Encyclopedia of Nanotechnology

Living Edition
| Editors: Bharat Bhushan

Prenucleation Clusters

  • Denis GebauerEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-94-007-6178-0_380-2

Keywords

Calcium Carbonate Calcium Oxalate Critical Nucleus Stable Cluster Classical Nucleation Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Synonyms

Definition

Prenucleation clusters are thermodynamically stable associates of atoms, ions, or molecules forming in solution, approximately 1–3 nm in size on average. They are solutes themselves and form based upon dynamic chemical equilibrium in undersaturated as well as supersaturated (metastable) solution states, playing a key role during nucleation of a second phase from the latter.

Overview

Relevance

How crystallization may be controlled is an important question, since many processes and applications depend on the control of crystal polymorphism, morphology, size, and other crystal characteristics. However, today, the design of bottom-up approaches to tailor-made crystalline materials is still widely settled in the realm of trial and error. In order to improve these empirical approaches, (nano)technology depends on a molecular understanding of the underlying processes [1]. A look at living nature shows that organisms are able to control crystallization in sophisticated ways, and form mineralized structures – biominerals like bone, teeth, or nacre – that show outstanding material properties that are tailor made with respect to function through advanced micro- and nanostructures [2]. Many studies have indicated that biomineralization processes can proceed via so-called nonclassical, that is, particle-mediated pathways, which may also involve liquid and/or amorphous intermediates [3]. In contrast, classical theories presented in most crystallization textbooks only consider ion-by-ion, atom-by-atom, or molecule-by-molecule reaction channels for nucleation and growth [4].

The notion of stable prenucleation clusters can be regarded as an important expansion of nonclassical concepts toward the most fundamental step in crystallization: nucleation [5]. The term “nucleation” refers to the onset of phase separation in a system that has become supersaturated. The existence of stable clusters is not taken into account within classical nucleation theory, which is the framework that is used to access nucleation phenomena in the majority of cases. Hence, an alternative reaction channel referred to as the “prenucleation cluster pathway” has been proposed [5], which includes a nanoscopic liquid-liquid separation as central event. In the proposed mechanism, stable prenucleation clusters play a key role as direct molecular solute precursors of phase-separated nanodroplets. There are strong indications that this pathway is relevant for many materials forming from aqueous solution, including the most important biominerals calcium carbonate and phosphate, as well as silica, iron oxides, calcium oxalate, but also small organic molecules like amino acids, urea, or citrate [5, 6].

Background: Classical Nucleation Theory

Nucleation means the onset of a phase transition, that is, the irreversible formation of the first nuclei of a nascent phase in a system that has become supersaturated. The work of Becker and Döring is commonly known as classical nucleation theory (CNT), which was originally derived for the formation of nuclei from supersaturated water vapors [7, 8]. The fundamental assumption of CNT is that the bulk energy of a forming nucleus drives nucleation, while the generation of a phase interface, and with it of interfacial surface, is the antagonist and impedes nucleus growth. The bulk energy (favorable, negative sign) scales with the cube of the radius of the nuclei, and their surface energy (unfavorable, positive sign) increases with the square of the radius. Hence, the bulk energy begins to balance the energetic costs due to the generation of a phase interface at a certain point (Fig. 1). A nucleus of this size is the critical nucleus. The critical size corresponds to a metastable state of equilibrium, and even infinitesimal changes toward smaller or larger sizes will lead to nucleus dissolution or growth without limit, respectively. The change in free enthalpy for the formation of (pre)critical nuclei is positive, hence formation of these species is thermodynamically improbable and can only occur through fluctuations on microscopic scales.
Fig. 1

Classical representation of the energy of a nucleus (blue line) in dependence of its radius in a supersaturated system. The surface energy gives a positive (unfavorable, red line) and the bulk energy a negative energetic contribution (green line), which are proportional to the square and the cube of the radius, respectively. Hence, at the critical size, the bulk term begins to balance the surface term

CNT makes several assumptions, among which the so-called capillary assumption is the most debatable. The oversimplification was realized already by Gibbs when he first formulated it: Nanoscopic nuclei of a nascent phase are assumed to behave as if they were macroscopic. There have been several empirical and semiempirical treatments of CNT that aim at the improvement of quantitative predictions of nucleation rates, which can deviate from measurements by many orders of magnitude [9]. Under purely qualitative considerations, though, CNT is successful in describing nucleation phenomena in principle. The hallmark of nucleation is the presence of a barrier, which scales with supersaturation (and temperature) and prevents nucleation from proceeding spontaneously, at least close to the saturation limit. CNT assumes that a nucleus of critical size is fundamental to the existence of this thermodynamic barrier.

Prenucleation Clusters: An Alternative Concept

Prenucleation clusters, as opposed to classical nuclei, are considered to be solutes. Their formation is thus not linked to the problem of phase separation, at least during the initial stages. Mechanistically, prenucleation cluster formation can be conceived of being analogous with polycondensation reactions, yielding mostly chain-like assemblies of monomers. Hence, solute association leads to Schulz-Flory-like size distributions of a population of clusters [10]. Since a broad distribution of many clusters is entropically favorable, thermodynamically stable clusters will not grow without limit to macroscopic sizes. Also, the solute clusters will not aggregate, because there is no driving force for this due to the absence of interfacial surfaces.

Accordingly, five key characteristics have been suggested to define chemical species as prenucleation clusters [5]:
  1. 1.

    They are composed of chemical entities that also constitute the final solid but may include additional molecules like water.

     
  2. 2.

    Prenucleation clusters are thermodynamically stable solutes, around 1–3 nm in size on average, and there is formally no phase boundary with the surrounding solution.

     
  3. 3.

    They are direct molecular precursors to phase-separated species.

     
  4. 4.

    Stable solute clusters are highly dynamic and change configuration on timescales of hundreds of picoseconds, typical for rearrangements in solution.

     
  5. 5.

    They can exhibit distinct structural motifs and thereby give rise to the phenomenon of polyamorphism as observed in transient solid intermediates [11].

     
Computer simulations evidence that upon reaching a certain size, prenucleation clusters can internally develop higher coordination numbers than in the initial chain-like forms. This slows down their dynamics distinctly; thus, the clusters become different from the solution and should then be regarded as nanodroplets of a second phase. The resulting phase interface is subsequently reduced via aggregation, yielding larger, eventually solid amorphous nanoparticles most likely through solidification. However, the direct formation of (nano)crystalline species from prenucleation clusters should not be categorically excluded [5]. Returning to the hallmark of nucleation, the barrier of phase separation close to the solubility limit in the prenucleation cluster pathway is considered to arise from considerable energetic costs for condensing small dynamic solute clusters toward bulk-like states with distinctly higher coordination. Only fluctuations toward larger cluster sizes can lead to the development of somewhat higher coordination numbers, slowing down the dynamics, and phase separation yielding at first liquid nanodroplets can be initiated as described above. Physically, this event can be conceived of as entering a nanoscopic liquid-liquid miscibility gap [5]. A schematic overview of the prenucleation cluster pathway is illustrated in Fig. 2.
Fig. 2

Schematic illustration of the prenucleation cluster pathway. Stable prenucleation clusters form in solution based on chemical equilibrium. They are direct molecular precursors to phase-separated nanodroplets, forming upon a nanoscopic liquid-liquid separation event. The key difference between prenucleation clusters and nanodroplets is the distinctly reduced dynamics of the latter. This corresponds to the emergence of interfacial surfaces, which are reduced via aggregation, yielding amorphous intermediates. These may solidify and eventually crystallize. For explanation see text

Key Research Findings

In case of electrolyte solutions, the prenucleation cluster concept essentially represents an expansion of classical ion-pairing models [5]. In older literature, it is postulated that ion association must be limited to ion pairs when corresponding experimental ion-binding profiles are linear. The basic argument in this case is that the formation of defined larger species would lead to curved ion-binding behavior, as can be shown easily utilizing the law of mass action [5]. The most prominent example for this observation is arguably calcium carbonate. The first central key research finding here is the realization that linear ion-binding profiles are in fact ambiguous and that the formation of higher associated states cannot be unequivocally ruled out based upon ion-binding profiles alone. This ambiguity arises when successive binding events that lead to the generation of larger associates (e.g., in case of calcium carbonate, binding of a calcium ion to a carbonate ion, binding of a calcium ion to a calcium carbonate ion pair, binding of an ion pair to an ion pair, and so forth) are assumed to be all equal and independent, that is, bound by equivalent energetics. Then, all association events are macroscopically indistinguishable in the first place and may appear like simple ion pairing from the point of view of the law of mass action, despite the presence of large clusters. While this basic assumption may seem like an oversimplification, extensive computer simulations do show that it is indeed sustainable [5]. Thus, in any case, the unambiguous identification, or exclusion, of higher associated states crucially depends upon additional techniques like analytical ultracentrifugation, which can also show that the bound ions quantitatively reside in entities that are much larger than ion pairs on average [5].

Second, the thermodynamic stability of prenucleation clusters (equilibrium constant of formation K >> 1 and a corresponding change in free enthalpy of ΔG < 0) is essential to explain the occurrence of a significant population of larger clusters, which can be analytically detected in the first place. In contrast, metastable species are in fact very rare (owing to an equilibrium constant of formation 0 < K < 1, and thus ΔG > 0) and usually cannot be detected analytically. Because a metastable state is regarded to be central to the nucleation event within the notions of CNT, stable species have to be regarded as inactive during phase separation processes according to this theoretical framework, because they cannot participate in metastable fluctuations that would lead to the random formation of a critical nucleus. Stable clusters would sit in a free energy trap and hamper formation of a critical nucleus, at least from a classical point of view [5, 12].

However, in the prenucleation cluster pathway, the stable clusters do not yield a solid metastable nucleus of critical size but form amorphous nanodroplets via a structurally more direct transformation, and these nanophases subsequently aggregate to form a new macroscopic phase. At this point, it is important to note that the existence of a nucleation barrier shows that phase separation is a generic consequence of metastable fluctuations, which do not necessarily require the existence of a classical critical nucleus. Thus, the third major key research finding is that metastable fluctuations can also occur in a stable cluster population. They lead to the random occurrence of large clusters through microscopic fluctuations, which correspond to metastable deviations from the equilibrium cluster size distribution. In turn, the random occurrence of a significant population of rather large clusters, which can condense internally as opposed to smaller ones, would be at first reversible and physically correspond to a binodal nanoscopic liquid-liquid separation event [5].

Future Directions for Research

Despite significant progress when it comes to the understanding of the prenucleation cluster pathway in the recent years, many open questions remain that need to be addressed. The following list does not demand to be complete and is supposed to give a rather generic overview:
  • Nucleation theory: It is most important to include the notion of stable prenucleation clusters into a revised quantitative theory of nucleation. In this context, modeling and simulation approaches appear to be crucial. The implementation concerns homogeneous nucleation theory, but cluster-based pathways do play a role in heterogeneous phase separation processes as well (Fig. 3). The latter are of immediate importance for various industrial and technological problems but also in biomineralization and medical issues.

  • Biomineralization and additive-controlled crystallization: It is now evident that prenucleation clusters play important roles during surface-induced crystallization in biomimetic approaches (Fig. 3), but their role in biological systems has not been shown directly. Importantly, the prenucleation cluster pathway can mechanistically explain the occurrence of liquid intermediate forms of minerals, which are considered to play a central role in biomineralization [13]. The latter phenomenon provides a direct link to additive-controlled mineralization, since such liquid intermediates can be stabilized by certain polymers. This immediately raises the question whether this phenomenon can be exploited more generally than previously assumed and how the prenucleation cluster pathway may improve the understanding of additive-controlled mineralization, as suggested for biomineralization [14].

  • Generality: Prenucleation clusters have been shown to exist for a series of compounds, including most biominerals but also small organic molecules. The prenucleation cluster pathway may be a more general phenomenon that may apply to the formation mechanism of many solids, perhaps not only in aqueous solution. The generality of the prenucleation cluster concept has to be tested, including the identification of conditions under which cluster-based mechanisms of phase separation may or may not dominate.

Fig. 3

Computer-aided 3D visualization of tomograms from cryo-TEM of different stages of the surface-induced mineralization of calcium phosphate from simulated body fluid. Prenucleation clusters (Stage 1) that are approximately 0.9 nm in size aggregate upon tranformation into nanodroplets on an extrinsic surface (Stages 2 & 3) to form initially amorphous nanoparticles (Stage 4), which subsequently crystallize (Stage 5; data kindly provided by A. Dey and N. A. J. M. Sommerdijk)

Cross-References

References

  1. 1.
    Rieger, J., Kellermeier, M., Nicoleau, L.: Formation of nanoparticles and nanostructures – an industrial perspective on CaCO3, cement and polymers. Angew. Chem. Int. Ed. 53, 12380–12396 (2014)Google Scholar
  2. 2.
    Lowenstam, H., Weiner, S.: On Biomineralization. Oxford University Press, New York (1989)Google Scholar
  3. 3.
    Cölfen, H., Antonietti, M.: Mesocrystals and Nonclassical Crystallization. Wiley, Chichester (2008)CrossRefGoogle Scholar
  4. 4.
    Mullin, J.: Crystallization. Butterworth-Heinemann, Oxford (2001)Google Scholar
  5. 5.
    Gebauer, D., Kellermeier, M., Gale, J.D., Bergström, L., Cölfen, H.: Pre-nucleation clusters as solute precursors in crystallisation. Chem. Soc. Rev. 43, 2348–2371 (2014)CrossRefGoogle Scholar
  6. 6.
    Davey, R.J., Schroeder, S.L.M., ter Horst, J.H.: Nucleation of organic crystals – a molecular perspective. Angew. Chem. Int. Ed. 52, 2166–2179 (2013)CrossRefGoogle Scholar
  7. 7.
    Nielsen, A.E.: Kinetics of Precipitation. Pergamon, New York (1964)Google Scholar
  8. 8.
    Kashchiev, D.: Nucleation: Basic Theory with Applications. Butterworth-Heinemann, Oxford (2000)Google Scholar
  9. 9.
    Vekilov, P.G.: The two-step mechanism of nucleation of crystals in solution. Nanoscale 2, 2346–2357 (2010)CrossRefGoogle Scholar
  10. 10.
    Flory, P.J.: Fundamental principles of condensation polymerization. Chem. Rev. 39, 137–197 (1946)CrossRefGoogle Scholar
  11. 11.
    Cartwright, J.H., Checa, A.G., Gale, J.D., Gebauer, D., Sainz-Díaz, C.I.: Calcium carbonate polyamorphism and its role in biomineralization: how many amorphous calcium carbonates are there? Angew. Chem. Int. Ed. 51, 11960–11970 (2012)CrossRefGoogle Scholar
  12. 12.
    De Yoreo, J.J.: Crystal nucleation: more than one pathway. Nat. Mater. 12, 284–285 (2013)CrossRefGoogle Scholar
  13. 13.
    Gower, L.B.: Biomimetic model systems for investigating the amorphous precursor pathway and its role in biomineralization. Chem. Rev. 108, 4551–4627 (2008)CrossRefGoogle Scholar
  14. 14.
    Evans, J.S.: “Liquid-like” biomineralization protein assemblies: a key to the regulation of non-classical nucleation. CrystEngComm 15, 8388–8394 (2013)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of Chemistry, Physical ChemistryUniversity of KonstanzKonstanzGermany