atomistic modeling of an electrochemical interface

The Pennsylvania State University

The Graduate School

Department of Chemical Engineering

ATOMISTIC MODELING OF AN

ELECTROCHEMICAL INTERFACE

A Thesis in

Chemical Engineering

by

Michael V Glasspool

2011 Michael V Glasspool

Submitted in Partial Fulfillment

of the Requirements

for the Degree of

Master of Science

August 2011

The thesis of Michael V Glasspool was reviewed and approved* by the following:

Janna K Maranas

Associate Professor of Chemical Engineering

Thesis Co-Advisor

Michael J Janik

Assistant Professor of Chemical Engineering

Thesis Co-Advisor

John J and Jean M Brennan Clean Energy Early Career Professor

Scott T Milner

Joyce Chair Professor in Chemical Engineering

Andrew Zydney

Department Head, Chemical Engineering

Walter L. Robb Chair and Professor of Chemical Engineering

*Signatures are on file in the Graduate School

iii

ABSTRACT

Electrochemical interfaces are present in a variety of applications. Despite their prevalence, the

electrode/electrolyte interface is not well understood from a molecular standpoint. Variations in

the electrolyte structure near an electrode surface give rise to fluctuations in the electric field

which can affect surface reaction kinetics. One device affected by such phenomena is the proton

exchange membrane fuel cell (PEMFC). The cathode half of a PEMFC, at which the oxygen

reduction reaction takes place, accounts for nearly 70% of the total performance losses during

typical operation. Characterizing the interfacial structure at a PEMFC cathode can give insight

into what causes these performance losses. In this study, we develop a new method to analyze an

electrochemical system. Molecular dynamics simulations can be used to describe systems with

atomistic detail, and explain macroscopic phenomena. Using the Central Force Model to describe

liquid water, and Electrode Charge Dynamics to account for electronic polarizability in a

platinum electrode, we will simulate the electrochemical interface in a manner than can produce a

more accurate characterization of the interfacial structure. We use sulfuric acid in the electrolyte

to approximate the behavior of the Nafion ® membrane used in PEM fuel cells. We describe

sulfuric acid in a reactive manner by incorporating the acid into the Central Force Model.

iv

TABLE OF CONTENTS

LIST OF FIGURES v

LIST OF TABLES vii

ACKNOWLEDGEMENTS viii

Chapter 1 Background and Motivation 1

Atomistic modeling techniques 4

Description of research plan 6

Selecting a model system 6

Chapter 2 Molecular Dynamics Force Field Selection 12

Selection of a fore field for liquid water 12

A brief review of available models for liquid water 13

Modeling water using reactive bonds 15

Ab initio molecular dynamics 20

Describing an electrode surface with atomistic resolution 22

Early simulations of electrochemical systems 23

Electrode charge dynamics 25

Incorporating ECD into a molecular dynamics simulation 26

Chapter 3 Molecular Dynamics Simulation of Aqueous Sulfuric Acid 29

Approximation the behavior of Nafion with sulfuric acid 29

Structural characterization of the sulfuric acid molecules 30

Developing a molecular dynamics description of sulfuric acid 32

Design of the intermolecular potentials 35

Finalizing the OS-H potential for sulfuric acid 44

Comparison of final screening tests for force field fitting 45

Chapter 4 Simulation Aqueous Sulfuric Acid between Platinum Electrodes 49

Parameterization of Pt(111) surface with aqueous sulfuric acid 49

Parameterization of the Pt(111) surface with water 50

Parameterization of the Pt(111) surface with sulfuric acid 54

Initial simulation of a full electrochemical system 56

Correcting the Pt/HSO4- force field interaction 61

Simulation of an electrochemical interface 63

Conclusions and future work 73

References 75

v

LIST OF FIGURES

1-1: Comparison of classical electrochemical interface to a more accurate 2

description attainable from simulations

1-2: The Gibb‟s energy of reaction (eV) for oxygen replaced by water at a 3

Pt(111) surface

1-3: Description of simulation scales from QM to continuum 4

1-4: A proton exchange membrane fuel cell 7

1-5: Proton transport through water is assisted by Grotthus hopping 9

1-6: Nafion is a polyfluorosulfonic structure with an active sulfate group on 10

its side chain

2-1: Various TIPnP models describe the water molecule using a different 13

number of charge centers

2-2: Increase in the size of biological system benchmarks historically 15

2-3: Comparison of reactive and non-reactive potentials used in MD simulations 17

2-4: Pair potentials used to describe liquid water in the revised central force model 18

2-4: The image-charge representation of interactions between charged species 24

and electrode surfaces

2-5: ECD description of electrode atoms 26

3-1: Geometric analysis of H2SO4 from VASP calculations 31

3-2: Molecules used in a MD simulation of H2SO4/H2O system (referenced) 33

3-3: Radial distribution function of sulfuric acid oxygen atoms with water 34

hydrogen atoms provided by an AIMD study for two acid concentrations

3-4: Pair potentials for the SO4 group for reactive MD simulation of H2SO4/H2O 36

3-5: Non-bonded interaction potential for S-OS and S-OW 38

3-6: Pair interaction potential for S-H in reactive sulfuric acid simulations 40

3-7: RDF for the S-H distance for CFM-1 and CFM-OO 43

3-8: CFM-2 prescreening S-H RDF 44

3-9: Final form of OS-H potential compared to that of CFM potential for OH 47

vi

3-10: Overlay of my OS-H RDF with that of Ikeshoji et al. 47

4-1: Comparison of initial water/Pt(111) fitting to expected surface adsorption sites 52

4-2: VMD image of the movement of water molecules (shown as oxygen 53

atoms) on a Pt(111) surface

4-3: View of the preferred bisulfate ion orientation on a Pt (111) surface 54

4-4: Comparison of MD fit for Pt-S interaction to abintio data for energy vs. 56

distance data for bisulfate/Pt (111)

4-5: Snapshot of our MD simulation of aqueous sulfuric acid between 56

platinum electrodes

4-6: Average charges on metal layers in solution for a neutral run and a highly 59

charged electrode case

4-7: Sulfur density plots from different time blocks within a 10 V charged 60

electrode simulation

4-8: Comparison of (a) initial configuration with sulfate groups forced 61

towards the electrode surface, and (b) a 9ps snapshot showing migration away from both

electrode surfaces

4-9: Comparison between MD and QM for the Pt/HSO4- energy for the final fitting 62

4-10: Distribution of sulfur atoms in the z-direction 64

4-11: Electric potential as a function of distance generated from Poisson‟s 65

equation for 3 different charged electrode cases

4-12: Distribution of water ions (H+, OH

- and H3O

+) through solution 66

at the start of all simulations

4-13: Distribution of water ions (H+, OH

- and H3O

+) through solution 67

during the 87.5 – 121.5 ps time block for the 6 V charged electrode simulation.

4-14: Average number of H atoms bound to OS atoms as a function of distance 70

for a 50 ps time block in the 10 V charged electrode simulation

4-15: Snapshot of SO4 groups in solution for the 10 V charged electrode 71

simulation (top) and uncharged electrode simulation (bottom) after 125 ps

4-16: OS distribution profiles for the 10 V charged electrode simulation (top) 72

and the uncharged electrode simulation during a 50 ps time block.

vii

LIST OF TABLES

2-1: Comparison of the diffusion coefficient for various water models 21

3-1: Atomic charges for reactive MD simulations 32

3-2: Interaction parameters for harmonic sulfate bonds 37

3-3: Integration analysis of various OS-H potentials for average sulfate 46

molecular configuration

4-1: Parameters for the initial force field interaction between water and Pt (111) 51

4-2: Interaction parameters for the new water/Pt(111) interaction using Equation 2-10 53

4-3: Parameters for initial Pt-S interaction fitting 55

4-4: Interaction parameters for final Pt-S and Pt-OS interaction from Equation 2-10 62

4-5: Statistical analysis of the proton dissociation from sulfuric acid 68

in a charged environment

viii

ACKNOWLEDGEMENTS

I would like to thank Dr. Michael Janik and Dr. Janna Maranas for their guidance and support

throughout my studies.

I would like the thank Kuan-Yu Yeh for all of her work in collaborating with me, for her useful

discussions, and for helping me to better understand my field.

Thank you to Erin Boland for her work in developing our code and assisting in my learning how

to run our MD simulations.

Thank you to the lab groups of Drs. Janna Maranas and Michael Janik, particularly those with

whom I have worked most closely, for providing an excellent working environment, helpful

discussions and a positive atmosphere.

Finally, thank you to Scott Milner for serving on this committee and his helpful discussions

following my presentation in April 2011.

1

Chapter 1

Background and Motivation

Electrochemical systems are prevalent in a great number of applications, such as fuel

cells, batteries, solar cells, and electrocatalysis. Despite the diversity of systems involving

electrochemical interfaces, or a charged electrode at which chemical reactions take place, there

has been little research in the way of computationally describing the solid/solution interface in a

manner that both provides atomistic detail to the metal electrode and can model reactions in

solution [1-5]. Changes in the interfacial structure, or the structure created in solution at an

electrode/electrolyte interface, lead to changes in the local electric field. Electrochemical

reactions are strongly dependent on the local electric field due to the kinetic dependence on

electrode potential [6,7]. Because the electric field is dependent on the local structure and

distribution of charges around an electrode surface, atomistic characterization of this region can

give insight to the interplay between the interfacial structure and the achievable reaction kinetics

under defined electrochemical conditions.

Classical electrochemistry describes the interface on a macroscopic scale using different

models such as the Helmholtz double layer or Gouy-Chapman models [6]. These models differ on

the level of detail considered, but the phenomenological consideration is similar. The electrode is

considered to be a flat layer of charge with no atomistic distinction. Counterions specifically

adsorb to the electrode surface in a uniform fashion, creating a well defined electric field normal

to the electrode surface. As distance increases from the electrode surface, the descriptions vary.

However, all models essentially describe a region of high counterion concentration outside the

adsorbed layer which slowly approaches bulk solution values. The important notes are the well-

defined electric field normal to the electrode surface and a lack of atomistic distinction. Because

of model limitations, double layer theory cannot describe time and spatial variations in surface

2

potentials, ion distribution near the surface, or dynamic interfacial structure; all of which lead to

an inaccurate description of the electric field [8]. The electric field plays an important role in

surface phenomena, which cannot be predicted through classical means. It is unclear how the

double layer prediction changes in systems with different species or surface potential, and the

model cannot easily differentiate between ions that may be present. Though these models may be

able to describe some macroscopic phenomena, an atomistically precise picture of the

electrochemical interface is not obtained. Figures 1-1.a,b show the approximation of the surface

given by classical considerations [9]. A more realistic surface would describe surfaces with

atomistic variations in charges and an electric field that reflects the ordering of species near the

electrode surface [3].

(a) (b)

(c) (d)

Figure 1-1: Comparison of classical electrochemical interface to a more accurate description attainable

from simulations. (a) Idealized electrochemical interface with specifically adsorbed counterions [9]. (b)

Stern layer description gives well defined electric field in all regions. The vertical lines represent the inner

(left) and outer (right) Helmholtz planes, and horizontal line define the potential at the Helmholtz planes.

(c) MD simulation snapshot showing distinct atomistic charges on metal [3]. (d) Z-direction variation in

electric potential due to an applied cell voltage in an MD study [3].

Series1, 0, 10

Series1, 1, 6 Series1

, 1.5, 4.8 Series1

, 2, 4 Series1, 3, 3.2

Series1, 4, 2.7

Series1, 5, 2.4

Series1, 6, 2.2 Series1, 7, 2.1 Series1, 8, 2.1 Series1, 9, 2.1

Series2, 1, 20

Series2, 1, 0

Series3, 2, 20

Series3, 2, 0

Series4, -0.3,

10

Series4, 0, 10

Series5, -0.3, 6

Series5, 1, 6

-0.3 2, -0.3, 4

-0.3 2, 2, 4 P

ote

nti

al/a

.u.

Distance from surface/a.u

3

A Quantum Mechanics (QM) study using the Vienna Ab Initio Simulation (VASP)

package has shown the strong influence of cell potential on the reaction kinetics in the reduction

of molecular oxygen to water [7]. Yeh et al also showed that the inclusion of water in these

models to solvate the surface using a variety of solvation techniques leads to a favorable initial

step in the reaction mechanism for the reduction of oxygen at all relevant potentials. Figure 1-2

shows how potential strongly affects surface phenomena, in this case the surface replacement of

water with oxygen.

Figure 1-2: The Gibb‟s energy of reaction (eV) for an oxygen molecule replacing a water

molecular at a Pt(111) surface shows strong dependence on potential (V), water density, and

water layer thickness ((a) has 36H2O and (b) 24H2O) [7].

Despite its importance in surface kinetics calculations, the description of water using QM

methods is not representative of that expected experimentally. Many studies have shown QM to

produce a more ice-like structure for water rather than what is known for the liquid structure

because water-water interactions are not properly represented [70-73]. Additionally, there is

disagreement on the structure of water near an electrode surface in a charged system. As Figure

1-2 shows, there are significant differences in the reaction energies depending on the local water

structure. It is important to maintain an accurate electronic description of the system for reaction

energy purposes, but a broader description including dispersive forces is necessary to describe the

liquid phase behavior of water.

4

Atomistic modeling techniques

QM is not able to describe the dynamic fluctuations and average structures that define an

electrochemical interface. Because this method is typically used to minimize the electronic

energy of a system to find the lowest energy structure, there is no description of time, or how the

structure of a system may change with time. To consider system fluctuations at an atomistic level,

a higher scale model such as Molecular Dynamics (MD) is required.

Figure 1-3: Description of simulation scales from QM to continuum. The highlighted point is the

longer time and length scales achievable through MD compared to QM (electronic structure) [10].

Figure 1-3 shows that MD can reach time and length scales upwards of 4-5 orders of

magnitude greater than QM, and thus simulation sizes can be significantly larger [10]. The larger

dimensions are important for describing electrochemical interfaces. QM techniques are limited by

approximately 100-200 atoms. To ensure that a reasonable explanation in attained, it is necessary

to have large enough simulations to realize sufficient bulk solution away from the electrode. The

length scales required for our problem are on to 10-100 Å scale with a 100 ps scale needed to

5

reach diffusive solution behavior [1]. However, surface reactions cannot be accurately described

using MD, so some combination of QM and MD is required.

In MD simulations, forces acting on atoms calculated from interatomic potentials, or a

force field, are used to determine the acceleration of each particle in the system using Newton‟s

second law [12]. Forces are calculated from defined intermolecular potentials using Equation 1-1,

which say that the force acting on the particles is equal and opposite to the slope of the interaction

potential curve at a given separation distance. Then, Newton‟s second law is solved to determine

the acceleration in each direction on each particle using Equation 1-2.

( )

( )

Equation 1-1

( ) ( ) Equation 1-2

It is possible, through the use of MD, to reach considerably higher length scales than QM

methods due to the decrease in complexity of the calculations that are used, as well as to resolve

these systems in time. Because MD simulations require the iterative solution to all interatomic

pair force calculations, more complex expressions lead to longer simulation times. Thus, there is

an inherent balance of complexity and computational expense that must be considered in MD.

Force fields can be as complex or simple as the user desires, and in many cases more simple force

fields can be used when certain features of the system do not need to be considered. Therefore, it

must be decided a priori which features of the system are required in the simulation, and the force

field can be designed to yield those features.

6

Description of research plan

Our method will look to capture the physical phenomena occurring at electrochemical

surfaces and, specifically, how the interfacial structure varies with simulation conditions and its

subsequent effect on reaction kinetics. Because neither QM nor MD is capable of describing the

system of interest independently, a multi-scale simulation technique will be developed. Our goal

is to build a MD force field capable of accurately describing the interaction of solution species

with electrode surfaces to produce images of the electrolyte structure present at the electrode

interface. With this force-field in place, simulations will be performed on an electrochemical

system of interest to characterize the interfacial structure. Results from this work can be used to

study the effect of our simulated interfacial structure on reaction kinetics using QM methods.

Selecting a model system

As stated, electrochemical interfaces are present in many applications. To begin our force

field development, we chose a specific electrochemical system to analyze. We have chosen the

proton exchange membrane fuel cell (PEMFC) as our first system of study due to its high profile

and potential use in transportation applications.

Petroleum based fuels and other nonrenewable sources have powered a great deal of the

daily lives of people for the majority of the last century. However, the large scale use of these

fuels has led to a diminishing long-term supply and negative effects on the climate. Primarily due

to these reasons, there has been a surge in the amount of research conducted on alternative

devices for fuel conversion.

7

Figure 1-4: A proton exchange membrane fuel cell uses hydrogen fuel at the anode and oxygen at

the cathode and converts the chemical energy to electrical energy with a maximum potential of

1.23 V [13].

One of the most heavily researched of these devices is the PEMFC depicted in Figure 1-4

[13]. In general, a fuel cell is a device capable of converting energy released from chemical

reactions into electrical energy for use in some external device. A PEMFC uses the production of

water from hydrogen fuel and oxygen. The device is split into two half cells, each of which is

responsible for a half reaction. Hydrogen fuel enters the anode where H2 molecules are oxidized

at the electrode surface into two protons and electrons as in Equation 1-3. The protons are

transported to the cathode side of the cell through a proton exchange membrane, which is

generally a polyfluorosulfonic membrane such as Nafion®. Electrons travel through an external

circuit, powering a device connected to the cell, and to the cathode. At the cathode, oxygen is

reduced by the free protons and electrons producing water and some residual heat as byproducts,

shown in Equation 1-4. The maximum cell voltage is 1.23 V, based on the total reaction energy

for Equation 1-5 [14].

8

Equation 1-3

Equation 1-4

Equation 1-5

The PEMFC has gained a lot of popularity due to its clean byproducts, its ability to

operate at low temperatures, and its high energy density. However, there are a number of

problems preventing fuel cells from becoming economically feasible [15]. Dr. Steven Chu, the

United States Secretary of Energy, has pointed out that there are four main problems preventing

the use of PEMFC‟s, or a hydrogen based economy, from being realized. He points to a lack of an

adequate source of hydrogen gas, difficulties in storing large amounts of hydrogen, the inability

to effectively distribute gas from manufacturers to customers on the scale required, and

inadequacies in the fuel cells themselves [16]. Of the fuel cell inefficiencies, cathodic losses make

up approximately 70% of the total overpotential at typical operating conditions [17].

Due to our interest in building a simulation technique capable of describing

electrochemical interfaces and the level of interest PEM fuel cells, we choose the cathode half of

the PEMFC as our first system of interest.

Because MD simulations rely on user specified force fields, before designing a force field

to describe a system it is important to consider the phenomena associated with that system that

must be described accurately. Atomistic simulation cannot consider all phenomena associated

with a system with reasonable computational expense, so it is necessary to sacrifice the

description of certain aspects of the system to describe those that are truly important.

As described previously, cell potential and electric field have been shown to strongly

affect reaction kinetics for the surface reaction that take place in fuel cells, and the local electric

field is determined by the ordering of charges near the electrode surface. We therefore wish to

build a model that can accurately describe the region near a metal surface in electrochemical

9

systems. Because of the importance of local structure on the electric field, we require a model that

is capable of mimicking the structure of species present near the surface. We will use a method

capable of matching the bulk dynamics of water to allow for reasonable simulation times and

proper structural rearrangement. Methods which cannot reproduce accurate dynamic behavior

may hinder the diffusion of simulation species towards electrode surfaces. Additionally, as we are

most interested in structural behavior in the region near the electrode surface, short range

interactions between species in solution and electrode atoms must be properly accounted for.

Many MD simulations have been performed using plane-of-charge, image-charge or other

methods to describe the electrode surface, which over predict the short range interactions [5]. We

will describe the metal atoms in a manner which allows for atomistic resolution and accurately

captures short-range phenomena and structure.

Because designing a simulation of a full cathode is an intensive process, we will make

approximations on the system. We first choose to let water represent the bulk solution. Water is

the main product of the PEMFC reaction, as it is produced via the oxygen reduction reaction, and

is required in the cell during normal operation to aid both the transport of species to the electrode

surface and the transfer of protons through the membrane.

Figure 1-5: Proton transport through water is assisted by Grotthus hopping. Solid lines denote full

bonds and dotted line denote hydrogen bonds. The charged species moves from the “first oxygen”

to the “third oxygen” with no molecular rearrangement. (White-H, Red-O)

The description of water must include the ability to break and form bonds. Hydrogen

diffusion through aqueous solutions relies on a process known as the Grotthus mechanism by

10

which free protons can bond to a water molecule forming a hydronium ion [18]. A different

hydrogen atom can then dissociate from the ion and form a bond with another water molecule,

thereby moving the positive charge with minimal atomic rearrangement. The Grotthus

mechanism is shown in Figure 1-5, in which the hydronium ion starts on the first water molecule

and moves to the third by rearranging the O-H bonds from direct to hydrogen bonds.

Figure 1-6: Nafion is a polyfluorosulfonic structure with an active sulfate group on its side chain

[19].

Secondly, we need to describe the proton exchange membrane by some representative

structure. Nafion is a popular electrolyte because of its ability to allow rapid proton diffusion

through the cell at low temperatures and not to break down during operation. Side groups on the

Nafion structure include active sulfate groups, which may prevent the diffusion of reactants to the

surface in some cases, or even adsorb and block active sites from catalyzing the reaction. The

Nafion ® structure is approximated by adding sulfuric acid to the simulation box. Nafion ®, as a

polyfluorosulfonic membrane, has very active sulfate groups, as shown in Figure 1-6 and Nafion

® has similar properties to sulfuric acid in solution [19,20]. These groups have the ability to

dissociate protons via the O-H bond on the sulfate group, and serve as sites for “proton hopping”

through solution. An accurate description of aqueous sulfuric acid over an electrode surface can

give insight on the behavior of the membrane layer and the importance of the interplay between

the electrode and electrolyte, including the effect that it may have upon interfacial structure, and

therefore upon the reaction kinetics.

11

Our goal is to build a molecular dynamics force field to describe aqueous sulfuric acid

over a platinum (111) electrode surface, because it is the most common electrode in a PEMFC

[21-25]. The force field will be reactive on all O-H bonds to mimic the Grotthus mechanism by

which protons are conducted through aqueous solutions. Additionally, the force field will

accommodate fluctuating charges on metal atoms to allow them to react to local environments, as

well as produce atomistically distinct charges on electrode atoms and accurately describe short

range interactions. The MD simulations will be carried out on a time scale of hundreds of

picoseconds, due to the computational expense involved with accurately describing electrode

surfaces, and the short time steps needed to accommodate the reactive O-H bonds. From these

simulations, we will analyze the effect of various simulations parameters on the local structure

that is obtained near the electrode surface, and determine the variation in electric field to see how

this deviates from classical double layer models of electrochemical surfaces. Upon completion,

we will have the ability to analyze the structure of aqueous sulfuric acid in electrochemical

systems, and infer as to the impact that electrolyte membranes have on structuring and transport

at these interfaces.

The following chapters will describe computational methods that will be used for the

project. Force field development for MD work is described in detail, as results are strongly

dependent on the form of the force field used. We validate our choice to describe liquid water,

which is the bulk component in our simulations. Then, we describe the addition of sulfuric acid to

water to approximate the activity of the electrolyte in an electrochemical cell. Finally, the whole

system is simulated through the addition of a platinum electrode, and we discuss the findings

from our full scale electrochemical simulations.

12

Chapter 2

Molecular Dynamics Force Field Selection

For the atomistic simulation of an electrochemical system, a force field must be selected to

represent attraction among system components. Our system will be described in this section,

along with the force fields that will be used to describe the majority components. Some

modifications to literature force fields are required for our work, and they will be discussed in

subsequent chapters.

Selection of a force field for liquid water

Water is the most abundant resource on the planet, so it is unsurprising that water is also

one of the most heavily researched compounds in simulation work. Because of the important role

that water plays as a solvent in many systems, there have been water force fields developed for

various applications. In many cases, describing water as nonreactive and nonpolarizable is

enough to describe the phenomena of interest in a problem. Much of the work carried out in

molecular dynamics has described water in this manner. MD simulations have had a profound

effect on the understanding of processes taking place at the atomistic scale over picosecond time

periods.

In many biological applications, or other studies in which water is viewed as a bulk

solvent, use of a water model as simple as TIP3P is sufficient [26]. The Amber Force Field

provides users with the ability to solvate any simulation box using TIP3P water [27]. The TIP3P

model describes water using a 104.52° fixed molecular angle with 0.95 Å O-H bond length and

three fixed point charges of 0.417 e and -0.834 e for H and O, respectively [27].

13

Figure 2-1: Various TIPnP models describe the water molecule using a different number of

charge centers for different levels of accuracy with dipole moments and intermolecular

interactions [28].

Other similar models try to make improvements to these approximations by changing the

charge distributions or using additional local charges to more accurately represent the charge

distribution around the water molecule and include more interaction sites for the molecule. These

geometries are summarized in Figure 2-1. The common theme amongst these models, however, is

that they all view water as a rigid molecule with fixed charges that cannot be changed based upon

the other charges in the system [28].

A brief review of available models for liquid water

A full comparison of all available water models would be an exhaustive undertaking.

Countless water models have been suggested by research groups, independent models have been

developed for specific simulations, and many models simply do not perform well under any

desired range of conditions. A good review of common classical and polarizable water models is

undertaken by Baranyai and Kiss. In this paper the common TIP4P, TIP5P and SPC classical

models, as well as various modifications to those models are examined for geometric analysis,

dynamic behavior and other important simulation qualities [28]. The authors also test a select few

14

polarizable models, including the BSV, DC, SWM4, and GCP force fields. Improvements to early

water models have been made and bulk solution descriptions of water have become more

accurate. However, most models cannot accurately describe liquid water entirely, due to their

inability to describe water‟s self-ionization and its ability to assist in proton transport. A

schematic of water in common TIPnP water force fields is shown in Figure 2-1, including

molecular geometries, charge distributions and van der Waals radii.

Newer models have looked to improve the performance and transferability of polarized

water models [29-32]. The goal of these models has been to create a model capable of accurately

describing both small water clusters with similar accuracy to quantum mechanics calculations,

and to describe bulk water. Recently, Baranyai has developed a new charge-on-spring water

model with the goal of making calculations less expensive [29]. This model uses fixed molecular

geometries from experimental values. Like many of the current models, positive charges of

0.557e are placed on the hydrogen atoms with the corresponding negative charge of 1.114 e

placed on the axis of rotation, a distance of 0.24 Å from the oxygen atom toward the positively

charged hydrogen atoms, thus adding a fourth point to the water molecule. The important feature

of this work is the inclusion of the charge-on-spring. Similar models have been constructed, but

the idea is to allow the negative charge in the center of the molecule to fluctuate in space [26].

The charge is considered a massless entity, and after each molecular movement time step, the

position of this spring is equilibrated with respect to other charges in the system. Equilibration of

this spring essentially allows for lengthening and shortening of the dipole on water with respect to

surrounding molecules. Considerations are made to maintain the dipole of each molecule near its

experimental value of 1.855 D, but the position of the dipole can change and its value can

fluctuate slightly. An important point reached in Baranyai‟s conclusions is the necessity for a

minimum of four points in all water models to accurately describe the geometries of the

molecules and allow for charge polarization.

15

Figure 2-2: Increase in the size of biological system benchmarks historically, semi-log to show

the exponential increase in simulation speed/efficiency [33].

Despite using fixed geometry, nonreactive water in biological applications allows for

accurate representation of the phenomena of interest in certain systems. Many areas, however,

require water to take on a flexible geometry, or have the ability to break and form bonds. As

computer speeds have increased and molecular simulation has become a more powerful tool, its

range of applications has increased dramatically. With the availability of computational resources

and the speed with which computers can process information constantly increasing, the

complexity of simulations can increase, as evidenced in Figure 2-2 [33]. The ability to describe

liquid water in a more accurate way is important in some non-biological systems, including water

at electrochemical interfaces. We will next survey current reactive force fields for liquid water.

Modeling water using reactive bonds

Though they are less frequently used, many models exist to describe water in a reactive

nature [34-38]. Reactive molecular dynamics allows for bonds to break and reform between

atoms, leading to molecular dissociation and the formation of ionic species. In liquid water, bond

16

reactivity is especially important because proton mobility in solutions is dependent upon it.

Protons diffuse readily through solution via the Grotthus mechanism by which protons bond to

water molecules and can transfer positive charge through a cluster of water molecules by the

movement of bonds rather than atoms [39]. For the purposes of describing electrochemical

systems and, in particular, a proton exchange membrane fuel cell, various reactive models of

liquid water were considered.

Mathematically, the difference between a reactive and nonreactive force field lies within

the two-body potential between atoms [12]. In a nonreactive simulation, two-body interactions for

bonded atoms are described using a harmonic potential which is typically symmetric about the

equilibrium bond distance. Because the force acting between particles is equal to the slope of this

potential, atoms are always forced to their equilibrium bond lengths. Atoms that are too close

together cause a repulsive interaction and atoms that are too far apart are attracted to one another

so that the actual bond length oscillates about the equilibrium distance.

( )

Equation 2-1

[.

/

.

/

] Equation 2-2

In reactive simulations, the attractive portion of the potential, or long range interaction, is

altered. Rather than mirroring the repulsive force, the attractive force typically tapers off to zero,

and the magnitude of the slope decreases with increasing distance. Eventually, the attractive force

becomes weak enough that the atoms are no longer bonded to one another, and these atoms can

form bonds with different atoms in the simulation box. General forms for the two types are given

in Equations 2-1,2 and the difference between these methods, shown with a Lennard-Jones

potential for the reactive force, is graphed in Figure 2-3. In Equation 2-1, k is a force constant,

adjustable for the flexibility of the bond, r is the interatomic distance and r0 is the equilibrium

17

bond distance. In Equation 2-2, ε serves a similar role to k as a force constant which controls the

well depth, and σ is a bond distance parameter which controls the location of the well.

Figure 2-3: Comparison of reactive and non-reactive potentials used in MD simulations

The first reactive water model was developed by Frank Stillinger in 1975 and

subsequently revised in 1977 [34-36]. This model, known as the central force model (CFM),

relies solely on pair potentials between oxygen and hydrogen atoms to describe liquid water,

unlike most nonreactive models which contain an additional three-body term to account for the

bending angle of water. The three pair interactions each have a unique form. The bonded term for

O-H, as alluded to previously, is a non-harmonic potential with an attractive well at the

equilibrium bond distance and eventually tapers off to equal the electrostatic interaction. The O-O

interaction is purely repulsive at all distances and deviates only slightly from the electrostatic

repulsion. The H-H interaction is quite unique. To account for the appropriate bending angle in

H2O, there is a small well in the interaction at the H-H distance typical of water molecules. This

well is followed by a short attractive region meant to hold the proper molecular geometry, and

Harmonic, 0.05, 625.535

Harmonic, 0.1, 564.285

Harmonic, 0.15, 505.535

Harmonic, 0.2, 449.285

Harmonic, 0.25, 395.535

Harmonic, 0.3, 344.285

Harmonic, 0.35, 295.535

Harmonic, 0.4, 249.285

Harmonic, 0.45, 205.535

Harmonic, 0.5, 164.285

Harmonic, 0.55, 125.535 Harmonic, 0.6, 89.285

Harmonic, 0.65, 55.535 Harmonic, 0.7, 24.285 Harmonic,

0.75, -4.465 Harmonic, 0.8, -30.715 Harmonic, 0.85, -54.465 Harmonic, 0.9, -75.715 Harmonic, 0.95, -94.465 Harmonic, 1, -

110.715 Harmonic, 1.05, -124.465

Harmonic, 1.1, -135.715

Harmonic, 1.15, -144.465

Harmonic, 1.2, -150.715

Harmonic, 1.25, -154.465

Harmonic, 1.3, -155.715

Harmonic, 1.35, -154.465

Harmonic, 1.4, -150.715

Harmonic, 1.45, -144.465

Harmonic, 1.5, -135.715

Harmonic, 1.55, -124.465

Harmonic, 1.6, -110.715

Harmonic, 1.65, -94.465

Harmonic, 1.7, -75.715

Harmonic, 1.75, -54.465

Harmonic, 1.8, -30.715

Harmonic, 1.85, -4.465

Harmonic, 1.9, 24.285

Harmonic, 1.95, 55.535

Harmonic, 2, 89.285

Harmonic, 2.05, 125.535

Harmonic, 2.1, 164.285

Harmonic, 2.15, 205.535

Harmonic, 2.2, 249.285

Harmonic, 2.25, 295.535

Harmonic, 2.3, 344.285

Harmonic, 2.35, 395.535

Harmonic, 2.4, 449.285

Harmonic, 2.45, 505.535

Harmonic, 2.5, 564.285

Harmonic, 2.55, 625.535

Harmonic, 2.6, 689.285

Harmonic, 2.65, 755.535

Harmonic, 2.7, 824.285

Harmonic, 2.75, 895.535

Harmonic, 2.8, 969.285 Harmonic,

2.85, 1045.535


2.95, 1205.535

Harmonic, 3, 1289.285

Harmonic, 3.05,

1375.535


3.15, 1555.535


3.25, 1745.535


3.35, 1945.535


3.45, 2155.535


3.55, 2375.535


3.65, 2605.535


3.75, 2845.535


3.85, 3095.535


3.95, 3355.535

Harmonic, 4, 3489.285

Harmonic, 4.05,

3625.535


4.15, 3905.535


4.25, 4195.535


4.35, 4495.535


4.45, 4805.535


4.55, 5125.535


4.65, 5455.535


4.75, 5795.535


4.85, 6145.535


4.95, 6505.535

Harmonic, 5, 6689.285

Harmonic, 5.05,

6875.535


5.15, 7255.535


5.25, 7645.535


5.35, 8045.535


5.45, 8455.535


5.55, 8875.535


5.65, 9305.535


5.75, 9745.535


5.85, 10195.535

Harmonic, 5.9,

10424.285

Harmonic, 5.95,

10655.535

Harmonic, 6, 10889.285

Harmonic, 6.05,

11125.535

Harmonic, 6.1,

11364.285

Harmonic, 6.15,

11605.535

Harmonic, 6.2,

11849.285

Harmonic, 6.25,

12095.535

Harmonic, 6.3,

12344.285

Harmonic, 6.35,

12595.535

Harmonic, 6.4,

12849.285

Harmonic, 6.45,

13105.535

Harmonic, 6.5,

13364.285

Harmonic, 6.55,

13625.535

Harmonic, 6.6,

13889.285

Harmonic, 6.65,

14155.535

Harmonic, 6.7,

14424.285

Harmonic, 6.75,

14695.535

Harmonic, 6.8,

14969.285

Harmonic, 6.85,

15245.535

Harmonic, 6.9,

15524.285

Harmonic, 6.95,

15805.535

Harmonic, 7, 16089.285

Harmonic, 7.05,

16375.535

Harmonic, 7.1,

16664.285

Harmonic, 7.15,

16955.535

Harmonic, 7.2,

17249.285

Harmonic, 7.25,

17545.535

Harmonic, 7.3,

17844.285

Harmonic, 7.35,

18145.535

Harmonic, 7.4,

18449.285

Harmonic, 7.45,

18755.535

Harmonic, 7.5,

19064.285

Harmonic, 7.55,

19375.535

Harmonic, 7.6,

19689.285

Harmonic, 7.65,

20005.535

Harmonic, 7.7,

20324.285

Harmonic, 7.75,

20645.535

Harmonic, 7.8,

20969.285

Harmonic, 7.85,

21295.535

Harmonic, 7.9,

21624.285

Harmonic, 7.95,

21955.535

Harmonic, 8, 22289.285

Harmonic, 8.05,

22625.535

Lennard Jones, 0.05,

2.12576E+18

Lennard Jones, 0.1,

5.18985E+14


4E+12

Lennard Jones, 0.2,

1.26705E+11

Lennard Jones, 0.25, 8706941844

Lennard Jones, 0.3,

976499269.6


153555969.1

Lennard Jones, 0.4,

30922266.07


7520731.797

Lennard Jones, 0.5,

2122409.766


675289.5207

Lennard Jones, 0.6,

237076.8212


90300.77579

Lennard Jones, 0.7,

36795.15483


15835.84371

Lennard Jones, 0.8,

7104.527175


3270.022111

Lennard Jones, 0.9,

1508.377175


667.8117836

Lennard Jones, 1,

254.3056343 Lennard Jones, 1.05,

46.30796018

Lennard Jones, 1.1, -

59.55158672 Lennard

Jones, 1.15, -113.2325637


139.6488092

Lennard Jones, 1.25, -151.573308


155.7152916

Lennard Jones, 1.35, -155.6729309


153.4093041

Lennard Jones, 1.45, -150.0094917


146.0781448

Lennard Jones, 1.55, -141.9527418


137.8201911

Lennard Jones, 1.65, -133.7816859


129.8893233

Lennard Jones, 1.75, -126.1670469


122.6227527

Lennard Jones, 1.85, -119.2553397


116.0588374

Lennard Jones, 1.95, -113.0248206

Lennard Jones, 2, -

110.1438173

Lennard Jones, 2.05, -107.4061162


104.8022189

Lennard Jones, 2.15, -102.3230799

Lennard Jones, 2.2, -99.9602198

Lennard Jones, 2.25, -97.70576648


95.55245328

Lennard Jones, 2.35, -93.49359431


91.52304825

Lennard Jones, 2.45, -89.63517704


87.82480377

Lennard Jones, 2.55, -86.08717175

Lennard Jones, 2.6, -84.417906

Lennard Jones, 2.65, -82.81297774


81.26867196

Lennard Jones, 2.75, -79.78155812


78.34846364

Lennard Jones, 2.85, -76.96645026


75.63279267

Lennard Jones, 2.95, -74.34495943

Lennard Jones, 3, -

73.10059586

Lennard Jones, 3.05, -71.89750868


70.73365223

Lennard Jones, 3.15, -69.60711603


68.51611363

Lennard Jones, 3.25, -67.45897256

Lennard Jones, 3.3, -66.4341252

Lennard Jones, 3.35, -65.44010059


64.47551692

Lennard Jones, 3.45, -63.53907483


62.62955123

Lennard Jones, 3.55, -61.74579366


60.88671528

Lennard Jones, 3.65, -60.05129011


59.23854882

Lennard Jones, 3.75, -58.44757483


57.67750068

Lennard Jones, 3.85, -56.92750481


56.19680846

Lennard Jones, 3.95, -55.48467294

Lennard Jones, 4, -

54.79039704

Lennard Jones, 4.05, -54.11331466


53.45279261

Lennard Jones, 4.15, -52.80822863


52.17904943

Lennard Jones, 4.25, -51.56470903

Lennard Jones, 4.3, -50.9646871

Lennard Jones, 4.35, -50.37848746


49.80563672

Lennard Jones, 4.45, -49.24568292


48.69819439

Lennard Jones, 4.55, -48.16275856


47.63898095

Lennard Jones, 4.65, -47.12648415


46.62490694

Lennard Jones, 4.75, -46.13390339


45.65314208

Lennard Jones, 4.85, -45.18230534


44.72108851

Lennard Jones, 4.95, -44.26919935

Lennard Jones, 5, -

43.82635733

Lennard Jones, 5.05, -43.39229309


42.96674789

Lennard Jones, 5.15, -42.54947309


42.14022962

Lennard Jones, 5.25, -41.73878759


41.34492579

Lennard Jones, 5.35, -40.95843132


40.57909918

Lennard Jones, 5.45, -40.20673195


39.84113937

Lennard Jones, 5.55, -39.48213809

Lennard Jones, 5.6, -39.1295513

Lennard Jones, 5.65, -38.78320848


38.44294511

Lennard Jones, 5.75, -38.1086024


37.78002705

Lennard Jones, 5.85, -37.45707102


37.13959129

Lennard Jones, 5.95, -36.82744965

Lennard Jones, 6, -

36.52051253

Lennard Jones, 6.05, -36.21865077


35.92173945

Lennard Jones, 6.15, -35.62965772


35.34228865

Lennard Jones, 6.25, -35.05951903


34.78123927

Lennard Jones, 6.35, -34.50734323


34.23772811

Lennard Jones, 6.45, -33.97229426


33.71094515

Lennard Jones, 6.55, -33.45358716


33.20012954

Lennard Jones, 6.65, -32.95048425

Lennard Jones, 6.7, -32.7045659

Lennard Jones, 6.75, -32.46229161


32.22358098

Lennard Jones, 6.85, -31.9883559


31.75654059

Lennard Jones, 6.95, -31.52806141

Lennard Jones, 7, -

31.30284685

Lennard Jones, 7.05, -31.0808274


30.86193554

Lennard Jones, 7.15, -30.64610564


30.43327386

Lennard Jones, 7.25, -30.22337817


30.01635821

Lennard Jones, 7.35, -29.81215526


29.61071222

Lennard Jones, 7.45, -29.41197348


29.21588495

Lennard Jones, 7.55, -29.02239396


28.83144923

Lennard Jones, 7.65, -28.64300081


28.45700006

Lennard Jones, 7.75, -28.27339959


28.09215324

Lennard Jones, 7.85, -27.91321601


27.73654404

Lennard Jones, 7.95, -27.56209458

Lennard Jones, 8, -

27.38982596

Lennard Jones, 8.05, -27.21969752

Bo

nd

En

erg

y (k

cal/

mo

l)

Bond Distance (Angstrom)

Harmonic

Lennard Jones

18

gradually reaches the pure electrostatic repulsion. The potentials, including electrostatic

interactions, are given in Equations 2-3 (O-O), 2-4 (H-H), and 2-5 (O-H), and are plotted in

Figure 2-4.

, ( )-

, ( )-

Equation 2-3

, ( )- , ( ) - Equation 2-4

, ( ) - , ( ) - Equation 2-5

Figure 2-4: Pair potentials used to describe liquid water in the revised central force model

The same group went on to develop a more complex model known as the polarization

model (PM) for liquid water in 1978 [37]. As an extension of the CFM, the PM contains many of

O-O, 0.7, 388554.9501 O-O, 0.7175, 322896.7206

O-O, 0.7354375, 268337.774

O-O, 0.753823438, 223001.7119

O-O, 0.772669023, 185329.3543

O-O, 0.791985749, 154025.1121

O-O, 0.811785393, 128012.4246

O-O, 0.832080028, 106396.7312

O-O, 0.852882028, 88434.70307

O-O, 0.874204079, 73508.67633

O-O, 0.896059181, 61105.40731

O-O, 0.91846066, 50798.41968

O-O, 0.941422177, 42233.33572

O-O, 0.964957731, 35115.68756

O-O, 0.989081675, 29200.78896

O-O, 1.013808717, 24285.31939

O-O, 1.039153934, 20200.33084

O-O, 1.065132783, 16805.43689

O-O, 1.091761102, 13983.98421

O-O, 1.11905513, 11639.04025

O-O, 1.147031508, 9690.059358

O-O, 1.175707296, 8070.112422

O-O, 1.205099978, 6723.584925

O-O, 1.235227478, 5604.264125

O-O, 1.266108165, 4673.749622

O-O, 1.297760869, 3900.132631

O-O, 1.330204891, 3256.898532

O-O, 1.363460013, 2722.014952

O-O, 1.397546513, 2277.174018

O-O, 1.432485176, 1907.162701

O-O, 1.468297305, 1599.339622

O-O, 1.505004738, 1343.200299

O-O, 1.542629856, 1130.015891

O-O, 1.581195603, 952.5330227

O-O, 1.620725493, 804.724349

O-O, 1.66124363, 681.5812898

O-O, 1.702774721, 578.9418062

O-O, 1.745344089, 493.3472909

O-O, 1.788977691, 421.9236522

O-O, 1.833702134, 362.2825016

O-O, 1.879544687, 312.4390463

O-O, 1.926533304, 270.7438616

O-O, 1.974696637, 235.8261977

O-O, 2.024064053, 206.5468696

O-O, 2.074665654,

181.95911

O-O, 2.126532295, 161.2760385

O-O, 2.179695603, 143.8436273

O-O, 2.234187993, 129.1182334

O-O, 2.290042692, 116.6479235

O-O, 2.34729376, 106.0569495

O-O, 2.405976104, 97.03284179

O-O, 2.466125506, 89.31567719

O-O, 2.527778644, 82.68915941

O-O, 2.59097311, 76.97321273

O-O, 2.655747438, 72.01784812

O-O, 2.722141124, 67.69810739

O-O, 2.790194652, 63.90992806

O-O, 2.859949518, 60.56679541

O-O, 2.931448256, 57.5970554

O-O, 3.004734463, 54.94175267

O-O, 3.079852824, 52.55283506

O-O, 3.156849145, 50.39154651

O-O, 3.235770373, 48.42683532

O-O, 3.316664633, 46.63366232

O-O, 3.399581249, 44.99121234

O-O, 3.48457078, 43.48116999

O-O, 3.571685049, 42.08635265

O-O, 3.660977175, 40.79001213

O-O, 3.752501605, 39.57596761

O-O, 3.846314145, 38.42944536

O-O, 3.942471999, 37.33820662

O-O, 4.041033799, 36.29341509

O-O, 4.142059644, 35.28982429

O-O, 4.245611135, 34.32519307

O-O, 4.351751413, 33.39917417

O-O, 4.460545198, 32.51208328

O-O, 4.572058828, 31.66389448

O-O, 4.686360299, 30.85362312

O-O, 4.803519306, 30.0790928

O-O, 4.923607289, 29.33701311

O-O, 5.046697471, 28.62329269

O-O, 5.172864908, 27.93351606

O-O, 5.302186531, 27.2634909

O-O, 5.434741194, 26.60974342

O-O, 5.570609724,

25.96984

O-O, 5.709874967, 25.34246119

O-O, 5.852621841,

24.727235

O-O, 5.998937387, 24.12441327

O-O, 6.148910822, 23.53451214

O-O, 6.302633593, 22.95802274

O-O, 6.460199432, 22.39524653

O-O, 6.621704418, 21.84625155

O-O, 6.787247029, 21.31090836

O-O, 6.956928204, 20.78895686

O-O, 7.130851409, 20.2800691

O-O, 7.309122695, 19.78389281

O-O, 7.491850762, 19.30007543

O-O, 7.679147031, 18.82827458

O-O, 7.871125707, 18.36816131

H-H, 0.7, 69.3937077 H-H, 0.7175, 68.08484738

H-H, 0.7354375,

66.79572337

H-H, 0.753823438, 65.52326148

H-H, 0.772669023, 64.26396483

H-H, 0.791985749, 63.01385216

H-H, 0.811785393, 61.76839694

H-H, 0.832080028, 60.52247203

H-H, 0.852882028, 59.27030643

H-H, 0.874204079, 58.0054636

H-H, 0.896059181, 56.72085309

H-H, 0.91846066, 55.40879094

H-H, 0.941422177, 54.06112713

H-H, 0.964957731, 52.66946129

H-H, 0.989081675, 51.22546957

H-H, 1.013808717, 49.72136527

H-H, 1.039153934, 48.1505124

H-H, 1.065132783, 46.50820364

H-H, 1.091761102, 44.79259983

H-H, 1.11905513, 43.00580739

H-H, 1.147031508, 41.15504093

H-H, 1.175707296, 39.25378171

H-H, 1.205099978, 37.32280176

H-H, 1.235227478, 35.39088141

H-H, 1.266108165, 33.49501484

H-H, 1.297760869, 31.67988266

H-H, 1.330204891, 29.99638698

H-H, 1.363460013, 28.49910447

H-H, 1.397546513, 27.24262625

H-H, 1.432485176, 26.27692035

H-H, 1.468297305, 25.64206121

H-H, 1.505004738, 25.36289137

H-H, 1.542629856, 25.44436704

H-H, 1.581195603, 25.86843416

H-H, 1.620725493, 26.59322761

H-H, 1.66124363, 27.55514459

H-H, 1.702774721, 28.67391483

H-H, 1.745344089, 29.86021699

H-H, 1.788977691, 31.0247027

H-H, 1.833702134, 32.08609085

H-H, 1.879544687, 32.97074746

H-H, 1.926533304, 33.56144869

H-H, 1.974696637, 33.32747168

H-H, 2.024064053, 29.73314215

H-H, 2.074665654, 21.41586306

H-H, 2.126532295, 17.26449239

H-H, 2.179695603, 16.3756822

H-H, 2.234187993, 16.02339209

H-H, 2.290042692, 15.69916869

H-H, 2.34729376, 15.35619197

H-H, 2.405976104, 15.00201261

H-H, 2.466125506, 14.64558256

H-H, 2.527778644, 14.29243111

H-H, 2.59097311, 13.94543308

H-H, 2.655747438, 13.60587649

H-H, 2.722141124, 13.27421495

H-H, 2.790194652, 12.95050987

H-H, 2.859949518, 12.63465886

H-H, 2.931448256, 12.32650007

H-H, 3.004734463, 12.0258545

H-H, 3.079852824, 11.73254112

H-H, 3.156849145, 11.44638161

H-H, 3.235770373, 11.16720157

H-H, 3.316664633, 10.8948308

H-H, 3.399581249, 10.62910322

H-H, 3.48457078, 10.3698568

H-H, 3.571685049, 10.11693346

H-H, 3.660977175, 9.87017899

H-H, 3.752501605, 9.629442917

H-H, 3.846314145, 9.394578456

H-H, 3.942471999, 9.165442396

H-H, 4.041033799, 8.94189502

H-H, 4.142059644, 8.72380002

H-H, 4.245611135, 8.511024409

H-H, 4.351751413, 8.303438448

H-H, 4.460545198, 8.100915559

H-H, 4.572058828, 7.903332253

H-H, 4.686360299, 7.710568052

H-H, 4.803519306, 7.522505416

H-H, 4.923607289, 7.339029674

H-H, 5.046697471, 7.160028951

H-H, 5.172864908, 6.985394098

H-H, 5.302186531, 6.815018632

H-H, 5.434741194, 6.648798666

H-H, 5.570609724, 6.486632845

H-H, 5.709874967, 6.328422287

H-H, 5.852621841, 6.174070524

H-H, 5.998937387, 6.023483438

H-H, 6.148910822, 5.876569208

H-H, 6.302633593, 5.733238252

H-H, 6.460199432, 5.593403173

H-H, 6.621704418, 5.456978705

H-H, 6.787247029, 5.323881663

H-H, 6.956928204, 5.194030891

H-H, 7.130851409, 5.067347211

H-H, 7.309122695, 4.943753376

H-H, 7.491850762, 4.823174026

H-H, 7.679147031, 4.705535635

H-H, 7.871125707, 4.590766473

O-H, 0.7, 48.61541352

O-H, 0.7175, 17.43188532

O-H, 0.7354375, -6.964879732

O-H, 0.753823438, -25.96490954

O-H, 0.772669023, -40.67549595

O-H, 0.791985749, -51.97863321

O-H, 0.811785393, -60.57675801

O-H, 0.832080028, -67.02912915

O-H, 0.852882028, -71.78065079

O-H, 0.874204079, -75.18442176

O-H, 0.896059181, -77.51862694

O-H, 0.91846066, -78.99719237

O-H, 0.941422177, -79.77102256

O-H, 0.964957731, -79.91125063

O-H, 0.989081675, -79.36096217

O-H, 1.013808717, -77.87996718

O-H, 1.039153934, -75.22858424

O-H, 1.065132783, -71.88440014

O-H, 1.091761102, -68.98957668

O-H, 1.11905513, -66.94883766

O-H, 1.147031508, -65.43012398

O-H, 1.175707296, -64.11295124

O-H, 1.205099978, -62.85207206

O-H, 1.235227478, -61.59996126

O-H, 1.266108165, -60.34645074

O-H, 1.297760869, -59.09312335

O-H, 1.330204891, -57.84430748

O-H, 1.363460013, -56.60426248

O-H, 1.397546513, -55.37644568

O-H, 1.432485176, -54.16342098

O-H, 1.468297305, -52.96693594

O-H, 1.505004738, -51.78802107

O-H, 1.542629856, -50.62707015

O-H, 1.581195603, -49.48389269

O-H, 1.620725493, -48.35773896

O-H, 1.66124363, -47.24730151

O-H, 1.702774721, -46.15069992

O-H, 1.745344089, -45.06545987

O-H, 1.788977691, -43.98850593

O-H, 1.833702134, -42.91619901

O-H, 1.879544687, -41.84446576

O-H, 1.926533304, -40.76908258

O-H, 1.974696637, -39.68618186

O-H, 2.024064053, -38.59302197

O-H, 2.074665654, -37.48898006

O-H, 2.126532295, -36.37657594

O-H, 2.179695603, -35.26215814

O-H, 2.234187993, -34.15579897

O-H, 2.290042692, -33.07010899

O-H, 2.34729376, -

32.018126

O-H, 2.405976104, -31.01093575

O-H, 2.466125506, -30.05587245

O-H, 2.527778644, -29.15585288

O-H, 2.59097311, -28.30983871

O-H, 2.655747438, -27.51398908

O-H, 2.722141124, -26.76296779

O-H, 2.790194652, -26.05103072

O-H, 2.859949518, -25.37274778

O-H, 2.931448256, -24.7233796

O-H, 3.004734463, -24.09900207

O-H, 3.079852824, -23.49647886

O-H, 3.156849145, -22.9133598

O-H, 3.235770373, -22.34775529

O-H, 3.316664633, -21.79821422

O-H, 3.399581249, -21.26361801

O-H, 3.48457078, -20.74309459

O-H, 3.571685049, -20.23595145

O-H, 3.660977175, -19.74162523

O-H, 3.752501605, -19.25964463

O-H, 3.846314145, -18.78960371

O-H, 3.942471999, -18.33114291

O-H, 4.041033799, -17.88393582

O-H, 4.142059644, -17.44768008

O-H, 4.245611135, -17.02209112

O-H, 4.351751413, -16.60689802

O-H, 4.460545198, -16.20184069

O-H, 4.572058828, -15.80666801

O-H, 4.686360299, -15.42113658

O-H, 4.803519306, -15.04500994

O-H, 4.923607289, -14.67805795

O-H, 5.046697471, -14.32005642

O-H, 5.172864908, -13.97078683

O-H, 5.302186531, -13.63003607

O-H, 5.434741194, -13.29759633

O-H, 5.570609724, -12.97326487

O-H, 5.709874967, -12.65684391

O-H, 5.852621841, -12.34814051

O-H, 5.998937387, -12.04696645

O-H, 6.148910822, -11.75313807

O-H, 6.302633593, -11.46647623

O-H, 6.460199432, -11.18680613

O-H, 6.621704418, -10.91395724

O-H, 6.787247029, -10.64776319

O-H, 6.956928204, -10.38806167

O-H, 7.130851409, -10.13469433

O-H, 7.309122695, -9.887506682

O-H, 7.491850762, -9.646347995

O-H, 7.679147031, -9.411071225

O-H, 7.871125707, -9.18153291

Ene

rgy

(kca

l/m

ol)

Distance (A)

O-O

H-H

O-H

19

the same terms. The PM consists of two different sets of potential forms. The first term, Φ1, is the

summation of pair-wise additive terms, which is the foundation of the CFM. However, PM alters

the first term in each equation to model the atoms using full atomic charges and also includes a

second term, Φ2, which is an electrostatic term that accounts for polarizability of particles. Within

the electrostatic polarization description is a screening function which softens the short range

interactions. Partial charges are used in most water models because full charges over-predict the

value of the dipole moment of water molecules. The PM very accurately represents many features

which cannot be described well by CFM such as bond stretching frequencies, bond energies, and

movement of charges. The model also is the only reactive water model to our knowledge that can

accurately reproduce reaction energies of forming water‟s bonds. However, the PM struggles with

structural information on large scales because it was designed for small water clusters, and thus

cannot be used to simulate the system sizes in which we are interested. Water‟s diffusion

coefficient is also greatly under predicted, and the PM leads to essentially stagnant behavior as

demonstrated by Erin Boland within our research group [40], and has not been used for bulk

water simulations to our knowledge.

The recent model from D‟Aguanno et al. was created using recursive fitting [38]. This

group used experimental radial distribution functions for water at three different sets of

experimental conditions; A – 268 K and 27 MPa, B – 298 K and 0.1 MPa, and C – 423 K and 10

MPa. The model maintains the central force description via the use of only pair-wise additive

potentials between atomic species to describe water. Hofmann demonstrated the existence of

proton transfer events predicted by the model for liquid water over a non-reactive, DREIDING

description of Nafion ® [41-42]. The DREIDING force field is a generic non-reactive force field

developed by Goddard III et al. for molecular simulations. Its details are not relevant to this

thesis, and can be found in reference 42. The reactive water model of D‟Aguanno et al. showed

20

good behavior in terms of structure at different temperatures, but was otherwise similar to the

CFM from which it was derived.

Another reactive molecular dynamics model is ReaxFF, designed by Goddard III et al

[43]. This model was originally designed as a reactive model for hydrocarbons, and has been

recently used to describe metals, mixed oxide surfaces and some biological applications [44-48].

ReaxFF is a variable bond order model parameterized from QM calculations. The force field is

very complex, and includes terms to describe bonding interactions for stretching, bending and

torsion; bond under and over-coordination terms to ensure proper bond distances for given bond

orders and overall bond order conservation; valence terms, conjugation energy terms, Coulombic

and van der Waals interactions, as well as energy penalty terms [43]. Though this force field is

precisely parameterized, it has not been shown to accurately depict liquid water, and the level of

parameterization required to add new species to the simulation system is very time consuming

and cannot be done without the force field creators.

Ab initio molecular dynamics

Another interesting method that has been used to describe water and aqueous solutions is

ab initio MD (AIMD). The field of ab initio MD began in 1985 through the work of Car and

Parrinello with the motivation to create a unified method of performing MD simulations without

the need to parameterize force fields [49]. AIMD is particularly useful for simulations involving

many different atom types or simulations in which the electronic structure of atoms is expected to

change drastically [50].

The basic principles of AIMD are relatively straightforward. In classical MD, all particles

are considered classically and force-fields are input to the simulations between these particles. In

ab initio calculations, all particles are considered with QM algorithms [50]. That is, the electronic

21

wave function is minimized for the system through the solution of the Schrodinger wave

equation. AIMD bridges the gap between the two. Nuclei in the system are considered classically,

whereas the forces between atoms are calculated based upon the electronic wave functions. This

method requires a separation of the nuclear and electronic terms in the time-dependent

Schrodinger equation. The Born-Oppenheimer approximation is therefore made, assuming that

electron distribution occurs on a much faster time scale than molecular or nuclear rearrangement.

Though AIMD is considered to be more accurate than MD in determining the forces

between atoms, it is very computationally expensive and parameters cannot be adjusted to

describe phenomena which are not accurately captured by the specific ab initio methods applied.

Because large length scales are required to generate an accurate picture of an electrochemical

interface due to the need to simulate large enough systems to reach bulk solution behavior away

from the electrode, AIMD is considered too expensive for these systems [1]. An additional

concern is the structure of water predicted by these methods. QM techniques struggle with

describing liquid water, and produce a more ice-like structure for water. Because AIMD relies

upon QM calculations for electronic structure, the bulk water structure may be misrepresented, as

shown by Galli et al [71,72]. A recent AIMD study of aqueous sulfuric acid found the diffusion

coefficient of water to be 0.05x10-5

cm2/s, which is significantly below that of the experimental

value of 2.3x10-5

cm2/s [51]. The diffusion coefficients of various water models from each class

of MD simulations are shown in Table 2-1 [52]. Non-reactive MD is able to reproduce liquid

dynamics quite accurately, but does not meet our requirements. Of the reactive models

considered, CFM most accurately predicts the liquid water self-diffusion coefficient. For

comparison, experimental values of the diffusion coefficient are given for each study. Differences

in these values from one study to the next are due to different simulation temperatures, for which

the diffusion coefficient is observed to change experimentally.

22

Table 2-1: Comparison of the diffusion coefficient for various water models [52]

Force Field Class

Diffusion Coefficient

(Experimental Value)

(x105 cm

2/s)

SPC Non-reactive MD 4.2 (2.3)

SPC/E Non-reactive MD 2.7 (2.3)

TIP3P Non-reactive MD 5.4 (2.3)

Central Force Model (1) Reactive MD 0.73 (2.1)

Central Force Model (2) Reactive MD 1.12 (2.4)

Polarization Model Reactive, polarizable MD ~0 (2.3)

Ikeshoji et al AIMD ab initio MD 0.05 (2.3)

Going forward, we choose the revised central force model of liquid water, developed by

Stillinger and Rahman, to describe water in our simulations [36]. We base this choice on the

ability of this method to describe bond breaking and forming events, which is a key feature in

systems in which proton transfer occurs, as well as its ability to accurately describe liquid water‟s

structure and diffusion coefficient. Because we are developing a method to describe the dynamic

structure near an electrical interface, we feel that structural and dynamic accuracy are requisite to

any model used in our simulations. The task of incorporating sulfuric acid into CFM is described

in Chapter 3.

Describing an electrode surface with atomistic resolution

With CFM being used to describe water, which will be the most prevalent species in our

electrochemical simulations, we next choose a method of describing the electrode surface.

Because the region of interest is that close to the electrode surface, the description must

accurately capture short range phenomena. For this reason, typical electrode simulations that view

the metal surface as a slab of charge or use image-charge techniques cannot be used. We require a

23

method capable of describing a metal surface with atomistic distinction, and with the ability to

influence the charges on atoms in response to local environment so that short range interactions

are not over predicted.

Early simulations of electrochemical systems

Some of the earliest use of molecular dynamics for the use of electrochemical systems

was performed by Spohr [53] and Philpott and Glosli [54]. At the time, computational power was

not great enough to provide atomistically distinct electrode surfaces in the manner in which we

wish to consider them; that is with polarizable electron clouds that can react to local

environments.

Spohr studied a 2.2 molal solution of NaCl in water over a metallic surface. The water in

this model is described using the SPC/E rigid water model [55]. In his study, an image-charge

consideration was adopted for the metal surface, and the identity of the metal was insignificant.

The image charge method allows the metal to interact differently with solution species at different

distances from the metal. Figure 2-4 shows how the method is implemented. If a charge

approaches a metal surface, a charge of equal but opposite magnitude is envisioned as an image

to the solution charge beneath the metal surface. The separation distance of these charges is twice

that of the separation distance between the real charge and the metal surface. This method can

reproduce long range interactions between a metal surface and a solution charge, but because the

interaction energy is inversely proportional to the square of the distance between charges, at short

ranges this method can severely over predict interaction energies. There is no means by which to

screen this interaction at short distances. However, Sphor was able to show that the classical

electrochemical models suffer from a lack of atomic description and cannot properly predict the

24

charge distribution near a surface due to atomic layering that cannot be described

macroscopically.

Figure 2-4: The image-charge representation of interactions between charged species and

electrode surfaces

Philpott used a plane of charge method for his electrode surface description. In this

method, NaCl salt is added to a SPC/E water box over a metal surface. To charge the simulation,

excess positive charges are added to the box, and the metal surface takes on an excess negative

charge to maintain a neutral solution. The model has similarities to the image-charge method, but

does not provide the same level of atomistic distinction. Rather than image charges being

envisioned for solution charges, an image plane of charge is placed at the center of the metal

nuclei to interact with solution charges. Forces between the charges and metal surface are then

calculated using both a dispersive interaction term, similar to that of a Lennard-Jones interaction,

25

and an electrostatic terms between the charge and metal plane of charge. This model also suffers

from inaccurate predictions of short range interactions. Despite lacking the precise description of

the metal surface we desire, both of these studies motivate the need to describe electrode surfaces

using methods that allow for atomistic resolution of the electrode/electrolyte interface. We wish

to use a method that provides for a more careful consideration of short range interactions to

obtain a more accurate description of the electric field at this interface.

Electrode charge dynamics

Electrode charge dynamics (ECD) is a method developed by Wheeler et al. which allows

for electronic polarizability of all metal atoms to mimic the charge fluctuation response these

atoms have to changes in local environments. Whereas previous simulations consider a flat plane

of charge, this method gives atomistic distinction to electrode atoms.

There are two main drawbacks to previous methods. First, these methods cannot give

atomistic distinction. Any point on the surface is considered equal with an image charge located

as a certain distance beneath the entire surface to respond to local charges. Second, because the

underlying equation is Poisson‟s equation, forces between the charge and image charge scale with

d-2

, where d represents the distance between them (or twice the distance between the charge and

metal surface). At short separation distances, this force becomes exaggerated and the description

of a local structure near an electrode surface can be dramatically affected by inaccuracies in the

short range interactions.

To correct these shortcomings, Wheeler‟s method is capable of essentially reproducing

the image-charge description at long ranges, and obtaining an accurate short range description

with atomistic resolution of the metal surface. The surface atoms are described in two parts. Each

26

metal atom has a positive, fixed charged center to represent the nucleus and core electrons as

point charges. The valence electrons are then described as a Gaussian distribution of negative

charge about the center. This Gaussian region of valence electrons can change its overall charge

in response to charges near the surface. If one envisions the surface of the electrode, the nucleus

and core electrons are within the surface at a fixed position with an overall positive charge. In a

neutral environment, the valence electrons can be spread evenly about a given center. Figure 2-5

shows what this description might look like in 2-D for a single surface atom.

Figure 2-5: ECD description of electrode atoms as a positive core surrounded by a Gaussian

distribution of negative charge representing the valence electrons. In this image, the horizontal

line can be thought of as the electrode surface. Nuclei are beneath the surface and valence

electrons extend away from the surface in a Gaussian distribution [5].

Incorporating ECD into a molecular dynamics simulation

The two mathematical requirements of the method, given in Equations 2-6, are that the

valence electron charge on each metal atom, qiv, cannot be greater than zero and that the sum of

all valence electron and core charges, qic, must equal the fixed total charge of the metal slab, Qtotal.

That is, a metal atom may essentially give up all valence electrons but cannot lose any core

electrons. Equation 2-6.b ensures that no electron density can be exchanged with the electrolyte.

This model does not have the ability to describe redox reactions at the electrode surface. The

27

actual valence charge on a metal atom at any point in time determines the size of the “electron

cloud.” This cloud is defined by a distribution function given in Equation 2-7, where ρ is the

probability density of electrons at a point in space, r, near a metal atom, i. The parameter γ is

defined as an inverse-width parameter related to the Fermi wave vector.

Equation 2-6.a

∑(

)

Equation 2-6.b

( ) (

) Equation 2-7

,∑(

) - ∑

Equation 2-8

∑∑

∑∑

∑∑

∑

Equation 2-9

( )

( )

Equation 2-10

During the simulation, ECD solves for the valence electron charge on each metal atom at

every time step to minimize the Coulombic potential energy of the metal. Because this charge

varies in response to local charges, the energy associated with all diffuse charge interaction is

minimized to determine the favored electronic configuration. This minimization is performed

using the Lagrangian shown in Equation 2-8, and μ and λ are solved to minimize the function.

The function U, given in Equation 2-9, defines the total system energy. The terms Cij and C*ij are

error functions designed to describe the overlap of their respective integrals (Equation 2-10), Φiset

is a term that allows a user specified charge difference over the electrode, and Uext consists of the

interaction of the electrode with non-electrode charges, such as those of the electrolyte. At any

28

given time, all values in the energy terms are fixed but for the value of the diffuse charge. This

charge is optimized for each atom in the system, and repeated as the local structure changes.

To incorporate ECD with the CFM description of water, force-field parameterization

based on QM calculations was performed in collaboration with Kuan-Yu Yeh. A small platinum

cluster arranged in a (111) surface geometry was used to represent the electrode. A water

molecule was placed above the surface in different orientations (with the hydrogen atoms toward

the surface, the plane of the molecule parallel to the surface, and the hydrogen atoms away from

the surface). For each orientation, QM energies were obtained at various distances from the

electrode. Then, using a genetic algorithm to minimize the error for a selected functional form,

parameters were fit to a MD function to match the energy vs. distance QM data. The functional

forms used were those reported by Wheeler et al. for the interaction of water with a Cu(111)

cluster. This potential is given in Equation 2-10.

( ) , ( * ( )+)

- Equation 2-10

Parameterization of our system, consisting of aqueous sulfuric acid over a platinum (111)

electrode surface with ECD, will be discussed in the final chapter of this work. We will next

describe the parameterization of CFM to include sulfuric acid to produce a novel description of

aqueous sulfuric acid including the ability to break and form bonds to simulate deprotonating acid

groups. After designing a model capable of describing aqueous sulfuric acid, we will be able to

move on to simulate that model in an electrochemical environment to approximate the behavior

of the electrode/electrolyte interface of a PEMFC cathode.

29

Chapter 3

Molecular Dynamics Simulation of Aqueous Sulfuric Acid

In proton exchange membrane fuel cells (PEMFC), the proton conducting polymer often

used is Nafion ®. Nafion is a polyfluorosulfonic membrane with high proton conductivity at low

temperatures. PEMFCs typically operate at or above room temperature, with maximum operating

temperatures near 80 °C [15]. At temperatures higher than this, water produced by the oxygen

reduction reaction (ORR) may begin to vaporize and the fuel cell no longer operates correctly.

Nafion ® will also begin to degrade around 90 °C, but it remains thermally stable at temperature

of interest to the system [56].

Approximating the behavior of Nafion with sulfuric acid

Because molecular dynamics (MD) simulations require parameterization for all atomic

pairs, it is a very long process to directly build a full simulation of a PEMFC cathode including

reacting species, water byproduct, metal slab and proton exchange membrane. For this thesis, we

approximate the behavior of Nafion ® through the simulation of aqueous sulfuric acid. The acidic

group on the end of the side chain on Nafion ® is SO3H, seen in Figure 1-6. This acid group

contains free oxygen atoms that can act as proton hopping sites to assist in the transport of

protons through the membrane. In addition to mimicking the proton exchange behavior, both

sulfuric acid and Nafion ® are acidic in nature and will donate protons to solution [20].

Finally, sulfur and sulfuric acid are known to be strong adsorbates in surface studies.

Markovic et al showed the activity of the ORR in rotating disk electrode experiments over a

platinum surface in sulfuric acid to be structure dependent [57]. The activity over a Pt(111)

surface was very low due to the adsorption of bisulfate anions deactivating the catalyst surface.

30

Though other surfaces may not be as active for bisulfate adsorption, the (111) surface cut is the

lowest energy surface and most likely to be exposed. Ishikawa et al. used QM calculations to

show that at potentials of interest, sulfuric acid is a strong adsorbate over the Pt(111) surface [58].

Adsorption begins at ~+0.40 V(NHE) and gets stronger with increased potential (the typical

PEMFC operating potential is ~+0.8 V). The bulk of the membrane, if it gets too near the

electrode surface, may also prohibit the diffusion of gaseous oxygen to the surface. Through the

simulation of aqueous sulfuric acid in an electrochemical environment, we hope to shed light on

the activity of a proton exchange membrane in a similar electrochemical environment. The results

from this work will provide a unique electrochemical description of aqueous sulfuric acid.

Structural characterization of the sulfuric acid molecule

To include sulfuric acid in our CFM description of water, our first consideration is the

structure of the H2SO4 molecule. There is little very structural information available on

experimental studies of sulfuric acid. In studies that have provided structural data, the data given

are of vibrational information. Thus, to determine the proper structure of the H2SO4 molecule,

quantum mechanical (QM) calculations were used to find the lowest energy electronic

configuration. All QM calculations were performed using the Vienna ab-initio simulation

package (VASP), developed at the Institute for Material Physics at the University of Vienna [59-

61]. For the study of a single H2SO4 molecule, the projected augmented wave method was used

for electron/ion interaction. A 400 eV cutoff for the plane-wave basis set was used and the

Brilloiun zone sampling was performed using the gamma point only [62]. The structure was

considered optimized when the forces acting on all atoms was less than 0.05 eV/Å.

31

Figure 3-1: Geometric analysis of H2SO4 from VASP calculations

There are two distinct bond distances for the S-O bonds in sulfuric acid. Those oxygen

atoms which bond protons have a weaker interaction with the central sulfur atom, and thus a

longer bond. This bond, denoted S-OH has a distance of 1.61 Å. The oxygen to which there is no

proton bonded has a shorter equilibrium bond distance with the sulfur atom and a formal double

bond. The bond distance for the “free” oxygen, denoted S-OF was calculated to be 1.43 Å. The

equilibrium bond distance for the H-OH bond is 0.979 Å.

The SO4 group does not have a tetrahedral geometry because the protons have an

interaction that attracts a second neighbor oxygen atom. The OF–S-OF angle is 124.3°, and that for

the OH-S-OH group is 101.8°. The two other types of angles seen are those for OF-S-OH for which

the hydrogen is angled toward the free oxygen and that for which the hydrogen is angled away

from the free oxygen. The former case has an angle of ~107.8°, while the latter has a slightly

smaller angle of ~106.3°.

Incorporating H2SO4 into the MD force field to run aqueous sulfuric acid is necessary

before the solution was simulated over platinum. The CFM description of atoms, in terms of

partial atomic charges and the description of liquid water, is maintained because water is the

primary component of our system. Partial charges are assigned to each atom to ensure proper

prediction of the dipole moment and correct water dynamics. The charge on the hydrogen atom,

32

qH, is assigned a value of 0.32983 e, and all other atoms in the system are scaled naturally from

the hydrogen charge [36].

Table 3-1: Atomic charges for reactive MD simulations

Atom Charge,qi (e)

H 0.32983

OW -0.65966

OS -0.65966

S 1.97898

Developing a molecular dynamics description of sulfuric acid

To parameterize H2SO4 with water, certain decisions had to be made a priori. First,

because there is no experimental data available, a structural basis for comparison was needed.

There have been several studies to consider aqueous sulfuric acid from an classical MD

simulation standpoint [63-65]. Most of these studies have used classical molecular dynamics with

fixed molecular geometries, and they do not allow for proton dissociation or other proton transfer

events to occur. Others look only at simulating small acidic clusters in water and use force fields

which are not computationally efficient for large scales. From the literature on aqueous H2SO4

simulation, only two papers were found to be relevant to the present study.

Laaksonen et al use the only example to our knowledge of classical MD simulations in

which oxygen atoms in sulfuric acid are differentiated (OH and OF are considered different atoms)

[63]. Differentiating between the two types of oxygen atoms allows for proper matching of

angular data for the sulfate cluster. This study was performed using non-reactive MD

parameterized from ab initio data. The bonds for the different oxygen atoms, S-OH and S-OF can

be fit explicitly to match the calculated equilibrium distances. A unique feature of the model of

Lasksonen et al. is the use of only pair potentials. That is, interactions between oxygen atoms

33

within a sulfate group are controlled using a bond-like potential rather than through the use of an

angular term on the O-S-O plane. Similar considerations are taken for all atomic interactions.

Laaksonen uses simulations of bisulfate (HSO4-) and hydronium (H3O

+) in water as well as

sulfuric acid (H2SO4) in water to show that the bisulfate anion is favored in solution when the

hydration in the system is large enough.

Figure 3-2: Molecules used in the MD simulation of H2SO4/H2O system with bisulfate anions and

hydronium cations using different potentials for sulfuric acid oxygen atoms for the

presence/absence of protons performed by Laaksonen et al.

Ikeshoji used ab initio molecular dynamics (AIMD) to study small H2SO4/H2O systems

[51]. The benefit of this method is the ability to study proton transfer events, and the electronic

structure calculations allow simulations to be run without the need for parameterization of all

interactions in the system. Ikeshoji, like Laaksonen, found that the bisulfate anion was most

stable in low concentration systems. This work went on to include electric field effects on the

structure of acid and solution dynamics through the application of a homogeneous electric field of

1.03 V/nm in one direction. These results showed that, under the influence of an external electric

field, sulfuric acid tends to dissociate more readily for low concentration systems. In a 0.84 molar

34

H2SO4 solution in water, 100% of the structures existed as HSO4- without electric field, whereas

application of the electric field caused 11% of the bisulfate anions to further dissociate to SO42-

.

Figure 3-3: Radial distribution function of sulfuric acid oxygen atoms with water hydrogen atoms

provided by an AIMD study for two acid concentrations [51].

Because AIMD cannot be used for the time and length scales that we would like to

consider in the construction of a MD model for electrochemical interfaces, a separate MD force

field description of the acid/water system is required. The RDFs for sulfuric acid in water from

Ikeshoji et al were used to add water to our sulfuric acid molecule because they are considered to

be the most reliable structural information available for the aqueous system. The main basis of

comparison for our parameterization, the RDF for sulfuric acid oxygen atoms with hydrogen

atoms, is shown in Figure 3-3 for two concentrations. Some deviation from these results is

expected because our method relies only on Newton‟s equations of motion and can more

accurately capture dynamics of aqueous systems. Ikeshoji et al. do not give information on the

structural information of water in their simulations, and it is unknown whether a more ice-like

configuration is reached. The dynamics associated with AIMD are also greatly under predicted.

35

Diffusion coefficients for water and sulfuric acid are two orders of magnitude lower than their

respective experimental values [66].

Design of the intermolecular potentials

To develop our description of the acid/water system it is necessary to parameterize

interactions for all new atom types. Firstly, the force-field is optimized to describe the sulfuric

acid group by itself. Because our force field will allow the breaking and forming of bonds

involving protons, we cannot provide atomistic distinction between OH and OF. If all oxygen

atoms in the acid cluster are treated equally, it will be equally likely for a free proton to bond to

or dissociate from any oxygen atom. To avoid confusion between oxygen in water molecules and

oxygen in sulfuric acid, the latter will henceforth be termed OS. Having decided that all OS atoms

will be treated equally, a compromise must be made on the equilibrium bond distance for S-OS, as

well as the geometric angle at which the S-OS bonds exist with one another.

As stated previously, the S-OS bond distances are longer for oxygen to which a proton is

bonded (1.613 Å compared to 1.434 Å). For all S-OS, an equilibrium distance of 1.51 Å was

selected. This distance was selected as a weighted average of QM bond lengths. Because research

has shown the bisulfate anion to be favored, the bond distance was selected to be closer to that of

the S-OF bond in H2SO4. Finally, because each OS will be considered identical, the equilibrium

molecular geometry is a tetrahedral orientation. Because all S-OS bond lengths are 1.51 Å, the

equilibrium OS-S-OS bond angle is 109.5°.

36

Figure 3-4: Pair potentials for the SO4 group for reactive MD simulation of H2SO4/H2O

Molecular dissociation of the SO4 group is not an event that would be expected under

reasonable conditions. Formation or breakup of the SO4 will not be included in our model, so

these bonds will not be considered reactive. Figure 3-4 shows the interaction potentials used for

the SO4 group in these simulations. Harmonic potentials will be used for all S-OS bonds with an

equilibrium distance of 1.51 Å. To maintain the two-body force field description characteristic of

the central force model for water, the method of Laaksonen is implemented to maintain molecular

geometry in the sulfate group [63,64]. Rather than describing OS-S-OS angles via a three body

angular term, identical two body interactions are used to OS-OS bonds. The atomic distance

between to OS atoms corresponding to a 109.5° OS-S-OS angle, with a S-OS bond distance of 1.51

Å, is 2.466 Å. To maintain the desired geometry, a harmonic potential with an equilibrium bond

distance of 2.466 Å is used for OS-OS pairs within a sulfate group. For S-OS pairs and OS-OS pairs

interacting between different sulfuric acid molecules, different potentials are used and will be

discussed. Harmonic potentials can be controlled via a force constant. These potentials are

analogous to Hooke‟s law in describing springs. A force constant controls the magnitude of the

S-Os, 0, 1140.05 S-Os, 0.1,

994.05 S-Os, 0.2, 858.05 S-Os, 0.3, 732.05 S-Os, 0.4, 616.05 S-Os, 0.5, 510.05 S-Os, 0.6, 414.05 S-Os, 0.7, 328.05 S-Os, 0.8,

252.05 S-Os, 0.9,

186.05 S-Os, 1, 130.05 S-Os, 1.1,

84.05 S-Os, 1.2,

48.05 S-Os, 1.3,

22.05 S-Os, 1.4,

6.05 S-Os, 1.5,

0.05

S-Os, 1.6, 4.05

S-Os, 1.7, 18.05

S-Os, 1.8, 42.05

S-Os, 1.9, 76.05

S-Os, 2, 120.05

S-Os, 2.1, 174.05

S-Os, 2.2, 238.05

S-Os, 2.3, 312.05

S-Os, 2.4, 396.05

S-Os, 2.5, 490.05

S-Os, 2.6, 594.05

S-Os, 2.7, 708.05

S-Os, 2.8, 832.05

S-Os, 2.9, 966.05

S-Os, 3, 1110.05

S-Os, 3.1, 1264.05

S-Os, 3.2, 1428.05

S-Os, 3.3, 1602.05

S-Os, 3.4, 1786.05

S-Os, 3.5, 1980.05 S-Os, 3.6, 2184.05 S-Os, 3.7, 2398.05 S-Os, 3.8, 2622.05 S-Os, 3.9, 2856.05 S-Os, 4, 3100.05

Os-Os, 0, 1512.9 Os-Os, 0.1,

1392.4 Os-Os, 0.2, 1276.9 Os-Os, 0.3, 1166.4 Os-Os, 0.4, 1060.9 Os-Os, 0.5,

960.4 Os-Os, 0.6, 864.9 Os-Os, 0.7, 774.4 Os-Os, 0.8, 688.9

Os-Os, 0.9, 608.4

Os-Os, 1, 532.9

Os-Os, 1.1, 462.4

Os-Os, 1.2, 396.9

Os-Os, 1.3, 336.4

Os-Os, 1.4, 280.9

Os-Os, 1.5, 230.4

Os-Os, 1.6, 184.9

Os-Os, 1.7, 144.4

Os-Os, 1.8, 108.9

Os-Os, 1.9, 78.4

Os-Os, 2, 52.9

Os-Os, 2.1, 32.4

Os-Os, 2.2, 16.9

Os-Os, 2.3, 6.4

Os-Os, 2.4, 0.9

Os-Os, 2.5, 0.4

Os-Os, 2.6, 4.9

Os-Os, 2.7, 14.4

Os-Os, 2.8, 28.9

Os-Os, 2.9, 48.4

Os-Os, 3, 72.9

Os-Os, 3.1, 102.4

Os-Os, 3.2, 136.9

Os-Os, 3.3, 176.4

Os-Os, 3.4, 220.9

Os-Os, 3.5, 270.4

Os-Os, 3.6, 324.9

Os-Os, 3.7, 384.4

Os-Os, 3.8, 448.9

Os-Os, 3.9, 518.4

Os-Os, 4, 592.9

Os-Os, 4.1, 672.4

Os-Os, 4.2, 756.9

Os-Os, 4.3, 846.4

Os-Os, 4.4, 940.9

Os-Os, 4.5, 1040.4

Os-Os, 4.6, 1144.9

Os-Os, 4.7, 1254.4

Os-Os, 4.8, 1368.9

Os-Os, 4.9, 1488.4

Os-Os, 5, 1612.9

Ene

rgy

(kca

l/m

ol)

Distance (A)

S-Os

Os-Os

37

force acting on particles to return them to the equilibrium position. Both sets of atomic pairs are

described with the same equation, Equation 2-1, and the constants are given in Table 3-2. Bond

flexibility can be controlled through the value of the force constant.

Table 3-2: Interaction parameters for harmonic sulfate bonds, functional form U(r)=0.5k(r-r0)2

Bond Pair Force Constant, k

(kcal.mol

-1.Å

-2)

Equilibrium Distance, r0

(Å)

S-OS

1000 1.51

OS-OS 600 2.466

For all OS non-bonded interactions, OS is considered identical to OW. The non-bonded

OS-OS or OS-OW is identical to that of the OW-OW interaction. Sulfur atoms on different sulfate

groups are limited in their approach by molecular sterics. Because each sulfur atom has four

oxygen atoms bound to it at a distance of 1.51 Å and the oxygen atoms themselves have a natural

tendency to repel one another, sulfur atoms cannot approach each other to a distance closer than

c.a. 4.5 Å at any time. Because this distance is well outside of that expected to have any strong

electronic effect, the S-S interaction is described in a purely repulsive electrostatic manner with

no additional force terms, given in Equation 3-1.

( )

Equation 3-1

Similarly, the approach between sulfur and oxygen atoms to which it is not bonded, both

OS atoms on other sulfate groups and OW, will not be very close. The closest expected approach

between these atomic pairs is outside of 3 Å. Because these pairs will always exist at distances

outside the primary influence of electrostatics, there will be only a weak attractive force between

the atoms due to their opposite charges. A simple Lennard-Jones interaction, given in Equation 3-

2, is used for these pairs and is identical for both non-bonded S-OS pairs and all S-OW pairs. The

38

weakness of this interaction leaves a force dominated by electrostatics, with a small region of

repulsive behavior at close distances, though these distances are closer than the atoms are

expected to approach during a simulation. Figure 3-5 shows how this interaction deviates only

slightly from, and is dominated by, the electrostatic potential. To give this fit, weak interactions

are required so as not to overpower the electrostatics. For the given function, σ is given as 12 Å

and ε is 1x10-7

kcal/mol.

( )

[.

/

.

/

] Equation 3-2

Figure3-5: Non-bonded interaction potential for S-OS and S-OW

The parameterization of the OS-H bond requires a balance of a bonding interaction and

the ability to dissociate protons. Because it has been shown that the bisulfate anion, HSO4- is the

most prevalent species at low acid concentrations in solution, a bond force must be designed so

that it is strong enough to hold a proton on the sulfate group, but weak enough to allow a proton

Non-bonded Potential, 0.1, 3.56644E+18

Non-bonded Potential,

0.15, 2.74878E+16



0.25, 5.98349E+13



0.35, 1.0554E+12



0.45, 51723126567

Non-bonded Potential, 0.5, 14608138031


0.55, 4654602435

Non-bonded Potential, 0.6, 1638399252


0.65, 627009601.3

Non-bonded Potential, 0.7, 257666170.3


0.75, 112589405.8



0.85, 25072575.28



0.95, 6599659.625

Non-bonded Potential, 1, 3566005.356


1.05, 1985513.471



1.15, 666215.5855



1.25, 244736.687



1.35, 97004.78621



1.45, 40988.3487



1.55, 18266.33756



1.65, 8495.59283



1.75, 4075.102208



1.85, 1984.662729



1.95, 957.4351087

Non-bonded Potential, 2, 653.8799767


2.05, 435.8814923



2.15, 163.872612



2.25, 19.1249073 Non-bonded Potential, 2.3, -25.7997649 Non-bonded

Potential, 2.35, -

58.80519933 Non-bonded

Potential, 2.4, -83.02857942


2.45, -100.7464184

Non-bonded Potential, 2.5, -113.6213912


2.55, -122.8753322



2.65, -133.9007486



2.75, -138.6206304



2.85, -139.7333256



2.95, -138.7840331

Non-bonded Potential, 3, -137.8336155


3.05, -136.6713187



3.15, -133.92422



3.25, -130.8569612



3.35, -127.6569727



3.45, -124.4358422



3.55, -121.2592809



3.65, -118.1650058



3.75, -115.1735517



3.85, -112.2948855



3.95, -109.5324923



4.05, -106.8859221



4.15, -104.3523857



4.25, -101.9277599



4.35, -99.60721998



4.45, -97.38563635



4.55, -95.25782156



4.65, -93.21868058



4.75, -91.26329951



4.85, -89.38699462



4.95, -87.58533609



5.05, -85.85415567



5.15, -84.18954449



5.25, -82.5878447



5.35, -81.04563776



5.45, -79.55973089



5.55, -78.12714285



5.65, -76.74508965



5.75, -75.41097061



5.85, -74.12235514



5.95, -72.87697017



6.05, -71.67268846



6.15, -70.50751775



6.25, -69.37959067



6.35, -68.28715549



6.45, -67.22856755



6.55, -66.20228146



6.65, -65.20684383



6.75, -64.24088666



6.85, -63.30312129



6.95, -62.39233275

Non-bonded Potential, 7, -

61.946694


7.05, -61.50737466



7.15, -60.64716448



7.25, -59.81067919



7.35, -58.99695125



7.45, -58.20506493



7.55, -57.4341529



7.65, -56.68339308



7.75, -55.95200575



7.85, -55.23925088



7.95, -54.54442558



8.05, -53.86686189



8.15, -53.20592458



8.25, -52.5610092



8.35, -51.93154022



8.45, -51.31696934



8.55, -50.71677391



8.65, -50.13045543



8.75, -49.55753817



8.85, -48.9975679



8.95, -48.45011068



9.05, -47.91475175



9.15, -47.39109448



9.25, -46.87875937



9.35, -46.37738317



9.45, -45.88661799



9.55, -45.40613052



9.65, -44.93560125



9.75, -44.4747238



9.85, -44.0232042



9.95, -43.58076032


Electrostatic Only, 0.1, -

4336.285906

Electrostatic Only, 0.15, -2890.857271


2168.142953



1445.428635



1084.071477



867.2571812



722.7143177



619.4694151



542.0357383



481.8095451


Electrostatic Only, 1, -

433.6285906



394.2078096



361.3571588



333.5604543



309.7347076



289.0857271



271.0178691



255.0756415



240.9047726





216.8142953





197.1039048



188.5341698



180.6785794



173.4514362



166.7802272



160.6031817



154.8673538



149.5271002



144.5428635



139.8801905



135.5089346



131.4026032



127.5378208





120.4523863



117.1969164





111.1868181



108.4071477



105.7630709



103.2449025



100.8438583



98.55195241



96.36190902



94.26708491



92.26140226



90.33928971



88.49563073



86.72571812



85.02521384



83.39011358



81.81671521



80.30159085



78.84156193



77.43367689



76.07519133





73.49637129



72.27143177





69.94009526



68.82993502



67.75446728



66.71209086



65.70130161



64.72068516



63.76891038



62.84472328



61.94694151



61.07444938



60.22619314



59.40117679



58.59845819



57.81714541





56.31540138



55.59340905



54.88969501



54.20357383





52.88153544



52.24440851



51.62245126



51.01512831



50.42192914



49.84236674





48.72231355



48.18095451



47.65149347



47.13354246



46.62673017



46.13070113





45.16964485



44.70397841



44.24781537



43.80086774



43.36285906

Ene

rgy

(kca

l/m

ol)

Distance (A)

Non-bondedPotential

Electrostatic Only

39

to dissociate. There are three interactions which play a role in the dissociation of protons from a

sulfate group. The most obvious interaction is the OS-H pair. The S-H and OW-H potentials also

affect a protons‟ tendency to dissociate. Because hydrogen atoms from water and sulfuric acid are

not considered different in our simulations, the OW-H bond potential does not change from that

described in CFM. Intuitively, the OS-H potential must then be designed to provide a force that is

weaker than that of the CFM O-H description, but not so weak so as to completely dissociate both

protons from sulfuric acid, yielding an average solution structure of HSO4-.

Meanwhile, there must be an attractive force between the sulfur atom and protons in an

acid molecule. Though this attraction may be counter-intuitive because both atoms have positive

charges, it is required in a simulation to attain the bending of the S-OS-H group. Without some

attractive force between the proton and molecular center, a 180° bend angle would be expected

for this group rather than the ~107.5° angle predicted by QM calculations, as shown in Figure 3-

1. The potential chosen for S-H follows a common form. As in the CFM description of H-H pair

interactions, our S-H interaction has a small attractive well at a distance corresponding to typical

S-H distance in H2SO4 of approximately 2.1 Å. This interaction potential is shown in Figure 3-6

and described in Equation 3-3. Using this potential, the average H-OS-S angle calculated is 121°.

It is important to note that the average angle for a fully bonded S-OS-H group may be slightly

different. Because our force-field is reactive the calculation method cannot differentiate protons

that are in the act of dissociating from those bonded to a OS, which may lead to an inaccurate

angle calculation.

40

Figure 3-6: Pair interaction potential for S-H in reactive sulfuric acid simulations

( )

( ( ) ( ( )) Equation 3-3

Because every atomic pair interaction in the system affects the structures that are

obtained, the potential for OS-H was the last to be parameterized in an attempt to simulate

aqueous sulfuric acid and produce bisulfate anions as the predominant sulfate form. To balance

the selective dissociation of protons from the H2SO4 group, a parametric design process was

performed to fit a potential for OS-H. Three different potential forms were studied. The first,

termed CFM-1 (Equation 3-4), is based on the potential form used by Stillinger and Rahman for

O-H in the original version of the CFM[34,35]. The second, termed CFM-2 (Equation 3-5), is the

same potential form used by Stillinger and Rahman for O-H in the CFM, which is the original

version of the force field used for liquid water [34,35]. The third, termed CFM-OO (Equation 3-

6), attempted to describe the OS-H interaction using a potential form used for O-O in the revised

CFM, but altered to produce an attractive interaction rather than a repulsive one [36]. The

functional forms are given, without electrostatic terms, in Equation 3-4,5,6.

Adjust_2, 0.01,

6305017178

Adjust_2, 0.02,

5426770750

Adjust_2, 0.03,

4670862762

Adjust_2, 0.04,

4020248030

Adjust_2, 0.05,

3460259212

Adjust_2, 0.06,

2978272580

Adjust_2, 0.07,

2563422947

Adjust_2, 0.08,

2206358616

Adjust_2, 0.09,

1899030531

Adjust_2, 0.1,

1634510814

Adjust_2, 0.11,

1406836595

Adjust_2, 0.12,

1210875583

Adjust_2, 0.13,

1042210380

Adjust_2, 0.14,

897038895

Adjust_2, 0.15,

772088639

Adjust_2, 0.16,

664542955.5

Adjust_2, 0.17,

571977525.9

Adjust_2, 0.18,

492305720.1

Adjust_2, 0.19,

423731559

Adjust_2, 0.2,

364709229

Adjust_2, 0.21,

313908236.3

Adjust_2, 0.22,

270183414.1

Adjust_2, 0.23,

232549108.5

Adjust_2, 0.24,

200156959.1

Adjust_2, 0.25,

172276775.3

Adjust_2, 0.26,

148280076.6

Adjust_2, 0.27,

127625924.3

Adjust_2, 0.28,

109848728.7

Adjust_2, 0.29,

94547752.56

Adjust_2, 0.3,

81378078.43

Adjust_2, 0.31,

70042833

Adjust_2, 0.32,

60286495.05

Adjust_2, 0.33,

51889135.43

Adjust_2, 0.34,

44661459.38

Adjust_2, 0.35,

38440539.36

Adjust_2, 0.36,

33086142.36

Adjust_2, 0.37,

28477568.68

Adjust_2, 0.38,

24510931.14

Adjust_2, 0.39,

21096813.22

Adjust_2, 0.4,

18158253.39

Adjust_2, 0.41,

15629010.24

Adjust_2, 0.42,

13452069.28

Adjust_2, 0.43,

11578357.66

Adjust_2, 0.44,

9965637.995

Adjust_2, 0.45,

8577556.231

Adjust_2, 0.46,

7382822.135

Adjust_2, 0.47,

6354503.957

Adjust_2, 0.48,

5469421.319

Adjust_2, 0.49,

4707622.687

Adjust_2, 0.5,

4051935.612

Adjust_2, 0.51,

3487579.632

Adjust_2, 0.52,

3001833.081

Adjust_2, 0.53,

2583746.32

Adjust_2, 0.54,

2223894.905

Adjust_2, 0.55,

1914167.143

Adjust_2, 0.56,

1647581.231

Adjust_2, 0.57,

1418127.878

Adjust_2, 0.58,

1220634.834

Adjust_2, 0.59,

1050650.305

Adjust_2, 0.6,

904342.5942

Adjust_2, 0.61,

778413.7282

Adjust_2, 0.62,

670025.115

Adjust_2, 0.63,

576733.5547

Adjust_2, 0.64,

496436.1652

Adjust_2, 0.65,

427322.9782

Adjust_2, 0.66,

367836.1391

Adjust_2, 0.67,

316634.7893

Adjust_2, 0.68,

272564.8407

Adjust_2, 0.69,

234632.9598

Adjust_2, 0.7,

201984.176

Adjust_2, 0.71,

173882.6088

Adjust_2, 0.72,

149694.8797

Adjust_2, 0.73,

128875.834

Adjust_2, 0.74,

110956.2526

Adjust_2, 0.75,

95532.2743

Adjust_2, 0.76,

82256.29217

Adjust_2, 0.77,

70829.11783

Adjust_2, 0.78,

60993.23706

Adjust_2, 0.79,

52527.00502

Adjust_2, 0.8,

45239.64987

Adjust_2, 0.81,

38966.97249

Adjust_2, 0.82,

33567.64507

Adjust_2, 0.83,

28920.02536

Adjust_2, 0.84,

24919.41465

Adjust_2, 0.85,

21475.69765

Adjust_2, 0.86,

18511.31118

Adjust_2, 0.87,

15959.49573

Adjust_2, 0.88,

13762.79066

Adjust_2, 0.89,

11871.73889

Adjust_2, 0.9,

10243.77214

Adjust_2, 0.91,

8842.251319

Adjust_2, 0.92,

7635.640695

Adjust_2, 0.93,

6596.797022

Adjust_2, 0.94,

5702.357712

Adjust_2, 0.95,

4932.214229

Adjust_2, 0.96,

4269.058829

Adjust_2, 0.97,

3697.994442

Adjust_2, 0.98,

3206.198887

Adjust_2, 0.99,

2782.635864

Adjust_2, 1, 2417.8062

Adjust_2, 1.01,

2103.533745

Adjust_2, 1.02,

1832.781091

Adjust_2, 1.03,

1599.490956

Adjust_2, 1.04,

1398.449669

Adjust_2, 1.05,

1225.169664

Adjust_2, 1.06,

1075.788345

Adjust_2, 1.07,

946.9810325

Adjust_2, 1.08,

835.8860461

Adjust_2, 1.09,

740.0402114

Adjust_2, 1.1,

657.3233568

Adjust_2, 1.11,

585.910539

Adjust_2, 1.12,

524.2309235

Adjust_2, 1.13,

470.932392

Adjust_2, 1.14,

424.8510807

Adjust_2, 1.15,

384.9851602

Adjust_2, 1.16,

350.4722687

Adjust_2, 1.17,

320.5700876

Adjust_2, 1.18,

294.6396236

Adjust_2, 1.19,

272.1308181

Adjust_2, 1.2,

252.5701623

Adjust_2, 1.21,

235.5500368

Adjust_2, 1.22,

220.7195356

Adjust_2, 1.23,

207.7765688

Adjust_2, 1.24,

196.461065

Adjust_2, 1.25,

186.5491206

Adjust_2, 1.26,

177.8479637

Adjust_2, 1.27,

170.1916198

Adjust_2, 1.28,

163.4371808

Adjust_2, 1.29,

157.4615942

Adjust_2, 1.3,

152.1588987

Adjust_2, 1.31,

147.4378455

Adjust_2, 1.32,

143.2198504

Adjust_2, 1.33,

139.4372317

Adjust_2, 1.34,

136.0316926

Adjust_2, 1.35,

132.9530159

Adjust_2, 1.36,

130.1579399

Adjust_2, 1.37,

127.609191

Adjust_2, 1.38,

125.2746508

Adjust_2, 1.39,

123.12664

Adjust_2, 1.4,

121.1413005

Adjust_2, 1.41,

119.2980651

Adjust_2, 1.42,

117.5792004

Adjust_2, 1.43,

115.9694127

Adjust_2, 1.44,

114.45551

Adjust_2, 1.45,

113.0261102

Adjust_2, 1.46,

111.6713902

Adjust_2, 1.47,

110.3828696

Adjust_2, 1.48,

109.1532253

Adjust_2, 1.49,

107.976131

Adjust_2, 1.5,

106.8461194

Adjust_2, 1.51,

105.7584638

Adjust_2, 1.52,

104.709076

Adjust_2, 1.53,

103.694418

Adjust_2, 1.54,

102.7114268

Adjust_2, 1.55,

101.7574489

Adjust_2, 1.56,

100.8301843

Adjust_2, 1.57,

99.92763808

Adjust_2, 1.58,

99.04807909

Adjust_2, 1.59,

98.19000381

Adjust_2, 1.6,

97.35210566

Adjust_2, 1.61,

96.53324837

Adjust_2, 1.62,

95.73244312

Adjust_2, 1.63,

94.94882879

Adjust_2, 1.64,

94.181655

Adjust_2, 1.65,

93.43026742

Adjust_2, 1.66,

92.69409517

Adjust_2, 1.67,

91.97263993

Adjust_2, 1.68,

91.26546652

Adjust_2, 1.69,

90.57219481

Adjust_2, 1.7,

89.8924927

Adjust_2, 1.71,

89.2260701

Adjust_2, 1.72,

88.57267362

Adjust_2, 1.73,

87.93208209

Adjust_2, 1.74,

87.30410263

Adjust_2, 1.75,

86.68856717

Adjust_2, 1.76,

86.08532954

Adjust_2, 1.77,

85.49426283

Adjust_2, 1.78,

84.91525712

Adjust_2, 1.79,

84.34821752

Adjust_2, 1.8,

83.79306236

Adjust_2, 1.81,

83.24972168

Adjust_2, 1.82,

82.71813581

Adjust_2, 1.83,

82.19825413

Adjust_2, 1.84,

81.69003397

Adjust_2, 1.85,

81.19343959

Adjust_2, 1.86,

80.70844123

Adjust_2, 1.87,

80.23501426

Adjust_2, 1.88,

79.7731384

Adjust_2, 1.89,

79.32279692

Adjust_2, 1.9,

78.88397599

Adjust_2, 1.91,

78.45666394

Adjust_2, 1.92,

78.04085066

Adjust_2, 1.93,

77.63652691

Adjust_2, 1.94,

77.24368374

Adjust_2, 1.95,

76.86231186

Adjust_2, 1.96,

76.49240104

Adjust_2, 1.97,

76.13393951

Adjust_2, 1.98,

75.7869134

Adjust_2, 1.99,

75.4513061

Adjust_2, 2, 75.12709772

Adjust_2, 2.01,

74.81426449

Adjust_2, 2.02,

74.51277815

Adjust_2, 2.03,

74.22260543

Adjust_2, 2.04,

73.94370745

Adjust_2, 2.05,

73.67603913

Adjust_2, 2.06,

73.4195487

Adjust_2, 2.07,

73.17417707

Adjust_2, 2.08,

72.93985738

Adjust_2, 2.09,

72.71651441

Adjust_2, 2.1,

72.50406414

Adjust_2, 2.11,

72.30241324

Adjust_2, 2.12,

72.11145866

Adjust_2, 2.13,

71.93108716

Adjust_2, 2.14,

71.76117496

Adjust_2, 2.15,

71.60158738

Adjust_2, 2.16,

71.45217855

Adjust_2, 2.17,

71.31279109

Adjust_2, 2.18,

71.18325599

Adjust_2, 2.19,

71.06339234

Adjust_2, 2.2,

70.95300729

Adjust_2, 2.21,

70.851896

Adjust_2, 2.22,

70.75984158

Adjust_2, 2.23,

70.67661526

Adjust_2, 2.24,

70.60197642

Adjust_2, 2.25,

70.53567289

Adjust_2, 2.26,

70.47744116

Adjust_2, 2.27,

70.42700671

Adjust_2, 2.28,

70.38408446

Adjust_2, 2.29,

70.34837919

Adjust_2, 2.3,

70.31958612

Adjust_2, 2.31,

70.29739149

Adjust_2, 2.32,

70.28147318

Adjust_2, 2.33,

70.27150152

Adjust_2, 2.34,

70.26713996

Adjust_2, 2.35,

70.26804596

Adjust_2, 2.36,

70.27387182

Adjust_2, 2.37,

70.28426562

Adjust_2, 2.38,

70.29887209

Adjust_2, 2.39,

70.31733367

Adjust_2, 2.4,

70.33929141

Adjust_2, 2.41,

70.36438602

Adjust_2, 2.42,

70.39225887

Adjust_2, 2.43,

70.42255299

Adjust_2, 2.44,

70.45491406

Adjust_2, 2.45,

70.48899143

Adjust_2, 2.46,

70.52443906

Adjust_2, 2.47,

70.56091648

Adjust_2, 2.48,

70.59808967

Adjust_2, 2.49,

70.63563198

Adjust_2, 2.5,

70.6732249

Adjust_2, 2.51,

70.71055889

Adjust_2, 2.52,

70.74733404

Adjust_2, 2.53,

70.78326082

Adjust_2, 2.54,

70.8180606

Adjust_2, 2.55,

70.85146627

Adjust_2, 2.56,

70.88322268

Adjust_2, 2.57,

70.91308706

Adjust_2, 2.58,

70.94082936

Adjust_2, 2.59,

70.96623258

Adjust_2, 2.6,

70.98909291

Adjust_2, 2.61,

71.00921994

Adjust_2, 2.62,

71.02643673

Adjust_2, 2.63,

71.04057983

Adjust_2, 2.64,

71.05149926

Adjust_2, 2.65,

71.05905839

Adjust_2, 2.66,

71.06313385

Adjust_2, 2.67,

71.06361528

Adjust_2, 2.68,

71.06040514

Adjust_2, 2.69,

71.05341839

Adjust_2, 2.7,

71.04258221

Adjust_2, 2.71,

71.02783561

Adjust_2, 2.72,

71.00912905

Adjust_2, 2.73,

70.98642406

Adjust_2, 2.74,

70.95969277

Adjust_2, 2.75,

70.92891748

Adjust_2, 2.76,

70.89409016

Adjust_2, 2.77,

70.85521201

Adjust_2, 2.78,

70.81229293

Adjust_2, 2.79,

70.76535108

Adjust_2, 2.8,

70.7144123

Adjust_2, 2.81,

70.65950971

Adjust_2, 2.82,

70.60068313

Adjust_2, 2.83,

70.53797865

Adjust_2, 2.84,

70.47144814

Adjust_2, 2.85,

70.40114874

Adjust_2, 2.86,

70.32714246

Adjust_2, 2.87,

70.24949569

Adjust_2, 2.88,

70.16827877

Adjust_2, 2.89,

70.08356561

Adjust_2, 2.9,

69.99543322

Adjust_2, 2.91,

69.90396141

Adjust_2, 2.92,

69.80923233

Adjust_2, 2.93,

69.71133018

Adjust_2, 2.94,

69.61034089

Adjust_2, 2.95,

69.50635172

Adjust_2, 2.96,

69.39945107

Adjust_2, 2.97,

69.2897281

Adjust_2, 2.98,

69.17727256

Adjust_2, 2.99,

69.06217446

Adjust_2, 3, 68.94452391

Adjust_2, 3.01,

68.82441086

Adjust_2, 3.02,

68.70192493

Adjust_2, 3.03,

68.57715523

Adjust_2, 3.04,

68.45019018

Adjust_2, 3.05,

68.32111738

Adjust_2, 3.06,

68.19002345

Adjust_2, 3.07,

68.0569939

Adjust_2, 3.08,

67.92211307

Adjust_2, 3.09,

67.78546397

Adjust_2, 3.1,

67.64712822

Adjust_2, 3.11,

67.50718598

Adjust_2, 3.12,

67.36571586

Adjust_2, 3.13,

67.22279487

Adjust_2, 3.14,

67.07849839

Adjust_2, 3.15,

66.93290009

Adjust_2, 3.16,

66.78607193

Adjust_2, 3.17,

66.63808414

Adjust_2, 3.18,

66.48900513

Adjust_2, 3.19,

66.33890159

Adjust_2, 3.2,

66.18783837

Adjust_2, 3.21,

66.03587855

Adjust_2, 3.22,

65.88308343

Adjust_2, 3.23,

65.72951248

Adjust_2, 3.24,

65.57522345

Adjust_2, 3.25,

65.42027227

Adjust_2, 3.26,

65.26471318

Adjust_2, 3.27,

65.10859865

Adjust_2, 3.28,

64.95197946

Adjust_2, 3.29,

64.79490472

Adjust_2, 3.3,

64.63742186

Adjust_2, 3.31,

64.47957672

Adjust_2, 3.32,

64.3214135

Adjust_2, 3.33,

64.16297486

Adjust_2, 3.34,

64.00430193

Adjust_2, 3.35,

63.84543433

Adjust_2, 3.36,

63.6864102

Adjust_2, 3.37,

63.52726626

Adjust_2, 3.38,

63.36803783

Adjust_2, 3.39,

63.20875886

Adjust_2, 3.4,

63.04946198

Adjust_2, 3.41,

62.89017852

Adjust_2, 3.42,

62.73093853

Adjust_2, 3.43,

62.57177088

Adjust_2, 3.44,

62.4127032

Adjust_2, 3.45,

62.25376201

Adjust_2, 3.46,

62.09497267

Adjust_2, 3.47,

61.93635949

Adjust_2, 3.48,

61.77794569

Adjust_2, 3.49,

61.61975349

Adjust_2, 3.5,

61.46180412

Adjust_2, 3.51,

61.30411784

Adjust_2, 3.52,

61.146714

Adjust_2, 3.53,

60.98961105

Adjust_2, 3.54,

60.83282657

Adjust_2, 3.55,

60.67637731

Adjust_2, 3.56,

60.52027919

Adjust_2, 3.57,

60.36454739

Adjust_2, 3.58,

60.2091963

Adjust_2, 3.59,

60.05423961

Adjust_2, 3.6,

59.89969029

Adjust_2, 3.61,

59.74556066

Adjust_2, 3.62,

59.59186236

Adjust_2, 3.63,

59.43860642

Adjust_2, 3.64,

59.28580327

Adjust_2, 3.65,

59.13346276

Adjust_2, 3.66,

58.98159416

Adjust_2, 3.67,

58.83020622

Adjust_2, 3.68,

58.67930718

Adjust_2, 3.69,

58.52890477

Adjust_2, 3.7,

58.37900623

Adjust_2, 3.71,

58.22961837

Adjust_2, 3.72,

58.08074754

Adjust_2, 3.73,

57.93239967

Adjust_2, 3.74,

57.78458027

Adjust_2, 3.75,

57.63729449

Adjust_2, 3.76,

57.49054707

Adjust_2, 3.77,

57.34434241

Adjust_2, 3.78,

57.19868457

Adjust_2, 3.79,

57.05357727

Adjust_2, 3.8,

56.9090239

Adjust_2, 3.81,

56.76502758

Adjust_2, 3.82,

56.6215911

Adjust_2, 3.83,

56.478717

Adjust_2, 3.84,

56.33640754

Adjust_2, 3.85,

56.19466472

Adjust_2, 3.86,

56.05349032

Adjust_2, 3.87,

55.91288586

Adjust_2, 3.88,

55.77285265

Adjust_2, 3.89,

55.63339177

Adjust_2, 3.9,

55.49450413

Adjust_2, 3.91,

55.3561904

Adjust_2, 3.92,

55.2184511

Adjust_2, 3.93,

55.08128655

Adjust_2, 3.94,

54.94469692

Adjust_2, 3.95,

54.8086822

Adjust_2, 3.96,

54.67324223

Adjust_2, 3.97,

54.53837672

Adjust_2, 3.98,

54.40408521

Adjust_2, 3.99,

54.27036713

Adjust_2, 4, 54.13722178

Adjust_2, 4.01,

54.00464833

Adjust_2, 4.02,

53.87264584

Adjust_2, 4.03,

53.74121325

Adjust_2, 4.04,

53.61034942

Adjust_2, 4.05,

53.4800531

Adjust_2, 4.06,

53.35032294

Adjust_2, 4.07,

53.22115751

Adjust_2, 4.08,

53.09255528

Adjust_2, 4.09,

52.96451467

Adjust_2, 4.1,

52.837034

Adjust_2, 4.11,

52.71011152

Adjust_2, 4.12,

52.58374543

Adjust_2, 4.13,

52.45793386

Adjust_2, 4.14,

52.33267486

Adjust_2, 4.15,

52.20796646

Adjust_2, 4.16,

52.0838066

Adjust_2, 4.17,

51.9601932

Adjust_2, 4.18,

51.83712411

Adjust_2, 4.19,

51.71459715

Adjust_2, 4.2,

51.59261011

Adjust_2, 4.21,

51.47116071

Adjust_2, 4.22,

51.35024666

Adjust_2, 4.23,

51.22986562

Adjust_2, 4.24,

51.11001525

Adjust_2, 4.25,

50.99069313

Adjust_2, 4.26,

50.87189686

Adjust_2, 4.27,

50.753624

Adjust_2, 4.28,

50.63587208

Adjust_2, 4.29,

50.51863861

Adjust_2, 4.3,

50.4019211

Adjust_2, 4.31,

50.28571701

Adjust_2, 4.32,

50.17002382

Adjust_2, 4.33,

50.05483897

Adjust_2, 4.34,

49.94015991

Adjust_2, 4.35,

49.82598405

Adjust_2, 4.36,

49.71230882

Adjust_2, 4.37,

49.59913162

Adjust_2, 4.38,

49.48644985

Adjust_2, 4.39,

49.37426091

Adjust_2, 4.4,

49.2625622

Adjust_2, 4.41,

49.15135109

Adjust_2, 4.42,

49.04062498

Adjust_2, 4.43,

48.93038124

Adjust_2, 4.44,

48.82061726

Adjust_2, 4.45,

48.71133042

Adjust_2, 4.46,

48.60251811

Adjust_2, 4.47,

48.4941777

Adjust_2, 4.48,

48.3863066

Adjust_2, 4.49,

48.27890218

Adjust_2, 4.5,

48.17196184

Adjust_2, 4.51,

48.06548299

Adjust_2, 4.52,

47.95946302

Adjust_2, 4.53,

47.85389936

Adjust_2, 4.54,

47.74878941

Adjust_2, 4.55,

47.6441306

Adjust_2, 4.56,

47.53992036

Adjust_2, 4.57,

47.43615613

Adjust_2, 4.58,

47.33283536

Adjust_2, 4.59,

47.22995551

Adjust_2, 4.6,

47.12751404

Adjust_2, 4.61,

47.02550843

Adjust_2, 4.62,

46.92393616

Adjust_2, 4.63,

46.82279472

Adjust_2, 4.64,

46.72208162

Adjust_2, 4.65,

46.62179439

Adjust_2, 4.66,

46.52193054

Adjust_2, 4.67,

46.42248762

Adjust_2, 4.68,

46.32346317

Adjust_2, 4.69,

46.22485476

Adjust_2, 4.7,

46.12665996

Adjust_2, 4.71,

46.02887636

Adjust_2, 4.72,

45.93150156

Adjust_2, 4.73,

45.83453316

Adjust_2, 4.74,

45.7379688

Adjust_2, 4.75,

45.64180611

Adjust_2, 4.76,

45.54604274

Adjust_2, 4.77,

45.45067635

Adjust_2, 4.78,

45.35570461

Adjust_2, 4.79,

45.26112523

Adjust_2, 4.8,

45.16693589

Adjust_2, 4.81,

45.07313432

Adjust_2, 4.82,

44.97971824

Adjust_2, 4.83,

44.8866854

Adjust_2, 4.84,

44.79403355

Adjust_2, 4.85,

44.70176047

Adjust_2, 4.86,

44.60986394

Adjust_2, 4.87,

44.51834175

Adjust_2, 4.88,

44.42719172

Adjust_2, 4.89,

44.33641168

Adjust_2, 4.9,

44.24599945

Adjust_2, 4.91,

44.1559529

Adjust_2, 4.92,

44.06626989

Adjust_2, 4.93,

43.9769483

Adjust_2, 4.94,

43.88798603

Adjust_2, 4.95,

43.79938098

Adjust_2, 4.96,

43.71113107

Adjust_2, 4.97,

43.62323425

Adjust_2, 4.98,

43.53568845

Adjust_2, 4.99,

43.44849164

Adjust_2, 5, 43.3616418

Adjust_2, 5.01,

43.27513691

Adjust_2, 5.02,

43.18897499

Adjust_2, 5.03,

43.10315404

Adjust_2, 5.04,

43.0176721

Adjust_2, 5.05,

42.93252721

Adjust_2, 5.06,

42.84771742

Adjust_2, 5.07,

42.76324081

Adjust_2, 5.08,

42.67909547

Adjust_2, 5.09,

42.59527948

Adjust_2, 5.1,

42.51179096

Adjust_2, 5.11,

42.42862803

Adjust_2, 5.12,

42.34578882

Adjust_2, 5.13,

42.26327149

Adjust_2, 5.14,

42.18107419

Adjust_2, 5.15,

42.09919511

Adjust_2, 5.16,

42.01763242

Adjust_2, 5.17,

41.93638433

Adjust_2, 5.18,

41.85544905

Adjust_2, 5.19,

41.7748248

Adjust_2, 5.2,

41.69450983

Adjust_2, 5.21,

41.61450237

Adjust_2, 5.22,

41.5348007

Adjust_2, 5.23,

41.45540309

Adjust_2, 5.24,

41.37630782

Adjust_2, 5.25,

41.2975132

Adjust_2, 5.26,

41.21901752

Adjust_2, 5.27,

41.14081912

Adjust_2, 5.28,

41.06291633

Adjust_2, 5.29,

40.98530749

Adjust_2, 5.3,

40.90799096

Adjust_2, 5.31,

40.83096512

Adjust_2, 5.32,

40.75422833

Adjust_2, 5.33,

40.677779

Adjust_2, 5.34,

40.60161553

Adjust_2, 5.35,

40.52573632

Adjust_2, 5.36,

40.45013982

Adjust_2, 5.37,

40.37482444

Adjust_2, 5.38,

40.29978865

Adjust_2, 5.39,

40.2250309

Adjust_2, 5.4,

40.15054966

Adjust_2, 5.41,

40.07634341

Adjust_2, 5.42,

40.00241064

Adjust_2, 5.43,

39.92874985

Adjust_2, 5.44,

39.85535956

Adjust_2, 5.45,

39.78223829

Adjust_2, 5.46,

39.70938457

Adjust_2, 5.47,

39.63679694

Adjust_2, 5.48,

39.56447396

Adjust_2, 5.49,

39.4924142

Adjust_2, 5.5,

39.42061622

Adjust_2, 5.51,

39.34907861

Adjust_2, 5.52,

39.27779997

Adjust_2, 5.53,

39.2067789

Adjust_2, 5.54,

39.136014

Adjust_2, 5.55,

39.06550391

Adjust_2, 5.56,

38.99524726

Adjust_2, 5.57,

38.92524269

Adjust_2, 5.58,

38.85548885

Adjust_2, 5.59,

38.7859844

Adjust_2, 5.6,

38.71672802

Adjust_2, 5.61,

38.64771837

Adjust_2, 5.62,

38.57895416

Adjust_2, 5.63,

38.51043408

Adjust_2, 5.64,

38.44215684

Adjust_2, 5.65,

38.37412114

Adjust_2, 5.66,

38.30632573

Adjust_2, 5.67,

38.23876933

Adjust_2, 5.68,

38.17145067

Adjust_2, 5.69,

38.10436853

Adjust_2, 5.7,

38.03752164

Adjust_2, 5.71,

37.97090879

Adjust_2, 5.72,

37.90452875

Adjust_2, 5.73,

37.8383803

Adjust_2, 5.74,

37.77246223

Adjust_2, 5.75,

37.70677336

Adjust_2, 5.76,

37.64131248

Adjust_2, 5.77,

37.57607842

Adjust_2, 5.78,

37.51107

Adjust_2, 5.79,

37.44628606

Adjust_2, 5.8,

37.38172543

Adjust_2, 5.81,

37.31738697

Adjust_2, 5.82,

37.25326954

Adjust_2, 5.83,

37.18937199

Adjust_2, 5.84,

37.12569321

Adjust_2, 5.85,

37.06223208

Adjust_2, 5.86,

36.99898747

Adjust_2, 5.87,

36.93595829

Adjust_2, 5.88,

36.87314344

Adjust_2, 5.89,

36.81054183

Adjust_2, 5.9,

36.74815238

Adjust_2, 5.91,

36.68597402

Adjust_2, 5.92,

36.62400566

Adjust_2, 5.93,

36.56224627

Adjust_2, 5.94,

36.50069477

Adjust_2, 5.95,

36.43935013

Adjust_2, 5.96,

36.3782113

Adjust_2, 5.97,

36.31727726

Adjust_2, 5.98,

36.25654697

Adjust_2, 5.99,

36.19601942

Adjust_2, 6, 36.13569359

Adjust_2, 6.01,

36.07556848

Adjust_2, 6.02,

36.01564309

Adjust_2, 6.03,

35.95591643

Adjust_2, 6.04,

35.89638751

Adjust_2, 6.05,

35.83705535

Adjust_2, 6.06,

35.77791898

Adjust_2, 6.07,

35.71897743

Adjust_2, 6.08,

35.66022975

Adjust_2, 6.09,

35.60167497

Adjust_2, 6.1,

35.54331215

Adjust_2, 6.11,

35.48514035

Adjust_2, 6.12,

35.42715864

Adjust_2, 6.13,

35.36936608

Adjust_2, 6.14,

35.31176174

Adjust_2, 6.15,

35.25434472

Adjust_2, 6.16,

35.1971141

Adjust_2, 6.17,

35.14006898

Adjust_2, 6.18,

35.08320845

Adjust_2, 6.19,

35.02653162

Adjust_2, 6.2,

34.97003761

Adjust_2, 6.21,

34.91372553

Adjust_2, 6.22,

34.8575945

Adjust_2, 6.23,

34.80164365

Adjust_2, 6.24,

34.74587212

Adjust_2, 6.25,

34.69027905

Adjust_2, 6.26,

34.63486357

Adjust_2, 6.27,

34.57962485

Adjust_2, 6.28,

34.52456204

Adjust_2, 6.29,

34.4696743

Adjust_2, 6.3,

34.41496079

Adjust_2, 6.31,

34.3604207

Adjust_2, 6.32,

34.30605318

Adjust_2, 6.33,

34.25185744

Adjust_2, 6.34,

34.19783265

Adjust_2, 6.35,

34.14397801

Adjust_2, 6.36,

34.09029272

Adjust_2, 6.37,

34.03677598

Adjust_2, 6.38,

33.98342699

Adjust_2, 6.39,

33.93024497

Adjust_2, 6.4,

33.87722914

Adjust_2, 6.41,

33.82437872

Adjust_2, 6.42,

33.77169293

Adjust_2, 6.43,

33.71917102

Adjust_2, 6.44,

33.6668122

Adjust_2, 6.45,

33.61461574

Adjust_2, 6.46,

33.56258087

Adjust_2, 6.47,

33.51070685

Adjust_2, 6.48,

33.45899292

Adjust_2, 6.49,

33.40743835

Adjust_2, 6.5,

33.35604241

Adjust_2, 6.51,

33.30480437

Adjust_2, 6.52,

33.25372349

Adjust_2, 6.53,

33.20279905

Adjust_2, 6.54,

33.15203035

Adjust_2, 6.55,

33.10141666

Adjust_2, 6.56,

33.05095728

Adjust_2, 6.57,

33.00065149

Adjust_2, 6.58,

32.95049861

Adjust_2, 6.59,

32.90049794

Adjust_2, 6.6,

32.85064878

Adjust_2, 6.61,

32.80095045

Adjust_2, 6.62,

32.75140226

Adjust_2, 6.63,

32.70200353

Adjust_2, 6.64,

32.65275359

Adjust_2, 6.65,

32.60365177

Adjust_2, 6.66,

32.5546974

Adjust_2, 6.67,

32.50588982

Adjust_2, 6.68,

32.45722837

Adjust_2, 6.69,

32.40871239

Adjust_2, 6.7,

32.36034123

Adjust_2, 6.71,

32.31211424

Adjust_2, 6.72,

32.26403079

Adjust_2, 6.73,

32.21609022

Adjust_2, 6.74,

32.16829192

Adjust_2, 6.75,

32.12063523

Adjust_2, 6.76,

32.07311954

Adjust_2, 6.77,

32.02574422

Adjust_2, 6.78,

31.97850865

Adjust_2, 6.79,

31.93141221

Adjust_2, 6.8,

31.88445428

Adjust_2, 6.81,

31.83763427

Adjust_2, 6.82,

31.79095155

Adjust_2, 6.83,

31.74440553

Adjust_2, 6.84,

31.69799561

Adjust_2, 6.85,

31.6517212

Adjust_2, 6.86,

31.60558169

Adjust_2, 6.87,

31.5595765

Adjust_2, 6.88,

31.51370505

Adjust_2, 6.89,

31.46796675

Adjust_2, 6.9,

31.42236103

Adjust_2, 6.91,

31.3768873

Adjust_2, 6.92,

31.331545

Adjust_2, 6.93,

31.28633356

Adjust_2, 6.94,

31.24125241

Adjust_2, 6.95,

31.19630098

Adjust_2, 6.96,

31.15147873

Adjust_2, 6.97,

31.10678509

Adjust_2, 6.98,

31.06221951

Adjust_2, 6.99,

31.01778145

Adjust_2, 7, 30.97347035

Adjust_2, 7.01,

30.92928567

Adjust_2, 7.02,

30.88522687

Adjust_2, 7.03,

30.84129342

Adjust_2, 7.04,

30.79748478

Adjust_2, 7.05,

30.75380042

Adjust_2, 7.06,

30.71023981

Adjust_2, 7.07,

30.66680242

Adjust_2, 7.08,

30.62348774

Adjust_2, 7.09,

30.58029524

Adjust_2, 7.1,

30.53722442

Adjust_2, 7.11,

30.49427474

Adjust_2, 7.12,

30.45144572

Adjust_2, 7.13,

30.40873683

Adjust_2, 7.14,

30.36614757

Adjust_2, 7.15,

30.32367744

Adjust_2, 7.16,

30.28132594

Adjust_2, 7.17,

30.23909258

Adjust_2, 7.18,

30.19697686

Adjust_2, 7.19,

30.15497829

Adjust_2, 7.2,

30.11309639

Adjust_2, 7.21,

30.07133066

Adjust_2, 7.22,

30.02968062

Adjust_2, 7.23,

29.9881458

Adjust_2, 7.24,

29.94672571

Adjust_2, 7.25,

29.90541989

Adjust_2, 7.26,

29.86422786

Adjust_2, 7.27,

29.82314915

Adjust_2, 7.28,

29.78218329

Adjust_2, 7.29,

29.74132982

Adjust_2, 7.3,

29.70058827

Adjust_2, 7.31,

29.6599582

Adjust_2, 7.32,

29.61943914

Adjust_2, 7.33,

29.57903063

Adjust_2, 7.34,

29.53873222

Adjust_2, 7.35,

29.49854348

Adjust_2, 7.36,

29.45846394

Adjust_2, 7.37,

29.41849316

Adjust_2, 7.38,

29.37863071

Adjust_2, 7.39,

29.33887614

Adjust_2, 7.4,

29.29922901

Adjust_2, 7.41,

29.2596889

Adjust_2, 7.42,

29.22025536

Adjust_2, 7.43,

29.18092796

Adjust_2, 7.44,

29.14170629

Adjust_2, 7.45,

29.10258991

Adjust_2, 7.46,

29.06357839

Adjust_2, 7.47,

29.02467133

Adjust_2, 7.48,

28.9858683

Adjust_2, 7.49,

28.94716887

Adjust_2, 7.5,

28.90857265

Adjust_2, 7.51,

28.87007921

Adjust_2, 7.52,

28.83168815

Adjust_2, 7.53,

28.79339906

Adjust_2, 7.54,

28.75521153

Adjust_2, 7.55,

28.71712516

Adjust_2, 7.56,

28.67913955

Adjust_2, 7.57,

28.64125429

Adjust_2, 7.58,

28.603469

Adjust_2, 7.59,

28.56578327

Adjust_2, 7.6,

28.52819671

Adjust_2, 7.61,

28.49070894

Adjust_2, 7.62,

28.45331956

Adjust_2, 7.63,

28.41602818

Adjust_2, 7.64,

28.37883443

Adjust_2, 7.65,

28.34173792

Adjust_2, 7.66,

28.30473826

Adjust_2, 7.67,

28.26783508

Adjust_2, 7.68,

28.23102801

Adjust_2, 7.69,

28.19431666

Adjust_2, 7.7,

28.15770066

Adjust_2, 7.71,

28.12117965

Adjust_2, 7.72,

28.08475325

Adjust_2, 7.73,

28.0484211

Adjust_2, 7.74,

28.01218283

Adjust_2, 7.75,

27.97603808

Adjust_2, 7.76,

27.93998649

Adjust_2, 7.77,

27.90402769

Adjust_2, 7.78,

27.86816133

Adjust_2, 7.79,

27.83238706

Adjust_2, 7.8,

27.79670451

Adjust_2, 7.81,

27.76111334

Adjust_2, 7.82,

27.72561319

Adjust_2, 7.83,

27.69020373

Adjust_2, 7.84,

27.65488459

Adjust_2, 7.85,

27.61965544

Adjust_2, 7.86,

27.58451593

Adjust_2, 7.87,

27.54946572

Adjust_2, 7.88,

27.51450447

Adjust_2, 7.89,

27.47963184

Adjust_2, 7.9,

27.4448475

Adjust_2, 7.91,

27.4101511

Adjust_2, 7.92,

27.37554233

Adjust_2, 7.93,

27.34102084

Adjust_2, 7.94,

27.3065863

Adjust_2, 7.95,

27.27223839

Adjust_2, 7.96,

27.23797679

Adjust_2, 7.97,

27.20380116

Adjust_2, 7.98,

27.16971118

Adjust_2, 7.99,

27.13570654

Adjust_2, 8, 27.10178691

Adjust_2, 8.01,

27.06795197

Adjust_2, 8.02,

27.0342014

Adjust_2, 8.03,

27.0005349

Adjust_2, 8.04,

26.96695215

Adjust_2, 8.05,

26.93345283

Adjust_2, 8.06,

26.90003663

Adjust_2, 8.07,

26.86670325

Adjust_2, 8.08,

26.83345238

Adjust_2, 8.09,

26.80028372

Adjust_2, 8.1,

26.76719695

Adjust_2, 8.11,

26.73419177

Adjust_2, 8.12,

26.70126789

Adjust_2, 8.13,

26.668425

Adjust_2, 8.14,

26.63566281

Adjust_2, 8.15,

26.60298101

Adjust_2, 8.16,

26.57037932

Adjust_2, 8.17,

26.53785744

Adjust_2, 8.18,

26.50541507

Adjust_2, 8.19,

26.47305193

Adjust_2, 8.2,

26.44076772

Adjust_2, 8.21,

26.40856215

Adjust_2, 8.22,

26.37643495

Adjust_2, 8.23,

26.34438582

Adjust_2, 8.24,

26.31241448

Adjust_2, 8.25,

26.28052064

Adjust_2, 8.26,

26.24870403

Adjust_2, 8.27,

26.21696436

Adjust_2, 8.28,

26.18530136

Adjust_2, 8.29,

26.15371475

Adjust_2, 8.3,

26.12220425

Adjust_2, 8.31,

26.09076959

Adjust_2, 8.32,

26.05941049

Adjust_2, 8.33,

26.02812668

Adjust_2, 8.34,

25.9969179

Adjust_2, 8.35,

25.96578387

Adjust_2, 8.36,

25.93472432

Adjust_2, 8.37,

25.90373898

Adjust_2, 8.38,

25.8728276

Adjust_2, 8.39,

25.8419899

Adjust_2, 8.4,

25.81122563

Adjust_2, 8.41,

25.78053452

Adjust_2, 8.42,

25.74991631

Adjust_2, 8.43,

25.71937073

Adjust_2, 8.44,

25.68889755

Adjust_2, 8.45,

25.65849648

Adjust_2, 8.46,

25.62816729

Adjust_2, 8.47,

25.59790972

Adjust_2, 8.48,

25.5677235

Adjust_2, 8.49,

25.5376084

Adjust_2, 8.5,

25.50756415

Adjust_2, 8.51,

25.47759052

Adjust_2, 8.52,

25.44768724

Adjust_2, 8.53,

25.41785408

Adjust_2, 8.54,

25.38809078

Adjust_2, 8.55,

25.35839711

Adjust_2, 8.56,

25.32877281

Adjust_2, 8.57,

25.29921765

Adjust_2, 8.58,

25.26973139

Adjust_2, 8.59,

25.24031377

Adjust_2, 8.6,

25.21096457

Adjust_2, 8.61,

25.18168354

Adjust_2, 8.62,

25.15247045

Adjust_2, 8.63,

25.12332506

Adjust_2, 8.64,

25.09424714

Adjust_2, 8.65,

25.06523645

Adjust_2, 8.66,

25.03629276

Adjust_2, 8.67,

25.00741584

Adjust_2, 8.68,

24.97860545

Adjust_2, 8.69,

24.94986137

Adjust_2, 8.7,

24.92118337

Adjust_2, 8.71,

24.89257122

Adjust_2, 8.72,

24.86402469

Adjust_2, 8.73,

24.83554356

Adjust_2, 8.74,

24.80712761

Adjust_2, 8.75,

24.77877661

Adjust_2, 8.76,

24.75049033

Adjust_2, 8.77,

24.72226856

Adjust_2, 8.78,

24.69411108

Adjust_2, 8.79,

24.66601767

Adjust_2, 8.8,

24.6379881

Adjust_2, 8.81,

24.61002217

Adjust_2, 8.82,

24.58211965

Adjust_2, 8.83,

24.55428033

Adjust_2, 8.84,

24.52650399

Adjust_2, 8.85,

24.49879043

Adjust_2, 8.86,

24.47113942

Adjust_2, 8.87,

24.44355077

Adjust_2, 8.88,

24.41602425

Adjust_2, 8.89,

24.38855965

Adjust_2, 8.9,

24.36115678

Adjust_2, 8.91,

24.33381541

Adjust_2, 8.92,

24.30653535

Adjust_2, 8.93,

24.27931638

Adjust_2, 8.94,

24.25215831

Adjust_2, 8.95,

24.22506093

Adjust_2, 8.96,

24.19802403

Adjust_2, 8.97,

24.17104741

Adjust_2, 8.98,

24.14413088

Adjust_2, 8.99,

24.11727423

Adjust_2, 9, 24.09047726

Adjust_2, 9.01,

24.06373977

Adjust_2, 9.02,

24.03706156

Adjust_2, 9.03,

24.01044245

Adjust_2, 9.04,

23.98388222

Adjust_2, 9.05,

23.9573807

Adjust_2, 9.06,

23.93093767

Adjust_2, 9.07,

23.90455295

Adjust_2, 9.08,

23.87822635

Adjust_2, 9.09,

23.85195768

Adjust_2, 9.1,

23.82574674

Adjust_2, 9.11,

23.79959334

Adjust_2, 9.12,

23.77349729

Adjust_2, 9.13,

23.74745841

Adjust_2, 9.14,

23.72147651

Adjust_2, 9.15,

23.6955514

Adjust_2, 9.16,

23.66968289

Adjust_2, 9.17,

23.64387081

Adjust_2, 9.18,

23.61811496

Adjust_2, 9.19,

23.59241516

Adjust_2, 9.2,

23.56677123

Adjust_2, 9.21,

23.54118299

Adjust_2, 9.22,

23.51565025

Adjust_2, 9.23,

23.49017284

Adjust_2, 9.24,

23.46475057

Adjust_2, 9.25,

23.43938328

Adjust_2, 9.26,

23.41407077

Adjust_2, 9.27,

23.38881287

Adjust_2, 9.28,

23.36360941

Adjust_2, 9.29,

23.3384602

Adjust_2, 9.3,

23.31336509

Adjust_2, 9.31,

23.28832388

Adjust_2, 9.32,

23.26333641

Adjust_2, 9.33,

23.2384025

Adjust_2, 9.34,

23.21352198

Adjust_2, 9.35,

23.18869468

Adjust_2, 9.36,

23.16392044

Adjust_2, 9.37,

23.13919907

Adjust_2, 9.38,

23.11453042

Adjust_2, 9.39,

23.0899143

Adjust_2, 9.4,

23.06535056

Adjust_2, 9.41,

23.04083903

Adjust_2, 9.42,

23.01637954

Adjust_2, 9.43,

22.99197193

Adjust_2, 9.44,

22.96761603

Adjust_2, 9.45,

22.94331167

Adjust_2, 9.46,

22.9190587

Adjust_2, 9.47,

22.89485695

Adjust_2, 9.48,

22.87070626

Adjust_2, 9.49,

22.84660646

Adjust_2, 9.5,

22.8225574

Adjust_2, 9.51,

22.79855892

Adjust_2, 9.52,

22.77461085

Adjust_2, 9.53,

22.75071304

Adjust_2, 9.54,

22.72686534

Adjust_2, 9.55,

22.70306757

Adjust_2, 9.56,

22.67931959

Adjust_2, 9.57,

22.65562124

Adjust_2, 9.58,

22.63197237

Adjust_2, 9.59,

22.60837282

Adjust_2, 9.6,

22.58482243

Adjust_2, 9.61,

22.56132105

Adjust_2, 9.62,

22.53786853

Adjust_2, 9.63,

22.51446472

Adjust_2, 9.64,

22.49110947

Adjust_2, 9.65,

22.46780262

Adjust_2, 9.66,

22.44454403

Adjust_2, 9.67,

22.42133354

Adjust_2, 9.68,

22.398171

Adjust_2, 9.69,

22.37505627

Adjust_2, 9.7,

22.35198921

Adjust_2, 9.71,

22.32896965

Adjust_2, 9.72,

22.30599746

Adjust_2, 9.73,

22.28307249

Adjust_2, 9.74,

22.26019459

Adjust_2, 9.75,

22.23736362

Adjust_2, 9.76,

22.21457944

Adjust_2, 9.77,

22.19184189

Adjust_2, 9.78,

22.16915085

Adjust_2, 9.79,

22.14650616

Adjust_2, 9.8,

22.12390768

Adjust_2, 9.81,

22.10135528

Adjust_2, 9.82,

22.07884881

Adjust_2, 9.83,

22.05638813

Adjust_2, 9.84,

22.0339731

Adjust_2, 9.85,

22.01160358

Adjust_2, 9.86,

21.98927944

Adjust_2, 9.87,

21.96700054

Adjust_2, 9.88,

21.94476673

Adjust_2, 9.89,

21.92257789

Adjust_2, 9.9,

21.90043387

Adjust_2, 9.91,

21.87833454

Adjust_2, 9.92,

21.85627977

Adjust_2, 9.93,

21.83426942

Adjust_2, 9.94,

21.81230335

Adjust_2, 9.95,

21.79038144

Adjust_2, 9.96,

21.76850354

Adjust_2, 9.97,

21.74666954

Adjust_2, 9.98,

21.72487929

Adjust_2, 9.99,

21.70313266

Adjust_2, 10, 21.68142953

Ene

rgy

(kca

l/m

ol)

Distance (A)

41

( )

Equation 3-4

( )

( ( ) Equation 3-5

( )

( ( ) ) ( ( ) ) Equation 3-6

All tests for sulfuric acid parameterization were performed using the Large-scale

Atomic/Molecular Massively Parallel Simulator (LAMMPS) Molecular Dynamics Simulator

[67]. These tests were designed to parameterize force parameters to produce our desired solution

structure of HSO4- and our desired RDF. LAMMPS is a classical molecular dynamics code

typically used for polymer, metal, biological or semiconductor systems capable of handling both

all-atom or coarse-grained simulations. Our simulations were done on all atoms. Force fields

were user specified in a tabular format, with 1000 equidistant bins for distances between 0 – 10 Å

for atom pairs with potential forms not included in the package. Harmonic bonds were specified

for OS-S and OS-OS pairs within a sulfate group and Lennard-Jones forms were specified for all

non-bonded sulfur-oxygen interactions with a cutoff of 9.0 Å. Charges were defined for all atoms

to be those previously specified per the CFM partial charges. The Verlet algorithm was used for

integration of Newton‟s equations and periodic boundary conditions were applied in all directions

to remove end effects. The simulation temperature was 300 K.

The simulation box was 19.403 X 19.204 X 23.36 Å3 consisting of 897 atoms. The

solution consists of six sulfuric acid molecules and 285 water molecules, corresponding to a

sulfuric acid concentration of 1.14 M and a solution density of 1.09 g/cm3, matching the

experimental value of density for the given concentration. The box size was chosen to facilitate

later simulations including the platinum surface and will be described in the next section. For pre-

screening runs to differentiate between functions, simulations were run for 2x106 steps with a

42

time step of 0.25 fs for a total of 500 ps. Short time steps are required due to the reactive nature of

the O-H bonds. Coordinates were output every 1000 steps, so the RDF plots were generated from

a sample of 2001 coordinate files (including the initial structure). Subsequent runs used to decide

on a final version of the force field used identical parameters and set up, but were run for 16x106

steps, or 4000 ps (4 ns).

For all potentials tested, the results were analyzed against two criteria, both of which

were based upon radial distribution function (RDF) plots. A RDF plots, as a function of distance,

the likelihood of finding an atom at a given position in space relative to another atom. Areas on

the chart in which the value of the RDF is greater than 1 denote a region in which atoms are more

likely to be found, and vice versa. All plots will reach a value of 1 at a distance far enough away

from the reference point, indicating that coordination is no longer a function of distance.

Of the two criteria, the first was the average coordination for OS-H in the first peak.

Because the bisulfate anion is favored in our simulation, information from the first peak can be

used to determine the average structure. The first peak in the OS-H RDF occurs near 1 Å in all of

the tests. Because there are four OS atoms on each sulfate group, and one proton is desired on the

sulfate group, a correct structure would provide a numerical integration of the first peak equal to

0.25, or 0.25 hydrogen atoms for every OS. The second criterion is a comparison to the only

available ab initio MD structural data for aqueous sulfuric acid [51]. All RDF plots were

compared to that provided by Ikeshoji et al, shown in Figure 3-3.

The three potential forms were differentiated primarily through the shape of the RDF

after the first peak. The first peak height and location can be tuned through the adjustment of the

first term parameters in the force equation (A/rB), so it was not considered as strongly in the

prescreening. However, for all values tested for the equations, a poor RDF was obtained. In the

case of CFM-1, there was no well defined second peak. Each fitting produced a continuous

increase in the value of the RDF until a maximum value at a distance of approximately 3.4 Å.

43

Instead, we expect a well defined second peak near 1.7 – 1.9 Å, followed by an obvious well and

a final peak feature at approximately 3.3 Å. The oscillations in peaks produced by CFM-1 were

reproducible for all runs and steered us away from the use of the CFM-1 description for a OS-H

potential.

Figure 3-7: RDF for the S-H distance for CFM-1 and CFM-OO (right image is zoomed in to

show the second peak information used to eliminate these potentials from consideration)

Results from CFM-OO also failed based on the shape of the second peak. In all tests

performed there was a strong region of vacuum-like space outside the first peak. This trend

showed that dissociated protons, or hydrogen atoms on water molecules, have a large region of

repulsive behavior outside of the equilibrium OS-H bond distance. In other words, if a proton

dissociates, it spends very little time near the atoms from which it dissociated. This feature is not

echoed in the AIMD studies. After this extended region of zero coordination, there is a slow rise

to a second peak which is not well defined, before reaching a well defined third peak similar to

the trend seen in CFM-1 studies. The CFM-OO potential form was also discarded based upon the

long range features in the OS-H RDF generated from the prescreening tests. Figure 3-7 shows the

RDF for both CFM-1 and CFM-OO used to decide against these potentials for our study.

CFM-2 potentials produced a much better fit against available data. Though trends in the

first peak were not indicative of our simulation producing an average bisulfate structure indicated

CFM_1, 0.024005, 0

CFM_1, 0.072015, 0

CFM_1, 0.120025, 0

CFM_1, 0.168035, 0

CFM_1, 0.216045, 0

CFM_1, 0.264055, 0

CFM_1, 0.312065, 0

CFM_1, 0.360075, 0

CFM_1, 0.408085, 0

CFM_1, 0.456095, 0

CFM_1, 0.504105, 0

CFM_1, 0.552115, 0

CFM_1, 0.600125, 0

CFM_1, 0.648135, 0

CFM_1, 0.696145, 0

CFM_1, 0.744155, 0

CFM_1, 0.792165, 0

CFM_1, 0.840175, 0

CFM_1, 0.8881

85, 0.0228

963

CFM_1, 0.9361

95, 4.5539

4

CFM_1, 0.9842

05, 18.480

8 CFM_1, 1.0322

2, 8.5518

4 CFM_1, 1.0802

3, 2.1044

3

CFM_1, 1.1282

4, 0.8352

43

CFM_1, 1.1762

5, 0.6293

17

CFM_1, 1.2242

6, 0.5420

21

CFM_1, 1.2722

7, 0.4591

62

CFM_1, 1.3202

8, 0.3600

54

CFM_1, 1.3682

9, 0.2588

68

CFM_1, 1.4163, 0.1829

49

CFM_1, 1.4643

1, 0.1514

12

CFM_1, 1.5123

2, 0.1739

98

CFM_1, 1.5603

3, 0.2588

58

CFM_1, 1.6083

4, 0.3645

56

CFM_1, 1.6563

5, 0.4675

25

CFM_1, 1.7043

6, 0.5572

34

CFM_1, 1.7523

7, 0.6230

99

CFM_1, 1.8003

8, 0.6350

59

CFM_1, 1.8483

9, 0.6735

06

CFM_1, 1.8964, 0.6448

61

CFM_1, 1.9444

1, 0.6494

54

CFM_1, 1.9924

2, 0.6460

99

CFM_1, 2.0404

2, 0.6123

34

CFM_1, 2.0884

4, 0.6176

42

CFM_1, 2.1364

5, 0.6175

63

CFM_1, 2.1844

5, 0.6349

58

CFM_1, 2.2324

6, 0.6555

84

CFM_1, 2.2804

8, 0.7130

34

CFM_1, 2.3284

9, 0.7984

63

CFM_1, 2.3765, 0.8825

09

CFM_1, 2.4245, 0.9918

28

CFM_1, 2.4725

2, 1.0812

7

CFM_1, 2.5205

3, 1.1225

3

CFM_1, 2.5685

4, 1.1269

6

CFM_1, 2.6165

4, 1.0523

6

CFM_1, 2.6645

6, 0.9979

15

CFM_1, 2.7125

7, 0.9593

96

CFM_1, 2.7605

8, 0.9085

03

CFM_1, 2.8085

8, 0.8664

54

CFM_1, 2.8565

9, 0.8647

75

CFM_1, 2.9046

1, 0.8691

57

CFM_1, 2.9526

2, 0.9271

53

CFM_1, 3.0006

2, 1.0174

8

CFM_1, 3.0486

3, 1.1178

7

CFM_1, 3.0966

5, 1.2317

2

CFM_1, 3.1446

6, 1.3613

3

CFM_1, 3.1926

7, 1.4452

2

CFM_1, 3.2406

7, 1.5045

1

CFM_1, 3.2886

9, 1.6376

8

CFM_1, 3.3367, 1.659

CFM_1, 3.3847

1, 1.504

CFM_1, 3.4327

1, 1.2162

6

CFM_1, 3.4807

3, 1.0373

1

CFM_1, 3.5287

4, 0.9839

09

CFM_1, 3.5767

5, 0.9819

63

CFM_1, 3.6247

5, 1.0473

1

CFM_1, 3.6727

7, 1.1065

9

CFM_1, 3.7207

8, 1.0641

6

CFM_1, 3.7687

9, 0.9387

72

CFM_1, 3.8167

9, 0.7998

99

CFM_1, 3.8648

1, 0.7286

57

CFM_1, 3.9128

2, 0.7037

05

CFM_1, 3.9608

3, 0.6927

7

CFM_1, 4.0088

4, 0.6961

58

CFM_1, 4.0568

5, 0.7148

12

CFM_1, 4.1048

6, 0.7143

34

CFM_1, 4.1528

7, 0.7255

99

CFM_1, 4.2008

7, 0.7309

58

CFM_1, 4.2488

9, 0.7382

65

CFM_1, 4.2969, 0.7596

86

CFM_1, 4.3449, 0.7566

34

CFM_1, 4.3929

2, 0.7643

14

CFM_1, 4.4409

3, 0.7736

84

CFM_1, 4.4889

4, 0.7917

03

CFM_1, 4.5369

5, 0.7791

99

CFM_1, 4.5849

5, 0.7962

88

CFM_1, 4.6329

7, 0.8132

73

CFM_1, 4.6809

8, 0.8218

6

CFM_1, 4.7289

9, 0.8391

87

CFM_1, 4.777, 0.8597

05

CFM_1, 4.825, 0.8783

79

CFM_1, 4.8730

2, 0.8978

5

CFM_1, 4.9210

3, 0.9188

48

CFM_1, 4.9690

3, 0.9331

85

CFM_1, 5.0170

5, 0.9661

05

CFM_1, 5.0650

6, 0.9881

38

CFM_1, 5.1130

7, 0.9925

33

CFM_1, 5.1610

8, 1.005

CFM_1, 5.2090

8, 1.0181

8

CFM_1, 5.2571, 1.0323

5

CFM_1, 5.3051

1, 1.0465

1

CFM_1, 5.3531

1, 1.0636

5

CFM_1, 5.4011

3, 1.0760

8

CFM_1, 5.4491

4, 1.0979

3

CFM_1, 5.4971

5, 1.1045

6

CFM_1, 5.5451

6, 1.1054

9

CFM_1, 5.5931

6, 1.1034

3

CFM_1, 5.6411

8, 1.0897

9

CFM_1, 5.6891

9, 1.0957

1

CFM_1, 5.7372, 1.0787

4

CFM_1, 5.7852

1, 1.0705

1

CFM_1, 5.8332

2, 1.0678

5

CFM_1, 5.8812

3, 1.0515

3

CFM_1, 5.9292

4, 1.0465

5

CFM_1, 5.9772

4, 1.0410

9

CFM_1, 6.0252

6, 1.0339

6

CFM_1, 6.0732

7, 1.0268

6

CFM_1, 6.1212

8, 1.0123

1

CFM_1, 6.1692

9, 1.0164

CFM_1, 6.2173, 1.0116

1

CFM_1, 6.2653

1, 1.0044

3

CFM_1, 6.3133

2, 1.0053

8

CFM_1, 6.3613

3, 1.0064

1

CFM_1, 6.4093

4, 0.9994

41

CFM_1, 6.4573

5, 0.9954

55

CFM_1, 6.5053

6, 1.0014

9

CFM_1, 6.5533

7, 0.9978

08

CFM_1, 6.6013

7, 1.0060

1

CFM_1, 6.6493

9, 0.9936

45

CFM_1, 6.6974, 1.0075

5

CFM_1, 6.7454

1, 1.0034

2

CFM_1, 6.7934

2, 1.0124

8

CFM_1, 6.8414

3, 1.0077

5

CFM_1, 6.8894

4, 1.0047

7

CFM_1, 6.9374

5, 1.0119

CFM_1, 6.9854

6, 1.0169

4

CFM_1, 7.0334

7, 1.0119

9

CFM_1, 7.0814

8, 1.0216

4

CFM_1, 7.1294

9, 1.0221

CFM_1, 7.1775, 1.0241

7

CFM_1, 7.2255

1, 1.0196

9

CFM_1, 7.2735

2, 1.0317

2

CFM_1, 7.3215

3, 1.0280

4

CFM_1, 7.3695

4, 1.0225

7

CFM_1, 7.4175

5, 1.0282

4

CFM_1, 7.4655

6, 1.0241

9

CFM_1, 7.5135

7, 1.0324

3

CFM_1, 7.5615

8, 1.0230

4

CFM_1, 7.6095

9, 1.0184

4

CFM_1, 7.6576, 1.0225

9

CFM_1, 7.7056

1, 1.0197

6

CFM_1, 7.7536

2, 1.0106

9

CFM_1, 7.8016

3, 1.0135

4

CFM_1, 7.8496

4, 1.0096

2

CFM_1, 7.8976

5, 1.0050

6

CFM_1, 7.9456

6, 1.0068

5

CFM_1, 7.9936

7, 1.0025

7

CFM_1, 8.0416

8, 0.9995

64

CFM_1, 8.0896

9, 0.9980

84

CFM_1, 8.1377, 1.0004

6

CFM_1, 8.1857

1, 0.9899

13

CFM_1, 8.2337

2, 0.9877

9

CFM_1, 8.2817

3, 0.9875

62

CFM_1, 8.3297

4, 0.9909

04

CFM_1, 8.3777

5, 0.9854

78

CFM_1, 8.4257

6, 0.9876

65

CFM_1, 8.4737

7, 0.9885

61

CFM_1, 8.5217

8, 0.9828

2

CFM_1, 8.5697

9, 0.9856

36

CFM_1, 8.6178, 0.9922

14

CFM_1, 8.6658

1, 0.9874

37

CFM_1, 8.7138

2, 0.9904

75

CFM_1, 8.7618

3, 0.9911

81

CFM_1, 8.8098

4, 0.9927

32

CFM_1, 8.8578

5, 0.9922

96

CFM_1, 8.9058

6, 0.9916

61

CFM_1, 8.9538

7, 0.9945

51

CFM_1, 9.0018

8, 1.0003

2

CFM_1, 9.0498

9, 1.0030

7

CFM_1, 9.0979, 1.0015

7

CFM_1, 9.1459

1, 1.0064

3

CFM_1, 9.1939

2, 1.0066

7

CFM_1, 9.2419

3, 1.0104

2

CFM_1, 9.2899

4, 1.0066

9

CFM_1, 9.3379

5, 1.0100

9

CFM_1, 9.3859

6, 1.0184

6

CFM_1, 9.4339

7, 1.0157

3

CFM_1, 9.4819

8, 1.0160

2

CFM_1, 9.5299

9, 1.0174

9

CFM_1, 9.578, 1.0161

9

CFM_OO,

0.024005, 0

CFM_OO,

0.072015, 0

CFM_OO,

0.120025, 0

CFM_OO,

0.168035, 0

CFM_OO,

0.216045, 0

CFM_OO,

0.264055, 0

CFM_OO,

0.312065, 0

CFM_OO,

0.360075, 0

CFM_OO,

0.408085, 0

CFM_OO,

0.456095, 0

CFM_OO,

0.504105, 0

CFM_OO,

0.552115, 0

CFM_OO,

0.600125, 0

CFM_OO,

0.648135, 0

CFM_OO,

0.696145, 0

CFM_OO,

0.744155, 0

CFM_OO,

0.792165, 0

CFM_OO,

0.840175, 0

CFM_OO,

0.888185,

0.0340174

CFM_OO,

0.936195,

5.69742

CFM_OO,

0.984205,

15.966

CFM_OO,

1.03222,

4.95576

CFM_OO,

1.08023,

0.779321

CFM_OO,

1.12824,

0.302066

CFM_OO,

1.17625,

0.245087

CFM_OO,

1.22426,

0.207993

CFM_OO,

1.27227,

0.160388

CFM_OO,

1.32028,

0.115182

CFM_OO,

1.36829,

0.0719537

CFM_OO,

1.4163, 0.0460

59

CFM_OO,

1.46431,

0.0389963

CFM_OO,

1.51232,

0.0309179

CFM_OO,

1.56033,

0.0390089

CFM_OO,

1.60834,

0.0540748

CFM_OO,

1.65635,

0.0874846

CFM_OO,

1.70436,

0.118874

CFM_OO,

1.75237,

0.157161

CFM_OO,

1.80038,

0.217844

CFM_OO,

1.84839,

0.268768

CFM_OO,

1.8964, 0.3270

95

CFM_OO,

1.94441,

0.39142

CFM_OO,

1.99242,

0.448329

CFM_OO,

2.04042,

0.520093

CFM_OO,

2.08844,

0.568055

CFM_OO,

2.13645,

0.596189

CFM_OO,

2.18445,

0.645234

CFM_OO,

2.23246,

0.665008

CFM_OO,

2.28048,

0.673134

CFM_OO,

2.32849,

0.717351

CFM_OO,

2.3765, 0.7617

76

CFM_OO,

2.4245, 0.8039

12

CFM_OO,

2.47252,

0.867478

CFM_OO,

2.52053,

0.895927

CFM_OO,

2.56854,

0.912118

CFM_OO,

2.61654,

0.879632

CFM_OO,

2.66456,

0.828881

CFM_OO,

2.71257,

0.771951

CFM_OO,

2.76058,

0.708555

CFM_OO,

2.80858,

0.664057

CFM_OO,

2.85659,

0.652488

CFM_OO,

2.90461,

0.671477

CFM_OO,

2.95262,

0.711751

CFM_OO,

3.00062,

0.794816

CFM_OO,

3.04863,

0.875391

CFM_OO,

3.09665,

0.982601

CFM_OO,

3.14466,

1.06427

CFM_OO,

3.19267,

1.1431

CFM_OO,

3.24067,

1.25512

CFM_OO,

3.28869,

1.38846

CFM_OO,

3.3367, 1.4640

5

CFM_OO,

3.38471,

1.31021

CFM_OO,

3.43271,

1.06583

CFM_OO,

3.48073,

0.925474

CFM_OO,

3.52874,

0.888731

CFM_OO,

3.57675,

0.874636

CFM_OO,

3.62475,

0.894168

CFM_OO,

3.67277,

0.940245

CFM_OO,

3.72078,

1.02412

CFM_OO,

3.76879,

1.03602

CFM_OO,

3.81679,

0.988862

CFM_OO,

3.86481,

0.910537

CFM_OO,

3.91282,

0.836813

CFM_OO,

3.96083,

0.791709

CFM_OO,

4.00884,

0.773695

CFM_OO,

4.05685,

0.778481

CFM_OO,

4.10486,

0.778973

CFM_OO,

4.15287,

0.777079

CFM_OO,

4.20087,

0.78978

CFM_OO,

4.24889,

0.79911

CFM_OO,

4.2969, 0.8049

21

CFM_OO,

4.3449, 0.8101

99

CFM_OO,

4.39292,

0.818587

CFM_OO,

4.44093,

0.82768

CFM_OO,

4.48894,

0.834227

CFM_OO,

4.53695,

0.825868

CFM_OO,

4.58495,

0.828675

CFM_OO,

4.63297,

0.841795

CFM_OO,

4.68098,

0.843721

CFM_OO,

4.72899,

0.851559

CFM_OO,

4.777, 0.8581

67

CFM_OO,

4.825, 0.8821

04

CFM_OO,

4.87302,

0.901436

CFM_OO,

4.92103,

0.908254

CFM_OO,

4.96903,

0.927227

CFM_OO,

5.01705,

0.954518

CFM_OO,

5.06506,

0.967374

CFM_OO,

5.11307,

0.984635

CFM_OO,

5.16108,

0.998726

CFM_OO,

5.20908,

1.00515

CFM_OO,

5.2571, 1.0113

6

CFM_OO,

5.30511,

1.02263

CFM_OO,

5.35311,

1.04915

CFM_OO,

5.40113,

1.05836

CFM_OO,

5.44914,

1.06805

CFM_OO,

5.49715,

1.08522

CFM_OO,

5.54516,

1.09015

CFM_OO,

5.59316,

1.09344

CFM_OO,

5.64118,

1.08404

CFM_OO,

5.68919,

1.0734

CFM_OO,

5.7372, 1.0795

7

CFM_OO,

5.78521,

1.06993

CFM_OO,

5.83322,

1.06172

CFM_OO,

5.88123,

1.06153

CFM_OO,

5.92924,

1.04737

CFM_OO,

5.97724,

1.04635

CFM_OO,

6.02526,

1.04611

CFM_OO,

6.07327,

1.03376

CFM_OO,

6.12128,

1.04432

CFM_OO,

6.16929,

1.03162

CFM_OO,

6.2173, 1.0247

5

CFM_OO,

6.26531,

1.02488

CFM_OO,

6.31332,

1.02391

CFM_OO,

6.36133,

1.02086

CFM_OO,

6.40934,

1.01486

CFM_OO,

6.45735,

1.02243

CFM_OO,

6.50536,

1.02154

CFM_OO,

6.55337,

1.02347

CFM_OO,

6.60137,

1.0055

CFM_OO,

6.64939,

1.01599

CFM_OO,

6.6974, 1.0103

3

CFM_OO,

6.74541,

1.01412

CFM_OO,

6.79342,

1.01425

CFM_OO,

6.84143,

1.017

CFM_OO,

6.88944,

1.01569

CFM_OO,

6.93745,

1.01373

CFM_OO,

6.98546,

1.01498

CFM_OO,

7.03347,

1.01106

CFM_OO,

7.08148,

1.01183

CFM_OO,

7.12949,

1.01871

CFM_OO,

7.1775, 1.0161

3

CFM_OO,

7.22551,

1.01627

CFM_OO,

7.27352,

1.0132

CFM_OO,

7.32153,

1.00906

CFM_OO,

7.36954,

1.01771

CFM_OO,

7.41755,

1.01763

CFM_OO,

7.46556,

1.01693

CFM_OO,

7.51357,

1.01576

CFM_OO,

7.56158,

1.01479

CFM_OO,

7.60959,

1.01309

CFM_OO,

7.6576, 1.0093

CFM_OO,

7.70561,

1.01266

CFM_OO,

7.75362,

1.01173

CFM_OO,

7.80163,

1.00434

CFM_OO,

7.84964,

0.999728

CFM_OO,

7.89765,

1.00253

CFM_OO,

7.94566,

1.00615

CFM_OO,

7.99367,

0.998472

CFM_OO,

8.04168,

1.00101

CFM_OO,

8.08969,

0.995962

CFM_OO,

8.1377, 0.9992

73

CFM_OO,

8.18571,

0.99321

CFM_OO,

8.23372,

0.994925

CFM_OO,

8.28173,

1.00028

CFM_OO,

8.32974,

0.995197

CFM_OO,

8.37775,

0.992023

CFM_OO,

8.42576,

0.996972

CFM_OO,

8.47377,

0.994456

CFM_OO,

8.52178,

0.992814

CFM_OO,

8.56979,

0.997093

CFM_OO,

8.6178, 0.9964

89

CFM_OO,

8.66581,

0.994702

CFM_OO,

8.71382,

0.999156

CFM_OO,

8.76183,

1.00444

CFM_OO,

8.80984,

1.00212

CFM_OO,

8.85785,

1.00459

CFM_OO,

8.90586,

1.00442

CFM_OO,

8.95387,

1.00513

CFM_OO,

9.00188,

1.00622

CFM_OO,

9.04989,

1.00833

CFM_OO,

9.0979, 1.0104

8

CFM_OO,

9.14591,

1.01381

CFM_OO,

9.19392,

1.01224

CFM_OO,

9.24193,

1.01477

CFM_OO,

9.28994,

1.01902

CFM_OO,

9.33795,

1.01722

CFM_OO,

9.38596,

1.01617

CFM_OO,

9.43397,

1.02014

CFM_OO,

9.48198,

1.02372

CFM_OO,

9.52999,

1.02169

CFM_OO,

9.578, 1.0192

5

RD

F

Distance (A)

CFM_1

CFM_OO

CFM_1, 0.024005, 0

CFM_1, 0.072015, 0

CFM_1, 0.120025, 0

CFM_1, 0.168035, 0

CFM_1, 0.216045, 0

CFM_1, 0.264055, 0

CFM_1, 0.312065, 0

CFM_1, 0.360075, 0

CFM_1, 0.408085, 0

CFM_1, 0.456095, 0

CFM_1, 0.504105, 0

CFM_1, 0.552115, 0

CFM_1, 0.600125, 0

CFM_1, 0.648135, 0

CFM_1, 0.696145, 0

CFM_1, 0.744155, 0

CFM_1, 0.792165, 0

CFM_1, 0.840175, 0

CFM_1, 0.8881

85, 0.0228

963

CFM_1, 0.9361

95, 4.5539

4

CFM_1, 0.9842

05, 18.480

8

CFM_1, 1.0322

2, 8.5518

4 CFM_1, 1.0802

3, 2.1044

3

CFM_1, 1.1282

4, 0.8352

43

CFM_1, 1.1762

5, 0.6293

17

CFM_1, 1.2242

6, 0.5420

21

CFM_1, 1.2722

7, 0.4591

62

CFM_1, 1.3202

8, 0.3600

54

CFM_1, 1.3682

9, 0.2588

68

CFM_1, 1.4163, 0.1829

49

CFM_1, 1.4643

1, 0.1514

12

CFM_1, 1.5123

2, 0.1739

98

CFM_1, 1.5603

3, 0.2588

58

CFM_1, 1.6083

4, 0.3645

56

CFM_1, 1.6563

5, 0.4675

25

CFM_1, 1.7043

6, 0.5572

34

CFM_1, 1.7523

7, 0.6230

99

CFM_1, 1.8003

8, 0.6350

59

CFM_1, 1.8483

9, 0.6735

06

CFM_1, 1.8964, 0.6448

61

CFM_1, 1.9444

1, 0.6494

54

CFM_1, 1.9924

2, 0.6460

99

CFM_1, 2.0404

2, 0.6123

34

CFM_1, 2.0884

4, 0.6176

42

CFM_1, 2.1364

5, 0.6175

63

CFM_1, 2.1844

5, 0.6349

58

CFM_1, 2.2324

6, 0.6555

84

CFM_1, 2.2804

8, 0.7130

34

CFM_1, 2.3284

9, 0.7984

63

CFM_1, 2.3765, 0.8825

09

CFM_1, 2.4245, 0.9918

28

CFM_1, 2.4725

2, 1.0812

7

CFM_1, 2.5205

3, 1.1225

3

CFM_1, 2.5685

4, 1.1269

6

CFM_1, 2.6165

4, 1.0523

6

CFM_1, 2.6645

6, 0.9979

15

CFM_1, 2.7125

7, 0.9593

96

CFM_1, 2.7605

8, 0.9085

03

CFM_1, 2.8085

8, 0.8664

54

CFM_1, 2.8565

9, 0.8647

75

CFM_1, 2.9046

1, 0.8691

57

CFM_1, 2.9526

2, 0.9271

53

CFM_1, 3.0006

2, 1.0174

8

CFM_1, 3.0486

3, 1.1178

7

CFM_1, 3.0966

5, 1.2317

2

CFM_1, 3.1446

6, 1.3613

3

CFM_1, 3.1926

7, 1.4452

2

CFM_1, 3.2406

7, 1.5045

1

CFM_1, 3.2886

9, 1.6376

8

CFM_1, 3.3367, 1.659

CFM_1, 3.3847

1, 1.504

CFM_1, 3.4327

1, 1.2162

6

CFM_1, 3.4807

3, 1.0373

1

CFM_1, 3.5287

4, 0.9839

09

CFM_1, 3.5767

5, 0.9819

63

CFM_1, 3.6247

5, 1.0473

1

CFM_1, 3.6727

7, 1.1065

9

CFM_1, 3.7207

8, 1.0641

6

CFM_1, 3.7687

9, 0.9387

72

CFM_1, 3.8167

9, 0.7998

99

CFM_1, 3.8648

1, 0.7286

57

CFM_1, 3.9128

2, 0.7037

05

CFM_1, 3.9608

3, 0.6927

7

CFM_1, 4.0088

4, 0.6961

58

CFM_1, 4.0568

5, 0.7148

12

CFM_1, 4.1048

6, 0.7143

34

CFM_1, 4.1528

7, 0.7255

99

CFM_1, 4.2008

7, 0.7309

58

CFM_1, 4.2488

9, 0.7382

65

CFM_1, 4.2969, 0.7596

86

CFM_1, 4.3449, 0.7566

34

CFM_1, 4.3929

2, 0.7643

14

CFM_1, 4.4409

3, 0.7736

84

CFM_1, 4.4889

4, 0.7917

03

CFM_1, 4.5369

5, 0.7791

99

CFM_1, 4.5849

5, 0.7962

88

CFM_1, 4.6329

7, 0.8132

73

CFM_1, 4.6809

8, 0.8218

6

CFM_1, 4.7289

9, 0.8391

87

CFM_1, 4.777, 0.8597

05

CFM_1, 4.825, 0.8783

79

CFM_1, 4.8730

2, 0.8978

5

CFM_1, 4.9210

3, 0.9188

48

CFM_1, 4.9690

3, 0.9331

85

CFM_1, 5.0170

5, 0.9661

05

CFM_1, 5.0650

6, 0.9881

38

CFM_1, 5.1130

7, 0.9925

33

CFM_1, 5.1610

8, 1.005

CFM_1, 5.2090

8, 1.0181

8

CFM_1, 5.2571, 1.0323

5

CFM_1, 5.3051

1, 1.0465

1

CFM_1, 5.3531

1, 1.0636

5

CFM_1, 5.4011

3, 1.0760

8

CFM_1, 5.4491

4, 1.0979

3

CFM_1, 5.4971

5, 1.1045

6

CFM_1, 5.5451

6, 1.1054

9

CFM_1, 5.5931

6, 1.1034

3

CFM_1, 5.6411

8, 1.0897

9

CFM_1, 5.6891

9, 1.0957

1

CFM_1, 5.7372, 1.0787

4

CFM_1, 5.7852

1, 1.0705

1

CFM_1, 5.8332

2, 1.0678

5

CFM_1, 5.8812

3, 1.0515

3

CFM_1, 5.9292

4, 1.0465

5

CFM_1, 5.9772

4, 1.0410

9

CFM_1, 6.0252

6, 1.0339

6

CFM_1, 6.0732

7, 1.0268

6

CFM_1, 6.1212

8, 1.0123

1

CFM_1, 6.1692

9, 1.0164

CFM_1, 6.2173, 1.0116

1

CFM_1, 6.2653

1, 1.0044

3

CFM_1, 6.3133

2, 1.0053

8

CFM_1, 6.3613

3, 1.0064

1

CFM_1, 6.4093

4, 0.9994

41

CFM_1, 6.4573

5, 0.9954

55

CFM_1, 6.5053

6, 1.0014

9

CFM_1, 6.5533

7, 0.9978

08

CFM_1, 6.6013

7, 1.0060

1

CFM_1, 6.6493

9, 0.9936

45

CFM_1, 6.6974, 1.0075

5

CFM_1, 6.7454

1, 1.0034

2

CFM_1, 6.7934

2, 1.0124

8

CFM_1, 6.8414

3, 1.0077

5

CFM_1, 6.8894

4, 1.0047

7

CFM_1, 6.9374

5, 1.0119

CFM_1, 6.9854

6, 1.0169

4

CFM_1, 7.0334

7, 1.0119

9

CFM_1, 7.0814

8, 1.0216

4

CFM_1, 7.1294

9, 1.0221

CFM_1, 7.1775, 1.0241

7

CFM_1, 7.2255

1, 1.0196

9

CFM_1, 7.2735

2, 1.0317

2

CFM_1, 7.3215

3, 1.0280

4

CFM_1, 7.3695

4, 1.0225

7

CFM_1, 7.4175

5, 1.0282

4

CFM_1, 7.4655

6, 1.0241

9

CFM_1, 7.5135

7, 1.0324

3

CFM_1, 7.5615

8, 1.0230

4

CFM_1, 7.6095

9, 1.0184

4

CFM_1, 7.6576, 1.0225

9

CFM_1, 7.7056

1, 1.0197

6

CFM_1, 7.7536

2, 1.0106

9

CFM_1, 7.8016

3, 1.0135

4

CFM_1, 7.8496

4, 1.0096

2

CFM_1, 7.8976

5, 1.0050

6

CFM_1, 7.9456

6, 1.0068

5

CFM_1, 7.9936

7, 1.0025

7

CFM_1, 8.0416

8, 0.9995

64

CFM_1, 8.0896

9, 0.9980

84

CFM_1, 8.1377, 1.0004

6

CFM_1, 8.1857

1, 0.9899

13

CFM_1, 8.2337

2, 0.9877

9

CFM_1, 8.2817

3, 0.9875

62

CFM_1, 8.3297

4, 0.9909

04

CFM_1, 8.3777

5, 0.9854

78

CFM_1, 8.4257

6, 0.9876

65

CFM_1, 8.4737

7, 0.9885

61

CFM_1, 8.5217

8, 0.9828

2

CFM_1, 8.5697

9, 0.9856

36

CFM_1, 8.6178, 0.9922

14

CFM_1, 8.6658

1, 0.9874

37

CFM_1, 8.7138

2, 0.9904

75

CFM_1, 8.7618

3, 0.9911

81

CFM_1, 8.8098

4, 0.9927

32

CFM_1, 8.8578

5, 0.9922

96

CFM_1, 8.9058

6, 0.9916

61

CFM_1, 8.9538

7, 0.9945

51

CFM_1, 9.0018

8, 1.0003

2

CFM_1, 9.0498

9, 1.0030

7

CFM_1, 9.0979, 1.0015

7

CFM_1, 9.1459

1, 1.0064

3

CFM_1, 9.1939

2, 1.0066

7

CFM_1, 9.2419

3, 1.0104

2

CFM_1, 9.2899

4, 1.0066

9

CFM_1, 9.3379

5, 1.0100

9

CFM_1, 9.3859

6, 1.0184

6

CFM_1, 9.4339

7, 1.0157

3

CFM_1, 9.4819

8, 1.0160

2

CFM_1, 9.5299

9, 1.0174

9

CFM_1, 9.578, 1.0161

9 CFM_O

O, 0.024005, 0

CFM_OO,

0.072015, 0

CFM_OO,

0.120025, 0

CFM_OO,

0.168035, 0

CFM_OO,

0.216045, 0

CFM_OO,

0.264055, 0

CFM_OO,

0.312065, 0

CFM_OO,

0.360075, 0

CFM_OO,

0.408085, 0

CFM_OO,

0.456095, 0

CFM_OO,

0.504105, 0

CFM_OO,

0.552115, 0

CFM_OO,

0.600125, 0

CFM_OO,

0.648135, 0

CFM_OO,

0.696145, 0

CFM_OO,

0.744155, 0

CFM_OO,

0.792165, 0

CFM_OO,

0.840175, 0

CFM_OO,

0.888185,

0.0340174

CFM_OO,

0.936195,

5.69742

CFM_OO,

0.984205,

15.966

CFM_OO,

1.03222,

4.95576

CFM_OO,

1.08023,

0.779321

CFM_OO,

1.12824,

0.302066

CFM_OO,

1.17625,

0.245087

CFM_OO,

1.22426,

0.207993

CFM_OO,

1.27227,

0.160388

CFM_OO,

1.32028,

0.115182

CFM_OO,

1.36829,

0.0719537

CFM_OO,

1.4163, 0.0460

59

CFM_OO,

1.46431,

0.0389963

CFM_OO,

1.51232,

0.0309179

CFM_OO,

1.56033,

0.0390089

CFM_OO,

1.60834,

0.0540748

CFM_OO,

1.65635,

0.0874846

CFM_OO,

1.70436,

0.118874

CFM_OO,

1.75237,

0.157161

CFM_OO,

1.80038,

0.217844

CFM_OO,

1.84839,

0.268768

CFM_OO,

1.8964, 0.3270

95

CFM_OO,

1.94441,

0.39142

CFM_OO,

1.99242,

0.448329

CFM_OO,

2.04042,

0.520093

CFM_OO,

2.08844,

0.568055

CFM_OO,

2.13645,

0.596189

CFM_OO,

2.18445,

0.645234

CFM_OO,

2.23246,

0.665008

CFM_OO,

2.28048,

0.673134

CFM_OO,

2.32849,

0.717351

CFM_OO,

2.3765, 0.7617

76

CFM_OO,

2.4245, 0.8039

12

CFM_OO,

2.47252,

0.867478

CFM_OO,

2.52053,

0.895927

CFM_OO,

2.56854,

0.912118

CFM_OO,

2.61654,

0.879632

CFM_OO,

2.66456,

0.828881

CFM_OO,

2.71257,

0.771951

CFM_OO,

2.76058,

0.708555

CFM_OO,

2.80858,

0.664057

CFM_OO,

2.85659,

0.652488

CFM_OO,

2.90461,

0.671477

CFM_OO,

2.95262,

0.711751

CFM_OO,

3.00062,

0.794816

CFM_OO,

3.04863,

0.875391

CFM_OO,

3.09665,

0.982601

CFM_OO,

3.14466,

1.06427

CFM_OO,

3.19267,

1.1431

CFM_OO,

3.24067,

1.25512

CFM_OO,

3.28869,

1.38846

CFM_OO,

3.3367, 1.4640

5

CFM_OO,

3.38471,

1.31021

CFM_OO,

3.43271,

1.06583

CFM_OO,

3.48073,

0.925474

CFM_OO,

3.52874,

0.888731

CFM_OO,

3.57675,

0.874636

CFM_OO,

3.62475,

0.894168

CFM_OO,

3.67277,

0.940245

CFM_OO,

3.72078,

1.02412

CFM_OO,

3.76879,

1.03602

CFM_OO,

3.81679,

0.988862

CFM_OO,

3.86481,

0.910537

CFM_OO,

3.91282,

0.836813

CFM_OO,

3.96083,

0.791709

CFM_OO,

4.00884,

0.773695

CFM_OO,

4.05685,

0.778481

CFM_OO,

4.10486,

0.778973

CFM_OO,

4.15287,

0.777079

CFM_OO,

4.20087,

0.78978

CFM_OO,

4.24889,

0.79911

CFM_OO,

4.2969, 0.8049

21

CFM_OO,

4.3449, 0.8101

99

CFM_OO,

4.39292,

0.818587

CFM_OO,

4.44093,

0.82768

CFM_OO,

4.48894,

0.834227

CFM_OO,

4.53695,

0.825868

CFM_OO,

4.58495,

0.828675

CFM_OO,

4.63297,

0.841795

CFM_OO,

4.68098,

0.843721

CFM_OO,

4.72899,

0.851559

CFM_OO,

4.777, 0.8581

67

CFM_OO,

4.825, 0.8821

04

CFM_OO,

4.87302,

0.901436

CFM_OO,

4.92103,

0.908254

CFM_OO,

4.96903,

0.927227

CFM_OO,

5.01705,

0.954518

CFM_OO,

5.06506,

0.967374

CFM_OO,

5.11307,

0.984635

CFM_OO,

5.16108,

0.998726

CFM_OO,

5.20908,

1.00515

CFM_OO,

5.2571, 1.0113

6

CFM_OO,

5.30511,

1.02263

CFM_OO,

5.35311,

1.04915

CFM_OO,

5.40113,

1.05836

CFM_OO,

5.44914,

1.06805

CFM_OO,

5.49715,

1.08522

CFM_OO,

5.54516,

1.09015

CFM_OO,

5.59316,

1.09344

CFM_OO,

5.64118,

1.08404

CFM_OO,

5.68919,

1.0734

CFM_OO,

5.7372, 1.0795

7

CFM_OO,

5.78521,

1.06993

CFM_OO,

5.83322,

1.06172

CFM_OO,

5.88123,

1.06153

CFM_OO,

5.92924,

1.04737

CFM_OO,

5.97724,

1.04635

CFM_OO,

6.02526,

1.04611

CFM_OO,

6.07327,

1.03376

CFM_OO,

6.12128,

1.04432

CFM_OO,

6.16929,

1.03162

CFM_OO,

6.2173, 1.0247

5

CFM_OO,

6.26531,

1.02488

CFM_OO,

6.31332,

1.02391

CFM_OO,

6.36133,

1.02086

CFM_OO,

6.40934,

1.01486

CFM_OO,

6.45735,

1.02243

CFM_OO,

6.50536,

1.02154

CFM_OO,

6.55337,

1.02347

CFM_OO,

6.60137,

1.0055

CFM_OO,

6.64939,

1.01599

CFM_OO,

6.6974, 1.0103

3

CFM_OO,

6.74541,

1.01412

CFM_OO,

6.79342,

1.01425

CFM_OO,

6.84143,

1.017

CFM_OO,

6.88944,

1.01569

CFM_OO,

6.93745,

1.01373

CFM_OO,

6.98546,

1.01498

CFM_OO,

7.03347,

1.01106

CFM_OO,

7.08148,

1.01183

CFM_OO,

7.12949,

1.01871

CFM_OO,

7.1775, 1.0161

3

CFM_OO,

7.22551,

1.01627

CFM_OO,

7.27352,

1.0132

CFM_OO,

7.32153,

1.00906

CFM_OO,

7.36954,

1.01771

CFM_OO,

7.41755,

1.01763

CFM_OO,

7.46556,

1.01693

CFM_OO,

7.51357,

1.01576

CFM_OO,

7.56158,

1.01479

CFM_OO,

7.60959,

1.01309

CFM_OO,

7.6576, 1.0093

CFM_OO,

7.70561,

1.01266

CFM_OO,

7.75362,

1.01173

CFM_OO,

7.80163,

1.00434

CFM_OO,

7.84964,

0.999728

CFM_OO,

7.89765,

1.00253

CFM_OO,

7.94566,

1.00615

CFM_OO,

7.99367,

0.998472

CFM_OO,

8.04168,

1.00101

CFM_OO,

8.08969,

0.995962

CFM_OO,

8.1377, 0.9992

73

CFM_OO,

8.18571,

0.99321

CFM_OO,

8.23372,

0.994925

CFM_OO,

8.28173,

1.00028

CFM_OO,

8.32974,

0.995197

CFM_OO,

8.37775,

0.992023

CFM_OO,

8.42576,

0.996972

CFM_OO,

8.47377,

0.994456

CFM_OO,

8.52178,

0.992814

CFM_OO,

8.56979,

0.997093

CFM_OO,

8.6178, 0.9964

89

CFM_OO,

8.66581,

0.994702

CFM_OO,

8.71382,

0.999156

CFM_OO,

8.76183,

1.00444

CFM_OO,

8.80984,

1.00212

CFM_OO,

8.85785,

1.00459

CFM_OO,

8.90586,

1.00442

CFM_OO,

8.95387,

1.00513

CFM_OO,

9.00188,

1.00622

CFM_OO,

9.04989,

1.00833

CFM_OO,

9.0979, 1.0104

8

CFM_OO,

9.14591,

1.01381

CFM_OO,

9.19392,

1.01224

CFM_OO,

9.24193,

1.01477

CFM_OO,

9.28994,

1.01902

CFM_OO,

9.33795,

1.01722

CFM_OO,

9.38596,

1.01617

CFM_OO,

9.43397,

1.02014

CFM_OO,

9.48198,

1.02372

CFM_OO,

9.52999,

1.02169

CFM_OO,

9.578, 1.0192

5

RD

F Distance (A)

CFM_1

CFM_OO

44

by very high OS-H coordination, the location of key features matches well with those presented

by Ikeshoji et al. CFM-2 was selected as the best potential form based on its ability to accurately

capture the location of key features on the RDF. The strong second peak, compared to the lack of

a second peak in the CFM-OO potential is depicted in Figure 3-8.

Figure 3-8: CFM-2 prescreening S-H RDF, shown against CFM-OO S-H RDF to highlight the

presence of the second peak at ~1.9 Å.

Finalizing the OS-H potential for sulfuric acid

A further parametric design was used to screen for the best combination of parameters in

the CFM-2 potential description of this interaction. From trends observed in the potential

selection previously described, it was noticed increased „A‟ values caused lowering of the first

peak and slight shifting to the right. For a given „A‟ value, increasing the value of „B‟ would shift

the peak right and change the peak height (some peak heights increased with B while other

CFM_2, 0.024005, 0

CFM_2, 0.072015, 0

CFM_2, 0.120025, 0

CFM_2, 0.168035, 0

CFM_2, 0.216045, 0

CFM_2, 0.264055, 0

CFM_2, 0.312065, 0

CFM_2, 0.360075, 0

CFM_2, 0.408085, 0

CFM_2, 0.456095, 0

CFM_2, 0.504105, 0

CFM_2, 0.552115, 0

CFM_2, 0.600125, 0

CFM_2, 0.648135, 0

CFM_2, 0.696145, 0

CFM_2, 0.744155, 0

CFM_2, 0.792165, 0

CFM_2, 0.840175, 0

CFM_2, 0.888185, 0.0117753

CFM_2, 0.936195, 3.58768

CFM_2, 0.984205, 15.9367

CFM_2, 1.03222, 8.15319

CFM_2, 1.08023, 1.66877 CFM_2,

1.12824, 0.411134

CFM_2, 1.17625, 0.189877

CFM_2, 1.22426, 0.188364

CFM_2, 1.27227, 0.203116

CFM_2, 1.32028, 0.233324

CFM_2, 1.36829, 0.253354

CFM_2, 1.4163,

0.254225

CFM_2, 1.46431, 0.289824

CFM_2, 1.51232, 0.381396

CFM_2, 1.56033, 0.536585

CFM_2, 1.60834, 0.758244

CFM_2, 1.65635, 1.0643

CFM_2, 1.70436, 1.40002

CFM_2, 1.75237, 1.74878

CFM_2, 1.80038, 2.00677

CFM_2, 1.84839, 2.27297

CFM_2, 1.8964, 2.44195

CFM_2, 1.94441, 2.4931

CFM_2, 1.99242, 2.35451

CFM_2, 2.04042, 2.15674

CFM_2, 2.08844, 1.87683

CFM_2, 2.13645, 1.58015

CFM_2, 2.18445, 1.30312

CFM_2, 2.23246, 1.13272

CFM_2, 2.28048, 1.05268

CFM_2, 2.32849, 1.00724

CFM_2, 2.3765, 1.01668

CFM_2, 2.4245, 1.00614

CFM_2, 2.47252, 1.01583

CFM_2, 2.52053, 1.01512

CFM_2, 2.56854, 0.991375

CFM_2, 2.61654, 0.940024

CFM_2, 2.66456, 0.875411

CFM_2, 2.71257, 0.818882

CFM_2, 2.76058, 0.792002

CFM_2, 2.80858, 0.765615

CFM_2, 2.85659, 0.773497

CFM_2, 2.90461, 0.785827

CFM_2, 2.95262, 0.845563

CFM_2, 3.00062, 0.956255

CFM_2, 3.04863, 1.1152

CFM_2, 3.09665, 1.3137

CFM_2, 3.14466, 1.49496

CFM_2, 3.19267, 1.61983

CFM_2, 3.24067, 1.66445

CFM_2, 3.28869, 1.63678

CFM_2, 3.3367, 1.56947

CFM_2, 3.38471, 1.42479

CFM_2, 3.43271, 1.24061

CFM_2, 3.48073, 1.13228

CFM_2, 3.52874, 1.14102

CFM_2, 3.57675, 1.20182

CFM_2, 3.62475, 1.21408

CFM_2, 3.67277, 1.16223

CFM_2, 3.72078, 1.02456

CFM_2, 3.76879, 0.895743

CFM_2, 3.81679, 0.781899

CFM_2, 3.86481, 0.707231

CFM_2, 3.91282, 0.664494

CFM_2, 3.96083, 0.639698

CFM_2, 4.00884, 0.639018

CFM_2, 4.05685, 0.660177

CFM_2, 4.10486, 0.668505

CFM_2, 4.15287, 0.685612

CFM_2, 4.20087, 0.712092

CFM_2, 4.24889, 0.726313

CFM_2, 4.2969,

0.746686

CFM_2, 4.3449,

0.754584

CFM_2, 4.39292, 0.767791

CFM_2, 4.44093, 0.766199

CFM_2, 4.48894, 0.771031

CFM_2, 4.53695, 0.768466

CFM_2, 4.58495, 0.764612

CFM_2, 4.63297, 0.759308

CFM_2, 4.68098, 0.762447

CFM_2, 4.72899, 0.759417

CFM_2, 4.777, 0.770129

CFM_2, 4.825, 0.780134

CFM_2, 4.87302, 0.791944

CFM_2, 4.92103, 0.816534

CFM_2, 4.96903, 0.84189

CFM_2, 5.01705, 0.859118

CFM_2, 5.06506, 0.894417

CFM_2, 5.11307, 0.927041

CFM_2, 5.16108, 0.942372

CFM_2, 5.20908, 0.978384

CFM_2, 5.2571, 1.00781

CFM_2, 5.30511, 1.03817

CFM_2, 5.35311, 1.05149

CFM_2, 5.40113, 1.06971

CFM_2, 5.44914, 1.08491

CFM_2, 5.49715, 1.09057

CFM_2, 5.54516, 1.10583

CFM_2, 5.59316, 1.10874

CFM_2, 5.64118, 1.10292

CFM_2, 5.68919, 1.12108

CFM_2, 5.7372, 1.11049

CFM_2, 5.78521, 1.10317

CFM_2, 5.83322, 1.11102

CFM_2, 5.88123, 1.10296

CFM_2, 5.92924, 1.09196

CFM_2, 5.97724, 1.08912

CFM_2, 6.02526, 1.07865

CFM_2, 6.07327, 1.06315

CFM_2, 6.12128, 1.05963

CFM_2, 6.16929, 1.04382

CFM_2, 6.2173, 1.03093

CFM_2, 6.26531, 1.01213

CFM_2, 6.31332, 1.00259

CFM_2, 6.36133, 0.99082

CFM_2, 6.40934, 0.989364

CFM_2, 6.45735, 0.979374

CFM_2, 6.50536, 0.976717

CFM_2, 6.55337, 0.982615

CFM_2, 6.60137, 0.98202

CFM_2, 6.64939, 0.979566

CFM_2, 6.6974,

0.983294

CFM_2, 6.74541, 0.993806

CFM_2, 6.79342, 0.995256

CFM_2, 6.84143, 0.995442

CFM_2, 6.88944, 1.00716

CFM_2, 6.93745, 1.01313

CFM_2, 6.98546, 1.0151

CFM_2, 7.03347, 1.01935

CFM_2, 7.08148, 1.02158

CFM_2, 7.12949, 1.03326

CFM_2, 7.1775, 1.02671

CFM_2, 7.22551, 1.02409

CFM_2, 7.27352, 1.02931

CFM_2, 7.32153, 1.03339

CFM_2, 7.36954, 1.02705

CFM_2, 7.41755, 1.02684

CFM_2, 7.46556, 1.02826

CFM_2, 7.51357, 1.0174

CFM_2, 7.56158, 1.01902

CFM_2, 7.60959, 1.01975

CFM_2, 7.6576, 1.01305

CFM_2, 7.70561, 1.01103

CFM_2, 7.75362, 1.0113

CFM_2, 7.80163, 1.00564

CFM_2, 7.84964, 1.00706

CFM_2, 7.89765, 0.998782

CFM_2, 7.94566, 0.990984

CFM_2, 7.99367, 0.999514

CFM_2, 8.04168, 0.989507

CFM_2, 8.08969, 0.99201

CFM_2, 8.1377,

0.987449

CFM_2, 8.18571, 0.985783

CFM_2, 8.23372, 0.992054

CFM_2, 8.28173, 0.988149

CFM_2, 8.32974, 0.988099

CFM_2, 8.37775, 0.982463

CFM_2, 8.42576, 0.988261

CFM_2, 8.47377, 0.978245

CFM_2, 8.52178, 0.985287

CFM_2, 8.56979, 0.978116

CFM_2, 8.6178,

0.985138

CFM_2, 8.66581, 0.986392

CFM_2, 8.71382, 0.98418

CFM_2, 8.76183, 0.985184

CFM_2, 8.80984, 0.984651

CFM_2, 8.85785, 0.988578

CFM_2, 8.90586, 0.990919

CFM_2, 8.95387, 0.991975

CFM_2, 9.00188, 0.990118

CFM_2, 9.04989, 0.991559

CFM_2, 9.0979, 1.00016

CFM_2, 9.14591, 0.998173

CFM_2, 9.19392, 1.00376

CFM_2, 9.24193, 1.00332

CFM_2, 9.28994, 1.00222

CFM_2, 9.33795, 1.00516

CFM_2, 9.38596, 1.01009

CFM_2, 9.43397, 1.00766

CFM_2, 9.48198, 1.00698

CFM_2, 9.52999, 1.00539

CFM_2, 9.578, 1.00839 CFM_OO,

0.024005, 0 CFM_OO,

0.072015, 0 CFM_OO,

0.120025, 0 CFM_OO,

0.168035, 0 CFM_OO,

0.216045, 0 CFM_OO,

0.264055, 0 CFM_OO,

0.312065, 0 CFM_OO,

0.360075, 0 CFM_OO,

0.408085, 0 CFM_OO,

0.456095, 0 CFM_OO,

0.504105, 0 CFM_OO,

0.552115, 0 CFM_OO,

0.600125, 0 CFM_OO,

0.648135, 0 CFM_OO,

0.696145, 0 CFM_OO,

0.744155, 0 CFM_OO,

0.792165, 0 CFM_OO,

0.840175, 0

CFM_OO, 0.888185, 0.0340174

CFM_OO, 0.936195, 5.69742

CFM_OO, 0.984205,

15.966

CFM_OO, 1.03222, 4.95576

CFM_OO, 1.08023, 0.779321

CFM_OO, 1.12824, 0.302066

CFM_OO, 1.17625, 0.245087

CFM_OO, 1.22426, 0.207993

CFM_OO, 1.27227, 0.160388

CFM_OO, 1.32028, 0.115182

CFM_OO, 1.36829,

0.0719537

CFM_OO, 1.4163,

0.046059

CFM_OO, 1.46431,

0.0389963

CFM_OO, 1.51232,

0.0309179

CFM_OO, 1.56033,

0.0390089

CFM_OO, 1.60834,

0.0540748

CFM_OO, 1.65635,

0.0874846

CFM_OO, 1.70436, 0.118874

CFM_OO, 1.75237, 0.157161

CFM_OO, 1.80038, 0.217844

CFM_OO, 1.84839, 0.268768

CFM_OO, 1.8964,

0.327095

CFM_OO, 1.94441, 0.39142

CFM_OO, 1.99242, 0.448329

CFM_OO, 2.04042, 0.520093

CFM_OO, 2.08844, 0.568055

CFM_OO, 2.13645, 0.596189

CFM_OO, 2.18445, 0.645234

CFM_OO, 2.23246, 0.665008

CFM_OO, 2.28048, 0.673134

CFM_OO, 2.32849, 0.717351

CFM_OO, 2.3765,

0.761776

CFM_OO, 2.4245,

0.803912

CFM_OO, 2.47252, 0.867478

CFM_OO, 2.52053, 0.895927

CFM_OO, 2.56854, 0.912118

CFM_OO, 2.61654, 0.879632

CFM_OO, 2.66456, 0.828881

CFM_OO, 2.71257, 0.771951

CFM_OO, 2.76058, 0.708555

CFM_OO, 2.80858, 0.664057

CFM_OO, 2.85659, 0.652488

CFM_OO, 2.90461, 0.671477

CFM_OO, 2.95262, 0.711751

CFM_OO, 3.00062, 0.794816

CFM_OO, 3.04863, 0.875391

CFM_OO, 3.09665, 0.982601

CFM_OO, 3.14466, 1.06427

CFM_OO, 3.19267, 1.1431

CFM_OO, 3.24067, 1.25512

CFM_OO, 3.28869, 1.38846

CFM_OO, 3.3367, 1.46405

CFM_OO, 3.38471, 1.31021

CFM_OO, 3.43271, 1.06583

CFM_OO, 3.48073, 0.925474

CFM_OO, 3.52874, 0.888731

CFM_OO, 3.57675, 0.874636

CFM_OO, 3.62475, 0.894168

CFM_OO, 3.67277, 0.940245

CFM_OO, 3.72078, 1.02412

CFM_OO, 3.76879, 1.03602

CFM_OO, 3.81679, 0.988862

CFM_OO, 3.86481, 0.910537

CFM_OO, 3.91282, 0.836813

CFM_OO, 3.96083, 0.791709

CFM_OO, 4.00884, 0.773695

CFM_OO, 4.05685, 0.778481

CFM_OO, 4.10486, 0.778973

CFM_OO, 4.15287, 0.777079

CFM_OO, 4.20087, 0.78978

CFM_OO, 4.24889, 0.79911

CFM_OO, 4.2969,

0.804921

CFM_OO, 4.3449,

0.810199

CFM_OO, 4.39292, 0.818587

CFM_OO, 4.44093, 0.82768

CFM_OO, 4.48894, 0.834227

CFM_OO, 4.53695, 0.825868

CFM_OO, 4.58495, 0.828675

CFM_OO, 4.63297, 0.841795

CFM_OO, 4.68098, 0.843721

CFM_OO, 4.72899, 0.851559

CFM_OO, 4.777,

0.858167

CFM_OO, 4.825,

0.882104

CFM_OO, 4.87302, 0.901436

CFM_OO, 4.92103, 0.908254

CFM_OO, 4.96903, 0.927227

CFM_OO, 5.01705, 0.954518

CFM_OO, 5.06506, 0.967374

CFM_OO, 5.11307, 0.984635

CFM_OO, 5.16108, 0.998726

CFM_OO, 5.20908, 1.00515

CFM_OO, 5.2571, 1.01136

CFM_OO, 5.30511, 1.02263

CFM_OO, 5.35311, 1.04915

CFM_OO, 5.40113, 1.05836

CFM_OO, 5.44914, 1.06805

CFM_OO, 5.49715, 1.08522

CFM_OO, 5.54516, 1.09015

CFM_OO, 5.59316, 1.09344

CFM_OO, 5.64118, 1.08404

CFM_OO, 5.68919, 1.0734

CFM_OO, 5.7372, 1.07957

CFM_OO, 5.78521, 1.06993

CFM_OO, 5.83322, 1.06172

CFM_OO, 5.88123, 1.06153

CFM_OO, 5.92924, 1.04737

CFM_OO, 5.97724, 1.04635

CFM_OO, 6.02526, 1.04611

CFM_OO, 6.07327, 1.03376

CFM_OO, 6.12128, 1.04432

CFM_OO, 6.16929, 1.03162

CFM_OO, 6.2173, 1.02475

CFM_OO, 6.26531, 1.02488

CFM_OO, 6.31332, 1.02391

CFM_OO, 6.36133, 1.02086

CFM_OO, 6.40934, 1.01486

CFM_OO, 6.45735, 1.02243

CFM_OO, 6.50536, 1.02154

CFM_OO, 6.55337, 1.02347

CFM_OO, 6.60137, 1.0055

CFM_OO, 6.64939, 1.01599

CFM_OO, 6.6974, 1.01033

CFM_OO, 6.74541, 1.01412

CFM_OO, 6.79342, 1.01425

CFM_OO, 6.84143,

1.017

CFM_OO, 6.88944, 1.01569

CFM_OO, 6.93745, 1.01373

CFM_OO, 6.98546, 1.01498

CFM_OO, 7.03347, 1.01106

CFM_OO, 7.08148, 1.01183

CFM_OO, 7.12949, 1.01871

CFM_OO, 7.1775, 1.01613

CFM_OO, 7.22551, 1.01627

CFM_OO, 7.27352, 1.0132

CFM_OO, 7.32153, 1.00906

CFM_OO, 7.36954, 1.01771

CFM_OO, 7.41755, 1.01763

CFM_OO, 7.46556, 1.01693

CFM_OO, 7.51357, 1.01576

CFM_OO, 7.56158, 1.01479

CFM_OO, 7.60959, 1.01309

CFM_OO, 7.6576, 1.0093

CFM_OO, 7.70561, 1.01266

CFM_OO, 7.75362, 1.01173

CFM_OO, 7.80163, 1.00434

CFM_OO, 7.84964, 0.999728

CFM_OO, 7.89765, 1.00253

CFM_OO, 7.94566, 1.00615

CFM_OO, 7.99367, 0.998472

CFM_OO, 8.04168, 1.00101

CFM_OO, 8.08969, 0.995962

CFM_OO, 8.1377,

0.999273

CFM_OO, 8.18571, 0.99321

CFM_OO, 8.23372, 0.994925

CFM_OO, 8.28173, 1.00028

CFM_OO, 8.32974, 0.995197

CFM_OO, 8.37775, 0.992023

CFM_OO, 8.42576, 0.996972

CFM_OO, 8.47377, 0.994456

CFM_OO, 8.52178, 0.992814

CFM_OO, 8.56979, 0.997093

CFM_OO, 8.6178,

0.996489

CFM_OO, 8.66581, 0.994702

CFM_OO, 8.71382, 0.999156

CFM_OO, 8.76183, 1.00444

CFM_OO, 8.80984, 1.00212

CFM_OO, 8.85785, 1.00459

CFM_OO, 8.90586, 1.00442

CFM_OO, 8.95387, 1.00513

CFM_OO, 9.00188, 1.00622

CFM_OO, 9.04989, 1.00833

CFM_OO, 9.0979, 1.01048

CFM_OO, 9.14591, 1.01381

CFM_OO, 9.19392, 1.01224

CFM_OO, 9.24193, 1.01477

CFM_OO, 9.28994, 1.01902

CFM_OO, 9.33795, 1.01722

CFM_OO, 9.38596, 1.01617

CFM_OO, 9.43397, 1.02014

CFM_OO, 9.48198, 1.02372

CFM_OO, 9.52999, 1.02169

CFM_OO, 9.578,

1.01925

RD

F

Distance (A)

CFM_2

CFM_OO

45

decreased). The desired first peak has a distance of approximately 0.97 Å and integrates to 0.25 to

a certain cutoff distance.

The parameterization on CFM-2 optimized each of the 5 parameters through a parametric

design process. That is, a range of values was selected for each parameter, and all permutations of

those values were simulated. After a range of values was tested, recommendations were made for

narrowing the range of values and the process was repeated. All prescreening runs were

performed for 500 ps. Of these runs the eight best, based on the appearance of all RDF features,

were selected for further simulation. The extended runs were carried out for 4 ns, and the optimal

parameters were chosen.

Comparison of final screening tests for force field fitting

To select the best parameter fit, RDF plots were created for the final 2 ns of each 4 ns

simulation. Analyzing only the final 2 ns would remove any initial configuration bias from the

plots and give an equilibrium indication of the features predicted by the force field. The RDF was

numerically integrated to a cutoff value to determine the average hydrogen coordination about

each sulfate group. Two cutoff distances were chosen for selecting the best fit. The first was the

“full-width at half-max” method. This method cut off the integration at the point at which the

value of the RDF reached the halfway point between the first maximum and the next minimum.

The second method was to cutoff the integration at a distance corresponding to 10% greater than

the equilibrium bond distance. For both of these tests, the “Fit 2” produced the best integration,

with both values being within 2% of the desired 0.25. Thus, “Fit 2” was chosen as the optimal

potential to describe the interaction between OS atoms and H atoms.

46

Table 3-3: Integration analysis of various OS-H potentials for average sulfate molecular

configuration

Fit First Max

(Å) RDF at first max Integrating to Max +10%

Integrating to “half max”

from 1st max to 1

st min

1 1.045 1.539 0.281 0.274

2 1.075 1.356 0.245 0.252

3 1.075 1.112 0.206 0.206

4 1.075 1.047 0.204 0.197

5 1.075 1.606 0.307 0.316

6 1.025 1.314 0.230 0.261

7 1.055 0.955 0.174 0.184

8 1.035 1.936 0.344 0.344

The final potential is one that is similar to the CFM description of O-H because it shares

the same functional form with differences in parameters. The OS-H fit potential has a minimum at

a similar distance, because the equilibrium bond distance is almost equal to that in water.

However, the well in the fit potential is not as weak, and the approach to equal the electrostatic

interaction is much more gradual. This decrease in steepness of the well in the attractive region

facilitates proton dissociation, as the force attracting the atoms back to their equilibrium bond

length is lessened. The final functional form is presented in Equation 3-7 and is compared to the

original CFM description of the O-H bond in Equation 3-8 and Figure 3-9, including electrostatic

interactions.

( )

, ( )- Equation 3-7

( )

, ( )- Equation 3-8

47

Figure 3-9: Final form of OS-H potential compared to that of CFM potential for OH

Figure 3-10: Overlay of my OS-H RDF with that of Ikeshoji et al. Ikeshoji removes the bonded

proton from consideration in RDF calculation, which is why there is no peak at ~1 Å

In the final chapter, aqueous sulfuric acid will be parameterized with platinum, which

serves as the electrode in our study, to run a full simulation. We will describe the

parameterization of sulfuric acid with platinum, and the simulation of the full electrochemical

CFM - OH, 0.01,

232346956892583000000000000000

0.0

CFM - OH, 0.02,

72396563830107200000

000000.0

CFM - OH, 0.03,

16735234631379100000

0000.0

CFM - OH, 0.04,

22557913064597800000

00.0

CFM - OH, 0.05,

79901700800757700000

.0

CFM - OH, 0.06,

5214501185666830000.

0

CFM - OH, 0.07,

518823130426959000.0

CFM - OH, 0.08,

70287789213875800.0

CFM - OH, 0.09,

12053873307097800.0

CFM - OH, 0.10,

2489642498235420.0

CFM - OH, 0.11,

597707206299114.0

CFM - OH, 0.12,

162477689821179.0

CFM - OH, 0.13,

49023577951130.8

CFM - OH, 0.14,

16165915138128.1

CFM - OH, 0.15,

5755073051599.2

CFM - OH, 0.16,

2190084382981.0

CFM - OH, 0.17,

883723971319.4

CFM - OH, 0.18,

375584435880.5

CFM - OH, 0.19,

167184334790.3

CFM - OH, 0.20,

77574315409.5

CFM - OH, 0.21,

37369229425.9

CFM - OH, 0.22,

18623849313.2

CFM - OH, 0.23,

9573511627.1

CFM - OH, 0.24,

5062612347.4

CFM - OH, 0.25,

2747736054.1

CFM - OH, 0.26,

1527516425.5

CFM - OH, 0.27,

868203040.5

CFM - OH, 0.28,

503710532.4

CFM - OH, 0.29,

297878109.0

CFM - OH, 0.30,

179321022.9

CFM - OH, 0.31,

109761867.1

CFM - OH, 0.32,

68240207.4

CFM - OH, 0.33,

43050781.4

CFM - OH, 0.34,

27535575.2

CFM - OH, 0.35,

17841575.1

CFM - OH, 0.36,

11702560.1

CFM - OH, 0.37,

7765079.7

CFM - OH, 0.38,

5209070.0

CFM - OH, 0.39,

3530825.8

CFM - OH, 0.40,

2416937.3

CFM - OH, 0.41,

1669995.3

CFM - OH, 0.42,

1164202.9

CFM - OH, 0.43,

818506.0

CFM - OH, 0.44,

580126.9

CFM - OH, 0.45,

414353.6

CFM - OH, 0.46,

298136.2

CFM - OH, 0.47,

216028.5

CFM - OH, 0.48,

157588.5

CFM - OH, 0.49,

115698.0

CFM - OH, 0.50,

85465.7

CFM - OH, 0.51,

63504.2

CFM - OH, 0.52,

47450.6

CFM - OH, 0.53,

35644.8

CFM - OH, 0.54,

26912.4

CFM - OH, 0.55,

20417.1

CFM - OH, 0.56,

15560.0

CFM - OH, 0.57,

11909.0

CFM - OH, 0.58, 9150.9

CFM - OH, 0.59, 7057.4

CFM - OH, 0.60, 5461.0

CFM - OH, 0.61, 4238.2

CFM - OH, 0.62, 3297.5

CFM - OH, 0.63, 2570.9

CFM - OH, 0.64, 2007.4

CFM - OH, 0.65, 1568.7

CFM - OH, 0.66, 1225.9 CFM - OH, 0.67, 957.2 CFM - OH, 0.68, 745.7 CFM - OH, 0.69, 578.8 CFM - OH, 0.70, 446.7 CFM - OH, 0.71, 341.8 CFM - OH, 0.72, 258.3 CFM - OH, 0.73, 191.6 CFM - OH, 0.74, 138.3 CFM - OH, 0.75, 95.6 CFM - OH, 0.76, 61.2

CFM - OH, 0.77, 33.6 CFM - OH, 0.78, 11.4 CFM - OH, 0.79, -6.6 CFM - OH, 0.80, -21.0 CFM - OH, 0.81, -32.7 CFM - OH, 0.82, -42.1 CFM - OH, 0.83, -49.7 CFM - OH, 0.84, -55.8 CFM - OH, 0.85, -60.6 CFM - OH, 0.86, -64.5 CFM - OH, 0.87, -67.6 CFM - OH, 0.88, -70.0 CFM - OH, 0.89, -71.9 CFM - OH, 0.90, -73.4 CFM - OH, 0.91, -74.5 CFM - OH, 0.92, -75.3 CFM - OH, 0.93, -75.8 CFM - OH, 0.94, -76.1 CFM - OH, 0.95, -76.3 CFM - OH, 0.96, -76.4 CFM - OH, 0.97, -76.3 CFM - OH, 0.98, -76.1

CFM - OH, 0.99, -75.9

CFM - OH, 1.00, -75.6

CFM - OH, 1.01, -75.2

CFM - OH, 1.02, -74.9

CFM - OH, 1.03, -74.4

CFM - OH, 1.04, -74.0

CFM - OH, 1.05, -73.5

CFM - OH, 1.06, -73.1

CFM - OH, 1.07, -72.6

CFM - OH, 1.08, -72.1

CFM - OH, 1.09, -71.6

CFM - OH, 1.10, -71.0

CFM - OH, 1.11, -70.5

CFM - OH, 1.12, -70.0

CFM - OH, 1.13, -69.5

CFM - OH, 1.14, -69.0

CFM - OH, 1.15, -68.5

CFM - OH, 1.16, -68.0

CFM - OH, 1.17, -67.5

CFM - OH, 1.18, -67.0

CFM - OH, 1.19, -66.5

CFM - OH, 1.20, -66.0

CFM - OH, 1.21, -65.5

CFM - OH, 1.22, -65.1

CFM - OH, 1.23, -64.6

CFM - OH, 1.24, -64.1

CFM - OH, 1.25, -63.7

CFM - OH, 1.26, -63.2

CFM - OH, 1.27, -62.8

CFM - OH, 1.28, -62.4

CFM - OH, 1.29, -61.9

CFM - OH, 1.30, -61.5

CFM - OH, 1.31, -61.1

CFM - OH, 1.32, -60.7

CFM - OH, 1.33, -60.3

CFM - OH, 1.34, -59.8

CFM - OH, 1.35, -59.4

CFM - OH, 1.36, -59.1

CFM - OH, 1.37, -58.7

CFM - OH, 1.38, -58.3

CFM - OH, 1.39, -57.9

CFM - OH, 1.40, -57.5

CFM - OH, 1.41, -57.2

CFM - OH, 1.42, -56.8

CFM - OH, 1.43, -56.4

CFM - OH, 1.44, -56.1

CFM - OH, 1.45, -55.7

CFM - OH, 1.46, -55.4

CFM - OH, 1.47, -55.0

CFM - OH, 1.48, -54.7

CFM - OH, 1.49, -54.4

CFM - OH, 1.50, -54.0

CFM - OH, 1.51, -53.7

CFM - OH, 1.52, -53.4

CFM - OH, 1.53, -53.1

CFM - OH, 1.54, -52.8

CFM - OH, 1.55, -52.5

CFM - OH, 1.56, -52.2

CFM - OH, 1.57, -51.8

CFM - OH, 1.58, -51.5

CFM - OH, 1.59, -51.2

CFM - OH, 1.60, -51.0

CFM - OH, 1.61, -50.7

CFM - OH, 1.62, -50.4

CFM - OH, 1.63, -50.1

CFM - OH, 1.64, -49.8

CFM - OH, 1.65, -49.5

CFM - OH, 1.66, -49.2

CFM - OH, 1.67, -49.0

CFM - OH, 1.68, -48.7

CFM - OH, 1.69, -48.4

CFM - OH, 1.70, -48.1

CFM - OH, 1.71, -47.9

CFM - OH, 1.72, -47.6

CFM - OH, 1.73, -47.4

CFM - OH, 1.74, -47.1

CFM - OH, 1.75, -46.8

CFM - OH, 1.76, -46.6

CFM - OH, 1.77, -46.3

CFM - OH, 1.78, -46.1

CFM - OH, 1.79, -45.8

CFM - OH, 1.80, -45.6

CFM - OH, 1.81, -45.3

CFM - OH, 1.82, -45.0

CFM - OH, 1.83, -44.8

CFM - OH, 1.84, -44.5

CFM - OH, 1.85, -44.3

CFM - OH, 1.86, -44.1

CFM - OH, 1.87, -43.8

CFM - OH, 1.88, -43.6

CFM - OH, 1.89, -43.3

CFM - OH, 1.90, -43.1

CFM - OH, 1.91, -42.8 CFM - OH, 1.92, -42.6

CFM - OH, 1.93, -42.3

CFM - OH, 1.94, -42.1

CFM - OH, 1.95, -41.8

CFM - OH, 1.96, -41.6

CFM - OH, 1.97, -41.4

CFM - OH, 1.98, -41.1

CFM - OH, 1.99, -40.9

CFM - OH, 2.00, -40.6

CFM - OH, 2.01, -40.4

CFM - OH, 2.02, -40.2

CFM - OH, 2.03, -39.9

CFM - OH, 2.04, -39.7

CFM - OH, 2.05, -39.4

CFM - OH, 2.06, -39.2

CFM - OH, 2.07, -38.9

CFM - OH, 2.08, -38.7

CFM - OH, 2.09, -38.5

CFM - OH, 2.10, -38.2

CFM - OH, 2.11, -38.0

CFM - OH, 2.12, -37.7

CFM - OH, 2.13, -37.5

CFM - OH, 2.14, -37.3

CFM - OH, 2.15, -37.0

CFM - OH, 2.16, -36.8

CFM - OH, 2.17, -36.6

CFM - OH, 2.18, -36.3 CFM - OH, 2.19, -36.1

CFM - OH, 2.20, -35.9 CFM - OH, 2.21, -35.6

CFM - OH, 2.22, -35.4

CFM - OH, 2.23, -35.2 CFM - OH, 2.24, -34.9

CFM - OH, 2.25, -34.7 CFM - OH, 2.26, -34.5

CFM - OH, 2.27, -34.3 CFM - OH, 2.28, -34.0 CFM - OH, 2.29, -33.8 CFM - OH, 2.30, -33.6 CFM - OH, 2.31, -33.4 CFM - OH, 2.32, -33.2 CFM - OH, 2.33, -33.0 CFM - OH, 2.34, -32.8 CFM - OH, 2.35, -32.6 CFM - OH, 2.36, -32.4 CFM - OH, 2.37, -32.2 CFM - OH, 2.38, -32.0 CFM - OH, 2.39, -31.8 CFM - OH, 2.40, -31.6 CFM - OH, 2.41, -31.4 CFM - OH, 2.42, -31.2 CFM - OH, 2.43, -31.1 CFM - OH, 2.44, -30.9 CFM - OH, 2.45, -30.7 CFM - OH, 2.46, -30.5 CFM - OH, 2.47, -30.4 CFM - OH, 2.48, -30.2 CFM - OH, 2.49, -30.0 CFM - OH, 2.50, -29.9 CFM - OH, 2.51, -29.7 CFM - OH, 2.52, -29.6 CFM - OH, 2.53, -29.4 CFM - OH, 2.54, -29.3 CFM - OH, 2.55, -29.1 CFM - OH, 2.56, -29.0 CFM - OH, 2.57, -28.8 CFM - OH, 2.58, -28.7 CFM - OH, 2.59, -28.5 CFM - OH, 2.60, -28.4 CFM - OH, 2.61, -28.3 CFM - OH, 2.62, -28.1 CFM - OH, 2.63, -28.0 CFM - OH, 2.64, -27.9 CFM - OH, 2.65, -27.7 CFM - OH, 2.66, -27.6 CFM - OH, 2.67, -27.5 CFM - OH, 2.68, -27.4 CFM - OH, 2.69, -27.2 CFM - OH, 2.70, -27.1 CFM - OH, 2.71, -27.0 CFM - OH, 2.72, -26.9 CFM - OH, 2.73, -26.8 CFM - OH, 2.74, -26.7 CFM - OH, 2.75, -26.6 CFM - OH, 2.76, -26.4 CFM - OH, 2.77, -26.3 CFM - OH, 2.78, -26.2 CFM - OH, 2.79, -26.1 CFM - OH, 2.80, -26.0 CFM - OH, 2.81, -25.9 CFM - OH, 2.82, -25.8 CFM - OH, 2.83, -25.7 CFM - OH, 2.84, -25.6 CFM - OH, 2.85, -25.5 CFM - OH, 2.86, -25.4 CFM - OH, 2.87, -25.3 CFM - OH, 2.88, -25.2 CFM - OH, 2.89, -25.1 CFM - OH, 2.90, -25.0 CFM - OH, 2.91, -25.0 CFM - OH, 2.92, -24.9 CFM - OH, 2.93, -24.8 CFM - OH, 2.94, -24.7 CFM - OH, 2.95, -24.6 CFM - OH, 2.96, -24.5 CFM - OH, 2.97, -24.4 CFM - OH, 2.98, -24.3 CFM - OH, 2.99, -24.2 CFM - OH, 3.00, -24.2 CFM - OH, 3.01, -24.1 CFM - OH, 3.02, -24.0 CFM - OH, 3.03, -23.9 CFM - OH, 3.04, -23.8 CFM - OH, 3.05, -23.8 CFM - OH, 3.06, -23.7 CFM - OH, 3.07, -23.6 CFM - OH, 3.08, -23.5 CFM - OH, 3.09, -23.4 CFM - OH, 3.10, -23.4 CFM - OH, 3.11, -23.3 CFM - OH, 3.12, -23.2 CFM - OH, 3.13, -23.1 CFM - OH, 3.14, -23.1 CFM - OH, 3.15, -23.0 CFM - OH, 3.16, -22.9 CFM - OH, 3.17, -22.8 CFM - OH, 3.18, -22.8 CFM - OH, 3.19, -22.7 CFM - OH, 3.20, -22.6 CFM - OH, 3.21, -22.5 CFM - OH, 3.22, -22.5 CFM - OH, 3.23, -22.4 CFM - OH, 3.24, -22.3 CFM - OH, 3.25, -22.3 CFM - OH, 3.26, -22.2 CFM - OH, 3.27, -22.1 CFM - OH, 3.28, -22.0 CFM - OH, 3.29, -22.0 CFM - OH, 3.30, -21.9 CFM - OH, 3.31, -21.8 CFM - OH, 3.32, -21.8 CFM - OH, 3.33, -21.7 CFM - OH, 3.34, -21.6 CFM - OH, 3.35, -21.6 CFM - OH, 3.36, -21.5 CFM - OH, 3.37, -21.5 CFM - OH, 3.38, -21.4 CFM - OH, 3.39, -21.3 CFM - OH, 3.40, -21.3 CFM - OH, 3.41, -21.2 CFM - OH, 3.42, -21.1 CFM - OH, 3.43, -21.1 CFM - OH, 3.44, -21.0 CFM - OH, 3.45, -21.0 CFM - OH, 3.46, -20.9 CFM - OH, 3.47, -20.8 CFM - OH, 3.48, -20.8 CFM - OH, 3.49, -20.7 CFM - OH, 3.50, -20.7 CFM - OH, 3.51, -20.6 CFM - OH, 3.52, -20.5 CFM - OH, 3.53, -20.5 CFM - OH, 3.54, -20.4 CFM - OH, 3.55, -20.4 CFM - OH, 3.56, -20.3 CFM - OH, 3.57, -20.2 CFM - OH, 3.58, -20.2 CFM - OH, 3.59, -20.1 CFM - OH, 3.60, -20.1 CFM - OH, 3.61, -20.0 CFM - OH, 3.62, -20.0 CFM - OH, 3.63, -19.9 CFM - OH, 3.64, -19.9 CFM - OH, 3.65, -19.8 CFM - OH, 3.66, -19.7 CFM - OH, 3.67, -19.7 CFM - OH, 3.68, -19.6 CFM - OH, 3.69, -19.6 CFM - OH, 3.70, -19.5 CFM - OH, 3.71, -19.5 CFM - OH, 3.72, -19.4 CFM - OH, 3.73, -19.4 CFM - OH, 3.74, -19.3 CFM - OH, 3.75, -19.3 CFM - OH, 3.76, -19.2 CFM - OH, 3.77, -19.2 CFM - OH, 3.78, -19.1 CFM - OH, 3.79, -19.1 CFM - OH, 3.80, -19.0 CFM - OH, 3.81, -19.0 CFM - OH, 3.82, -18.9 CFM - OH, 3.83, -18.9 CFM - OH, 3.84, -18.8 CFM - OH, 3.85, -18.8 CFM - OH, 3.86, -18.7 CFM - OH, 3.87, -18.7 CFM - OH, 3.88, -18.6 CFM - OH, 3.89, -18.6 CFM - OH, 3.90, -18.5 CFM - OH, 3.91, -18.5 CFM - OH, 3.92, -18.4 CFM - OH, 3.93, -18.4 CFM - OH, 3.94, -18.3 CFM - OH, 3.95, -18.3 CFM - OH, 3.96, -18.3 CFM - OH, 3.97, -18.2 CFM - OH, 3.98, -18.2 CFM - OH, 3.99, -18.1 CFM - OH, 4.00, -18.1 CFM - OH, 4.01, -18.0 CFM - OH, 4.02, -18.0 CFM - OH, 4.03, -17.9 CFM - OH, 4.04, -17.9 CFM - OH, 4.05, -17.8 CFM - OH, 4.06, -17.8 CFM - OH, 4.07, -17.8 CFM - OH, 4.08, -17.7 CFM - OH, 4.09, -17.7 CFM - OH, 4.10, -17.6 CFM - OH, 4.11, -17.6 CFM - OH, 4.12, -17.5 CFM - OH, 4.13, -17.5 CFM - OH, 4.14, -17.5 CFM - OH, 4.15, -17.4 CFM - OH, 4.16, -17.4 CFM - OH, 4.17, -17.3 CFM - OH, 4.18, -17.3 CFM - OH, 4.19, -17.2 CFM - OH, 4.20, -17.2 CFM - OH, 4.21, -17.2 CFM - OH, 4.22, -17.1 CFM - OH, 4.23, -17.1 CFM - OH, 4.24, -17.0 CFM - OH, 4.25, -17.0 CFM - OH, 4.26, -17.0 CFM - OH, 4.27, -16.9 CFM - OH, 4.28, -16.9 CFM - OH, 4.29, -16.8 CFM - OH, 4.30, -16.8 CFM - OH, 4.31, -16.8 CFM - OH, 4.32, -16.7 CFM - OH, 4.33, -16.7 CFM - OH, 4.34, -16.7 CFM - OH, 4.35, -16.6 CFM - OH, 4.36, -16.6 CFM - OH, 4.37, -16.5 CFM - OH, 4.38, -16.5 CFM - OH, 4.39, -16.5 CFM - OH, 4.40, -16.4 CFM - OH, 4.41, -16.4 CFM - OH, 4.42, -16.4 CFM - OH, 4.43, -16.3 CFM - OH, 4.44, -16.3 CFM - OH, 4.45, -16.2 CFM - OH, 4.46, -16.2 CFM - OH, 4.47, -16.2 CFM - OH, 4.48, -16.1 CFM - OH, 4.49, -16.1 CFM - OH, 4.50, -16.1 CFM - OH, 4.51, -16.0 CFM - OH, 4.52, -16.0 CFM - OH, 4.53, -16.0 CFM - OH, 4.54, -15.9 CFM - OH, 4.55, -15.9 CFM - OH, 4.56, -15.8 CFM - OH, 4.57, -15.8 CFM - OH, 4.58, -15.8 CFM - OH, 4.59, -15.7 CFM - OH, 4.60, -15.7 CFM - OH, 4.61, -15.7 CFM - OH, 4.62, -15.6 CFM - OH, 4.63, -15.6 CFM - OH, 4.64, -15.6 CFM - OH, 4.65, -15.5 CFM - OH, 4.66, -15.5 CFM - OH, 4.67, -15.5 CFM - OH, 4.68, -15.4 CFM - OH, 4.69, -15.4 CFM - OH, 4.70, -15.4 CFM - OH, 4.71, -15.3 CFM - OH, 4.72, -15.3 CFM - OH, 4.73, -15.3 CFM - OH, 4.74, -15.2 CFM - OH, 4.75, -15.2 CFM - OH, 4.76, -15.2 CFM - OH, 4.77, -15.2 CFM - OH, 4.78, -15.1 CFM - OH, 4.79, -15.1 CFM - OH, 4.80, -15.1 CFM - OH, 4.81, -15.0 CFM - OH, 4.82, -15.0 CFM - OH, 4.83, -15.0 CFM - OH, 4.84, -14.9 CFM - OH, 4.85, -14.9 CFM - OH, 4.86, -14.9 CFM - OH, 4.87, -14.8 CFM - OH, 4.88, -14.8 CFM - OH, 4.89, -14.8 CFM - OH, 4.90, -14.7 CFM - OH, 4.91, -14.7 CFM - OH, 4.92, -14.7 CFM - OH, 4.93, -14.7 CFM - OH, 4.94, -14.6 CFM - OH, 4.95, -14.6 CFM - OH, 4.96, -14.6 CFM - OH, 4.97, -14.5 CFM - OH, 4.98, -14.5 CFM - OH, 4.99, -14.5 CFM - OH, 5.00, -14.5 CFM - OH, 5.01, -14.4 CFM - OH, 5.02, -14.4 CFM - OH, 5.03, -14.4 CFM - OH, 5.04, -14.3 CFM - OH, 5.05, -14.3 CFM - OH, 5.06, -14.3 CFM - OH, 5.07, -14.3 CFM - OH, 5.08, -14.2 CFM - OH, 5.09, -14.2 CFM - OH, 5.10, -14.2 CFM - OH, 5.11, -14.1 CFM - OH, 5.12, -14.1 CFM - OH, 5.13, -14.1 CFM - OH, 5.14, -14.1 CFM - OH, 5.15, -14.0 CFM - OH, 5.16, -14.0 CFM - OH, 5.17, -14.0 CFM - OH, 5.18, -14.0 CFM - OH, 5.19, -13.9 CFM - OH, 5.20, -13.9 CFM - OH, 5.21, -13.9 CFM - OH, 5.22, -13.8 CFM - OH, 5.23, -13.8 CFM - OH, 5.24, -13.8 CFM - OH, 5.25, -13.8 CFM - OH, 5.26, -13.7 CFM - OH, 5.27, -13.7 CFM - OH, 5.28, -13.7 CFM - OH, 5.29, -13.7 CFM - OH, 5.30, -13.6 CFM - OH, 5.31, -13.6 CFM - OH, 5.32, -13.6 CFM - OH, 5.33, -13.6 CFM - OH, 5.34, -13.5 CFM - OH, 5.35, -13.5 CFM - OH, 5.36, -13.5 CFM - OH, 5.37, -13.5 CFM - OH, 5.38, -13.4 CFM - OH, 5.39, -13.4 CFM - OH, 5.40, -13.4 CFM - OH, 5.41, -13.4 CFM - OH, 5.42, -13.3 CFM - OH, 5.43, -13.3 CFM - OH, 5.44, -13.3 CFM - OH, 5.45, -13.3 CFM - OH, 5.46, -13.2 CFM - OH, 5.47, -13.2 CFM - OH, 5.48, -13.2 CFM - OH, 5.49, -13.2 CFM - OH, 5.50, -13.1 CFM - OH, 5.51, -13.1 CFM - OH, 5.52, -13.1 CFM - OH, 5.53, -13.1 CFM - OH, 5.54, -13.0 CFM - OH, 5.55, -13.0 CFM - OH, 5.56, -13.0 CFM - OH, 5.57, -13.0 CFM - OH, 5.58, -13.0 CFM - OH, 5.59, -12.9 CFM - OH, 5.60, -12.9 CFM - OH, 5.61, -12.9 CFM - OH, 5.62, -12.9 CFM - OH, 5.63, -12.8 CFM - OH, 5.64, -12.8 CFM - OH, 5.65, -12.8 CFM - OH, 5.66, -12.8 CFM - OH, 5.67, -12.7 CFM - OH, 5.68, -12.7 CFM - OH, 5.69, -12.7 CFM - OH, 5.70, -12.7 CFM - OH, 5.71, -12.7 CFM - OH, 5.72, -12.6 CFM - OH, 5.73, -12.6 CFM - OH, 5.74, -12.6 CFM - OH, 5.75, -12.6 CFM - OH, 5.76, -12.5 CFM - OH, 5.77, -12.5 CFM - OH, 5.78, -12.5 CFM - OH, 5.79, -12.5 CFM - OH, 5.80, -12.5 CFM - OH, 5.81, -12.4 CFM - OH, 5.82, -12.4 CFM - OH, 5.83, -12.4 CFM - OH, 5.84, -12.4 CFM - OH, 5.85, -12.4 CFM - OH, 5.86, -12.3 CFM - OH, 5.87, -12.3 CFM - OH, 5.88, -12.3 CFM - OH, 5.89, -12.3 CFM - OH, 5.90, -12.2 CFM - OH, 5.91, -12.2 CFM - OH, 5.92, -12.2 CFM - OH, 5.93, -12.2 CFM - OH, 5.94, -12.2 CFM - OH, 5.95, -12.1 CFM - OH, 5.96, -12.1 CFM - OH, 5.97, -12.1 CFM - OH, 5.98, -12.1 CFM - OH, 5.99, -12.1 CFM - OH, 6.00, -12.0 CFM - OH, 6.01, -12.0 CFM - OH, 6.02, -12.0 CFM - OH, 6.03, -12.0 CFM - OH, 6.04, -12.0 CFM - OH, 6.05, -11.9 CFM - OH, 6.06, -11.9 CFM - OH, 6.07, -11.9 CFM - OH, 6.08, -11.9 CFM - OH, 6.09, -11.9 CFM - OH, 6.10, -11.8 CFM - OH, 6.11, -11.8 CFM - OH, 6.12, -11.8 CFM - OH, 6.13, -11.8 CFM - OH, 6.14, -11.8 CFM - OH, 6.15, -11.8 CFM - OH, 6.16, -11.7 CFM - OH, 6.17, -11.7 CFM - OH, 6.18, -11.7 CFM - OH, 6.19, -11.7 CFM - OH, 6.20, -11.7 CFM - OH, 6.21, -11.6 CFM - OH, 6.22, -11.6 CFM - OH, 6.23, -11.6 CFM - OH, 6.24, -11.6 CFM - OH, 6.25, -11.6 CFM - OH, 6.26, -11.5 CFM - OH, 6.27, -11.5 CFM - OH, 6.28, -11.5 CFM - OH, 6.29, -11.5 CFM - OH, 6.30, -11.5 CFM - OH, 6.31, -11.5 CFM - OH, 6.32, -11.4 CFM - OH, 6.33, -11.4 CFM - OH, 6.34, -11.4 CFM - OH, 6.35, -11.4 CFM - OH, 6.36, -11.4 CFM - OH, 6.37, -11.3 CFM - OH, 6.38, -11.3 CFM - OH, 6.39, -11.3 CFM - OH, 6.40, -11.3 CFM - OH, 6.41, -11.3 CFM - OH, 6.42, -11.3 CFM - OH, 6.43, -11.2 CFM - OH, 6.44, -11.2 CFM - OH, 6.45, -11.2 CFM - OH, 6.46, -11.2 CFM - OH, 6.47, -11.2 CFM - OH, 6.48, -11.2 CFM - OH, 6.49, -11.1 CFM - OH, 6.50, -11.1 CFM - OH, 6.51, -11.1 CFM - OH, 6.52, -11.1 CFM - OH, 6.53, -11.1 CFM - OH, 6.54, -11.1 CFM - OH, 6.55, -11.0 CFM - OH, 6.56, -11.0 CFM - OH, 6.57, -11.0 CFM - OH, 6.58, -11.0 CFM - OH, 6.59, -11.0 CFM - OH, 6.60, -11.0 CFM - OH, 6.61, -10.9 CFM - OH, 6.62, -10.9 CFM - OH, 6.63, -10.9 CFM - OH, 6.64, -10.9 CFM - OH, 6.65, -10.9 CFM - OH, 6.66, -10.9 CFM - OH, 6.67, -10.8 CFM - OH, 6.68, -10.8 CFM - OH, 6.69, -10.8 CFM - OH, 6.70, -10.8 CFM - OH, 6.71, -10.8 CFM - OH, 6.72, -10.8 CFM - OH, 6.73, -10.7 CFM - OH, 6.74, -10.7 CFM - OH, 6.75, -10.7 CFM - OH, 6.76, -10.7 CFM - OH, 6.77, -10.7 CFM - OH, 6.78, -10.7 CFM - OH, 6.79, -10.6 CFM - OH, 6.80, -10.6 CFM - OH, 6.81, -10.6 CFM - OH, 6.82, -10.6 CFM - OH, 6.83, -10.6 CFM - OH, 6.84, -10.6 CFM - OH, 6.85, -10.6 CFM - OH, 6.86, -10.5 CFM - OH, 6.87, -10.5 CFM - OH, 6.88, -10.5 CFM - OH, 6.89, -10.5 CFM - OH, 6.90, -10.5 CFM - OH, 6.91, -10.5 CFM - OH, 6.92, -10.4 CFM - OH, 6.93, -10.4 CFM - OH, 6.94, -10.4 CFM - OH, 6.95, -10.4 CFM - OH, 6.96, -10.4 CFM - OH, 6.97, -10.4 CFM - OH, 6.98, -10.4 CFM - OH, 6.99, -10.3 CFM - OH, 7.00, -10.3 CFM - OH, 7.01, -10.3 CFM - OH, 7.02, -10.3 CFM - OH, 7.03, -10.3 CFM - OH, 7.04, -10.3 CFM - OH, 7.05, -10.3 CFM - OH, 7.06, -10.2 CFM - OH, 7.07, -10.2 CFM - OH, 7.08, -10.2 CFM - OH, 7.09, -10.2 CFM - OH, 7.10, -10.2 CFM - OH, 7.11, -10.2 CFM - OH, 7.12, -10.2 CFM - OH, 7.13, -10.1 CFM - OH, 7.14, -10.1 CFM - OH, 7.15, -10.1 CFM - OH, 7.16, -10.1 CFM - OH, 7.17, -10.1 CFM - OH, 7.18, -10.1 CFM - OH, 7.19, -10.1 CFM - OH, 7.20, -10.0 CFM - OH, 7.21, -10.0 CFM - OH, 7.22, -10.0 CFM - OH, 7.23, -10.0 CFM - OH, 7.24, -10.0 CFM - OH, 7.25, -10.0 CFM - OH, 7.26, -10.0 CFM - OH, 7.27, -9.9 CFM - OH, 7.28, -9.9 CFM - OH, 7.29, -9.9 CFM - OH, 7.30, -9.9 CFM - OH, 7.31, -9.9 CFM - OH, 7.32, -9.9 CFM - OH, 7.33, -9.9 CFM - OH, 7.34, -9.8 CFM - OH, 7.35, -9.8 CFM - OH, 7.36, -9.8 CFM - OH, 7.37, -9.8 CFM - OH, 7.38, -9.8 CFM - OH, 7.39, -9.8 CFM - OH, 7.40, -9.8 CFM - OH, 7.41, -9.8 CFM - OH, 7.42, -9.7 CFM - OH, 7.43, -9.7 CFM - OH, 7.44, -9.7 CFM - OH, 7.45, -9.7 CFM - OH, 7.46, -9.7 CFM - OH, 7.47, -9.7 CFM - OH, 7.48, -9.7 CFM - OH, 7.49, -9.6 CFM - OH, 7.50, -9.6 CFM - OH, 7.51, -9.6 CFM - OH, 7.52, -9.6 CFM - OH, 7.53, -9.6 CFM - OH, 7.54, -9.6 CFM - OH, 7.55, -9.6 CFM - OH, 7.56, -9.6 CFM - OH, 7.57, -9.5 CFM - OH, 7.58, -9.5 CFM - OH, 7.59, -9.5 CFM - OH, 7.60, -9.5 CFM - OH, 7.61, -9.5 CFM - OH, 7.62, -9.5 CFM - OH, 7.63, -9.5 CFM - OH, 7.64, -9.5 CFM - OH, 7.65, -9.4 CFM - OH, 7.66, -9.4 CFM - OH, 7.67, -9.4 CFM - OH, 7.68, -9.4 CFM - OH, 7.69, -9.4 CFM - OH, 7.70, -9.4 CFM - OH, 7.71, -9.4 CFM - OH, 7.72, -9.4 CFM - OH, 7.73, -9.3 CFM - OH, 7.74, -9.3 CFM - OH, 7.75, -9.3 CFM - OH, 7.76, -9.3 CFM - OH, 7.77, -9.3 CFM - OH, 7.78, -9.3 CFM - OH, 7.79, -9.3 CFM - OH, 7.80, -9.3 CFM - OH, 7.81, -9.3 CFM - OH, 7.82, -9.2 CFM - OH, 7.83, -9.2 CFM - OH, 7.84, -9.2 CFM - OH, 7.85, -9.2 CFM - OH, 7.86, -9.2 CFM - OH, 7.87, -9.2 CFM - OH, 7.88, -9.2 CFM - OH, 7.89, -9.2 CFM - OH, 7.90, -9.1 CFM - OH, 7.91, -9.1 CFM - OH, 7.92, -9.1 CFM - OH, 7.93, -9.1 CFM - OH, 7.94, -9.1 CFM - OH, 7.95, -9.1 CFM - OH, 7.96, -9.1 CFM - OH, 7.97, -9.1 CFM - OH, 7.98, -9.1 CFM - OH, 7.99, -9.0 CFM - OH, 8.00, -9.0 CFM - OH, 8.01, -9.0 CFM - OH, 8.02, -9.0 CFM - OH, 8.03, -9.0 CFM - OH, 8.04, -9.0 CFM - OH, 8.05, -9.0 CFM - OH, 8.06, -9.0 CFM - OH, 8.07, -9.0 CFM - OH, 8.08, -8.9 CFM - OH, 8.09, -8.9 CFM - OH, 8.10, -8.9 CFM - OH, 8.11, -8.9 CFM - OH, 8.12, -8.9 CFM - OH, 8.13, -8.9 CFM - OH, 8.14, -8.9 CFM - OH, 8.15, -8.9 CFM - OH, 8.16, -8.9 CFM - OH, 8.17, -8.8 CFM - OH, 8.18, -8.8 CFM - OH, 8.19, -8.8 CFM - OH, 8.20, -8.8 CFM - OH, 8.21, -8.8 CFM - OH, 8.22, -8.8 CFM - OH, 8.23, -8.8 CFM - OH, 8.24, -8.8 CFM - OH, 8.25, -8.8 CFM - OH, 8.26, -8.7 CFM - OH, 8.27, -8.7 CFM - OH, 8.28, -8.7 CFM - OH, 8.29, -8.7 CFM - OH, 8.30, -8.7 CFM - OH, 8.31, -8.7 CFM - OH, 8.32, -8.7 CFM - OH, 8.33, -8.7 CFM - OH, 8.34, -8.7 CFM - OH, 8.35, -8.7 CFM - OH, 8.36, -8.6 CFM - OH, 8.37, -8.6 CFM - OH, 8.38, -8.6 CFM - OH, 8.39, -8.6 CFM - OH, 8.40, -8.6 CFM - OH, 8.41, -8.6 CFM - OH, 8.42, -8.6 CFM - OH, 8.43, -8.6 CFM - OH, 8.44, -8.6 CFM - OH, 8.45, -8.6 CFM - OH, 8.46, -8.5 CFM - OH, 8.47, -8.5 CFM - OH, 8.48, -8.5 CFM - OH, 8.49, -8.5 CFM - OH, 8.50, -8.5 CFM - OH, 8.51, -8.5 CFM - OH, 8.52, -8.5 CFM - OH, 8.53, -8.5 CFM - OH, 8.54, -8.5 CFM - OH, 8.55, -8.5 CFM - OH, 8.56, -8.4 CFM - OH, 8.57, -8.4 CFM - OH, 8.58, -8.4 CFM - OH, 8.59, -8.4 CFM - OH, 8.60, -8.4 CFM - OH, 8.61, -8.4 CFM - OH, 8.62, -8.4 CFM - OH, 8.63, -8.4 CFM - OH, 8.64, -8.4 CFM - OH, 8.65, -8.4 CFM - OH, 8.66, -8.3 CFM - OH, 8.67, -8.3 CFM - OH, 8.68, -8.3 CFM - OH, 8.69, -8.3 CFM - OH, 8.70, -8.3 CFM - OH, 8.71, -8.3 CFM - OH, 8.72, -8.3 CFM - OH, 8.73, -8.3 CFM - OH, 8.74, -8.3 CFM - OH, 8.75, -8.3 CFM - OH, 8.76, -8.3 CFM - OH, 8.77, -8.2 CFM - OH, 8.78, -8.2 CFM - OH, 8.79, -8.2 CFM - OH, 8.80, -8.2 CFM - OH, 8.81, -8.2 CFM - OH, 8.82, -8.2 CFM - OH, 8.83, -8.2 CFM - OH, 8.84, -8.2 CFM - OH, 8.85, -8.2 CFM - OH, 8.86, -8.2 CFM - OH, 8.87, -8.1 CFM - OH, 8.88, -8.1 CFM - OH, 8.89, -8.1 CFM - OH, 8.90, -8.1 CFM - OH, 8.91, -8.1 CFM - OH, 8.92, -8.1 CFM - OH, 8.93, -8.1 CFM - OH, 8.94, -8.1 CFM - OH, 8.95, -8.1 CFM - OH, 8.96, -8.1 CFM - OH, 8.97, -8.1 CFM - OH, 8.98, -8.0 CFM - OH, 8.99, -8.0 CFM - OH, 9.00, -8.0 CFM - OH, 9.01, -8.0 CFM - OH, 9.02, -8.0 CFM - OH, 9.03, -8.0 CFM - OH, 9.04, -8.0 CFM - OH, 9.05, -8.0 CFM - OH, 9.06, -8.0 CFM - OH, 9.07, -8.0 CFM - OH, 9.08, -8.0 CFM - OH, 9.09, -8.0 CFM - OH, 9.10, -7.9 CFM - OH, 9.11, -7.9 CFM - OH, 9.12, -7.9 CFM - OH, 9.13, -7.9 CFM - OH, 9.14, -7.9 CFM - OH, 9.15, -7.9 CFM - OH, 9.16, -7.9 CFM - OH, 9.17, -7.9 CFM - OH, 9.18, -7.9 CFM - OH, 9.19, -7.9 CFM - OH, 9.20, -7.9 CFM - OH, 9.21, -7.8 CFM - OH, 9.22, -7.8 CFM - OH, 9.23, -7.8 CFM - OH, 9.24, -7.8 CFM - OH, 9.25, -7.8 CFM - OH, 9.26, -7.8 CFM - OH, 9.27, -7.8 CFM - OH, 9.28, -7.8 CFM - OH, 9.29, -7.8 CFM - OH, 9.30, -7.8 CFM - OH, 9.31, -7.8 CFM - OH, 9.32, -7.8 CFM - OH, 9.33, -7.7 CFM - OH, 9.34, -7.7 CFM - OH, 9.35, -7.7 CFM - OH, 9.36, -7.7 CFM - OH, 9.37, -7.7 CFM - OH, 9.38, -7.7 CFM - OH, 9.39, -7.7 CFM - OH, 9.40, -7.7 CFM - OH, 9.41, -7.7 CFM - OH, 9.42, -7.7 CFM - OH, 9.43, -7.7 CFM - OH, 9.44, -7.7 CFM - OH, 9.45, -7.6 CFM - OH, 9.46, -7.6 CFM - OH, 9.47, -7.6 CFM - OH, 9.48, -7.6 CFM - OH, 9.49, -7.6 CFM - OH, 9.50, -7.6 CFM - OH, 9.51, -7.6 CFM - OH, 9.52, -7.6 CFM - OH, 9.53, -7.6 CFM - OH, 9.54, -7.6 CFM - OH, 9.55, -7.6 CFM - OH, 9.56, -7.6 CFM - OH, 9.57, -7.6 CFM - OH, 9.58, -7.5 CFM - OH, 9.59, -7.5 CFM - OH, 9.60, -7.5 CFM - OH, 9.61, -7.5 CFM - OH, 9.62, -7.5 CFM - OH, 9.63, -7.5 CFM - OH, 9.64, -7.5 CFM - OH, 9.65, -7.5 CFM - OH, 9.66, -7.5 CFM - OH, 9.67, -7.5 CFM - OH, 9.68, -7.5 CFM - OH, 9.69, -7.5 CFM - OH, 9.70, -7.5 CFM - OH, 9.71, -7.4 CFM - OH, 9.72, -7.4 CFM - OH, 9.73, -7.4 CFM - OH, 9.74, -7.4 CFM - OH, 9.75, -7.4 CFM - OH, 9.76, -7.4 CFM - OH, 9.77, -7.4 CFM - OH, 9.78, -7.4 CFM - OH, 9.79, -7.4 CFM - OH, 9.80, -7.4 CFM - OH, 9.81, -7.4 CFM - OH, 9.82, -7.4 CFM - OH, 9.83, -7.4 CFM - OH, 9.84, -7.3 CFM - OH, 9.85, -7.3 CFM - OH, 9.86, -7.3 CFM - OH, 9.87, -7.3 CFM - OH, 9.88, -7.3 CFM - OH, 9.89, -7.3 CFM - OH, 9.90, -7.3 CFM - OH, 9.91, -7.3 CFM - OH, 9.92, -7.3 CFM - OH, 9.93, -7.3 CFM - OH, 9.94, -7.3 CFM - OH, 9.95, -7.3 CFM - OH, 9.96, -7.3 CFM - OH, 9.97, -7.2 CFM - OH, 9.98, -7.2 CFM - OH, 9.99, -7.2

CFM - OH, 10.00, -7.2

Acid - OH, 0.01,

1549992770.9

Acid - OH, 0.02,

96871384.4

Acid - OH, 0.03,

19133391.4

Acid - OH, 0.04,

6052878.7

Acid - OH, 0.05,

2478552.6

Acid - OH, 0.06,

1194781.1

Acid - OH, 0.07,

644529.9

Acid - OH, 0.08,

377512.6

Acid - OH, 0.09,

235439.5

Acid - OH, 0.1,

154275.3

Acid - OH, 0.11,

105208.1

Acid - OH, 0.12,

74145.0

Acid - OH, 0.13,

53711.9

Acid - OH, 0.14,

39829.5

Acid - OH, 0.15,

30133.5

Acid - OH, 0.16,

23197.4

Acid - OH, 0.17,

18131.1

Acid - OH, 0.18,

14361.8

Acid - OH, 0.19,

11511.3

Acid - OH, 0.2, 9324.1

Acid - OH, 0.21, 7623.8

Acid - OH, 0.22, 6286.2

Acid - OH, 0.23, 5222.6

Acid - OH, 0.24, 4368.7

Acid - OH, 0.25, 3676.9

Acid - OH, 0.26, 3111.9

Acid - OH, 0.27, 2646.9

Acid - OH, 0.28, 2261.6

Acid - OH, 0.29, 1940.3 Acid - OH,

0.3, 1670.7 Acid - OH,

0.31, 1443.2 Acid - OH,

0.32, 1250.3 Acid - OH,

0.33, 1086.0 Acid - OH,

0.34, 945.3 Acid - OH,

0.35, 824.4 Acid - OH,

0.36, 720.1 Acid - OH,

0.37, 629.7 Acid - OH,

0.38, 551.2 Acid - OH,

0.39, 482.7 Acid - OH, 0.4, 422.8 Acid - OH,

0.41, 370.3 Acid - OH,

0.42, 324.0 Acid - OH,

0.43, 283.3 Acid - OH,

0.44, 247.3 Acid - OH,

0.45, 215.4 Acid - OH,

0.46, 187.1 Acid - OH,

0.47, 161.9 Acid - OH,

0.48, 139.4 Acid - OH,

0.49, 119.4 Acid - OH, 0.5, 101.5 Acid - OH, 0.51, 85.4 Acid - OH, 0.52, 71.0 Acid - OH, 0.53, 58.1 Acid - OH, 0.54, 46.5 Acid - OH, 0.55, 36.0 Acid - OH, 0.56, 26.6 Acid - OH, 0.57, 18.0 Acid - OH, 0.58, 10.4 Acid - OH, 0.59, 3.4

Acid - OH, 0.6, -2.9

Acid - OH, 0.61, -8.5 Acid - OH, 0.62, -13.7 Acid - OH, 0.63, -18.3 Acid - OH, 0.64, -22.5 Acid - OH, 0.65, -26.4 Acid - OH, 0.66, -29.8 Acid - OH, 0.67, -32.9 Acid - OH, 0.68, -35.8 Acid - OH, 0.69, -38.4 Acid - OH, 0.7, -40.7 Acid - OH, 0.71, -42.8 Acid - OH, 0.72, -44.7 Acid - OH, 0.73, -46.4 Acid - OH, 0.74, -48.0 Acid - OH, 0.75, -49.4 Acid - OH, 0.76, -50.6 Acid - OH, 0.77, -51.8 Acid - OH, 0.78, -52.8 Acid - OH, 0.79, -53.7 Acid - OH, 0.8, -54.5 Acid - OH, 0.81, -55.2 Acid - OH, 0.82, -55.9 Acid - OH, 0.83, -56.4 Acid - OH, 0.84, -56.9 Acid - OH, 0.85, -57.3 Acid - OH, 0.86, -57.7 Acid - OH, 0.87, -58.0 Acid - OH, 0.88, -58.3 Acid - OH, 0.89, -58.5 Acid - OH, 0.9, -58.7 Acid - OH, 0.91, -58.8 Acid - OH, 0.92, -58.9 Acid - OH, 0.93, -59.0 Acid - OH, 0.94, -59.0 Acid - OH, 0.95, -59.0 Acid - OH, 0.96, -59.0 Acid - OH, 0.97, -59.0 Acid - OH, 0.98, -58.9 Acid - OH, 0.99, -58.9 Acid - OH, 1,

-58.8 Acid - OH, 1.01, -58.7 Acid - OH, 1.02, -58.5 Acid - OH, 1.03, -58.4 Acid - OH, 1.04, -58.2 Acid - OH, 1.05, -58.1 Acid - OH, 1.06, -57.9 Acid - OH, 1.07, -57.7 Acid - OH, 1.08, -57.5 Acid - OH, 1.09, -57.3 Acid - OH, 1.1, -57.1

Acid - OH, 1.11, -56.9 Acid - OH, 1.12, -56.7

Acid - OH, 1.13, -56.4

Acid - OH, 1.14, -56.2

Acid - OH, 1.15, -56.0

Acid - OH, 1.16, -55.7

Acid - OH, 1.17, -55.5

Acid - OH, 1.18, -55.2

Acid - OH, 1.19, -55.0

Acid - OH, 1.2, -54.7

Acid - OH, 1.21, -54.5

Acid - OH, 1.22, -54.2

Acid - OH, 1.23, -54.0

Acid - OH, 1.24, -53.7

Acid - OH, 1.25, -53.5

Acid - OH, 1.26, -53.2

Acid - OH, 1.27, -52.9

Acid - OH, 1.28, -52.7

Acid - OH, 1.29, -52.4

Acid - OH, 1.3, -52.1

Acid - OH, 1.31, -51.9

Acid - OH, 1.32, -51.6

Acid - OH, 1.33, -51.4

Acid - OH, 1.34, -51.1

Acid - OH, 1.35, -50.8

Acid - OH, 1.36, -50.6

Acid - OH, 1.37, -50.3

Acid - OH, 1.38, -50.1

Acid - OH, 1.39, -49.8

Acid - OH, 1.4, -49.6

Acid - OH, 1.41, -49.3

Acid - OH, 1.42, -49.0

Acid - OH, 1.43, -48.8

Acid - OH, 1.44, -48.5

Acid - OH, 1.45, -48.3

Acid - OH, 1.46, -48.0 Acid - OH, 1.47, -47.8

Acid - OH, 1.48, -47.5

Acid - OH, 1.49, -47.3

Acid - OH, 1.5, -47.1

Acid - OH, 1.51, -46.8

Acid - OH, 1.52, -46.6

Acid - OH, 1.53, -46.3

Acid - OH, 1.54, -46.1 Acid - OH, 1.55, -45.9

Acid - OH, 1.56, -45.6

Acid - OH, 1.57, -45.4

Acid - OH, 1.58, -45.2

Acid - OH, 1.59, -44.9

Acid - OH, 1.6, -44.7

Acid - OH, 1.61, -44.5 Acid - OH, 1.62, -44.3 Acid - OH, 1.63, -44.0 Acid - OH, 1.64, -43.8

Acid - OH, 1.65, -43.6 Acid - OH, 1.66, -43.4 Acid - OH, 1.67, -43.2 Acid - OH, 1.68, -42.9 Acid - OH, 1.69, -42.7 Acid - OH, 1.7, -42.5 Acid - OH, 1.71, -42.3 Acid - OH, 1.72, -42.1 Acid - OH, 1.73, -41.9 Acid - OH, 1.74, -41.7 Acid - OH, 1.75, -41.5 Acid - OH, 1.76, -41.2 Acid - OH, 1.77, -41.0 Acid - OH, 1.78, -40.8 Acid - OH, 1.79, -40.6 Acid - OH, 1.8, -40.4 Acid - OH, 1.81, -40.2 Acid - OH, 1.82, -40.0 Acid - OH, 1.83, -39.8 Acid - OH, 1.84, -39.6 Acid - OH, 1.85, -39.4 Acid - OH, 1.86, -39.3 Acid - OH, 1.87, -39.1 Acid - OH, 1.88, -38.9 Acid - OH, 1.89, -38.7 Acid - OH, 1.9, -38.5 Acid - OH, 1.91, -38.3 Acid - OH, 1.92, -38.1 Acid - OH, 1.93, -37.9 Acid - OH, 1.94, -37.7 Acid - OH, 1.95, -37.5 Acid - OH, 1.96, -37.4 Acid - OH, 1.97, -37.2 Acid - OH, 1.98, -37.0 Acid - OH, 1.99, -36.8 Acid - OH, 2,

-36.6 Acid - OH, 2.01, -36.4 Acid - OH, 2.02, -36.3 Acid - OH, 2.03, -36.1 Acid - OH, 2.04, -35.9 Acid - OH, 2.05, -35.7 Acid - OH, 2.06, -35.6 Acid - OH, 2.07, -35.4 Acid - OH, 2.08, -35.2 Acid - OH, 2.09, -35.0 Acid - OH, 2.1, -34.9 Acid - OH, 2.11, -34.7 Acid - OH, 2.12, -34.5 Acid - OH, 2.13, -34.4 Acid - OH, 2.14, -34.2 Acid - OH, 2.15, -34.0 Acid - OH, 2.16, -33.8 Acid - OH, 2.17, -33.7 Acid - OH, 2.18, -33.5 Acid - OH, 2.19, -33.4 Acid - OH, 2.2, -33.2 Acid - OH, 2.21, -33.0 Acid - OH, 2.22, -32.9 Acid - OH, 2.23, -32.7 Acid - OH, 2.24, -32.5 Acid - OH, 2.25, -32.4 Acid - OH, 2.26, -32.2 Acid - OH, 2.27, -32.1 Acid - OH, 2.28, -31.9 Acid - OH, 2.29, -31.8 Acid - OH, 2.3, -31.6 Acid - OH, 2.31, -31.5 Acid - OH, 2.32, -31.3 Acid - OH, 2.33, -31.2 Acid - OH, 2.34, -31.0 Acid - OH, 2.35, -30.9 Acid - OH, 2.36, -30.7 Acid - OH, 2.37, -30.6 Acid - OH, 2.38, -30.5 Acid - OH, 2.39, -30.3 Acid - OH, 2.4, -30.2 Acid - OH, 2.41, -30.0 Acid - OH, 2.42, -29.9 Acid - OH, 2.43, -29.8 Acid - OH, 2.44, -29.6 Acid - OH, 2.45, -29.5 Acid - OH, 2.46, -29.4 Acid - OH, 2.47, -29.3 Acid - OH, 2.48, -29.1 Acid - OH, 2.49, -29.0 Acid - OH, 2.5, -28.9 Acid - OH, 2.51, -28.8 Acid - OH, 2.52, -28.6 Acid - OH, 2.53, -28.5 Acid - OH, 2.54, -28.4 Acid - OH, 2.55, -28.3 Acid - OH, 2.56, -28.2 Acid - OH, 2.57, -28.0 Acid - OH, 2.58, -27.9 Acid - OH, 2.59, -27.8 Acid - OH, 2.6, -27.7 Acid - OH, 2.61, -27.6 Acid - OH, 2.62, -27.5 Acid - OH, 2.63, -27.4 Acid - OH, 2.64, -27.3 Acid - OH, 2.65, -27.1 Acid - OH, 2.66, -27.0 Acid - OH, 2.67, -26.9 Acid - OH, 2.68, -26.8 Acid - OH, 2.69, -26.7 Acid - OH, 2.7, -26.6 Acid - OH, 2.71, -26.5 Acid - OH, 2.72, -26.4 Acid - OH, 2.73, -26.3 Acid - OH, 2.74, -26.2 Acid - OH, 2.75, -26.1 Acid - OH, 2.76, -26.0 Acid - OH, 2.77, -25.9 Acid - OH, 2.78, -25.8 Acid - OH, 2.79, -25.7 Acid - OH, 2.8, -25.7 Acid - OH, 2.81, -25.6 Acid - OH, 2.82, -25.5 Acid - OH, 2.83, -25.4 Acid - OH, 2.84, -25.3 Acid - OH, 2.85, -25.2 Acid - OH, 2.86, -25.1 Acid - OH, 2.87, -25.0 Acid - OH, 2.88, -24.9 Acid - OH, 2.89, -24.8 Acid - OH, 2.9, -24.8 Acid - OH, 2.91, -24.7 Acid - OH, 2.92, -24.6 Acid - OH, 2.93, -24.5 Acid - OH, 2.94, -24.4 Acid - OH, 2.95, -24.3 Acid - OH, 2.96, -24.3 Acid - OH, 2.97, -24.2 Acid - OH, 2.98, -24.1 Acid - OH, 2.99, -24.0 Acid - OH, 3,

-23.9 Acid - OH, 3.01, -23.9 Acid - OH, 3.02, -23.8 Acid - OH, 3.03, -23.7 Acid - OH, 3.04, -23.6 Acid - OH, 3.05, -23.5 Acid - OH, 3.06, -23.5 Acid - OH, 3.07, -23.4 Acid - OH, 3.08, -23.3 Acid - OH, 3.09, -23.2 Acid - OH, 3.1, -23.2 Acid - OH, 3.11, -23.1 Acid - OH, 3.12, -23.0 Acid - OH, 3.13, -22.9 Acid - OH, 3.14, -22.9 Acid - OH, 3.15, -22.8 Acid - OH, 3.16, -22.7 Acid - OH, 3.17, -22.7 Acid - OH, 3.18, -22.6 Acid - OH, 3.19, -22.5 Acid - OH, 3.2, -22.5 Acid - OH, 3.21, -22.4 Acid - OH, 3.22, -22.3 Acid - OH, 3.23, -22.2 Acid - OH, 3.24, -22.2 Acid - OH, 3.25, -22.1 Acid - OH, 3.26, -22.0 Acid - OH, 3.27, -22.0 Acid - OH, 3.28, -21.9 Acid - OH, 3.29, -21.8 Acid - OH, 3.3, -21.8 Acid - OH, 3.31, -21.7 Acid - OH, 3.32, -21.6 Acid - OH, 3.33, -21.6 Acid - OH, 3.34, -21.5 Acid - OH, 3.35, -21.5 Acid - OH, 3.36, -21.4 Acid - OH, 3.37, -21.3 Acid - OH, 3.38, -21.3 Acid - OH, 3.39, -21.2 Acid - OH, 3.4, -21.1 Acid - OH, 3.41, -21.1 Acid - OH, 3.42, -21.0 Acid - OH, 3.43, -21.0 Acid - OH, 3.44, -20.9 Acid - OH, 3.45, -20.8 Acid - OH, 3.46, -20.8 Acid - OH, 3.47, -20.7 Acid - OH, 3.48, -20.7 Acid - OH, 3.49, -20.6 Acid - OH, 3.5, -20.5 Acid - OH, 3.51, -20.5 Acid - OH, 3.52, -20.4 Acid - OH, 3.53, -20.4 Acid - OH, 3.54, -20.3 Acid - OH, 3.55, -20.3 Acid - OH, 3.56, -20.2 Acid - OH, 3.57, -20.2 Acid - OH, 3.58, -20.1 Acid - OH, 3.59, -20.0 Acid - OH, 3.6, -20.0 Acid - OH, 3.61, -19.9 Acid - OH, 3.62, -19.9 Acid - OH, 3.63, -19.8 Acid - OH, 3.64, -19.8 Acid - OH, 3.65, -19.7 Acid - OH, 3.66, -19.7 Acid - OH, 3.67, -19.6 Acid - OH, 3.68, -19.6 Acid - OH, 3.69, -19.5 Acid - OH, 3.7, -19.5 Acid - OH, 3.71, -19.4 Acid - OH, 3.72, -19.3 Acid - OH, 3.73, -19.3 Acid - OH, 3.74, -19.2 Acid - OH, 3.75, -19.2 Acid - OH, 3.76, -19.1 Acid - OH, 3.77, -19.1 Acid - OH, 3.78, -19.0 Acid - OH, 3.79, -19.0 Acid - OH, 3.8, -18.9 Acid - OH, 3.81, -18.9 Acid - OH, 3.82, -18.8 Acid - OH, 3.83, -18.8 Acid - OH, 3.84, -18.7 Acid - OH, 3.85, -18.7 Acid - OH, 3.86, -18.7 Acid - OH, 3.87, -18.6 Acid - OH, 3.88, -18.6 Acid - OH, 3.89, -18.5 Acid - OH, 3.9, -18.5 Acid - OH, 3.91, -18.4 Acid - OH, 3.92, -18.4 Acid - OH, 3.93, -18.3 Acid - OH, 3.94, -18.3 Acid - OH, 3.95, -18.2 Acid - OH, 3.96, -18.2 Acid - OH, 3.97, -18.1 Acid - OH, 3.98, -18.1 Acid - OH, 3.99, -18.1 Acid - OH, 4,

-18.0 Acid - OH, 4.01, -18.0 Acid - OH, 4.02, -17.9 Acid - OH, 4.03, -17.9 Acid - OH, 4.04, -17.8 Acid - OH, 4.05, -17.8 Acid - OH, 4.06, -17.7 Acid - OH, 4.07, -17.7 Acid - OH, 4.08, -17.7 Acid - OH, 4.09, -17.6 Acid - OH, 4.1, -17.6 Acid - OH, 4.11, -17.5 Acid - OH, 4.12, -17.5 Acid - OH, 4.13, -17.4 Acid - OH, 4.14, -17.4 Acid - OH, 4.15, -17.4 Acid - OH, 4.16, -17.3 Acid - OH, 4.17, -17.3 Acid - OH, 4.18, -17.2 Acid - OH, 4.19, -17.2 Acid - OH, 4.2, -17.2 Acid - OH, 4.21, -17.1 Acid - OH, 4.22, -17.1 Acid - OH, 4.23, -17.0 Acid - OH, 4.24, -17.0 Acid - OH, 4.25, -17.0 Acid - OH, 4.26, -16.9 Acid - OH, 4.27, -16.9 Acid - OH, 4.28, -16.8 Acid - OH, 4.29, -16.8 Acid - OH, 4.3, -16.8 Acid - OH, 4.31, -16.7 Acid - OH, 4.32, -16.7 Acid - OH, 4.33, -16.6 Acid - OH, 4.34, -16.6 Acid - OH, 4.35, -16.6 Acid - OH, 4.36, -16.5 Acid - OH, 4.37, -16.5 Acid - OH, 4.38, -16.5 Acid - OH, 4.39, -16.4 Acid - OH, 4.4, -16.4 Acid - OH, 4.41, -16.3 Acid - OH, 4.42, -16.3 Acid - OH, 4.43, -16.3 Acid - OH, 4.44, -16.2 Acid - OH, 4.45, -16.2 Acid - OH, 4.46, -16.2 Acid - OH, 4.47, -16.1 Acid - OH, 4.48, -16.1 Acid - OH, 4.49, -16.1 Acid - OH, 4.5, -16.0

Acid - OH, 4.51, -16.0 Acid - OH, 4.52, -16.0 Acid - OH, 4.53, -15.9 Acid - OH, 4.54, -15.9 Acid - OH, 4.55, -15.8 Acid - OH, 4.56, -15.8 Acid - OH, 4.57, -15.8 Acid - OH, 4.58, -15.7 Acid - OH, 4.59, -15.7 Acid - OH, 4.6, -15.7




Acid - OH, 4.91, -14.7 Acid - OH, 4.92, -14.7 Acid - OH, 4.93, -14.6 Acid - OH, 4.94, -14.6 Acid - OH, 4.95, -14.6 Acid - OH, 4.96, -14.5 Acid - OH, 4.97, -14.5 Acid - OH, 4.98, -14.5 Acid - OH, 4.99, -14.5

Acid - OH, 5, -14.4











Acid - OH, 6, -12.0











Acid - OH, 7, -10.3











Acid - OH, 8, -9.0











Acid - OH, 9, -8.0










Acid - OH, 9.91, -7.3 Acid - OH, 9.92, -7.3 Acid - OH, 9.93, -7.3 Acid - OH, 9.94, -7.3 Acid - OH, 9.95, -7.3 Acid - OH, 9.96, -7.3 Acid - OH, 9.97, -7.2 Acid - OH, 9.98, -7.2 Acid - OH, 9.99, -7.2 Acid - OH,

10, -7.2 En

erg

y (k

cal/

mo

l)

Distance (A)

CFM - OH

Acid - OH

48

system. Results from these simulations will be discussed for various potentials and future

recommendations for continuing this work will be given.

49

Chapter 4

Simulating Aqueous Sulfuric Acid between Platinum Electrodes

We have developed a molecular dynamics (MD) force field capable of describing

aqueous sulfuric acid in a reactive manner. The force field has been parameterized to allow for

selective proton dissociation to obtain an average solution structure of HSO4-, which is the most

abundant species in aqueous sulfuric acid at low concentrations. Sulfuric acid was chosen to

represent the activity of a Nafion proton exchange membrane in solution. This chapter will

discuss the incorporation of electrode charge dynamics (ECD) into our force field to provide

atomistic distinction to platinum metal atoms of an electrode surface and the running of our full

scale electrochemical system, with preliminary data analysis.

Parameterization of Pt (111) surface with aqueous sulfuric acid

To accurately describe average structure at the electrode/electrolyte interface in

electrochemical systems, short range interactions must be represented correctly. Because image-

charge methods cannot mimic the interaction expected near an electrode surface, ECD is used in

its place [5]. Forces defined between metal atoms and atoms in the electrolyte/solution region are

parameterized from ab initio calculations in which single point calculations are performed to

determine the energy for a system as a function of adsorbate distance away from a metal surface.

In our calculations, water molecules and bisulfate anions were separately considered over a Pt

(111) metal cluster consisting of 25 metal atoms in four layers. The (111) surface of platinum is

used because it is the most energetically favorable surface cut, and is the most active for the

ORR. For description of the platinum metal, parameters from Equations 2-6, 2-7 are needed. The

core charges, qic, are assigned a value of 1 e, leading to an initial value of -1 e for all diffuse

charges, qid, to yield a neutral surface. During simulation, the diffuse charges change from their

50

initial values in response to local charges. The width parameter, γ, is given a value of 0.751 Å-1

,

as per Guymon et al for Cu (111) and Cummings et al for Pt (111) [5, 68].

Parameterization of the Pt (111) surface with water

The first interaction considered in developing a force field to include a platinum electrode

was that of the Pt (111) surface with water. To obtain data for this interaction, ab initio

calculations were run using VASP to give an energy landscape for a water molecule above a Pt

(111) surface. Three different water molecule orientations were considered; one with the dipole

pointing into the surface (0°) , one with the dipole parallel to the surface (90°), and one with the

dipole pointing out of the surface (180°). For each orientation single point calculations were

performed for a range of 10 H20-Pt distances, including the equilibrium distance. Fitting to ab

intio data was then performed using a genetic algorithm relying on a global minimization to

system energy from MD compared to QM [69]. The function fitting is described by Erin Boland,

with the results of the fitting of O-Pt and H-Pt being described by Equation 4-1, with parameters

given in Table 4-1 [40].

( ) 0 { ( ( ))}

1

( )

Equation 4-1

51

Table 4-1: Parameters for the initial force field interaction between water and Pt (111)

Parameter Hydrogen Oxygen

ε (kcal/mol) 0.0140742 39.3183

A (Å-1

) 1.4712 1.00555

re (Å) 0.26348 0.556786

A2 (kcal Å/mol) 39095.6 19502.4

A3 (Å-1

) 825.29 608.289

B (ÅC) 109379 8604.8

C 18.7382 7.11049

Face centered cubic (FCC) metals with a (111) surface exposed have 4 primary

adsorption sites because they arrange in a 3 layer repeating structure (ABCABC); atop, FCC

hollow, HCP hollow, and bridge. With atop adsorption, an atom adsorbs directly above a metal

atom on the top layer. The bridging adsorption occurs when an atom bridges between two metal

atoms and interacts directly with both. Hollow sites are created between 3 atoms on the top layer,

where a “gap” is seen in the layer and the adsorption interacts with all 3 metal atoms. HCP

(hexagonal closed packed) hollow sites have an atom in the second layer directly below the “gap”

and are so named because all hollow sites exist with this feature in HCP metals. FCC hollow sites

exist with no atom from the second layer beneath the hollow site, but have an atom from the third

metal layer below the adsorption site. These sites are so named because they are specific to metal

with a FCC structure.

52

(a) (b)

Figure 4-1: Comparison of initial water/Pt(111) fitting to expected surface adsorption sites. (a)

Equilibrated surface structure from initial MD runs with adsorption to FCC hollow site (H

removed). (b) Non-reactive MD simulation of water over a platinum surface adsorbing to the atop

site [3].

After using this potential, we noted that the interaction yielded an unfavorable

organization of water molecules on the metal surface. Though the interfacial structure is not well

known, and has not been structurally characterized, it can be shown through QM calculations that

the preferred adsorption site of water is in an atop site. Our first water/Pt interaction yielded a

surface structure in which water molecules adsorbed to FCC hollow sites. Figure 4-1 compares

the adsorption events we saw in our simulations to those that would be expected of a surface

organization of water on Pt (111) [3]. For clarity in Figure 4-1a, the hydrogen atoms have been

removed from the water molecules, and the top two metal layers are shown to demonstrate

adsorption over the FCC hollow site.

To correct this, we had to alter our force field between water and platinum. Due to the

lack of clarity as to the arrangement of water at an electrode surface, two different potentials were

used, both of which follow the same modified Morse potential described in Equation 2-10. The

first fitting, termed the “weak potential,” was taken from a computational study performed by

Cummings et al on ssDNA electrophoresis which included a model for non-reactive TIP3P water

over a Pt (111) surface [68]. The second fitting, termed the “strong potential,” used the same

53

length parameters with a greater strength of interaction, obtained through doubling the energy

parameter. The two fittings were used to determine the effect of interaction potential on the

interfacial structure. Table 4-2 gives the parameters for the two force fields used.

Table 4-2: Interaction parameters for the new water/Pt(111) interaction using Equation 2-10

Parameter Weak – O Weak – H Strong- O Strong -H

ε (kcal/mol) 0.19880 0.38779 0.39761 0.7756

A (Å-1

) 2.00 2.320 2.00 2.320

ro (Å) 3.073 2.768 3.073 2.768

The newly fit interaction provides a more mobile surface structure without the strong

affinity to stay locked in hollow sites. Figure 4-2 shows a time resolved surface structure. This

image, creating using Visual Molecular Dynamics, shows how the oxygen atoms in the first layer

move over a 25 ps time period. The color of the dot denotes the position of the atom relative to its

starting position, with red being used for the initial positions and changing to blue over the time

period. The figure shows that water molecules can escape hollow sites and are mobile on the

surface.

Figure 4-2: VMD image of the movement of water molecules (shown as oxygen atoms) on a

Pt(111) surface during an MD simulation using updated water/Pt force field

54

Parameterization of the Pt(111) surface with sulfuric acid

With a force field developed for the simulation of reactive water over a platinum

electrode using central force model water with electrode charge dynamics, we move on to

complete our force field description for our electrochemical system. Sulfuric acid is used to

approximate the activity of Nafion in solution. Chapter 3 described our incorporation of sulfuric

acid into the central force water description to provide a reactive description of the acid. In this

section we will discuss parameterizing sulfuric acid with Pt (111).

Because the most prevalent species in solution at the concentration of sulfuric acid that

we are studying is the bisulfate anion, we developed our force field based upon the interaction of

the bisulfate anion with a Pt (111) cluster. We have shown that the energetically favorable

configuration of HSO4- on a Pt (111) surface is with 3 O atoms directed downward over Pt atop

sites, and the O atom with the bound H pointing away from the surface. This surface orientation

is depicted in Figure 4-3.

(a) (b)

Figure 4-3: View of the preferred bisulfate ion orientation on a Pt (111) surface. (a) Side view (b)

Top view

Given the surface configuration and the data obtained for a description of the change in

energy with distance from the surface, a force field was parameterized using the same genetic

algorithm which was used for water/Pt interaction fitting. Only the Pt-S interaction was fit, as the

55

Pt-Os interaction was initially decided to be the same as that of the Pt-OW to simplify the force

field. A number of potential forms were considered to find an interaction that yielded the least

error between MD energy predicted and the calculated ab initio data. The best fit was obtained

using Equation 4-2, which is a modified Lennard-Jones potential. Because the Os-Pt interaction

was maintained to the be same as that for OW-Pt, a fitting was done for both the “strong” and

“weak” H2O-Pt potentials. The parameters for each case are given in Table 4-3, and the fit is

compared against QM data in Figure 4-4. Note, MD data are only included in the figure for the

force field fit involving the weak Pt-H2O parameters, as the strong Pt-H2O data would overlie

them.

( ) [(

)

(

)

] Equation 4-2

Table 4-3: Parameters for initial Pt-S interaction fitting

Parameter Strong Weak

ε (kcal/mol) 1400 2200

A (Å) 3.215 3.250

B 5.800 5.430

C 4.900 4.960

56

Figure 4-4: Comparison of MD fit for Pt-S interaction to ab intio data for energy vs. distance data

for bisulfate/Pt (111)

Initial simulation of a full electrochemical system

Our electrochemical system consists of aqueous sulfuric acid between platinum

electrodes. The MD simulations of our system were performed using a C++ code written within

the research group to combine central force water with the electrode charge dynamics description

of the metal surface. A snapshot of our simulation is shown in Figure 4-5. The coordinates are

defined as such; x: into the paper, y: up-down, z: left-right.

Figure 4-5: Snapshot of our MD simulation of aqueous sulfuric acid between platinum electrodes

Because of the use of periodic boundary conditions in all directions, we chose a number

of electrode layers that provides a “mirrored” FCC (111) stacking arrangement, which requires

3N+1 metal layers for the same surface to be exposed to both sides of the system, where N is any

57

integer value. We chose to simulate 7 (ABCABCA) layers of the electrode, as this allows for a

distinct charge difference between two sides of an electrode, while simultaneously being more

computationally efficient than larger systems and still providing enough metal layers to allow the

charge to diffuse through the metal layers to a conserved value.

To determine the size of the box in the x and y directions, it was necessary to decide what

cut-off distance would be implemented in our force field equations. Because periodic boundary

conditions lead to “images” of all system particles, it is required that the cutoff distance for all

forces be less than half of the box size, so that a particle cannot mathematically interact with its

own “image.” The cutoff distance was chosen to be 9 Å, leading to a minimum box size in the x

and y directions of 18 Å. Due to the stacking arrangement and bond distances in a Pt (111)

layered structure, the x-y sizing is 19.204 Å x 19.406 Å. The sizing in the z-direction was chosen

so as to allow for a sufficient region of bulk solution between the electrodes. To simulate a

system with oppositely charged electrodes, enough bulk solution must be included so as to reach

a region of neutral solution that is essentially unaffected by the presence of the electrodes

[1,3,5,54,54]. To ensure that this bulk solution region was reached, we choose a z-direction length

of 63 Å, corresponding to a length of 51.6 Å between the electrode surfaces. This box size also

motivated the box size studied in LAMMPS simulations on aqueous sulfuric acid discussed

previously, as the box was chosen to represent half of the occupied regions between the platinum

surfaces (accounting for the ~2.5 Å between the metal and first layer of solution). All starting

structures for the full electrochemical system were taken from a 6 ns simulation of aqueous

H2SO4 carried out in LAMMPS. To use these structures in the new system, the boxes were

doubled in the z-direction. This method allowed for a pre-equilibrated solution structure, which

aided in computational efficiency because our LAMMPS simulations run over 100X faster than

our ECD simulations.

58

Using this pre-equilibrated structure, we then carried out simulations of the

acid/water/electrode system using our group code. Periodic boundary conditions were applied in

all directions using a 3D Ewald summation for long range forces. A time step of 0.25 fs was

imposed to allow the reactive bonds sufficiently fast updating. Before applying a potential across

the electrodes, the system was run in a zero-charge system over a neutral electrode. The pre-

equilibrated structure was started from a static state (no velocity on all particles). Metal atoms are

fixed during the simulation, as movement of the electrode would not be expected. All simulations

using charged electrodes were started from a structure obtained after 50 ps of simulation over a

neutral electrode. We chose to analyze 6 different cases for charged systems; neutral, 0.8 V, 1.23

V, 4 V, 6 V, and 10 V. The 0.8 V and 1.23 V cases were chosen because they represent the

typical operating potential and maximum theoretical voltage encountered in PEMFC‟s. The latter

three cases were chosen as extremes, which are not expected to be encountered in an actual

PEMFC, to study the effect of very large electric fields.

For early times during the simulations, we monitored the distribution of solution species

through the simulation box, charge density throughout the solution, and considered the charge on

metal atoms. We expect, for runs with charged electrodes, to see a migration of charges toward

their respective counter-electrodes, as well as a decrease in potential across the solution from one

electrode to the other, as illustrated previously in Figure 1-1. We impose the potential difference

between the layers at the ends of the simulation box, or the point at which the periodic boundary

is defined normal to the electrode surface. In Figure 4-6, metal layers 1 and 7 are in contact with

solution and metal layers 3 and 4 represent the far right side of our box and the far left side of our

box, respectively, as seen in Figure 4-5. Platinum was shown to observe the expected behavior, in

which metal layers show variation in charge due to nearby charges. Because the extreme potential

difference is imposed between layers 3 and 4, a very negative and a very positive charge is

59

produced. The remaining layers alternate between positive and negative, giving the charge

distribution shown in Figure 4-6.

Figure 4-6: Average charges on metal layers in solution for a neutral run and a highly charged

electrode case

Despite the proper behavior shown in the electrode layers, structural data did not follow

expected trends. For all cases, it would be expected for bisulfate anions to be attracted to the

metal surfaces, and especially so in highly charged cases. Despite proving the charge on the metal

atoms, there was no migration towards the electrodes in any of our simulations. This lack of

migration can be seen when comparing density profiles for sulfur atoms in a simulation. The

density profiles were generated from 47.25 ps time blocks. Figure 4-7 shows the sulfur atom

density profile two separate time blocks for our most charged electrode case (10 V) averaged in

the z-direction. Narrow peaks of high density indicate regions in which the atoms have little

movement in the z-direction. Other peaks with a wider distribution indicate more mobile sulfate

groups. In both time blocks, the sulfur atoms appear to be “locked” at a certain distance from the

electrode, and cannot approach any closer. This sort of behavior may be reasonable in the case of

10 V , 1, -0.13871951

8

10 V , 2, 0.08193175

10 V , 3, -0.34541385

7

10 V , 4, 0.35882817

9

10 V , 5, -0.07568791

1

10 V , 6, -0.01442542

9

10 V , 7, 0.13348667

9

Nuetral, 1, -0.01382941

1

Nuetral, 2, 0.02162958

9

Nuetral, 3, -0.01012571

4

Nuetral, 4, 0.00636014

3

Nuetral, 5, -0.00930171

4

Nuetral, 6, 0.02100437

5

Nuetral, 7, -0.01573735

7

Ave

rage

Ch

arge

(e

)

Metal Layer

10 V

Nuetral

60

an adsorbed anion, but for an anion in bulk solution at a distance of ~10Å from the electrode

surface, the behavior is non-physical.

Figure 4-7: Sulfur density plots from different time blocks within a 10 V charged electrode

simulation. Time block A: 40.5 – 87.75 ps. Time block B: 121.5 – 168.75 ps.

The behavior in Figure 4-7 led us to believe there was a force field coding error between

the platinum electrode and sulfur atoms. Because the OS atoms had an identical interaction with

platinum to that of the OW atoms, the problem was most likely in the Pt-S force field. To confirm

that the problem existed between this pair, sulfate groups were forced closer to the surface. Two

anionic sulfate groups were placed near the positive electrode, and one anion sulfate group was

placed near the counter-electrode. In both cases the sulfate groups were placed outside of the first

water layer, so as to not produce any undesired effects from an unstable surface structure. The

new configuration was built using Materials Studio 4.6, to visually verify that no atoms were

placed too close together and cause highly repulsive interaction behavior. All other run

parameters remained the same, and the 10 V charged case was studied. After only a very brief

simulation time (< 9 ps) it was seen that the sulfate groups had migrated away from both

electrodes to the same distance seen in the peak locations in Figure 4-7. This test confirmed that

Time Block A, 0, 0

Time Block A, 0.051696, 0





















































































































































































Time Block A, 9.408763, 0.000476

Time Block A, 9.46046, 0.000714

Time Block A, 9.512156, 0.000476

Time Block A, 9.563852, 0.001429

Time Block A, 9.615549, 0.004048 Time Block A, 9.667246, 0.002143

Time Block A, 9.718942, 0.004762

Time Block A, 9.770638, 0.005714

Time Block A, 9.822335, 0.004762

Time Block A, 9.874031, 0.004762

Time Block A, 9.925728, 0.006667

Time Block A, 9.977424, 0.006429

Time Block A, 10.029121, 0.006429 Time Block A,

10.080817, 0.004524 Time Block A,

10.132514, 0.002857

Time Block A, 10.184211, 0.001905

Time Block A, 10.235907, 0.003571

Time Block A, 10.287603, 0.003571

Time Block A, 10.3393, 0.003095


10.442693, 0.001667

Time Block A, 10.494389, 0.001905


10.597782, 0.00119

Time Block A, 10.649479, 0.000714

Time Block A, 10.701175, 0.000952

Time Block A, 10.752872, 0.001429

Time Block A, 10.804568,

0.00119


0.00119

Time Block A, 10.907962, 0.001905

Time Block A, 10.959658, 0.002857

Time Block A, 11.011354, 0.004524

Time Block A, 11.063051, 0.003333


0.005


0.005

Time Block A, 11.21814, 0.004762

Time Block A, 11.269837, 0.005714

Time Block A, 11.321533, 0.007381

Time Block A, 11.37323, 0.004524


0.005


0.00619 Time Block A,

11.528319, 0.005238 Time Block A,

11.580016, 0.003333

Time Block A, 11.631713, 0.003095

Time Block A, 11.683409, 0.002143

Time Block A, 11.735105, 0.002857

Time Block A, 11.786802, 0.002381

Time Block A, 11.838499, 0.000952

Time Block A, 11.890195, 0.000952

Time Block A, 11.941891, 0.000476

Time Block A, 11.993588, 0.000476

Time Block A, 12.045284, 0.000238

Time Block A, 12.096981, 0.000238

Time Block A, 12.148677, 0.000952


0.00119

Time Block A, 12.252071, 0.000476

Time Block A, 12.303767, 0.000476

Time Block A, 12.355464, 0.000952

Time Block A, 12.40716, 0.00119

Time Block A, 12.458856, 0.000952

Time Block A, 12.510553, 0.001667

Time Block A, 12.56225, 0.002143

Time Block A, 12.613946, 0.001905

Time Block A, 12.665642, 0.003571

Time Block A, 12.717339, 0.002143

Time Block A, 12.769035, 0.003333

Time Block A, 12.820732, 0.003333

Time Block A, 12.872428, 0.004048

Time Block A, 12.924125, 0.006905


0.00381

Time Block A, 13.027518, 0.003095

Time Block A, 13.079215, 0.003571

Time Block A, 13.130911, 0.002143

Time Block A, 13.182607, 0.003571

Time Block A, 13.234304, 0.004762


13.337697, 0.002857

Time Block A, 13.389393, 0.003571


0.005 Time Block A,

13.492786, 0.002619


13.596179, 0.001429

Time Block A, 13.647876, 0.002857


13.751269, 0.000714

Time Block A, 13.802966, 0.002143

Time Block A, 13.854662, 0.001429

Time Block A, 13.906358, 0.000476

Time Block A, 13.958055, 0.000952


0.00119

Time Block A, 14.061448, 0.001905

Time Block A, 14.113144, 0.001667

Time Block A, 14.164841, 0.001667

Time Block A, 14.216537, 0.003095

Time Block A, 14.268234, 0.003333


14.371627, 0.004524

Time Block A, 14.423324, 0.003095

Time Block A, 14.47502, 0.005238

Time Block A, 14.526717, 0.004524



14.630109, 0.004762

Time Block A, 14.681806, 0.005476

Time Block A, 14.733503, 0.004762


14.836895, 0.002619

Time Block A, 14.888592, 0.001429

Time Block A, 14.940288, 0.002381

Time Block A, 14.991985, 0.002619

Time Block A, 15.043681, 0.002857

Time Block A, 15.095378, 0.001905

Time Block A, 15.147075, 0.000952

Time Block A, 15.198771, 0.000714

Time Block A, 15.250468, 0.000476

Time Block A, 15.302164, 0.000476

Time Block A, 15.35386, 0.000238

Time Block A, 15.405557, 0 Time Block A, 15.457254, 0 Time Block A, 15.50895, 0

Time Block A, 15.560646, 0 Time Block A, 15.612343, 0 Time Block A, 15.664039, 0 Time Block A, 15.715736, 0 Time Block A, 15.767432, 0 Time Block A, 15.819129, 0 Time Block A, 15.870826, 0 Time Block A, 15.922522, 0 Time Block A, 15.974219, 0 Time Block A, 16.025915, 0 Time Block A, 16.077611, 0 Time Block A, 16.129308, 0 Time Block A, 16.181005, 0 Time Block A, 16.232701, 0 Time Block A, 16.284397, 0 Time Block A, 16.336094, 0 Time Block A, 16.387791, 0 Time Block A, 16.439487, 0 Time Block A, 16.491183, 0 Time Block A, 16.54288, 0


Time Block A, 16.749666, 0 Time Block A, 16.801362, 0 Time Block A, 16.853059, 0 Time Block A, 16.904756, 0 Time Block A, 16.956452, 0 Time Block A, 17.008148, 0 Time Block A, 17.059845, 0 Time Block A, 17.111542, 0 Time Block A, 17.163238, 0 Time Block A, 17.214934, 0 Time Block A, 17.266631, 0 Time Block A, 17.318327, 0 Time Block A, 17.370024, 0 Time Block A, 17.421721, 0 Time Block A, 17.473417, 0 Time Block A, 17.525113, 0 Time Block A, 17.57681, 0

Time Block A, 17.628507, 0 Time Block A, 17.680203, 0 Time Block A, 17.731899, 0 Time Block A, 17.783596, 0 Time Block A, 17.835293, 0 Time Block A, 17.886989, 0 Time Block A, 17.938685, 0 Time Block A, 17.990382, 0 Time Block A, 18.042078, 0 Time Block A, 18.093775, 0 Time Block A, 18.145472, 0 Time Block A, 18.197168, 0 Time Block A, 18.248864, 0 Time Block A, 18.300561, 0 Time Block A, 18.352258, 0

Time Block A, 18.403954, 0.000238

Time Block A, 18.45565, 0.000476

Time Block A, 18.507347, 0.001905

Time Block A, 18.559044, 0.000476

Time Block A, 18.61074, 0.001667

Time Block A, 18.662436, 0.000238


18.765829, 0.000476

Time Block A, 18.817526, 0.001905

Time Block A, 18.869223, 0.003095

Time Block A, 18.920919, 0.003333

Time Block A, 18.972615, 0.002857

Time Block A, 19.024312, 0.003571

Time Block A, 19.076009, 0.003095

Time Block A, 19.127705, 0.002619

Time Block A, 19.179401, 0.002619

Time Block A, 19.231098, 0.003333

Time Block A, 19.282795, 0.003571


0.005 Time Block A,

19.386187, 0.004048


Time Block A, 19.541277, 0.002619

Time Block A, 19.592974, 0.004286

Time Block A, 19.64467, 0.003095



19.748063, 0.002619

Time Block A, 19.79976, 0.00381

Time Block A, 19.851456, 0.002381

Time Block A, 19.903152, 0.003333

Time Block A, 19.954849, 0.000952

Time Block A, 20.006546, 0.000952

Time Block A, 20.058242, 0.000476

Time Block A, 20.109938, 0.000476

Time Block A, 20.161635, 0

Time Block A, 20.213331, 0.000238

Time Block A, 20.265028, 0.000714

Time Block A, 20.316725, 0 Time Block A, 20.368421, 0 Time Block A, 20.420117, 0 Time Block A, 20.471814, 0

Time Block A, 20.523511, 0.000476

Time Block A, 20.575207, 0.000238

Time Block A, 20.626903, 0.000952

Time Block A, 20.6786, 0.000476


0.00119

Time Block A, 20.781993, 0.000952

Time Block A, 20.833689, 0.002619

Time Block A, 20.885386, 0.002143

Time Block A, 20.937082, 0.002143

Time Block A, 20.988779, 0.002619

Time Block A, 21.040476, 0.002619


21.143868, 0.002619

Time Block A, 21.195565, 0.004048


0.005

Time Block A, 21.298958, 0.004286

Time Block A, 21.350654, 0.003571

Time Block A, 21.402351, 0.002381

Time Block A, 21.454048, 0.002619

Time Block A, 21.505744, 0.002857

Time Block A, 21.55744, 0.002381

Time Block A, 21.609137, 0.002381

Time Block A, 21.660833, 0.002857

Time Block A, 21.71253, 0.004524

Time Block A, 21.764227, 0.003333


0.005


0.00119

Time Block A, 21.919316, 0.003095

Time Block A, 21.971013, 0.001667

Time Block A, 22.022709, 0.002381

Time Block A, 22.074405, 0.001667

Time Block A, 22.126102, 0.001667


0.00119

Time Block A, 22.229495, 0.000476

Time Block A, 22.281191, 0.000476

Time Block A, 22.332888, 0.000714

Time Block A, 22.384584, 0 Time Block A, 22.436281, 0 Time Block A, 22.487978, 0 Time Block A, 22.539674, 0 Time Block A, 22.59137, 0


Time Block A, 22.798156, 0 Time Block A, 22.849853, 0 Time Block A, 22.901549, 0 Time Block A, 22.953246, 0 Time Block A, 23.004942, 0 Time Block A, 23.056639, 0 Time Block A, 23.108335, 0 Time Block A, 23.160032, 0 Time Block A, 23.211729, 0 Time Block A, 23.263425, 0 Time Block A, 23.315121, 0 Time Block A, 23.366818, 0 Time Block A, 23.418515, 0 Time Block A, 23.470211, 0 Time Block A, 23.521907, 0 Time Block A, 23.573604, 0 Time Block A,

23.6253, 0 Time Block A, 23.676997, 0 Time Block A, 23.728694, 0 Time Block A, 23.78039, 0








Time Block A, 27.088966, 0 Time Block A, 27.140662, 0 Time Block A, 27.192359, 0 Time Block A, 27.244055, 0 Time Block A, 27.295752, 0 Time Block A, 27.347449, 0 Time Block A, 27.399145, 0 Time Block A, 27.450841, 0

Time Block A, 27.502538, 0.000238

Time Block A, 27.554235, 0.000238

Time Block A, 27.605931, 0.000952

Time Block A, 27.657627, 0.000476

Time Block A, 27.709324, 0.000476

Time Block A, 27.761021, 0.000476

Time Block A, 27.812717, 0.001667

Time Block A, 27.864413, 0.002381

Time Block A, 27.91611, 0.00119

Time Block A, 27.967806, 0.001667

Time Block A, 28.019503, 0.003571

Time Block A, 28.0712, 0.003333

Time Block A, 28.122896, 0.004762


28.226289, 0.002857

Time Block A, 28.277986, 0.004524

Time Block A, 28.329682, 0.004286



28.433075, 0.004762


0.00381


0.00381

Time Block A, 28.588164, 0.005714

Time Block A, 28.639861, 0.003333

Time Block A, 28.691557, 0.002619

Time Block A, 28.743254, 0.002143

Time Block A, 28.794951, 0.002857

Time Block A, 28.846647, 0.002381

Time Block A, 28.898343, 0.003333

Time Block A, 28.95004, 0.003333

Time Block A, 29.001737, 0.001905

Time Block A, 29.053433, 0.001667

Time Block A, 29.105129, 0.001429

Time Block A, 29.156826, 0.001667

Time Block A, 29.208523, 0.000238

Time Block A, 29.260219, 0.003333

Time Block A, 29.311915, 0.003333

Time Block A, 29.363612, 0.004048

Time Block A, 29.415308, 0.004524

Time Block A, 29.467005, 0.004048

Time Block A, 29.518702, 0.002619

Time Block A, 29.570398, 0.004286

Time Block A, 29.622094, 0.004762

Time Block A, 29.673791, 0.004762

Time Block A, 29.725488, 0.005238


Time Block A, 29.880577, 0.005238

Time Block A, 29.932274, 0.004286


0.005 Time Block A,

30.035666, 0.002619

Time Block A, 30.087363, 0.001667

Time Block A, 30.139059, 0.003095

Time Block A, 30.190756, 0.002857

Time Block A, 30.242453, 0.002381


30.345845, 0

Time Block A, 30.397542, 0.000952

Time Block A, 30.449239, 0.000238


Time Block A, 30.914507, 0 Time Block A, 30.966204, 0 Time Block A,











Time Block A, 35.773978, 0.000238


0.00119


0.00119


35.980764, 0.00119

Time Block A, 36.032461, 0.002143

Time Block A, 36.084157, 0.003333

Time Block A, 36.135853, 0.004524

Time Block A, 36.18755, 0.004762

Time Block A, 36.239247, 0.004048

Time Block A, 36.290943, 0.004048

Time Block A, 36.342639, 0.005952


0.005

Time Block A, 36.446033, 0.004524

Time Block A, 36.497729, 0.007143

Time Block A, 36.549425, 0.007381

Time Block A, 36.601122, 0.004048

Time Block A, 36.652819, 0.005238

Time Block A, 36.704515, 0.004524


36.807908, 0.001429

Time Block A, 36.859604, 0.002143

Time Block A, 36.911301, 0.000714

Time Block A, 36.962998, 0.000238

Time Block A, 37.014694, 0.000238

Time Block A, 37.06639, 0.000714

Time Block A, 37.118087, 0.000476

Time Block A, 37.169784, 0.000476

Time Block A, 37.22148, 0.001429

Time Block A, 37.273176, 0.002143

Time Block A, 37.324873, 0.003571

Time Block A, 37.37657, 0.002857

Time Block A, 37.428266, 0.004524


0.00381

Time Block A, 37.531659, 0.004524

Time Block A, 37.583355, 0.006667


0.01

Time Block A, 37.686749, 0.006667

Time Block A, 37.738445, 0.007381

Time Block A, 37.790141, 0.004286

Time Block A, 37.841838, 0.007381

Time Block A, 37.893535, 0.009048

Time Block A, 37.945231, 0.004762

Time Block A, 37.996927, 0.005476

Time Block A, 38.048624, 0.007381

Time Block A, 38.100321, 0.003333

Time Block A, 38.152017, 0.002857

Time Block A, 38.203714, 0.002619

Time Block A, 38.25541, 0.00381


0.00381

Time Block A, 38.358803, 0.004048


38.462196, 0.002619


0.00381

Time Block A, 38.565589, 0.003571

Time Block A, 38.617286, 0.002857

Time Block A, 38.668982, 0.003095

Time Block A, 38.720678, 0.002619

Time Block A, 38.772375, 0.001667

Time Block A, 38.824072, 0.001667

Time Block A, 38.875768, 0.001429

Time Block A, 38.927465, 0.001905

Time Block A, 38.979161, 0.001905


0.00119


0.00119

Time Block A, 39.134251, 0.002619

Time Block A, 39.185947, 0.002381


0.00381

Time Block A, 39.28934, 0.004762

Time Block A, 39.341037, 0.001905

Time Block A, 39.392733, 0.001667

Time Block A, 39.444429, 0.001667

Time Block A, 39.496126, 0.000714

Time Block A, 39.547823, 0.000238

Time Block A, 39.599519, 0.000238

Time Block A, 39.651216, 0.000238

Time Block A, 39.702912, 0 Time Block A, 39.754608, 0 Time Block A, 39.806305, 0 Time Block A, 39.858002, 0 Time Block A, 39.909698, 0 Time Block A, 39.961394, 0 Time Block A, 40.013091, 0 Time Block A, 40.064788, 0 Time Block A, 40.116484, 0 Time Block A, 40.16818, 0


Time Block A, 40.374967, 0 Time Block A, 40.426663, 0 Time Block A, 40.478359, 0 Time Block A, 40.530056, 0 Time Block A, 40.581753, 0 Time Block A, 40.633449, 0 Time Block A, 40.685145, 0 Time Block A, 40.736842, 0 Time Block A, 40.788539, 0 Time Block A, 40.840235, 0 Time Block A, 40.891931, 0 Time Block A, 40.943628, 0 Time Block A, 40.995325, 0 Time Block A, 41.047021, 0 Time Block A, 41.098718, 0 Time Block A, 41.150414, 0

Time Block A, 41.20211, 0.000238

Time Block A, 41.253807, 0.000238

Time Block A, 41.305504, 0.000238

Time Block A, 41.3572, 0.000238

Time Block A, 41.408896, 0.000238

Time Block A, 41.460593, 0.000476


Time Block A, 41.563986, 0.000952

Time Block A, 41.615682, 0.002381



41.719076, 0.002619

Time Block A, 41.770772, 0.005476

Time Block A, 41.822469, 0.007381

Time Block A, 41.874165, 0.009762

Time Block A, 41.925861, 0.010476

Time Block A, 41.977558, 0.010714


42.080951, 0.005952


0.005 Time Block A, 42.184344, 0.002857

Time Block A, 42.236041, 0.002381

Time Block A, 42.287737, 0.001905

Time Block A, 42.339433, 0.001429

Time Block A, 42.39113, 0.000952



Time Block A, 43.476757, 0 Time Block A, 43.528453, 0 Time Block A, 43.580149, 0 Time Block A, 43.631846, 0 Time Block A, 43.683543, 0 Time Block A, 43.735239, 0 Time Block A, 43.786935, 0 Time Block A, 43.838632, 0 Time Block A, 43.890329, 0 Time Block A, 43.942025, 0 Time Block A, 43.993722, 0 Time Block A, 44.045418, 0 Time Block A, 44.097114, 0 Time Block A, 44.148811, 0 Time Block A, 44.200508, 0 Time Block A, 44.252204, 0 Time Block A,










Time Block A, 48.646406, 0 Time Block A, 48.698103, 0 Time Block A,

48.7498, 0 Time Block A, 48.801496, 0 Time Block A, 48.853193, 0 Time Block A, 48.904889, 0 Time Block A, 48.956586, 0 Time Block A, 49.008282, 0 Time Block A, 49.059979, 0 Time Block A, 49.111675, 0 Time Block A, 49.163371, 0 Time Block A, 49.215068, 0 Time Block A, 49.266765, 0 Time Block A, 49.318461, 0 Time Block A, 49.370157, 0 Time Block A, 49.421854, 0 Time Block A, 49.473551, 0 Time Block A, 49.525247, 0 Time Block A, 49.576944, 0 Time Block A, 49.62864, 0




Time Block A, 51.593107, 0 Time Block A, 51.644804, 0

Time Block B, 0, 0

Time Block B, 0.051696, 0























































































































































































Time Block B, 9.512156, 0.000714

Time Block B, 9.563852, 0.000238


Time Block B, 9.667246, 0.000476

Time Block B, 9.718942, 0.000714

Time Block B, 9.770638, 0.001667

Time Block B, 9.822335, 0.000952

Time Block B, 9.874031, 0.000952

Time Block B, 9.925728, 0.00119

Time Block B, 9.977424, 0.001667

Time Block B, 10.029121, 0.000476

Time Block B, 10.080817, 0.000952

Time Block B, 10.132514, 0.000238

Time Block B, 10.184211, 0 Time Block B, 10.235907, 0 Time Block B, 10.287603, 0

Time Block B, 10.3393, 0.000714

Time Block B, 10.390997, 0.000476

Time Block B, 10.442693, 0.000714

Time Block B, 10.494389, 0

Time Block B, 10.546086, 0.001667

Time Block B, 10.597782, 0.000952

Time Block B, 10.649479, 0.000952

Time Block B, 10.701175, 0.002857

Time Block B, 10.752872,

0.00381


0.00381

Time Block B, 10.856265, 0.004762

Time Block B, 10.907962, 0.002381

Time Block B, 10.959658, 0.003333

Time Block B, 11.011354, 0.004048

Time Block B, 11.063051, 0.003095

Time Block B, 11.114748, 0.004286

Time Block B, 11.166444, 0.003333

Time Block B, 11.21814, 0.003095

Time Block B, 11.269837, 0.002619

Time Block B, 11.321533, 0.004286

Time Block B, 11.37323, 0.003095

Time Block B, 11.424926, 0.003333

Time Block B, 11.476623, 0.003333

Time Block B, 11.528319, 0.002143


0.00381 Time Block B, 11.631713, 0.002619

Time Block B, 11.683409, 0.002381

Time Block B, 11.735105, 0.001667

Time Block B, 11.786802, 0.001429

Time Block B, 11.838499, 0.000476

Time Block B, 11.890195, 0.002381


0.00119

Time Block B, 11.993588, 0.004762

Time Block B, 12.045284, 0.004048

Time Block B, 12.096981, 0.004286

Time Block B, 12.148677, 0.006429 Time Block B,

12.200374, 0.004762

Time Block B, 12.252071, 0.006429

Time Block B, 12.303767, 0.008571

Time Block B, 12.355464, 0.007619

Time Block B, 12.40716, 0.007857

Time Block B, 12.458856, 0.010952

Time Block B, 12.510553, 0.005476

Time Block B, 12.56225, 0.008095

Time Block B, 12.613946, 0.010952


12.717339, 0.008571

Time Block B, 12.769035, 0.008333

Time Block B, 12.820732, 0.007381

Time Block B, 12.872428, 0.006429

Time Block B, 12.924125, 0.008095

Time Block B, 12.975822, 0.004762


0.005 Time Block B, 13.079215, 0.004048

Time Block B, 13.130911, 0.001667

Time Block B, 13.182607, 0.001429

Time Block B, 13.234304, 0.000952

Time Block B, 13.286001, 0.000714

Time Block B, 13.337697, 0.000476


0.00119

Time Block B, 13.44109, 0.000952

Time Block B, 13.492786, 0.000238

Time Block B, 13.544483, 0 Time Block B, 13.596179, 0 Time Block B, 13.647876, 0 Time Block B, 13.699573, 0 Time Block B, 13.751269, 0 Time Block B, 13.802966, 0 Time Block B, 13.854662, 0 Time Block B, 13.906358, 0

Time Block B, 13.958055, 0.000476

Time Block B, 14.009752, 0

Time Block B, 14.061448, 0.000714

Time Block B, 14.113144, 0.000238

Time Block B, 14.164841, 0.000714

Time Block B, 14.216537, 0.002143


0.00119

Time Block B, 14.31993, 0.004286

Time Block B, 14.371627, 0.005476

Time Block B, 14.423324, 0.002381

Time Block B, 14.47502, 0.004048


0.005

Time Block B, 14.578413, 0.005238

Time Block B, 14.630109, 0.002619

Time Block B, 14.681806, 0.002857

Time Block B, 14.733503, 0.004762

Time Block B, 14.785199, 0.004762

Time Block B, 14.836895, 0.004286


14.940288, 0.002143

Time Block B, 14.991985, 0.003333

Time Block B, 15.043681, 0.002143

Time Block B, 15.095378, 0.002381

Time Block B, 15.147075, 0.002619

Time Block B, 15.198771, 0.001667

Time Block B, 15.250468, 0.002143

Time Block B, 15.302164, 0.000952

Time Block B, 15.35386, 0.00119

Time Block B, 15.405557, 0.001429

Time Block B, 15.457254, 0.001429

Time Block B, 15.50895, 0.000714


0.00119

Time Block B, 15.612343, 0.000952


0.00119

Time Block B, 15.715736, 0.000952


15.819129, 0 Time Block B, 15.870826, 0

Time Block B, 15.922522, 0.000238

Time Block B, 15.974219, 0 Time Block B, 16.025915, 0 Time Block B, 16.077611, 0 Time Block B, 16.129308, 0 Time Block B, 16.181005, 0 Time Block B, 16.232701, 0 Time Block B, 16.284397, 0 Time Block B, 16.336094, 0 Time Block B, 16.387791, 0 Time Block B, 16.439487, 0 Time Block B, 16.491183, 0 Time Block B, 16.54288, 0


Time Block B, 16.749666, 0 Time Block B, 16.801362, 0 Time Block B, 16.853059, 0 Time Block B, 16.904756, 0 Time Block B, 16.956452, 0 Time Block B, 17.008148, 0 Time Block B, 17.059845, 0 Time Block B, 17.111542, 0 Time Block B, 17.163238, 0 Time Block B, 17.214934, 0 Time Block B, 17.266631, 0 Time Block B, 17.318327, 0 Time Block B, 17.370024, 0 Time Block B, 17.421721, 0 Time Block B, 17.473417, 0 Time Block B, 17.525113, 0 Time Block B, 17.57681, 0

Time Block B, 17.628507, 0 Time Block B, 17.680203, 0 Time Block B, 17.731899, 0 Time Block B, 17.783596, 0 Time Block B, 17.835293, 0 Time Block B, 17.886989, 0 Time Block B, 17.938685, 0 Time Block B, 17.990382, 0

Time Block B, 18.042078, 0.000238

Time Block B, 18.093775, 0.000238

Time Block B, 18.145472, 0

Time Block B, 18.197168, 0.000238

Time Block B, 18.248864, 0

Time Block B, 18.300561, 0.000714

Time Block B, 18.352258, 0.000476

Time Block B, 18.403954, 0.000476

Time Block B, 18.45565, 0.00119

Time Block B, 18.507347, 0.001905

Time Block B, 18.559044, 0.000476

Time Block B, 18.61074, 0.000476

Time Block B, 18.662436, 0.002381

Time Block B, 18.714133, 0.002381


0.00119

Time Block B, 18.817526, 0.002381


18.920919, 0.000952

Time Block B, 18.972615, 0.002143

Time Block B, 19.024312, 0.002381


0.00381

Time Block B, 19.127705, 0.003571

Time Block B, 19.179401, 0.004048

Time Block B, 19.231098, 0.004762

Time Block B, 19.282795, 0.005238

Time Block B, 19.334491, 0.002381

Time Block B, 19.386187, 0.002143

Time Block B, 19.437884, 0.002619

Time Block B, 19.48958, 0.002143


0.00119

Time Block B, 19.592974, 0.002619

Time Block B, 19.64467, 0.002857

Time Block B, 19.696366, 0.002857

Time Block B, 19.748063, 0.001905

Time Block B, 19.79976, 0.002143


0.00119

Time Block B, 19.903152, 0.000952

Time Block B, 19.954849, 0.001429


0.00119


0.00119

Time Block B, 20.109938, 0.003095

Time Block B, 20.161635, 0.002857

Time Block B, 20.213331, 0.002619

Time Block B, 20.265028, 0.002143

Time Block B, 20.316725, 0.004286


20.420117, 0.001429


0.005 Time Block B, 20.523511, 0.002857

Time Block B, 20.575207, 0.002857


0.005

Time Block B, 20.6786, 0.005238

Time Block B, 20.730297, 0.004286

Time Block B, 20.781993, 0.005714

Time Block B, 20.833689, 0.005952


20.937082, 0.005952


21.040476, 0.003095

Time Block B, 21.092172, 0.003095

Time Block B, 21.143868, 0.003333

Time Block B, 21.195565, 0.003333

Time Block B, 21.247262, 0.000714


0.00119

Time Block B, 21.350654, 0.000952

Time Block B, 21.402351, 0.000714

Time Block B, 21.454048, 0.000238

Time Block B, 21.505744, 0.000476

Time Block B, 21.55744, 0.000238

Time Block B, 21.609137, 0.000238

Time Block B, 21.660833, 0.000238


Time Block B, 21.764227, 0

Time Block B, 21.815923, 0.000238

Time Block B, 21.867619, 0 Time Block B, 21.919316, 0 Time Block B, 21.971013, 0 Time Block B, 22.022709, 0 Time Block B, 22.074405, 0 Time Block B, 22.126102, 0 Time Block B, 22.177798, 0 Time Block B, 22.229495, 0 Time Block B, 22.281191, 0 Time Block B, 22.332888, 0 Time Block B, 22.384584, 0 Time Block B, 22.436281, 0 Time Block B, 22.487978, 0 Time Block B, 22.539674, 0 Time Block B, 22.59137, 0


Time Block B, 22.798156, 0 Time Block B, 22.849853, 0 Time Block B, 22.901549, 0 Time Block B, 22.953246, 0 Time Block B, 23.004942, 0 Time Block B, 23.056639, 0 Time Block B, 23.108335, 0 Time Block B, 23.160032, 0 Time Block B, 23.211729, 0 Time Block B, 23.263425, 0 Time Block B, 23.315121, 0 Time Block B, 23.366818, 0 Time Block B, 23.418515, 0 Time Block B, 23.470211, 0 Time Block B, 23.521907, 0 Time Block B, 23.573604, 0 Time Block B,

23.6253, 0 Time Block B, 23.676997, 0 Time Block B, 23.728694, 0 Time Block B, 23.78039, 0





Time Block B, 25.899947, 0 Time Block B, 25.951643, 0 Time Block B, 26.003339, 0 Time Block B, 26.055036, 0

Time Block B, 26.106733, 0.000476

Time Block B, 26.158429, 0.000476

Time Block B, 26.210125, 0.000476

Time Block B, 26.261822, 0.000714

Time Block B, 26.313519, 0.000238


0.00119


0.00119


0.00119

Time Block B, 26.520304, 0.003333

Time Block B, 26.572001, 0.002857

Time Block B, 26.623698, 0.002381

Time Block B, 26.675394, 0.002381

Time Block B, 26.72709, 0.002619


0.005

Time Block B, 26.830484, 0.006429

Time Block B, 26.88218, 0.005476

Time Block B, 26.933876, 0.005476

Time Block B, 26.985573, 0.005952

Time Block B, 27.03727, 0.005952

Time Block B, 27.088966, 0.002857

Time Block B, 27.140662, 0.004048


0.005 Time Block B, 27.244055, 0.003571

Time Block B, 27.295752, 0.003571

Time Block B, 27.347449, 0.002619

Time Block B, 27.399145, 0.002619

Time Block B, 27.450841, 0.001429

Time Block B, 27.502538, 0.001905


0.00119

Time Block B, 27.605931, 0.000476

Time Block B, 27.657627, 0.000238

Time Block B, 27.709324, 0 Time Block B, 27.761021, 0 Time Block B, 27.812717, 0 Time Block B, 27.864413, 0 Time Block B, 27.91611, 0

Time Block B, 27.967806, 0 Time Block B, 28.019503, 0 Time Block B,

28.0712, 0 Time Block B, 28.122896, 0 Time Block B, 28.174592, 0 Time Block B, 28.226289, 0 Time Block B, 28.277986, 0 Time Block B, 28.329682, 0 Time Block B, 28.381378, 0

Time Block B, 28.433075, 0.000238

Time Block B, 28.484772, 0.000238

Time Block B, 28.536468, 0

Time Block B, 28.588164, 0.000476

Time Block B, 28.639861, 0.000952

Time Block B, 28.691557, 0.001429

Time Block B, 28.743254, 0.001429

Time Block B, 28.794951, 0.000952


0.00119

Time Block B, 28.898343, 0.000714


29.001737, 0.001905

Time Block B, 29.053433, 0.004524

Time Block B, 29.105129, 0.003571

Time Block B, 29.156826, 0.003571

Time Block B, 29.208523, 0.005476

Time Block B, 29.260219, 0.005238

Time Block B, 29.311915, 0.004762

Time Block B, 29.363612, 0.004048

Time Block B, 29.415308, 0.004286

Time Block B, 29.467005, 0.003333

Time Block B, 29.518702, 0.004286

Time Block B, 29.570398, 0.004762


0.005 Time Block B, 29.673791, 0.002857

Time Block B, 29.725488, 0.003571

Time Block B, 29.777184, 0.004286

Time Block B, 29.82888, 0.001905

Time Block B, 29.880577, 0.000952


0.00119

Time Block B, 29.98397, 0.000714


30.087363, 0 Time Block B, 30.139059, 0

Time Block B, 30.190756, 0.000238

Time Block B, 30.242453, 0 Time Block B, 30.294149, 0 Time Block B, 30.345845, 0 Time Block B, 30.397542, 0 Time Block B, 30.449239, 0 Time Block B, 30.500935, 0 Time Block B, 30.552631, 0 Time Block B, 30.604328, 0 Time Block B, 30.656025, 0 Time Block B, 30.707721, 0 Time Block B, 30.759417, 0 Time Block B, 30.811114, 0 Time Block B, 30.86281, 0








Time Block B, 34.171386, 0

Time Block B, 34.223083, 0.000238


Time Block B, 34.326476, 0.000238

Time Block B, 34.378172, 0

Time Block B, 34.429869, 0.000476

Time Block B, 34.481566, 0.000952

Time Block B, 34.533262, 0.000952

Time Block B, 34.584959, 0.001429

Time Block B, 34.636655, 0.002381


0.00119

Time Block B, 34.740048, 0.003571

Time Block B, 34.791745, 0.005238

Time Block B, 34.843441, 0.006429

Time Block B, 34.895137, 0.006429

Time Block B, 34.946834, 0.006429

Time Block B, 34.998531, 0.005714


35.101923, 0.006905 Time Block B, 35.15362,

0.005


0.005 Time Block B, 35.257013, 0.002619

Time Block B, 35.30871, 0.003333

Time Block B, 35.360406, 0.002143

Time Block B, 35.412102, 0.002143

Time Block B, 35.463799, 0.001429


0.00119


0.00119

Time Block B, 35.618888, 0.000714

Time Block B, 35.670585, 0

Time Block B, 35.722282, 0.000476

Time Block B, 35.773978, 0.000476

Time Block B, 35.825674, 0 Time Block B, 35.877371, 0

Time Block B, 35.929068, 0.000238

Time Block B, 35.980764, 0.000238

Time Block B, 36.032461, 0.000476

Time Block B, 36.084157, 0.000952

Time Block B, 36.135853, 0.000238

Time Block B, 36.18755, 0.001905


0.00119

Time Block B, 36.290943, 0.002619


0.00119

Time Block B, 36.394336, 0.002381


36.497729, 0.002381

Time Block B, 36.549425, 0.002857

Time Block B, 36.601122, 0.002381

Time Block B, 36.652819, 0.002857


0.00381


0.00381 Time Block B, 36.807908,

0.00119

Time Block B, 36.859604, 0.002381

Time Block B, 36.911301, 0.001429

Time Block B, 36.962998, 0.002619

Time Block B, 37.014694, 0.001905

Time Block B, 37.06639, 0.001905

Time Block B, 37.118087, 0.001905

Time Block B, 37.169784, 0.001429

Time Block B, 37.22148, 0.001667

Time Block B, 37.273176, 0.001905

Time Block B, 37.324873, 0.003095

Time Block B, 37.37657, 0.003333

Time Block B, 37.428266, 0.003571


0.005


0.00619

Time Block B, 37.583355, 0.006429

Time Block B, 37.635052, 0.006667


37.738445, 0.007381

Time Block B, 37.790141, 0.010238

Time Block B, 37.841838, 0.009286

Time Block B, 37.893535, 0.010952


37.996927, 0.006429

Time Block B, 38.048624, 0.004048


0.005 Time Block B, 38.152017, 0.002619

Time Block B, 38.203714, 0.002381

Time Block B, 38.25541, 0.000952


0.00119

Time Block B, 38.358803, 0.000714

Time Block B, 38.4105, 0.000714

Time Block B, 38.462196, 0.000238

Time Block B, 38.513892, 0 Time Block B, 38.565589, 0 Time Block B, 38.617286, 0 Time Block B, 38.668982, 0 Time Block B, 38.720678, 0 Time Block B, 38.772375, 0 Time Block B, 38.824072, 0 Time Block B, 38.875768, 0 Time Block B, 38.927465, 0 Time Block B, 38.979161, 0 Time Block B, 39.030857, 0 Time Block B, 39.082554, 0 Time Block B, 39.134251, 0 Time Block B, 39.185947, 0 Time Block B, 39.237643, 0 Time Block B, 39.28934, 0






Time Block B, 41.563986, 0 Time Block B, 41.615682, 0 Time Block B, 41.667379, 0 Time Block B, 41.719076, 0 Time Block B, 41.770772, 0 Time Block B, 41.822469, 0 Time Block B, 41.874165, 0 Time Block B, 41.925861, 0 Time Block B, 41.977558, 0

Time Block B, 42.029255, 0.000238

Time Block B, 42.080951, 0.000238

Time Block B, 42.132647, 0.000714

Time Block B, 42.184344, 0.000952

Time Block B, 42.236041, 0.000714

Time Block B, 42.287737, 0.002381

Time Block B, 42.339433, 0.002381

Time Block B, 42.39113, 0.004048

Time Block B, 42.442827, 0.003333

Time Block B, 42.494523, 0.004286

Time Block B, 42.54622, 0.01


0.01

Time Block B, 42.649612, 0.013333

Time Block B, 42.701309, 0.014524

Time Block B, 42.753006, 0.010238

Time Block B, 42.804702, 0.005238

Time Block B, 42.856398, 0.000714

Time Block B, 42.908095, 0 Time Block B, 42.959792, 0 Time Block B, 43.011488, 0 Time Block B, 43.063184, 0 Time Block B, 43.114881, 0 Time Block B, 43.166578, 0 Time Block B, 43.218274, 0 Time Block B, 43.269971, 0 Time Block B, 43.321667, 0 Time Block B, 43.373363, 0 Time Block B, 43.42506, 0

Time Block B, 43.476757, 0 Time Block B, 43.528453, 0 Time Block B, 43.580149, 0 Time Block B, 43.631846, 0 Time Block B, 43.683543, 0 Time Block B, 43.735239, 0 Time Block B, 43.786935, 0 Time Block B, 43.838632, 0 Time Block B, 43.890329, 0 Time Block B, 43.942025, 0 Time Block B, 43.993722, 0 Time Block B, 44.045418, 0 Time Block B, 44.097114, 0 Time Block B, 44.148811, 0 Time Block B, 44.200508, 0 Time Block B, 44.252204, 0 Time Block B,











48.7498, 0 Time Block B, 48.801496, 0 Time Block B, 48.853193, 0 Time Block B, 48.904889, 0 Time Block B, 48.956586, 0 Time Block B, 49.008282, 0 Time Block B, 49.059979, 0 Time Block B, 49.111675, 0 Time Block B, 49.163371, 0 Time Block B, 49.215068, 0 Time Block B, 49.266765, 0 Time Block B, 49.318461, 0 Time Block B, 49.370157, 0 Time Block B, 49.421854, 0 Time Block B, 49.473551, 0 Time Block B, 49.525247, 0 Time Block B, 49.576944, 0 Time Block B, 49.62864, 0




Time Block B, 51.593107, 0 Time Block B, 51.644804, 0

Time BlockATime BlockB

61

there was an unnatural repulsive behavior between the sulfate groups and electrode surfaces that

needed to be corrected. Figure 4-8 shows snapshots of the initial simulation configuration (a) and

the configuration that showed migration of sulfate groups away from the platinum surface (b).

Platinum atoms have been removed from the image, however the positive electrode is to the left

of solution and the negative electrode is to the right.

(a)

(b)

Figure 4-8: Comparison of (a) initial configuration with sulfate groups forced towards the

electrode surface, and (b) a 9ps snapshot showing migration away from both electrode surfaces.

Correcting the Pt/HSO4- force field interaction

Motivated from the results seen in Figure 4-7 and Figure 4-8, a new force field was

developed for platinum/bisulfate. A few initial coding errors were found in the development of

the first interaction potential. The same QM data were used for force field fitting, and various

potential forms were tested to determine the best description of the interaction. To minimize the

mean-square error, a new interaction was simultaneously parameterized for Pt-OS. Because a new

62

fitting was being used for Pt-OS, it was unnecessary to fit sulfuric acid potentials for both the

“strong” and “weak” water potentials. The potential form described in Equation 2-10 yielded the

most accurate description for both interaction pairs, and their parameters are given in Table 4-4,

and a comparison between the force field fitting and QM data is provided in Figure 4-9.

Table 4-4: Interaction parameters for final Pt-S and Pt-OS interaction from Equation 2-10

Parameter Pt-S Pt-OS

ε (kcal/mol) 6.56 340.6

A (Å-1

) 0.651 1.382

ro (Å) 6.180 1.727

Figure 4-9: Comparison between MD and QM for the Pt/HSO4- energy for the final fitting

Simulation of an electrochemical interface

Using the revised force-field we fit to describe an electrochemical system, we have begun

to simulate aqueous sulfuric acid between platinum electrodes. Due to the time limitations on this

thesis, and the computational expense of the code, simulations have only been completed to 150 -

200 ps for all charged and uncharged simulation conditions. However, because the simulations

QM Data, 1.787,

116.9384363

QM Data, 1.937,

100.0070253

QM Data, 2.087,

80.69074675

QM Data, 2.237,

56.54890376

QM Data, 2.387,

31.67293077

QM Data, 2.537,

12.5481233

QM Data, 2.637,

4.710584948

QM Data, 2.687,

2.268896429

QM Data, 2.737,

0.719993946

QM Data,

2.787, 0

QM Data, 2.837,

0.025966087

QM Data, 2.987,

2.995762394

QM Data, 3.287,

14.56994987

QM Data, 3.587,

23.96270927

QM Data, 3.787,

27.50777202

QM Data, 3.987,

29.34488424

QM Data, 4.537,

32.82563134

QM Data, 4.987,

31.45736151

QM Data, 5.287,

31.57637659

QM Data, 5.787,

31.4627346

Force Field Fit,

1.787, 118.282

Force Field Fit,

1.937, 97.7244

Force Field Fit,

2.087, 79.5149

Force Field Fit,

2.237, 57.2828

Force Field Fit,

2.387, 33.6915

Force Field Fit,

2.537, 14.5114

Force Field Fit,

2.637, 6.04634

Force Field Fit,

2.687, 3.19802

Force Field Fit,

2.737, 1.21026

Force Field Fit, 2.787, -0.53297

Force Field Fit,

2.837, 0.852062

Force Field Fit,

2.987, 9.05678

Force Field Fit,

3.287, 16.5695

Force Field Fit,

3.587, 20.4101

Force Field Fit,

3.787, 23.6609

Force Field Fit,

3.987, 30.5335

Force Field Fit,

4.537, 33.3752

Force Field Fit,

4.987, 33.7518

Force Field Fit,

5.287, 32.2637

Force Field Fit,

5.787, 29.6624

Ene

rgy

(kca

l/m

ol)

Distance (A)

QM Data

Force Field Fit

63

were started from equilibrated bulk structures, some information can be taken from these

abbreviated run times. Additionally, in the original presentation of the ECD method, Wheeler‟s

simulation times were only 400 ps due to the computational expense of the code. Considering the

shorter time steps required for a reactive water model, our run times are reasonable.

We showed previously that sulfuric acid tended to migrate away from the electrode

surface very rapidly in our initial simulations. After developing the new interaction potential

between sulfuric acid and platinum, this problem was resolved. A density profile of sulfur atoms

as a function of distance away from the electrode surface is shown in Figure 4-10. This figure was

developed using atomic coordinates between 54 – 101 ps in our most highly charged electrode

case. Whereas previously we saw migration away from the electrode almost immediately, our

current simulations show that the acid groups can maintain a close proximity to the electrode. To

begin the simulation, two acid molecules were placed near the positive electrode and one acid

molecule was placed near the negative electrode. Figure 4-10 shows that each acid finds an

equilibrium-like position near each electrode at which the sulfur is less mobile. The wider peaks

in solution are indicative of a more mobile bulk solution.

Series1, 6.840696, 0

Series1, 6.892393, 0

Series1, 6.944089, 0

Series1, 6.995786, 0

Series1, 7.047483, 0

Series1, 7.099179, 0

Series1, 7.150875, 0

Series1, 7.202572, 0

Series1, 7.254268, 0

Series1, 7.305965, 0

Series1, 7.357661, 0

Series1, 7.409358, 0

Series1, 7.461054, 0

Series1, 7.512751, 0

Series1, 7.564447, 0

Series1, 7.616144, 0

Series1, 7.66784, 0

Series1, 7.719537, 0

Series1, 7.771233, 0

Series1, 7.82293, 0

Series1, 7.874626, 0

Series1, 7.926323, 0

Series1, 7.978019, 0

Series1, 8.029716, 0

Series1, 8.081412, 0

Series1, 8.133109, 0

Series1, 8.184805, 0

Series1, 8.236502, 0

Series1, 8.288199, 0

Series1, 8.339895, 0

Series1, 8.391592, 0

Series1, 8.443288, 0

Series1, 8.494984, 0

Series1, 8.546681, 0

Series1, 8.598377, 0

Series1, 8.650074, 0

Series1, 8.701771, 0

Series1, 8.753467, 0

Series1, 8.805163, 0

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De

nsi

ty o

f su

lfu

r at

om

s (n

orm

aliz

ed

)

Z-position (A)

64

Figure 4-10: Distribution of sulfur atoms in the z-direction (electrode surfaces are located at 6.79

Å and 58.5 Å)

Performing the same density analysis on all species in solution gives the distribution of

charges through the system. Poisson‟s equation can be used to calculate the electric field from

this distribution. The charge density distribution (ρ), according to Poisson‟s equation, is the

product of the second derivative of the charge density (φ) and the permittivity of the solution (εo).

Equation 4-3 was used to determine the average potential in the Z-direction through solution for

cases of different charge. This charge density distribution is due only to the electrolyte, and does

not include the charges present in the electrode.

Equation 4-3

This analysis is ongoing, in an effort to correctly define the integration constants, but the

potential difference between electrodes and the variation in electric field with charge can be seen

in Figure 4-11. Periodic oscillations in the z-direction are an artifact of the computational method.

Because the z-length is greater than the x and y-lengths, the cutoff length in the Ewald summation

must be adjusted in future simulations to dampen out these fluctuations. However, despite the

presence of oscillating potential, the electric field can still be determined qualitatively.

65

Figure 4-11: Electric potential as a function of distance generated from Poisson‟s equation for 3

different charged electrode cases (0 Å represent the surface of the positive electrode)

Because long simulation times are needed to see normal movement of the acid groups

towards the electrode, there is no sufficient data to show the movement of SO4 groups toward or

away from either electrode. However, water does not require the same time scales to form ions

near surfaces. Because water is the bulk species and is able to form ions through the movement of

hydrogen bonds, an ionic analysis on the states of water shows a preference for ionic species to be

located near their respective counter electrodes. We considered three forms for our ionic analysis.

Two positive ions were considered, H+ and H3O

+, and one negative ion, OH

-. To classify the

existence of these species, cutoff distances were selected. The equilibrium distance for the O-H

bond in water is 0.98 Å. A free proton, H+, was classified as a proton which was greater than 1.15

Å away from the nearest oxygen atom. A hydronium ion was classified as an oxygen atom with 3

hydrogen atoms within 1.115 Å. A shorter cutoff distance was chosen for the hydronium ion to

differentiate truly cationic species from water molecules that were closely packed. Hydroxide

anions were classified as oxygen atoms with only one neighboring hydrogen atom within 1.15 Å.

1.23 V, 0.051696, -

1.70E-02

1.23 V, 0.103393, -

3.40E-02

1.23 V, 0.155089, -

5.10E-02

1.23 V, 0.206786, -

6.80E-02

1.23 V, 0.258483, -

8.50E-02

1.23 V, 0.310179, -

1.02E-01

1.23 V, 0.361875, -

1.19E-01

1.23 V, 0.413572, -

1.36E-01

1.23 V, 0.465268, -

1.53E-01

1.23 V, 0.516965, -

1.70E-01

1.23 V, 0.568661, -

1.87E-01

1.23 V, 0.620358, -

2.04E-01

1.23 V, 0.672054, -

2.21E-01

1.23 V, 0.723751, -

2.38E-01

1.23 V, 0.775447, -

2.55E-01

1.23 V, 0.827144, -

2.72E-01

1.23 V, 0.87884, -2.89E-01

1.23 V, 0.930537, -

3.06E-01

1.23 V, 0.982233, -

3.23E-01

1.23 V, 1.03393, -3.40E-01

1.23 V, 1.085626, -

3.57E-01

1.23 V, 1.137323, -

3.74E-01

1.23 V, 1.189019, -

3.91E-01

1.23 V, 1.240716, -

4.08E-01

1.23 V, 1.292412, -

4.25E-01

1.23 V, 1.344109, -

4.42E-01

1.23 V, 1.395805, -

4.59E-01

1.23 V, 1.447502, -

4.76E-01

1.23 V, 1.499199, -

4.93E-01

1.23 V, 1.550895, -

5.10E-01

1.23 V, 1.602592, -

5.27E-01

1.23 V, 1.654288, -

5.44E-01

1.23 V, 1.705984, -

5.61E-01

1.23 V, 1.757681, -

5.78E-01

1.23 V, 1.809377, -

5.95E-01

1.23 V, 1.861074, -

6.12E-01

1.23 V, 1.912771, -

6.30E-01

1.23 V, 1.964467, -

6.48E-01

1.23 V, 2.016163, -

6.69E-01

1.23 V, 2.06786, -6.93E-01

1.23 V, 2.119556, -

7.24E-01

1.23 V, 2.171253, -

7.66E-01

1.23 V, 2.22295, -8.20E-01

1.23 V, 2.274646, -

8.88E-01

1.23 V, 2.326343, -

9.70E-01

1.23 V, 2.378039, -1.06E+00

1.23 V, 2.429735, -1.15E+00

1.23 V, 2.481432, -1.24E+00

1.23 V, 2.533128, -1.30E+00

1.23 V, 2.584825, -1.35E+00

1.23 V, 2.636522, -1.37E+00

1.23 V, 2.688218, -1.37E+00

1.23 V, 2.739914, -1.33E+00

1.23 V, 2.791611, -1.28E+00

1.23 V, 2.843307, -1.21E+00

1.23 V, 2.895004, -1.13E+00

1.23 V, 2.946701, -1.04E+00

1.23 V, 2.998397, -

9.38E-01

1.23 V, 3.050094, -

8.34E-01

1.23 V, 3.10179, -7.29E-01

1.23 V, 3.153486, -

6.23E-01

1.23 V, 3.205183, -

5.20E-01

1.23 V, 3.256879, -

4.19E-01

1.23 V, 3.308576, -

3.23E-01

1.23 V, 3.360272, -

2.31E-01

1.23 V, 3.411969, -

1.46E-01

1.23 V, 3.463665, -

6.50E-02

1.23 V, 3.515362, 1.04E-02

1.23 V, 3.567058, 8.03E-02

1.23 V, 3.618755, 1.45E-01

1.23 V, 3.670452, 2.05E-01

1.23 V, 3.722148, 2.61E-01

1.23 V, 3.773845, 3.16E-01

1.23 V, 3.825541, 3.70E-01

1.23 V, 3.877237, 4.23E-01

1.23 V, 3.928934, 4.76E-01

1.23 V, 3.98063, 5.28E-01

1.23 V, 4.032327, 5.81E-01

1.23 V, 4.084023, 6.34E-01

1.23 V, 4.13572, 6.86E-01

1.23 V, 4.187416, 7.36E-01

1.23 V, 4.239113, 7.82E-01

1.23 V, 4.290809, 8.24E-01

1.23 V, 4.342506, 8.61E-01

1.23 V, 4.394203, 8.92E-01

1.23 V, 4.445899, 9.15E-01

1.23 V, 4.497596, 9.31E-01

1.23 V, 4.549292, 9.40E-01

1.23 V, 4.600988, 9.42E-01

1.23 V, 4.652685, 9.39E-01

1.23 V, 4.704381, 9.33E-01

1.23 V, 4.756078, 9.25E-01

1.23 V, 4.807774, 9.16E-01

1.23 V, 4.859471, 9.09E-01

1.23 V, 4.911167, 9.06E-01

1.23 V, 4.962864, 9.04E-01

1.23 V, 5.01456, 9.00E-01

1.23 V, 5.066257, 8.87E-01

1.23 V, 5.117954, 8.62E-01

1.23 V, 5.16965, 8.27E-01

1.23 V, 5.221347, 7.91E-01

1.23 V, 5.273043, 7.56E-01

1.23 V, 5.324739, 7.28E-01

1.23 V, 5.376436, 7.05E-01

1.23 V, 5.428132, 6.90E-01

1.23 V, 5.479829, 6.80E-01

1.23 V, 5.531525, 6.73E-01

1.23 V, 5.583222, 6.69E-01

1.23 V, 5.634918, 6.66E-01

1.23 V, 5.686615, 6.62E-01

1.23 V, 5.738311, 6.58E-01

1.23 V, 5.790008, 6.52E-01

1.23 V, 5.841705, 6.44E-01

1.23 V, 5.893401, 6.34E-01

1.23 V, 5.945098, 6.22E-01

1.23 V, 5.996794, 6.10E-01

1.23 V, 6.04849, 5.98E-01

1.23 V, 6.100187, 5.85E-01

1.23 V, 6.151883, 5.72E-01

1.23 V, 6.20358, 5.59E-01

1.23 V, 6.255276, 5.46E-01

1.23 V, 6.306973, 5.35E-01

1.23 V, 6.358669, 5.25E-01

1.23 V, 6.410366, 5.15E-01

1.23 V, 6.462062, 5.06E-01

1.23 V, 6.513759, 4.96E-01

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4.50E+00

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4.52E+00

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4.54E+00

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4.55E+00

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5.01E+00

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5.06E+00

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5.08E+00

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5.10E+00

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5.12E+00

10 V, 32.93067, -5.14E+00

10 V, 32.982367, -

5.15E+00

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5.17E+00

10 V, 33.08576, -5.18E+00

10 V, 33.137457, -

5.20E+00

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5.21E+00

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10 V, 33.292546, -

5.23E+00

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5.24E+00

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5.25E+00

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5.26E+00

10 V, 33.499332, -

5.28E+00

10 V, 33.551029, -

5.29E+00

10 V, 33.602725, -

5.30E+00

10 V, 33.654421, -

5.31E+00

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5.32E+00

10 V, 33.757815, -

5.33E+00

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5.34E+00

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5.35E+00

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5.35E+00

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5.48E+00

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5.53E+00

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5.53E+00

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5.52E+00

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5.52E+00

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5.52E+00

10 V, 35.15362, -5.51E+00

10 V, 35.205317, -

5.51E+00

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5.50E+00

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5.48E+00

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5.43E+00

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5.43E+00

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5.42E+00

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5.41E+00

10 V, 35.929068, -

5.40E+00

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5.39E+00

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5.38E+00

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5.38E+00

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5.37E+00

10 V, 36.290943, -

5.36E+00

10 V, 36.342639, -

5.36E+00

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5.35E+00

10 V, 36.446033, -

5.35E+00

10 V, 36.497729, -

5.35E+00

10 V, 36.549425, -

5.34E+00

10 V, 36.601122, -

5.34E+00

10 V, 36.652819, -

5.33E+00

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5.33E+00

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5.31E+00

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5.30E+00

10 V, 36.911301, -

5.29E+00

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5.28E+00

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5.28E+00

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10 V, 37.118087, -

5.25E+00

10 V, 37.169784, -

5.24E+00

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5.21E+00

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5.20E+00

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5.16E+00

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5.12E+00

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5.04E+00

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5.02E+00

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5.02E+00

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5.01E+00

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5.00E+00

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5.00E+00

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4.99E+00

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5.00E+00

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5.02E+00

10 V, 38.668982, -

5.03E+00

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5.05E+00

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5.07E+00

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5.16E+00

10 V, 38.979161, -

5.20E+00

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5.24E+00

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5.28E+00

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5.32E+00

10 V, 39.185947, -

5.36E+00

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5.39E+00

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10 V, 39.341037, -

5.46E+00

10 V, 39.392733, -

5.49E+00

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5.52E+00

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5.55E+00

10 V, 39.547823, -

5.58E+00

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5.61E+00

10 V, 39.651216, -

5.63E+00

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5.70E+00

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5.72E+00

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5.73E+00

10 V, 39.961394, -

5.74E+00

10 V, 40.013091, -

5.75E+00

10 V, 40.064788, -

5.76E+00

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10 V, 40.219877, -

5.77E+00

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5.78E+00

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5.78E+00

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6.54E+00

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6.60E+00

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6.60E+00

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6.60E+00

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6.60E+00

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6.60E+00

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6.59E+00

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6.58E+00

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6.55E+00

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6.55E+00

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6.55E+00

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6.55E+00

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6.57E+00

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6.59E+00

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6.57E+00

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6.50E+00

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10 V, 48.077745, -

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10 V, 48.181138, -

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10 V, 48.284531, -

7.25E+00

10 V, 48.336228, -

7.34E+00

10 V, 48.387924, -

7.44E+00

10 V, 48.43962, -7.54E+00

10 V, 48.491317, -

7.65E+00

10 V, 48.543014, -

7.76E+00

10 V, 48.59471, -7.87E+00

10 V, 48.646406, -

7.97E+00

10 V, 48.698103, -

8.08E+00

10 V, 48.7498, -8.17E+00

10 V, 48.801496, -

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10 V, 48.853193, -

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10 V, 48.904889, -

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10 V, 48.956586, -

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10 V, 49.008282, -

8.46E+00

10 V, 49.059979, -

8.44E+00

10 V, 49.111675, -

8.40E+00

10 V, 49.163371, -

8.33E+00

10 V, 49.215068, -

8.25E+00

10 V, 49.266765, -

8.15E+00

10 V, 49.318461, -

8.05E+00

10 V, 49.370157, -

7.96E+00

10 V, 49.421854, -

7.88E+00

10 V, 49.473551, -

7.82E+00

10 V, 49.525247, -

7.79E+00

10 V, 49.576944, -

7.77E+00

10 V, 49.62864, -7.77E+00

10 V, 49.680337, -

7.78E+00

10 V, 49.732033, -

7.80E+00

10 V, 49.78373, -7.83E+00

10 V, 49.835426, -

7.85E+00

10 V, 49.887122, -

7.88E+00

10 V, 49.938819, -

7.90E+00

10 V, 49.990516, -

7.93E+00

10 V, 50.042212, -

7.96E+00

10 V, 50.093908, -

7.98E+00

10 V, 50.145605, -

8.01E+00

10 V, 50.197302, -

8.04E+00

10 V, 50.248998, -

8.06E+00

10 V, 50.300695, -

8.09E+00

10 V, 50.352391, -

8.12E+00

10 V, 50.404088, -

8.14E+00

10 V, 50.455784, -

8.17E+00

10 V, 50.507481, -

8.20E+00

10 V, 50.559177, -

8.22E+00

10 V, 50.610873, -

8.25E+00

10 V, 50.66257, -8.28E+00

10 V, 50.714267, -

8.30E+00

10 V, 50.765963, -

8.33E+00

10 V, 50.817659, -

8.36E+00

10 V, 50.869356, -

8.38E+00

10 V, 50.921053, -

8.41E+00

10 V, 50.972749, -

8.44E+00

10 V, 51.024446, -

8.46E+00

10 V, 51.076142, -

8.49E+00

10 V, 51.127839, -

8.52E+00

10 V, 51.179535, -

8.54E+00

10 V, 51.231232, -

8.57E+00

10 V, 51.282928, -

8.60E+00

10 V, 51.334624, -

8.62E+00

10 V, 51.386321, -

8.65E+00

10 V, 51.438018, -

8.68E+00

10 V, 51.489714, -

8.70E+00

10 V, 51.54141, -8.73E+00

10 V, 51.593107, -

8.76E+00

Po

ten

tial

(V

)

Distance from positive electrode (A)

1.23 V

6 V

10 V

66

Figure 4-12: Distribution of water ions (H

+, OH

- and H3O

+) through solution at the start of all

simulations (taken from initial 30 snapshots of uncharged simulation).

As stated, we began our simulations from a pre-equilibrated, bulk sulfuric acid solution.

This solution had no positional dependence of ions in solution. To show this, the plots in Figure

4-12 show the number of instances of each water-derived ionic species. These data were taken

from the first 4 ps of simulation in our 6 V charged electrode simulation. The time period

considered is very short to demonstrate only the initial configuration with no effects from

simulation. The x-axis denotes position through the box between electrodes, and the y-axis gives

the number of times each configuration was found. There were 30 data snapshots considered, so

numbers greater than 1 on the y-axis may refer to the same oxygen atom maintaining its

configuration for multiple snapshots. Figure 4-12 shows that the instances of each water

configuration were very low at the beginning of the simulation and, more importantly, that there

was no positional bias to the location of ions in solution.

Series1, 0, 0

Series1, 0.15, 0 Series1, 0.25, 0 Series1, 0.35, 0 Series1, 0.475, 0 Series1, 0.59, 0 Series1, 0.705, 0 Series1, 0.82, 0 Series1, 0.935, 0 Series1, 1.05, 0 Series1, 1.165, 0 Series1, 1.28, 0 Series1, 1.395, 0 Series1, 1.51, 0 Series1, 1.625, 0 Series1, 1.74, 0 Series1, 1.855, 0 Series1, 1.97, 0 Series1, 2.085, 0 Series1,

2.2, 0 Series1, 2.315, 0 Series1, 2.43, 0 Series1, 2.545, 0 Series1, 2.66, 0 Series1, 2.775, 0 Series1, 2.89, 0 Series1, 3.005, 0 Series1, 3.12, 0 Series1, 3.235, 0 Series1, 3.35, 0 Series1, 3.465, 0 Series1, 3.58, 0 Series1, 3.695, 0 Series1, 3.81, 0 Series1, 3.925, 0 Series1, 4.04, 0 Series1, 4.155, 0 Series1, 4.27, 0 Series1, 4.385, 0 Series1,



9.1, 0 Series1, 9.215, 0 Series1, 9.33, 0 Series1, 9.445, 0 Series1, 9.56, 0 Series1, 9.675, 0 Series1, 9.79, 0 Series1, 9.905, 0 Series1, 10.02, 0

Series1, 10.135,

0

Series1, 10.25, 0

Series1, 10.365,

0

Series1, 10.48, 0

Series1, 10.595,

0

Series1, 10.71, 0

Series1, 10.825,

1 Series1, 10.94, 0

Series1, 11.055,

0

Series1, 11.17, 0

Series1, 11.285,

1

Series1, 11.4, 2

Series1, 11.515,

0

Series1, 11.63, 0

Series1, 11.745,

0

Series1, 11.86, 0

Series1, 11.975,

0

Series1, 12.09, 0

Series1, 12.205,

0

Series1, 12.32, 0

Series1, 12.435,

0

Series1, 12.55, 1 Series1, 12.665,

0

Series1, 12.78, 0

Series1, 12.895,

0

Series1, 13.01, 1 Series1, 13.125,

0

Series1, 13.24, 0

Series1, 13.355,

0

Series1, 13.47, 0

Series1, 13.585,

0

Series1, 13.7, 0

Series1, 13.815,

0

Series1, 13.93, 0

Series1, 14.045,

0

Series1, 14.16, 0

Series1, 14.275,

0

Series1, 14.39, 0

Series1, 14.505,

0

Series1, 14.62, 0

Series1, 14.735,

0

Series1, 14.85, 0

Series1, 14.965,

0

Series1, 15.08, 0

Series1, 15.195,

0

Series1, 15.31, 0

Series1, 15.425,

0

Series1, 15.54, 1 Series1, 15.655,

0

Series1, 15.77, 0

Series1, 15.885,

0

Series1, 16, 0

Series1, 16.115,

0

Series1, 16.23, 0

Series1, 16.345,

0

Series1, 16.46, 0

Series1, 16.575,

0

Series1, 16.69, 0

Series1, 16.805,

0

Series1, 16.92, 0

Series1, 17.035,

0

Series1, 17.15, 0

Series1, 17.265,

0

Series1, 17.38, 0

Series1, 17.495,

0

Series1, 17.61, 1 Series1, 17.725,

0

Series1, 17.84, 0

Series1, 17.955,

0

Series1, 18.07, 0

Series1, 18.185,

0

Series1, 18.3, 0

Series1, 18.415,

0

Series1, 18.53, 0

Series1, 18.645,

0

Series1, 18.76, 0

Series1, 18.875,

0

Series1, 18.99, 0

Series1, 19.105,

1

Series1, 19.22, 1 Series1, 19.335,

0

Series1, 19.45, 0

Series1, 19.565,

0

Series1, 19.68, 0

Series1, 19.795,

0

Series1, 19.91, 1

Series1, 20.025,

1 Series1, 20.14, 0

Series1, 20.255,

0

Series1, 20.37, 0

Series1, 20.485,

0

Series1, 20.6, 0

Series1, 20.715,

0

Series1, 20.83, 0

Series1, 20.945,

0

Series1, 21.06, 0

Series1, 21.175,

0

Series1, 21.29, 0

Series1, 21.405,

0

Series1, 21.52, 0

Series1, 21.635,

0

Series1, 21.75, 0

Series1, 21.865,

0

Series1, 21.98, 0

Series1, 22.095,

0

Series1, 22.21, 0

Series1, 22.325,

0

Series1, 22.44, 0

Series1, 22.555,

0

Series1, 22.67, 0

Series1, 22.785,

0

Series1, 22.9, 0

Series1, 23.015,

0

Series1, 23.13, 0

Series1, 23.245,

0

Series1, 23.36, 0

Series1, 23.475,

0

Series1, 23.59, 0

Series1, 23.705,

0

Series1, 23.82, 0

Series1, 23.935,

0

Series1, 24.05, 0

Series1, 24.165,

0

Series1, 24.28, 0

Series1, 24.395,

0

Series1, 24.51, 0

Series1, 24.625,

0

Series1, 24.74, 0

Series1, 24.855,

0

Series1, 24.97, 0

Series1, 25.085,

0

Series1, 25.2, 0

Series1, 25.315,

0

Series1, 25.43, 0

Series1, 25.545,

1 Series1, 25.66, 0

Series1, 25.775,

0

Series1, 25.89, 0

Series1, 26.005,

0

Series1, 26.12, 0

Series1, 26.235,

0

Series1, 26.35, 0

Series1, 26.465,

0

Series1, 26.58, 0

Series1, 26.695,

0

Series1, 26.81, 0

Series1, 26.925,

0

Series1, 27.04, 0

Series1, 27.155,

0

Series1, 27.27, 0

Series1, 27.385,

0

Series1, 27.5, 1 Series1, 27.615,

0

Series1, 27.73, 0

Series1, 27.845,

0

Series1, 27.96, 0

Series1, 28.075,

0

Series1, 28.19, 0

Series1, 28.305,

0

Series1, 28.42, 0

Series1, 28.535,

0

Series1, 28.65, 0

Series1, 28.765,

0

Series1, 28.88, 0

Series1, 28.995,

0

Series1, 29.11, 0

Series1, 29.225,

0

Series1, 29.34, 0

Series1, 29.455,

0

Series1, 29.57, 0

Series1, 29.685,

0

Series1, 29.8, 0

Series1, 29.915,

0

Series1, 30.03, 0

Series1, 30.145,

0

Series1, 30.26, 0

Series1, 30.375,

0

Series1, 30.49, 0

Series1, 30.605,

0

Series1, 30.72, 0

Series1, 30.835,

0

Series1, 30.95, 0

Series1, 31.065,

0

Series1, 31.18, 0

Series1, 31.295,

0

Series1, 31.41, 0

Series1, 31.525,

0

Series1, 31.64, 0

Series1, 31.755,

0

Series1, 31.87, 0

Series1, 31.985,

0

Series1, 32.1, 0

Series1, 32.215,

0

Series1, 32.33, 0

Series1, 32.445,

0

Series1, 32.56, 0

Series1, 32.675,

0

Series1, 32.79, 0

Series1, 32.905,

0

Series1, 33.02, 0

Series1, 33.135,

1 Series1, 33.25, 0

Series1, 33.365,

0

Series1, 33.48, 0

Series1, 33.595,

0

Series1, 33.71, 0

Series1, 33.825,

0

Series1, 33.94, 0

Series1, 34.055,

0

Series1, 34.17, 1 Series1, 34.285,

0

Series1, 34.4, 0

Series1, 34.515,

0

Series1, 34.63, 1

Series1, 34.745,

2

Series1, 34.86, 0

Series1, 34.975,

0

Series1, 35.09, 0

Series1, 35.205,

0

Series1, 35.32, 0

Series1, 35.435,

0

Series1, 35.55, 0

Series1, 35.665,

0

Series1, 35.78, 0

Series1, 35.895,

1 Series1, 36.01, 0

Series1, 36.125,

0

Series1, 36.24, 0

Series1, 36.355,

1 Series1, 36.47, 0

Series1, 36.585,

0

Series1, 36.7, 0

Series1, 36.815,

0

Series1, 36.93, 0

Series1, 37.045,

0

Series1, 37.16, 0

Series1, 37.275,

0

Series1, 37.39, 0

Series1, 37.505,

0

Series1, 37.62, 0

Series1, 37.735,

0

Series1, 37.85, 0

Series1, 37.965,

0

Series1, 38.08, 0

Series1, 38.195,

0

Series1, 38.31, 0

Series1, 38.425,

0

Series1, 38.54, 0

Series1, 38.655,

0

Series1, 38.77, 0

Series1, 38.885,

1 Series1,

39, 0

Series1, 39.115,

0

Series1, 39.23, 0

Series1, 39.345,

0

Series1, 39.46, 0

Series1, 39.575,

0

Series1, 39.69, 0

Series1, 39.805,

0

Series1, 39.92, 0

Series1, 40.035,

0

Series1, 40.15, 0

Series1, 40.265,

0

Series1, 40.38, 0

Series1, 40.495,

0

Series1, 40.61, 0

Series1, 40.725,

0

Series1, 40.84, 0

Series1, 40.955,

1 Series1, 41.07, 0

Series1, 41.185,

0

Series1, 41.3, 0

Series1, 41.415,

0

Series1, 41.53, 0

Series1, 41.645,

0

Series1, 41.76, 0

Series1, 41.875,

0

Series1, 41.99, 0

Series1, 42.105,

0

Series1, 42.22, 0

Series1, 42.335,

0

Series1, 42.45, 1

Series1, 42.565,

1 Series1, 42.68, 0

Series1, 42.795,

0

Series1, 42.91, 0

Series1, 43.025,

0

Series1, 43.14, 0

Series1, 43.255,

1

Series1, 43.37, 1 Series1, 43.485,

0

Series1, 43.6, 0

Series1, 43.715,

0

Series1, 43.83, 0

Series1, 43.945,

0

Series1, 44.06, 0

Series1, 44.175,

0

Series1, 44.29, 0

Series1, 44.405,

0

Series1, 44.52, 0

Series1, 44.635,

0

Series1, 44.75, 0

Series1, 44.865,

0

Series1, 44.98, 0

Series1, 45.095,

0

Series1, 45.21, 0

Series1, 45.325,

0

Series1, 45.44, 0

Series1, 45.555,

0

Series1, 45.67, 0

Series1, 45.785,

0

Series1, 45.9, 0

Series1, 46.015,

0

Series1, 46.13, 0

Series1, 46.245,

0

Series1, 46.36, 0

Series1, 46.475,

0

Series1, 46.59, 0

Series1, 46.705,

0

Series1, 46.82, 0

Series1, 46.935,

0

Series1, 47.05, 0

Series1, 47.165,

0

Series1, 47.28, 0

Series1, 47.395,

0

Series1, 47.51, 0

Series1, 47.625,

0

Series1, 47.74, 0

Series1, 47.855,

0

Series1, 47.97, 0

Series1, 48.085,

0

Series1, 48.2, 0

Series1, 48.315,

0

Series1, 48.43, 0

Series1, 48.545,

0

Series1, 48.66, 0

Series1, 48.775,

0

Series1, 48.89, 1 Series1, 49.005,

0

Series1, 49.12, 0

Series1, 49.235,

0

Series1, 49.35, 0

Series1, 49.465,

0

Series1, 49.58, 0

Series1, 49.695,

0

Series1, 49.81, 0

Series1, 49.925,

0

Series1, 50.04, 0

Series1, 50.155,

0

Series1, 50.27, 0

Series1, 50.385,

0

Series1, 50.5, 0

Series1, 50.615,

0

Series1, 50.73, 0

Series1, 50.845,

1 Series1, 50.96, 0

Series1, 51.075,

0

Series1, 51.19, 0

Series1, 51.305,

0

Series1, 51.42, 0

Series1, 51.535,

0

Series1, 51.65, 0

Series1, 51.765,

0

Series1, 51.88, 0

Series1, 51.995,

0

Series1, 52.11, 0

Series1, 52.225,

0

Series1, 52.34, 0

Series1, 52.455,

0

Series1, 52.57, 0

Series1, 52.685,

0

Series1, 52.8, 0

Series1, 52.915,

0

Series1, 53.03, 0

Series1, 53.145,

0

Series1, 53.26, 0

Series1, 53.375,

0

Series1, 53.49, 0

Series1, 53.605,

0

Series1, 53.72, 0

Series1, 53.835,

0

Series1, 53.95, 0

Series1, 54.065,

0

Series1, 54.18, 0

Series1, 54.295,

0

Series1, 54.41, 0

Series1, 54.525,

0

Series1, 54.64, 0

Series1, 54.755,

0

Series1, 54.87, 0

Series1, 54.985,

0

Series1, 55.1, 0

Series1, 55.215,

0

Series1, 55.33, 0

Series1, 55.445,

0

Series1, 55.56, 0

Series1, 55.675,

0

Series1, 55.79, 0

Series1, 55.905,

0

Series1, 56.02, 0

Series1, 56.135,

0

Series1, 56.25, 0

Series1, 56.365,

0

Series1, 56.48, 0

Series1, 56.595,

0

Series1, 56.71, 0

Series1, 56.825,

0

Series1, 56.94, 0

Series1, 57.055,

0

Series1, 57.17, 0

Series1, 57.285,

0

Series1, 57.4, 0

Series1, 57.515,

0

Series1, 57.63, 0

Series1, 57.745,

0

Series1, 57.86, 0

Series1, 57.975,

0

Series1, 58.09, 0

Series1, 58.205,

0

Series1, 58.32, 0

Series1, 58.435,

0

Series1, 58.55, 0

Series1, 58.665,

0

Series1, 58.78, 0

Series1, 58.895,

0

Series1, 59.01, 0

Series1, 59.125,

0

Series1, 59.24, 0

Series1, 59.355,

0

Series1, 59.47, 0

Series1, 59.585,

0

Series1, 59.7, 0

Series1, 59.815,

0

Series1, 59.93, 0

Series1, 60.045,

0

Series1, 60.16, 0

Series1, 60.275,

0

Series1, 60.39, 0

Series1, 60.505,

0

Series1, 60.62, 0

Series1, 60.735,

0

Series1, 60.85, 0

Series1, 60.965,

0

Series1, 61.08, 0

Series1, 61.195,

0

Series1, 61.31, 0

Series1, 61.425,

0

Series1, 61.54, 0

Series1, 61.655,

0

Series1, 61.77, 0

Series1, 61.885,

0

Series1, 62, 0

Series1, 62.115,

0

Series1, 62.23, 0

Series1, 62.345,

0

Series1, 62.46, 0

Series1, 62.575,

0

Series1, 62.69, 0

Series1, 62.805,

0

Series1, 62.92, 0

Series1, 63.035,

0

Series1, 63.15, 0

Series1, 63.265,

0

Series1, 63.38, 0

Series1, 63.495,

0

Series1, 63.61, 0

Series1, 63.725,

0

Nu

mb

er

of

Hyd

ron

ium

ca

tio

ns

Z-coordinate (A)

Series1, 0, 0

Series1, 0.15,

0

Series1, 0.25,

0

Series1, 0.35,

0

Series1,

0.475, 0

Series1, 0.59,

0

Series1,

0.705, 0

Series1, 0.82,

0

Series1,

0.935, 0

Series1, 1.05,

0

Series1,

1.165, 0

Series1, 1.28,

0

Series1,

1.395, 0

Series1, 1.51,

0

Series1,

1.625, 0

Series1, 1.74,

0

Series1,

1.855, 0

Series1, 1.97,

0

Series1,

2.085, 0

Series1, 2.2, 0

Series1,

2.315, 0

Series1, 2.43,

0

Series1,

2.545, 0

Series1, 2.66,

0

Series1,

2.775, 0

Series1, 2.89,

0

Series1,

3.005, 0

Series1, 3.12,

0

Series1,

3.235, 0

Series1, 3.35,

0

Series1,

3.465, 0

Series1, 3.58,

0

Series1,

3.695, 0

Series1, 3.81,

0

Series1,

3.925, 0

Series1, 4.04,

0

Series1,

4.155, 0

Series1, 4.27,

0

Series1,

4.385, 0

Series1, 4.5, 0

Series1,

4.615, 0

Series1, 4.73,

0

Series1,

4.845, 0

Series1, 4.96,

0

Series1,

5.075, 0

Series1, 5.19,

0

Series1,

5.305, 0

Series1, 5.42,

0

Series1,

5.535, 0

Series1, 5.65,

0

Series1,

5.765, 0

Series1, 5.88,

0

Series1,

5.995, 0

Series1, 6.11,

0

Series1,

6.225, 0

Series1, 6.34,

0

Series1,

6.455, 0

Series1, 6.57,

0

Series1,

6.685, 0

Series1, 6.8, 0

Series1,

6.915, 0

Series1, 7.03,

0

Series1,

7.145, 0

Series1, 7.26,

0

Series1,

7.375, 0

Series1, 7.49,

0

Series1,

7.605, 0

Series1, 7.72,

0

Series1,

7.835, 0

Series1, 7.95,

0

Series1,

8.065, 0

Series1, 8.18,

0

Series1,

8.295, 0

Series1, 8.41,

0

Series1,

8.525, 0

Series1, 8.64,

0

Series1,

8.755, 0

Series1, 8.87,

0

Series1,

8.985, 0

Series1, 9.1, 0

Series1,

9.215, 0

Series1, 9.33,

1

Series1,

9.445, 1

Series1, 9.56,

0

Series1,

9.675, 2

Series1, 9.79,

0

Series1,

9.905, 0

Series1,

10.02, 0

Series1,

10.135, 0

Series1,

10.25, 0

Series1,

10.365, 0

Series1,

10.48, 0

Series1,

10.595, 0

Series1,

10.71, 0

Series1,

10.825, 0

Series1,

10.94, 0

Series1,

11.055, 0

Series1,

11.17, 0

Series1,

11.285, 0

Series1, 11.4,

0

Series1,

11.515, 0

Series1,

11.63, 0

Series1,

11.745, 0

Series1,

11.86, 0

Series1,

11.975, 0

Series1,

12.09, 0

Series1,

12.205, 0

Series1,

12.32, 0

Series1,

12.435, 0

Series1,

12.55, 0

Series1,

12.665, 0

Series1,

12.78, 0

Series1,

12.895, 0

Series1,

13.01, 0

Series1,

13.125, 0

Series1,

13.24, 0

Series1,

13.355, 0

Series1,

13.47, 0

Series1,

13.585, 0

Series1, 13.7,

0

Series1,

13.815, 0

Series1,

13.93, 0

Series1,

14.045, 0

Series1,

14.16, 0

Series1,

14.275, 0

Series1,

14.39, 0

Series1,

14.505, 0

Series1,

14.62, 0

Series1,

14.735, 0

Series1,

14.85, 0

Series1,

14.965, 0

Series1,

15.08, 0

Series1,

15.195, 0

Series1,

15.31, 0

Series1,

15.425, 0

Series1,

15.54, 0

Series1,

15.655, 0

Series1,

15.77, 0

Series1,

15.885, 0

Series1, 16, 0

Series1,

16.115, 0

Series1,

16.23, 0

Series1,

16.345, 0

Series1,

16.46, 0

Series1,

16.575, 0

Series1,

16.69, 0

Series1,

16.805, 0

Series1,

16.92, 0

Series1,

17.035, 0

Series1,

17.15, 0

Series1,

17.265, 0

Series1,

17.38, 0

Series1,

17.495, 0

Series1,

17.61, 0

Series1,

17.725, 0

Series1,

17.84, 0

Series1,

17.955, 0

Series1,

18.07, 0

Series1,

18.185, 0

Series1, 18.3,

0

Series1,

18.415, 0

Series1,

18.53, 0

Series1,

18.645, 0

Series1,

18.76, 0

Series1,

18.875, 0

Series1,

18.99, 0

Series1,

19.105, 0

Series1,

19.22, 0

Series1,

19.335, 0

Series1,

19.45, 0

Series1,

19.565, 0

Series1,

19.68, 0

Series1,

19.795, 0

Series1,

19.91, 0

Series1,

20.025, 0

Series1,

20.14, 0

Series1,

20.255, 0

Series1,

20.37, 0

Series1,

20.485, 0

Series1, 20.6,

0

Series1,

20.715, 0

Series1,

20.83, 0

Series1,

20.945, 0

Series1,

21.06, 1

Series1,

21.175, 0

Series1,

21.29, 0

Series1,

21.405, 0

Series1,

21.52, 0

Series1,

21.635, 0

Series1,

21.75, 0

Series1,

21.865, 0

Series1,

21.98, 0

Series1,

22.095, 1

Series1,

22.21, 0

Series1,

22.325, 0

Series1,

22.44, 0

Series1,

22.555, 0

Series1,

22.67, 0

Series1,

22.785, 0

Series1, 22.9,

0

Series1,

23.015, 0

Series1,

23.13, 0

Series1,

23.245, 0

Series1,

23.36, 0

Series1,

23.475, 0

Series1,

23.59, 0

Series1,

23.705, 0

Series1,

23.82, 0

Series1,

23.935, 0

Series1,

24.05, 0

Series1,

24.165, 0

Series1,

24.28, 0

Series1,

24.395, 0

Series1,

24.51, 0

Series1,

24.625, 0

Series1,

24.74, 0

Series1,

24.855, 0

Series1,

24.97, 0

Series1,

25.085, 0

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Series1, 51.995,

0

Series1, 52.11, 0

Series1, 52.225,

0

Series1, 52.34, 0

Series1, 52.455,

0

Series1, 52.57, 0

Series1, 52.685,

0

Series1, 52.8, 0

Series1, 52.915,

0

Series1, 53.03, 0

Series1, 53.145,

0

Series1, 53.26, 0

Series1, 53.375,

0

Series1, 53.49, 0

Series1, 53.605,

0

Series1, 53.72, 0

Series1, 53.835,

0

Series1, 53.95, 0

Series1, 54.065,

0

Series1, 54.18, 0

Series1, 54.295,

0

Series1, 54.41, 0

Series1, 54.525,

0

Series1, 54.64, 0

Series1, 54.755,

0

Series1, 54.87, 0

Series1, 54.985,

0

Series1, 55.1, 0

Series1, 55.215,

0

Series1, 55.33, 1 Series1, 55.445,

0

Series1, 55.56, 1

Series1, 55.675,

2

Series1, 55.79, 0

Series1, 55.905,

0

Series1, 56.02, 0

Series1, 56.135,

0

Series1, 56.25, 0

Series1, 56.365,

0

Series1, 56.48, 0

Series1, 56.595,

0

Series1, 56.71, 0

Series1, 56.825,

0

Series1, 56.94, 0

Series1, 57.055,

0

Series1, 57.17, 0

Series1, 57.285,

0

Series1, 57.4, 0

Series1, 57.515,

0

Series1, 57.63, 0

Series1, 57.745,

0

Series1, 57.86, 0

Series1, 57.975,

0

Series1, 58.09, 0

Series1, 58.205,

0

Series1, 58.32, 0

Series1, 58.435,

0

Series1, 58.55, 0

Series1, 58.665,

0

Series1, 58.78, 0

Series1, 58.895,

0

Series1, 59.01, 0

Series1, 59.125,

0

Series1, 59.24, 0

Series1, 59.355,

0

Series1, 59.47, 0

Series1, 59.585,

0

Series1, 59.7, 0

Series1, 59.815,

0

Series1, 59.93, 0

Series1, 60.045,

0

Series1, 60.16, 0

Series1, 60.275,

0

Series1, 60.39, 0

Series1, 60.505,

0

Series1, 60.62, 0

Series1, 60.735,

0

Series1, 60.85, 0

Series1, 60.965,

0

Series1, 61.08, 0

Series1, 61.195,

0

Series1, 61.31, 0

Series1, 61.425,

0

Series1, 61.54, 0

Series1, 61.655,

0

Series1, 61.77, 0

Series1, 61.885,

0

Series1, 62, 0

Series1, 62.115,

0

Series1, 62.23, 0

Series1, 62.345,

0

Series1, 62.46, 0

Series1, 62.575,

0

Series1, 62.69, 0

Series1, 62.805,

0

Series1, 62.92, 0

Series1, 63.035,

0

Series1, 63.15, 0

Series1, 63.265,

0

Series1, 63.38, 0

Series1, 63.495,

0

Series1, 63.61, 0

Series1, 63.725,

0

Nu

mb

er

of

Hyd

roxi

de

A

nio

ns

Z-coordinate (A)

67

After simulation, trends in the position of water-derived ions in solution were noticed.

The positively charged ions have a preference to be located closer to the negative electrode (right

hand side of the simulation box, and a higher z-coordinate), and the hydroxide ions tend toward

the negative electrode. Figures 4-13 shows the same analysis as Figure 4-12 for the 6 V charged

electrode case for the time period spanning 87.5 – 121.5 ps. The figures show a clear migration of

charge toward counter electrodes in our electrochemical system.

Figure 4-13: Distribution of water ions (H

+, OH

- and H3O

+) through solution during the 87.5 –

121.5 ps time block for the 6 V charged electrode simulation.

Application of an electric field has been shown to increase the dissociation of protons

from sulfuric acid. Analysis of our systems has shown a similar trend thus far. For our 6

simulations, a different level of average sulfuric acid structure is observed. A similar analysis was

Series1, 0, 0





9.1, 0 Series1, 9.215, 0 Series1, 9.33, 0 Series1, 9.445, 0 Series1, 9.56, 0 Series1, 9.675, 0 Series1, 9.79, 0 Series1, 9.905, 0 Series1, 10.02, 0

Series1, 10.135,

0

Series1, 10.25, 0

Series1, 10.365,

0

Series1, 10.48, 0

Series1, 10.595,

0

Series1, 10.71, 0

Series1, 10.825,

0

Series1, 10.94, 0

Series1, 11.055,

0

Series1, 11.17, 0

Series1, 11.285,

0

Series1, 11.4, 0

Series1, 11.515,

0

Series1, 11.63, 0

Series1, 11.745,

0

Series1, 11.86, 0

Series1, 11.975,

0

Series1, 12.09, 0

Series1, 12.205,

0

Series1, 12.32, 0

Series1, 12.435,

0

Series1, 12.55, 0

Series1, 12.665,

0

Series1, 12.78, 0

Series1, 12.895,

0

Series1, 13.01, 0

Series1, 13.125,

0

Series1, 13.24, 0

Series1, 13.355,

0

Series1, 13.47, 0

Series1, 13.585,

3

Series1, 13.7, 3 Series1, 13.815,

0

Series1, 13.93, 8

Series1, 14.045,

7 Series1, 14.16, 4

Series1, 14.275,

6

Series1, 14.39, 7

Series1, 14.505,

15

Series1, 14.62,

12

Series1, 14.735,

14 Series1, 14.85, 5

Series1, 14.965,

11 Series1, 15.08, 3

Series1, 15.195,

4

Series1, 15.31, 4

Series1, 15.425,

6 Series1, 15.54, 4

Series1, 15.655,

3

Series1, 15.77, 2

Series1, 15.885,

3

Series1, 16, 4

Series1, 16.115,

3

Series1, 16.23, 7 Series1, 16.345,

4

Series1, 16.46, 4

Series1, 16.575,

3

Series1, 16.69, 7 Series1, 16.805,

4

Series1, 16.92, 6

Series1, 17.035,

8 Series1, 17.15, 1

Series1, 17.265,

1

Series1, 17.38, 3

Series1, 17.495,

3

Series1, 17.61,

10 Series1, 17.725,

1

Series1, 17.84, 9

Series1, 17.955,

11 Series1, 18.07, 7

Series1, 18.185,

8

Series1, 18.3, 10 Series1, 18.415,

4

Series1, 18.53, 4 Series1, 18.645,

2 Series1, 18.76, 0

Series1, 18.875,

0

Series1, 18.99, 2

Series1, 19.105,

1

Series1, 19.22, 0

Series1, 19.335,

1

Series1, 19.45, 1

Series1, 19.565,

3

Series1, 19.68, 3

Series1, 19.795,

5

Series1, 19.91, 7 Series1, 20.025,

5 Series1, 20.14, 1

Series1, 20.255,

10 Series1, 20.37, 3

Series1, 20.485,

3

Series1, 20.6, 4

Series1, 20.715,

3

Series1, 20.83, 3 Series1, 20.945,

0

Series1, 21.06, 2

Series1, 21.175,

1

Series1, 21.29, 3

Series1, 21.405,

11 Series1, 21.52, 5 Series1, 21.635,

2

Series1, 21.75, 5 Series1, 21.865,

3

Series1, 21.98, 3

Series1, 22.095,

2

Series1, 22.21, 6 Series1, 22.325,

2

Series1, 22.44, 9

Series1, 22.555,

9 Series1, 22.67, 4

Series1, 22.785,

3

Series1, 22.9, 3

Series1, 23.015,

2

Series1, 23.13, 4 Series1, 23.245,

2

Series1, 23.36, 2

Series1, 23.475,

2

Series1, 23.59, 3 Series1, 23.705,

1

Series1, 23.82, 0

Series1, 23.935,

4 Series1, 24.05, 1

Series1, 24.165,

2

Series1, 24.28, 1

Series1, 24.395,

4 Series1, 24.51, 1

Series1, 24.625,

4

Series1, 24.74, 3

Series1, 24.855,

4 Series1, 24.97, 1

Series1, 25.085,

2 Series1, 25.2, 0

Series1, 25.315,

2

Series1, 25.43, 3

Series1, 25.545,

4

Series1, 25.66, 5 Series1, 25.775,

2

Series1, 25.89, 4

Series1, 26.005,

5 Series1, 26.12, 2

Series1, 26.235,

4

Series1, 26.35, 6 Series1, 26.465,

4 Series1, 26.58, 1

Series1, 26.695,

1

Series1, 26.81, 2

Series1, 26.925,

1

Series1, 27.04, 0

Series1, 27.155,

1

Series1, 27.27, 0

Series1, 27.385,

0

Series1, 27.5, 0

Series1, 27.615,

0

Series1, 27.73, 0

Series1, 27.845,

0

Series1, 27.96, 0

Series1, 28.075,

0

Series1, 28.19, 0

Series1, 28.305,

0

Series1, 28.42, 0

Series1, 28.535,

0

Series1, 28.65, 0

Series1, 28.765,

0

Series1, 28.88, 0

Series1, 28.995,

0

Series1, 29.11, 0

Series1, 29.225,

0

Series1, 29.34, 0

Series1, 29.455,

0

Series1, 29.57, 0

Series1, 29.685,

0

Series1, 29.8, 0

Series1, 29.915,

0

Series1, 30.03, 0

Series1, 30.145,

0

Series1, 30.26, 0

Series1, 30.375,

0

Series1, 30.49, 0

Series1, 30.605,

0

Series1, 30.72, 0

Series1, 30.835,

0

Series1, 30.95, 0

Series1, 31.065,

0

Series1, 31.18, 0

Series1, 31.295,

0

Series1, 31.41, 0

Series1, 31.525,

0

Series1, 31.64, 0

Series1, 31.755,

0

Series1, 31.87, 0

Series1, 31.985,

0

Series1, 32.1, 0

Series1, 32.215,

0

Series1, 32.33, 0

Series1, 32.445,

0

Series1, 32.56, 0

Series1, 32.675,

0

Series1, 32.79, 1

Series1, 32.905,

1

Series1, 33.02, 0

Series1, 33.135,

2

Series1, 33.25, 3

Series1, 33.365,

4

Series1, 33.48, 7

Series1, 33.595,

8 Series1, 33.71, 3

Series1, 33.825,

3

Series1, 33.94, 2

Series1, 34.055,

2 Series1, 34.17, 0

Series1, 34.285,

3 Series1, 34.4, 1

Series1, 34.515,

4 Series1, 34.63, 1

Series1, 34.745,

0

Series1, 34.86, 2

Series1, 34.975,

2 Series1, 35.09, 0

Series1, 35.205,

0

Series1, 35.32, 1

Series1, 35.435,

0

Series1, 35.55, 0

Series1, 35.665,

0

Series1, 35.78, 0

Series1, 35.895,

0

Series1, 36.01, 0

Series1, 36.125,

2

Series1, 36.24, 1

Series1, 36.355,

3

Series1, 36.47, 2

Series1, 36.585,

1

Series1, 36.7, 1

Series1, 36.815,

1

Series1, 36.93, 2

Series1, 37.045,

1

Series1, 37.16, 1

Series1, 37.275,

4

Series1, 37.39, 5

Series1, 37.505,

8 Series1, 37.62, 4

Series1, 37.735,

6

Series1, 37.85, 7

Series1, 37.965,

10 Series1, 38.08, 7 Series1, 38.195,

5 Series1, 38.31, 3

Series1, 38.425,

9 Series1, 38.54, 6

Series1, 38.655,

7 Series1, 38.77, 5 Series1, 38.885,

3

Series1, 39, 2

Series1, 39.115,

2

Series1, 39.23, 1

Series1, 39.345,

0

Series1, 39.46, 0

Series1, 39.575,

0

Series1, 39.69, 0

Series1, 39.805,

0

Series1, 39.92, 0

Series1, 40.035,

1

Series1, 40.15, 1

Series1, 40.265,

4

Series1, 40.38, 5

Series1, 40.495,

6

Series1, 40.61, 9

Series1, 40.725,

11 Series1, 40.84, 4 Series1, 40.955,

2

Series1, 41.07, 5 Series1, 41.185,

2

Series1, 41.3, 1

Series1, 41.415,

1

Series1, 41.53, 1

Series1, 41.645,

2

Series1, 41.76, 2

Series1, 41.875,

1

Series1, 41.99, 3

Series1, 42.105,

3

Series1, 42.22, 5

Series1, 42.335,

5

Series1, 42.45, 4

Series1, 42.565,

4

Series1, 42.68, 5

Series1, 42.795,

5 Series1, 42.91, 2

Series1, 43.025,

4 Series1, 43.14, 0

Series1, 43.255,

0

Series1, 43.37, 2 Series1, 43.485,

0

Series1, 43.6, 0

Series1, 43.715,

1

Series1, 43.83, 3

Series1, 43.945,

2

Series1, 44.06, 3

Series1, 44.175,

4

Series1, 44.29, 9 Series1, 44.405,

7

Series1, 44.52,

12 Series1, 44.635,

8 Series1, 44.75, 4

Series1, 44.865,

12 Series1, 44.98, 6

Series1, 45.095,

15

Series1, 45.21, 4

Series1, 45.325,

10

Series1, 45.44,

14 Series1, 45.555,

8

Series1, 45.67,

12

Series1, 45.785,

9 Series1, 45.9, 2

Series1, 46.015,

2

Series1, 46.13, 5

Series1, 46.245,

4

Series1, 46.36, 4 Series1, 46.475,

2

Series1, 46.59, 3

Series1, 46.705,

3

Series1, 46.82, 2

Series1, 46.935,

4

Series1, 47.05, 3 Series1, 47.165,

0

Series1, 47.28, 1

Series1, 47.395,

1

Series1, 47.51, 3 Series1, 47.625,

0

Series1, 47.74, 1

Series1, 47.855,

1

Series1, 47.97, 1

Series1, 48.085,

0

Series1, 48.2, 0

Series1, 48.315,

2

Series1, 48.43, 1

Series1, 48.545,

2

Series1, 48.66, 4 Series1, 48.775,

1

Series1, 48.89, 5

Series1, 49.005,

5 Series1, 49.12, 3 Series1, 49.235,

1

Series1, 49.35, 1

Series1, 49.465,

0

Series1, 49.58, 1

Series1, 49.695,

0

Series1, 49.81, 0

Series1, 49.925,

0

Series1, 50.04, 0

Series1, 50.155,

0

Series1, 50.27, 0

Series1, 50.385,

0

Series1, 50.5, 6 Series1, 50.615,

3

Series1, 50.73, 4

Series1, 50.845,

10

Series1, 50.96,

11

Series1, 51.075,

15

Series1, 51.19,

16

Series1, 51.305,

17

Series1, 51.42, 4

Series1, 51.535,

12

Series1, 51.65, 0

Series1, 51.765,

1

Series1, 51.88, 1

Series1, 51.995,

0

Series1, 52.11, 0

Series1, 52.225,

0

Series1, 52.34, 0

Series1, 52.455,

0

Series1, 52.57, 0

Series1, 52.685,

1

Series1, 52.8, 2

Series1, 52.915,

3

Series1, 53.03,

12

Series1, 53.145,

18

Series1, 53.26,

29

Series1, 53.375,

37

Series1, 53.49,

35 Series1, 53.605,

30 Series1, 53.72,

26

Series1, 53.835,

11

Series1, 53.95,

11 Series1, 54.065,

6 Series1, 54.18, 2 Series1, 54.295,

0

Series1, 54.41, 0

Series1, 54.525,

0

Series1, 54.64, 0

Series1, 54.755,

0

Series1, 54.87, 0

Series1, 54.985,

0

Series1, 55.1, 0

Series1, 55.215,

0

Series1, 55.33, 0

Series1, 55.445,

0

Series1, 55.56, 0

Series1, 55.675,

0

Series1, 55.79, 1

Series1, 55.905,

2

Series1, 56.02, 1

Series1, 56.135,

3 Series1, 56.25, 1

Series1, 56.365,

0

Series1, 56.48, 0

Series1, 56.595,

0

Series1, 56.71, 0

Series1, 56.825,

0

Series1, 56.94, 0

Series1, 57.055,

0

Series1, 57.17, 0

Series1, 57.285,

0

Series1, 57.4, 0

Series1, 57.515,

0

Series1, 57.63, 0

Series1, 57.745,

0

Series1, 57.86, 0

Series1, 57.975,

0

Series1, 58.09, 0

Series1, 58.205,

0

Series1, 58.32, 0

Series1, 58.435,

0

Series1, 58.55, 0

Series1, 58.665,

0

Series1, 58.78, 0

Series1, 58.895,

0

Series1, 59.01, 0

Series1, 59.125,

0

Series1, 59.24, 0

Series1, 59.355,

0

Series1, 59.47, 0

Series1, 59.585,

0

Series1, 59.7, 0

Series1, 59.815,

0

Series1, 59.93, 0

Series1, 60.045,

0

Series1, 60.16, 0

Series1, 60.275,

0

Series1, 60.39, 0

Series1, 60.505,

0

Series1, 60.62, 0

Series1, 60.735,

0

Series1, 60.85, 0

Series1, 60.965,

0

Series1, 61.08, 0

Series1, 61.195,

0

Series1, 61.31, 0

Series1, 61.425,

0

Series1, 61.54, 0

Series1, 61.655,

0

Series1, 61.77, 0

Series1, 61.885,

0

Series1, 62, 0

Series1, 62.115,

0

Series1, 62.23, 0

Series1, 62.345,

0

Series1, 62.46, 0

Series1, 62.575,

0

Series1, 62.69, 0

Series1, 62.805,

0

Series1, 62.92, 0

Series1, 63.035,

0

Series1, 63.15, 0

Series1, 63.265,

0

Series1, 63.38, 0

Series1, 63.495,

0

Series1, 63.61, 0

Series1, 63.725,

0

Nu

mb

er

of

Hyd

ron

ium

ca

tio

ns

Z-coordinate (A)

Series1, 0, 0




6.8, 0 Series1, 6.915, 0 Series1, 7.03, 0 Series1, 7.145, 0 Series1, 7.26, 0 Series1, 7.375, 0 Series1, 7.49, 0 Series1, 7.605, 0 Series1, 7.72, 0 Series1, 7.835, 0 Series1, 7.95, 0 Series1, 8.065, 0 Series1, 8.18, 0 Series1, 8.295, 0 Series1, 8.41, 0 Series1, 8.525, 0 Series1, 8.64, 0 Series1, 8.755, 0

Series1, 8.87, 1 Series1, 8.985, 1

Series1, 9.1, 4

Series1, 9.215,

12

Series1, 9.33, 16 Series1, 9.445,

12

Series1, 9.56, 10 Series1, 9.675, 4 Series1, 9.79, 3 Series1, 9.905, 2 Series1, 10.02, 1

Series1, 10.135,

1

Series1, 10.25, 0

Series1, 10.365,

1

Series1, 10.48, 1

Series1, 10.595,

0

Series1, 10.71, 1

Series1, 10.825,

1

Series1, 10.94, 3

Series1, 11.055,

1

Series1, 11.17, 1

Series1, 11.285,

0

Series1, 11.4, 0

Series1, 11.515,

1

Series1, 11.63, 1

Series1, 11.745,

3

Series1, 11.86, 4

Series1, 11.975,

7

Series1, 12.09,

13

Series1, 12.205,

13 Series1, 12.32, 9

Series1, 12.435,

6

Series1, 12.55, 8 Series1, 12.665,

0

Series1, 12.78, 2

Series1, 12.895,

3

Series1, 13.01, 2

Series1, 13.125,

2

Series1, 13.24, 1

Series1, 13.355,

0

Series1, 13.47, 0

Series1, 13.585,

0

Series1, 13.7, 0

Series1, 13.815,

0

Series1, 13.93, 0

Series1, 14.045,

1

Series1, 14.16, 1

Series1, 14.275,

1

Series1, 14.39, 2

Series1, 14.505,

5 Series1, 14.62, 1

Series1, 14.735,

4

Series1, 14.85, 2

Series1, 14.965,

4

Series1, 15.08, 2

Series1, 15.195,

2

Series1, 15.31, 5

Series1, 15.425,

7

Series1, 15.54, 5

Series1, 15.655,

3

Series1, 15.77, 2

Series1, 15.885,

3

Series1, 16, 6

Series1, 16.115,

5

Series1, 16.23,

12

Series1, 16.345,

7

Series1, 16.46,

11

Series1, 16.575,

7

Series1, 16.69,

15

Series1, 16.805,

16 Series1, 16.92, 6

Series1, 17.035,

7

Series1, 17.15, 5

Series1, 17.265,

7

Series1, 17.38, 6

Series1, 17.495,

12 Series1, 17.61, 7

Series1, 17.725,

14

Series1, 17.84,

10

Series1, 17.955,

11

Series1, 18.07, 8

Series1, 18.185,

8

Series1, 18.3, 19

Series1, 18.415,

17

Series1, 18.53,

19

Series1, 18.645,

12

Series1, 18.76,

20

Series1, 18.875,

17 Series1, 18.99, 9

Series1, 19.105,

15

Series1, 19.22,

18

Series1, 19.335,

15

Series1, 19.45,

14

Series1, 19.565,

13

Series1, 19.68,

14 Series1, 19.795,

4

Series1, 19.91, 9 Series1, 20.025,

3

Series1, 20.14, 2

Series1, 20.255,

1

Series1, 20.37, 0

Series1, 20.485,

3

Series1, 20.6, 2

Series1, 20.715,

6

Series1, 20.83, 4

Series1, 20.945,

1

Series1, 21.06, 0

Series1, 21.175,

1

Series1, 21.29, 0

Series1, 21.405,

1

Series1, 21.52, 1

Series1, 21.635,

0

Series1, 21.75, 1

Series1, 21.865,

3

Series1, 21.98, 2

Series1, 22.095,

2

Series1, 22.21, 5

Series1, 22.325,

5

Series1, 22.44, 2

Series1, 22.555,

3

Series1, 22.67, 1

Series1, 22.785,

3

Series1, 22.9, 3

Series1, 23.015,

3

Series1, 23.13, 0

Series1, 23.245,

5 Series1, 23.36, 1

Series1, 23.475,

3

Series1, 23.59, 6

Series1, 23.705,

6

Series1, 23.82, 5 Series1, 23.935,

0

Series1, 24.05, 2

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Nu

mb

er

of

Hyd

roxi

de

An

ion

s

Z-coordinate (A)

68

performed to find the average structure of sulfuric acid as was employed in classifying the ionic

forms of water. A cutoff distance of 1.15 Å was chosen for the presence of a proton on an OS

atom. Though longer simulation times are needed to confirm the results given here due to the

time required for reactions to take place, trends show an increasing level of deprontonation from

sulfuric acid with increased electrode potential. Table 4-5 summarizes the findings to this point.

All numbers given are in terms of the number of non-dissociated hydrogen atoms on each sulfuric

acid cluster, using a cutoff distance of 1.15 Å.

Table 4-5: Statistical analysis of the proton dissociation from sulfuric acid in a charged

environment. Averages given are the average number of protons bound to an SO4 group during a

34 ps time block. A bond is defined as an OS-H distance of less than 1.15 Å.

0 V 0.8 V 1.23 V 4 V 6 V 10 V

Average 1.377 1.266 1.110 1.249 1.241 0.982

Standard Deviation 0.215 0.198 0.185 0.189 0.180 0.178

Variance 0.554 0.471 0.413 0.429 0.390 0.378

All cases other than the 10 V simulation have an average sulfuric acid structure

consisting of more than one proton per cluster. This finding contradicts what we saw from our

radial distribution function analysis of sulfuric acid in bulk solution discussed in Chapter 3 of this

thesis. The trend suggests that a greater number of protons are attached to a sulfate anion between

electrodes than in our equilibrated bulk solution structure. A possible explanation is the higher

level of dissociated water molecules in solution due to the presence of the electrodes. More free

water-derived protons in solution may lead to a decrease in the ability of sulfuric acid protons to

dissociate. However, longer simulation times are needed to confirm that this is a trend in the

simulations and is not due to poor statistics.

For those protons that are bound to SO4 groups, there is no clear trend in a positional

dependence. We expect to simulate an electric field that is greater near the surface of the

69

electrodes, and less significant in bulk solution. This expectation, together with the knowledge

that the application of an electric field leads to higher proton dissociation from sulfuric acid,

would lead us to believe that the more deprotonated acid molecules would be nearer the positive

surface. However, in analyzing the average coordination between OS atoms and hydrogen atoms

throughout the simulation box, there is no clear trend which shows electric field dependence of

proton dissociation. For the 10 V charged electrode case, we mapped the position of each OS

atom, and the average number of protons to which it was bound for a 50 ps time block. The

movement in the z-direction of OS atoms was no more than 3.5 Å for any atoms and it was

neglected for graphical purposes. Figure 4-14 shows the average hydrogen coordination for each

OS atom in the simulation. The positions plotted for each of the 48 atoms represent their positions

at the end of the 50 ps time block. Though there is no clear trend in the bulk region, it does seem

as if acid molecules closer to the positive electrode (left hand side of the figure) experience more

deprotonation. The cluster about 10 Å represents 2 SO4 groupings, and shows that the grouping

spends the majority of the time block completely dissociated, with 1 OS atom protonated less than

25% of the time. There also seems to be less protonation on the right-most SO4 group, which is

nearest the negative electrode, but the data are less conclusive here.

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286

Ave

rage

H/O

s ra

tio

Z-coordinate (A)

70

Figure 4-14: Average number of H atoms bound to OS atoms as a function of distance for a 50 ps

time block in the 10 V charged electrode simulation. Data are given as H atoms per OS atom. To

determine the H atoms per S atom, the four OS atoms in a sulfate anion must be added.

Due to the different charge at each electrode surface, we also see a slight

difference in the orientation of sulfuric acid at each platinum surface in charged systems. Near the

positive electrode, sulfuric acid orients itself with three oxygen atoms pointing toward the

surface, similarly to the preferred adsorption mechanism discussed earlier and seen in Figure 4-3.

Because the oxygen atoms are negative and the core sulfur is positively charged, the orientation

with 3 oxygen atoms towards to surface is electrostatically favored. At the negative electrode, the

oxygen atoms are more repulsed from the surface, and they orient themselves farther away than at

the positive electrode. This behavior, at both electrodes, is shown for the 10 V charged case in

Figure 4-15, with a comparison to the uncharged electrode case. The top figure represents the 10

V charged electrode case. The 2 left-most SO4 seem to prefer to have three oxygen atoms

pointing towards the positive surface, whereas in the bottom image (uncharged) the same

configuration is not seen. At the right-hand electrode, the top image shows clearly only one

oxygen pointing toward the negative surface, with no straightforward conclusion drawn about the

uncharged image.

71

Figure 4-15: Snapshot of SO4 groups in solution for the 10 V charged electrode simulation (top)

and uncharged electrode simulation (bottom) after 125 ps. In the charged electrode snapshot

(top), the positive electrode is on the left and the negative electrode is on the right.

Though snapshots are not necessarily indicative of average simulation behavior, the OS

density plots for each simulation seem to show the same trend over a time average of ~ 50 ps.

These trends are difficult to ascertain solely from the density profiles, but together with the

snapshot give the idea that charged electrodes force certain structural arrangements in sulfuric

acid near the surface. We do not see the specific adsorption of anions demonstrated

experimentally, but longer simulations times may allow for reorganization of surface layers to

allow this adsorption to occur.

Figure 4-16 shows the density profiles for OS as a function of its z-coordinate for the

same two cases explored in Figure 4-15. The peaks of note are the left-most and right-most peaks.

In the charged electrode simulation, near the positive electrode (left), there are only two distinct

peaks, suggesting a grouping of the oxygen atoms into two layers. The first of these distinct peaks

is significantly wider, and is consistent with three oxygen atoms from each SO4 group facing

toward the surface. The next peak is much narrower, and is consistent with the one oxygen atom

in the SO4 group directed away from the surface.

72

Figure 4-16: OS distribution profiles for the 10 V charged electrode simulation (top) and the

uncharged electrode simulation during a 50 ps time block.

The right-most grouping in the charged simulations‟ density profile is consistent with the

image of the SO4 group with one oxygen atom directed toward the surface. There are three

distinct peaks. The middle peak in this grouping is taller, and of a similar width to the peaks

nearest to it, suggesting one oxygen atom is directed toward the surface, one oxygen atom is

directed away from the surface, and two oxygen atoms share a plane nearly parallel to the surface.

This orientation is consistent with the snapshot image seen in the right-most SO4 group shown in

the top figure of Figure 4-15.

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57.865142, 0 Series1,

57.916839, 0 Series1,

57.968535, 0 Series1,

58.020232, 0 Series1,

58.071928, 0 Series1,

58.123624, 0 Series1,

58.175321, 0 Series1,

58.227018, 0 Series1,

58.278714, 0 Series1,

58.33041, 0 Series1,

58.382107, 0 Series1,

58.433804, 0

No

rmal

ize

d O

s d

en

sity

(u

nch

arge

d)

Z-Coordinate (A)

73

These trends are not as distinct in the uncharged electrode case. Though similar

arguments can be made for some of the structural features seen in the density profile for the

uncharged electrode, there is no reason to assume an orientation was dictated by the electrode.

Further simulations need to be carried out on the electrochemical system to validate the structural

findings reported in this Chapter.

Conclusions and future work

In this thesis I have described the development of our atomistic modeling technique for

electrochemical interfaces. The purpose of our work was to design a model capable of accurately

predicting short range interactions at electrode surfaces and characterizing the resultant structure

and electric field. The electrode/electrolyte interface plays a significant role in surface reaction

kinetics impacting devices such as fuel cells, batteries and solar cells. We chose to study the

cathode half-cell of the proton-exchange membrane fuel cell to determine what affects the

interfacial structure can have on the oxygen reduction reaction kinetics.

We modeled aqueous sulfuric acid over a platinum (111) electrode surface as a first step

towards modeling the aqueous behavior of Nafion in an electrochemical environment. We

developed a novel modeling technique capable of describing aqueous sulfuric acid in a reactive

manner over an electrode surface with atomistic resolution, as well as the capability to account

for electronic polarizablity of the metal surface. We validated our aqueous acid model against

previous ab initio molecular dynamics simulations of the same system.

Simulations of our full electrochemical systems have begun, and the initial results are

promising. Currently, our method predicts some trends that would be expected of our system. We

have seen migration of ions towards counter electrodes, and we observe proper trends in cell

potential, with a decreasing electric field with distance away from the positive electrode.

74

Exposing aqueous sulfuric acid to an external electric field leads to more de--protonation of the

acidic protons, which is a trend we have observed in our simulations with increased cell potential.

Finally, we have observed changes in the interfacial structure in terms of the orientation of

sulfuric acid groups near the electrode surface in the presence of an electric field.

To this point, we have proven that we are capable of modeling the chosen

electrochemical system of interest using our developed modeling techniques. In the future, longer

simulations must be performed to validate the results that have been discussed in this paper. The

diffusion rate of sulfate groups is a problem which must be addressed. We have seen a certain

level of sulfate movement in the bulk liquid away from the electrode surface, but the sulfate

groups nearest the electrode surface are immobile in the Z-direction. These molecules maintain a

fixed distance from the electrode surface in the second atomic layer. The lack of stronger

molecular adsorption may be due to an over-predicted attraction of water molecules to the

platinum surface. Analysis of the movement of species parallel to the surface may give insight as

to the cause of this lack of movement in the Z-direction. Finally, with a solution to the value of

the electric field from our charge distributions, we can classify the electric field quantitatively

near the electrode surface, and analyze gas phase reaction energies to determine how the ORR

kinetics are altered by the interfacial structures predicted by our MD simulations.

75

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atomistic modeling of an electrochemical interface

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