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.

Size and temperature dependent shapes of copper nanocrystals using parallel tempering molecular dynamics

We performed parallel-tempering molecular dynamics simulations to predict the temperature- and size-dependent equilibrium shapes of a series of Cu nanocrystals in the 100- to 200-atom size range. Our study indicates that temperature-dependent, solid-solid shape transitions occur frequently for Cu nanocrystals in this size range. Complementary calculations with electronic density functional theory indicate that vibrational entropy favors nanocrystals with a shape intermediate between a decahedron and an icosahedron. Overall, we find that entropy plays a significant role in determining the shapes Cu nanocrystals, so studies aimed at determining minimum-energy shapes may fail to correctly predict shapes observed at experimental temperatures. We also observe significant shape changes with nanocrystal size - sometimes with changes in a single atom. The information from this study could be useful in efforts to devise processing routes to achieve selective nanocrystal shapes.

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.

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.

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.

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.

Chloride enables the growth of Ag nanocubes and nanowires by making PVP binding facet-selective

Solution-phase synthesis of metal nanocrystals with multiple additives is a common strategy for control over nanocrystal shape, and thus control over their properties. However, few rules are available to predict the effect of multiple capping agents on metal nanocrystal shapes, making it hard to rationally design synthetic conditions. This work uses a combination of seed-mediated growth, single-crystal electrochemistry, and DFT calculations to determine the roles of PVP and Cl^- in the anisotropic growth of single-crystal and penta-twinned silver nanocrystals. Single-crystal seeds grow into truncated octahedra bounded by a mixture of {111} and {100} facets in the presence of 0.03-30 mM PVP, but when 3-6 μM Cl^- is added with PVP, the single-crystal seeds grow into cubes bounded by {100} facets. Electrochemical measurements on Ag(100) and Ag(111) single-crystal electrodes show PVP is a capping agent but it exhibits no selectivity for a particular facet. Addition of Cl^- to PVP further passivates Ag(100) but not Ag(111), leading to conditions that favor formation of nanocubes. DFT calculations indicate the preferential binding of Cl^- to Ag(100) causes preferential binding of PVP to Ag(100). The combined results indicate the presence or absence of Cl^- modulates binding of PVP to (100) facets, leading to the formation of nanocubes with Cl^-, or truncated octahedra without it.

Green chemistry and first-principles theory enhance catalysis: synthesis and 6-fold catalytic activity increase of sub-5 nm Pd and Pt@Pd nanocubes

Synthesizing metal nanoparticles with fine control of size, shape and surface properties is of high interest for applications such as catalysis, nanoplasmonics, and fuel cells. In this contribution, we demonstrate that the citrate-coated surfaces of palladium (Pd) and platinum (Pt)@Pd nanocubes with a lateral length <5 nm and low polydispersity in shape achieve superior catalytic properties. The synthesis achieves great control of the nanoparticle's physico-chemical properties by using only biogenic reagents and bromide ions in water while being fast, easy to perform and scalable. The role of the seed morphology is pivotal as Pt single crystal seeds are necessary to achieve low polydispersity in shape and prevent nanorods formation. In addition, electrochemical measurements demonstrate the abundancy of Pd{100} surface facets at a macroscopic level, in line with information inferred from TEM analysis. Quantum density functional theory calculations indicate that the kinetic origin of cubic Pd nanoshapes is facet-selective Pd reduction/deposition on Pd(111). Moreover, we underline both from an experimental and theoretical point of view that bromide alone does not induce nanocube formation without the synergy with formic acid. The superior performance of these highly controlled nanoparticles to perform the catalytic reduction of 4-nitrophenol was proved: polymer-free and surfactant-free Pd nanocubes outperform state-of-the-art materials by a factor >6 and a commercial Pd/C catalyst by more than one order of magnitude.

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 the OptiBoost protocol is an effective way to advance the applicability of HD simulations.

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.

Solution-Phase Growth of Cu Nanowires with Aspect Ratios Greater Than 1000: Multiscale Theory

Penta-twinned metal nanowires are finding widespread application in existing and emerging technologies. However, little is known about their growth mechanisms. We probe the origins of chloride- and alkylamine-mediated, solution-phase growth of penta-twinned Cu nanowires from first-principles using multiscale theory. Using quantum density functional theory (DFT) calculations, we characterize the binding and surface diffusion of Cu atoms on chlorine-covered Cu(100) and Cu(111) surfaces. We find stronger binding and slower diffusion of Cu atoms on chlorinated Cu(111) than on chlorinated Cu(100), which is a reversal of the trend for bare Cu surfaces. We also probe interfacet diffusion and find that this proceeds faster from Cu(100) to Cu(111) than the reverse. Using the DFT rates for hopping between individual sites at Ångstrom scales, we calculate coarse-grained, interfacet rates for nanowires of various lengths─up to hundreds of micrometers─and diameters in the 10 nm range. We predict nanowires with aspect ratios of ∼100, based on surface diffusion alone. We also account for the influence of a self-assembled alkylamine layer that covers most of the {100} facets, but is absent or thin and disordered on the {111} facets and in an "end zone" near the {100}/{111} boundary. With an end zone, we predict a wide range of nanowire aspect ratios in the experimental ranges. Our work reveals the mechanisms by which a halide─chloride─promotes the growth of high-aspect-ratio nanowires.

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.

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.

Synthesis of Citrate-Coated Penta-twinned Palladium Nanorods and Ultrathin Nanowires with a Tunable Aspect Ratio

Green and scalable methodologies for the preparation of metal nanoparticles with fine control of shape and size are of high interest in many areas including catalysis, nanomedicine, and nanodiagnostics. In this contribution, we describe a new synthetic method for the production of palladium (Pd) penta-twinned nanowires and nanorods utilizing sodium citrate, formic acid, ascorbic acid, and potassium bromide (KBr) in water, without the use of surfactants or polymers. The synthesis is green, fast, and without the need of complex setups. Interestingly, a microwave-assisted scale-up process has been developed. The combination of a synthetic protocol for seeds and the seed-mediated growth process allows us to synthesize nanorods and nanowires by modulating the concentration of KBr. The synthesized nanomaterials have been physicochemically characterized. High-resolution transmission electron microscopy shows that the nanorods and nanowires have a penta-twinned structure enclosed by {100} lateral facets. Moreover, the absence of sticky molecules or toxic byproducts guarantees the biocompatibility of the nanomaterials, while leaving the surface clean to perform enzymatic activities.

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.

Oriented attachment mechanism of triangular Ag nanoplates: a molecular dynamics study

We use molecular-dynamics simulations to probe the experimentally observed aggregation of PVP-covered triangular Ag nanoplates to form 2D sheets in solution. We find lateral plate attachment is the most favorable aggregation pathway - consistent with experiment. The mechanism is general and suggests new processing strategies for creating 2D architectures in solution-phase syntheses.

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.

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)β2(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)β2(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.

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.

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.

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.

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(111) (left) and Cu(100) (right).

How Structure-Directing Agents Control Nanocrystal Shape: Polyvinylpyrrolidone-Mediated Growth of Ag Nanocubes

The importance of structure-directing agents (SDAs) in the shape-selective synthesis of colloidal nanostructures has been well documented. However, the mechanisms by which SDAs actuate shape control are poorly understood. In the polyvinylpyrrolidone (PVP)-mediated growth of {100}-faceted Ag nanocrystals, this capability has been attributed to preferential binding of PVP to Ag(100). We use molecular dynamics simulations to probe the mechanisms by which Ag atoms add to Ag(100) and Ag(111) in ethylene glycol solution with PVP. We find that PVP induces kinetic Ag nanocrystal shapes by regulating the relative Ag fluxes to these facets. Stronger PVP binding to Ag(100) leads to a larger Ag flux to Ag(111) and cubic nanostructures through two mechanisms: enhanced Ag trapping by more extended PVP films on Ag(111) and a reduced free-energy barrier for Ag to cross lower-density films on Ag(111). These flux-regulating capabilities depend on PVP concentration and chain length, consistent with experiment.

Effects of Hierarchical Surface Roughness on Droplet Contact Angle

Superhydrophobic surfaces often incorporate roughness on both micron and nanometer length scales, although a satisfactory understanding of the role of this hierarchical roughness in causing superhydrophobicity remains elusive. We present a two-dimensional thermodynamic model to describe wetting on hierarchically grooved surfaces by droplets for which the influence of gravity is negligible. By creating wetting phase diagrams for droplets on surfaces with both single-scale and hierarchical roughness, we find that hierarchical roughness leads to greatly expanded superhydrophobic domains in phase space over those for a single scale of roughness. Our results indicate that an important role of the nanoscale roughness is to increase the effective Young's angle of the microscale features, leading to smaller required aspect ratios (height to width) for the surface structures. We then show how this idea may be used to design a hierarchically rough surface with optimally high contact angles.

Kinetics of droplet wetting mode transitions on grooved surfaces: forward flux sampling

The wetting configuration of a liquid droplet on a rough or physically patterned surface is typically characterized by either the Cassie wetting mode, in which the droplet resides on top of the roughness, or the Wenzel mode, in which the droplet penetrates into the roughness. For a fixed surface topology and droplet size, one of these modes corresponds to the global free-energy minimum. However, the other state is often metastable and long-lived due to a free-energy barrier that hinders the transition between the two wetting states. Metastable wetting states have been observed experimentally, and we also observe them in molecular dynamics (MD) simulations of a droplet on a grooved surface. Using forward flux sampling, we study the kinetics of the Cassie to Wenzel and Wenzel to Cassie transitions for two-dimensional droplets on periodically grooved substrates. The global-minimum wetting states that emerge from our nanoscale MD approach are consistent with those predicted by a macroscopic model based on free energy minimization. We find that the free-energy barriers for these transitions depend on the droplet size and surface topology. A committor analysis indicates that the transition-state ensemble consists of droplets that are on the verge of initiating/breaking contact with the substrate at the bottom of the grooves.

Mechanisms of oriented attachment of TiO2 nanocrystals in vacuum and humid environments: reactive molecular dynamics

Oriented attachment (OA) of nanocrystals is now widely recognized as a key process in the solution-phase growth of hierarchical nanostructures. However, the microscopic origins of OA remain unclear. We perform molecular dynamics simulations using a recently developed ReaxFF reactive force field to study the aggregation of various titanium dioxide (anatase) nanocrystals in vacuum and humid environments. In vacuum, the nanocrystals merge along their direction of approach, resulting in a polycrystalline material. By contrast, in the presence of water vapor the nanocrystals reorient themselves and aggregate via the OA mechanism to form a single or twinned crystal. They accomplish this by creating a dynamic network of hydrogen bonds between surface hydroxyls and surface oxygens of aggregating nanocrystals. We determine that OA is dominant on surfaces that have the greatest propensity to dissociate water. Our results are consistent with experiment, are likely to be general for aqueous oxide systems, and demonstrate the critical role of solvent in nanocrystal aggregation. This work opens up new possibilities for directing nanocrystal growth to fabricate nanomaterials with desired shapes and sizes.

Asymmetric van der Waals forces drive orientation of compositionally anisotropic nanocylinders within smectic arrays: experiment and simulation

Understanding how micro- and nanoparticles interact is important for achieving bottom-up assembly of desired structures. Here, we examine the self-assembly of two-component, compositionally asymmetric nanocylinders that sediment from solution onto a solid surface. These particles spontaneously formed smectic arrays. Within the rows of an array, nanocylinders tended to assemble such that neighboring particles had the same orientation of their segments. As a probe of interparticle interactions, we classified nanocylinder alignments by measuring the segment orientations of many sets of neighboring particles. Monte Carlo simulations incorporating an exact expression for the van der Waals (vdW) energy indicate that differences in the vdW interactions, even when small, are the key factor in producing observed segment alignment. These results point to asymmetrical vdW interactions as a potentially powerful means of controlling orientation in multicomponent cylinder arrays, and suggest that designing for these interactions could yield new ways to control self-assembly.

A local superbasin kinetic Monte Carlo method

We present a local superbasin kinetic Monte Carlo (LSKMC) method that efficiently treats multiple-time-scale problems in kinetic Monte Carlo (KMC). The method is designed to solve the small-barrier problem created by groups of recurrent free-energy minima connected by low free-energy barriers and separated from the full phase space of the system by high barriers. We propose an algorithm to detect, on the fly, groups of recurrent free-energy minima connected by low free-energy barriers and to consolidate them into "superbasins," which we treat with rate equations and/or absorbing Markov chains. We discuss various issues involved with implementing LSKMC simulations that contain local superbasins and non-superbasin events concurrently. These issues include the time distribution of superbasin escapes and interactions between superbasin and non-superbasin states. The LSKMC method is exact, as it introduces no new approximations into conventional KMC simulations. We demonstrate various aspects of LSKMC in several examples, which indicate that significant increases in computational efficiency can be achieved using this method.

Wetting on physically patterned solid surfaces: the relevance of molecular dynamics simulations to macroscopic systems

We used molecular dynamics (MD) simulations to study the wetting of Lennard-Jones cylindrical droplets on surfaces patterned with grooves. By scaling the surface topography parameters with the droplet size, we find that the preferred wetting modes and contact angles become independent of the droplet size. This result is in agreement with a mathematical model for the droplet free energy at small Bond numbers for which the effects of gravity are negligible. The MD contact angles for various wetting modes are in good agreement with those predicted by the mathematical model. We construct phase diagrams of the dependence of the wetting modes observed in the MD simulations on the topography of the surface. Depending on the topographical parameters characterizing the surface, multiple wetting modes can be observed, as is also seen experimentally. Thus, our studies indicate that MD simulations can yield insight into the large-length-scale behavior of droplets on patterned surfaces.

A theory for the morphological dependence of wetting on a physically patterned solid surface

We present a theoretical model for predicting equilibrium wetting configurations of two-dimensional droplets on periodically grooved hydrophobic surfaces. The main advantage of our model is that it accounts for pinning/depinning of the contact line at step edges, a feature that is not captured by the Cassie and Wenzel models. We also account for the effects of gravity (via the Bond number) on various wetting configurations that can occur. Using free-energy minimization, we construct phase diagrams depicting the dependence of the wetting modes (including the number of surface grooves involved in the wetting configuration) and their corresponding contact angles on the geometrical parameters characterizing the patterned surface. In the limit of vanishing Bond number, the predicted wetting modes and contact angles become independent of drop size if the geometrical parameters are scaled with drop radius. Contact angles predicted by our continuum-level theoretical model are in good agreement with corresponding results from nanometer-scale molecular dynamics simulations. Our theoretical predictions are also in good agreement with experimentally measured contact angles of small drops, for which gravitational effects on interface deformation are negligible. We show that contact-line pinning is important for superhydrophobicity and that the contact angle is maximized when the droplet size is comparable to the length scale of the surface pattern.

Molecular thin films on solid surfaces: mechanisms of melting

We use molecular dynamics simulations to study the melting of pentane and hexane monolayers adsorbed on the basal plane of graphite. For both of these systems, the temperature-dependent structures and the melting temperatures agree well with experiment. A detailed analysis reveals that a mechanism involving the promotion of molecules to the second layer underlies melting in these systems. In the second-layer promotion mechanism, a small fraction of molecules transition into the second layer around the melting temperature, leaving vacant space in the first layer to facilitate disordering. The second-layer promotion mechanism arises because of the weaker molecule-surface interaction in our study than that in previous studies. The weaker molecule-surface interaction is consistent with experimental temperature-programmed desorption studies.

Adsorption of polyvinylpyrrolidone on Ag surfaces: insight into a structure-directing agent

We use density functional theory to resolve the role of polyvinylpyrrolidone (PVP) in the shape-selective synthesis of Ag nanostructures. At the segment level, PVP binds more strongly to Ag(100) than Ag(111) because of a surface-sensitive balance between direct binding and van der Waals attraction. At the chain level, correlated segment binding leads to a strong preference for PVP bind to Ag(100). Our study underscores differences between small-molecule and polymeric structure-directing agents.

Entropic forces and directed alignment of hard squares in suspensions of rods and disks

We use Monte Carlo simulations in two dimensions to study the depletion forces between two hard squares in a suspension of hard rods or disks. We determine the effects of size and concentration of rods and disks on the potential of mean force between the squares. Both rods and disks produce a short-range depletion attraction between the two squares. The depletion interaction can be strong enough to outweigh the (rotational) entropic repulsion between the squares at certain sizes and concentrations of the rods and disks. We also probe the relative orientation that two squares adopt as they approach each other and we observe rich behavior, in which the relative orientation depends on the size, concentration, and shape of the depletion agent. Simple models based on the ideas of Asakura and Oosawa [J. Chem. Phys. 22, 1255 (1954)] can explain trends in the potentials of mean force obtained from the simulations.

Assembly of gold nanowires by sedimentation from suspension: Experiments and simulation

We investigated the ordering of gold nanowires that settled from aqueous suspension onto a glass substrate due to gravity. The nanowires, ca. 300 nm in cross-sectional diameter and ca. 2, 4, or 7 microns in length, were coated with 2-mercaptoethanesulfonic acid to provide electrostatic repulsion and prevent aggregation. The layer of nanowires in direct contact with the substrate was examined from below using optical microscopy and found to exhibit smectic-like ordering. The extent of smectic ordering depended on nanowire length with the shortest (2 μm) nanowires exhibiting the best ordering. To understand the assembly in this system, we used canonical Monte Carlo simulations to model the two-dimensional ordering of the nanowires on a substrate. We accounted for van der Waals and electrostatic interactions between the nanowires. The simulations reproduced the experimental trends and showed that roughness at the ends of the nanowires, which locally increased electrostatic repulsion, is critical to correctly predicting the experimentally observed smectic ordering.

Molecular dynamics simulation of the aggregation of titanium dioxide nanocrystals: preferential alignment

We use classical molecular-dynamics simulations to study the aggregation of various titanium dioxide (anatase) nanocrystals in vacuum. In all cases, we observe a strong tendency for the nanocrystals to aggregate with certain preferred orientations in a "hinge" mechanism. Although some of the nanocrystals possess significant dipole moments, dipole-dipole interactions do not direct aggregation, implying that higher-order multipole moments are the driving force for preferential alignment. These high-order multipole moments originate from under-coordinated O and Ti surface atoms on the edges between nanocrystal facets, which create localized regions of positive and negative charge. The observed mechanism for preferential alignment may be a driving force for oriented attachment and the growth of anisotropic structures during crystallization.