Predicting kinetic nanocrystal shapes through multi-scale theory and simulation: Polyvinylpyrrolidone-mediated growth of Ag nanocrystals

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.

Preparation and SERS applications of Ta2O5 composite nanostructures

Noble metal and semiconductor composite substrates possess high sensitivity, excellent stability, good biocompatibility, and selective enhancement, making them an important research direction in the field of surface-enhanced Raman scattering (SERS). Ta2O5, as a semiconductor material with high thermal stability, corrosion resistance, outstanding optical properties, and catalytic performance, has great potential in SERS research. This study aims to design and fabricate a composite SERS substrate based on Ta2O5 nanostructures, achieving optimal detection performance by combining the urchin-like structure of Ta2O5 with silver nanoparticles (Ag NPs). The urchin-like Ta2O5 nanostructures were prepared using a hydrothermal reaction method. The bandgap was modulated through structure design and the self-doping technique, the charge transfer efficiency and surface plasmon resonance effects were improved, thereby achieving better SERS performance. The composite substrate enables highly sensitive quantitative detection. This composite SERS substrate combines the electromagnetic enhancement mechanism (EM) and chemical enhancement mechanism (CM), achieving ultra-low detection limits of 10-13 M for R6G. Within the concentration range above 10-12 M, there is a good linear relationship between concentration and peak intensity, demonstrating excellent quantitative analysis capabilities. Furthermore, this composite SERS substrate is capable of precise detection of analytes such as crystal violet (CV) and methylene blue (MB), holding broad application prospects in areas such as food safety and environmental monitoring.

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.

Molecular Driving Force for Facet Selectivity of Sequence-Defined Amphiphilic Peptoids at Au-Water Interfaces

Shape-controlled colloidal nanocrystal syntheses often require facet-selective solution-phase chemical additives to regulate surface free energy, atom addition/migration fluxes, or particle attachment rates. Because of their highly tunable properties and robustness to a wide range of experimental conditions, peptoids represent a very promising class of next-generation functional additives for control over nanocrystal growth. However, understanding the origin of facet selectivity at the molecular level is critical to generalizing their design. Herein we employ molecular dynamics simulations and biased sampling methods and report stronger selectivity to Au(111) than to Au(100) for Nce3Ncp6, a peptoid that has been shown to assist the formation of 5-fold twinned Au nanostars. We find that facet selectivity is achieved through synergistic effects of both peptoid-surface and solvent-surface interactions. Moreover, the amphiphilic nature of Nce3Ncp6 together with the order of peptoid-peptoid and peptoid-surface binding energies, that is, peptoid-Au(100) < peptoid-peptoid < peptoid-Au(111), further amplifies its distinct collective behavior on different Au surfaces. Our studies provide a fundamental understanding of the molecular origin of facet-selective adsorption and highlight the possibility of future designs and uses of sequence-defined peptoids for predictive syntheses of nanocrystals with designed shapes and properties.

Adsorption of ethylenediamine on Cu surfaces: attributes of a successful capping molecule using first-principles calculations

The shape-controlled synthesis of Cu nanocrystals can benefit a wide range of applications, though challenges exist in achieving high and selective yields to a particular shape. Capping agents play a pivotal role in controlling shape, but their exact role remains ambiguous. In this study, the adsorption of ethylenediamine (EDA) on Cu(100) and Cu(111) was investigated with quantum density functional theory (DFT) to reveal the complex roles of EDA in promoting penta-twinned Cu nanowire growth. We find EDA has stronger binding on Cu(100) than on Cu(111), which agrees the general expectation that penta-twinned Cu nanowires express facets with stronger capping-molecule binding. Despite this stronger binding, ab initio thermodynamics reveals the surface energy of EDA-covered Cu(111) is lower than that EDA-covered Cu(100) at all solution-phase EDA chemical potentials, so there is no thermodynamic driving force for penta-twinned nanowires. We also investigated the capability of EDA to protect Cu surfaces from oxidation in water by quantifying energy barriers for a water molecule to diffuse through EDA layers on Cu(100) and Cu(111). The energy barrier on Cu(100) is significantly lower, which supports observations of faster oxidation of Cu(100) in electrochemical experiments. Thus, we elucidate another possible function of a capping agent - to enable selective oxidation of crystal facets. This finding adds to the general understanding of successful attributes of capping agents for shape-selective nanocrystal growth.

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.

Chemical Identity of Poly(N-vinylpyrrolidone) End Groups Impact Shape Evolution During the Synthesis of Ag Nanostructures

Ag nanocubes (AgNCs) are predominantly synthesized by the polyol method, where the solvent (ethylene glycol) is considered the reducing agent and poly(N-vinylpyrrolidone) (PVP) the shape-directing agent. An experimental phase diagram for the formation of Ag nanocubes as a function of PVP monomer concentration (C_m) and molecular weight (M_w) demonstrated end groups of PVP impact the final Ag product. Measured rates of the initial Ag⁺ reduction at different PVP C_m and M_w confirmed the reducing effect originates from end-groups. PVP with well-defined aldehyde and hydroxyl end groups lead to the formation of Ag nanocubes and nanowires respectively, indicating the faster reducing agent formed kinetically preferred nanowires. We demonstrate PVP end-groups induce initial reduction of Ag⁺ to form seeds followed by autocatalytic reduction of Ag⁺ by ethylene glycol (and not solvent oxidation products) to form Ag nanostructures. The current study enabled a quantitative description of the role of PVP in nanoparticle shape-control and demonstrates a unique opportunity to design nanostructures by combining nanoparticle synthesis with polymer design to introduce specific physicochemical properties.

Growth Mechanism of Five-Fold Twinned Ag Nanowires from Multiscale Theory and Simulations

Five-fold twinned metal nanowires can be synthesized with high aspect ratios via solution-phase methods. The origins of their anisotropic growth, however, are poorly understood. We combine atomic-scale, mesoscale, and continuum theoretical methods to predict growth morphologies of Ag nanowires from seeds and to demonstrate that high aspect ratio nanowires can originate from anisotropic surface diffusion induced by the strained nanowire structure. Nanowire seeds are similar to Marks decahedra, with {111} "notches" that accelerate diffusion along the nanowire axis to facilitate one-dimensional growth. The strain distribution on the {111} facets induces heterogeneous atom aggregation and leads to atom trapping at the nanowire ends. We predict that decahedral Ag seeds can grow to become nanowires with aspect ratios in the experimental range. Our studies show that there is a complex interplay between atom deposition, diffusion, seed architecture, and nanowire aspect ratio that could be manipulated experimentally to achieve controlled nanowire syntheses.

Revisiting the Polyol Synthesis of Silver Nanostructures: Role of Chloride in Nanocube Formation

Chloride (Cl^-) is often used together with polyvinylpyrrolidone (PVP) in the polyol synthesis of Ag nanocubes. In the literature, shape control is attributed predominantly to the preferential binding of PVP to Ag(100) facets compared to Ag(111) facets, whereas the role of Cl^- has not been well studied. Several hypotheses have been proposed regarding the role of Cl^-; however, there is still no consensus regarding the exact influence of Cl^- in the shape-controlled synthesis of Ag nanocubes. To examine the influence of Cl^-, we undertook a joint theoretical-experimental study. Experimentally, we examined the influence of Cl^- concentration on the shape of Ag nanoparticles (NPs) at constant H⁺ concentration. In the presence of H⁺, in situ formed HNO₃ etches the initially formed Ag seeds and slows down the overall reduction of Ag⁺, which promotes the formation of monodisperse Ag NPs. Ex situ experiments probed the evolution of Cl^- during the growth of Ag nanocubes, which involves the initial formation of AgCl nanocubes, and their subsequent dissolution to release Cl^-, which adsorbs onto the surfaces of single crystal seeds to impact shape evolution through apparent thermodynamic control. The formation of cubes is independent of the source of AgCl, indicating temporal control of the Cl^- chemical potential in solution leads to high-yield synthesis of Ag nanocubes. Increasing the concentration of Cl^- alone leads to a progression in shape from truncated octahedra, to cuboctahedra, truncated cubes, and ultimately cubes, directly demonstrating the importance of Cl^- in Ag NP shape control. We used ab initio thermodynamics calculations based on density functional theory to probe the role of Cl^- in directing shape control. With increasing Cl chemical potential (surface coverage), calculated surface energies γ of Ag facets transition from γ₁₁₁ < γ₁₀₀ to γ₁₀₀ < γ₁₁₁ and predict Wulff shapes terminated with an increasing (100) contribution, consistent with experimental observations. The combination of theory and experiment is beneficial for advancing the understanding of nanocrystal formation.

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).