A classical view on nonclassical nucleation PNAS PLUS 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 CHEMISTRY 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. www.pnas.org/cgi/doi/10.1073/pnas.1700342114 PNAS Early Edition | 1of9 Downloaded by guest on September 28, 2021 are able to nucleate from solution—bounded by a limit of solution A B 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 pre- sent 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 av- erage 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