Stephen Whitelam

Crystallization by particle attachment in synthetic, biogenic, and geologic environments

Growing crystals by attaching particles Crystals grow in a number a ways, including pathways involving the assembly of other particles and multi-ion complexes. De Yoreo et al. review the mounting evidence for these nonclassical pathways from new observational and computational techniques, and the thermodynamic basis for these growth mechanisms. Developing predictive models for these crystal growth and nucleation pathways will improve materials synthesis strategies. These approaches will also improve fundamental understanding of natural processes such as biomineralization and trace element cycling in aquatic ecosystems. Science, this issue 10.1126/science.aaa6760 Materials nucleate and grow by the assembly of small particles and multi-ion complexes. BACKGROUND Numerous lines of evidence challenge the traditional interpretations of how crystals nucleate and grow in synthetic and natural systems. In contrast to the monomer-by-monomer addition described in classical models, crystallization by addition of particles, ranging from multi-ion complexes to fully formed nanocrystals, is now recognized as a common phenomenon. This diverse set of pathways results from the complexity of both the free-energy landscapes and the reaction dynamics that govern particle formation and interaction. Whereas experimental observations clearly demonstrate crystallization by particle attachment (CPA), many fundamental aspects remain unknown—particularly the interplay of solution structure, interfacial forces, and particle motion. Thus, a predictive description that connects molecular details to ensemble behavior is lacking. As that description develops, long-standing interpretations of crystal formation patterns in synthetic systems and natural environments must be revisited. Here, we describe the current understanding of CPA, examine some of the nonclassical thermodynamic and dynamic mechanisms known to give rise to experimentally observed pathways, and highlight the challenges to our understanding of these mechanisms. We also explore the factors determining when particle-attachment pathways dominate growth and discuss their implications for interpreting natural crystallization and controlling nanomaterials synthesis. ADVANCES CPA has been observed or inferred in a wide range of synthetic systems—including oxide, metallic, and semiconductor nanoparticles; and zeolites, organic systems, macromolecules, and common biomineral phases formed biomimetically. CPA in natural environments also occurs in geologic and biological minerals. The species identified as being responsible for growth vary widely and include multi-ion complexes, oligomeric clusters, crystalline or amorphous nanoparticles, and monomer-rich liquid droplets. Particle-based pathways exceed the scope of classical theories, which assume that a new phase appears via monomer-by-monomer addition to an isolated cluster. Theoretical studies have attempted to identify the forces that drive CPA, as well as the thermodynamic basis for appearance of the constituent particles. However, neither a qualitative consensus nor a comprehensive theory has emerged. Nonetheless, concepts from phase transition theory and colloidal physics provide many of the basic features needed for a qualitative framework. There is a free-energy landscape across which assembly takes place and that determines the thermodynamic preference for particle structure, shape, and size distribution. Dynamic processes, including particle diffusion and relaxation, determine whether the growth process follows this preference or another, kinetically controlled pathway. OUTLOOK Although observations of CPA in synthetic systems are reported for diverse mineral compositions, efforts to establish the scope of CPA in natural environments have only recently begun. Particle-based mineral formation may have particular importance for biogeochemical cycling of nutrients and metals in aquatic systems, as well as for environmental remediation. CPA is poised to provide a better understanding of biomineral formation with a physical basis for the origins of some compositions, isotopic signatures, and morphologies. It may also explain enigmatic textures and patterns found in carbonate mineral deposits that record Earth’s transition from an inorganic to a biological world. A predictive understanding of CPA, which is believed to dominate solution-based growth of important semiconductor, oxide, and metallic nanomaterials, promises advances in nanomaterials design and synthesis for diverse applications. With a mechanism-based understanding, CPA processes can be exploited to produce hierarchical structures that retain the size-dependent attributes of their nanoscale building blocks and create materials with enhanced or novel physical and chemical properties. Major gaps in our understanding of CPA. Particle attachment is influenced by the structure of solvent and ions at solid-solution interfaces and in confined regions of solution between solid surfaces. The details of solution and solid structure create the forces that drive particle motion. However, as the particles move, the local structure and corresponding forces change, taking the particles from a regime of long-range to short-range interactions and eventually leading to particle-attachment events. Field and laboratory observations show that crystals commonly form by the addition and attachment of particles that range from multi-ion complexes to fully formed nanoparticles. The particles involved in these nonclassical pathways to crystallization are diverse, in contrast to classical models that consider only the addition of monomeric chemical species. We review progress toward understanding crystal growth by particle-attachment processes and show that multiple pathways result from the interplay of free-energy landscapes and reaction dynamics. Much remains unknown about the fundamental aspects, particularly the relationships between solution structure, interfacial forces, and particle motion. Developing a predictive description that connects molecular details to ensemble behavior will require revisiting long-standing interpretations of crystal formation in synthetic systems, biominerals, and patterns of mineralization in natural environments.

Real-time imaging of Pt3Fe nanorod growth in solution.

Growing in Liquid The ability to control the growth of materials at the nanometer scale is key to nanotechnology. Materials grown in liquids, however, are difficult to track on a particle-by-particle basis during growth. Two studies used an in situ liquid cell to follow the formation of larger nanoparticles or nanorods grown in solvents using high-resolution transmission electron microscopes. Liao et al. (p. 1011) watched platinum iron nanorods form from kinked chains of connected nanoparticles that gradually reoriented and straightened to form rigid rods. Li et al. (p. 1014) observed the coalescence of iron oxyhydroxide nanoparticles through an oriented attachment mechanism, whereby two similar particles rotated until their corresponding crystal lattices aligned. An in situ liquid stage is used to study the formation of nanowires from solution in a transmission electron microscope. The growth of colloidal nanocrystal architectures by nanoparticle attachment is frequently reported as an alternative to the conventional growth by monomer attachment. However, the mechanism whereby nanoparticle attachment proceeds microscopically remains unclear. We report real-time transmission electron microscopy (TEM) imaging of the solution growth of Pt3Fe nanorods from nanoparticle building blocks. Observations revealed growth of winding polycrystalline nanoparticle chains by shape-directed nanoparticle attachment followed by straightening and orientation and shape corrections to yield single-crystal nanorods. Tracking nanoparticle growth trajectories allowed us to distinguish the force fields exerted by single nanoparticles and nanoparticle chains. Such quantification of nanoparticle interaction and understanding the growth pathways are important for the design of hierarchical nanomaterials and controlling nanocrystal self-assembly for functional devices.

Microscopic Evidence for Liquid-Liquid Separation in Supersaturated CaCO3 Solutions

Making Crystals The initial transition from a disordered solution to the formation of nuclei that grow into crystals continues to be a puzzle. Recent experiments suggested the formation of stable ordered clusters that appear prior to the formation of the first nuclei. Wallace et al. (p. 885; see the Perspective by Myerson and Trout) used molecular dynamics to look at the potential structure and dynamics of these clusters and lattice gas simulations to explore the population dynamics of the cluster populations prior to nucleation. A liquid-liquid phase separation process was observed whereby one phase becomes more concentrated in ions and becomes the precursor for nuclei to form. The preordering seen during calcium carbonate crystallization may be due to a liquid-liquid separation process. [Also see Perspective by Myerson and Trout] Recent experimental observations of the onset of calcium carbonate (CaCO3) mineralization suggest the emergence of a population of clusters that are stable rather than unstable as predicted by classical nucleation theory. This study uses molecular dynamics simulations to probe the structure, dynamics, and energetics of hydrated CaCO3 clusters and lattice gas simulations to explore the behavior of cluster populations before nucleation. Our results predict formation of a dense liquid phase through liquid-liquid separation within the concentration range in which clusters are observed. Coalescence and solidification of nanoscale droplets results in formation of a solid phase, the structure of which is consistent with amorphous CaCO3. The presence of a liquid-liquid binodal enables a diverse set of experimental observations to be reconciled within the context of established phase-separation mechanisms.

Dynamic Criticality in Glass-Forming Liquids

We propose that the dynamics of supercooled liquids and the formation of glasses can be understood from the existence of a zero-temperature dynamical critical point. To support our proposal, we derive a dynamic field theory for a generic kinetically constrained model, which we expect to describe the dynamics of a supercooled liquid. We study this field theory using the renormalization group (RG). Its long time behavior is dominated by a zero-temperature critical point, which for d>2 belongs to the directed percolation universality class. Molecular dynamics simulations seem to confirm the existence of dynamic scaling behavior consistent with the RG predictions.

Peptoid nanosheets exhibit a new secondary-structure motif

A promising route to the synthesis of protein-mimetic materials that are capable of complex functions, such as molecular recognition and catalysis, is provided by sequence-defined peptoid polymers—structural relatives of biologically occurring polypeptides. Peptoids, which are relatively non-toxic and resistant to degradation, can fold into defined structures through a combination of sequence-dependent interactions. However, the range of possible structures that are accessible to peptoids and other biological mimetics is unknown, and our ability to design protein-like architectures from these polymer classes is limited. Here we use molecular-dynamics simulations, together with scattering and microscopy data, to determine the atomic-resolution structure of the recently discovered peptoid nanosheet, an ordered supramolecular assembly that extends macroscopically in only two dimensions. Our simulations show that nanosheets are structurally and dynamically heterogeneous, can be formed only from peptoids of certain lengths, and are potentially porous to water and ions. Moreover, their formation is enabled by the peptoids’ adoption of a secondary structure that is not seen in the natural world. This structure, a zigzag pattern that we call a Σ(‘sigma’)-strand, results from the ability of adjacent backbone monomers to adopt opposed rotational states, thereby allowing the backbone to remain linear and untwisted. Linear backbones tiled in a brick-like way form an extended two-dimensional nanostructure, the Σ-sheet. The binary rotational-state motif of the Σ-strand is not seen in regular protein structures, which are usually built from one type of rotational state. We also show that the concept of building regular structures from multiple rotational states can be generalized beyond the peptoid nanosheet system.

The Statistical Mechanics of Dynamic Pathways to Self-Assembly

This review describes some important physical characteristics of the pathways (i.e., dynamical processes) by which molecular, nanoscale, and micrometer-scale self-assembly occurs. We highlight the existence of features of self-assembly pathways that are common to a wide range of physical systems, even though those systems may differ with respect to their microscopic details. We summarize some existing theoretical descriptions of self-assembly pathways and highlight areas-notably, the description of self-assembly pathways that occur far from equilibrium-that are likely to become increasingly important.

Control of pathways and yields of protein crystallization through the interplay of nonspecific and specific attractions.

We use computer simulation to study crystal-forming model proteins equipped with interactions that are both orientationally specific and nonspecific. Distinct dynamical pathways of crystal formation can be selected by tuning the strengths of these interactions. When the nonspecific interaction is strong, liquidlike clustering can precede crystallization; when it is weak, growth can proceed via ordered nuclei. Crystal yields are in certain parameter regimes enhanced by the nonspecific interaction, even though it promotes association without local crystalline order. Our results suggest that equipping nanoscale components with weak nonspecific interactions (such as depletion attractions) can alter both their dynamical pathway of assembly and optimize the yield of the resulting material.

Transformation from spots to waves in a model of actin pattern formation.

Actin networks in certain single-celled organisms exhibit a complex pattern-forming dynamics that starts with the appearance of static spots of actin on the cell cortex. Spots soon become mobile, executing persistent random walks, and eventually give rise to traveling waves of actin. Here we describe a possible physical mechanism for this distinctive set of dynamic transformations, by equipping an excitable reaction-diffusion model with a field describing the spatial orientation of its chief constituent (which we consider to be actin). The interplay of anisotropic actin growth and spatial inhibition drives a transformation at fixed parameter values from static spots to moving spots to waves.

There and (Slowly) Back Again: Entropy-Driven Hysteresis in a Model of DNA Overstretching

When pulled along its axis, double-stranded DNA elongates abruptly at a force of approximately 65 pN. Two physical pictures have been developed to describe this overstretched state. The first proposes that strong forces induce a phase transition to a molten state consisting of unhybridized single strands. The second picture introduces an elongated hybridized phase called S-DNA. Little thermodynamic evidence exists to discriminate directly between these competing pictures. Here we show that within a microscopic model of DNA we can distinguish between the dynamics associated with each. In experiment, considerable hysteresis in a cycle of stretching and shortening develops as temperature is increased. Since there are few possible causes of hysteresis in a system whose extent is appreciable in only one dimension, such behavior offers a discriminating test of the two pictures of overstretching. Most experiments are performed upon nicked DNA, permitting the detachment (unpeeling) of strands. We show that the long-wavelength progression of the unpeeled front generates hysteresis, the character of which agrees with experiment only if we assume the existence of S-DNA. We also show that internal melting can generate hysteresis, the degree of which depends upon the nonextensive loop entropy of single-stranded DNA.

Limit of validity of Ostwald's rule of stages in a statistical mechanical model of crystallization.

We have only rules of thumb with which to predict how a material will crystallize, chief among which is Ostwalds rule of stages. It states that the first phase to appear upon transformation of a parent phase is the one closest to it in free energy. Although sometimes upheld, the rule is without theoretical foundation and is not universally obeyed, highlighting the need for microscopic understanding of crystallization controls. Here we study in detail the crystallization pathways of a prototypical model of patchy particles. The range of crystallization pathways it exhibits is richer than can be predicted by Ostwalds rule, but a combination of simulation and analytic theory reveals clearly how these pathways are selected by microscopic parameters. Our results suggest strategies for controlling self-assembly pathways in simulation and experiment.