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.

Nanoparticle Assembly and Oriented Attachment: Correlating Controlling Factors to the Resulting Structures.

Nanoparticle assembly and attachment are common pathways of crystal growth by which particles organize into larger scale materials with hierarchical structure and long-range order. In particular, oriented attachment (OA), which is a special type of particle assembly, has attracted great attention in recent years because of the wide range of material structures that result from this process, such as one-dimensional (1D) nanowires, two-dimensional (2D) sheets, three-dimensional (3D) branched structures, twinned crystals, defects, etc. Utilizing in situ transmission electron microscopy techniques, researchers observed orientation-specific forces that act over short distances (∼1 nm) from the particle surfaces and drive the OA process. Integrating recently developed 3D fast force mapping via atomic force microscopy with theories and simulations, researchers have resolved the near-surface solution structure, the molecular details of charge states at particle/fluid interfaces, inhomogeneity of surface charges, and dielectric/magnetic properties of particles that influence short- and long-range forces, such as electrostatic, van der Waals, hydration, and dipole-dipole forces. In this review, we discuss the fundamental principles for understanding particle assembly and attachment processes, and the controlling factors and resulting structures. We review recent progress in the field via examples of both experiments and modeling, and discuss current developments and the future outlook.

Uneven Strain Distribution Induces Consecutive Dislocation Slipping, Plane Gliding, and Subsequent Detwinning of Penta-Twinned Nanoparticles.

Twin structures possess distinct physical and chemical properties by virtue of their specific twin configuration. However, twinning and detwinning processes are not fully understood on the atomic scale. Integrating in situ high resolution transmission electron microscopy and molecular dynamic simulations, we find tensile strain in the asymmetrical 5-fold twins of Au nanoparticles leads to twin boundary migration through dislocation sliding (slipping of an atomic layer) along twin boundaries and dislocation reactions at the 5-fold axis under an electron beam. Migration of one or two layers of twin planes is governed by energy barriers, but overall, the total energy, including surface, lattice strain, and twin boundary energy, is relaxed after consecutive twin boundary migration, leading to a detwinning process. In addition, surface rearrangement of 5-fold twinned nanoparticles can aid in the detwinning process.

Elucidating the Role of Reduction Kinetics in the Phase-Controlled Growth on Preformed Nanocrystal Seeds: A Case Study of Ru.

This study demonstrates the crucial role of reduction kinetics in phase-controlled synthesis of noble-metal nanocrystals using Ru nanocrystals as a case study. We found that the reduction kinetics played a more important role than the templating effect from the preformed seed in dictating the crystal structure of the deposited overlayers despite their intertwined effects on successful epitaxial growth. By employing two different polyols, a series of Ru nanocrystals with tunable sizes of 3-7 nm and distinct patterns of crystal phase were synthesized by incorporating different types of Ru seeds. Notably, the use of ethylene glycol and triethylene glycol consistently resulted in the formation of Ru shell in natural hexagonal close-packed (hcp) and metastable face-centered cubic (fcc) phases, respectively, regardless of the size and phase of the seed. Quantitative measurements and theoretical calculations suggested that this trend was a manifestation of the different reduction kinetics associated with the precursor and the chosen polyol, which, in turn, affected the reduction pathway (solution versus surface) and packing sequence of the deposited Ru atoms. This work not only underscores the essential role of reduction kinetics in controlling the packing of atoms and thus the phase taken by Ru nanocrystals but also suggests a potential extension to other noble-metal systems.

Diffusion growth mechanism of penta-twinned Ag nanocrystals from decahedral seeds.

Crystals with penta-twinned structures can be produced from diverse fcc metals, but the mechanisms that control the final product shapes are still not well understood. By using the theory of absorbing Markov chains to account for the growth of penta-twinned decahedral seeds via atom deposition and surface diffusion, we predicted the formation of various types of products: decahedra, nanorods, and nanowires. We showed that the type of product depends on the morphology of the seed and that small differences between various seed morphologies can lead to significantly different products. For the case of uncapped decahedra seeds, we compared predictions from our model to nanowire morphologies obtained in two different experiments and obtained favorable agreement. Possible extensions of our model are indicated.

The influence of iodide on the solution-phase growth of Cu microplates: a multi-scale theoretical analysis from first principles.

We use first-principles density functional theory (DFT) to quantify the role of iodide in the solution-phase growth of Cu microplates. Our calculations show that a Cu adatom binds more strongly to hcp hollow sites than fcc hollow sites on iodine-covered Cu(111) - the basal facet of two-dimensional (2D) Cu plates. This feature promotes the formation of stacking faults during seed and plate which, in turn, promotes 2D growth. We also found that iodine adsorption leads to strong Cu atom binding and prohibitively slow diffusion of Cu atoms on Cu(100) - a feature that promotes Cu atom accumulation on the {100} site facets of a growing 2D plate. Incorporating these insights into analog experiments, in which we initiated the growth of Cu plates from small seeds consisting of magnetic spheres, we confirmed that two or more stacking faults are required for lateral plate growth, consistent with prior studies. Moreover, plates can take on a variety of shapes during growth: from triangular and truncated triangular to round and hexagonal - consistent with experiment. Using absorbing Markov chain calculations, we assessed the propensity for 2D vs. 3D kinetic growth of the plates. At experimental temperatures, we predict plates can grow to achieve lateral dimensions in the 1-10 micron range, as observed in experiments.

OptiBoost: A method for choosing a safe and efficient boost for the bond-boost method in accelerated molecular dynamics simulations with hyperdynamics.

Accelerated molecular-dynamics (MD) simulations based on hyperdynamics (HD) can significantly improve the efficiency of MD simulations of condensed-phase systems that evolve via rare events. However, such simulations are not generally easy to apply since appropriate boosts are usually unknown. In this work, we developed a method called OptiBoost to adjust the value of the boost in HD simulations based on the bond-boost method. We demonstrated the OptiBoost method in simulations on a cosine potential and applied it in three different systems involving Ag diffusion on Ag(100) in vacuum and in ethylene glycol solvent. In all cases, OptiBoost was able to predict safe and effective values of the boost, indicating that the OptiBoost protocol is an effective way to advance the applicability of HD simulations.

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.

Influence of Gravity on the Sliding Angle of Water Drops on Nanopillared Superhydrophobic Surfaces.

Molecular dynamics (MD) simulations were used to study the effects of gravity, solid surface energy, and the fraction of water-solid interface area on the water droplet sliding angles on nanopillared surfaces. To effectively simulate the influence of gravity on drop sliding, we developed a protocol in which we scale the value of gravitational acceleration used in our simulations according to the Bond number (Bo). In this way, we approximate the behavior of drops larger than we can effectively simulate using MD. The sliding angle decreased with an increase in Bo, while it increased with an increase in the liquid-solid surface interaction. The sliding angles exhibit a minimum with an increase in the fraction of water-solid interface area, due to meniscus formation at high fractions. Trends predicted by our model are in agreement with experiment. Using our model, we investigated the mechanisms of droplet movement along nanopillared surfaces. Depending on the pinning state of the droplets at equilibrium, either the advancing or the receding contact angle initiates motion. Moreover, the minimum dynamic advancing and receding contact angles of drops with gravity are close to the static contact angle and the intrinsic contact angle, respectively, while the maxima of both angles are as large as 180°. We find that the drops move through a combination of sliding and rolling, in agreement with experiment. Our studies offer clarity to conflicting experimental reports and present new results awaiting experimental confirmation.

Development and initial applications of an e-ReaxFF description of Ag nanoclusters.

Metal nanocrystals are of considerable scientific interest because of their uses in electronics, catalysis, and spectroscopy, but the mechanisms by which nanocrystals nucleate and grow to achieve selective shapes are poorly understood. Ab initio calculations and experiments have consistently shown that the lowest energy isomers for small silver nanoparticles exhibit two-dimensional (2D) configurations and that a transition into three-dimensional (3D) configurations occurs with the addition of only a few atoms. We parameterized an e-ReaxFF potential for Ag nanoclusters (N ≤ 20 atoms) that accurately reproduces the 2D-3D transition observed between the Ag5 and Ag7 clusters. This potential includes a four-body dihedral term that imposes an energetic penalty to 3D structures that is significant for small clusters but is overpowered by the bond energy from out-of-plane Ag-Ag bonds in larger 3D clusters. The potential was fit to data taken from density-functional theory and coupled-cluster calculations and compared to an embedded atom method potential to gauge its quality. We also demonstrate the potential of e-ReaxFF to model redox reactions in silver halides and plasmon motion using molecular dynamics simulations. This is the first case in which e-ReaxFF is used to describe metals. Furthermore, the inclusion of a bond-order dependent dihedral angle in this force field is a unique solution to modeling the 2D-3D transition seen in small metal nanoclusters.

Single-Crystal Electrochemistry Reveals Why Metal Nanowires Grow.

Shape-control is used to tune the properties of metal nanostructures in applications ranging from catalysts to touch screens, but the origins of anisotropic growth of metal nanocrystals in solution are unknown. We show single-crystal electrochemistry can test hypotheses for why nanostructures form and predict conditions for anisotropic growth by quantifying the degree to which different species cause facet-selective metal deposition. Electrochemical measurements show disruption of alkylamine monolayers by chloride ions causes facet-selective Cu deposition. An intermediate range of chloride concentrations maximizes facet-selective Cu deposition on single crystals and produces the highest aspect ratio nanowires in a solution-phase synthesis. DFT calculations similarly show an intermediate monolayer coverage of chloride displaces the alkylamine capping agent from the ends but not the sides of a nanowire, facilitating anisotropic growth.

Dynamic Contact Angles and Mechanisms of Motion of Water Droplets Moving on Nanopillared Superhydrophobic Surfaces: A Molecular Dynamics Simulation Study.

In this work, we investigate the dynamic advancing and receding contact angles, and the mechanisms of motion of water droplets moving across nanopillared superhydrophobic surfaces using molecular-dynamics simulation. We obtain equilibrium Cassie states of droplets on nanopillared surfaces with different pillar heights, groove widths, and intrinsic contact angles. We quantitatively evaluate the dynamic advancing and receding contact angles along the advancing direction of an applied body force, and find that they depend on the roughness parameters and the applied body force in a predictable way. The maximum dynamic advancing contact angle is 180°, and the minimum dynamic advancing contact angle is close to the static contact angle. On the receding side, the maximum dynamic receding contact angle is as large as 180°, while the minimum dynamic receding contact angle is close to the intrinsic contact angle of smooth surface. Interestingly, water droplets exhibit a "rolling" mechanism as they move across the surface, which is confirmed by movies of interfacial water molecules, as well as droplet velocity profiles.

The diffusion of a Ga atom on GaAs(001)ß2(2 × 4): Local superbasin kinetic Monte Carlo.

We use first-principles density-functional theory to characterize the binding sites and diffusion mechanisms for a Ga adatom on the GaAs(001)ß2(2 × 4) surface. Diffusion in this system is a complex process involving eleven unique binding sites and sixteen different hops between neighboring binding sites. Among the binding sites, we can identify four different superbasins such that the motion between binding sites within a superbasin is much faster than hops exiting the superbasin. To describe diffusion, we use a recently developed local superbasin kinetic Monte Carlo (LSKMC) method, which accelerates a conventional kinetic Monte Carlo (KMC) simulation by describing the superbasins as absorbing Markov chains. We find that LSKMC is up to 4300 times faster than KMC for the conditions probed in this study. We characterize the distribution of exit times from the superbasins and find that these are sometimes, but not always, exponential and we characterize the conditions under which the superbasin exit-time distribution should be exponential. We demonstrate that LSKMC simulations assuming an exponential superbasin exit-time distribution yield the same diffusion coefficients as conventional KMC.

Effect of Gravity on the Configuration of Droplets on Two-Dimensional Physically Patterned Surfaces.

Wetting of solid surfaces is important for many potential applications, including the design of low-drag and antifouling/self-cleaning surfaces, and it is usually quantified by the contact angle and by contact angle hysteresis. Both the chemistry and the physical patterning of the surface are known to affect the contact angle. In studying the wetting of such surfaces, most models focus on the small Bond number (Bo) limit in which the effect of gravity is negligible, which simplifies free energy calculations. In this work, we employ a thermodynamic model for surfaces patterned with two-dimensional asperities, which remains applicable for nonzero Bo. We employ two versions of the model: one in which we require the liquid-vapor interface to remain a circular cap, and another in which we allow the liquid-vapor interface to deform. We find that the effects of gravity are twofold. First, drops with larger Bo tend to flatten and spread across the surface relative to the same size drops with Bo = 0. Second, gravity makes it more favorable for drops to penetrate surface asperities compared to the case of Bo = 0, which also tends to lower the contact angles. The main effect of droplet deformation is to produce larger contact angles for the same wetting configuration. Finally, we compare our model predictions with relevant experimental observations. We find very close agreement with the experiments, thereby validating our theoretical model.

Surfactant Binding to Polymer-Water Interfaces in Atomistic Simulations.

Attractive interactions between additive molecules and particle surfaces are key parameters in the design of waterborne suspensions and coatings. We use atomistic molecular dynamics (MD) simulations to determine the potential of mean force for a commonly used industrial surfactant sodium dodecyl sulfate (SDS) interacting with acrylate latex particles. We investigate how the potential of mean force and binding free energy depend on the amount of SDS adsorbed, solution ionic strength, and presence of other charged groups on the particle surface. We show that the potential of mean force for SDS is a sum of two independent terms, from the hydrophobic surfactant tail and charged headgroup: dragging the surfactant tail into solution contributes a linear potential of about kT per CH2 group, while the headgroup is repelled by like charges on the surface with a potential of about the zeta potential. Commercial acrylate latex particles also bear multivalent charged "hairs" as a remnant of their synthesis. These charged hairs result in a heterogeneously charged surface, for which SDS binds more or less strongly depending on the local environment.

Atomistic Molecular Dynamics Simulations of Charged Latex Particle Surfaces in Aqueous Solution.

Charged particles in aqueous suspension form an electrical double layer at their surfaces, which plays a key role in suspension properties. For example, binder particles in latex paint remain suspended in the can because of repulsive forces between overlapping double layers. Existing models of the double layer assume sharp interfaces bearing fixed uniform charge, and so cannot describe aqueous binder particle surfaces, which are soft and diffuse, and bear mobile charge from ionic surfactants as well as grafted multivalent oligomers. To treat this industrially important system, we use atomistic molecular dynamics simulations to investigate a structurally realistic model of commercial binder particle surfaces, informed by extensive characterization of particle synthesis and surface properties. We determine the interfacial profiles of polymer, water, bound and free ions, from which the charge density and electrostatic potential can be calculated. We extend the traditional definitions of the inner and outer Helmholtz planes to our diffuse interfaces. Beyond the Stern layer, the simulated electrostatic potential is well described by the Poisson-Boltzmann equation. The potential at the outer Helmholtz plane compares well to the experimental zeta potential. We compare particle surfaces bearing two types of charge groups, ionic surfactant and multivalent oligomers, with and without added salt. Although the bare charge density of a surface bearing multivalent oligomers is much higher than that of a surfactant-bearing surface at realistic coverage, greater counterion condensation leads to similar zeta potentials for the two systems.

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(100) and Cu(111). HDA forms self-assembled layers on these surfaces, analogous to alkanethiols on various metal surfaces, and it binds by donating electrons in the amine group to the Cu surface atoms, consistent with experiment. van der Waals interactions between the alkyl tails of HDA molecules are stronger than the interaction between the amine group and the Cu surfaces. Strong HDA-tail interactions lead to coverage-dependent tilting of the HDA layers, such that the tilt angle is larger for lower coverages. At full monolayer coverage, the energetically preferred binding configuration for HDA on Cu(100) is a (5 × 3) pattern - although we cannot rule out incommensurate structures - while the pattern is preferred on Cu(111). A major motivation for this study is to understand the experimentally observed capability of HDA as a capping agent for producing {100}-faceted Cu nanocrystals. Consistent with experiment, we find that HDA binds more strongly to Cu(100) than to Cu(111). This strong binding stems from the capability of HDA to form more densely packed layers on Cu(100), which leads to stronger HDA-tail interactions, as well as the stronger binding of the amine group to Cu(100). We estimate the surface energies of HDA-covered Cu(100) and Cu(111) surfaces and find that these surfaces are nearly isoenergetic. By drawing analogies to previous theoretical work, it seems likely that HDA-covered Cu nanocrystals could have kinetic shapes that primarily express {100} facets, as is seen experimentally.