Development of Interatomic Potentials with Applications to Nanoscale Surface Science

DEVELOPMENT OF INTERATOMIC POTENTIALS WITH APPLICATIONS TO NANOSCALE SURFACE SCIENCE

ANDREW ANTONY

A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2017

To the metallurgists who inspire me most: Dad, Uncle Mike, and my late grandfather, Ken Antony (Grandpa)

ACKNOWLEDGMENTS

First and foremost, I would like to express a heartfelt appreciation toward my parents who have provided unconditional love and support throughout my academic career. They are wonderful people and I hope that the hard work put into this dissertation reflects the dedication and sacrifices they have made for me throughout my life. In addition, I want to acknowledge three people who have been most influential in my decision to study materials science and engineering: my father, his twin brother (my uncle), and my late grandfather. Being surrounded by metallurgists my whole life had a tremendous impact on my appreciation for engineering and critical scientific inquiry.

While a researcher in California, my grandfather began taking foreign language courses as an admission requirement to graduate school. When he and my grandmother realized they would be raising twins, my grandfather ended his pursuit of a doctoral degree to take care of his family. This dissertation is dedicated to him.

I am sincerely appreciative for my advisor, Dr. Sinnott, and coadvisor, and Dr.

Phillpot, for leading a research group that fostered academic excellence, created strong interpersonal relationships, and stimulated intellectual creativity. The dedication and care they put into mentoring all students and researchers has made graduate school an incredible life experience for me. Dr. Sinnott exemplifies collegial professionalism and her guidance has been instrumental in helping me through a time of uncertainty as a young researcher. Our countless discussions on career choices, scientific research, and professional involvement have been paramount in helping me discover my own aspirations. I would also like to thank Dr. Richard Hennig for his scientific expertise and useful discussions while I was studying at UF.

A huge thank you is also extended to the research group at UF, Florida

Laboratory for Advanced Materials and Simulations (FLAMES). The people in this group are incredible individuals and their intellectual support and friendship have followed me even after moving to Penn State. I am forever grateful particularly for Dr. Tao Liang whose expertise in atomic materials theory has helped me develop a mindset structured by logical and practical science.

Ironically, the research I was working on as a student at UF was a collaborative project with a chemical engineering group at Penn State. Dr. Michael Janik and Sneha

Akhade both provided significant contributions to our scientific work and immediately welcomed me into the Penn State community after I moved from UF to Penn State.

Many thanks to both for being encouraging researchers and friends.

I want to thank all my classmates and friends at UF with whom I have shared courses, class projects, and countless memories in Gainesville and Florida. In addition,

I thank all the members of the racquetball clubs at UF and Penn State for their support and camaraderie while I was in graduate school.

Although I moved away from my home state of Louisiana, my two brothers continued to support and motivate me, and even visited me at both UF and Penn State.

We are a close-knit brotherhood and I thank them for everything they have done for me.

Finally, I want to thank my girlfriend, Casey Phifer, for her never-ending support and companionship. She has stuck with me while we were both researching at schools a country apart and words alone cannot express how much I love her and cherish our relationship.

TABLE OF CONTENTS

page

ACKNOWLEDGMENTS ...... 4

LIST OF TABLES ...... 8

LIST OF FIGURES ...... 9

LIST OF ABBREVIATIONS ...... 11

ABSTRACT ...... 12

CHAPTER

1 INTRODUCTION ...... 14

1.1 Electrochemical Systems ...... 14 1.2 Nanoscale Water-Metal Interactions ...... 15 1.3 Platinum Catalysts ...... 16 1.4 Objectives and Outline ...... 17

2 COMPUTATIONAL METHODOLOGIES ...... 21

2.1 Overview ...... 21 2.2 Empirical Interatomic Potentials ...... 22 2.2.1 Many-Body Potentials ...... 23 2.2.2 Charge Optimized Many Body (COMB) Reactive Potential ...... 24 2.2.2.1 Charge- and distance-dependent interactions ...... 25 2.2.2.2 Distance-dependent interactions ...... 30 2.2.2.3 Charge equilibration scheme ...... 31 2.2.2.4 Electrochemical modeling developments ...... 32 2.2.2.5 Parameterization of COMB3 ...... 33 2.3 Molecular Dynamics (MD) ...... 35 2.4 Geometry Optimization and Energy Minimization ...... 37

3 COMB3 POTENTIAL FOR PLATINUM METAL AND Pt/O/H INTERACTIONS ...... 40

3.1 Interatomic Potential Developments ...... 40 3.2 Parameterization of Pt Metal ...... 42 3.2.1 γ Surface Energies ...... 43 3.2.2 Tensile Test Simulation ...... 44 3.3 Parameterization of Pt/O Interactions ...... 45 3.4 Parameterization of Pt/H and Pt/O/H Interactions ...... 47

4 PLATINUM AND GOLD NANOPARTICLES ...... 59

4.1 Metal Nanoparticles ...... 59 4.2 Wulff-Constructed Nanoparticles ...... 59 4.3 High Temperature Nanoparticle Simulations ...... 60 4.3.1 Shape Change of Nanoparticles at Elevated Temperatures ...... 61 4.3.2 Diffusion of Nanoparticle Surface Atoms ...... 64

5 SURFACE PHENOMENA ON PLATINUM METAL SURFACES ...... 74

5.1 Overview of Adsorption on Pt ...... 74 5.2 O* and H* Adsorption on Pt(111) ...... 76 5.3 OH* and H2O* adsorption on Pt(111) ...... 77 5.4 Interfacial Molecular Ordering of Multilayer H2O on Pt(111) ...... 79 5.5 Summary of COMB3 Pt/O/H ...... 83

6 DYNAMIC SIMULATIONS OF WATER/METAL INTERFACES ...... 91

6.1 Overview of Cu/H2O Interfaces ...... 91 6.2 DFT Calculations of H2O on Cu(111) ...... 93 6.3 COMB3 Water ...... 94 6.4 Water Adsorption on Cu(111) ...... 97 6.5 Dynamic Simulations of Water on Copper Surfaces ...... 99 6.5.1 Spreading Mechanism of a Water Droplet on Cu ...... 101 6.5.2 Effect of Surface Chemistry on Spreading Rate ...... 105 6.6 Electrochemical Simulations of Cu/H2O Systems ...... 108 6.7 COMB3 Cu/H2O Synopsis ...... 112

7 CONCLUSIONS ...... 130

APPENDIX: POTENTIAL PARAMETERS FOR Pt-O-H COMB3 POTENTIAL ...... 133

LIST OF REFERENCES ...... 135

BIOGRAPHICAL SKETCH ...... 149

LIST OF TABLES

Table page

3-1 Fitted properties of Pt metal ...... 50

3-2 Fitted heat of formation energies of Pt/O solid state phases ...... 51

3-3 Fitted adsorption energies for O* on Pt(111) ...... 51

3-4 Fitted adsorption energies for H* on low-index Pt surfaces ...... 51

3-5 Fitted adsorption energies for OH* on Pt(111)...... 51

3-6 Fitted adsorption energies for molecular H2O* on Pt(111)...... 52

4-1 Relative surface energy ratios for Pt and Au...... 67

5-1 Adsorption energies for 0.11 ML H* adsorption on Pt(111) ...... 84

5-2 Adsorption energies for 0.25 ML O* adsorption on Pt(111) ...... 84

5-3 Adsorption energies for 0.11 ML OH* on Pt(111) ...... 84

5-4 Adsorption energies for 0.11 ML H2O* on Pt(111) ...... 84

6-1 List of properties of H2O systems ...... 113

6-2 Bulk liquid water properties...... 114

A-1 COMB3 parameters for Pt, O, and H ...... 133

A-2 Two-body parameters developed for Pt metal...... 133

A-3 Two-body parameters developed for Pt/O/H ...... 134

A-4 Three-body Legendre polynomial parameters for Pt metal, Pt/O, and Pt/H ...... 134

A-5 Three-body Legendre polynomial parameters for Pt/O/H ...... 134

LIST OF FIGURES

Figure page

1-1 Solid-liquid interface in aqueous environments present in fuel cells ...... 19

1-2 Volcano plot of oxygen reduction activity for transition metals ...... 20

2-1 Schematic diagrams of electrochemistry simulation methods...... 39

3-1 Pt stacking faults...... 53

3-2 Simulated tensile test of polycrystalline Pt ...... 54

3-3 Pt/O bulk structures included in the COMB3 fitting database ...... 55

3-4 Adsorption sites on Pt(111) ...... 56

3-5 Hydrogen adsorption on low index Pt surfaces...... 57

3-6 Hexagonal water adsorbed on Pt(111) ...... 58

4-1 Pt and Au Wulff-constructed NPs ...... 68

4-2 Pt and Au nanoparticles simulated at high temperatures ...... 69

4-3 Radial distribution functionsfor high temperature Pt and Au nanoparticles...... 70

4-4 Energy and coordination change of Pt and Au nanoparticles ...... 71

4-5 MSD of Pt and Au nanoparticle surface atoms ...... 72

4-6 Arrhenius plot of activation energy for surface self-diffusion ...... 73

5-1 Adsorbed oxygen on Pt(111) in a p(2x2) ordering ...... 85

5-2 Coverage dependent oxygen adsorption energy on Pt(111) ...... 86

5-3 Water/Pt(111) interface ...... 87

5-4 Atomic distribution at the water/Pt interface ...... 88

5-5 Wetting layer on Pt(111) ...... 89

5-6 Ring structures of the first wetting layer on Pt(111)...... 90

6-1 Radial distribution functions of liquid water...... 115

6-2 Configuration of water monomers adsorbed on Cu(111) ...... 116

6-3 Water hexamer adsorbed on Cu(111)...... 117

6-4 Regions of a water droplet ...... 118

6-5 Time evolution of a water droplet on Cu...... 119

6-6 Simulated base radius of water droplet on Cu ...... 120

6-7 Low temperature structure of water droplets on Cu...... 121

6-8 Diffusivity of water droplet regions ...... 122

6-9 Oxygenated and hydroxylated Cu surfaces ...... 123

6-10 Spreading rate of water on O* and OH* covered Cu...... 124

6-11 Precursor film schematic and molecular wetting mechanism ...... 125

6-12 Cu/H2O/Cu simulated electrochemical cell ...... 126

6-13 Average atomic charge at the electrochemical interface ...... 127

6-14 Water density profile as a function of applied potential ...... 128

6-15 Potential profiles from simulated electrochemistry methods ...... 129

LIST OF ABBREVIATIONS

CNA Common Neighbor Analysis

DFT Density Functional Theory

EDLC Electrochemical double-layer capacitor

EE Electronegativity Equalization

LJ Lennard-Jones

MD Molecular Dynamics

ML Monolayer

NP Nanoparticle

PF Precursor film

QEq Charge Equilibration

SF Stable stacking fault

SFE Stacking fault energy

USF Unstable stacking fault vdW Van der Waals

X* Indicates atomic or molecular species (X) adsorbed on a surface (*)

Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy

DEVELOPMENT OF INTERATOMIC POTENTIALS WITH APPLICATIONS TO NANOSCALE SURFACE SCIENCE

Andrew Antony

May 2017

Chair: Susan B. Sinnott Cochair: Simon R. Phillpot Major: Materials Science and Engineering

Technologically advanced fuel cells currently contain Pt as the catalytic material that improves device performance. The economically high cost of Pt limits the amount of material used in these electrochemical devices. Fundamentally, the electrocatalytic reactions take place when atoms or molecules encounter atoms on the electrode surface. In order to develop and improve understanding of the precious metal and its role in atomic-scale processes, computational models and simulations are constructed to mimic the physical behavior at the heterogeneous interface.

An empirical interatomic potential based on the third generation charge optimized many body (COMB3) formalism is first developed for pure Pt metal followed by validation and testing that confirms reliability of the potential. High temperature molecular dynamics simulations are performed on Pt and Au nanoparticles to compare atomic surface diffusion and nanoparticle shape change. Analysis of the simulations is based on the overall atomic coordination distribution for each nanoparticle and the diffusivity of surface atoms at elevated temperatures.

Adsorbed species such as O, H, OH, and H2O are then considered at a Pt surface and the potential undergoes further optimization. Multilayer water films are simulated on a Pt(111) surface and the structure of the first wetting layer is determined to exhibit a buckled structure including short and long range interactions between water molecules and Pt surface atoms. Atomic density profiles at the interface verify these observations and we compare the degenerate molecular structure and charge density distributions that occur on Pt and Cu surfaces.

The final part of this work reports dynamic wetting simulations of water on copper surfaces. Properties of liquid water as predicted by COMB3 are reported along with molecular interaction with a copper surface. The wetting mechanism for a water droplet on a bare Cu(111) is determined by calculating relative displacement of water molecules from different regions of the droplet. Next, the Cu surface is chemically altered by the addition of adsorbed O and OH species which decreases the spreading rate and degree of spreading. Analysis of atomic charge at the water/Cu interface of these simulations indicates a retarded spreading rate due to stronger Coulombic interactions between H2O molecules and adsorbed O or OH compared to H2O molecules and Cu surface atoms.

Thus, this work presents a variety of surface phenomena at the nanoscale (from atomic diffusion on nanoparticle surfaces to wetting behavior of water on chemically modified Cu) based on molecular dynamics simulations and provides a new empirical potential that enables simulations of Pt/O/H systems.

CHAPTER 1 INTRODUCTION

1.1 Electrochemical Systems

Currently, several technologically relevant devices take advantage of electrochemical reactions that occur inside a battery, fuel cell, or any other applied voltage circuit. Providing powerful electrochemical energy conversion and storage devices is currently one of society’s most challenging engineering tasks. If a voltage is used to increase or control the rate of reactions in an electrochemical cell, the process is termed electrocatalysis. In fuel cells, chemical energy stored in fuels such as hydrogen gas is directly converted to electrical energy with water as a byproduct.1 For these electrochemical devices, the hydrogen oxidation reaction (HOR) and oxygen reduction reaction (ORR) are the chemical reactions to be catalyzed.2-3 Conversely, when molecular water is split into gaseous hydrogen and oxygen, the device is called a water electrolyser1. In either case, some catalytic electrode material comes into contact with liquid water in order for the reaction to proceed and thus, the material chosen for the anode and cathode ultimately determines the efficiency of the device. A molecular representation of such fuel cell interactions is shown in Figure 1-1 where water molecules form a hydration shell around electrolytic metal cations. This schematic validates the scientific importance of developing atomic-scale models and simulation capabilities for O2, H2, OH, and H2O at some electrode interface.

Various chemical reactions can be catalyzed in electrochemical devices depending on the operating conditions (e.g., overpotential, temperature, or humidity) and materials used as the electrodes and electrolyte.4 Due to the intimate relationship between device performance and properties of their materials, research and

development to realize state-of-the-art batteries and fuel cells is focused on identifying promising electrode materials.

1.2 Nanoscale Water-Metal Interactions

Nanostructured electrocatalysts have received significant attention recently due to favorable properties that arise when particles approach length scales below a few hundred nanometers.4-5 Instead of microstructural features that determine material functionality, nanoscale materials and their surfaces possess inherent atomic-scale surface defects. As an example, nanosurfaces tend to deviate from atomically planar terminations and form imperfections such as terraces, step edges, kinks, and other atomic scale defects. These defects play a significant role in chemical and physical processes especially in the context of heterogeneous interactions. For example, the role of surface edges has been shown to accelerate dissociative adsorption of water on metal surfaces in ultra-high vacuum (UHV) conditions.6

It is important here to differentiate the behavior of water on a solid surface depending on the simulation/experimental setup and environmental conditions. One such water-metal interaction that has been given significant scientific attention is the adsorption of individual water molecules at low temperatures and UHV environments, as mentioned above. When molecular water comes into contact with a metal surface, formation of a thin film of molecules occurs at the interface. Initially, the structure of this molecularly thin layer was thought to resemble a hexagonal bilayer7 resembling the

(001) basal plane of ice-I due to the presence of proton ordering. In the 1990s, experimental advances allowed researchers the ability to fully characterize the structure of a water overlayer on any surface.8 With further improvements of experimental techniques and DFT calculations, researchers have identified molecularly adsorbed

structures of water clusters, 1D ice chains (1 nm wide) on Cu9-10 and a mixture of pentagonal, hexagonal, and heptagonal rings of water molecules on Pt(111).11-13

Conversely, experiments and especially MD simulations also consider the dynamic interaction of a liquid droplet on a solid surface where behavior such as spreading rate, wettability, and contact angle are studied.14-16 The wetting process of water on metal surfaces involves the formation of a molecularly thin precursor film

(PF)15 which diffuses across a surface driven by the interplay between the droplet’s surface tension and the metal surface energy. Admittedly, these studies are often aimed at studying more general behavior of liquid/solid wetting interactions and specific research on water-metal interfaces represents one subset of this broad spectrum.

For the case of fuel cells and other electrochemical devices, operating temperature and pressure are well above conditions that characterize the structural nature of the first wetting layer. In addition, the electrolyte is an aqueous environment where water molecules behave as a liquid, so only considering the first wetting layer of low-temperature (below 200 K) molecular adsorption is not reasonable. While the wetting behavior of a water droplet on an infinitely large surface is an ideal process to study using MD tools, electrolytic movement (i.e., liquid water from aqueous solution) in a fuel cell is confined between two electrodes. Nonetheless, water dynamics still occur at the first interfacial wetting layer and subsequent layers in a confined cell; therefore,

MD simulations can provide atomic-scale information that relates dynamic water behavior to the molecular structure at the metal-water interface.

1.3 Platinum Catalysts

While electrochemical devices are promising because they emit non-harmful byproducts like water, their efficiency is dependent on the selection of catalytic material

at the electrode. Platinum-based materials are widely studied for their catalytic properties in several applications, ranging from fuel cell electrodes to electrocatalysts in biological systems. Although Pt is a promising catalyst in most cases, the high cost of the precious metal is a serious drawback which enforces technological constraints on device performance.17 The economic cost of Pt has driven researchers to develop methods and materials that optimize the amount of Pt while retaining or improving catalytic performance. The development of such materials has been closely related to the concept of a volcano plot18-19 which links the electrocatalytic rate of reaction to a more fundamental material “descriptor” as shown in Figure 1-2. From the figure, oxygen reduction activities for several transition metals are plotted as a function of the DFT calculated oxygen binding energy and Pt exhibits the highest predicted activity.

As scientists and engineers seek to design better materials as the electrocatalyst in high functioning fuel cells, relevant nanoscale models and simulations are needed to complement experimental approaches and large-scale device modelling. Developing interatomic potentials for MD simulations allows for mechanistic studies that corroborate empirical findings which may not be fully understood using first principles methods alone. Furthermore, a potential specifically parameterized to capture Pt metal interaction with water or other O/H containing chemical species can elucidate material specific processes which are necessary to progress the field of Pt nanoscience and catalysis.

1.4 Objectives and Outline

The work described in this dissertation builds on the prior work described in

Section 1.3 and provides new mechanistic insights at the level of the atomic scale. In particular, the objectives are to provide a detailed description of the computer

simulation methodology and present the subsequent development of interatomic potentials for Pt/O/H systems. These developments are then applied during simulations to provide a mechanistic understanding of nanoscale surface phenomena that may occur at a heterogeneous metal/liquid or metal/gas interface. The major impact of the work summarized here is the dissemination of a scientifically valuable interatomic potential for Pt/O/H systems which researchers can utilize in future studies. Unlike previous classical MD models of the Pt/H2O interface, the COMB3 Pt/O/H potential predicts interfacial configurations in line with experiments and DFT calculations.

Furthermore, this dissertation initiates a framework for making additional developments for aqueous Pt catalysis or other Pt-based MD simulations. For example, researchers studying organic catalysis on Pt should include reaction-specific products and reactants on a Pt surface in the fitting database to fully utilize the reactive nature of COMB3.

Figure 1-1. Solid-liquid interface in aqueous environments present in fuel cells. [From V. R. Stamenkovic et al. ‘Energy and fuels from electrochemical interfaces’, Nature Materials, 2017(1), 57-69.]

Figure 1-2. Volcano plot of oxygen reduction activity plotted as a function of DFT- calculated oxygen binding energies for transition metals. [From J. K. Nørskov et al. ‘Origin of the overpotential for oxygen reduction at a fuel-cell cathode’, The Journal of Physical Chemistry B, 2004, 108(46), 17886-17892.]

CHAPTER 2 COMPUTATIONAL METHODOLOGIES

2.1 Overview

Theoretical investigations of materials science and engineering problems span length and time scales from atomic interactions that occur over a few nanoseconds (10-9 s) to mechanical materials properties that affect the stability of materials such as structural alloys over days or months. The advent of computational tools to study these types of problems has created a scientifically-rich field for researchers studying atomic- scale phenomena. Classical molecular dynamics (MD) is one such tool that provides researchers the capability of investigating atomic motion in nanometer-size simulations.

The primary advantage of these simulations is their ability to provide an understanding of the mechanisms that underlie larger scale phenomena. Another advantage of computational research is that outputs from MD simulations can be used as the input to some mesoscale (10-6 m) model that predicts microstructural evolution which helps connect the time- and length-scale discontinuity.

This chapter lays the foundation for understanding the relationship between MD and the interatomic potentials used within MD simulations to describe the materials system of interest. Throughout this dissertation, an emphasis is placed on the development of potentials under the third generation charge optimized many-body

(COMB3) formalism and their application to surface science studies in the presence of a heterogeneous interface (e.g. water on metal, Pt/PtO2 interface). A method for simulating electrochemistry within a variable charge potential is provided and a general outline of the parameterization procedure used during development of COMB3 materials systems is discussed at the end of the COMB3 formalism section.

2.2 Empirical Interatomic Potentials

For classical simulation methods, such as MD, the energy that describes inter- and/or intra- atomic interactions is termed a potential in the convention of materials scientists or a force field in the convention of chemists and biological scientists. In MD simulations, the forces on particles or atoms are derived from a potential energy function U, which depend on atomic positions:

퐹 = −∇푈(푟1 … 푟푁) (2-1)

During molecular dynamics computer simulations, the interatomic potential is responsible for determining atomic motion and producing a scientifically accurate output. These potentials take on mathematical functional forms and parameterizations with the goal of describing interactions that arise from quantum mechanical principles.

Initially, selecting an analytical form for the potential was often done using pairwise terms where the energy only depends on the relative distance between atomic pairs. As an example, one of the earliest (and simplest) potentials is a classical 12-6

Lennard-Jones (LJ)20 which is a pairwise potential between two atoms in the following equation:

휎 휎 푈퐿퐽 = 4휀 [( )12 − ( )6] (2-2) 푟 푟

This potential is often presented in an introductory materials science or physics context and is suitable for describing simple systems such as a diatomic inert gas molecule where a lack of valence electrons means only weak van der Waals forces are present.

For advanced researchers studying more complicated systems that include two or more atomic species in a 3D crystal lattice, the construction of a new potential is warranted.

2.2.1 Many-Body Potentials

Interatomic potentials have undergone significant developments so that the potential energy can be described as a function of many-body (two-, three-, or higher body) interactions instead of a pair potential sum. The pioneering many-body potentials developed during the 1980’s were generally used to simulate specific solid state materials systems. One such implementation of bond order was presented in a Tersoff potential21 to more accurately describe elastic properties of Si. In this formalism, atomic interactions are mathematically described using repulsive (푓푅(푟푖푗)) and attractive

(푓퐴(푟푖푗)) terms:

푇푒푟푠표푓푓 푈 = ∑푖,푗 푉푖푗 (2-3)

푉푖푗 = 푓푐{푎푖푗푓푅(푟푖푗) + 푏푖푗푓퐴(푟푖푗)} (2-4)

Another common potential with two-body and three-body terms to model solid and liquid

Si was introduced and subsequently named Stillinger-Weber potential.22

During the same decade, an embedded atom method (EAM) potential was developed to mathematically describe metallic bonding for fcc metals and their alloys.23-

24 The starting point of EAM is the approximation that the total electron density in a metal is a linear superposition of atomic densities. In the EAM description, an embedding function, Fi, is determined by the density of a host atom, ρi, where each density is assumed to take the form of a locally uniform electron gas. The total EAM

퐸퐴푀 energy function, 푈 , adds a distance-dependent pair potential, 휑푖푗, to the embedding function:

1 푈퐸퐴푀 = ∑ 퐹 (휌 ) + ∑ ∑ 휑 (푅 ) 푖 푖 2 푖푗 푖푗 (2-5) 푖 푖 푗≠푖

Large-scale computer simulations using EAM are computationally feasible and require a similar amount of work compared to simple pair potentials. This precedent has made

EAM a widely used potential when studying, e.g., grain boundary phenomena and deformation mechanisms in metals and alloys.

The original modified EAM (MEAM) potential was developed for Si and Ge25 to model the differences between metallic and covalent bonding by including angle- dependent terms in the host electron density. The modification of the density results in bond-bending forces inherent to covalent bonding. Later, MEAM was extended to include elements with cubic crystal structures (namely, bcc and fcc metals) using the same analytical form.26

In the interest of modeling chemical systems and their reactions, the reactive force field (ReaxFF) was developed by van Duin et al.27 In ReaxFF, the system energy

(푈푅푒푎푥퐹퐹) is divided into various partial energy contributions in the following equation:

푈푅푒푎푥퐹퐹 = 푈푏표푛푑 + 푈표푣푒푟 + 푈푢푛푑푒푟 + 푈푣푎푙푒푛푐푒 + 푈푝푒푛푎푙푡푦 + 푈푡표푟푠푖표푛 + 푈푐표푛푗 (2-6) + 푈푣푑푊 + 푈퐶표푢푙표푚푏

The bond order, which is assumed to be obtained directly from interatomic distance, is captured within the 푈푏표푛푑 term. Compared to quantum chemical or first principles approaches, ReaxFF is faster which allows simulations of molecular dissociation and bond formation in large hydrocarbon systems.

2.2.2 Charge Optimized Many Body (COMB) Reactive Potential

Much of this thesis contains MD simulations that use potentials parameterized under the third-generation charge optimized many body (COMB3) formalism. This section contains equations that outline how the energy function is calculated for such

systems. It should be noted that the main goal of the COMB formalism is to model dissimilar materials systems with transferability to describe complex bonding environments. The progress of the potential has been achieved through two important developments: the bond order concept and self-consistent charge equilibration. This section details the concepts and theories, including bond order and self-consistent charge equilibration, which govern how system energies are calculated using the third generation COMB (COMB3) potential.

The total energy of a system in the COMB328 potential series is represented by four separate energy terms:

푈푡표푡[{푞}, {푟}] = 푈푒푠[{푞}, {푟}] + 푈푠ℎ표푟푡[{푞}, {푟}] + 푈푣푑푤[{푟}] + 푈푐표푟푟[{푟}] (2-7)

Where 푈푒푠[{푞}, {푟}] represents electrostatic energies, 푈푠ℎ표푟푡[{푞}, {푟}] are short-range interactions, 푈푣푑푤[{푟}] are van der Waals energies, and 푈푐표푟푟[{푟}] are correction terms.

In Equation 2-2, {푞} and {푟} represent the charge and coordinate array of the system, respectively.

2.2.2.1 Charge- and distance-dependent interactions

There are only two energy terms in Equation 2-2 whose values are both charge and distance dependent: electrostatic (푈푒푠[{푞}, {푟}]) and short-range (푈푠ℎ표푟푡[{푞}, {푟}]) energies. The electrostatic energy can be broken into the following terms which are also functions of charge and distance:

푈푒푠[{푞}, {푟}] = 푈푠푒푙푓 + 푈푞푞 + 푈푞푍 + 푈푝표푙푎푟 (2-8)

self 푖표푛푖푧푒 The self-energy (U ) consists of ionization energy of an isolated atom, 푉푖 (푞푖), which is also the energy required for the atom to form its own charge. COMB3 adopts the self-energy function according to Mortier et al.29 who showed that the energy and

chemical potential of an atom, 푖, can be expressed as a function of charge by using a

Taylor series expansion (truncated at second order):

2 푖표푛푖푧푒 0 휕퐸 1 휕 퐸 2 푉푖 (푞푖) = 퐸푖 + 푞푖 + 2 푞푖 (2-9) 휕푞푖 2 휕푞푖

We now define the electron affinity (EA) as an atom having a negative charge (−1) and the ionization potential (IP) as the atom having a positive charge (+1) By solving this equation for 푞 = 0, +1, and −1 we yield the following two equations:

휕퐸 1 = (퐼푃 + 퐸퐴) = 휒푖 (2-10) 휕푞푖 2

휕2퐸 푞푞 2 = (퐼푃 − 퐸퐴) = 퐽푖푖 (2-11) 휕푞푖

Where the first derivative of energy with respect to charge is equivalent to the atom’s electronegativity and the second derivative is defined as the chemical hardness which describes the interaction between valence electrons in the same atom. This is now useful because we have established a way to relate the change in atomic energy with respect to charge with either calculated or experimentally measured values, ionization potentials and electron affinities. This definition of electronegativity will be proven useful in later sections when a detailed description of self-consistent charge equilibration is provided. In COMB3, a field-effect correction term that accounts for change in chemical hardness when an atom is embedded in a molecule of bulk oxide is added to the chemical hardness coefficient (Equation 2-6). Using the definitions from Equations 2-5 and 2-6 and expanding the ionization energy (Equation 2-4), the short-range interaction in COMB3 takes the form:

푠푒푙푓 2 3 4 푓푖푒푙푑 푈 [{푞}, {푟}] = 휒푖푞푖 + 퐽푖푞푖 + 퐾푖푞푖 + 퐿푖푞푖 + 퐸푖 (푟푖푗, 푞푖, 푞푗) (2-12)

휒 푃 푞 푃퐽 푞2 푓푖푒푙푑 1 푁푁 푖푗 푗 푖푗 푗 퐸푖 (푟푖푗, 푞푖, 푞푗) = ∑푗≠푖 ( 휒 + 퐽 ) (2-13) 4휋휀0 퐴 퐴 푟3 +( 푖푗)3 5 푖푗 5 푖푗 푟푖푗+( ) 푟푖푗 푟푖푗 where 푃휒, 푃퐽, 퐴휒, 퐴퐽 are parameters to be fit.

Coulombic electrostatic interactions between ions are calculated according to the electrostatic potential (ES+) model described by Streitz and Mintmire.30 Pointing out that the fixed ionic charge model is incorrect at the metal/metal oxide interface, ES+ allows the valence state of a metal atom to vary depending on the local chemical environment.

In COMB3, the second energy term in Equation 2-3 models charge-charge interactions as the sum of Coulombic integrals over radial charge density distribution functions, ρi(r):

1 푈푞푞[{푞}, {푟}] = ∑ ∑ 푞 퐽푞푞푞 (2-14) 2 푖 푗≠푖 푖 푖푗 푗

푞푞 3 휌푖(풓1)휌푗(풓2) 3 퐽푖푗 = [휌푖|휌푗] = ∫ 푑 풓1 ∫ 푑 풓2 (2-15) |풓1−풓2−풓푖푗|

Using a similar Coulombic integral, the nuclear-attraction energy (UqZ) is expressed based on interaction between the atomic valence shell and effective core charge:

1 푈푞푍[{푞}, {푟}] = ∑ ∑ 푞 퐽푞푍푍 (2-16) 2 푖 푗≠푖 푖 푖푗 푗

푞푍 퐽푖푗 = [푗|휌푖] − [휌푖|휌푗] (2-17)

3 휌푖(푟) [푗|휌푖] = ∫ 푑 풓1 (2-18) |풓−풓푖| where Zi is the core charge and the charge density distributions are based on Slater S- type orbitals.31 Calculating the density distribution function integrals yields exponentially

푞푞 푞푍 decaying functions for 퐽푖푗 and 퐽푖푗 . The last term in the electrostatic energy is a

polarization contribution which represents self-dipole, dipole-dipole, and charge-dipole interactions:

2 푝표푙푎푟 휇⃗⃗ 푖 ⃗ 푞 푈 [{푞}, {푟}] = ∑푖 + ∑푖 휇 푖 ∙ 퐸푖 + ∑푖 ∑푗>푖 휇 푖푇푖푗휇 푗 (2-19) 2푃푖

푞 where 휇푖 is the point dipole moment, 푃푖 is the polarizability tensor, 퐸푖 is the electrostatic field generated by atomic charges, and 푇푖푗 is the damped dipole-field tensor. The inclusion of explicit electronic polarization terms permits distortion of charge distribution so that small polarizable molecules such as O2 and water can redistribute electron density based on a response to some external electric field (or charge-dependent environment).

The bond order concept32 underlies short-range energies in COMB3 in which the bond strength is regulated by atomic environment. Interatomic potentials that implement either separated or integrated formats of bond order are capable of determining bond strength on-the-fly and are grouped into the class of reactive potentials (Section 2.1.1).

The ensuing COMB3 short-range terms are based on the Tersoff potential formalism for

Si.33 Within COMB3, short-range interactions are modeled as a sum of pair-wise

퐴 푅 attractive (푉 ) and repulsive (푉 ) terms which also depend on a cut-off function, 퐹푐(푟푖푗):

푏 +푏 푈푠ℎ표푟푡[{푞}, {푟}] = ∑ ∑ {퐹 (푟 ) [푉푅(푟 , 푞 , 푞 ) − 푖푗 푗푖 푉퐴(푟 , 푞 , 푞 )]} (2-20) 푖 푗>푖 푐 푖푗 푖푗 푖 푗 2 푖푗 푖 푗

Where the bond order average is coupled to the attractive interaction. In the same manner as the Tersoff potential, 푉퐴 and 푉푅 both exponentially decay with separation distance:

1 푉푅(푞 , 푞 , 푟 ) = 퐴 푒푥푝 {−휆 푟 + 휆∗[퐷 (푞 ) + 퐷 (푞 )]} (2-21) 푖 푗 푖푗 푖푗 푖푗 푖푗 2 푖 푖 푖 푗 푗

1 푉퐴(푞 , 푞 , 푟 ) = 퐵∗ (푞 , 푞 ) 푒푥푝 { [훼 퐷 (푞 ) + 훼 퐷 (푞 )]} ∑3 [퐵푛 푒푥푝(−훼푛 푟 )] (2-22) 푖 푗 푖푗 푖푗 푖 푗 2 푖푖 푖 푖 푗푗 푗 푗 푛=1 푖푗 푖푗 푖푗

Where 퐴푖푗, 휆푖푗, 퐵푖푗, and 훼푖푗 are parameters to be fit. The sum associated with the attraction term (Equation 2-17) provides flexibility in order to correctly predict stacking faults in anisotropic hcp metals and other energetics associated with oxides. The

∗ 34 functions 퐷푖(푞푖) and 퐵푖푗(푞푖, 푞푗) constructed by Yasukawa are an extension of the

Tersoff potential that can regulate bond energy according to the valence electron configuration and associated charges of two bonded atoms. If both atomic charges are zero (i.e., 푞푖 = 푞푗 = 0) then the bond energy is unchanged and the potential is equivalent to the Tersoff potential. The term 퐹푐(푟푖푗) in Equation 2-20 is a Tersoff cut-off

푚푖푛 function that terminates atomic interactions between a minimum (푟푖푗 ) and maximum

푚푎푥 (푟푖푗 ) distance:

푚푖푛 1 푖푓 푟푖푗 ≤ 푟푖푗 1 푟 − 푟푚푖푛 퐹 (푟 , 푟푚푖푛, 푟푚푎푥) = [ 푖푗 푖푗 ] 푚푖푛 푚푎푥 (2-23) 푐 푖푗 푖푗 푖푗 1 + cos (휋 푚푎푥 푚푖푛) 푖푓 푟푖푗 < 푟푖푗 ≤ 푟푖푗 2 푟푖푗 − 푟푖푗 푚푎푥 { 0 푖푓 푟푖푗 > 푟푖푗

The charge-dependent terms presented above illustrate variable charge distributions present in real heterogeneous systems. A system containing some metal/oxide interface is a standard example to describe how COMB3 captures different chemical bonding environments. Away from the interface, the metal-oxygen bonding in the oxide is mostly electrostatic (ionic). Atoms close to the interface have a mixed metallic and ionic bonding where both Equations (2-8) and (2-20) determine the overall interatomic energy. In the bulk metal, atomic charges are essentially zero (negligible electrostatic

interactions) and the overall bond character is captured as short-range interactions as expressed in Equation (2-20).

2.2.2.2 Distance-dependent interactions

Two terms in the COMB3 total energy formula from Equation (2-7) are exclusively dependent on the distance between atoms and have relatively simple formalisms compared to the charge-dependent energies. The van der Waals interaction energy, EvdW, is a classical Lennard-Jones potential with the form:

푁푁 푁푁 12 6 휎푣푑푊 휎푣푑푊 푣푑푊 푣푑푊 푣푑푊 푖푗 푖푗 푈 [{푟}] = ∑ ∑ 푉 (푟푖푗) = ∑ ∑ 4휀푖푗 [( ) − ( ) ] (2-24) 푟푖푗 푟푖푗 푖 푗>푖 푖 푗>푖

푣푑푊 푣푑푊 The two terms 휀푖푗 and 휎푖푗 reflect the strength and equilibrium distance of the van

푣푑푊 der Waals interactions. After 0.95휎푖푗 , a cubic spline function is used to smoothly terminate the vdW interactions at the maximum cutoff distance.

The correction terms on bond angles take the form of Legendre polynomials and consider third nearest neighbor interactions, including the case of distinguishing fcc-Cu and hcp-Cu, at the expense of computational cost.28 Yu et al. first implemented

Legendre polynomials to correct underestimated Cu surface energies using the equation:

푁푁 푁푁 6 푐표푟푟 푈 [{푟}] = ∑ ∑ ∑ {퐹퐶(푟푖푗)퐹퐶(푟푖푘) ∑ 퐿푃푛(cos(휃푖푗푘))} (2-25) 푖 푗>푖 푘≠푖 푛=1

th Where LPn(x) is the n order polynomial function and the parameters to be fit are coefficients of each polynomial function.

2.2.2.3 Charge equilibration scheme

Within the COMB3 formalism, atoms are assigned an atomic charge which is capable of fluctuating based on the atomic environment. Within the atomic position equilibration algorithm is a charge equilibration model that allows the atomic charge to vary. In DFT, the electronegativity of an atom, χi, is equal to the derivative of the electrostatic energy

푒푠 with respect to atomic charge, 휕퐸 /휕푞푖, which is equivalent to the negative value of the chemical potential (−휇푖). The charge dependent energy of COMB3, U[{q}], is comprised of electrostatic (Equation (2-8)) and short-range (Equation (2-20)) terms which are the energies accounted for during the charge equilibration scheme:

휕푈[{푞}] 휒푖 = −휇푖 = (2-26) 휕푞푖

Electronegativity equalization (EE)35-36 is based on the thermodynamic principle that the electronegativity (negative chemical potential) at all sites in a closed system are equal under chemical equilibrium conditions. By enforcing this constraint on atoms within a dynamic charge system such as COMB3, the charges are solved self-consistently. The charge equilibration (QEq)37-38 scheme implemented in COMB3 solves the dynamic charge equation in a similar manner to the real space equations of motion:

푀푄푞̈푖 = 휒̅ − 휒푖 + 휈푞̇푖 (2-27)

Where 휒̅ is the average electronegativity of all atoms in the system and ν is an empirically determined damping factor. The charge equation of motion above is solved using a velocity Verlet algorithm [cite] for each atom assuming fixed ion positions in real

space. Once the charges are equilibrated and the EE principle is satisfied, the ions are allowed to move.

2.2.2.4 Electrochemical modeling developments

Electrochemical reactions that occur under an external voltage between a cathode and anode often take place at or near the electrode/electrolyte interface. It is fitting that the electrochemistry developments follow the charge equilibration scheme since Electrode-COMB3 (ECOMB3) alters the charge equations of motion and charge constraints during simulation. Two separate methods, both within the COMB3 charge equilibration scheme, are presented: χ-offset and Q-offset. In the χ-offset method schematically shown in Figure 2-1A, the applied voltage, V, is modeled as the electronegativity difference (Equation (2-26)) between the cathode, C and anode, A:

휕푈 휕푈 푉 = 퐶 − 퐴 (2-28) 휕푞푖 휕푞푖

The new charge equations of motion are then expressed as following:

퐸: 푀푄푞̈푖 = 휒̅ − 휒푖 + 휈푞̇푖 (2-29a)

푁퐴 퐶: 푀푄푞̈푖 = 휒̅ + 푉 − 휒푖 + 휈푞̇푖 (2-29b) 푁퐴 + 푁퐶

푁퐶 퐴: 푀푄푞̈푖 = 휒̅ − 푉 − 휒푖 + 휈푞̇푖 (2-29c) 푁퐴 + 푁퐶

If the number of atoms considered the anode and cathode are equal, the voltage prefactor reduces to 1/2 and the voltage offset becomes ±푉/2.

The Q-offset method from Figure 2-1B considers the electrodes to be parallel plate capacitors (Ccathode and Canode) in the form of an electrochemical double-layer capacitor (EDLC). In this model, the induced charge on the cathode and anode is ±Q

while the cumulative charge within the electrolyte is zero. The new charge equations of motion and charge constraints are:

퐸: 푀푄푞̈푖 = 휒퐸̅ − 휒푖 + 휈푞̇푖 푎푛푑 ∑ 푞푖 = 0 (2-30a) 푖

퐶: 푀푄푞̈푖 = 휒퐶̅ − 휒푖 + 휈푞̇푖 푎푛푑 ∑ 푞푖 = +푄 (2-30b) 푖

퐴: 푀푄푞̈푖 = 휒퐴̅ − 휒푖 + 휈푞̇푖 푎푛푑 ∑ 푞푖 = −푄 (2-30c) 푖

Within this model, QEq is applied separately to the anode, cathode, and electrolyte so that atomic charge is not allowed to migrate between the electrodes and electrolyte.

Although the charge constraints prohibit charge transfer across the electrode/electrolyte interface, local charge segregation within the anode or cathode can still induce atomic motion via electrostatic interactions at the interface.

2.2.2.5 Parameterization of COMB3

Because of the complex functional form of COMB3, there are dozens of parameters to fit even for just a single element system. When developing COMB3 potentials, it is important to provide users with a parameter set that is both rigorous and flexible. This means that the potential should be capable of accurately reproducing important physical properties of the material (i.e. lattice constant and bond length, elastic constants, bulk modulus, etc.) and accurately capture the physics of systems not specified during parameterization. This primary aim of COMB3 makes the potential development process strenuous and challenging. It also means that developers must be

extremely careful when constructing the database and choosing target values to which the parameters are fit.

The Potential Optimization Software for Materials (POSMat)39 computer code is used within this work as a tool to optimize and generate parameter sets for the COMB3 potential. The parameterization process begins with identifying and including bulk crystal phases (‘structures’) into a fitting database (also called training set or training database). The next step in the fitting process is defining the ‘target values’ to which each structure calculation will be compared to. The target values are materials properties relevant to the application of the potential. A target value is chosen for each structure either from DFT calculations or experimental values found in previous literature. Often, researchers will generate specific DFT calculations to include in the database to the application of interest. From an initial parameter set, a user-defined calculation (i.e. cohesive energies, bulk modulus, defect formation energies, etc.) is performed for each structure in the database. Using a least squares fitting method, a cost function for each material property (value) is calculated based on a weighted difference between the target and calculated values:

2 퐶표푠푡푖 = 푊푒푖푔ℎ푡푖×(퐶푎푙푐푢푙푎푡푒푑 푣푎푙푢푒푖 − 푇푎푟푔푒푡 푣푎푙푢푒푖) (2-31)

The individual costs are then added to a total cost function which is minimized using a simplex optimization algorithm.40 The iterative process of cost function minimizations uses different weighting schemes and including more parameters in the fitting procedure until a suitable parameter set is obtained and the cost function is minimized.

More details on the fitting database and parameter sets for Pt metal and Pt/O/H systems are provided in later chapters.

Developing interatomic potentials with the purpose of simulating complex bonding environments present in solid state systems or chemisorption at a surface is undoubtedly a challenging task. Generating a transferrable elemental parameter set that can predict correct behavior of both chemical reactions and solid state systems using identical parameters is an even more challenging.41 The advent of reactive, dynamic charge potentials like COMB3 has made simulation of these physical phenomena possible at the expense of computational cost, primarily due to the additional charge equilibration schemes. Nonetheless, theorists and computational researchers continue to pursue development of these complex force fields because they provide such an indispensable tool for future researchers. So while the benefits of developing reactive interatomic potentials may not be immediately realized, there is optimism that the developed potentials will be utilized by theoretical and experimental researchers alike during future studies.

2.3 Molecular Dynamics (MD)

In density functional theory (DFT), also known as first principles or ab initio calculations, the energy of a system is defined by a functional of the electron density where electrons and their many-body interactions are explicitly included in the calculation. The calculations are generally performed with electrons in their ground state and no temperature effects taken into account. Analytic forms of the potential energy are devised by making approximations to these quantum mechanical effects and excluding the explicit electronic interactions.

The computational cost of DFT calculations limits their system size to only a few hundred atoms even with the fastest available supercomputers. By using mathematical functions (i.e., empirical potentials) that do not include quantum mechanical calculations, we can extend the size of the system to hundreds of thousands or millions of atoms. A classical approach to simulate a particle (atomic) system based on

Newton’s equation of motion was developed in 1957 by Alder and Wainwright.42

Throughout this work, atomic systems are studied; therefore, ‘atoms’ are the particles of interest. The potential energy, 푈, of each atom is correlated to its position, 푟푖, in the following way:

휕 퐹푖 = 푚푖푟푖̈ = − 푈 (2-32) 휕푟푖

Where the net force acting on an atom 푖 is 퐹푖, which is equal to the atomic mass, 푚푖, multiplied by the second derivative of its position with respect to time, 푟푖̈ . This relation of force, mass, and position can then be expressed as the first derivative of the energy function with respect to atom 푖’s position. The iterative process of updating such positions and forces on atoms until dynamical equilibrium is reached is termed

Molecular Dynamics (MD). Equation (2-32) is at the heart of MD simulations and it is evident that an accurate energy function is necessary to describe the physics of such a system.

Time integration algorithms are finite difference methods used to predict atomic coordinates after some small time evolution of the MD system. The time increment between successive atomic positions is termed the simulation timestep, ∆t. Two such algorithms are Verlet43 and predictor-corrector which generate new atomic coordinates based on a truncated Taylor series expansion. To obtain new atomic positions after one

timestep, 푟(푡 + ∆푡), the Verlet algorithm combines Taylor series expansions for positions at a previous 푟(푡 − ∆푡) and future time, where a is the acceleration of the atom, which produces in the following equation:

푟(푡 + ∆푡) = 2푟(푡) − 푟(푡 − ∆푡) + 풂(푡)∆푡2 + 푂(∆푡4) (2-33)

Thermodynamic ensembles are used during MD simulations to regulate thermodynamic state variables such as number of atoms (N), volume (V), energy (E), temperature (T), and pressure (P). Simulating a system according to these ensembles is also known as thermostatting or barostatting, depending on the ensemble. In the microcanonical ensemble (NVE), the number of atoms, volume, and energy remain at a fixed value during the simulation. Other ensembles include canonical (NVT), isothermal- isobaric (NPT), and isenthalpic (NPH; where H is the enthalpy state variable).44-47

2.4 Geometry Optimization and Energy Minimization

The geometry of any initial input structure to a computer program can be optimized using an energy minimization approach. An energy minimization iteratively adjusts atoms until the configuration is near a local potential energy minimum.

Oftentimes, this optimized structure now becomes the starting point for our MD simulation. The most popularly used minimization command, and the one employed throughout this thesis, is the conjugate gradient (CG) algorithm.

As described previously, MD simulations utilize the numerical solution to

Newton’s equations of motion for a given initial structural configuration. The simulation is carried out via numerical integration where each atom’s position and velocity is updated every finite time step, ∆푡. Utilizing a relatively short time-step means that deterministic algorithm for simulating atomic trajectories enables the dynamic evolution

of a system over a few to tens of nanoseconds. Though this is may be considered a short simulation by meso- or macro-scale researchers, these timescales are not accessible by DFT and can often elucidate mechanisms that occur on this time scale.

Thus, this capability of MD provides another advantage over the first principles calculations.

The software used to carry out the MD simulations presented in this work is an open source code called Large-scale Atomic/Molecular Massively Parallel Simulator

(LAMMPS)48 distributed by researchers at Sandia National Lab. Its ease of use and customizability make it useful tool to study some of the most complex problems in materials science and engineering. The COMB3 potential is incorporated into this code which provides researchers around the world access to our developments.

Figure 2-1. Schematic diagrams of electrochemistry methods in MD simulations. A) χ- offset model using electronegativity differences. B) Q-offset model. An applied voltage (V) is applied across a simulation cell consisting of cathode (C), anode (A), and electrolyte (E).

CHAPTER 3 COMB3 POTENTIAL FOR PLATINUM METAL AND Pt/O/H INTERACTIONS

3.1 Interatomic Potential Developments

As discussed in Chapter 1, practical applications employ Pt as a catalyst to improve device functionality. Improvements are often made by tailoring the nanoscale surface properties of Pt (i.e., in nanoparticles or nanorods) to improve reactivity or selectivity. Obtaining a better understanding of physical phenomena at the atomic or nanoscale often elucidates fundamental mechanisms that cannot be discerned through experiments alone. It is common for the suitability of these nanoscale properties to be investigated using first principles approaches such as density functional theory (DFT) calculations, which are used to understand atomic-level processes that determine structure-property relationships. While useful and of high fidelity, it is computationally expensive to use DFT to simulate the dynamics of NP systems for time scales relevant to catalysis and electrochemical. For researchers studying greater length and longer time-scales at the atomistic level, classical molecular dynamics (MD) is the tool of choice. The forces on each particle (and the resulting trajectories) during MD simulations are determined by the first derivative of the classical, empirical interatomic potential function. In order to simulate the relevant physics within a material system, researchers are tasked with developing appropriate interatomic potentials.

In general, the dynamical behavior of fcc metals has been investigated in detail using two-body and many-body interatomic potentials. There are many such force field in the literature; in particular, the many-body, empirical embedded atom method

Some of this chapter is included in a manuscript titled “Charge Optimized Many Body potentials for Pt and Au” by A.C. Antony et al., submitted to Journal of Physics: Condensed Matter

(EAM)23, 49-53 and modified-EAM (MEAM)54 potentials have been used to model the dynamical properties of Pt. The Adams, Foiles and Wolfer (AFW)49 parameterization of the EAM potential functions was developed to examine mono- and di-vacancy mediated diffusion in fcc and Pt. The functions were fitted in order to predict better agreement with the experimentally measured self-diffusion rates and activation energies. The authors concluded that the AFW parameterization is capable of accurately predicting activation energies for both vacancy mediated self-diffusion and impurity diffusion. These potentials were later used to investigate surface self-diffusion51 and to calculate activation energies for single adatom diffusion on (111), (100), (110), (311), and (331) surfaces for Pt as well as six other fcc metals (Ni, Cu, Al, Ag, Pd, Au).

There is substantial literature for both the COMB355-57 and the ReaxFF58-60 formalisms; for the sake of concision, here we will emphasize these potentials developed for Pt-Pt interactions, as this is a necessary first step towards further development. The ReaxFF Pt potential61 was optimized to reproduce energies and structures for bulk Pt obtained from DFT calculations. The potential was also reported to exhibit transferability to low- and high-index surfaces.

Developing a Pt potential within a dynamic charge, reactive potential framework such as the third-generation charge optimized many-body (COMB3)28 or ReaxFF27 potentials, provides the possibility of coupling the existing single element or material- specific potentials to multi-component systems. The primary advantage, yet still challenging task for developers, is that these potentials can be extended to describe complex chemical bonding environments using the same potential framework, allowing for the investigation of heterogeneous material systems. For example, the COMB3 Zr

metal potential has been extended to include Zr-H and Zr-O interactions62-63 and used

62 to investigate oxygen clustering at Zr surfaces and dissociation of O2 on Zr(0001). The

COMB3 Cu potential has undergone several parameter optimizations and extensions and arguably possesses the highest fidelity of all the COMB3 potentials to date. One such parameterization extension was used to simulate deposition of Cu clusters on ZnO surfaces55 and subsequent film growth where Cu forms a 2D structure on ZnO(101̅0).

The final two sections of this chapter present developments similar to the ones described above where binary and ternary interactions (Pt-O, Pt-H, and Pt-O-H) are introduced into the fitting database. Simulations that employ these newly developed potentials are presented in Chapter 5.

3.2 Parameterization of Pt Metal

The training database used to parameterize the Pt potential included five stable crystal phases (spacegroup in parenthesis): fcc (퐹푚3̅푚), hcp (푃63/푚푚푐), bcc (퐼푚3̅푚), sc (푃푚3̅푚), and diamond (퐹푚3̅푚). Also included in the fitting database are the hypothetical Pt dimer; the Pt(100), Pt(110), and Pt(111) surfaces, the formation energies for the Pt interstitial (Ei) and Pt vacancy (Ev), the stable stacking fault

(훾퐼푆퐹〈121̅〉) and two unstable stacking faults (훾푈푆퐹〈121̅〉 and 훾푆퐹〈101〉). The elastic constants and bulk modulus are also included in our fitting database to correctly capture

Pt metal’s response to elastic deformation.

The fitting database and target values used during the parameterization are provided in Table 3-1. In the table, COMB3 fit values based on the current parameterization are compared to experimental values, DFT calculations, and other empirical potentials including Foiles, Baskes, and Daw (FBD)-EAM23 and previously

mentioned (AFW)-EAM potentials, modified EAM (MEAM), and ReaxFF. COMB3 is capable of more accurately reproducing experimental bulk modulus values by underestimating C11 and C12 elastic constants compared to EAM potentials. COMB3 reproduces the unstable stacking fault (usf) energy, which is underestimated by the

EAM potentials. The results from Table 3-1 also illustrate that surface energy calculations using COMB3 and MEAM agree well with DFT calculations, while (FBD)-

EAM and (AFW)-EAM potentials are less accurate. It should be noted, however, that the

FBD functions of the EAM potential provide the most fidelity with regard to energy differences between stable crystal phases and the AFW functions are fit specifically to reproduce vacancy formation energy (Ev), which is within 0.03 eV of our DFT calculation. Similarly, ReaxFF slightly underestimates surface energies but reproduces the bulk modulus within 5% of experimental findings and predicts correct phase order.

These property tradeoffs from Table 3-1 indicate variability between interatomic potentials and can guide researchers when choosing a potential for a specific application.

3.2.1 γ Surface Energies

Mapping the γ surface energy, also known as the generalized-stacking-fault energy (GSFE) surface, can be achieved by rigidly moving the atoms belonging to the

{111} planes in 〈121〉 and 〈101〉 perpendicular directions and calculating the energy difference with respect to the perfect structure. For Pt (a=3.92 Å), the 〈121〉 direction is

4.80 Å and 〈101〉 is 2.77 Å. These distances correspond to the length of vectors along which the atoms are displaced to create gamma surface energies (Figure 3-1). The stacking fault energies (SFEs) of Pt have been previously studied and the calculated

results of their stable (SF) and unstable stacking fault (USF) energies vary depending on interatomic potential or calculation method.64-65 SF and USF energies are important quantities determining the mechanical behavior of metals66 and Table 3-1 provides numerical values of SFEs predicted by COMB3 and obtained from the literature. The energy difference relative to the perfect crystal structure is calculated and a 2D contour plot and one-dimensional SFE curve along the [101] and [121̅] directions are presented in Figure 3-1. COMB3 predicts the 〈101〉 SF energy to be 1270 mJ/m2 and the SF and

USF energies along 〈121̅〉 to be 330 mJ/m2 and 433 mJ/m2, respectively, for Pt. These values slightly overestimate the SFEs when compared to the EAM potential parameterized in Ref. 53. The agreement in qualitative and quantitative behavior between EAM and COMB3 is remarkably good, especially considering they are two very different formalisms. It is unlikely that both potentials would provide qualitatively consistent behavior arising from equivalent errors, so we judge that these results are reliable.

3.2.2 Tensile Test Simulation

A uniaxial tensile test is performed on polycrystalline Pt using MD. The simulated polycrystal contains 186,613 atoms that comprise 16 grains. The initial cubic box dimensions are 14.1 nm in all directions. The tensile test was carried out using a constant strain rate of 8.0 × 108 s-1, typical for such computational tensile tests, and the temperature was maintained at 300 K. The high strain rate is typical for MD simulations describing physical deformation of materials because of the relatively short time scales accessible by MD using short 0.25 fs timesteps.67 Snapshots from the simulation are visualized using Atomeye software.68 The stress-strain curve from the simulation along

with a common neighbor analysis (CNA) of the strained structure is presented in Figure

3-2. In addition, a close-up visualization of observed stacking faults is shown in white outline. From the stress-strain curve, we use a linear fit up to the yield point to predict the elastic modulus (Young’s modulus). Our results indicate a predicted elastic modulus for polycrystalline Pt to be ~183 GPa. This simulated value compares well with experimental measurements of ~165 GPa for 0.45 mm Pt wire.69 More recent experiments using 400 nm thick Pt films measure Young’s modulus as a function of strain rate. The researchers report a range of values between 177-193 GPa70 which are in closest agreement with our simulations. Thus, the newly developed COMB3 Pt potential satisfactorily describes mechanical behavior of the bulk fcc phase and further developments can be pursued.

3.3 Parameterization of Pt/O Interactions

Parameters for the COMB3 Pt/O potential were developed to accurately reproduce bulk platinum oxide structures and adsorbed oxygen on Pt(111). To construct the fitting database, bulk structures and their formation energy are chosen either from the Materials Project website71, previous DFT calculations for Pt bulk oxide phases and surfaces found in the literature72-75, or DFT calculations specific to the parameterization

(e.g., point defects and surfaces). Adsorption energy calculations from first principles are used as the target values for atomic and molecular oxygen site adsorption on

Pt(111). The bulk structures included in the fitting database are (structure type and space group in parenthesis): β-PtO2 (CaCl2-type; 푃푛푛푚), Pt3O4 (simple cubic; 푃푚3̅푛), α-

PtO2 (CdI2-type; 푃3̅푚1), PtO (PtS-type; 푃42/푚푚푐), PtO2 (fluorite; 퐹푚3푚), and PtO

(rocksalt; 퐹푚3̅푚). Atomic representations of the bulk structures from the fitting database

are shown in Figure 3-3. The target value for all bulk platinum oxide compounds (PtxOy) is the formation energy per formula unit:

[ ] ∆퐻푓 = (퐸푃푡푥푂푦 ∙ 푥 + 푦 ) − (휇푃푡 ∙ 푥 + 휇푂 ∙ 푦) (3-1)

Where 퐸푃푡푥푂푦 is the calculated energy per atom of the compound, and 휇푃푡 and 휇푂 are the reference chemical potentials for Pt and O, respectively. The chemical potential for

Pt is the calculated cohesive energy of fcc bulk Pt and the oxygen chemical potential is the energy per atom of an isolated O2 molecule. Table 3-2 presents the results of fitting the COMB3 Pt/O potential to bulk structures, point defects, and oxide surfaces and benchmarks the predictions against DFT calculations and the ReaxFF potential

61 developed for Pt/O. The α-PtO2 and β-PtO2 have both been reported to have equal formation energies76 and COMB3 reproduces equivalent values for both structures although the formation energy. During the fitting procedure, correctly predicting relative surface site adsorption energies for atomic and molecular species is favored at the expense of bulk oxide and Pt vacancy point defect formation energies. Thus, a higher weighting factor is placed on point defect formation energies and adsorption energies to more accurately capture these kinetic contributions.

Three adsorption structures are included in the fitting database to correctly capture site preference of atomic oxygen adsorbed on Pt(111). Table 3-3 lists the adsorption sites, adsorbate (O* or O2*), coverage, DFT target values and results from the COMB3 potential. Adsorption energies, Eads, for any coverage are calculated per atomic adsorbate (O* or H*, X* in Equation 3-2) in the following manner:

퐸푎푑푠 = (퐸푠푙푎푏+푋∗ − (퐸푠푙푎푏 + 푛푋∗퐸푋))/푛푋∗ (3-2)

Where 퐸푠푙푎푏+푋∗ is the energy of the Pt(111) slab with X*, 퐸푠푙푎푏 is the energy of the

Pt(111) slab with no adsorbates, 퐸푋 is the reference adsorbate energy, which is taken to be gas phase for O* and H*, and 푛푋∗ is the number of adsorbates.

As mentioned in the previous paragraph, priority during fitting is given to the reproducibility of adsorption site preference and relative adsorption site energies, especially in the case of atomic oxygen. Per DFT calculations, the fcc site is more energetically favorable for oxygen adsorption rather than the atop site.

3.4 Parameterization of Pt/H and Pt/O/H Interactions

Pt does not form any bulk hydride structures and DFT calculations of several

Pt/H bulk compounds reveal positive formation energies for PtH and PtH2 stoichiometries. Still, these high energy bulk structures are included in the fitting database so the potential does not predict formation of bulk hydride during dynamic simulations. Due to the very positive formation energy, low weights are placed on the

Pt/H structures so long as the COMB3 calculated heat of formation is also positive.

More importantly, predicting correct behavior of hydrogen adsorption on Pt(111),

Pt(110), and Pt(100) is the primary objective of fitting the Pt/H interactions. The fcc, hcp, atop, and bridge adsorbate sites are fitted for H* on Pt(111) and low and high adsorbate coverages (up to 1 ML) are fitted for H* on Pt(110) and Pt(100). Atomic-scale renderings of low coverage (1/9 to 1/4 ML) H* adsorption on Pt(111), Pt(110), and

Pt(100) is shown in Figure 3-5. The fitting results in Table 3-4 indicate that the magnitude of COMB3 adsorption energies closely match DFT calculations for the

Pt(111) surface which is the primary surface of interest for our MD simulations. COMB3 predicts lowest adsorption energy to be -0.57 eV/atom at the atop site which is 0.04 eV

lower than adsorption at the hollow hcp site (-0.53 eV/atom) and 0.08 eV lower than the hollow fcc site (-0.49 eV/atom). In comparison, DFT calculations indicate that the atop site adsorption energy (-0.43 eV/atom) is less favorable than fcc adsorption (-0.45 eV/atom) and more favorable than hcp adsorption (-0.39 eV/atom). These small energy

∗ ∗ ∗ ∗ barriers between adsorption sites (0.02 eV for 퐻푓푐푐 → 퐻푎푡표푝 and 0.04 for 퐻푎푡표푝 → 퐻ℎ푐푝) mean that H* atoms can readily diffuse across the Pt(111) surface without the presence of strong external forces (e.g., at low temperatures). Surfaces like Pt(110) and Pt(100) have a smaller atomic packing fraction in the surface plane compared to Pt(111). Thus,

H* atoms are more strongly bound to the Pt surface atoms due to a lack of surrounding surface atoms (Figure 3-5). DFT calculations from Table 3-4 show that regardless of H* coverage, adsorption energies on both Pt(110) and Pt(100) are between -0.55 and -0.57 eV/atom, a range higher than low coverage adsorption on Pt(111). The COMB3 potential also reflects the stronger adsorption energies on open surfaces, albeit with less overall accuracy compared to DFT (0.15 eV lower for H* on Pt(100) at 1/9 ML coverage and 0.28 eV lower for H* on Pt(110) at low and high coverages).

After parameterizing Pt/O and Pt/H terms, OH* and H2O* molecules adsorbed on

Pt(111) are included in the training database and the three-body Legendre polynomial parameters (Equation 2-25) are fitted. The four OH* structures from Table 3-5 are

∗ ∗ ∗ ∗ included in the fitting database: 푂퐻푎푡표푝, 푂퐻ℎ푐푝, 푂퐻푓푐푐 (푂−푑표푤푛), and 푂퐻푓푐푐 (퐻−푑표푤푛) in addition to adsorbates on (100) and (110) surfaces. The DFT adsorption energies

(target values in Table 3-5) are calculated using OH* in its gaseous state as the reference adsorbate. Reported DFT adsorption energies for nx OH* molecules adsorbed on Pt surface are calculated in the following equation:

퐸푎푑푠 = (퐸푠푙푎푏+푂퐻∗ − (퐸푠푙푎푏 + 푛푂퐻∗퐸푂퐻(푔)))/푛푋∗ (3-3)

Where 퐸푠푙푎푏+푂퐻∗ is the energy of the Pt(111) slab with OH*, 퐸푠푙푎푏 is the energy of the

Pt(111) slab with no adsorbates, and 퐸푂퐻(푔) is the OH* reference adsorbate energy.

Finally, we fit the COMB3 Pt/O/H parameters to DFT calculations of water adsorbed on Pt(111). We consider three configurations for monomer adsorption: atop, fcc (O-down), and fcc (H-down) and Table 3-6 includes calculated values for these adsorption configurations. Furthermore, we fit the hydrogen bonded hexamer where the adsorbate structure from the DFT calculation is shown in Figure 3-6. Extensive measures have been taken to ensure that the potential is capable of simulating physical behavior of water on Pt. For example, after fitting the parameters to adsorption energies of OH and H2O, the potential is re-optimized so that water formation and dissociation reaction energies are accurate enough so that water does not readily dissociate on the surface. In Chapter 5, simulations of the Pt/water interface are carried out using the

COMB3 Pt/O/H potential and qualitatively the potential does quite well when it comes to capturing physically verified configurations of water molecules near Pt(111). Tables of the developed Pt/O/H parameters are provided in the appendix.

Table 3-1. Fitted properties of Pt metal compared with DFT calculations, experimental values, and other common empirical potentials. Structure Exp. or (FBD)- (AFW)- MEAM54 ReaxFF61 COMB3 DFT EAM23 EAM49 FCC bulk phase a0 (Å) 3.92 3.92 3.92 3.92 3.95 3.92 E0 (eV/atom) -5.77 -5.77 -5.77 -5.77 -5.77 a C11 (GPa) 347 303 307 358 283 a C12 (GPa) 251 273 272 254 198 a C44 (GPa) 77 68 72 78 82 B (GPa) 280a, 282 283 239 228 228-270b Phase transitions (eV/atom) ∆E (fcc→hcp) 0.03 0.03d 0.02 0.00 0.07 ∆E (fcc→bcc) 0.16 0.16d 0.28 0.12 0.32 ∆E (fcc→sc) 0.37 0.39d 0.76 1.24 0.21 ∆E (fcc→diam) 1.17 1.16d 1.71 1.80 0.75 Defect formation Energies (eV) Ev 1.80 1.50 1.77 1.50 1.78 Ei (octahedral site) 5.49 4.99 6.64 5.44 (dumbbell) Planar defects (mJ/m2) c d f 휸푰푺푭〈ퟏퟐퟏ̅〉 330 121 110 330 c d 휸푼푺푭〈ퟏퟐퟏ̅〉 422 320 433 휸푺푭〈ퟏퟎퟏ〉 1173 1270 Surface energies

(J/m2) 휸(ퟏퟏퟏ) 1.71 1.34 1.61e 1.71 1.68 1.71 휸(ퟏퟎퟎ) 2.28 1.55 1.71e 2.29 1.89 2.22 휸(ퟏퟏퟎ) 2.32 1.68 1.82e 2.33 2.02 2.38 a Ref. 77 b Ref. 78 c Ref. 64 d Ref. 53 e Ref. 51 f Ref. 26

Table 3-2. Fitted heat of formation energies of Pt/O solid state phases as predicted by the COMB3 potential and compared with DFT calculations. Values with an asterisk (*) are from Materials Project website.71 Property DFT (target) COMB3 Formation energy (eV) α-PtO2 (CdI2-type) -2.82* -2.01 β-PtO2 (CaCl2-type) -2.81* -1.29 Pt3O4 -5.92* -3.38 PtO2 (fluorite) -1.36 -2.25 PtO (PtS-type) -1.09 -0.91 PtO (rocksalt) 0.39* -1.49

Table 3-3. Fitted adsorption energies for O* on Pt(111). Adsorption site Coverage (ML) Adsorption energy (eV/species) DFT (target) COMB3 fcc 0.25 -1.65 -1.03 atop 0.25 -0.21 -1.92

Table 3-4. Fitted adsorption energies for H* on low-index Pt surfaces. Surface Adsorption site Coverage (ML) Adsorption energy (eV/species) DFT (target) COMB3 fcc 0.11 -0.45 -0.49 hcp 0.11 -0.39 -0.53 Pt(111) atop 0.11 -0.43 -0.57 bridge 0.11 -0.40 -0.41 atop (H2) 0.11 -0.44 -0.13

Pt(100) bridge 0.11 -0.55 -0.70 bridge 1.00 -0.56 -0.68

Pt(110) bridge 0.25 -0.57 -0.85 bridge 0.75 -0.56 -0.84

Table 3-5. Fitted adsorption energies for OH* on Pt(111). Reference adsorbate energies for OH* are taken as the free energy of OH in H2O. Surface Adsorption site Coverage (ML) Adsorption energy (eV/species) DFT (target) COMB3 atop 0.11 -2.80 -4.51 Pt(111) hcp 0.11 -2.39 -4.16 fcc 0.11 -2.55 -2.90

Table 3-6. Fitted adsorption energies for molecular H2O* on Pt(111). Adsorbate configuration Adsorption energy (eV/species) DFT (target) COMB3 atop (O-down) -0.23 -0.27 hcp -0.06 -0.02 atop (H-down) -0.03 -0.02 hexamer H2O -0.51 -0.60

Figure 3-1. 2D contour plot and corresponding 1D energy plot of Pt stacking fault energies from COMB3 potential. The green line shows the SFE along [121̅] and the black line shows SFE along [101]. Contour plots are only from COMB3 calculations.

Figure 3-2. Stress-strain curve and corresponding simulation snapshots from a MD simulated tensile test of Pt polycrystal. Snapshots to the right are structures near the yield point (10% strain for Pt and 8% strain for Au) with atoms colored according to common neighbor analysis (CNA). Dark blue represent atoms in a fcc-coordinated environment, dark red represent atoms in a disordered environment (lacking 12-fold coordination), light blue represents atoms in hcp environment. A zoomed in snapshot of stacking fault structures (outlined in white) observed in strained 16-grain polycrystalline Pt is shown below the full simulation cell.

Figure 3-3. Pt/O bulk structures included in the fitting database. Pt atoms are grey and O atoms are red.

Figure 3-4. Schematic representation of 3x3 Pt(111) with adsorption sites: (A) atop, (B) hcp, (C) fcc, (D) bridge. Atomic colors distinguish layers in the ABC stacking sequence.

Figure 3-5. Top-down (above) and side view (below) of hydrogen adsorption. A) H* on Pt(111). B) H* on Pt(100). C) H* on Pt(110). Different shades of green represent first, second, and third atomic layers (darker means closer to surface). AB stacking sequence for (100) and (110) hides the third layer of atoms in the top-down views. H* atoms are orange. Adsorbate coverage is 1/9 ML for Pt(111) and Pt(100) and 1/4 ML for Pt(110).

Figure 3-6. Buckled hexagonal arrangement of water molecules on Pt(111). Molecules configure themselves to form a non-planar hydrogen bonded network. Left is a side view, right is a plan view of the 2/3 ML covered surface. The 3x3 unit cell from DFT calculations is contained within the black dotted lines.

CHAPTER 4 PLATINUM AND GOLD NANOPARTICLES

4.1 Metal Nanoparticles

Nanoparticles (NPs) of precious metals, such as Au and Pt, are currently being considered for a wide variety of applications ranging from catalysis79-83 to electrochemical approaches for biosensing and nanomedicine.84 Using NPs for catalysis means optimizing the amount of material in order to provide a high surface area-volume ratio. This is most beneficial because the amount of these expensive precious metals can be reduced while retaining or even improving their catalytic efficiency for the oxygen reduction reaction (ORR). For example, highly active Pt-based catalysts have been prepared by rationally manipulating the surface chemisorption properties by tuning exposed facets in certain chemical environments.81 In addition, Au NPs have novel applicability because of their biocompatibility which has proven useful by tuning spectroscopic and electrochemical characteristics of Au NPs with its substrate (DNA, sugars, and other biological molecules).85

4.2 Wulff-Constructed Nanoparticles

The most common method for generating NP models is a Wulff construction based on relative surface energies of the material.86 In short, the NPs are constructed from a single crystal bulk fcc metal (Pt or Au). We cut a plane normal to the [hkl] vector that has a distance 푑ℎ푘푙 = 푐 ∗ 훾ℎ푘푙 from the origin (in this case, center of the NP), where c is a scaling factor related to the size of the NP, and 훾ℎ푘푙 is the surface energy of the

(hkl) surface. For the models used in this dissertation, we construct 30 nm NPs (i.e.,

Most of this chapter appears as a section of the article titled “Charge Optimized Many Body potentials for Pt and Au” by A.C. Antony et al., submitted to Journal of Physics: Condensed Matter

the radius is 30 nm) based on the surface energies as calculated by COMB3. Since

(111) is the lowest energy surface facet for both Pt and Au, we report the relative surface energies as the ratio γ(hkl):γ(111) in Table 4-1. COMB3 predicts similar ratios that are also consistent with DFT calculations. For practical purposes, the NP shape will be determined by its chemical environment and the change in surface energy when atoms or molecules adsorb on different surfaces of the particle. In contrast, these reported ratios for bare low-index surfaces produce NP shapes where only Pt-Pt or Au-

Au interactions are considered.

A Wulff construction using the COMB3 surface energies produces a truncated octahedron shape for both Au and Pt, shown in Figure 4-1. For both NPs, the

훾(110): 훾(111) ratio is higher than 훾(100): 훾(111). Upon construction of the NP, it is noted that (110) facets are not formed because of its high energy relative to the (111) surface. Comparison of COMB3 Pt and Au surface energy ratios reveals that the Au NP should have a slightly larger (100) facet than Pt. In Figure 4-1 the Au(100) facets measure 3.13 nm2 and the Pt(100) facets are 1.92 nm2. The Visualization for Electronic and STructural Analysis (VESTA)87 software program is used to visualize the constructed NPs seen in Figure 4-1. The NPs in Figures 4-1A and 4-1C show distinct edge and corner atoms that have lower coordination than (111) and (100) surface atoms. Displacement of the edge and corner atoms at higher temperatures will be discussed later in the context of surface self-diffusion and the kinetic barrier associated with diffusion along edges of the NP.

4.3 High Temperature Nanoparticle Simulations

The as-built Wulff constructed NPs are first equilibrated by MD at 300 K for 1 ns.

In order to determine the shape change of NPs at higher temperatures and to calculate

the activation energy for surface self-diffusion, the equilibrated NPs are subject to annealing at elevated temperatures (700, 1100, 1500, 1900, 2300, and 2700 K for Pt;

600, 900, 1200, 1500, 1800 K for Au). During the simulated heating process, the NP is held at each temperature increment for 1 ns to allow for atomic diffusion. After holding the NP at the elevated temperature, the simulation undergoes a step-wise cooling process to 300 K where the cooling increment is 100 K for every 20 ps. Both annealing and cooling processes are performed under the NVT ensemble with a timestep of 0.2 fs.

The snapshots of the simulated NPs in Figure 4-2 are taken from the end of the simulation (after cooling to room temperature) using Atomeye68 software.

4.3.1 Shape Change of Nanoparticles at Elevated Temperatures

To understand the morphology change of the NP, we visualize a 2D slice of the center of the NP where atoms are colored according to their coordination number (CN).

Figure 4-2A displays snapshots of the NPs after cooling to 300 K from the indicated temperature and a histogram of CN is shown in Figure 4-2B. Due to structural similarities between Pt and Au (i.e., both are fcc metals with a lattice constant that differs by only ~0.16 Å), we expect both metal NPs to undergo similar shape changes.

Figure 4-2A shows that the shape of both NPs becomes spherical at higher temperatures, the only difference being the temperature at which this transition occurs

(1800 K for Au, 2700 K for Pt). The radial distribution of both NPs at their peak temperature is shown in Figure 4-3 and indicates that the Au NP has fully melted at

1800 K and Pt has melted at 2700 K. Upon cooling the Au NP from 600 K or 900 K there is little change in the average CN and the NP visually resembles the 300 K equilibrated structure. At 1500 K there are a high number of surface atoms with low CNs which explains the continuous decrease in average CN. When the Au NP reaches 1800

K, the shape from the Wulff-construction is lost and the NP becomes a spherical liquid.

From the 2D slice of the NP, there are a high number of bulk atoms with 13-fold coordination (~17% of all atoms have CN=13) due to kinetically capturing the Au NP in its liquid state. From a 3D view of the entire NP, Pt and Au look similar, but a 2D slice reveals a reordering of bulk Pt atoms upon cooling from high temperatures. A 2D cross- section of the Pt NP core at 2700 K in Figure 4-2A exposes atoms in their low-energy fcc crystal structure (CN=12). The recrystallization process of the Pt NP appears to generate randomly oriented grains where atoms lacking 12-fold coordination (yellow and red atoms in Figure 4-2) represent grain boundaries. In summary, a similar shape change initiated near corner atoms is evident during both simulations, while recrystallization of bulk Pt atoms into separate fcc grains and Au atoms arranged in their liquid phase result from differences of NP dynamics.

Several trends related to the NP shape change are identified in the histograms in

Figure 4-2B. As the NPs are heated, surface atoms become kinetically active, causing diffusion and rearrangement at the surface. A lack of fully coordinated fcc atoms at the corners of the NP means atoms near these sites are the most dynamically unstable for deformation to initiate. From Figure 4-2B, the percentage of perfectly coordinated (111) atoms (CN=9) decreases at high temperatures. At peak temperature, the reduction in 9- fold coordinated atoms is accompanied by a decrease in 12-fold coordinated atoms. For

Au, the reduction is nearly half, but more than 60% of Pt NP atoms retain their coordination. This observation is supported by the recrystallization of Pt atoms seen in

Figure 4-2A. The percentage of atoms with coordination 13 and 14 indicate the

relatively amorphous shape of both NPs, although the liquidus center of the Au NP has a larger number of highly coordinated atoms.

We further analyze the morphological evolution of the NPs upon cooling to 300 K by plotting the average atomic coordination number (CN) as the Pt and Au NPs are cooled from higher temperatures. The cutoff distance for determining whether two atoms are coordinated is 20% larger than the bond length for either metal (3.33 Å for Pt and 3.46 Å for Au). We report the difference in CN (∆CN in Figure 4-4) with respect to the equilibrated structure at 300 K and compare this value to the change in energy with respect to the structure at 300 K (∆E in Figure 4-4).

For the Au NP, ∆CN decreases for temperatures up to 1500 K due to deformation of surface atoms near step edges, kinks, and corners. At 1800 K, the particle becomes spherical and atoms near the center of the NP possess an average coordination number greater than perfect fcc atoms. As mentioned previously, the Pt NP exhibits reordering of atoms after high temperature simulation. At 2700 K, the average coordination number for the Pt NP is still less than the initial structure because of the high percentage of atoms recrystallizing into their fcc structure and a higher percentage of Pt atoms coordinated by eight, ten, and eleven atoms. The similar energy profiles for both NPs show less than 0.01 eV/atom difference from the starting structure up to some critical temperature (1500 for Au and 2300 for Pt). After cooling the NPs from peak temperature, the energy difference is notably higher due to the overall shape-change of the NP compared to the initial Wulff construction in addition to local changes in atomic coordination as indicated by the cross-sectional view in Figure 4-2.

4.3.2 Diffusion of Nanoparticle Surface Atoms

Understanding surface phenomena of NPs is relevant to our study because of the catalytic importance of both Pt and Au NPs. Since surface atoms are the preferred site for catalytic reactions to occur, it is useful to determine how these atoms dynamically rearrange themselves. During the MD simulations, the surface self-diffusion coefficient, Dsurf, for Pt and Au NPs is related to the slope of the total mean-squared displacement (MSD) by the Einstein relation:

1 2 퐷푠푢푟푓 = lim[〈|푟 (푡) − 푟 (0)| 〉/∆푡] (4-1) 4 푡→∞

Where 푟 (푡) − 푟 (0) is the distance traveled by surface atom i over some short time ∆푡 and |푟 (푡) − 푟 (0)|2 is the MSD. Thus, the term lim[〈|푟 (푡) − 푟 (0)|2〉/∆푡] is taken to be the 푡→∞ slope of the MSD curve from our MD simulations. Here, a surface atom is defined as any atom having a CN less than 10 (Pt/Au(111) atoms have CN=9). Figure 4-5 provides the MSD plots of atoms with CN<10 for Pt and Au NPs at elevated temperatures. At low temperatures, the diffusion coefficient of the Pt NP is 1×10-9 cm2/s at 700 K and reaches

4.3×10-8 cm2/s at 1100 K. Similarly, the diffusivity of the Au NP is 1.3×10-9 cm2/s at 900

K and 6.8×10-8 cm2/s at 1200 K which indicates that the surface atoms of the Au NP are more diffusive at similar temperatures. At 1500 K, the calculated diffusivity of Pt NP surface atoms reaches the same value as Au surface atoms at 1200 K.

Calculating D at elevated temperatures provides necessary dynamic information about the system which allows us to estimate the activation energy for surface self- diffusion. An Arrhenius equation is used to determine the relation between surface atom self-diffusion coefficients and the activation energy for which the kinetic process occurs:

퐸푎푐푡 퐷(푇) = 퐷0푒푥푝 (− ⁄ ) (4-2) 푘퐵푇

In the above equation, 퐸푎푐푡 is the activation energy, 퐷0 is a pre-exponential factor, kB is

Boltzmann constant, and T is temperature. The results of our activation energy barrier calculations are presented as an Arrhenius plot in Figure 4-6 where the dashed red line and is a linear fit for the Au NP and the dotted black line is a linear fit for the Pt NP.

The diffusion of surface atoms occurs primarily along surface defects (i.e., corners and step edges) of the NP. To determine the activation energy, we multiply the negative slope of the linear fit by kB (in units eV/K). The activation barriers for surface self-diffusion are estimated to be 0.62 ± 0.16 eV on the Pt NP and 1.44 ± 0.06 eV on Au

NP. The COMB3 barrier for surface self-diffusion on Pt underestimates experimentally measured values on Pt(110) of 0.84 ± 0.1 eV88 and 1.12 ± 0.1 eV.89 This result may be explained by the high Pt surface energies predicted by COMB3, and the termination by facets more stable than 110, which would cause surface atoms to become diffusive with relatively lower kinetic contributions. Recent high-resolution transmission electron microscopy (HRTEM) studies90 on Au NPs report activation energies to be as low as

0.55 eV for exchange diffusion on a flat Au(100) surface. In previous MD studies, eight different diffusion mechanisms on small Au clusters (201 total atoms) have been reported, with activation energies in the range of 0.11 to 0.41 eV.91 To explain these discrepancies in calculated activation energies, we note that the simulations from which we measure diffusion coefficients are executed at a high temperature. Since our potentials are parameterized under static conditions, it is possible that simulations at elevated temperatures do not reproduce exact experimental findings.

The high kinetic barrier calculated for surface self-diffusion on Au NPs warrants more discussion, particularly in terms of calculated Dsurf at different temperatures. At

1800 K, the Au NP has melted and therefore, Dsurf at this temperature is not included in the Arrhenius activation energy calculation. In addition, calculations of Dsurf at low temperatures are extremely low, on the order of 1.0-1.3 × 10-5 Å2/ps (1.0-1.3 × 10-9 cm2/s) for Pt NP at 700 K and Au NP at 900 K (Figure 4-5). These values indicate that

MSD of surface atoms at low temperatures is negligible although it is necessary to calculate activation barriers. The temperature-dependent diffusion coefficients (linear slope from the MSD curve) in Figure 4-5 are then used determine the Arrhenius relationship in Figure 4-6. From Figure 4-6, if the lowest temperature (high 1/T) data point for Pt is excluded from the activation energy calculation, the Pt barrier increases to

1.24 eV. Overestimation of the Au NP activation barrier for surface self-diffusion is attributed to the inability of COMB3 to capture all kinetically determined physical phenomena of complex systems. Still, the stability of Wulff constructed NPs during MD simulations and evidence of morphological change at high temperatures provides qualitatively reliable results so that the developed COMB3 potentials may be suitable for additional applications.

Table 4-1. Relative surface energy ratios from DFT and empirical interatomic potentials used for determining Wulff constructions of Pt and Au NPs. References for Pt values can be found in Table 3-1. Expt. or DFT EAM MEAM ReaxFF COMB3 Pt surface energy ratios 휸(ퟏퟎퟎ): 휸(ퟏퟏퟏ) 1.33 1.06, 1.16 1.34 1.13 1.33 휸(ퟏퟏퟎ): 휸(ퟏퟏퟏ) 1.36 1.13, 1.25 1.36 1.20 1.39 Au surface energy ratios 휸(ퟏퟎퟎ): 휸(ퟏퟏퟏ) 1.33a 1.16b, 1.16c 1.23d 1.13e 1.29 휸(ퟏퟏퟎ): 휸(ퟏퟏퟏ) 1.38a 1.24b, 1.26c 1.27d 1.19e 1.39 a Ref. 92 b Ref. 53 c Ref. 23 d Ref. 54 e Ref. 93

Figure 4-1. Wulff-constructed NPs with RNP = 30 nm. A) atomic representation of Au NP. B) Polyhedral representation of Au NP. C) atomic representation of Pt NP. B) Polyhedral representation of Pt.

Figure 4-2. Visualized snapshots of a 2D cross-section of the Au and Pt NPs and corresponding histogram of coordination numbers. A) Snapshots after cooling from indicated temperature to room temperature where atoms are colored per local CN. B) Histogram of atomic CN as a function of temperature for Au and Pt NPs.

Figure 4-3. Radial distribution functions, g(r), for NPs at different temperatures. A) Pt NP. B) Au NP.

Figure 4-4. Change in average atomic coordination number (∆CN) and energy (∆E) after cooling the NPs from indicated temperature to 300 K. Au ∆CN and ∆E overlap after 1500 K.

Figure 4-5. MSD of atoms with CN<10 from MD simulations. A) MSD profiles for Pt NP at elevated temperatures. B) MSD profiles for Au NP surface atoms at elevated temperatures. Data for 900 K and 1200 K in B overlap.

Figure 4-6. Arrhenius plot of surface diffusivity vs. inverse temperature for Pt (solid black line) and Au (dashed red line).

CHAPTER 5 SURFACE PHENOMENA ON PLATINUM METAL SURFACES

5.1 Overview of Adsorption on Pt

As a bulk metal, Pt is widely regarded for its ability to selectively catalyze chemical reactions with a high rate of reactivity. Because of the versatility of Pt catalysts, surface adsorption and subsequent chemical reactions of have been the focus of both experiments and computational research94-97. Adsorption energies and site preferences are dependent on physical features such as crystallographic plane, surface defects (i.e., kinks and step edges), and adsorbate coverage. Furthermore, adsorption behavior shows an environmental dependence, for instance, in the presence of solvated ions in liquid water. Because exact adsorbate geometry, energies, and reaction mechanisms cannot be fully characterized with an exclusively experimental approach, DFT calculations and MD simulations are often used to confirm or elucidate experimental findings. Two of the most studied adsorbates on Pt are atomic hydrogen

(H) and oxygen (O) (or any molecular combination of the two) because of their relevance in catalytic processes and capability to form adsorbed OH or H2O as reactants, intermediates, or products at the surface98-100.

The thermodynamically most stable Pt(111) facet forms a hexagonal arrangement of surface Pt atoms with four primary adsorption sites (Figure 3-3): atop, fcc, hcp, and bridge. For atomic or molecular adsorbates, the preferred adsorption site can be predicted using DFT calculations. Reports of 0.25 ML surface coverage H* on a five layer thick Pt(111) slab indicate similar adsorption energies for fcc (-0.53 eV), hcp (-

0.50 eV), atop (-0.49 eV), and bridge (-0.48 eV) sites, resulting in an evenly distributed site occupancy and a low energy barriers (0.05 eV for bridge*→fcc*) for H* surface

diffusion.101 Considering the size of a hydrogen atom and the fact that Pt and H do not form a stable crystal structure, these adsorption energies indicate overestimation of the binding of H* on Pt(111). Above a saturation surface coverage of 1 ML (i.e., 1 H* atom per Pt surface atom), subsurface diffusion is initiated and H atoms occupy subsurface tetrahedral sites.102

Below ~120 K, oxygen molecularly adsorbs on Pt(111) while in the temperature range 150 to 500 K, O2 will kinetically dissociate and adsorb as two separate oxygen atoms.103-104 Compared to DFT calculations of H* on Pt(111), the adsorption energies for O* are disparate for fcc (-3.87 eV), hcp (-3.43 eV), and atop (-2.46 eV).94 Ordering of adsorbates in a p(2x2) phase with O* atoms in fcc sites (Figure 5-1) has been reported for coverages of 1/4 ML by experiments105-106 and thermodynamic first principles calculations of the O*-Pt(111) phase diagram.107 Furthermore, results from scanning tunneling microscopy (STM) experiments reveal formation of 1D oxide chains on

Pt(111) during the early stages of oxidation. The p(2x1) 1D chain-like structure at 0.5

ML O* has also been reported to be the most energetically favorable formation according to DFT calculations which also find that the O* atoms above the surface cause buckling of Pt atoms.107-108 As the coverage reaches 3/4 ML, the chains develop into interconnected Y-shaped structures with localized honeycomb regions.106 Above

0.5 ML, research has suggested that oxygen may begin to occupy subsurface tetrahedral and octahedral sites which causes surface Pt atoms to reconstruct away from the bulk in order to accommodate the oxygen atom.108

The interplay between intermediary OH* species is critical in the electrochemical and catalytic formation or dissociation of molecular H2O on Pt. Experimental work by

Fisher and Sexton109 indicates formation of adsorbed OH on Pt(111) can exist as an intermediate by adsorption and subsequent dissociation of H2O on an O* covered Pt surface at low temperatures (150-200 K). Further temperature desorption

110 experiments determined the 2:1 (H2O:O) stoichiometric reaction for hydroxyl formation on Pt(111) as:

∗ ∗ ∗ ∗ 2H2O + O → 3OH + H (5-1)

More recent DFT calculations by Michaelides and Hu98 distinguish low-coverage and medium-coverage regimes for OH* on Pt(111). At low coverages (1/9 ML to 1/3 ML) the adsorption energy is about -2.25 eV and at medium coverages (1/2 ML to 1 ML) OH* chemisorption energy is about -2.5 eV (atop site is preferred for all coverages). The more favorable adsorption of high coverage OH* is attributed to the H bonding network formed by adjacent OH* species.

5.2 O* and H* Adsorption on Pt(111)

Although we include several adsorption structures in the COMB3 fitting database

(Chapter 3), the static structures that are fitted should be tested in classical MD simulations. Throughout this chapter, dynamic adsorption behavior and surface kinetics for atomic and molecular species on low index Pt surfaces are studied using the newly developed COMB3 Pt/O/H potential. Following calculations and results presented in

Chapter 3, the results from Table 5-1 and 5-2 compare DFT and COMB3 adsorption energies for H* and O*, respectively, where the adsorption energy calculation is the same as Equation (3-2). The calculated adsorption energies for H* on Pt(111) from DFT indicate no overwhelming site preference and suggest that H* can occupy the four identified Pt surface adsorption sites with similar binding energies. The COMB3

potential predicts atop as the most stable site for H*, but the hollow site (fcc and hcp) values are both within 0.08 eV.

As mentioned previously, the binding energy for O* is much different for atop, fcc, hcp, and bridge sites, resulting in a stronger preference to adsorb in one configuration.

Compared to DFT calculations of 1/9 ML O* on Pt(111) in Table 5-2, COMB3 overestimates adsorption energies at all surface sites. The largest discrepancy between

푎푡표푝 O* adsorption energies from COMB3 and DFT is at the atop site; 퐸푎푑푠 is -0.21 eV/atom from DFT and -1.51 eV/atom in COMB3. While COMB3 largely overestimates the binding energy at this site, it has the least negative adsorption energy, a result that is consistent with DFT calculations. COMB3 adsorption energy for O* in the bridge site is -

1.13 eV/atom and -2.47 eV/atom from DFT. These results indicate that adsorption at bridge sites is favorable at low coverages and adsorption atop Pt surface atoms is kinetically less likely. Trends in adsorption energy as a function of O* coverage and

Pt(111) surface site are plotted in Figure 5-2. At coverages less than ~0.63 ML more O* atoms are expected to adsorb at hollow hcp and fcc sites, but above this coverage the atop site has a stronger adsorption energy. Thus, it is expected that more O* atoms will occupy atop adsorption sites when the coverage approaches 1 ML.

5.3 OH* and H2O* adsorption on Pt(111)

Calculations of hyxdroxyl (OH*) adsorption energy on Pt(111) depend on the reference state from which the species is adsorbed. The adsorption energy calculation for OH* is provided in Chapter 3 (Equation 3-3). If the gaseous reference state is used to calculate adsorption energy, 퐸푂퐻 = 퐸푂퐻(푔), where energy is taken from an isolated

OH molecule. When calculating adsorption energy of OH* from the water reference state, the energy of the adsorbate is taken to be the same as Equation 3-4:

1 퐸 = 퐸 = 퐸 − 퐸 (5-2) 푂퐻 푂퐻/퐻2푂 퐻2푂 2 퐻2(푔)

Where 퐸퐻2푂 is the energy per molecule for an isolated water molecule. Table 5-3 reports the adsorption energies for OH* in the gas phase and Table 5-4 reports adsorption energies assuming aqueous OH*. The OH*(g) reference energy is calculated to be -7.09 eV from DFT and -4.36 from COMB3. The OH*(aq) reference energy is -10.82 eV in DFT and -7.65 eV in COMB3. Comparing the DFT adsorption energy calculations for these two reference states, the adsorption behavior is strongly dependent on the surrounding environment of the hydroxyl group. Negative adsorption energies from the OH*(g) reference state are calculated using DFT which COMB3 reproduces. When using the

OH* aqueous reference state, the COMB3 potential predicts negative adsorption energy as opposed to DFT calculations which indicate unfavorable adsorption of OH* from a liquid water molecule. This sacrifice in accuracy of OH* adsorption energy is made to better predict formation and dissociation energies of H2O on Pt.

Previously reported water adsorption energies from the fitted COMB3 Pt/O/H potential (Table 3-6) remain the same for the present discussion, where the most stable configuration for a single water molecule adsorbate is with the O atom closest to the Pt surface. Presence of hydrogen bonding in the water hexamer configuration (Figure 3-5) stabilizes the adsorbate and increases the molecular binding energy. Again, discrepancies between DFT and COMB3 H2O adsorption energies are acceptable since the parameters are optimized so that water remains intact when encountering a Pt surface.

5.4 Interfacial Molecular Ordering of Multilayer H2O on Pt(111)

The following section contains simulations of liquid water using the COMB3 force field. Properties of molecular, liquid, and solid phases of water using COMB3 are reported in Section 3.6. It is noted that COMB3 does not reproduce certain properties as well as potentials designed specifically for liquid water. However, since COMB3 is a variable charge model, the charge distribution within the simulation can be altered depending on local chemical environment. Combined with the bond order concept which controls the bond strength according to the atomic environment, COMB3 provides a reliable and advanced potential which captures many physiochemical complexities of the Pt/water interface.

Multilayer water films are simulated on Pt(111) with the intent to study the molecular structure and charge density profile of liquid water at the metal/liquid interface. The Pt slab is six atomic layers thick (504 atoms per layer) surface area of the

Pt slab is 5.6 nm × 5.8 nm (32.5 nm2) Three different thicknesses of water films are studied: 576 molecules or ~0.4 nm, 768 molecules or ~1.0 nm, and 1440 molecules or

~2.0 nm. Each simulation is carried out for 2 ns (0.25 fs time step) at a constant temperature of 300 K. The temperature of the system is subject to constraint via the

NVT ensemble for the Pt slab and the NVE ensemble with Langevin thermostat for water molecules. Charges on the atoms are optimized every 50 time steps (12.5 fs) using the QEq scheme.111

Throughout the simulations a wetting layer of molecules forms near the Pt surface, a result which has been reported in several previous MD studies of the Pt/water interface. A visualized snapshot of the 1440-molecule multilayer simulation and close-

up of the wetting layer configuration are shown in Figure 5-3. Ordering of molecules near the surface is visible and molecules closer to the Pt surface are designated with a

Pt-O bond in the figure. These bonds are meant to indicate short-range interactions between Pt surface atoms and O atoms from water molecules.

Atomic oxygen and hydrogen densities near the metal/water interface are taken from the end of the 576-molecule multilayer simulation and results are presented in

Figure 5-4. Firstly, we notice that there are two distinct oxygen peaks in the buckled wetting layer. The first peak at ~2.3 Å from the Pt surface indicates water molecules that exhibit short-range interactions with Pt (shown by Pt-O bonds in Figure 5-3) where atomic oxygen density in this first buckled layer is ~0.1 atoms/Å3. Previous ab initio MD

(AIMD) studies of the wetting RT39 bilayer structure observed in low temperature STM experiments match closely with our predictions, where the reported first oxygen density peak is 2.23 Å from the Pt surface and has a value of 0.1 atoms/Å3. Similarly, the first H peak in Figure 5-4 is ~2.5 Å in the COMB3 simulation and 2.33 Å in Meng’s112 AIMD study. Nonetheless, there are disparities in our COMB3 simulation results with respect to previous MD simulations and additional DFT calculations. Most previous MD simulations of the Pt/water interface113-119 treat the water as a fixed charge model (TIP series, extended simple point charge (SPC/E), or modified central force (mCF)) and parameterize a separate function to mathematically describe the interaction between water molecules and the metal surface. Another drawback of using these potentials is the constraint of fixed O-H bond lengths. In most of these simulations, a large oxygen density peak in closer proximity to the Pt surface (values vary from 2.31-2.50 Å)115-116 precedes a smaller peak. The large peak indicates strong planar densification in the

wetting layer closest to the surface. Indeed, Raghavan et al.114 report MD simulations where 80% of Pt(111) atop surface sites are occupied by water molecules. Their analysis shows a 2D arrangement of the planar wetting layer which displays an overall hexagonal arrangement where most water molecules occupy atop sites and some vacant sites create patches in the wetting layer. Subsequent MD simulations have also observed similar structures of the wetting layer on Pt(111).120

The number of molecules in the first and second buckled water layers varies as the thickness of the multilayer water film increases, as indicated by the change in oxygen density peaks from Figure 5-5A. After simulating 1440 H2O molecules on

Pt(111) for 2 ns, the number of water molecules in the total buckled layer is 505 compared to 504 surface Pt atoms. In comparison, there are 483 water molecules in the entire buckled layer for the 576-molecule film. The relative ratio of molecules in the first and second buckled layers is visualized in Figure 5-5B where a top-down view from the end of each simulation is shown. From the figure, a multilayer of greater than 1 ML

(576-molecule multilayer) produces a wetting layer with a surface coverage of ~0.96

ML. When the multilayer size increases to greater than 2 ML, the Pt surface becomes saturated with water molecules and surface coverage reaches 1 ML. The primary difference between these wetting layers is the distribution of molecules between the first and second buckled layers. The 576-molecule multilayer has a higher percentage of molecules in the first buckled layer compared to the 1440-molecule multilayer. These results suggest that bulk-like water molecules interact with the buckled wetting layer to maximize the hydrogen bonding network between the wetting layer and bulk region. For the film containing 576 molecules, the hydrogen bonding network above the wetting

layer is incomplete due to a deficiency of molecules in the bulk region and more molecules tend to form short-range bonds with Pt surface atoms. This explains the relatively large number of molecules in the first buckled layer. As the opportunity to form hydrogen bonded networks increases by including more water molecules above the buckled layer (768- and 1440-molecule multilayers), water molecules break their bonds with Pt surface atoms and become a part of the second buckled layer due to the affinity for hydrogen to orient towards O atoms from bulk H2O molecules.

Figure 5-6 is a snapshot of the entire wetting layer from the end of the 576- molecule multilayer simulation. The overall surface coverage of water molecules on

Pt(111) is ~0.96 ML (483 molecules in the wetting layer and 504 Pt surface atoms). This predicted surface coverage is higher than DFT calculations since we simulate coverages over 1 ML and DFT calculations are too computationally intensive to consider even hundreds of water molecules on a metal surface. Nonetheless, COMB3 simulations predict atop site adsorption of the wetting layer although not all sites are occupied. This results in local arrangements of molecules that include pentagons, hexagons, and heptagons in the wetting layer (labeled 5, 6, or 7 in Figure 5-4). Low temperature scanning tunneling microscopy (STM) experiments report images of submonolayer covered Pt(111) where the wetting layer is characterized to consist of 5-,

6-, and 7-membered rings of water molecules.11-12 Thus, the COMB3 simulations of the

Pt/water interface indicate significant improvement over previous MD studies and an accuracy that predicts wetting configurations consistent with DFT calculations and experimental observations.

5.5 Summary of COMB3 Pt/O/H

Previous MD simulations of the Pt/water interface using simplified interaction potentials between H2O and Pt provided a relatively accurate atomic description of the wetting layer, but the inclusion of many-body terms and Pt-O interactions from the metal oxide phase predict a more accurate molecular configuration. After parameterizing the

COMB3 Pt/O/H potential for adsorption energies, and re-optimizing to dissociation and formation energies, simulations of multilayer water in contact with Pt are analyzed. This is the first interatomic potential to-date that has the capabilities of reproducing a buckled wetting layer that is experimentally verified and supported by DFT calculations. Given the reactive nature of COMB3, it is suitable that future validation of this potential is aimed at studying chemical reactions that occur on a Pt surface. Of course, the absence of explicit electronic contributions in any empirical potential make proton (i.e., H+) transfer more difficult to capture.

Table 5-1. Adsorption energies for 0.11 ML H* adsorption on Pt(111). Adsorption site Adsorption energy (eV/species) DFT (this work) DFT literature COMB3 fcc -0.45 -0.49102†, -0.2996 -0.49 hcp -0.39 -0.45102†, -0.2696 -0.53 atop -0.43 -0.48101‡, -0.2696 -0.57 bridge -0.40 -0.47101‡, -0.2696 -0.41 †Values reported for 0.25 ML coverage ‡Values reported for 0.08 ML coverage

Table 5-2. Adsorption energies for 0.25 ML O* adsorption on Pt(111). Adsorption site Adsorption energy (eV/species) DFT (this work) DFT literature COMB3 fcc -1.65 -1.1496 -1.03 hcp -1.25 -0.6896 -1.03 atop -0.21 0.1496 -1.92

Table 5-3. Adsorption energies for 0.11 ML OH* on Pt(111) with OH(g) as the reference adsorbate. OH* is adsorbed with the O atom nearest to Pt (O-down). Adsorption site Adsorption energy (eV/species) DFT (this work) DFT literature COMB3 atop -2.80 -2.7196 -5.45 fcc -2.56 -2.4696 -5.63 hcp -2.39 -2.1996 -5.32

Table 5-4. Adsorption energies for 0.11 ML H2O* on Pt(111). Adsorption site Adsorption energy (eV/species) DFT (this work) DFT literature COMB3 atop -0.23 -0.30121, -0.30122 -1.23 hcp -0.06 -0.10122 hexamer (atop) -0.51 -0.52122 -0.66

Figure 5-1. Adsorbed oxygen (red atoms) on Pt(111) (grey atoms) in a p(2x2) ordering. The region contained within the dashed line represents one unit cell.

Figure 5-2. Coverage dependent adsorption energy for O* on Pt(111) adsorbed in fcc, hcp, and atop sites using COMB3 Pt/O/H potential; adsorption energies of hcp and fcc sites have <0.01 eV difference at all coverages.

Figure 5-3. Snapshot from the simulation of 1440-molecule water multilayer on Pt(111). Zoomed-in snapshot highlights the distinct buckled wetting layer at the surface. Large grey atoms are Pt, red atoms are O, and small grey atoms are H.

Figure 5-4. Local structure of water molecules at the Pt/water interface. A) atomic density distributions of the Pt(111)/water interface for oxygen and hydrogen. B) Only the buckled wetting layer densities (area inside black line) are shown.

Figure 5-5. Distribution of water molecules from the wetting layer on Pt(111) as a function of multilayer size. A) atomic oxygen distribution of the Pt/water interface and a zoomed-in plot of the dotted outline. B) plan view of the entire buckled wetting layer for varying thicknesses of multilayer water on Pt(111). C) side-view snapshot showing the first buckled layer (short range Pt-O interactions) as blue atoms and second buckled layer as red atoms.

Figure 5-6. Plan view showing only the buckled wetting layer of the 576-molecule water multilayer. Water molecules occupy a high percentage of atop sites with visible 5-, 6-, and 7- molecule rings in the wetting layer.

CHAPTER 6 DYNAMIC SIMULATIONS OF WATER/METAL INTERFACES

6.1 Overview of Cu/H2O Interfaces

Solids are in constant contact with water in a vast number of applications with important consequences. Corrosion of alloys in underwater environments,123 electrocatalysis,124-125 and electrodeposition all may occur at water/solid interfaces.

Solution phase heterogeneous catalysis,126 as well as frictional and wear characteristics of metals under water lubricating conditions127-128 are of interest for these ubiquitous applications. A molecular level understanding of this significant interface is desirable to guide control of processes in these surface science applications.

Many surface science studies6, 129-131 of water/metal interfaces have focused on the first water layer formed on wettable metal surfaces. The structure of the first water layer on metals, characterized using low-energy electron diffraction (LEED), was thought to be comprised of a two-dimensional (2D) epitaxial arrangement of molecules that resembles the (001) basal plane of ice I, often called the bilayer model.7 With the use of high resolution spectroscopy techniques, including scanning tunneling microscopy (STM), improved structural insight of the local water arrangement on the metal surface was developed. Low-temperature STM studies report different water arrangements on Pt(111), Cu(110), and Cu(111),12, 132-133 indicating that the structure of the first water layer varies with both the type of metal and the surface facet. Analysis of the STM images further indicates that water forms three-dimensional (3D) clusters when adsorbed at or below 20 K and annealed to 130 K on Cu(111) which has been defined129 as non-wetting behavior. This observation is in contrast to data from contact angle measurements of water droplets on oxygen-free, polycrystalline Cu films by

Schrader134 under ultra-high vacuum conditions, where the droplets exhibited a 0° contact angle, which is an indication of complete wetting.

The behavior of liquid droplets on solid surfaces can provide detailed insight into the underlying structure and dynamics at the metal-liquid interface. The dynamic motion of precursor films (PFs) originating from liquid droplets on solid substrates has been extensively reviewed by Popescu et al.15 and observed experimentally using ellipsometry,135 atomic force microscopy,136 and more recently fluorescence microscopy.137 Classical molecular dynamics (MD) studies report the propagation mechanism of the water PF on Au substrates as molecules diffuse from the droplet surface to the outer edge of the PF, finding that once molecules become part of the PF region, they are no longer mobile along the metal surface.138

These MD simulations have typically used rigid fixed charge water potentials such as extended simple point charge (SPC/E)139 and TIP4P140 which do an excellent job of describing molecular adsorption to the underlying surface but allow for only limited (if any) variations in atomic charges in response to changes in the surrounding environment. Additionally, the standard Lennard-Jones (LJ) pairwise potential used to describe liquid/solid interactions16, 141 lacks the complexity needed to capture both the underlying physics of the liquid water and chemical bonding in solid metals and metal oxides.

Here, we use a single, classical potential to model water molecules and liquid water in contact with surfaces of bare, oxidized, and hydroxylated copper using a single set of parameters. In particular, we use the formalism of the third-generation charge optimized many body (COMB3) potential to calculate the energy of our systems. First,

the adsorption of water molecules and molecular clusters on Cu(111) surfaces are determined and the COMB3 predictions are compared to adsorption energies and geometries calculated using DFT. Second, the dynamic wetting of Cu(111) by a water droplet is considered at 20, 130 and 300 K. The findings are compared to predictions of previous MD studies and to STM data. Third, the same water droplet is deposited at 300

K on reconstructed, oxidized Cu(111) and hydroxylated Cu(111) and the spreading behavior is characterized as a function of initial oxygen and hydroxide coverage. The chapter concludes with a summary of the new insights gained from the classical simulations performed here.

6.2 DFT Calculations of H2O on Cu(111)

Electronic structure calculations were performed using the Vienna Ab-initio

Simulation Package (VASP v. 5.3.5),142-144 a DFT plane-wave pseudopotential code implementing the Projector Augmented Wave (PAW)145-146 method for core-valence treatment. The Perdew-Burke-Ernzerhof (PBE)147 exchange-correlation functional described within the Generalized Gradient Approximation (GGA)148 was employed for all calculations. The plane-wave cutoff energy was 450 eV. A Fermi smearing (σ) of 0.2 eV for Cu containing systems and 0.003 eV for isolated water molecules was applied using the Methfessel-Paxton149 scheme. Geometric optimizations were conducted using the

Quasi-Newton150 optimization algorithm until the nuclei force convergence limit of 0.02 eV Å-1 was achieved. The self-consistent electronic convergence limit was set to 1×10-5 eV. The potential energy, interatomic forces and the stress tensor were corrected to include van der Waals contributions using the DFT-D3 method151 with Becke-Jonson152 damping. The Brillouin zones of surfaces were sampled using a 5×5×1 Monkhorst-

Pack153 mesh.

A periodic copper slab model was constructed using an experimental lattice constant of 3.62 Å. The Cu(111) surface consisted of a 3×3 hexagonal supercell with four atomic layers that contained 9 atoms per layer. The bottom two layers of the slab were fixed while the top two layers were allowed to relax. A 15 Å vacuum thickness was added in the surface normal direction to exclude the interaction between periodic slab models. Water adsorption on the Cu(111) slab was considered at coverages of 1/9

(monomer), 2/9 (dimer), and 2/3 (hexamer).

6.3 COMB3 Water

The total potential energy within the COMB3 formalism is detailed in Chapter 2

(Equation (2-7)). To ensure transferability of the COMB3 O/H parameters, we included heats of formation for the following structures in the fitting database: hydroxyl radical

(OH), hydrogen peroxide (H2O2), H2O, H3O, and H3O2 molecules and crystalline ice-Ih.

Table 6-1 reports energies and structural details predicted by COMB3 for a single H2O molecule and crystalline ice-Ih. This newly developed COMB3 potential for H2O systems was seamlessly coupled with previously developed COMB3 potentials for the copper-

154 56 hydrocarbon systems and Cu2O . The supplemental material contains a table of all the calculated heats of formation of the molecular structures listed above and a list of

COMB3 parameters used in the present work.

The COMB3 potentials reported here were implemented in the open source

Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) software package48 distributed by Sandia National Laboratory.

The data in Table 6-1 indicates that COMB3 accurately reproduces the energetics and geometry of a single H2O molecule and Ih-type crystalline ice. More importantly, the charges on the atoms dynamically adjust in response to the

environment, a feature absent in non-reactive fixed charge water models such as TIP4P and SPC/E. For example, the charge on an oxygen atom in ice-Ih is -0.71 e, which is lower than its value of -0.87 e in an isolated H2O molecule. The O-O dipole moment of

H2O can be estimated using a point charge model as qO × 0.6 eÅ, where qO is the charge on an O atom and 0.6 Å is the distance between positive and negative charge centers. Using this estimation, the calculated dipole moment using COMB3 is 0.42 eÅ

(2.02 D) for an isolated H2O molecule and 0.53 eÅ (2.55 D) in Ih ice, which is in close agreement with the predictions of first principles calculations155 and about 0.11 eÅ less than the theoretical value calculated by Batista et al. 156 using a self-consistent induction model.

It should be emphasized that COMB3 is a reactive potential, which means that the water molecules are not rigid and can change geometry or dissociate in response to changes in their physical environment. These unique features enable COMB3 to describe environmental dependent properties of water such as the standard heat of formation, induced dipole moment, and hydrogen bonds in water, as discussed in the next section.

The efficacy of COMB3 is tested by computing molecular and bulk scale properties of liquid water. Table 6-2 presents some properties of liquid water obtained from canonical ensemble MD simulations with COMB3. The system consisted of 297

3 water molecules in a 18.17 Å × 18.17 Å × 18.17 Å supercell (ρH2O = 0.99 g/cm ). A

Langevin thermostat was applied to all of the molecules to regulate a simulation temperature of 300 K. The simulation ran for 5 ns and included 1 ns of equilibration time. The table also provides a comparison of liquid water properties calculated using

COMB3 and those predicted with the rigid, fixed charge water potentials TIP3P140,

TIP4P140, SPC139, and SPC/E139 as well as with neutron diffraction experimental data.

The predicted heat of formation for liquid water using COMB3 is -2.81 eV/H2O or -271 kJ/mol, which is about 5% higher than the experimental value of the heat of formation for liquid water at 300 K and 1 atm. The optimal density of water at 300 K predicted by

COMB3 is 1.00 g/cm3, in agreement with experimental values. The COMB3 potential yields a dipole moment that is smaller than the value measured experimentally with a deviation of comparable magnitude to the deviation of predictions from both the TIP4P and SPC/E potentials from experiment. While TIP4P and SPC/E both overestimate the diffusion coefficient somewhat, TIP3P overestimates the diffusion coefficient by more than a factor of two. The value predicted by COMB3 also deviates from the experimental diffusion by underestimating the experimental value by a factor of two.

The radial distribution function g_ij(r) (RDF) was computed to provide a structural description of the bonding interactions between water molecules. Figure 6-1 illustrates the radial distribution functions g_OO(r), g_HH(r) and g_OH(r) calculated using either

COMB3 or SPC/E, along with data from neutron diffraction experiments157. The RDFs for liquid water predicted by COMB3 have qualitative merit but Figure 6-1 shows that peak heights are inconsistent with, and shifted relative to, both the SPC/E model and neutron diffraction data.

These comparisons illustrate that the COMB3 potential provides a reasonable qualitative description of the properties of liquid bulk water, but shortcomings with regard to self-diffusion coefficient and RDFs are apparent. Both of these inaccuracies may be attributed to the transferability of this complex, reactive, dynamic charge

potential. In this instance, transferability is used to mean that the O-H parameters used for liquid water simulations are the same elemental parameters used for the simulations in Section 6.4 of this chapter where OH is adsorbed at a metal surface. These parameters can also be employed for any system containing oxygen and hydrogen atoms (including ice-Ih, C-H-O systems, ZrH, Cu-SiO2, Cu adsorption on ZnO, among several others28). We did not fit the COMB3 potential to reproduce specific properties of liquid water, but rather included O/H molecules and crystalline ice-Ih for transferability.

For reactive, dynamic charge potentials, generating a single parameter set for atoms in different physical environments is an arduous task due to the inclusion of many varied structures (and thus, bonding environments) in the fitting database. Thus, although

COMB3 sacrifices a degree of quantitative accuracy for some liquid water properties, we highlight the importance of its ability to retain transferability.

In particular, as this work is focused on obtaining a mechanistic understanding of the behavior of wetting on bare and chemically variant copper surfaces, the influence of the variable charge scheme on the interfacial structure and dynamics of water is important. Future efforts to improve upon the reproducibility of the water self-diffusion coefficient are planned but are outside the scope of the present work.

6.4 Water Adsorption on Cu(111)

In this section we report adsorption energies and structural information for molecular water on Cu(111). The results are used to determine whether the previously developed COMB3 Cu/O/H parameters154 reproduce the correct geometries and energetics of molecular adsorption on Cu. Thus, the results from the DFT calculations reported here were not included in the COMB3 fitting database (i.e. adsorption energy

(Eads) of H2O hexamer on Cu(111)).

Water adsorption energies and geometries on Cu(111) using the COMB3 potential were determined using a conjugate gradient energy minimization method. The substrate for these calculations was a 31 Å × 31 Å Cu(111) surface consisting of 168 surface atoms and nine atomic layers for a total of 1512 atoms in the Cu slab; 10 Å of vacuum was included above the surface to prevent periodic slab-to-slab interactions in the surface normal direction. Adsorption energy minimization was performed for a water monomer, dimer, and a 2/3 (112 water molecules) surface coverage arranged in a hexagonal ice (ice Ih) configuration. In particular, adsorption energies (Eads) were calculated as:

퐻2푂+퐶푢 (퐸푡표푡 − 퐸퐶푢(111) − 퐸퐻2푂 ∗ 푛퐻2푂) 퐸푎푑푠 = (6-1) 푛퐻2푂

퐻2푂+퐶푢 where 퐸푡표푡 is the total energy of the Cu(111) surface with adsorbed H2O molecules,

퐸퐶푢(111) is the total energy of the bare Cu(111) slab, 퐸퐻2푂 is the per-molecule energy of

isolated water molecules, and 푛퐻2푂 is the number of water molecules adsorbed on the surface.

For single water molecule adsorption, two Cu(111) surface sites were identified as possible adsorption locations: one directly above a Cu surface atom (‘atop’), and one directly above the center of three adjacent surface atoms (‘hollow’).158-160 DFT and

COMB3 predict negative adsorption energies for both of these configurations indicating that both atop and hollow sites are favorable for molecular water adsorption. Figure 6-2 illustrates the geometric configuration of a single water molecule absorbed on atop and hollow sites as predicted by COMB3. For the atop adsorption site, the angle (θdipole) that the water molecule forms with the surface normal direction is 83.7° as calculated by

DFT and 78.9° using COMB3 (Figure 6-2). DFT calculations indicate a Cu-O distance of

2.35 Å while COMB3 predicts a distance of 2.52 Å, a value within 0.2 Å of the DFT results.

Adsorption energies of a H2O monomer, dimer, and 2/3 surface coverage

(hexamer) are reported in Table 6-3 and compared to DFT calculations that include van der Waals corrections, as discussed in Section 6.1. COMB3 predicts the opposite order of adsorption site stability (atop versus hollow) for monomers compared to DFT. We attribute this discrepancy to using universal, fully transferrable Cu-O and Cu-H parameters that were previously developed for organic-copper interactions.56 This observation may result in isolated H2O molecules at the Cu(111) surface occupying a larger fraction of hollow sites.

For adsorbed dimer and hexamer water clusters, the average Cu-O distances predicted by COMB3 are 2.77 Å and 2.80 Å, respectively. DFT calculations predict distances of 2.60 Å (dimer) and 3.14 Å (hexamer) between O atoms and Cu(111) surface atoms. We define the 2/3 ML coverage as two absorbed water molecules per three surface Cu atoms, as illustrated in Figure 6-3. The hexagonal geometry of the 2/3

ML coverage is retained after energy minimization for both DFT and COMB3 calculations.

The data in Table 6-3 indicates that COMB3 adequately predicts trend of stronger molecular adsorption with increasing water surface coverage, a result of hydrogen bonding among water molecules.

6.5 Dynamic Simulations of Water on Copper Surfaces

Classical MD simulations with COMB3 are used to examine the dynamics associated with water droplets with an initial diameter of 2.82 nm interacting with

Cu(111) at three different temperatures; the droplet contains 576 H2O molecules. The structure of the initial H2O configuration is obtained by running an NPT MD simulation of ice-Ih at 300 K for 200 ps, causing the hexagonal structure to become amorphous. The ice-Ih simulation cell is orthorhombic, resulting in a non-spherical shape for the initial water droplet. The copper surface consists of three layers with a surface area of 142 Å

× 143 Å and 10,752 Cu atoms. Throughout this work, the Z-axis is defined as the surface normal direction and the radial direction is defined as √푋2 + 푌2 (labeled as the

XY-axis). These axes are clearly marked in a side-view simulation snapshot depicted in

Figure 6-4.

The system is maintained at a constant-volume, constant-temperature ensemble at 300 K. The bottom layer of the Cu slab is held rigid while the water droplet and the top two Cu layers are coupled to a Langevin thermostat with a damping time constant of

100.0 ps. Using a Langevin thermostat adds thermal energy forces to the preexisting forces from the employed COMB3 potential. Thermal energy transfer occurs between hydrogen bonds in water, which in COMB3 are represented within the Coulombic energy term. The forces added from the Langevin thermostat are a small fractional number of the bond energy found in Cu (short range metallic bonding) but large compared to hydrogen bonding in water. To account for the larger relative forces, and to reduce the amount of charge fluctuation, the input simulation temperature for liquid water is 370 K in order to produce an output of 300 K. On the other hand, an input temperature of 300 K for Cu atoms results in an output temperature of 300 K.

Simulations were carried out at three different temperatures: 300, 130, and 20 K.

The simulations considering the interaction of the water droplet with the Cu surface at

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300 K are comparable to conditions used in the contact angle experiments of

Schrader.134 A simulation temperature of 130 K is used to compare simulation results with annealing conditions of experimental STM conditions. The results of these experiments132 carried out by Morgenstern’s group report the onset of crystallization from amorphous solid water (ASW) at 130 K. At this annealing temperature, STM images show formation of islands on the Cu(111) surface. More importantly, these images show a higher degree of clustering at increasing temperatures, indicating a tendency of H2O molecules to spread across Cu(111) and form large clusters at or above 130 K. The simulation results at 20 K are compared to low-temperature STM data where molecular water is dosed onto Cu(111). Results of low-temperature STM experiments from the Morgenstern group161-162 show that for temperatures at or below

20 K, water forms large amorphous clusters with no apparent order. During dissociation experiments, the group reports that the Cu(111) samples are cooled to below 20 K in order to avoid clustering of water molecules during deposition.

6.5.1 Spreading Mechanism of a Water Droplet on Cu

To describe the mechanism by which the droplet spreads during the 300 K simulation, we identify four dynamic molecular regions of the droplet using terminology that is similar to that of Yuan and Zhao138: interfacial, precursor film (PF), droplet surface, and bulk water. A schematic of these regions is illustrated in Figure 6-4. The interfacial region of the droplet (region 3 in Figure 6-4) indicates water molecules located directly above the Cu surface and directly below the bulk water and droplet surface regions. The PF region (region 2 in Figure 6-4) is denoted by molecules directly above the Cu surface that form a single molecular layer beyond the nominal contact region. Molecules at the surface of the droplet are expected to have higher mobility due

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to a deficiency in atomic interaction. Thus, we identify the droplet surface region (region

1 in Figure 6-4) as molecules located in a hemispherical, shell-like geometry that surrounds the spherical shape of the water droplet. Lastly, the bulk water region (region

4 in Figure 6-4) identifies molecules in which short range interactions are representative of molecules in the liquid state (i.e. single H2O completely surrounded by H2O molecules).

The dynamics of water molecules on a metal surface are distinctly different from their dynamics in bulk water due to competition between the presence of hydrogen bonding in bulk water and the metal-water attraction at the interface.118 The dynamic mean-square displacement (MSD) of water molecules gives a measure of their translational mobility, and the MSD of water molecules perpendicular to the surface

(MSD_Z) is shown in Figure 6-5. Complete wetting of the droplet across the surface occurs after approximately 0.8 ns, after which the MSD_Z nears convergence. The ratio of bulk water molecules relative to the entire droplet is also illustrated in Figure 6-5. The ratio of molecules considered as part of the bulk region (Nbulk/Ndroplet) decreases until the droplet has completely spread (Nbulk/Ndroplet ≈ 0 at 0.8 ns) and all molecules are assigned to the interfacial region.

The effective radius (RXY) as a function of the droplet height is determined to be

푅푋푌(푍) = √퐴(푍)⁄휋, where A(Z) is the area of water droplet at height Z. Using this terminology, RXY(0) is the effective base radius, an important measurement of water spreading rate. The spreading rate of the water droplet is determined by monitoring the change in effective base radius as the nanodroplet spreads. The effective base radius,

RXY(0), is plotted versus simulation time in Figure 6-6 to determine the profile of the

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spreading power law. The results from our simulation indicate that the water droplet follows a power law R ~ t0.16, which is in agreement with the predictions of previous MD studies138.

The inset of Figure 6-6 displays a zoomed in, top-down snapshot of the front of the PF to demonstrate surface coverage of the radially displaced PF. The PF has a dynamically changing H2O:Cu surface coverage ratio that is best approximated as 0.7, a coverage slightly greater than the 2/3 ML surface coverage calculated by DFT from

Figure 6-3. The atoms in the inset are colored according to atomic charge using the same color scheme as that used in Figure 6-10. From the snapshot, Cu surface atoms directly below the PF have increased positive charge (orange atoms) compared to the

Cu surface atoms outside of the PF region (yellow atoms).

At temperatures of 20 and 130 K, COMB3 predicts negligible change with time of the base radius as illustrated in Figure 6-7. Specifically, the base radius of the droplet at

130 K averaged over the simulation time is ~1.7 nm and the base radius at 20 K is ~1.6 nm. No spreading of the droplet occurs during these low-temperature simulations, a result consistent with reported STM data of water on Cu(111) at this temperature.132

The molecular level information from the 300 K simulation allows analysis of the physical mechanism of droplet progression. To more accurately describe the wetting process, the mean square displacement of wetting (MSD_W) is used. If a molecule is moving outward from the center of the droplet, i.e. the radial displacement rXY increases with time, MSD_W of that molecule is positive. Otherwise, the molecule is moving towards the center of the droplet and MSD_W is negative. By this definition,

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푀푆퐷_푊 = 푀푆퐷_푋푌푖푛푤푎푟푑 − 푀푆퐷_푋푌표푢푡푤푎푟푑 (6-2)

The predicted MSD_XY and MSD_W is illustrated in Figure 6-8A for the four regions of the droplet at 0.4 ns. In addition, MSD_W is reported as a function of droplet height in Figure 6-8B. Since the number of molecules in each region is dynamic and unequal, we present the data in Figure 6-8 relative to the average MSD_XY and

MSD_W of all molecules in the droplet. Analyzing the data in this manner ensures that we are not overestimating the displacement of molecules in one region solely because it contains more molecules than the others.

We address the issue of whether the PF itself is not diffusive, as described by

Yuan and Zhao.138 By including molecules directly below bulk water as part of the PF, their work concludes that the PF is not diffusive and exhibits the least mobility relative to the other molecules in the droplet. Our results agree with these findings for the interfacial and PF regions, both of which exhibit the smallest relative MSD_XY of the water droplet. Similarly, both studies find significant diffusion of droplet surface molecules to the nominal contact region and metal surface. As shown in Figure 6-8A, the radial diffusivity of the droplet’s surface is five times higher than the diffusivity of any other region in the droplet. Besides the droplet surface region, only the PF region exhibits higher MSD_W relative to MSD_XY. The difference between MSD_W and

MSD_XY is 0.1 in the PF region and 2.1 in the surface droplet region. These results indicate that the PF is relatively stationary while the droplet surface region constitutes a larger fraction of molecules at the surface near the end of the simulation. Additionally, although bulk water is more diffusive than the PF in the entire XY-plane, molecular movement parallel to the surface is random and is predicted to exhibit negative

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MSD_W, meaning that the radial displacement of bulk molecules has almost no contribution to the water droplet wetting. The dashed vertical lines in Figure 6-8B indicate that the average MSD_W of the droplet surface and PF coincide with the

MSD_W values from Figure 6-8A. Furthermore, Figure 6-8B indicates that molecules near the top of the droplet (~12 Å above the Cu surface) display greater radial displacement in order to move to the outer edge of the droplet’s surface instead of moving directly toward the Cu surface. Conversely, molecules closer to the nominal contact region (intersection of PF region and droplet surface region) do not demonstrate as much radial displacement as they are already near the outermost edge of the droplet surface.

From the above results, we note that the diffusion of water molecules from the surface of the droplet to the nominal contact region supplies additional molecules that can expand the PF region. Contrary to the highly diffusive molecules near the droplet’s surface, molecules closer to the nominal contact region remain stationary. From these observations and the 2D vantage point of Figure 6-4, we conclude that the droplet

“unwraps” itself so that molecules originally near the top of the droplet surface region

(region 1 in Figure 6-4) become part of the outer edge of the advancing water PF (inset of Figure 6-6). This conclusion is consistent with Yuan’s report concluding that the molecules near the nominal contact region do not propagate across the surface, but rather, molecules from the droplet’s surface move downward to form the final PF.

6.5.2 Effect of Surface Chemistry on Spreading Rate

To demonstrate transferability of the COMB3 potential, we investigate the effect of Cu(111) surface oxidation and hydroxyl coverage on the spreading rate of water. We reduce the dimensions of the Cu(111) slab to have surface dimensions 11.0 nm x 11.0

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nm in the X- and Y-directions and increase the thickness to 1.0 nm (6 atomic layers).

Oxygen atoms are placed 1.9 Å from the Cu surface atoms at a coverage of 0.50 ML. In this work, we define O* atoms as adsorbed oxygen atoms to differentiate them from O atoms found in H2O. The O* atoms are placed in random adsorption sites to replicate an oxidized Cu surface.163 Energy minimization is performed on the system using a conjugate gradient algorithm implemented in LAMMPS to allow the surface layer atoms to optimize their positions. The surface Cu atoms reconstruct to form a corrugated surface in good agreement with experimental data164 and the predictions of other computational studies165 for high coverage O adsorption on Cu(111).

For the final simulation, we consider a Cu(111) surface with OH* coverage of

0.50 ML (OH* representing adsorbed hydroxyl groups). Again, a conjugate gradient energy minimization used in the previous sections is performed on the Cu(111)-OH* surface prior to introducing water molecules into the system and running molecular dynamics.

After structural relaxation and using simulation details similar to those outlined previously, we perform NVT simulation of liquid water interacting with O* and OH* covered Cu(111). Snapshots of the initial MD simulation structure for both O* and OH* surfaces and their respective structures after 1.0 ns of simulation time are shown in

Figure 6-9.

For both O* and OH* covered Cu(111), the droplet exhibits a lower spreading rate compared to the bare surface. These spreading rates are compared in Figure 6-10, which indicates that water on O* and OH* covered Cu(111) has a spreading rate in closer agreement to the molecular-kinetic theory prediction166 of R ~ t1/7 compared to

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bare Cu(111). More interestingly, these droplets exhibit a smaller final base radius (~3.0 nm for O* surface and ~2.5 nm for OH* surface), indicating that the degree to which the droplet spreads is reduced on these surfaces. Classical MD simulations analyzing spontaneous spreading of a nanodroplet on surfaces with varying wettability indicate that decreasing the wettability of a surface reduces the rate at which the droplet spreads.141 Our results indicate that both the degree of spreading and spreading rate are reduced on O* and OH* covered Cu(111). This finding indicates that O* and OH* decreases the wettability of water on Cu(111).

Here, we propose a mechanism by which the spreading rate changes based on the pinning effects of Cu-O* or Cu-OH* bonds and the charge-charge interactions at the interface. To clarify the mechanism, a detailed schematic of the chemical species and their charges at the interface is shown in Figure 6-11. On bare Cu, hydrogen bonds within H2O compete with Cu-O Coulombic interactions at the surface. The Cu surface atoms have an approximate charge of +0.15 e and the O atoms from the H2O molecules in contact with the surface exhibit a charge of -0.88 e. These Cu-O interactions may therefore be thought of as relatively weak which allows the H2O molecules to readily move across the surface.

When the Cu(111) surface is oxidized the simulation results indicate that Cu atoms in Cu-O* bonds carry a charge of 0.80 e, O* atoms have an approximate charge of -0.75 e and H atoms have a charge of +0.33 e. The resulting stronger Coulombic interactions between Cu and O* atoms make the Cu-O* bonds stationary throughout the simulation. These immobile Cu-O* bonds can pin H2O molecules and thus slow down the water spreading rate on the surface. Similarly, Cu-OH* bonds at the hydroxylated

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Cu(111)/H2O interface are immobile, which can dramatically reduce the spreading rate of water molecules. In addition, the H atoms from OH* carry a charge of +0.40 e and O atoms from the surface contact layer of H2O have an approximate atomic charge of -

0.91 e, which results in a greater charge difference than was present in either the bare or oxidized Cu surface/water interface. The resulting strong hydrogen bonding at this interface cause the greatest reduction in water spreading rate.

6.6 Electrochemical Simulations of Cu/H2O Systems

An atomic description of water dynamics and electrochemical properties at the electrode/electrolyte interface is presented in this section. The two methodologies outlined in section 2.2.2.4 are used to simulate an electrochemical cell that consists of two Cu(111) electrodes and water as the electrolyte, as shown in Figure 6-12. The density of the liquid water is 1.0 g∙cm-3, which is the predicted value by COMB3 for bulk liquid water167. A vacuum of width 20 Å is added along the surface normal to avoid interactions between electrodes and periodic boundary conditions are applied in all three directions. The MD simulations are considered under the NVT ensemble and a

Nose-Hoover algorithm is used as the thermostat. It is worthwhile to point out that despite the constant volume constraint on the system, the distance between the two electrodes (102.0 Å in Figure 6-12) is allowed to change during the simulations. Thus, both the vacuum region and electrolyte region are capable of undergoing volume changes while retaining the initial supercell volume. are run for 2000 ps (2 ns) to allow full relaxation of water dipoles.

First, we compare the atomic charge distribution and density profile of water between the χ-offset and Q-offset methods. The data presented are time averaged

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values of the last 20 ps of simulation. To better quantify the charge distribution, the system is divided into seven regions as indicated in Figure 6-12, where Eb represents the bulk water region. The thickness of the interfacial electrolyte (EC and EA in Figure 6-

12) is set to 10 Å from the cathode and anode surfaces, where EC and EA combined takes up about 30% of the total electrolyte.

In the χ-offset method (Figure 6-14A), the average atomic charge increases from

0.22 e to 0.28 e for cathode Cu atoms (CE) and decreases from 0.22 e to 0.12 e for anode Cu atoms (AE) as V increases from 0 to 2.5 V. The average atomic charge is about -0.03 e for interfacial water (EC and EA regions) and -0.01 e for bulk water for all three applied potentials. This leads the net charge on the electrolyte to be about -112 e.

Such net charge accumulation in the electrolyte is the result of applying EE condition to the entire system. As exemplified in this study, the mean electronegativity is about 4.5 V for the copper slabs and 7.6 V for bulk water molecules, which gives a mean electronegativity of 6.0 V for the total system. After applying QEq to the whole system, the charges are transferred from higher electronegativity site to lower electronegativity

th site with the driving force (휒̅ − 휒푖) on the charge of every i atom. As a result, the net charge on the electrolyte is -112 e for 2240 water molecules for the case of V = 0.0 V.

Correspondingly, there is a net charge of about 56 e each on both the cathode and anode to maintain neutrality of the total system. This significant amount of charge accumulation occurring in the electrolyte is unphysical. When the charge transfer reaches a steady state, there should be no accumulated charge within the electrolyte region as a response to the applied potential.

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For the Q-offset method (Figure 6-13B), the average atomic charges of different electrolyte regions, i.e. EC, Eb and EA water molecules in Figure 6-13B, fluctuate around zero. For CE Cu atoms, the average atomic charge is 0.005 e for 0 V and 0.03 e for 2.5

V. At V=2.5 V, the average atomic charge of anode Cu atoms (AE) is -0.008 e. Since charge conservation is enforced on the cathode, anode and electrolyte separately, no charge accumulation in the electrolyte is observed for all three applied charge levels.

Figure 6-14 shows the density profiles of water as a function of the applied potentials for both, in which the horizontal line is 1.00 g∙cm-3 to indicate the COMB3 predicted density of bulk liquid water at 300 K. For the χ-offset method, the distance between the Cu electrodes (x-axis in Figure 6-14) has decreased from 66 Å to about 56

Å and thus the average density of water has increased to about 1.17 g∙cm-3 for the three applied voltage levels. The accumulated charge in the electrolyte and the larger qO and qH values result in stronger Coulomb interactions and hydrogen bonds and thus strong densification of water molecules in Figure 6-14A. For Q-offset method, the length of the electrolyte remains 66 Å throughout the simulation and the density of bulk water oscillates around 1.00 g∙cm-3. For water molecules near the interface, strong densification near the electrode area is understandable since negatively charged O atoms have oriented toward positively charged Cu electrodes.

The density profile of the electrolyte near the electrode surfaces is dependent on the orientation of the water molecules. Atoms with a charge value that has the opposite charge sign with the electrode surface charges, i.e. either negatively charged O or positively charged H atoms in water molecules, tend to orientate to the electrode surface. Cathode atoms in the χ-offset method exhibit more positive charges than those

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from the Q-offset method which leads to more planar ordering of oxygen atoms and thus higher density at the cathode interface. For the case of Q-offset method with 2.50

V, the density near the anode surface is 0.3 g∙cm-3, which indicates that the H atoms have orientated to the negatively charged (-0.008 e) Cu atom.

So the χ-offset method results in unphysical transfer of charge to the electrolyte which causes densification of the water. Using the charge density profile, the potential

(V) of the simulation is calculated using Poisson’s equation:

2 휌푞(푧) ∇ 푉푐푎푙 = − (6-3) 휀휀0 where 휌푞(푧) is the charge density profile normal to the electrode surface (summed atomic charges divided by unit volume). The resulting potentials, Vcal, for the χ-offset and Q-offset methods are presented in Figure 6-15. The parabolic shape of the χ-offset potential is caused by the net flow of charge to water molecules in the electrolyte. On the other hand, the Q-offset method results in a linear potential difference between the electrodes which is more qualitatively consistent with experimental measurements.

In conclusion, the χ-offset method is unreliable for simulating electrochemical systems due to charge accumulation at dissimilar interfaces. Similarly, applying constant charges on the electrodes in the Q-offset method is unphysical since the countercharge on or capacitance of the EDLC dynamically changes with time. A compromising methodology that merges these two concepts is proposed, in which QEq is applied to the cathode, anode, and electrolyte separately as in the Q-offset method and the electronegativity is only offset at the electrodes. Applying this method to the final configurations of the previous simulations results in a linear potential drop between the cathode and anode.

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6.7 COMB3 Cu/H2O Synopsis

This chapter presented a COMB3 potential capable of simulating solid copper and liquid water within the same dynamic charge framework. Results from COMB3 calculations indicate the ability of the potential to capture changes in oxygen charge and dipole moment with varying environments (Table 6-1). COMB3 adsorption properties are compared to DFT calculations for adsorbed water molecules on a Cu(111) surface.

The results show that COMB3 overestimates binding energies for a single molecule, dimer, and 2/3 ML coverage. The COMB3 potential is utilized to simulate the spreading of a water droplet over a Cu(111) substrate at surface areas greater than 50 nm2. The dynamic description of a liquid water nanodroplet wetting across the Cu surface is summarized by the pronounced radial diffusivity of droplet surface molecules so that the final PF (image at 1.6 ns in Figure 6-5) primarily consists of molecules originally part of the droplet’s surface. Additionally, it is found that pre-adsorbed O* and OH* decreases the degree of spreading over Cu(111) and reduces the spreading rate to a value in closer agreement with the molecular kinetic theory value of R ~ t1/7. Electrochemical simulation methods are then tested using a Cu/water/Cu simulation cell and the drawbacks and successes of both methods are detailed. The work presented here, especially the development of a dynamic charge potential capable of capturing liquid water in contact with a chemically variant metal surface, provides an advanced computational technique for probing the properties of interfacial phenomena where charge transfer plays a crucial role.

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Table 6-1. List of properties of H2O systems calculated with COMB3 and compared with the predictions of common empirical water potentials TIP3P,140 TIP4P,140 SPC,139 and SPC/E,139 and experimental data. The dipole moment within TIP3P, TIP4P, SPC, SPC/E, and COMB3 was estimated using qO × 0.6, where 0.6 Å is the distance between positive and negative charge centers. All 168 experimental properties for molecular H2O are from Ref. . Properties TIP3P TIP4P SPC SPC/E Exp./DFT COMB3

H2O O-H length 0.96 0.96 1.0 1.0 0.95 0.95 H-O-H angle (º) 104.5 104.5 109.5 109.5 104.5 107.6 ΔHf (eV/mole.) - - - - -2.50 -2.41 Charge on O, qO (e) -0.83 -1.04 -0.82 -0.82 - -0.71 Dipole moment (eÅ) 0.50 0.62 0.49 0.49 0.39 0.42 Ice Ih a (Å) - 4.49a - 4.63b 4.52c 4.55 c (Å) - 7.32a - 7.18b 7.36c 7.39 O-O distance (Å) 2.74d 2.68d 2.70d - 2.76e 2.78 f ΔHf (eV/mole.) - - - - -3.02 -3.16 Charge on O, qO (e) -0.83 -1.04 -0.82 -0.82 - -0.87 Dipole moment (eÅ) 0.50 0.62 0.49 0.49 0.52g, 0.53 0.64h 휸ퟎퟎퟎퟏ (basal plane) - - - - 0.010- 0.010 0.018i 휸ퟏퟎퟏ̅ퟎ (prism plane) - - - - 0.012- 0.017 0.016i aRef. 169 bRef. 170 cRef. 171 dRef. 172 eRef. 173 fRef. 174 gRef. 155, calculated value hRef. 156, calculated value iRef. 175

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Table 6-2. Comparison of bulk water properties from MD simulations using COMB3 or non-reactive water potentials (TIP3P, TIP4P, SPC, and SPC/E) with data from neutron diffraction experiments. Properties TIP3P176 TIP4P SPC176 SPC/E Experiment COMB3

ΔHf (eV/H2O) - - - - -2.96 -2.81 Density (g/cm3) 0.99 0.99 0.98 1.02 1.00 1.00 Average water 0.49 0.45 0.47 0.49 0.60a 0.45 dipole moment (eÅ) Diffusion coefficient 5.30 3.9 4.02 2.52 2.3b 0.96 (10-5 cm2/s) aRef. 177 bRef. 178

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Figure 6-1. Radial distribution functions of liquid water. Data is shown from experimental neutron diffraction data, SPC/E, and COMB3. A) Oxygen- oxygen rdf. B) Hydrogen-hydrogen rdf. C) Oxygen-hydrogen. Experimental and SPC/E results overlap in A.

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Figure 6-2. Configuration of water monomers adsorbed on the Cu(111). Side view and top-down view are shown for both adsorption sites. The molecule’s dipole vector forms an angle, θdipole, with the Cu(111) surface normal vector. Cu atoms are yellow, O atoms are red, and H atoms are grey. A) atop site adsorption. B) hollow site adsorption.

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Figure 6-3. Equilibrated 2/3 ML water surface structure from DFT calculations (top- down view). The figure includes periodic images from the 3×3 hexagonal unit cell (blue region). The color scheme is: Cu atoms are yellow, O atoms are red, H atoms are white.

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Figure 6-4. Side-view snapshot from the MD simulation of a water droplet forming on a Cu(111) surface at 300 K. Dsurf is the thickness of droplet surface water and Dint is the thickness of interfacial water. RXY(Z) is the effective radius of droplet at height Z, the area of such a circle is equal to the area of the water droplet max at that height. RZ is the maximum height of the droplet. Water droplet regions are identified as: (1) droplet surface (rZ > Dint and rXY > RXY(Z)-Dsurf or max rZ > Dint and rZ >RZ -Dsurf); (2) PF (rZ <= Dint and rXY > RXY(Dint)); (3) interfacial region (rZ <= Dint and rXY <= RXY(Dint)); and (4) bulk water (molecules not accounted for in other regions).

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Figure 6-5. MSD of water in the direction perpendicular to the surface (MSD_Z) and fraction of bulk water molecules (Nbulk/Ndroplet) as a function of MD simulation time. The increasing solid curve corresponds to the left vertical axis and the decreasing dotted curve corresponds to the right vertical axis. Insets are side- view snapshots of the simulation.

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Figure 6-6. The propagation of the base radius as wetting of the droplet progresses (300 K simulation temperature). The dotted line is a power law curve fitted to the data. A top-down snapshot from the simulation and a zoomed-in view of the PF illustrates surface coverage (~0.7 ML) as the droplet spreads across the surface.

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Figure 6-7. Static non-wetting structures of low temperature water droplets on Cu(111). A) Base radius of water droplets at 20 and 130 K. B) Top-down and side-view snapshots of the simulations at 0.8 ns.

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Figure 6-8. Water droplet displacement profiles. The dotted horizontal line distinguishes molecules in the droplet surface from PF molecules. Dashed vertical lines represent average MSD_W of the two regions as seen in A. All calculations are taken at 0.4 ns. A) MSD_XY and MSD_W of each region of the droplet illustrated in Figure 6-4. The values are reported relative to MSD_XY and MSD_W of all the droplet molecules. B) MSD of wetting (MSD_W) is calculated for droplet surface molecules as a function of droplet height.

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Figure 6-9. Perspective views of the initial setup of H2O interacting with Cu surfaces. Oxygen atoms from O* and OH* species are blue and O atoms from H2O are red. Hydrogen atoms from OH* species are white and H atoms from H2O are grey. Cu atoms are yellow. A) An oxidized Cu(111) surface (0.50 ML O*). B) Hydroxylated Cu(111) surface with 0.50 ML OH* coverage. C) Snapshot of the O* surface after 1.0 ns of simulation time. D) Snapshot of the OH* surface after 1.0 ns of simulation time.

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Figure 6-10. Spreading rate of single crystal Cu(111) surface (bare) and 0.50 ML O* and OH* covered Cu(111) after 1.5 ns of simulation time. The surfaces with pre-adsorbed species exhibit a lower degree of spreading and a slower spreading rate.

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Figure 6-11. Cartoon rendering of the water molecules from the PF and their interaction with (top) bare Cu, (middle) O* covered Cu, and (bottom) OH* covered Cu. Solid lines represent short-range bonding, dashed lines represent non- bonded Coulombic interactions (H-bonding in water and adsorbate-water interactions). Chemisorbed OH* and O* on Cu are colored red, atoms from liquid water are colored blue.

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Figure 6-12. System configuration of the Cu/H2O/Cu electrochemical cell. Seven regions of the cell are identified: bulk cathode (Cb), cathode atoms in contact with electrolyte (CE), electrolyte at the cathode (EC), bulk electrolyte (Eb), electrolyte at the anode (EA), anode atoms in contact with electrolyte (AE), and bulk anode (Ab). Yellow atoms are Cu, red atoms are O, and white atoms are H.

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Figure 6-13. Atomic charge distributions: average charge per atom of different regions from Figure 6-12. A) Charge distribution from χ-offset method. B) Charge distribution from Q-offset method.

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Figure 6-14. Water density profile as a function of applied potential for Cu/water/Cu system. A) Density using χ-offset method. B) Density using Q-offset method.

128

Figure 6-15. Potential profiles for electrochemical simulations. Vertical lines denote the anode and cathode surfaces. The legends are the same as Figure 6-14. A) Potential from χ-offset method. B) Potential from Q-offset method.

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CHAPTER 7 CONCLUSIONS

The primary content of this dissertation is separated into 1) theory and development of a Pt/O/H interatomic potential and 2) application of such potentials to

MD simulations involving nanoscale surfaces and dynamic interactions at heterogeneous interfaces. Details of the COMB3 parameterization show that the potential is developed to satisfactorily capture energetic transitions between crystal phases of pure Pt metal, defect formation energies, and surface energies. In addition, the γ surface energy is mapped for fcc-Pt and a simulated tensile test demonstrates efficacy of the potential by capturing mechanical deformation in polycrystalline Pt.

Extended development of the potential is presented in Sections 3.2 and 3.3 where Pt/O,

Pt/H, and Pt/O/H interactions are parameterized in the interest of simulating Pt surfaces with chemically adsorbed species (i.e., O*, H*, OH*, and H2O*).

High temperature MD simulations comparing Pt and Au NPs are executed using the COMB3 potential. Simulated step-wise heating of the particles to sufficiently high temperatures provides enough kinetic energy to the system to overcome the energy barrier associated with surface self-diffusion. Such diffusion is initiated via an Arrhenius relationship and t3he thermally activated surface self-diffusion begins with under- coordinated corner and edge atoms, followed by subsequent loss of an atomically well- defined particle shape (i.e., Wulff-constructed particles). The resulting morphological change causes the particle to become spherical even after step-wise cooling of the NP to room temperature. The difference in melting temperature between Pt and Au is captured in the COMB3 simulations, while the activation energy for surface self-diffusion

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is a more difficult kinetic property to correctly predict from a large (~30 nm radius) NP simulation.

Adsorption properties of the COMB3 Pt/O/H potential are reported and we perform MD simulations to of multilayer water on Pt(111). The structure of liquid water at the Pt surface during the simulations agrees with low temperature STM experiments,

AIMD simulations, and DFT calculations where the wetting layer displays a molecularly buckled configuration of pentagons, hexagons, and heptagons. In previous classical MD studies, the wetting layer was predicted to consist of a densely packed unary plane of oxygen atoms which marked the wetting layer of Pt(111). While these predictions were suitable for prior studies, the development of a COMB3 Pt/O/H potential that predicts

Pt/water configurations consistent with recent experiments and ab initio data is a significant progression in terms of modelling the Pt/water interface on time and length scales inaccessible to DFT. Of course, additional simulations of other Pt/O/H systems are necessary to further benchmark the potential and determine its suitability for reproducing chemically reactive scenarios.

The final chapter of this dissertation presents MD simulations of the dynamic wetting process of a liquid water droplet on bare Cu surfaces at 20, 130, and 300 K.

Low temperature simulations (130 K and below) indicate that the droplet is stationary and does not dynamically wet the surface. At room temperature, the droplet spreads over the surface and forms a molecularly thin PF which diffuses radially outward along

Cu surface atoms. A mechanism for this type of wetting behavior is identified in agreement with previous studies. The PF consists of water molecules initially at the surface of the droplet where molecules near the top of the droplet comprise the

131

outermost edge of the PF. The simulated spreading rate of liquid water on bare Cu at room temperature is compared to the spreading of water on O* or OH* covered Cu.

Simulation results indicate that increased hydrogen bonding opportunities present on O* and OH* Cu slows the overall spreading rate of the water droplet.

In summary, developments and applications of the COMB3 interatomic potential are demonstrated using MD simulations. The results provide mechanistic insight into physical and chemical processes that occur on the atomic (nano) scale. Transition metal surface interactions are emphasized in the simulations based on the applicability of these metals in catalysis and electrochemistry.

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APPENDIX POTENTIAL PARAMETERS FOR Pt-O-H COMB3 POTENTIAL

Table A-1. COMB3 parameters for Pt, O, and H Parameters Pt O H χ 5.14710000 6.59963000 5.35930500 J 3.41860000 5.95509700 8.24060300 K 0.45130000 0.76043340 0.00000000 L 0.00000000 0.00938801 0.00000000 ξ 1.53355500 1.37179400 2.00000000 Pχ 1.50166500 3.25885400 1.94835300 PJ 0.20000000 0.30569000 0.00000000 Z 0.03856610 -1.53917000 1.00000000 QL -0.90000000 -2.00000000 -0.53665160 QU 4.00000000 6.00000000 1.00000000 DL 0.01000000 0.00766441 0.01058483 DU -0.18623300 -1.21395100 -0.05714735 η 1.00000000 1.00000000 1.00000000 m 1.00000000 1.00000000 1.00000000

Table A-2. Two-body parameters developed for Pt metal. Pt-Pt Aij 671.33931301 1 B ij 45.42360220 2 B ij 154.85553293 λ 3.00354208 1 α ij 0.90555249 2 α ij 3.76066121 β 1.31555410 b6 0.00000000 b5 0.00000000 b4 0.53980186 b3 1.14275392 b2 0.22721410 b1 -0.15923395 b0 0.21824740 Rmin 2.70000000 Rmax 3.00000000 cosm1 0.24692924 cosm2 1.13742476

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Table A-3. Two-body parameters developed for Pt/O/H Pt-O O-Pt Pt-H H-Pt Aij 671.33931301 671.33931301 382.59472726 2292.53500000 1 B ij 45.42360220 45.42360220 45.32817241 45.32817241 2 B ij 154.85553293 154.85553293 0.00000000 0.00000000 λ 3.00354208 3.00354208 2.99378203 2.99378203 1 α ij 0.90555249 0.90555249 1.10167131 1.10167131 2 α ij 3.76066121 3.76066121 0.00000000 0.00000000 β 1.31555410 0.02281461 2.52061837 2.59739684 b6 0.00000000 0.00000000 0.00000000 -0.69790450 b5 0.00000000 0.00000000 0.00000000 -0.25151940 b4 0.53980186 0.05352012 0.78275591 1.47748100 b3 1.14275392 0.04509326 -0.15337997 0.22985150 b2 0.22721410 0.47256054 0.17570863 -0.95410160 b1 -0.15923395 0.16149080 0.70638840 0.38233600 b0 0.21824740 12.69966199 0.97587061 2.29128450 Rmin 2.70000000 3.05000000 2.20000000 2.20000000 Rmax 3.00000000 3.35000000 2.50000000 2.50000000 cosm1 0.24692924 0.42081750 0.44823789 -0.00123505 cosm2 1.13742476 0.94095990 0.94771773 0.00096295

Table A-4. Three-body Legendre polynomial parameters for Pt metal, Pt/O, and Pt/H Pt-Pt-Pt O-Pt-O Pt-O-Pt Pt-O-O O-O-Pt Pt-H-Pt

LP0 0.000000 0.049596 0.005756 1.262730 -0.545622 0.001270 LP1 0.012106 0.000000 0.000000 0.000000 0.000000 0.000000 LP2 -0.007398 0.000000 0.000000 0.000000 0.000000 0.000000 LP3 0.031373 0.000000 0.000000 0.000000 0.000000 0.000000 LP4 -0.007354 0.000000 0.000000 0.000000 0.000000 0.000000 LP5 0.009095 0.000000 0.000000 0.000000 0.000000 0.000000 LP6 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

Table A-5. Three-body Legendre polynomial parameters for Pt/O/H O-Pt-H H-Pt-O Pt-O-H H-O-Pt Pt-H-O O-H-Pt

LP0 0.000393 1.136920 -3.044120 -0.102090 0.258772 0.469840 LP1 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 LP2 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 LP3 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 LP4 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 LP5 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 LP6 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

134

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BIOGRAPHICAL SKETCH

Andrew (Drew) Antony was born in Indianapolis and spent his youth in suburban

Chicago. After moving to Louisiana for middle and high school, he attended Louisiana

State University (LSU) where he received a Bachelor of Science (B.S.) in physics in

2013. Working with Dr. Jiandi Zhang in an experimental condensed matter physics laboratory at LSU helped Drew realize his desire to pursue graduate studies in materials science and engineering. In the fall of 2013, he started graduate school at University of

Florida and began coursework and received research guidance under Dr. Susan B.

Sinnott in the Department of Materials Science and Engineering. Drew received a

Master of Science (M.S.) degree from the department in spring 2015. Shortly after, Dr.

Sinnott was named Department Chair at Pennsylvania State University and Drew moved to State College, PA to continue working with the Sinnott research group. As a visiting scholar in Penn State’s Department of Materials Science and Engineering, he became involved with the university’s club racquetball team and coached the men’s and women’s teams during the 2016-2017 season. During doctoral research, he interned with QuesTek Innovations LLC in Evanston, IL where he applied materials modelling and simulation techniques to improve superalloy design and processing. After returning from the internship, Drew completed his doctoral research and received his Ph.D. in

Materials Science and Engineering from University of Florida in May 2017.

149