 3 À in these simulations). 27 The enhanced strength of the D-O bond in DCO 3 À stabilises DCO 3 À relative to HCO 3 À , significantly decreasing the acid dissociation constant (pK D a À pK H a = 0.748) 28 and therefore the extent to which it will replace consumed CO 3 2À ions.
Electrochemical methods have been used extensively in the study of inorganic precipitation reactions, usually to report on average properties, such ion activities with ion selective electrodes, in bulk solution. 11,17,29 The use of nanopores, however, allows for convenient analysis of precipitation at the nanoscale by using an applied potential to mix solutions inside a confined volume and monitor the resulting changes in the ion current. Previously, the precipitation of weakly soluble phosphate salts of Zn, 30 Ca, 31 Co, 31 as well as CoCl 2 , 32 and even organic crystals 33 have been studied. We have used this approach to measure induction times for ACC precipitation in the presence of various scale inhibitors. 34 This method has several advantages over other techniques based on bulk conductivity, 35 turbidimetry 16 or (high speed) imaging, 36 as mixing is well defined, occurs on small time (10 À3 s) and length (10 À8 m) scales and is readily reversed (either via dissolution or migration of the particle away from the orifice 30 ) to reset the system for the collection of hundreds of repeat measurements. The fast time resolution allows rapid precipitation events to be quantified, enabling measurements at high supersaturations that other techniques are not able to access easily. This allows experimental exploration of solution conditions closer to the limit of solution stability, where molecular dynamics simulations of CaCO 3 solutions are often performed. 12,14,27 Furthermore, since precipitation in confined volumes stabilises ACC against further crystallisation, 37-41 products formed in the nanopore can subsequently be characterised ex situ, e.g. with Raman spectroscopy and electron microscopy, without further work up.
Here, we have measured the induction times and imaged the products formed from the reaction of a CaCl 2 solution with a solution containing a range of CO 3 2À concentrations (corresponding to a range of pH values) and compared the results between H 2 O and D 2 O. These experimental conditions were further investigated through detailed finite element method (FEM) simulations of the mixing process in order to understand the resulting temporal-spatial changes in supersaturation during these measurements.

Experimental
Single-barrelled quartz nanopipettes, with tip diameters between 20-50 nm were used as reaction centres for the precipitation of ACC. For most studies, the nanopipettes were filled with a solution of 100 mM NaHCO 3 titrated to a particular CO 3 2À concentration and were placed in a bath of 20 mM CaCl 2 (Fig. 1A). All solutions were made up using either 18 ) and K sp represent the activity of Ca 2+ , the activity of CO 3 2À , and the solubility product of ACC, respectively, where K sp is taken to be 3.8 Â 10 À8 M 2 . 17,42 Upon application of the negative tip bias, precipitation occurred, with precipitate filling the end of the nanopipette and blocking the current completely. The distinctive currenttime trace provided a well-defined end point for statistical analysis of many such ion current blocking transients. Significantly, the tip bias could be returned to the positive value to remove the blockage and restore the ion current to the 'open' value. This ability to restore the initial conditions allowed the process to be repeated multiple times in a single experiment across the 3 nanopipettes.
These precipitation and dissolution events were found to have a high degree of reproducibility (Fig. 1B). By monitoring the variations in current as a function of time, the real-time precipitation of ACC in a small, well-defined region of solution was observed. From the current transients, we define the induction time, t ind , the time between creating a supersaturated solution and forming an appreciable amount of new phase, 43 as being the time taken for the current to decrease to 1% of its maximum value following the voltage step to the negative nanopipette potential. As with any practical measurement, this will necessarily include some element of growth time, however we note that by limiting the growth to a few tens of nanometers an upper limit is placed on the contribution of this time to t ind which would be difficult to achieve with other techniques.
Through the repeated precipitation and dissolution of these precipitates, followed by an automated analysis using a Matlab script, we determined the mean induction time and its standard deviation for a variety of conditions. Care was also taken to ensure that repetitive precipitation events were truly independent, by checking that the induction time was independent of the repeat number (Fig. S1, ESI †).
To enable comparison of rate measurements between H 2 O and D 2 O at different CO 3 2À activities, without relying on pH/pD measurement and speciation models, the CO 3 2À concentration was determined spectroscopically for each solution. 44 The protocol is discussed in detail in the ESI † (Section S2). Briefly, the CO 3 2À and HCO 3 À ions show distinctive Raman scattering in both H 2 O and D 2 O solutions. Concentration analysis was conducted by making a solution of 100 mM NaHCO 3 in each solvent system, and titrating it to a high pH with NaOH (or NaOD) until only a CO 3 2À peak (and no HCO 3 À peak) was visible in the Raman spectrum. Through serial dilution, an accurate set of peak areas for a range of concentration values was obtained, from which a calibration curve was constructed allowing solutions of specific [CO 3 2À ] to be prepared by titration with Na 2 CO 3 while monitoring the area of the CO 3 2À peak.
Concentrations determined in this way typically had a 95% confidence interval of AE30%. Nanopipettes were fabricated using quartz capillaries with filaments (outer diameter 1.0 mm, inner diameter 0.5 mm, custom manufactured, Friedrich and Dimmock) using a laser puller (P-2000, Sutter Instruments; parameters of: Line 1: Heat 750, Fill 4, Vel 30, Del 150, Pull 80; Line 2: Heat 650, Fil 3, Vel 40, Del 135, Pull 150) to give a tip opening diameter of approximately 20-50 nm. The electrometer and current-voltage converter used were home built, while the user control of voltage output and data collection was via custom made programs in LabVIEW (2013, National Instruments) through an FPGA card (7852R, National Instruments). Raman spectroscopy was conducted using a Raman microscope (Horiba LabRam HR Evolution) fitted with a charged couple device (CCD) detector and a 488 nm OPSS laser. A 50Â (0.5 NA) objective and 600 line mm À1 grating was employed for mapping experiments with 10 Â 2 s acquisitions averaged per spectrum, giving a spectral resolution of 1.3 cm À1 and a nominal lateral resolution of 595 nm. A 10 mm path length quartz cuvette in a double pass accessory with an 1800 line mm À1 grating was used for measurements in solution with 4 Â 60 s acquisitions averaged per spectrum to give a spectral resolution of 0.34 cm À1 . Pulled nanopipettes were characterized regarding their inner radius and overall probe geometry by scanning transmission electron microscopy (STEM) using a Zeiss Gemini 500 SEM.

Results and discussion
Characterisation of the precipitate The goal of this study was to characterise the effect of pH and solvent on the kinetics of ACC formation. It was therefore necessary to confirm the presence of ACC within the nanopipette after precipitation. Although often unstable with respect to crystallisation into a more stable polymorphs, ACC has been shown to be stabilised when under confinement, 39 and such an environment is provided by a nanopipette. After precipitation was induced by the applied negative nanopipette potential, as summarised in the experimental section, nanopipettes were removed from solution and quickly submerged in ethanol to remove solution left on the outside of the nanopipette and to further inhibit transformation of the ACC.  Fig. 2A-F, false coloured for clarity). This region was not observed in either as-pulled nanopipettes or nanopipettes which had been filled with NaHCO 3 solution and then dipped in CaCl 2 bath solution without electrochemical mixing (Fig. S4, ESI †), and is therefore attributed to the precipitate. While formation of further precipitates along the nanopipette cannot be ruled out, due to the difficulty in imaging through the increasingly thick quartz walls further from the end, the formation of a precipitate at the very tip of the nanopipette is consistent with this region reaching the highest supersaturation and is supported by FEM modelling of the mixing process, vide infra. At lower concentrations ( Fig. 2A, B, D and E), precipitates were consistently observed within the first 100 nm of the tip of the nanopipette, and appeared to completely occlude the nanopipette (light grey arrows). The images were comparable between H 2 O and D 2 O experiments. For the highest concentration ( Fig. 2C and F), in addition to the particles observed in the first 100 nm, a darker region with a curved meniscus is observed further into the pipette (dark grey arrows). The presence of such meniscus-like forms are observed at various positions throughout the first 2-3 mm of all nanopipettes imaged used at the highest CO 3 2À concentrations and are absent from those used in the lower concentrations (ESI, † Section S3 and Table S1). This will be discussed later in relation to the mass transport simulations. Raman maps of nanopipettes used in experiments at CO 3 2À concentrations of 7.7, 16 and 36 mM (in a 20 mM CaCl 2 bath) did not reveal any CO 3 2À -related signals in the region of the nanopipette, as expected due to the small size and low density of the nanoparticles observed in the STEM images. However, Raman spectra from the nanopipette used in the 49 mM CO 3 2À experiment (20 mM CaCl 2 bath) yielded spectra with a single peak at 1080 cm À1 , 45 with no peaks at 711 cm À1 which would have indicated calcite, 16 or at 1043 cm À1 which would have indicated NaHCO 3 , 46 confirming the precipitate is ACC (Fig. S5, ESI †). Mapping over the region of the nanopipette tip showed the 1080 cm À1 signal was present throughout the 35 mm long section studied (Fig. 2G). Thus, at lower concentrations (supersaturations), precipitation is confined to the nanopipette tips, while at the highest concentrations it occurs over a more significant region from the nanopipette end.   positive to negative. An important aspect of these data is whether the growth of the precipitate is under kinetic or mass transport control. This can be assessed by comparing the total flux of ions through the nanopipette during the precipitation (available from the integrated ion current) with an estimate of the total number of ions required to form the precipitate observed in STEM (ESI, † Section S5). At 7.7 mM CO 3 2À the amount of Ca 2+ transferred within the induction time (t ind = 21 s) is 6.77 Â 10 À15 mol, while an upper estimate for the amount of Ca 2+ in the precipitate is 5.52 Â 10 À18 mol, suggesting that mass transport should not limit the rate of precipitation. In contrast, the much shorter induction time (t ind = 18 ms) at 49 mM CO 3 2À means the amount of Ca 2+ transferred is only 8.79 Â 10 À18 mol, while the precipitate is estimated to require 2.60 Â 10 À18 mol, suggesting that growth will be under mixed kinetic and mass transport control under these conditions. By pulsing the potential between mixing/blocking and unmixing/unblocking regimes it was possible to record 4100 induction times for each pH, across several nanopipettes. The huge influence of CO 3 2À concentration on the induction time is confirmed in histograms of the repeat measurements (Fig. 4).

Kinetics of ACC formation
As expected, an increase in CO 3 2À concentration, which leads to a higher supersaturation upon mixing, results in a decrease in induction time. When Àlog(t ind ) is plotted against log[CO 3 2À ] directly (Fig. 5A) the data reveal a third-order dependence of induction time on [CO 3 2À ]. A similarly high reaction order of 4 was reported previously for the induction time for vaterite crystals. 29 However, it is generally more insightful to study the relationship between the supersaturation, S, and t ind as this can be compared to theoretical predictions based on various precipitation mechanisms. 47 Where the nucleation time either dominates, or is comparable to the growth time, the relation is expected to hold, where T is temperature and A and B are constants, such that log t ind is proportional to log À2 S. 47 In contrast, were the growth time dominates the induction time, assuming mononuclear growth, the equivalent expression becomes where C and D are different constants and log t ind is instead expected to be proportional to log À1 S. 47 To determine if these two cases could be resolved graphically, log t ind was plotted as a function of both log À1 S* (Fig. 5B) and log À2 S* (Fig. 5C), with estimates of maximum supersaturation, S*, based on the perfect mixing of the starting solutions. Straight lines of best fit were determined for both plots, however although measurements were made over a significant pH range, the limited effective range of S* meant that the goodness of fit for both plots was similar, preventing reliable discrimination between the two cases. As a result further analysis to extract e.g. the surface energy of the critical nucleus was not attempted. The mean induction time for transients from each nanopipette run was calculated (   50 The data were also analysed based on fitting the cumulative probability distribution derived from each experiment (points, Fig. 4), assuming a classical nucleation model. The probability, P(t), to detect crystals at a time, t, which were nucleated at an earlier time is given by eqn (4), where J is the stationary nucleation rate and t g is the time taken for a nucleus to grow to an appreciable (detectable) size. 51 This distribution function was fitted to each data set (lines, Fig. 4) and the parameters extracted (Table 1 and Table S2 in ESI †). While some cumulative distributions are well fitted by the model, most are not. Of the distributions that do fit well, they follow the expected Poisson distribution with a tail towards longer times, however this trend is time-dependent (Fig. S1, ESI †), rather than stochastic, leading us to conclude that precipitation in these nanopipettes is not well described by existing models of induction time.
Simulations of the development of supersaturation over time In order to understand why the precipitate is formed within the first 100 nm of the pipette, the time-dependent evolution of the solution composition inside the nanopipette upon mixing was simulated using FEM calculations (Fig. 6). A full description of the model is given in the ESI † (Section S7) and is summarised here. Briefly, the Poisson-Nernst-Planck equations were used to describe the relationship between the electric field generated between the QRCEs in the nanopipette and bulk solution, and the transport of species by diffusion and migration, with an additional term in the continuity equation to ensure that the various chemical equilibria between species were satisfied. The simulation geometry was constructed based on STEM images of typical nanopipettes, with boundaries representing the bulk in the nanopipette and the bath each located 50 mm from the end of the nanopipette (Fig. S7, ESI †). The equilibria and subsequent calculations of S were based on the species activity, calculated from concentrations and activity coefficients derived from the Davies equation applying the local ionic strength.
Simulations reveal that S changes dramatically upon application of the potential step, reaching steady state within 100 ms (Fig. S9A, ESI †). Each concentration investigated gives rise to a different steady state value of S after around 100 ms. At this time, the position of maximum supersaturation is found to be between 250 to 625 nm into the nanopipette, from the end ( Fig. 6A and Fig. S9D, ESI †). Comparison with the STEM images in Fig. 2 shows good agreement between these simulations and experimental results -the precipitate forms in the region where there is a significant increase in supersaturation. Although the location of maximum S varies depending on the initial experimental concentration, it remains in the first 600 nm of the nanopipette, where the radius is only 2.5 times larger than at the tip. Similarly, while the half rise time of S varies with concentration (Fig. S9C, ESI †), steady state is reached by 100 ms for all concentrations, which is significantly faster than the induction time for all but the highest concentration blocking experiment. This finding agrees with the experimental assessment, based on the ionic current, that mass transport is only likely to limit growth in the [CO 3 2À ] = 48 mM case. The simulations also show that, within the approximations used (S7, ESI †), D 2 O will have only small effect on the mass transport,  (3)). (C) Relationship between t ind and log À2 S*. The relationship is linear in the case that nucleation time dominates, or is comparable to, the growth time (eqn (2)). A similar goodness of fit to the lines of best fit is observed in B and C. The legend applied to all panels: squares and solid lines represent measurements in H 2 O, circles and dashed lines are from D 2 O. Black, red and blue colours indicate data from replicates 1, 2 and 3. Error bars show relative standard deviation.
not modifying the value of supersaturation reached by more than 6% from the H 2 O case. This suggests that at 7, 15 and 36 mM CO 3 2À the evolution of supersaturation is controlled by the initial concentration itself, such that the value of S is comparable between the H 2 O and D 2 O cases. The absolute value of S is significant, however, as at steady state, in all cases, it exceeds the spinodal, estimated to be between 3-4 mM in stoichiometric CaCO 3 solution, 15 corresponding to an ion activity product (IAP) of between 5-8 Â 10 À7 M, 42 or a value of S between 13 and 21. In all cases the system reaches S = 21 in the simulations on a much shorter timescale than t ind . Given that decomposition of the unstable region will occur within microseconds of the spinodal being reached, 55 formation of a dense liquid phase by itself cannot explain the decrease in current magnitude (although diffusion coefficients, and hence ion currents, within the dense liquid phase are expected to be up to three orders of magnitude lower than in typical dilute solutions 12 ). It is therefore suggested that it is the formation of the solid ACC phase within the dense phase which is responsible for the observed current blockade and observed induction time. It is noted that particles must grow to almost the diameter of the pipette before the current flow is significantly perturbed (Fig. S10, ESI †).
Finally, it is interesting to compare the apparent differences in the STEM images of the pipettes after precipitation from different CO 3 2À concentrations (Fig. 2, Section S3 and Table S1, ESI †), with the differences in ion fluxes and distributions obtained from simulation (Fig. 6). As expected, the gradient of S along the centre of the nanopipette is steeper at higher [CO 3 2À ], leading to greater ion fluxes. A higher flux would enable a larger region of solution to exceed the spinodal, leading to larger dense liquid regions. Since the transformation from dense liquid to solid must involve loss of water into the dilute phase at the phase boundary, regions with lower surface area-volume ratios would require longer to complete this transformation. It is tentatively suggested that this may explain the liquid-like appearance of the residues from the [CO 3 2À ] = 48 mM experiments, where the larger volume of dense phase was not able to solidify on the timescale of the experiment. We note a novel aspect of the experimental approach is the ability to monitor such small regions of solution. As methods for preparing nanopipettes of smaller dimensions improve, this technique may be able to probe effects related to confinement, where mass transport properties can change dramatically. [52][53][54] Conclusions A system where ACC can be reliably and repeatedly precipitated and dissolved under the confined conditions of a nanopipette has been demonstrated. This system allows high resolution induction time measurements to be made, and the kinetics of individual, readily characterisable precipitates to be studied. It is observed that under the present conditions, relatively small increases in CO 3 2À concentration can decrease induction times by orders of magnitude, consistent with the expected change in supersaturation. Consideration of mass transport, and approximation of the observed precipitate volume, suggest that at low CO 3 2À concentrations, the process is kinetically controlled, but Values of t ind show the mean of the individual nanopipette means AE the standard error of the means. Individual nanopipette data is shown in Table S2, ESI. at the highest concentration ACC growth become limited by mass transport. The similarity of induction times between H 2 O and D 2 O solutions of equivalent CO 3 2À concentration suggests that neither ion desolvation nor HCO 3 À deprotonation represent significant energetic barriers for the growth of ACC, as predicted in previous molecular dynamics simulations. Differences in the appearance of precipitates formed at higher CO 3 2À concentrations are observed and rationalised using differences in the local ion flux. The system demonstrated in this work provides a useful platform for studying the effect of confinement and electric fields on the nucleation and growth of crystals from solution.

Conflicts of interest
There are no conflicts to declare.