Versatile stochastic model for predictive KMC simulation of fcc metal nanostructure evolution with realistic kinetics

Stochastic lattice-gas models provide the natural framework for analysis of the surface diffusion-mediated evolution of crystalline metal nanostructures on the appropriate time scale (often 101-104 s) and length scale. Model behavior can be precisely assessed by kinetic Monte Carlo simulation, typically incorporating a rejection-free algorithm to efficiently handle the broad range of Arrhenius rates for hopping of surface atoms. The model should realistically prescribe these rates, or the associated barriers, for a diversity of local surface environments. However, commonly used generic choices for barriers fail, even qualitatively, to simultaneously describe diffusion for different low-index facets, for terrace vs step edge diffusion, etc. We introduce an alternative Unconventional Interaction-Conventional Interaction formalism to prescribe these barriers, which, even with few parameters, can realistically capture most aspects of behavior. The model is illustrated for single-component fcc metal systems, mainly for the case of Ag. It is quite versatile and can be applied to describe both the post-deposition evolution of 2D nanostructures in homoepitaxial thin films (e.g., reshaping and coalescence of 2D islands) and the post-synthesis evolution of 3D nanocrystals (e.g., reshaping of nanocrystals synthesized with various faceted non-equilibrium shapes back to 3D equilibrium Wulff shapes).

Nanocrystal Assemblies: Current Advances and Open Problems

We explore the potential of nanocrystals (a term used equivalently to nanoparticles) as building blocks for nanomaterials, and the current advances and open challenges for fundamental science developments and applications. Nanocrystal assemblies are inherently multiscale, and the generation of revolutionary material properties requires a precise understanding of the relationship between structure and function, the former being determined by classical effects and the latter often by quantum effects. With an emphasis on theory and computation, we discuss challenges that hamper current assembly strategies and to what extent nanocrystal assemblies represent thermodynamic equilibrium or kinetically trapped metastable states. We also examine dynamic effects and optimization of assembly protocols. Finally, we discuss promising material functions and examples of their realization with nanocrystal assemblies.

Mesomorphology of clathrate hydrates from molecular ordering

Clathrate hydrates are crystals formed by guest molecules that stabilize cages of hydrogen-bonded water molecules. Whereas thermodynamic equilibrium is well described via the van der Waals and Platteeuw approach, the increasing concerns with global warming and energy transition require extending the knowledge to non-equilibrium conditions in multiphase, sheared systems, in a multiscale framework. Potential macro-applications concern the storage of carbon dioxide in the form of clathrates, and the reduction of hydrate inhibition additives currently required in hydrocarbon production. We evidence porous mesomorphologies as key to bridging the molecular scales to macro-applications of low solubility guests. We discuss the coupling of molecular ordering with the mesoscales, including (i) the emergence of porous patterns as a combined factor from the walk over the free energy landscape and 3D competitive nucleation and growth and (ii) the role of molecular attachment rates in crystallization-diffusion models that allow predicting the timescale of pore sealing. This is a perspective study that discusses the use of discrete models (molecular dynamics) to build continuum models (phase field models, crystallization laws, and transport phenomena) to predict multiscale manifestations at a feasible computational cost. Several advances in correlated fields (ice, polymers, alloys, and nanoparticles) are discussed in the scenario of clathrate hydrates, as well as the challenges and necessary developments to push the field forward.

Minimum Free-Energy Shapes of Ag Nanocrystals: Vacuum vs Solution

We use two variants of replica-exchange molecular dynamics (MD) simulations, parallel tempering MD and partial replica exchange MD, to probe the minimum free-energy shapes of Ag nanocrystals containing 100-200 atoms in a vacuum, ethylene glycol (EG) solvent, and EG solvent with a PVP polymer containing 100 repeat units. Our simulations reveal a shape intermediate between a Dh and an Ih, a Dh-Ih, that has distinct structural signatures and magic sizes. We find several prominent features associated with entropy: pure FCC nanocrystals are less common than FCC crystals containing stacking faults, and crystals with the minimum potential energy are not always preferred over the range of relevant temperatures. The shapes of the nanocrystals in solution are influenced by the chemical identities of the solution-phase molecules. Comparing Ag nanocrystal shapes in EG to those in an EG+PVP solution, we find more icosahedra in EG and more decahedra in EG+PVP across all of the nanocrystal sizes probed in this study. At certain critical sizes, nanocrystal shapes can change dramatically with the addition and removal of a single atom or with a change in temperature at a fixed size. The information in our study could be useful in efforts to devise processing routes to achieve selective nanocrystal shapes.

Theory of Anisotropic Metal Nanostructures

A significant challenge in the development of functional materials is understanding the growth and transformations of anisotropic colloidal metal nanocrystals. Theory and simulations can aid in the development and understanding of anisotropic nanocrystal syntheses. The focus of this review is on how results from first-principles calculations and classical techniques, such as Monte Carlo and molecular dynamics simulations, have been integrated into multiscale theoretical predictions useful in understanding shape-selective nanocrystal syntheses. Also, examples are discussed in which machine learning has been useful in this field. There are many areas at the frontier in condensed matter theory and simulation that are or could be beneficial in this area and these prospects for future progress are discussed.

Adsorption of alkylamines on Cu surfaces: identifying ideal capping molecules using first-principles calculations

We used dispersion-corrected density-functional theory to perform an in silico search over a series of primary alkylamines, including linear, branched, and cyclic molecules, to identify capping molecules for shape-selective Cu nanocrystal synthesis. We identify several attributes associated with successful capping agents. Generally, molecules with good geometric matching to the Cu surfaces possessed the strongest molecule-surface chemical bonds. However, non-bonding van der Waals interactions and molecular packing constraints can play a more significant role in determining the overall binding energy, the surface coverage, and the likely efficacy of the capping molecule. Though nearly all the molecules exhibited stronger binding to Cu(100) than to Cu(111), all predicted Wulff shapes are primarily {111}-faceted, based on ab initio thermodynamics calculations. From predicted capping-molecule densities on Cu(100) and Cu(111) for various solution environments, we identified several candidate molecules to produce {100}- or {111}-faceted nanocrystals with kinetic shapes, based on synthesis conditions used to grow Cu nanowires with ethylenediamine capping agent. Our study reveals the complexity of capping-molecule binding and important considerations that go into the selection of a successful capping agent.

Going beyond the equilibrium crystal shape: re-tracing the morphological evolution in group 5 tetradymite nanocrystals

Nanocrystals of group 5 tetradymites M₂X₃ (where M = Bi and Sb, X = Se and Te) are of high technological relevance in modern topological nanoelectronics. However, there is a current lack of a systematic understanding to predict the preferred nanocrystal morphology in experiments where commonly-used equilibrium thermodynamic models appear to fail. In this work, using first-principles DFT calculations with a rationally-extended ab initio atomistic thermodynamics approach coupled to implicit solvation models and Gibbs-Wulff shape constructions, we demonstrate that this absence of predictive power stems from the limitation of equilibrium thermodynamics. By re-tracing and carefully addressing with a more realistic chemical potential definition, we illustrate this shortcoming can be overcome and afford a more rational route to size-engineer and shape-design highly-functional group 5 tetradymite nanoparticles for targeted applications.

Self-Assembly of a Linear Alkylamine Bilayer around a Cu Nanocrystal: Molecular Dynamics

Copper nanocrystals are often grown with the help of alkylamine capping agents, which direct the nanocrystal shape. However, the role of these molecules is still unclear. We characterized the assembly of aqueous tetradecylamine (TDA) around a Cu nanocrystal and found that TDA exhibits a temperature-dependent bilayer structure. The bilayer involves an inner layer, in which TDA binds to Cu via the amine group and tends to orient the alkyl tail perpendicular to the surface, and an outer layer whose structure depends on temperature. At low temperatures, alkylamines in the inner layer form bundles with no apparent relation to the crystal facets. Alkylamines in the outer layer tend to orient their long axes perpendicular to the Cu surfaces, with interdigitation into the inner layer. At high temperatures, alkylamines in the inner layer lose their bundle structure, and outer-layer alkylamines tend to orient themselves tangential to the Cu surfaces, forming a "web" above inner-layer TDA. TDA exhibits a rapid interlayer exchange at typical synthesis temperatures, consistent with experiment. The variety in the assemblies seen here and in other studies of alkanethiols around gold nanocrystals indicates a richness in the assemblies that can be achieved by modulating the interaction between the strongly binding end group and the surface.

Understanding the Solution-Phase Growth of Cu and Ag Nanowires and Nanocubes from First Principles

In this feature article, we provide an account of the Langmuir Lecture delivered by Kristen Fichthorn at the Fall 2020 Virtual Meeting of the American Chemical Society. We discuss how multiscale theory and simulations based on first-principles DFT were useful in uncovering the intertwined influences of kinetics and thermodynamics on the shapes of Ag and Cu cubes and nanowires grown in solution. We discuss how Ag nanocubes can form through PVP-modified deposition kinetics and how the addition of chloride to the synthesis can promote thermodynamic cubic shapes for both Ag and Cu. We discuss kinetic factors contributing to nanowire growth: in the case of Ag, we show that high-aspect-ratio nanowires can form as a consequence of Ag atom surface diffusion on the strained surfaces of Marks-like decahedral seeds. On the other hand, solution-phase chloride enhances Cu nanowire growth due to a synergistic interaction between adsorbed chloride and hexadecylamine (HDA), which leaves the {111} nanowire ends virtually bare while the {100} sides are fully covered with HDA. For each of these topics, a synergy between theory and experiment led to significant progress.

Molecular dynamics simulations of the formation of Ag nanoparticles assisted by PVP

Understanding the formation mechanisms of nanoparticles is essential for the synthesis of nanomaterials with controlled properties. In solution synthesis, capping agents are used to mediate this process and control the final size and shape of the particles. In this work, the synthesis of silver nanoparticles, with polyvinylpyrrolidone (PVP) as the capping agent, is studied through molecular dynamics simulations. Nucleation of clusters of atoms and subsequent growth to form nanoparticles are analyzed, with focus on the role of PVP. No finite critical nucleus is detected, and amorphous particles seem to form by spinodal growth. In this timescale, PVP seems to have no effect on particle growth, which is ascribed to the competition between the protective effect and "bridging" (where a molecule of PVP is adsorbed to two different clusters, bringing them together). As the process evolves, a sequence of ordered structures appears within the particles: icosahedral, BCC, and FCC, the last one being the equilibrium configuration of bulk silver. In addition, for a low PVP content an apparent acceleration is observed in particle growth after these ordered phases appear, indicating that the growth of ordered particles from the solution is faster than the growth of amorphous particles. For a high PVP content, this acceleration is not observed, indicating that the protective effect prevails on particle growth in this regime. In addition, due to the bridging effect, the final overall configuration is strongly dependent on the PVP content. In the absence of PVP, large but dispersed particles are observed. When the PVP content is low, due to strong bridging, particles form agglomerates (with no strong coalescence in the timescale of simulations). When the PVP content is large enough, particles are smaller in size and do not show a strong tendency to agglomerate.

Synthesis, growth mechanisms, and applications of palladium-based nanowires and other one-dimensional nanostructures

Palladium-based nanostructures have attracted the attention of researchers due to their useful catalytic properties and unique ability to form hydrides, which finds application in hydrogen storage and hydrogen detection. Palladium-based nanowires have some inherent advantages over other Pd nanomaterials, combining high surface-to-volume ratio with good thermal and electron transport properties, and exposing high-index crystal facets that can have enhanced catalytic activity. Over the past two decades, both synthesis methods and applications of 1D palladium nanostructures have advanced greatly. In this review, we start by discussing different types of 1D palladium nanostructures before moving on to the different synthesis approaches that can produce them. Next, we discuss factors including kinetic vs. thermodynamic control of growth, oxidative etching, and surface passivation that affect palladium nanowire synthesis. We also review efforts to gain insight into growth mechanisms using different characterization tools. We discuss the effects of concentration of capping agents, reducing agents, metal halides, pH, and sacrificial oxidation on the growth of Pd-based nanowires in solution, from shape control, to yield, to aspect ratio. Various applications of palladium and palladium alloy nanowires are then discussed, including electrocatalysis, hydrogen storage, and sensing of hydrogen and other chemicals. We conclude with a summary and some perspectives on future research directions for this category of nanomaterials.

TiO2 Facets Shaped by Concentration-Dependent Surface Diffusion of Dopamine

Facet engineering highlights the fundamental understanding of kinetic growth of facets with capping agents. Here, we provide a roadmap for modulating TiO₂ facets using dopamine as a capping agent inspired by density functional theory calculations and molecular dynamics simulations. Our calculations revealed that the surface diffusion of dopamine and their facet-specific affinity direct the kinetic growth of TiO₂{100} and {101} facets into a nonequilibrium crystal shape. Our TiO₂ synthesis agreed well with the theoretical predictions, suggesting that the concentration-dependent diffusion is central in accurately tuning a desirable ratio of mixed facets. Our findings shed new light on the diffusion-limited kinetically controlled facet growth mechanism, and this fine-tuning of mixed facets on a single crystal provides a general approach to design and fabricate facets on metal oxides.

Poly(vinyl alcohol) as a water protecting agent for silver nanoparticles: the role of polymer size and structure

Chemical modification of silver nanoparticles (AgNPs) with a stabilizing agent, such as poly(vinyl alcohol) (PVA), plays an important role in shape-controlled seeded-growth and colloidal stability. However, theoretical aspects of the stabilizing mechanism of PVA are still poorly understood. To gain a better understanding of the role of PVA in water protecting effects for silver nanoparticles, we developed an atomistic model of a AgNP grafted with single-chain PVA of various lengths. Our model, designed for classical molecular dynamics (MD) simulations, approximates the AgNP as a quasi-spherical silver nanocrystal with 3.9 nm diameter and uses a united-atom representation for PVA with its polymer chain length varying from 220 up to 1540 repeating units. We found that PVA adsorbs onto the AgNP surface through multiple non-covalent interactions, among which non-covalent bonding of the hydroxyl groups plays a key role. The analysis of adsorption isotherms by using the Hill, Scatchard, and McGhee & von Hippel models exhibits evidence for positive binding cooperativity with the cooperativity parameter varying from 1.55 to 2.12. Our results indicate that the size of the PVA polymer rather than its structure plays a crucial role in providing water protecting effects for the AgNP core, varying from 40% up to 91%. The water-protecting efficiency was well approximated by the Langmuir-Freundlich equation, allowing us to predict that the saturated coverage of the nanoparticle of a given diameter of 3.9 nm should occur when the PVA molecular weight approaches 115 kDa, which corresponds to the number of vinyl alcohol monomers being equal to 3100 units.

Theory of the thermodynamic influence of solution-phase additives in shape-controlled nanocrystal synthesis

Though many experimental studies have documented that certain solution-phase additives can play a key role in the shape-selective synthesis of metal nanocrystals, the origins and mechanisms of this shape selectivity are still unclear. One possible role of such molecules is to thermodynamically induce the equilibrium shape of a nanocrystal by altering the interfacial free energies of the facets. Using a multi-scheme thermodynamic integration method that we recently developed [J. Chem. Phys., 2016, 145, 194108], we calculate the solid-liquid interfacial free energies γ_sl and investigate the propensity to achieve equilibrium shapes in such syntheses. We first apply this method to Ag(100) and Ag(111) facets in ethylene glycol solution containing polyvinylpyrrolidone (PVP), to mimic the environment in polyol synthesis of Ag nanocrystals. We find that although PVP has a preferred binding to Ag(100), its selectivity is not sufficient to induce a thermodynamic preference for {100}-faceted nanocubes, as has been observed experimentally. This indicates that PVP promotes Ag nanocube formation kinetically rather than thermodynamically. We further quantify the thermodynamic influence of adsorbed solution-phase additives for generic molecules, by building a γ_sl ratio/nanocrystal shape map as a function of zero-temperature binding energies. This map can be used to gauge the efficacy of candidate additive molecules for producing targeted thermodynamic nanocrystal shapes. The results indicate that only additives with a strong facet selectivity can impart significant thermodynamic-shape change. Therefore, many of the nanocrystals observed in experiments are likely kinetic products.

Self-assembled monolayer structures of hexadecylamine on Cu surfaces: density-functional theory

We used dispersion-corrected density-functional theory to probe possible structures for adsorbed layers of hexadecylamine (HDA) on Cu(111) (left) and Cu(100) (right).