A Classical View on Nonclassical Nucleation

A classical view on nonclassical nucleation

Paul J. M. Smeetsa,b,c,1,2, Aaron R. Finneyd,e,f,1,3, Wouter J. E. M. Habrakena,b,g, Fabio Nudelmana,b,h, Heiner Friedricha,b,c, Jozua Lavena,b, James J. De Yoreoi,j, P. Mark Rodgerd,e,4, and Nico A. J. M. Sommerdijka,b,c,3

aLaboratory of Materials and Interface Chemistry, Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands; bCenter for Multiscale Electron Microscopy, Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands; cInstitute for Complex Molecular Systems, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands; dCentre for Scientific Computing, University of Warwick, Coventry CV4 7AL, United Kingdom; eDepartment of Chemistry, University of Warwick, Coventry CV4 7AL, United Kingdom; fDepartment of Materials Science and Engineering, University of Sheffield, Sheffield S1 3JD, United Kingdom; gDepartment of Biomaterials, Max Planck Institute of Colloids and Interfaces, Research Campus Golm, D-14424 Potsdam, Germany; hEaStCHEM, School of Chemistry, University of Edinburgh, Edinburgh EH9 3FJ, United Kingdom; iPhysical Sciences Division, Pacific Northwest National Laboratory, Richland, WA 99352; and jDepartment of Materials Science and Engineering, University of Washington, Seattle, WA 98195

Edited by Patricia M. Dove, Virginia Polytechnic Institute and State University, Blacksburg, VA, and approved July 28, 2017 (received for review January 6, 2017) Understanding and controlling nucleation is important for many in biological systems, time-dependent spectroscopy measurements crystallization applications. Calcium carbonate (CaCO3) is often indicated that a hydrated amorphous calcium carbonate (ACC) is used as a model system to investigate nucleation mechanisms. first deposited and then undergoes dehydration before crystalli- Despite its great importance in geology, biology, and many indus- zation (10). Liquid–liquid phase separation has been proposed to trial applications, CaCO3 nucleation is still a topic of intense dis- occur in CaCO3 solutions. Faatz et al. (11) presented the basis for cussion, with new pathways for its growth from ions in solution a phase stability diagram including liquid–liquid phase separation. proposed in recent years. These new pathways include the so- Wolf et al. (12) performed experiments in acoustically levitated called nonclassical nucleation mechanism via the assembly of ther- droplets and observed the formation of emulsion-like structures in modynamically stable prenucleation clusters, as well as the formation transmission electron microscopy (TEM), which were proposed to of a dense liquid precursor phase via liquid–liquid phase separation. be a dense liquid phase (DLP). Bewernitz et al. (13) performed Here, we present results from a combined experimental and com- titration experiments at moderate pH levels, in which they sup- putational investigation on the precipitation of CaCO3 in dilute ported the proposed emergence of a DLP by 13C nuclear magnetic aqueous solutions. We propose that a dense liquid phase (contain- resonance (NMR) T relaxation and 13C pulsed field gradient – 2 ing 4 7H2O per CaCO3 unit) forms in supersaturated solutions stimulated-echo self-diffusion NMR measurements. Later, Wallace through the association of ions and ion pairs without significant et al. (14) developed the phase stability diagram to include regions participation of larger ion clusters. This liquid acts as the precursor for direct nucleation of solid CaCO3. They also performed lattice for the formation of solid CaCO3 in the form of vaterite, which + gas simulations, which showed that upon classical nucleation of a grows via a net transfer of ions from solution according to z Ca2 + − dense liquid close to the critical temperature, a wide distribution of z CO 2 → z CaCO . The results show that all steps in this process can 3 3 cluster sizes could be found in dilute solution. Recently, Zou et al. be explained according to classical concepts of crystal nucleation and (15) proposed a stability diagram for calcium carbonate with a growth, and that long-standing physical concepts of nucleation can metastable solution region—where mineral phases or dense liquids describe multistep, multiphase growth mechanisms.

calcium carbonate | nucleation | crystal growth | cryo-electron Significance microscopy | molecular simulation Nucleation is the process by which constituent building blocks n the process of forming a solid phase from a supersaturated first assemble to form a new substance. In the case of mineral Isolution, nucleation is the key step governing the timescale of formation from initially free ions in solution, the emergence of the transition. Controlling nucleation is an essential aspect in intermediary phases often determines the thermodynamics many crystallization processes, where distinct crystal polymorphism, and kinetics of formation for the most stable phase. Our work size, morphology, and other characteristics are required. It is, on CaCO3 mineralization reevaluates a topic of intense discus- therefore, important to obtain a fundamental understanding of sion: Can nucleation be explained by theories established over nucleation mechanisms. a century ago, or should new physical concepts, as recently More than 150 years ago, a basic theoretical framework, proposed, be adopted? Our data show that classical theories classical nucleation theory (CNT) (1, 2), was developed to describe can indeed be used to describe complex mechanisms of crys- such nucleation events. CNT describes the formation of nuclei tallization. In addition, we provide information about the from the dynamic and stochastic association of monomeric units properties of intermediate phases, which will aid in the design (e.g., ions, atoms, or molecules) that overcome a free-energy bar- of additives to control mineralization. rier at a critical nucleus size and grow out to a mature bulk phase. Author contributions: P.J.M.S., A.R.F., P.M.R., and N.A.J.M.S. designed research; P.J.M.S. Calcium carbonate (CaCO3) is a frequently used model system to and A.R.F. performed research; P.J.M.S. and A.R.F. analyzed data; and P.J.M.S., A.R.F., study nucleation (3–5); however, despite the many years of effort, W.J.E.M.H., F.N., H.F., J.L., J.J.D.Y., P.M.R., and N.A.J.M.S. wrote the paper. there are still phenomena associated with CaCO3 crystal formation The authors declare no conflict of interest. where the applicability of classical nucleation concepts have been This article is a PNAS Direct Submission. questioned (6). These include certain microstructures and habits of Freely available online through the PNAS open access option. biominerals formed by organisms (7), or geological mineral deposits 1P.J.M.S. and A.R.F. contributed equally to this work. with unusual mineralogical and textural patterns (8). 2Present address: Department of Materials Science and Engineering, Northwestern Uni- Three anhydrous crystalline polymorphs of CaCO3 are observed versity, Evanston, IL 60208. in nature: vaterite, aragonite, and calcite in order of increasing 3To whom correspondence may be addressed. Email: [email protected] or thermodynamic stability. In many cases, the precipitation of CaCO3 [email protected]. from solution is described as a multistep process, with amorphous 4Deceased March 23, 2017. phases first precipitated before transformation to more stable This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. crystalline forms according to Ostwald’sruleofstages(9).Moreover, 1073/pnas.1700342114/-/DCSupplemental.

E7882–E7890 | PNAS | Published online September 5, 2017 www.pnas.org/cgi/doi/10.1073/pnas.1700342114 Downloaded by guest on October 2, 2021 are able to nucleate from solution—bounded by a limit of solution A B PNAS PLUS stability at 3–4 mM calcium and carbonate concentrations (under standard conditions). At a limit of solution stability, dense liquids or solids and dilute ionic (“lean”) solution phases spontaneously phase separate (i.e., they undergo spinodal decomposition). Transformations from free ions in solution to dense liquid or solid phases may occur according to classical concepts. However, recent studies have described so-called nonclassical nucleation pathways (16) involving thermodynamically stable, nanometer- sized prenucleation clusters (PNCs) (17, 18) that are already present in undersaturated solutions. In fact, ∼75% of bound calcium CD in solution was proposed to be present in PNCs in typical titration experiments (17). In this scenario, the first solid mineral phase is produced upon aggregation of PNCs, as indicated by an increase in the sedimentation coefficients for solution species in analytical ultracentrifugation (AUC) measurements (17). Computer simulations indicate that PNCs are dynamically ordered liquid-like oxyanion polymers (DOLLOPs) with an average twofold cation–anion coordination (18). The loose binding of ions allows for a wide range of cluster configurations, and a limiting size to clusters was attributed to the pH dependence of Fig. 1. (A) Titration curve for n = 10 experiments showing the average + + bicarbonate incorporation. While the structural and dynamical development of concentration of free Ca2 ions as measured by the Ca2 -ISE 2+ 2+ properties of DOLLOPs may appear similar to nanodroplets of [c(Ca free); red line] compared with the total average concentration of Ca 2+ dense liquids, PNCs are defined as stable solutes, that is, they do dosed [c(Ca tot); black line] as a function of time normalized with respect to 2+ not have a phase boundary with the surrounding solution (19). the time of maximum c(Ca free): tσ max. The average concentration of bound 2+ 2+ = 2+ − 2+ Recently, evidence from AUC (17) and cryogenic TEM (cryo- Ca [c(Ca bound) c(Ca total) c(Ca free)] is given by the blue curve. Error 2+ TEM) (20) reporting PNCs with well-defined (sub)nanometer bars show SDs of the distribution. (B) Ratio of bound and total Ca ion concentrations up until tσ max (intervals are 100 s). The arrow indicates nu- sizes has been disputed (21). The role of PNCs in the nucleation 2+ cleation at ∼0.90 tσ max, as the fraction of bound Ca starts to increase process has also been questioned, considering that their pro- 2+ 2+ compared with the constant ratio of c(Ca bound)/c(Ca tot) determined in posed thermodynamic stability should increase the barrier to 2+ 2+ the prenucleation stage (K0.90 tσ max). The deviation of c(Ca bound)/c(Ca tot) nucleation, relative to the one from ions in solution (22). at K0.1 tσ max is attributed to electrode signal instability during the cali- Attempts have been made to incorporate PNCs into pathways bration at very low ionic strength. Error bars are standard errors of mea- – 2+ 2+ for liquid liquid separation (13, 19); nevertheless, no direct evi- surement (SEMs). (C) MINTEQ model data for c(Ca free), c(Ca bound), and 2+ dence for these mechanisms have been provided. Computer sim- c(Ca total), shown as red, blue, and black squares, respectively, overlaid on – the experimentally measured time-dependent concentration curves with the ulations have shown that liquid liquid separation provides the + + possibility for a wide distribution of cluster sizes in solution, but no same color. (D) The concentration of free Na in solution c(Na free) as determined by the MINTEQ speciation program (magenta squares) and the special thermodynamic status for clusters of a well-defined size + = + was demonstrated (14). Thus, an open debate remains about the average c(Na free) determined from n 3Na -ISE measurements (magenta line), with corresponding SDs of the distribution. involvement of stable PNCs in the nucleation of CaCO3. In this work, a combined experimental and computational investigation of CaCO3 precipitation is reported using a titration setup for the stochastic nature of nucleation. The high reproducibility of with ion-selective electrodes (ISEs) as described by Gebauer et al. the experiments is then evident in Fig. 1. (17), and molecular-dynamics (MD) simulations of clusters and free The difference between the total concentration of titrated CHEMISTRY ions in water with the force field reported by Demichelis et al. (18). 2+ 2+ 2+ Ca , c(Ca tot), and c(Ca free), defines the concentration of This system is additionally studied using cryo-TEM with image 2+ 2+ bound Ca in solution: c(Ca bound). Fig. 1B shows that, in ac- analysis, TEM simulations, and dynamic light scattering (DLS). Our cordance with previous data (17), on average 65–75 ± 1.0% > 2+ + studies confirm that a significant fraction ( 60%) of Ca in so- (mean ± SE) of the Ca2 was bound in solution before nucleation. lution is bound before nucleation, in agreement with earlier During the prenucleation stage (K0.90 tσ max), the activity ratio of studies (17, 18). However, we find no evidence for the formation bound to free calcium ions in solution (SI Appendix,Fig.S3), and of PNCs. Before nucleation of solid CaCO3 in the form of vaterite, concentration ratio of bound to total calcium ions in solution (Fig. we find the emergence of a dense liquid calcium carbonate phase 1B) was nearly constant until the nucleation point (the deviation at in both experiments and simulations. In titration experiments, the t K 0.1 tσ max is attributed to electrode signal instability during the vaterite grows following nucleation via a net transfer of stoichio- calibration at very low ionic strength, see SI Appendix,section2.3). + metric calcium and carbonate ions from solution, which eventually At the same time, during linear Ca2 addition, the linear addition exhibits Ostwald ripening as determined from DLS measurements. rate of NaOH to maintain the pH indicated a constant chemical All of the observed results can be completely explained within the composition of the reaction mixture in the prenucleation stage (SI concepts of classical nucleation in a multiple-step, multiple-phase Appendix,Fig.S4). It can be concluded from these considerations reaction from predominantly free ions and ion pairs in solution. that the carbonate activity is virtually constant. Results From the definition of the equilibrium for any prenucleation species of the type Ca (CO ) , it follows that Prenucleation Species. As in the report of Gebauer et al. (17), a x 3 y typical LaMer curve (23) was obtained (Fig. 1A) with high re- 2ðx–yÞ a Ca ðCO Þ − producibility, which showed a steady increase in the concentration x 3 y + x 1 2+ 2+ = constant · a Ca2 . of free Ca , c(Ca free), followed by a sudden drop indicating the + x free 2+ a Ca2 nucleation of a new phase. Following nucleation, c(Ca free) con- free verged toward the equilibrium solution concentration of the newly + formed solid phase. In the following, we used a dimensionless time, This is true if over a large range of Ca2 concentrations x = 1 (see 2+ tσ max, normalized by the time of maximum c(Ca free) to account SI Appendix,section2.3.4, for more details), and suggests that

Smeets et al. PNAS | Published online September 5, 2017 | E7883 Downloaded by guest on October 2, 2021 + bound calcium in solution is therefore present in single Ca2 -based 0 A ion association complexes, such as the classical ion pair CaCO3 , B similar to what was previously demonstrated for the case of calcium phosphate (24). Complexes with y = 2, 3... and containing bicarbonate would also agree with these data. An alternative that has C 1 been proposed could be the formation of polymeric assemblies of 0.8 0.6 Ca-C thetype[ionassociationcomplex]n, where, using a multiple binding P Ca-2C approach, the free energy of binding would be equal for all sub- 0.4 Ca-3C 0.2 sequent additions of monomeric units to n = 2, 3, 4... assemblies. 0 0 5 10 15 0 t (ns) Such polymeric assemblies were indeed proposed for [CaCO3 ]n on 0.6 30 the basis of AUC (17) and molecular simulations (18), and for [Ca D E 2− 0.5 1 25

(HPO4 )3]n on the basis of titration experiments and cryo-TEM ) 0.8

observations (24). 0.4 Ca-C 0.6 20 ) ( N 0.4 ) g P ions To verify whether the titration data could indeed be fully 0.3 0.2 R 15 f ( ( N explained by the formation of classical species, the activities of all P 0 123 4 0.2 10 2+ 2− – + – – NCa-C relevant ions (Ca ,CO3 ,HCO3 ,Na ,Cl,OH)werecalculated, taking into account the ionic strength at different time points, and 0.1 5 0 0 entered into an equilibrium speciation model (Visual MINTEQ; SI 0 1 2 345 6 7 8910 0 0.1 0.2 0.3 0.4 R (nm) Appendix,section2.4). The model not only correctly described the Nions g experimentally determined concentrations of calcium (Fig. 1C)and – sodium (Fig. 1D),butalsorequiresthatthe only relevant species Fig. 2. Simulations at low CaCO3 concentrations starting from (A C)a preformed cluster and (D–E) a random distribution of ions in solution. before nucleation are dissolved ions and the classical ion pairs + Snapshots of (A) a cluster present at the beginning of a simulation (where 0 + CaCO3 and CaHCO3 in a 96/4 ratio (SI Appendix,TableS4). This the initial Ca2 concentration was 32 mM), and (B) ionic species found at contrasts the suggestion that relatively large ionic assemblies are equilibrium in a 20-ns MD simulation. Calcium, carbon of carbonate, and accessible to the system. Indeed, DLS did not indicate any signifi- carbon of bicarbonate are shown in yellow, purple, and blue, respectively. cant population of nanoparticles in the prenucleation stage com- Green lines show carbon and calcium within 4.2 Å. (C) Time dependence of pared with the buffer background (SI Appendix,Fig.S5). the relative probability for calcium to bind to one (black), two (blue), or Cryo-TEM was used to investigate the presence of ionic as- three (red) (bi)carbonates. (D) Size probability distribution at equilibrium (in 0 number of ions, Nions; Nions = 1 indicates free ions) for ionic species in water semblies of the type [CaCO3 ]n in the prenucleation stage. An + for a system with an initial Ca2 concentration of 26 mM; averages were example TEM image is shown in SI Appendix,Fig.S5, demon- + obtained from the final 2 ns of simulation. Inset is the probability of a Ca2 strating that no such objects were found in any of the acquired ion coordinating to NCa-C carbon atoms (black) in associated species recorded images. At the applied imaging conditions, objects ≥0.9 nm (25) 2− over the same time window. Red and blue data are for binding to CO3 and − can be detected, which would permit the observation of polymeric HCO , respectively. Error bars represent 1 SD in the distribution. (E) Radius – 3 prenucleation clusters for which average diameters of 2 3nmhave of gyration (Rg, in nanometers) probability densities for ionic species in so- been proposed (19). The obtained images were also systematically lution at equilibrium for the simulation described in D. The peak at Rg = 0is analyzed using an in-house computational process (SI Appendix, due to free calcium, which is modeled as a charged point mass. section 1.9), but no prenucleation clusters were found to be present in solution. Specifically, at K0.90 tσ max, a significant population of clusters with sizes ≥0.9 nm, as proposed for PNCs (17, 26), was not clusters were equivalent. Furthermore, while density fluctuations in — — observed in cryo-TEM, in good agreement with titration analysis all simulations produced albeit rarely larger clusters, these and DLS measurements. quickly dissociated. While the system size may limit the size to The lack of polynuclear assemblies contrasts with the proposed which clusters can grow in solution, multiple simulations with stability of DOLLOPs, which were shown to emerge spontaneously varying total numbers of ions produced, qualitatively, the same in computer simulations and proposed as the structural form for exponential decay in cluster size distribution that is predicted by + PNCs (18). For high Ca2 concentrations (500 mM), 50- to 70-ns classical theories (SI Appendix,Fig.S12). – simulations identified DOLLOPs containing up to ∼60 ions at In the present work, 60 65% of the bound calcium was found pH = 10. Using a speciation model incorporating the multiple in ion pairs in the system where the pH at equilibrium was 8.3 ± 0.8, 2+ binding assumption, Demichelis et al. (18) predicted that, at these and we would expect this to be higher still for lower Ca con- + pH levels and c(Ca2 ) = 0.4 mM, around 25% and 75% of bound centrations, in line with the speciation model data above. The calcium would be present in ion pairs and DOLLOPs, respectively. affinities for calcium binding to carbonate or bicarbonate showed 0 To investigate cluster sizes at close-to-experimental concentrations, a preference for CaCO3 ion pairs in all simulations (Fig. 2D, we performed similar simulations, generating trajectories of at least Inset, and SI Appendix, section 3.1). In the random system at + 20 ns and using total Ca2 concentrations (20–30 mM) and pH equilibrium, the same ionic species were also found, with 66% of 0 values as close as computationally feasible to those used in the the ion pairs being of the type CaCO3 (SI Appendix, Fig. S13). experiments (SI Appendix,TableS1). During the simulation, the pH decreased due to the preferred 2+ 2− − At equilibrium, the concentrations of free calcium and (bi)car- binding of Ca to CO3 , which enriches the solution in HCO3 . bonate were measured as 3–5and16–26 mM, respectively (SI Another simulation performed at higher initial pH (pH = 10.3) 0 Appendix,TableS1). In agreement with previous simulations (18), showed an increased preference for the formation of CaCO3 ion from an initial single cluster in water, polymeric chains with char- pairs (87%) and a further reduction of the larger clusters, with + acteristics of DOLLOP were observed during the first few nano- only 3% of the Ca2 bound to two carbons (Fig. 2D, Inset). 0 + seconds of simulation. However, upon continuing the simulation Values closer to the predicted 96/4 ratio for CaCO3 /CaHCO3 up to 10 ns, these polymers dissociated into free ions, ion pairs, (SI Appendix, Table S4) are expected at higher equilibrium pH, and, occasionally, clusters of at most four ions in size with any but simulations very much larger in system size would be re- reasonable probability (Fig. 2). A second series of simulations was quired to obtain statistically meaningful values. initiated from random distributions of free ions (Materials and The size of clusters was determined according to radius of gy- Methods). These equilibrated to the same cluster size distribution ration, Rg.Fig.2E shows Rg probability densities for a simulation found with the first series (Fig. 2 and SI Appendix,section3.1)and which started from a random distribution of ions. The distribution the frequencies for both ion attachment and detachment to/from indicates a high probability to find clusters with Rg = 0.2 nm (ion

E7884 | www.pnas.org/cgi/doi/10.1073/pnas.1700342114 Smeets et al. Downloaded by guest on October 2, 2021 PNAS PLUS pairs), while larger clusters (up to a maximum of Rg = 0.4–0.5 nm) were found with only very low probability. Thus, no larger clusters A CC160 ≥0.9 nm could be found, entirely consistent with our cryo-TEM data. 150 − As HCO3 limits DOLLOP growth, simulations at moderately 140

basic pH could lead to an underestimation of equilibrium cluster 130 sizes. Therefore, we investigated a series of cluster simulations Intensity (a.u.) 120 from an initial (CaCO3)20 structure, where ionic coordination 0 200 400 600 Distance (nm) and ionic density were consistent with the structure of liquid-like clusters, at the limit of high pH and at 20–50 mM. These clusters D dissociated at all concentrations, with the dissolution rate being highest at the lowest concentration. Here, ion pairs (70%) and a low probability of clusters containing four ions were found after 45 ns of simulation (SI Appendix, section 3.2 and Table S7).

While some dissolution of clusters in water might be expected, (a.u.) Intensity 0.2 0.3 0.4 0.5 the continued, gradual dissociation of smaller polymeric species B d-spacing (nm) over tens of nanoseconds is further suggestive of the instability of liquid-like clusters in homogeneous, low-salinity solutions. E F 450 Wallace et al. (14) showed the free energy of liquid-like clusters cryoTEM 400 DLS from a low-density calcium carbonate solution to consistently de- DLP 350 crease with cluster size in replica exchange simulations sampling 300 – background 300 400 K at 15 mM. While their all-atom approach is adequate to T = 5.6688 250 understand the energetics of cluster growth, it does not provide the DLP P-value = 0.0051 200 150 equilibrium cluster size distribution at low concentrations. 100 To summarize, we do not observe larger nanometer-sized 0.36 0.37 0.38 0.39

Average size (nm) 50 d polymeric species at our experimental conditions in cryo-TEM, -spacing (nm) 0 nor detect them by DLS, and additionally demonstrate that PNCs dissipate in solution via our simulations. Instead, MINTEQ cal- Fig. 4. (A and B) Cryo-TEM image of the DLP in titration experiments in culations, titration data, and our simulations demonstrate that ion supersaturated solution conditions at (A) 0.92 tσ max and (B) 0.96 tσ max ∼ ∼ pair formation of the form of CaCO 0 dominates calcium-bound showing objects with diameters of 320 and 420 nm, respectively (white 3 arrows). (Scale bars: A and B, 500 nm.) C shows a line scan through the upper object in B (indicated in B by the black dashed line). The black dashed lines in C indicate the object boundaries, while the blue line indicates the mean intensity value of the dilute background solution. The low contrast related A B to the maximum intensity in the line scan indicates a high degree of hydration. (D) Low-dose selected area electron diffraction (LDSAED) shows the − amorphous nature of the objects in B. (Scale bar: 2 nm 1.) The Inset shows the integrated radial average profile over the diffraction pattern in D, with the large peak reflecting the ring closest to the center. (E) Bar plots in-

dicating the d-spacing of the background solution of the DLP at 0.96 tσ max (red), and of the submicrometer-sized DLP at 0.96 tσ max (blue) of n = 5samples with corresponding error bars (SD of the distribution). Statistical analysis (via a Welch–Aspin generalized T test; SI Appendix,section2.7) shows a significant difference between the DLP and its background solution by the indicated ± CDP value. (F)Meansize SD for the DLP particles in cryo-TEM (blue) and the DLS CHEMISTRY size distribution at 0.96 tσ max (green). DLS distributions correspond to the first decay in the correlation function recorded at 0.96 tσ max (Fig. 3B).

species in solution. Therefore, we are confident that we can ex- clude the formation of PNCs to describe our data.

Nucleation of a DLP. Before 0.96 tσ max, DLS showed an initial increase in the count rate starting from ≥0.90 tσ max, indicating Fig. 3. DLS results showing (A) evolution of the derived count rate (black the nucleation of a new phase (Fig. 3A). The associated corre-

dashed line) during 0.8–1.2 tσ max around the nucleation point at ∼0.90 tσ max lation diagrams (Fig. 3B) indicated that around these time points (red arrow). The dotted red line indicates the average count rate in the (∼0.88–0.96 tσ max) objects with a size of ∼200–400 nm were prenucleation stage, while the blue curve represents the amount of free present (Fig. 3C). DLS demonstrated that after 0.96 tσ a 2+ max Ca (right axis). (B) The correlation coefficient (G′) given for the time points A – further increase in count rate and particle size occurred (Fig. 3 1 4inA, showing a significant increase between measurement 2 and 3. The and B, and SI Appendix, Fig. S9) where the average particle ra- purple arrow indicates the single descent in curves 1 and 2, as also found for ∼ 1/3 the carbonate buffer solution. Pink arrows point at two distinct descents in dius, r, at time, t, scales approximately as r(t) t (Fig. 3D), curves 3 and 4 indicating the presence of a populations of micrometer-sized which fits particle growth through coalescence by Brownian particles (around 105 μs) alongside a population of smaller particles (at 102–103 μs) collisions (27) and through coarsening by Ostwald ripening (28, ′ > 0 μ after 0.96 tσ max. The intercept G 1at1.01tσ max at 10 sisindicativeof 29) (SI Appendix, section 2.7.2). sedimentation. (C) Volume size distribution of a typical DLS measurement To investigate the evolution of morphology and structure of between 0.88 and 0.96 tσ max (at 0.92 tσ max; bin size, 33 nm) demonstrating ∼ – the formed CaCO3 in more detail, samples for cryo-TEM were the presence of 200 400 nm particles in solution. (D) Rate of particle taken from the titration experiment at time points close before Ostwald ripening/coalescence as determined by DLS. The average radius 1/3 tσ and vitrified by plunge freezing (Materials and Methods). r at time t scales with r(t) ∼ t from approximately ∼0.90–0.96 tσ max max 2 onward, as indicated by the linear fits with corresponding R for n = 3 At >0.90 tσ max, cryo-TEM images showed the presence of round measurements in red, blue, and black. amorphous objects of ∼200–400 nm (Fig. 4 A, B, and D), with

Smeets et al. PNAS | Published online September 5, 2017 | E7885 Downloaded by guest on October 2, 2021 image contrast that was very low compared with what would be line with predictions from lattice-gas simulations of liquid–liquid expected for solid CaCO3 particles of the same size (30). For this phase separation (14). While the initial ion concentrations here system, the observed low contrast implies a phase of low density, were much higher than in experiments, this was chosen to reduce and therefore it is sensible to assume that the objects contain a any barrier to nucleation. At still higher concentrations (1.1 and 1.7 high degree of hydration. Amorphous calcium carbonate with M), cylindrical ionic networks spanned the periodic simulation cells high levels of hydration behaved as a liquid in computer models (Fig. 5B and SI Appendix, section 3.3.1). This transition is explained (14). Furthermore, low image contrast in TEM was observed for by a crossover in the minimum surface energy between a sphere a polymer-induced liquid precursor phase (31), as well as in and percolating cylinder at limited system sizes, as would be tetrahydrofuran–water mixtures which underwent liquid–liquid expected for a liquid phase. The concentrations of free ions in lean phase separation (32). Importantly, the ion activity product de- solution at equilibrium (SI Appendix,TableS2) were comparable to rived from the titration curve at all times remained significantly those found from solutions at relatively low concentrations, and + below the solubility of ACC as reported by Breˇcevic and Nielsen calcium concentrations [c(Ca2 ) = 1–2 mM] were less than that (33) (see Fig. 8A). This also contrasts with the earlier assignment proposed for the limit of solution stability at 300 K (15), further of the solubility to different forms of ACC, which—although supporting the proposed phase separation mechanism. having similar ion activity products—were not corrected for the From our analyses, the structure and dynamic properties of influence of ionic strength (17, 34). The fact that we still observe dense liquid CaCO3 at all concentrations were consistent and + an amorphous phase, and considering the above discussion, we comparable to a viscous fluid (SI Appendix, section 3.4). Ca2 in propose that the observed objects are vitrified droplets of a DLP, the DLP was found to bind preferentially to two carbonates rich in calcium carbonate that forms from the solution through a (∼45%, Fig. 5C; see SI Appendix, section 3.3.2, for details); an + liquid–liquid phase separation process. We note, however, that increase in three-coordinate Ca2 was observed compared with our TEM data cannot provide information surrounding the dy- ionic associates in lean solution, but not enough (35%) to con- namical behavior of ions in the observed objects. Low-dose se- dense and rigidify the dense liquid. Our coordination levels were lected area electron diffraction (LDSAED) was used to assess in reasonable agreement with those found in the high pH sim- the differences in short range order between the background ulations of Demichelis et al. (18) and for dense liquid nano- solution after nucleation and the DLP (at 0.96 tσ max). This particles simulated by Wallace et al. (14), where the average analysis revealed broad rings indicating the absence of any long- coordination in the largest clusters was around 2.8. Further range order in the DLP (Fig. 4D) and representing a d-spacing analysis showed that ion coordination was relatively high in the larger than that of the background solution (Fig. 4E), in line with core of the DLP, while a gradual decrease was observed away an increased ion density within the droplets (20). from the core in a wide and diffuse interfacial region (Fig. 5 E Simulations at high calcium and carbonate concentrations sup- and F, and SI Appendix, section 3.3.2). Ion diffusion coefficients, port the experimental observations. From initially free ions in Dion, varied as a function of distance from the center of the dense 2+ 2− −8 −6 2 water at 0.57 M, a Ca and CO3 ion-rich liquid domain formed liquid toward the interfacial region and were 10 to 10 cm /s over 40 ns of MD simulation. The spherical-like nanoparticle (with (SI Appendix, section 3.4): at least two orders of magnitude diameter ∼3.0 nm; Fig. 5A) which emerged was in equilibrium with higher than Dion in ACC with a 1:1 CaCO3:H2O stoichiometry a lean aqueous solution containing free ions, ion pairs, and occa- (35). The dynamic nature of ion coordination was confirmed by sional larger associates (SI Appendix, Figs. S18 and S19). This is in short Ca–C coordination lifetimes (Fig. 5D and SI Appendix,

A B

Fig. 5. (A and B) Snapshots taken from simulations

demonstrating the existence of a DLP in CaCO3 solutions at initial concentrations of (A) 0.57 M and (B) 1.1 M. Averages were measured from the final 5 ns of simulation. Calcium and carbonate are shown as purple and yellow, respectively, and a van der Waals surface (from ion atom centers) is highlighted. In B,a d (pixel) 16-Å slice through a large cylindrical cluster is taken, C 0.5 D G 100 200 300 400 which intersected the simulation cell boundaries. Water 0.4 molecules are represented by the blue circles. (C) Cluster ) ) 100 160 2+ 0.3 coordination probabilities for Ca to bind to NCa–C car- Ca-C Ca-C N N bons with corresponding SD at 1.1 M. (D) Probability , ( 0.2 t P

f ( 140 – 0.1 1 density for Ca C bond lifetimes (distance cutoff: 4.2 Å) at 1.1 M, with data smoothed using a running average. (E)

0 intensity (a.u.) 0 1 23456 01234 5 Mass density, ρ, of ions (red) and water (blue) in the DLP NCa-C t (ns) as a function of distance from the center of mass at 1.1 M with regression curves fitted (bandwidth: 0.6 nm). E F 8 1500 (F) Coordination probability map generated from in- 1.4 2+ ) terpolated data. Ca coordination numbers in the first -3 water 6 + 1000 coordination shell to carbonate oxygen atoms, Ca2 co- + 1.0 ordination, and water, Ca2 solvation, are plotted with

500 solvation 4 ρ (kg m ions 2+ the distance of calcium from the center of mass high- 0 Ca 2 lighted by the map color on the right (scale in nano- 0 1.0 2.0 3.0 1234 5 6 0.6 r (nm) meters). (G) Calculated TEM image at 1.7 M. Bottom to r (nm) Ca2+ coordination Top: a schematic of the supercell used in the calculation, showing orientation of the DLP with respect to the in- cident electrons; a selected region of the calculated TEM - image; smoothed line scans taken from the image as e shown by the blue and black curves.

E7886 | www.pnas.org/cgi/doi/10.1073/pnas.1700342114 Smeets et al. Downloaded by guest on October 2, 2021 PNAS PLUS AC (300 CaCO3 units) and a varying number of water molecules (CaCO3·n H2O, where n = 0 ̶7; SI Appendix, section 1.12.4). Radial distribution functions confirmed an amorphous arrange- ment of ions and the final configuration was then used in TEM image simulations. Supercells were created to ensure the sample depth was set approximately equal to that of the experimental TEM analysis (i.e., 130 nm). Fig. 7A shows the simulated electron intensities measured at the detector for ACC, as informed by calculating mean intensities of a number of line scans from simulated TEM images in the region of the bulk phases. The mean intensities show that the contrast is greatest for ACC with low water content. Experimentally obtained relative mean values for ACC intensities were close to those for BD160 160 simulated CaCO3·1H2O(67%vs.76± 4%). As both the samples in ) . ~14 simulation and experiment are approximately equal in depth, the ) 140 140 u . . u a .

( difference in relative intensities is most likely due to the difference a

~50 y ( t y 120 i 120 t s in the defocus parameters adopted (the chosen defocus did not i n s e n t

e affect the assignment of DLP vs. ACC in the experiments; SI Ap- n t 100 I

n 100 I ~110 nm ~ 420 nm pendix,section3.5.1). Within uncertainties, the electron intensity measured for the 80 80 0200400 0 200 400 600 800 1000 1200 1400 1600 DLP in simulations is in good agreement with ACC containing Distance (nm) Distance (nm) 5–7H2O/CaCO3 (Fig. 7A), that is, distinctly different from ACC Fig. 6. (A) Cryo-TEM image showing a line scan (red box) through one of the with CaCO3:1H2O. The experimentally determined TEM elec- two ACC particles in the direction of the red arrow. The width of the line scan is tron intensity for the DLP also falls within this range; hence, taken as ∼0.5 times the observed particle diameter. (B) Intensity vs. distance of these data show that it is possible to quantitatively differentiate thelinescaninA, where the boundaries of the ACC particle are indicated by between low hydration amorphous solids and dense liquids using the two black dashed lines. The intensity difference with the mean intensity of TEM. We can compare the mass density of the DLP from sim- – the background solution (dark blue line) is given by the indicated black arrow ulations (ρ = 970–1,500 kg·m 3; Figs. 5E and 7B) to the mass and value. (C) Cryo-TEM image of Fig. 4B with indicated line scan (light blue box) through a DLP particle in the direction of the blue arrow. The width of the densities of bulk ACC with varying levels of hydration (Fig. 7B). line scan is taken as ∼0.5 times the observed DLP diameter. (D) Intensity vs. Both the total mass and ionic mass densities of the DLP are – distance of the line scan in C, where the DLP droplet boundaries are indicated consistent with ACC containing 4 6H2O/CaCO3. Combined, by the two black dashed lines. The intensity difference with the mean intensity these results allow us to place bounds on the hydration level in of the background solution (dark blue line) is given by the indicated arrow and the DLP as 4–7H2O/CaCO3, which is consistent with the results value. (Scale bars: A,100nm;B,500nm.) from structural analyses in SI Appendix, section 3.3.3.

Formation of Vaterite. Following the prenucleation stage and for- section 3.3.2). In the core of the dense phase, the water was mation of the DLP, at ∼0.96 tσ max an increase in the amount of relatively tightly bound and on average a high level of hydration was found (4–7H2O/CaCO3; SI Appendix, section 3.3.3). TEM images for these dense phases (Fig. 5G) were calculated using a multislice algorithm (SI Appendix,section1.12) and based AB on the method by Rullgård et al. (36). These were in good ± agreement with the experimental cryo-TEM data showing 85 CHEMISTRY 5% vs. ∼93% transmission compared with the low-density background solution, respectively (see Figs. 4C and 5G, noting that the size of the simulated system limits the defocus values that can be used; SI Appendix, section 3.5.1). This agrees with our cryo-TEM observations which gave no evidence for clusters >1.1 nm within and surrounding the DLP phase (SI Appendix,Fig.S10). To substantiate the estimated levels of hydration in the DLP in our simulations, experimental cryo-electron micrographs of the Fig. 7. (A) Electron transmission intensities measured for bulk ACC with DLP droplets were compared with those of solid ACC. Since our varying levels of hydration; and (B) comparison of mass densities of ACC and vitreous ice layers have a thickness of ∼130 nm (37), which is DLP in simulations. (A) Mean electron intensities measured at the detector in smaller than the measured lateral diameter of a DLP droplet TEM simulations for bulk ACC with a range of hydration levels, n (i.e., · (Fig. 4 A and B), we propose that the observed DLP droplets are CaCO3 nH2O) are given by black data points. The data were averaged using a number of line scans, and errors shown in black are 1 SD of the sampled oblate structures that fit the thickness of the ice layer. We distribution. The blue and red lines are the mean intensities measured for therefore compared these with spherical ACC particles (miner- bulk water and DLP (with SD in the blue shaded area) using the same input

alized and analyzed in situ according to ref. 38), having a di- parameters. The mean intensity of low concentration CaCO3 solution was ameter approximately equal to the ice layer thickness. Analysis the same as that for pure water within statistical uncertainties. The experi- of such images showed that the contrast of an ACC particle mental mean intensity for the DLP was ∼135 (i.e., ∼93% of the background relative to the background solution and the carbon support film solution; Fig. 4C) and for ACC ∼100 (i.e., 67% relative to the background (i.e., independent of imaging conditions) was significantly higher solution; Fig. 6B), and we note the difference in the microscope parameters than that of the DLP (≈3.5 times, as demonstrated in Fig. 6). in experiments compared with TEM simulations. (B) Calculated mass densi- To obtain quantitative information on differences in hydration ties from simulations of bulk ACC with n water molecules per calcium carbonate (i.e., CaCO3·nH2O), where the blue data show the ionic mass density level between the DLP and ACC from the cryo-TEM experiments, in ACC and the red data provide the total mass density (i.e., ions and water). we compared electron transmission properties of ACC with varying The shaded blue and red areas provide the ionic and total mass densities in hydration in TEM simulations. As a primary step, ACC was pro- the core region of the DLP observed in high concentration simulations (Fig. duced in MD simulations by relaxing random distributions of ions 5E and SI Appendix, Fig. S21).

Smeets et al. PNAS | Published online September 5, 2017 | E7887 Downloaded by guest on October 2, 2021 A from the titration curve exhibited a good resemblance to the solubility product of vaterite (Fig. 7A, dotted line). We note that we do −1 not observe a shift in the carbonate ν2 band from 863 cm (ACC) − toward 873 cm 1 (vaterite), which would indicate that vaterite grows at the expense of ACC (40). This agrees with our data in Fig. 8A that we never surpass the solubility of ACC in our titration experiments. Discussion

We present an extensive study of the nucleation of CaCO3 from a B D supersaturated solution that forms via liquid–liquid phase separation. Experiments and simulations agree that no clusters, or polymeric assemblies thereof, larger than 0.9 nm in size are stable before nucleation. Furthermore, they demonstrate that the bound calcium in solution is predominantly present in the form of ion pairs alongside a population of clusters stochastically formed from the association of ions/ion pairs, of which the abundance decays C rapidly with increasing cluster size in accordance with CNT. Our results are incongruent with the findings of Gebauer et al. (17). However, it is important to note that, after initially pro- posing a narrow size distribution for PNCs based on AUC experiments, it was later realized that the sharp peaks in the AUC traces reflected the average value for all species in equilibrium on the timescale of the experiment (>8 h), rather than a distribution of cluster sizes (21). Particle sizes were determined Fig. 8. (A) Free ion product development vs. normalized time (black solid line) – during a typical titration experiment. The black dashed line indicates the solu- according to the Stokes Einstein equation or by using the sedi-

bility product Ksp, compared with the reported solubility product of ACC (Ksp ACC) mentation coefficients and the densities of ACC and ikaite, after (33) and vaterite (Ksp vat)(56).(B) POM indicating micrometer-sized entities at fitting with a discrete species model. However, considering that 1.03 tσ max (yellow arrows), which show birefringence when the surrounding Stokes–Einstein breaks down for systems where the solute size solution (dark gray) retracts (Inset). (C) SEM at 1.03 tσ max showing a typical approaches that of the solvent (41), and that DOLLOPs are spherical–framboidal vaterite morphology. (D)InsituATR-FTIRspectrafrom −1 2− likely to have a much lower density than any phase of reference, tσ max to 1.40 tσ max showing typical vibrations of vaterite at 875 cm (CO3 ν2 −1 2− we remain skeptical about the inference of particle size from the out of plane bend), 1,087/1,072 cm (CO3 ν1 symmetric stretch), and −1 2− AUC data. Moreover, to date, analysis of AUC data has not 1,467 cm (CO , ν asymmetric bond stretch) (57) gradually increasing in time. 3 3 accounted for the impact on cluster size distribution that must The Top Inset shows an enlargement of the ν1 peak at 1.40 tσ max,whilethe spectrum on the far Right displays the magnified ν2 spectral region. arise in the concentration gradient caused by the centrifugation process. Hence, the interpretation of the small associates found here as thermodynamically stable prenucleation clusters hinges on NaOH required to maintain a constant pH of 9.75 (due to release the proposed binding model for cluster formation in which the + of H in solution) marked the nucleation and growth of the first equilibrium binding energy for every ion pair is equal (17) and solid CaCO3. This increase reflects the withdrawal of carbonate ions negative by about 20 kJ/mol (18). Based on ratios of species con- from the buffer equilibrium while its binding behavior implies that centrations in our simulations, we find that the binding constant, β, growth of CaCO3 occurs via a net transfer of ions from solution for ion pairing is entirely consistent with earlier measurements (i.e., onto the growing CaCO3 according to the below (SI Appendix, section 2.5):

2+ + 2- → z Cafree z CO3 z CaCO3.

Simultaneously, at 0.96 tσ max, polarized optical microscopy (POM) showed objects with diameters of 1–3 μm that did not show birefringence when viewed through crossed polarizers (i.e., the material showed optically isotropic behavior; SI Appendix, Fig. S7), but these observations did not give any indication about the liquid or solid nature of the objects. From 1.03 tσ max onward, the particles displayed birefringence during or after drying of the surrounding solution, implying a rapid transformation of the disordered precursor to one of the crystalline forms of CaCO3 (Fig. 8B). SEM demonstrated that these birefringent particles had a corrugated spherical morphology characteristic of vaterite (39) (Fig. 8C and SI Appendix,Fig.S8). This identification was confirmed by in situ attenuated total reflection–

Fourier transform infrared spectroscopy (ATR-FTIR) (Fig. 8D), Fig. 9. Schematic demonstrating the development of CaCO3 structure which showed the growth over time of vibrational peaks charac- during the titration experiment in dilute calcium carbonate solutions. In the −1 −1 −1 0 + teristic of vaterite at 875 cm ,1,072cm ,and1,087cm (SI prenucleation stage, predominantly CaCO3 and CaHCO3 ion pairs exist ∼ Appendix,Fig.S8). In contrast to the report of Gebauer et al. (17), alongside free ions in solution. After a critical concentration at 0.90 tσ max,a liquid–liquid phase separation leads to the formation of a dense liquid phase no experimental evidence was obtained that indicated the formation (DLP) and a lean ionic solution of free ions and ion pairs. At the nucleation of solid ACC. ATR-FTIR did not show characteristic peaks asso- 2+ 2− point (∼0.96 tσ max), the DLP reacts with free Ca and free CO3 under + ciated with ACC, nor did the SEM results demonstrate a typical macroscopic release of H and after ∼tσ max converts to vaterite, until after solid, spherical morphology. Indeed, the ion activity product derived ∼1.30 tσ max equilibrium has been reached.

E7888 | www.pnas.org/cgi/doi/10.1073/pnas.1700342114 Smeets et al. Downloaded by guest on October 2, 2021 4 PNAS PLUS ∼10 )(18,42).Theformationof(CaCO3)2 in a single step from Ostwald ripening (50). The light-scattering data do not allow us to two ion pairs, on the other hand, suggests that β is reduced by distinguish between either of the two mechanisms for liquid–liquid orders of magnitude. While small system sizes limit statistical ac- phase separation; however, we note that we do not observe α curacy and activities are not included, the large difference in β values coarsening behavior displaying power-law regimes of the form t raises doubts about the assumptions which underlie the model. with α ≠ 1/3 as is often associated with late postseparation pro- Wolf et al. (43) and Pouget et al. (20) both suggested the cesses in spinodal decomposition in light-scattering data (51–53) presence of PNCs in an outgassing supersaturated Ca(HCO3)2 (for details, see SI Appendix, section 2.7.2). Moreover, our simu- solution—the “Kitano method” (44)—using mass spectrometry lations predict a noticeable free-energy barrier to the nucleation of and cryo-TEM in combination with AUC, respectively. However, dense liquid clusters at relatively low supersaturation (SI Appendix, the injection in the vacuum system of a mass spectrometer will section 3.3.1). We therefore propose that the formation of the drive the outgassing of the solution and the resulting increase in ∼200-nm liquid droplets occurs through density fluctuations that supersaturation will promote the formation of clusters with larger subsequently ripen/coalesce to form larger (sub)micrometer-sized diameters, similar to what has been observed in simulations at high objects, from which eventually vaterite nucleates. concentration (18, 45, 46). Moreover, the defocus conditions that In summary, our work provides a comprehensive reevaluation Pouget et al. applied for HRTEM imaging on the same electron of the nucleation mechanism for CaCO3 in controlled dilute microscope, are of the order of microns. The corresponding con- solutions (as presented in Fig. 9). Although the nucleation pro- trast transfer function (CTF) in this case (Materials and Methods cess depends critically on many parameters, such as temperature, and SI Appendix,section1.9) indicates a direct interpretable res- pH, and composition, we conclude that nucleation can be de- olution substantially larger than 1 nm, and we thus conclude that scribed by the concepts of CNT. While the mechanism of growth these data cannot prove the existence of 0.6-nm clusters, as was involves intermediate phases, the fundamental concepts of indicated in the original publication. Since, as indicated previously, classical nucleation still hold, as for the recently reported cases it is now realized that also the AUC data do not unambiguously of calcium phosphate (24) and iron oxide (54) nucleation. prove the presence of clusters with a defined particle size, we therefore conclude that neither of these reports provide solid evi- Materials and Methods dence supporting the formation of prenucleation clusters. Titration Experiments. In the titration experiment, a 10 mM CaCl2 solution was Our results also run counter to the conclusions from a study slowly added into a 10 mM carbonate buffer at 20 ± 1 °C and pH 9.75 (SI where CaCO3 was nucleated in the presence of a silica precursor, Appendix, section 1.1–1.4). This pH was selected since it reflects a high in which nanometer-sized objects observed by cryo-TEM and binding tendency of calcium with carbonate species due to the high fraction + DLS in solution were attributed to PNCs (26). These results can of carbonate ions in the carbonate buffer (17). The free Ca2 concentration 2+ 2+ be explained by the presence of silica primary particles, as [c(Ca free)] was monitored using a Ca -ISE, and the amount of NaOH added demonstrated recently (47). In fact, it is not possible to dis- to maintain a constant pH was registered. In addition, we measured the free + + + criminate between primary particles of silica and the proposed Na concentration [c(Na free)] using a Na -ISE (SI Appendix, section 1.3). PNCs based on the data presented in that study (26). To analyze solution species, samples were extracted from the titration At higher supersaturation, we provide evidence for the formation experiment at regular time intervals. In the prenucleation stage, DLS was used of objects consistent with a dense liquid before the growth of solid to detect nanometer-sized objects in solution (SI Appendix, section 1.5). In mineral phases, which has recently been proposed to feature in addition, cryo-TEM was used to investigate the presence of clusters, as was done in calcium phosphate experiments (24). To this end, the samples were a multistep CaCO3 mineralization pathway (6, 14). Amorphous · vitrified by plunge freezing (SI Appendix, section 1.9). For imaging, we used a CaCO3 is commonly considered to have the formula CaCO3 1H2O, Titan Krios microscope, which offers high resolution, detector sensitivity, and and to our knowledge the highest water content reported for ACC is detector size (4,000 × 4,000 pixels CCD). Imaging contrast was optimized by ∼1.4 H2O/CaCO3 (48), which is still clearly distinct from the 4–7 applying a nominal defocus of −0.5 μm. This defocus value resulted in a CTF H2O/CaCO3 we suggest for the DLP. Recently, Nielsen et al. (49) that allowed the direct interpretation of dark contrast objects ≥0.9 nm (25).

investigated CaCO3 nucleation with the use of in situ liquid phase Formed CaCO3 after the prenucleation stage was observed in (polarized)

TEM and observed that the dissolution behavior of amorphous light microscopy, SEM, and cryo-TEM (FEI Tecnai G2 operated at 200 kV and CHEMISTRY particles under the electron beam showed extreme qualitative dif- equipped with a LaB6 filament). Analysis was performed using in situ ATR- ferences and that dissolution rates differed by more than an order of FTIR, DLS, and electron diffraction. magnitude. They tentatively related these differences to either solid or liquid-like behavior of the particles (where liquid-like particles Simulations. MD at 298 K and 1 atm was used to investigate the speciation of dissolve faster). It is important to note, however, that these observed calcium (bi)carbonate in solution (see SI Appendix, section 1.10, for full details). Configurations were prepared to achieve an initial pH of 9.9 by setting differences in dissolution rate will also depend on other factors such 2− − the CO3 /HCO3 ratio determined by the Henderson–Hasselbalch equation as the difference in particle size, thickness of the imaged liquid layer, − 2− + 2+ and using a pKa of 10.328 for HCO3 ⇄ CO3 + H . Subsequently, Ca was + and applied electron dose rate. In any case, the apparent difference added to neutralize the total charge in the system, generating total Ca2 in electron-scattering intensities between these particles showing concentrations of 20–30 mM (SI Appendix, Table S1, provides the initial different dissolution rates is significantly lower compared with the system compositions). Two different initial arrangements of the ions were difference we observe between the ACC and the DLP, and suggests used: in the first type of simulation (cluster system), ions were inserted into a a significantly lower degree of hydration for any of the amorphous box of water as a single, low-energy cluster with an average ionic co- phases reported by Nielsen compared with the DLP observed here. ordination consistent with DOLLOP, as taken from extensive random struc- In contrast to the scenarios proposed previously for other sys- ture searches (45), and allowed to relax. In the second type (random system), tems (11, 14), we conclude that liquid–liquid separation in the ions were randomly introduced into a volume of water and equilibrated. studied system happens via an activated process. Our total calcium The 20-ns trajectories were generated with averages calculated in 2-ns windows at equilibrium. The total number of ions and water molecules was and carbonate concentrations of ∼1mMattσ max are well below the same in both the cluster and random systems. the spinodal limit reported by Zou et al. (15), although we note + Random systems were also prepared for simulations at high initial free Ca2 that their solutions were not prepared identically. Moreover, it is 2+ 2+ concentrations [c(Ca free)] of 0.57, 1.1, and 1.7 M (SI Appendix, Table S2). These unlikely that the slow addition of Ca ions allows the system to simulations contained only carbonate anions; otherwise, they were prepared cross the spinodal line before the appearance of the DLP. Thus, – following the methods used for lower concentration simulations. Simulations liquid liquid separation in our experiment is more likely to involve were performed at 298 K and 1 atm for 60 ns, with the final 5-ns window used nucleation and growth of the DLP within the binodal regime. Our to analyze equilibrium states. TEM simulations were performed using a multi- DLSdatainFig.2D fits the growth of phase-separated domains slice algorithm for the system at 1.7 M initially and bulk amorphous phases with both through coalescence by Brownian collisions and through varying degrees of hydration. For full details, see SI Appendix, section 1.12.

Smeets et al. PNAS | Published online September 5, 2017 | E7889 Downloaded by guest on October 2, 2021 The force field of Demichelis et al. (18) was used to model the interactions Research Technology Platform (Warwick University), the MidPlus Regional between atoms. This is an adaptation of earlier force fields and has been shown e-Infrastructure Centre (Grant EP/K000128/1), and ARCHER, the UK national to accurately reproduce the properties of bulk phases and, crucially, the free supercomputing service. The work of P.J.M.S. and N.A.J.M.S. is supported by a energies of solvation for ions in water (18, 42, 55). Clusters were defined VICI grant of the Netherlands Organization for Scientific Research. The work of according to a geometric criterion where the distance between Ca and C (of A.R.F. and P.M.R. was supported under Engineering and Physical Sciences carbonate and bicarbonate) was within 4.2 Å: slightly larger than the minimum Research Council Grant EP/I001514/1, and A.R.F. acknowledges support from

in Ca–C radial distribution functions for low-density amorphous CaCO3 clusters. the University of Sheffield under a Doctoral Prize Fellowship. The work of J.J.D.Y. was supported by the US Department of Energy, Office of Basic Energy Sciences, ACKNOWLEDGMENTS. Experimental work was performed at the Eindhoven Division of Materials Science and Engineering at the Pacific Northwest National University of Technology. The computational part of this study was performed at Laboratory (PNNL). PNNL is operated by Battelle for the US Department of the Centre for Scientific Computing and Department of Chemistry (University of Energy under Contract DE-AC05-76RL01830. This work is dedicated to the Warwick). Computational resources were provided by the Scientific Computing memory of P.M.R., who sadly passed away on March 23, 2017.

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