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.

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 Pt(3)Fe 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.

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.

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 behaviour 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 behaviour consistent with the RG predictions.PACS numbers: 64.60. Cn, 47.20.Bp, 47.54.+r, The recipe for making a glass is simple [1]: rapidly cool a liquid through its melting point to avoid crystallization. Cool it further, and the liquid eventually becomes so viscous that it forms a non-crystalline solid, or glass. Glasses are common in nature, but our theoretical understanding of their formation is poor [2]. Here we offer analytical and numerical results to support the proposition that the dynamics of glass-forming supercooled liquids is controlled by a zero temperature dynamic critical point.Our starting point is the real-space description of supercooled liquids studied in [3,4] and based on ideas and models originally proposed in [5,6,7]. In this approach the phenomenon of dynamic heterogeneity [8, 9, 10] plays a central role. The link between dynamic heterogeneity and glass formation is the subject of much current research. If this link is verified it will be an indication that the slow dynamics of glass formers is governed by dynamic spatial fluctuations (see [11,12] for alternatives based on thermodynamics), in contrast with the assumption of homogeneity of mode coupling theories [13,14].The microscopic coarse-grained approach of [3,4] relies on two observations: (i) at low temperature very few particles are mobile, and these mobility excitations are localized in space; (ii) mobile regions are needed to allow neighbouring regions to themselves become mobile. This is the concept of dynamic facilitation [5,7]. We show that this picture can be cast as a dynamical field theory and its scaling behaviour derived from a dynamic renormalization group (RG) analysis. We find that scaling properties are determined by a zero temperature critical point. For the simple case we consider, and for d > 2, this critical point is that of directed percolation (DP) [15]. We also show, by performing extensive molecular dynamics simulations, that supercooled Lennard-Jones binary mixtures display scaling behaviour consistent with that predicted by RG.We build an effective microscopic model as follows. A supercooled fluid in d spatial dimensions is coarse-grained into cells of linear size of the order of the static correlation length as given by the pair correlation function. Cells are labeled by a scalar mobility field, n i , identified by coarsegraining the system on a microscopic time scale. Mobile regions carr...

We describe some of the important physical characteristics of the 'pathways', i.e. dynamical processes, by which molecular, nanoscale and micron-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 be different in respect of 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.

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.

Two-dimensional (2D) atomically defined organic nanomaterials are an important material class with broad applications. However, few general synthetic methods exist to produce such materials in high yields and to precisely functionalize them. One strategy to form ordered 2D organic nanomaterials is through the supramolecular assembly of sequence-defined synthetic polymers. Peptoids, one such class of polymer, are designable bioinspired heteropolymers whose main-chain length and monomer sequence can be precisely controlled. We have recently discovered that individual peptoid polymers with a simple sequence of alternating hydrophobic and ionic monomers can self-assemble into highly ordered, free-floating nanosheets. A detailed understanding of their molecular structure and supramolecular assembly dynamics provides a robust platform for the discovery of new classes of nanosheets with tunable properties and novel applications. In this Account, we discuss the discovery, characterization, assembly, molecular modeling, and functionalization of peptoid nanosheets. The fundamental properties of peptoid nanosheets, their mechanism of formation, and their application as robust scaffolds for molecular recognition and as templates for the growth of inorganic minerals have been probed by an arsenal of experimental characterization techniques (e.g., scanning probe, electron, and optical microscopy, X-ray diffraction, surface-selective vibrational spectroscopy, and surface tensiometry) and computational techniques (coarse-grained and atomistic modeling). Peptoid nanosheets are supramolecular assemblies of 16-42-mer chains that form molecular bilayers. They span tens of microns in lateral dimensions and freely float in water. Their component chains are highly ordered, with chains nearly fully extended and packed parallel to one another as a result of hydrophobic and electrostatic interactions. Nanosheets form via a novel interface-catalyzed monolayer collapse mechanism. Peptoid chains first assemble into a monolayer at either an air-water or oil-water interface, on which peptoid chains extend, order, and pack into a brick-like pattern. Upon mechanical compression of the interface, the monolayer buckles into stable bilayer structures. Recent work has focused on the design of nanosheets with tunable properties and functionality. They are readily engineerable, as functional monomers can be readily incorporated onto the nanosheet surface or into the interior. For example, functional hydrophilic "loops" have been displayed on the surfaces of nanosheets. These loops can interact with specific protein targets, serving as a potentially general platform for molecular recognition. Nanosheets can also bind metal ions and serve as 2D templates for mineral growth. Through our understanding of the formation mechanism, along with predicted features ascertained from molecular modeling, we aim to further design and synthesize nanosheets as robust protein mimetics with the potential for unprecedented functionality and stability.

The simplest prescription for building a patterned structure from its constituents is to add particles, one at a time, to an appropriate template. However, self-organizing molecular and colloidal systems in nature can evolve in much more hierarchical ways. Specifically, constituents (or clusters of constituents) may aggregate to form clusters (or clusters of clusters) that serve as building blocks for later stages of assembly. Here we evaluate the character and consequences of such collective motion in a set of prototypical assembly processes. We do so using computer simulations in which a system's capacity for hierarchical dynamics can be controlled systematically. By explicitly allowing or suppressing collective motion, we quantify its effects. We find that coarsening within a two dimensional attractive lattice gas (and an analogous off-lattice model in three dimensions) is naturally dominated by collective motion over a broad range of temperatures and densities. Under such circumstances, cluster mobility inhibits the development of uniform coexisting phases, especially when macroscopic segregation is strongly favored by thermodynamics. By contrast, the assembly of model viral capsids is not frustrated but is instead facilitated by collective moves, which promote the orderly binding of intermediates consisting of several monomers.