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Designing solid materials from their solute state: a shift in paradigms towards a holistic approach in functional materials chemistry Denis Gebauer, and Stephan E Wolf J. Am. Chem. Soc., Just Accepted Manuscript • Publication Date (Web): 12 Feb 2019 Downloaded from http://pubs.acs.org on February 12, 2019
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Journal of the American Chemical Society
Designing solid materials from their solute state: a shift in paradigms towards a holistic approach in functional materials chemistry Denis Gebauer,†,‡,* and Stephan E. Wolf§,‡,⁋,* †Department
of Chemistry, Physical Chemistry, University of Konstanz, Universitätsstraße 10, 78457 Konstanz, Germany of Materials Science and Engineering (WW), Institute of Glass and Ceramics (WW3), Friedrich-AlexanderUniversity Erlangen-Nuremberg (FAU), Martensstrasse 5, 91058 Erlangen, Germany. §Department
⁋Interdisciplinary
Center for Functional Particle Systems (FPS), Friedrich-Alexander University Erlangen-Nürnberg (FAU), Haberstrasse 9a, 91058 Erlangen, Germany. ABSTRACT: “Non-classical” notions consider formation pathways of crystalline materials where larger species than monomeric chemical constituents, i.e., ions or single molecules, play crucial roles, which are not covered by the classical theories dating back to the 1870s and 1920s. Providing an outline of “non-classical” nucleation, we demonstrate that pre-nucleation clusters (PNCs) can lie on alternative pathways to phase separation, where the very event of demixing is not primarily based on the sizes of the species forming, as in the classical view, but their dynamics. Rationalizing, on the other hand, that precursors that can be analytically detected in pre-nucleation stages and that play a role in phase separation must be considered PNCs and cannot be explained by classical notions, we outline a variety of systems where PNCs are important. Indeed, in recent years, with the advent of “non-classical” theories, a primary focus of research concentrated on the fundamental understanding of oligomeric/polymeric and particulate species involved in nucleation and crystallization processes, respectively. At the same time, the near-to unfathomable potential of “non-classical” routes for the synthesis of inorganic functional materials slowly unfolds. An overview over recent developments in the fundamental and mechanistical understanding of “non-classical” nucleation and crystallization in this perspective then allows us mapping out the potential of cluster/particle-driven mineralization pathways to intrinsically tailor the properties of inorganic functional (hybrid) materials via structuration from the nano- to the mesoscale. This is of utter importance for the functionality and performance of materials as it may even confer emergent properties such as self-healing. Biominerals — often formed via particle accretion mechanisms— demonstrate this impressively and thus can serve as further source of inspiration how to exploit nonclassical crystallization routes for syntheses of structured and functional materials. These new avenues to synthetic approaches may finally provide a holistic material concept, in which fundamental chemistry and materials science synergistically alloy.
theories was realized early on,2,3 chemical aspects and peculiarities of specific systems are still commonly neglected. Justifiably so, Bøjesen and Iversen argued that it is time to introduce a shift in paradigms and to move away from a "one model fits all" to a chemistry-based approach to nucleation and crystallization.4 In a big step in this direction, Wall et al.5 made very recently a key contribution by introducing a model of reaction-driven nucleation theory, which is successful in predicting magic-sized clusters for gold nucleation as opposed to classical models. A thorough chemical understanding of a given system is thus at the heart of so-called “non-classical” nucleation and “nonclassical” crystallization frameworks.6-8 While a quantitative "non-classical" theory is still lacking, classical expressions can be parametrized to force quantitative agreement with experiments. But still, detailed aspects of micro- and nanoscale processes must often be included to accurately describe experimental observations, for instance, in macroscopic modeling approaches.9 The 'fixing' of classical expressions via parametrization is a direct consequence of their conceptual character, although real observations clearly differ from the predictions of the simplified models.10 In our opinion, microscopic and, ultimately, atomistic insights into the early stages of nucleation and crystallization will inevitably
INTRODUCTION Across all subfields of chemistry, nucleation and crystallization are phenomena of fundamental importance and literally ubiquitous. Our daily life is affected by these processes, while critical industrial issues arise from phase separation.1 Theoretical frameworks successful in explaining, describing and predicting related phenomena are crucially needed, both on qualitative and quantitative levels. In recent years, the existing textbook knowledge on nucleation and crystallization, however, has been continuously challenged. The corresponding theories seem to be at odds with many experimental observations, questioning both their explanatory and predictive powers. This is mainly because the established classical models only consider monomeric building blocks during the formation of nascent particles — atoms, ions or molecules, depending on the specific chemical system. The potential roles of stable oligomeric or polymeric species as nucleation precursors and of nanoscopic species as building units in crystal growth processes are mostly neglected in classical concepts. Moreover, quantitative expressions derived for nucleation rates typically rely on the assumption that physical properties of macroscopic phases are representative for nuclei. While the latter oversimplification of classical textbook
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only thermodynamic factors but also kinetic and mechanistic effects operating at different scales in space and time play important roles.19 We propose that the unification of “nonclassical” notions of nucleation and crystallization pave the way to holistic approaches where chemistry, rather than oversimplified physical notions, rationalizes the phase separation and growth mechanisms. This “non-classical” understanding is ultimately required in order to allow exploiting these crystallization modes as potent tools for directed and target-oriented synthesis of tailored structured functional materials. Before we can turn our attention to these discussions, we briefly summarize the main notions and characteristics of classical and "non-classical" models and theories. Advanced readers may proceed directly to the discussions section. Classical nucleation theory (CNT). Following CNT,3,20,21 nanoscopic nuclei can be assumed to behave as if they were macroscopic. The consideration of the size dependence of the bulk and interfacial free energies then shows that the excess free energy due to the nuclei's surface dominates at small sizes, whereas the favorable bulk free energy takes over at larger sizes. The point at which the two contributions are balanced is the nucleus of critical size (Fig. 1, top), which is characterized by a positive standard free energy that depends on supersaturation. The thermodynamics of the critical nucleus are thus assumed to govern the transition state to nucleation by imposing a 'thermodynamic' barrier that is progressively reduced by increasing supersaturation, while additional kinetic barriers that do not depend on supersaturation (e.g., due to dehydration of the monomeric constituents upon nucleus formation) are typically neglected. The established notion of 'two-step nucleation'22-24 then refers to a process, where a liquidcondensed phase is nucleated initially, and nucleation of solid particles in the formed intermediate phase proceeds according to the notions of CNT. Strictly speaking, even though often labeled a "non-classical" pathway, 'two-step nucleation' essentially relies on the same physical mechanism as CNT and can be seen as a subvariant of the Ostwald-Lussac law of stages: the formation of the new phase(s) is not fueled by the accretion of colloidal entities but it is driven by an ion-by-ion or molecule-by-molecule growth mode. That said, it becomes clear that semi-empirical equations for 'two-step nucleation'24 represent a parametrization of CNT, so as to explain experimentally determined nucleation rates that are much larger than predicted based on original CNT expressions. 'Two-step nucleation' is usually assumed to be applicable to protein nucleation in particular,25 however, it has been argued that it is more generally important.20 On the contrary, recent results imply that the 'two-step nucleation' mechanism does not always reflect the microscopic picture of nucleation, even for cases that were previously assumed to represent prime examples for 'twostep nucleation'.26,27 The pre-nucleation cluster (PNC) pathway. A truly "nonclassical" mechanism of nucleation has been established with the concept of the so-called pre-nucleation cluster (PNC) pathway, which is arguably most relevant for precipitation processes occurring in aqueous solutions (Fig. 1, bottom).28 PNCs are chemical clusters, e.g. multinuclear coordination complexes, which exist in solution before nucleation and which are characterized by five major traits28: (i) they are composed of the constituent atoms, molecules, or ions of a forming solid, but can also contain additional chemical species; (ii) they are small and, on ergodic average, thermodynamically stable solutes, and there is thus formally no phase boundary between the clusters
challenge the generalized views of established classical notions —and, in fact, already do. This represents a typical tide of events in scientific research of testing theories in search of their limits—reflecting the very idea of critical rationalism of Popper and the epistemological limits of science. This quest for limitations of established theories should not be perceived as an assault on the soundness of the derivation of those merited theories, but rather their supposedly general applicability. From the material chemist’s and material scientist’s point of view, the outcome of a “non-classical”, i.e., colloid-driven mineralization trajectory is clearly distinct from those of classical processes. In ion-by-ion, or monomer-by-monomer, driven processes, the crystal morphology is strictly governed by the anisotropic surface energy landscape of the pure bulk material. Surface energy minimization enforces the preferred expression of specific facets. Likewise, porosity is energetically highly unfavorable and generally obviated since it increases the surface area and, thus, the surface energy. The gain in bulk free energy fuels classical crystal growth and generally decreases upon incorporation of foreign chemical species. This limits the capability of classical systems to incorporate other chemical constituents, be they of organic nature or ionic dopants. Only because of this, recrystallization is an efficient and prevailing method for product purification, both in chemical labs and in industrial contexts: the molecular and ionic selection processes taking place at the crystal growth steps considerably restrict the compositional freedom of the final bulk material. Many of the synthetical and morphological constraints of classical crystallization can be alleviated in “non-classical” processes as these synthesis trajectories combinatorically implement nanoparticle synthesis, their stabilization and in situ surface functionalization of the colloids together with a subsequent selfassembly to form a mesostructured mineral body. Shifting gears from a crystallization process to a self-assembly process of reactive colloidal intermediates suppresses the dominant role of the crystal/solution interface in classical settings. Ostwald ripening is pushed into the background, either due to kinetic control or by colloid-stabilizing additives, and, similarly, shapes that would contradict Wulff’s rule can be kinetically stabilized on the microscale by generation of superstructures. This clears the way to a wide range of non-equilibrium morphologies. Aggregates with reduced symmetry, which are low in dimension or which feature high aspect-ratios are readily accessible by utilizing either stereoselective surfactants or exploiting intrinsic high-energy facets of the nanoscale building blocks.11-17 This results in highly fissured and jagged morphologies whose habit witness the nanoparticulate building block; and even highly complex shaped crystal superstructures such as helical bundles are feasible.18 In this perspective, we first rationalize that any species that can be experimentally detected in (metastable) pre-nucleation solutions and that participate in phase separation can be regarded as PNCs, following the definition that we reflect in the next but one paragraph. We then proceed to review recent, selected literature in order to illustrate the significance of PNCs during nucleation in a broad range of chemical systems. Turning to the potential modes of additive-directed nucleation and crystallization, we then review the colloidal reaction channels observed in biomineralization and bio-inspired materials chemistry within a unifying framework. Ultimately, this leads us to conclude that a paradigm shift away from CNT is fundamentally required for obtaining an improved understanding of the early stages of precipitation, where not
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Journal of the American Chemical Society
and the surrounding solution; (iii) PNCs are molecular precursors to the phase nucleating from solution, and hence participate in the process of phase separation; (iv) they are highly dynamic entities, and change configuration on timescales typical for molecular rearrangements in solution (i.e., within hundreds of picoseconds); note that this criterion does, on principle, not contradict the existence of a stable ergodic population; (v) they may have encoded structural motifs resembling, or relating to, one of the corresponding crystalline polymorphs, or forms.
PNCs reduce their dynamics.28,35,36 This event formally brings about the development of an interfacial surface, defined by a discontinuous change in dynamics upon leaving the solution and entering the, now, post-nucleation, clusters. In this sense, the PNCs become nanodroplets, which subsequently aggregate in order to decrease the as-developed interfacial surface area in the system, and then dehydrate to form solid amorphous intermediates, which later transform into crystals. PNCs can be thus seen as building blocks of an amorphous transient phase, and in case of a (quasi) solid-to-solid transformation also of the final crystalline phase. In analogy to CNT, but as opposed to 'two-step nucleation',26 there is one main barrier for phase separation in the PNC pathway. As opposed to CNT, though, the origin of the barrier is not based on the size of the nuclei, but on a structural change within PNCs that reduces their dynamics and creates interfacial surface.
DISCUSSION Pre-nucleation clusters (PNCs) versus classical nucleation theory (CNT). Although the limitations of CNT are generally acknowledged, 37 recent studies claimed nevertheless that CNT fully suffices to rationalize “non-classical” observations.30,38 These studies, however, provided no conclusive experimental evidence against PNCs and merely rested on (erroneous) interpretations of results from computer simulations, an issue that is discussed elsewhere in detail.10 Zahn rationalized the existence of precursor clusters and non-classical nucleation processes by analogous concepts based on competing interface and bulk energy terms, however, going well beyond CNT.39 The explanatory and predictive power of these ideas, which are based on computer simulations, should be tested experimentally. In any case, statistical tools to analyze crystallization trajectories and identify the transition mechanisms by computer simulations will continue to be of ultimate relevance for a better understanding of nucleation processes.40 Improving existing interatomic potentials and currently available enhanced sampling methods will certainly help bringing simulations and experiments closer together.41-43 As a matter of fact, any attempted proof of the validity of CNT, based on the experimental detection of as-defined pre-/critical nuclei, is paradoxical. Thermodynamics dictates that the concentration of CNT-like (pre-)critical nuclei is minuscule due to their excess standard free energy.2,3,10 Already this consideration unequivocally demonstrates that any larger species detected in (meta-)stable pre-nucleation solutions have to be "non-classical". Only thermodynamically stable species can be reproducibly found in such experiments, thus rendering these species either PNCs, if they participate in phase separation, or thermodynamically stable spectators that do not play a role in nucleation. In any case, decaying size distributions of experimentally found pre-nucleation species do not contradict thermodynamic stability, which can only be assessed unambiguously by exploring absolute populations within a (pseudo-) equilibrium perspective.10 In the future, it will be the ultimate task that we trace in systems suspected to behave “nonclassically” the fate of solutes, such as ions, coordination complexes and/or clusters, and to unequivocally demonstrate which species finally serve as “building blocks” of a given separating phase. General "non-classical" advances. Wills et al.44 provided direct support for thermodynamically stable multimeric clusters in aqueous solutions using a Group Additivity approach
Figure 1. Schematic illustration of the mechanism of nucleation according to classical nucleation theory (CNT, top) and the prenucleation cluster (PNC) pathway (bottom). For different polymorphs or forms, the accessibility depends on the level of supersaturation. The sizes of the different species are system specific and cannot be fully generalized; the critical size (top, middle) for realistic supersaturation levels is typically within tens of ions, i.e. smaller than approximately 3-4 nm in diameter.29 PNCs are similar in size but thermodynamically stable, and thus significantly more abundant than classical (pre-) critical nuclei that cannot occur macroscopically, from a thermodynamic point of view. The smallest sizes of phase separated nano-droplets, which directly emerge from the PNC precursors, are thus also in the lower nanometer regime. Upon aggregation and coalescence, dense liquid droplets with sizes up to several hundred nanometers can be formed.30 Consequently, depending on the kinetics of aggregation and dehydration, the size of solid amorphous intermediates can range from ca. 20 nm to hundreds of micrometer in size.31,32 For further explanation see the text. Figure and caption reproduced from ref.33
It is crucial to highlight that, seen from the viewpoint of CNT, PNCs are stuck in a free energy trap since they are even further away from the supposedly relevant transition state —the critical nucleus— than the monomeric constituents.34 Depending on the thermodynamic stability of PNCs, it is thus not necessarily impossible to form CNT-type critical nuclei from PNC species, but at least highly improbable from the viewpoint of Boltzmann statistics. It can be argued that the truly "non-classical" aspect of the PNC pathway is the realization that the CNT-type transition state is not necessarily required for nucleation or phase seperation.10 PNCs can lie on alternative pathways to phase separation, where the very event of demixing is not primarily based on the sizes of the species forming, as strictly predicted in CNT, but their dynamics. This mechanistically bypasses the CNT-type critical nucleus, which does not necessarily lie on the thermodynamic pathway either. According to the PNC pathway, changes in the structure of the
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towards a complete speciation from computations. Using molecular simulation coupled with experiments, Anwar et al.45 obtained "non-classical" insight into the mechanism of secondary nucleation based on such species. They revealed that molecular aggregates in solution, which, in our opinion, correspond to PNCs (see above), undergo nucleation to form new crystallites when they come in contact with seeds (Fig. 2). Due to the weak interaction between the newly formed crystals and the seed surface, the surface of the seeds becomes available for another nucleation event, and the new crystallites can serve as seeds.
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understanding may also open up new avenues for the design of environmentally friendly scaling inhibitors, such as cellulosebased antiscalants.50 Similarly, Walton and Wynne presented a rationale to explain laser-induced nucleation, thereby suggesting new ways of triggering local phase separation. 51 Expanding on this in a dental clinical context, Sun and coworkers demonstrated that laser and chelating agents can be synergistically combined to allow for a biomimetic enamel restoration 52 Also in geological contexts, non-classical processes may play an important role in mineral-solution equilibration processes which occur by dissolution-precipitation reactions leading to pseudomorphic minerals.53 While in this instance, fluid-mineral interactions are important, it becomes generally more and more evident that the solvent plays central roles in nucleation and crystallization, which is typically neglected in classical theories and may go well beyond influencing the self-assembly and clustering of solute molecules prior to nucleation (as to the latter, see below).54 But even for single-component systems, the treatment of nucleation as a multi-dimensional process sheds new light, e.g., on the issue of polymorph selection,55 where "non-classical" behavior was interpreted as a decoupling of positional and orientational symmetry breaking.56 Calcium carbonate. While calcium carbonate remains an essential model system for the further development and refinement of the PNC pathway,28,57 it is also the system where the pivotal role of the solvent, water, during the early stages of crystallization is now crystal clear. The release of hydration water is the entropic key contribution, which drives prenucleation ion association,58 beyond the ion pair,59 and allowing for the formation of even larger PNCs.60 The role of the solvent plays a key role when Mg is introduced, by inhibiting calcite growth and directly promoting aragonite nucleation in the early stages of CaCO3 formation.61 The assessment of water dynamics allowed the localization of the liquid-liquid binodal limit, at which PNCs become nanodroplets of a new phase,36 while water can control the pre-structuring in the as-formed amorphous intermediates.62 Presuming that amorphous calcium carbonate (ACC) can only form via spinodal decomposition, on the other hand, Zou et al.63 developed a phase diagram associated with a higher critical solution temperature that seems to be at odds with previous investigations.35,64 Future research will be required to elucidate the phase diagram of the aqueous calcium carbonate system in detail. Wolf et al. demonstrated, by means of a contact-free levitation technique, that at the onset of calcium carbonate formation at near-neutral pH conditions, a liquid-like precursor phase occurs and that the morphological appearance and life-time of this transient and liquid-condensed intermediate can be manipulated by the use of polymeric additives.65-67 Recently, Dietzsch et al. further confirmed that extended liquid-like networks served as a precursor phase for solid ACC particles also in presence of polymers.68 On the other hand, as-stabilized liquid-like precursors may play a role in calcite crystal growth as suggested by AFM studies.69 Layerby-layer attachment of ACC nanoparticles, followed by their restructuring and fusion with a calcite surface was observed by Rodriguez-Navarro et al.70 and similar processes were reported for siderite mesocrystals.71 A Double pulse procedure to investigate nucleation of calcium carbonate suggested that the growth of crystals can occur due to the agglomeration of nuclei.72
Figure 2. Snapshots from a molecular dynamics simulation trajectory showing the stepwise formation of crystalline structures on the surface of the seed crystal for a moderately supersaturated system (Lennard–Jones solute–solvent affinity parameter =3.0 kJ/mol). a) Configuration showing the emergence of clusters of solute molecules in the solvent (15 nanoseconds into the simulation); the solvent is not shown. b) Nucleation of solute clusters on coming in contact with the crystal surface (120 ns). c) Nucleation of a solute cluster on coming in contact with a previously nucleated structure in contact with the seed crystal surface (135ns). d) Yet another nucleation event as a disordered cluster nucleates on coming in contact with the aggregated crystallite structure (225ns). Figure and caption reproduced with permission from ref.45 Towards advancing the understanding of further phenomena associated with nucleation, Chibowski and Szczes46 reviewed the literature on magnetic water treatment effects, which are especially important in anti-scaling approaches,47 highlighting the remarkable progress achieved by Coey.48 Here, the formation of PNCs of the structural form of ‘dynamicallyordered liquid-like oxyanion polymers’49 (DOLLOPs) can potentially explain the efficacy of magnetic field treatments for anti-scaling; a phenomenon which would remain fully counterintuitive within the notions of CNT. This new
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Journal of the American Chemical Society to that of ferrihydrite nanoparticles formed, revealing that nucleation proceeded via a cluster aggregation-based “nonclassical” pathway.92 In fact, a combination of various experimental techniques showed that at low driving force for phase separation, olation clusters form first, which are the PNCs of the aqueous Fe(III) system.93 The change in the dynamics of these olation PNCs, which triggers phase separation, is based on the onset of oxolation93 which can be intimately influenced in the presence of polycarboxylates94. A liquid-jet photoelectron-spectroscopy experiment allowed the investigation of the electronic structure of the occurring ironoxo oligomers.95 Evidence for the role of Keggin clusters in the pathway of ferrihydrite formation during base hydrolysis was provided by Weatherill et al.96 Last but not least, the preparation of ligand-free and ligand-protected amorphous iron oxide clusters (
