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Computer Simulations of Self-Assembled Monolayers on the Au(111) Surface

Permanent Link: http://ufdc.ufl.edu/UFE0024209/00001

Material Information

Title: Computer Simulations of Self-Assembled Monolayers on the Au(111) Surface
Physical Description: 1 online resource (97 p.)
Language: english
Creator: Alkis, Sabri
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: assembled, au, calculations, computer, dft, dynamics, molecular, monolayers, self, simulations
Chemistry -- Dissertations, Academic -- UF
Genre: Chemistry thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Many polymer and organic molecule assemblies have been investigated recently because of their applications in molecular electronics, surface chemistry and bio-sensors. These assemblies are often used in surface studies because they are simple structurally, stable thermodynamically and have well-defined order. Great effort has been made to understand the properties of these systems both experimentally and theoretically. Computer simulations in collaboration with experiments help us understand these systems in greater detail. In the first project, heterogeneous systems containing of a host alkanethiol molecule (dodecanethiol) monolayer with a thiol-terminated azobenzene molecules were considered. Classical molecular dynamics simulations showed a phase transition that was characterized by the change in the tilt angle, heat capacity and diffusion constant of the host molecules. The results for the pure monolayer were compared to the heterogeneous systems and the results were used to describe recent experiments. The phase transition was found to occur at about 350K for all three systems which is in good agreement with the experimental results. In the second project, motions of Au atoms on alkanethiol monolayers were described using classical molecular dynamics in conjunction with first principle calculations. Based on quantum-mechanical calculations, the interaction between Au atoms and the monolayer was calibrated and then the motions of the atoms were investigated as a function of coverage and temperature. We found good agreement with experimental results. Gold atoms were observed to penetrate inside the monolayer at room temperature but not below room temperature. In the third project, inspired by recent experiments, we used classical molecular dynamics to study the motions of Agn clusters with various sizes on alkanethiol self-assembled monolayers. Detailed results on the dynamics, diffusion and sintering processes of these nano-clusters were reported.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Sabri Alkis.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Krause, Jeffrey L.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2009-11-30

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Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024209:00001

Permanent Link: http://ufdc.ufl.edu/UFE0024209/00001

Material Information

Title: Computer Simulations of Self-Assembled Monolayers on the Au(111) Surface
Physical Description: 1 online resource (97 p.)
Language: english
Creator: Alkis, Sabri
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: assembled, au, calculations, computer, dft, dynamics, molecular, monolayers, self, simulations
Chemistry -- Dissertations, Academic -- UF
Genre: Chemistry thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Many polymer and organic molecule assemblies have been investigated recently because of their applications in molecular electronics, surface chemistry and bio-sensors. These assemblies are often used in surface studies because they are simple structurally, stable thermodynamically and have well-defined order. Great effort has been made to understand the properties of these systems both experimentally and theoretically. Computer simulations in collaboration with experiments help us understand these systems in greater detail. In the first project, heterogeneous systems containing of a host alkanethiol molecule (dodecanethiol) monolayer with a thiol-terminated azobenzene molecules were considered. Classical molecular dynamics simulations showed a phase transition that was characterized by the change in the tilt angle, heat capacity and diffusion constant of the host molecules. The results for the pure monolayer were compared to the heterogeneous systems and the results were used to describe recent experiments. The phase transition was found to occur at about 350K for all three systems which is in good agreement with the experimental results. In the second project, motions of Au atoms on alkanethiol monolayers were described using classical molecular dynamics in conjunction with first principle calculations. Based on quantum-mechanical calculations, the interaction between Au atoms and the monolayer was calibrated and then the motions of the atoms were investigated as a function of coverage and temperature. We found good agreement with experimental results. Gold atoms were observed to penetrate inside the monolayer at room temperature but not below room temperature. In the third project, inspired by recent experiments, we used classical molecular dynamics to study the motions of Agn clusters with various sizes on alkanethiol self-assembled monolayers. Detailed results on the dynamics, diffusion and sintering processes of these nano-clusters were reported.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Sabri Alkis.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Krause, Jeffrey L.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2009-11-30

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024209:00001


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1 COMPUTER SIMULATIONS OF SELFASSEMBLED MONOLAYERS ON THE AU (111) SURFACE By SABRI ALKIS A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2009

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2 2009 Sabri Alkis

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3 To my family

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4 ACKNOWLEDG E MENTS I thank my pa rents and my research committee members, Nicolo Omenetto, Adrian Roitberg, Hai -Ping Cheng and So Hirata for support. I also would like to acknowledge my research group members Julio Palma, Christina Crecca, Luis Agapito, Josh McClellan. Their help is great ly appreciated in this work. I also thank Department of Energy (DOE) for supporting our research.

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5 TABLE OF CONTENTS ACKNOWLEDGEMENTS .................................................................................................... 4 page LIST OF TABLES ................................................................................................................. 7 LIST OF FIGURES ............................................................................................................... 8 ABSTRACT .........................................................................................................................10 CHAPTER 1 INTRODUCTION ..........................................................................................................12 Prologue ........................................................................................................................12 Self Assembled Monolayers, Structure and Formation ......................................................12 Applications ...................................................................................................................14 From Experiment to Theory ............................................................................................15 Overview of Research Projects ........................................................................................15 First Project: Simulations of Azobenzene Containing Alkanethiol SAMs on the Au(111) Surface ...................................................................................................16 Second Project: Molecular Dynamics Simulations of Au Penetration Through Alkanethiol Molecules on the Au(111) Surface ......................................................16 Third Project: Dynamics of Silver Clusters on Alkanethiol Molecules on the Au(111) Surface ...................................................................................................16 2 METHOD ......................................................................................................................17 Molecular Dynamics .......................................................................................................17 Potentials Used ...............................................................................................................17 Thermostat .....................................................................................................................20 Verlet Leapfrog Algorithm ..............................................................................................21 Periodic Boundary Conditions .........................................................................................22 Density Functional Theory ..............................................................................................23 Hohenberg -Kohn Theorems ............................................................................................24 Formalism of DFT ..........................................................................................................24 Density of States ............................................................................................................26 3 MOLECULAR DYNAMICS SIMULATIONS OF ALKANETHIOL MONOLAYERS WITH AZOBENZENE MOLECULES ON THE AU (111) SURFACE ............................28 Introduction ...................................................................................................................28 Systems, Simulation Model, and Computational Details ...................................................31 Results ...........................................................................................................................33

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6 Tests of Molecule -Surface Potentials, 0 K Structures .................................................33 Phase Transitions .....................................................................................................36 Conclusions ...................................................................................................................39 4 MOLECULAR DYNAMICS SIMULATIONS OF AU PENETRATION THROUGH ALKANETHIOL MONOLAYERS ON THE AU (111) SURFACE ................................. 56 Introduction ...................................................................................................................56 Computational Details ....................................................................................................58 Results ...........................................................................................................................60 Binding Energy of Au on Alkanethiol SAMs .............................................................60 Molecular Dynamics ................................................................................................61 Density of States and Charge Transfer ......................................................................62 Conclusions ...................................................................................................................64 5 DYNAMICS OF SILVER CLUSTERS ON ALKANETHIOL MONOLAYERS ON AU(111) SURFACE .......................................................................................................76 Introduction ...................................................................................................................76 Computational Details ....................................................................................................77 Results ...........................................................................................................................7 9 Conclusions ...................................................................................................................80 6 CONCLUSIONS ............................................................................................................87 LIST OF REFERENCES .......................................................................................................89 BIOGRAPHICAL SKETCH ................................................................................................. 97

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7 LIST OF TABLES Table page 4 -1 Charge transfer (per molecule) from the Au surface and charge transfer to alkanethiol molecules ................................................................................................. 63

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8 LIST OF FIGURES Figure page 3 -1 Azobenzene molecule ................................................................................................41 3 -2 Surface structures .......................................................................................................42 3 -3 Au -S C angles ...........................................................................................................43 3 -4 CH3S monolayer on the Au(111) surface (4x4 unit cell) ...............................................44 3 -5 Different atomic sites and energy curve .......................................................................45 3 -6 Caloric curves ............................................................................................................46 3 -7 Equilibrium configuration of the pure alkanethiol monolayer .......................................47 3 -8 Tilt angle ...................................................................................................................48 3 -9 Radial Distribution functions ......................................................................................50 3 -10 Diffusion process .......................................................................................................52 3 -11 Angle Distributions and guest molecule relation ..........................................................53 4 -1 Snaphots of a system with four tilted alkanethiol molecu les attached to a model of the Au(111) surface with an Au ad-atom after relaxation with DFT ..............................66 4 -2 Snaphots of a system wit h four vertical alkanethiol molecules attached to a model of the Au(111) surface with an Au ad-atom after relaxation with DFT ..............................66 4 -3 Binding energy of the Au ad-atom with respect to the distance above the the Au/S interface ....................................................................................................................67 4 -4 Snapshots from the molecular dynamics simulations for 9 atoms placed on the alkanethiol SAMs ......................................................................................................68 4 -5 Snapshots from the molecular dynamics simulations for 9 atoms placed on the alkanethiol SAMs ......................................................................................................69 4 -6 Average histograms of z, the distance of the Au ad -atom above the surface, for 9 atoms on the SAMs ....................................................................................................70 4 -7 Average histograms of z, the distance of the Au ad -atom above the surface, for 18 atoms on the SAMs ....................................................................................................71 4 -8 DOS and PDOS for th e system without the Au ad -atom ...............................................72

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9 4 -9 DOS and PDOS of the system with the Au ad-atom .....................................................73 4 -10 Pure Au surface, S, P and D projected DOS and the total DOS. ....................................74 4 -11 Renormalized PDOS for the topmost layer in the upper panel and the rest of the surface in the lower panel. ..........................................................................................75 5 -1 Typical cluster/alkanethiol SAM/gold surface configuration for the n=55 cluster. ..........82 5 -2 Projected x y trajectories of cluster center of mass for Ag clusters wit h n=55,147 and 1289 atoms (counterclockwise from top left) ...............................................................83 5 -3 Velocity frequency spectra P(f), normalized by velocity va riance, as a function of frequency f ................................................................................................................84 5 -4 Root mean square displacement 2 1 2t R averaged over a trajectory as a function of time t for n=55, n=147 and n=1289 (top to bottom) ..................................................85 5 -5 Velocity anisotropy: histogram of fractional devia tion from isotropy for velocity as a function of direction for n=55, n=147 and n=1289 (top to bottom) ................................86

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10 A bstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy COMPUTER SIMULATIONS OF SELFASSEMBLED MONOLAYERS ON THE AU (111) SURFACE By Sabri Alkis May 2009 Chair: Jeffrey Krause Major: Chemistr y Many polymer and organic molecule assemblies have been investigated recently because of their applications in molecular electronics, surface chemistry and bio -sensors. T hese assemblies are often used in surface studies because they are simple structural ly, stable thermodynamically and have well -defined order. Great effort has been made to understand the properties of these systems both experimentally and theoretically. Computer simulations in collaboration with experiments help us understand these system s in greater detail. In the first project, heterogeneous systems containing of a host alkanethiol molecule (dodecanethiol) monolayer with a thiol -terminated azobenzene molecules were considered. Classical molecular dynamics simulations showed a phase trans ition that was characterized by the change in the tilt angle, heat capacity and diffusion constant of the host molecules. The results for the pure monolayer were compared to the heterogeneous systems and the re sults were used to describe recent experiments The phase tra nsition was found to occur at about 350K for all three systems which is in good agreement with the experimental results. In the second project, motions of Au atoms on alkanethiol monolayers were described using classical molecular dynamics i n conjunction with first princ iple calculations. Based on quantum mechanical calculations, the interaction between Au atoms and the monolayer was

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11 calibrated and then the motions of the atoms were investigated as a function of coverage and temperature. W e f ound good agreement with experimental results. Gold atoms were observed to penetrate inside the monolayer at roo m temperature but not below room temperature. In the third project, inspired by recent experiments, we used classical molecular dynamics to stud y the motions of Agn clu sters with various sizes on alkanethiol self -assembled monolayers. Detailed results on the dynamics, diffusion and sintering process es of these nanoclusters were reported.

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12 CHAPTER 1 INTRODUCTION Prologue Self -assembled monolayers (SAMs) offer researchers great opportunities to understand self organization and structure property relationship,1 as they are highly ordered and oriented. Therefore, it is possible to produce a variety of surfaces with specific interactions. It is possible to change both the tail s and the head groups of the molecules, which provides the opportun ity to unde rstand intermolecular, molecule -substrate and molecule -solvent interactions.2 These systems are well defined and they are easily accessible, which makes them good model systems to study chemistry and physics in two dimensions.2 Since they have a dense and a fairly st able structure, SAMs hav e potential applications in corrosion prevention and wear protection.3 They a lso have a b iocompatible nature, which makes them applicable in chemical and bio-chemical sensing. They are high ly ordered and are ideal components in electrooptic devices.4 In this chapter general information about self -assembled monolayers, their preparation and their chem ical applications is presented. P ioneering theoretical work to study these monolayers is also described. Final ly, a n overview of the research projects in the thesis is presented. Self Assembled Monolayers, Structure and Formation Self -assembly can be described as the formation of complex structures from small building blocks. In nature, self -assembly is observed i n the formation of membranes from lipid molecules. Living cells are also good examples of self -assembly. Adsorption of a surfactant with a specific affinity to a substrate leads to the formation of self -assembled monolayers.5 Chemical bond formation of molecules with surface and intermolecular interactions act s as a driving force for t he formation of self -assembled monolayers.5

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13 These types of assemblies are importa nt because they can be prepared easily. Their surface propert ies can be changed easily through the modification of molecular structure and functions. It is also possible to use self -assembled monolayers as building blocks in more comp lex structures. They c an be used, for example, to dock additional layers to a surface.5 Over the last 15 years, the field of self -assembled monolayers has been a very popular research topic and many self -assembled monolay ers have been investigated. T he monolayers of organosulfur adsorbates (e.g., alkanethiols ) on gold are probably the most w ell -studied.2 Sulfur compounds are known to have a strong affinity to transition metal surfaces such as the gold surface.6, 7 The reason is the possibility of forming multiple bonds with the surf ace metal.8 A variety of organosulfur deriva tives have now been studied. Some of these derivatives are di n -alky-sulfate,9, 10 thiophenols,11, 12 mercaptopyridines12 and mercaptoanilines.13 Among these derivatives, alkanethiols on Au(111) are the most well -studied and best understood.12 Adsorption of alkanethiols on a Au(111) surface occ urs in two steps: A very fast step that takes only a few minutes and a slow step which takes several hours. At the end of the fi rst step, the thickness reaches the 80-90 % of i ts maxim um value. After the second step the thickness and the contact angles reach their final value s .14 This two ste p mechanism is confirmed by X ray photoelectron spectroscopy ( XPS ) measurements,15, 16 and near edge X -ray absorption fine structure (NEXAFS) studies.17 Results fr om the electron diffraction studies show that t he monolayers of alkanethiols on a Au(111) surface have hexagonal symmetry with an S S spacing of 4.97 The calculated area per molecule is 21.4 2. The structure is a simple 0 lattice which is confirmed by helium diffraction18 and atomic force microscopy (AFM)19 studies.

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14 Alkanethiolates on a Au(111) surface are tilted 26280 from the sur fac e normal at around 50 K and ha ve 52 550 rotation about the molecular axis. The alkanethiols tilt to reestablish van der Waals contact in an assembly with S -S distances of about 5 This distance is larger t han the distance of 4.6 that is reported for perpendicular alkyl chains.2 Applications SAMs have seve ral technical applications such as surface coatings, molecular electronics and active elements in sensors.5 One application of SAMs is corrosion protection.2024 They can also be employed in mec hanical protection of surfaces. SAMs have been used to modify ir on and steel surfaces to make them more resistant.25, 26 It is also possible to change t he endgroup s (hydrophobic, hydrophilic) to control the wettin g properties Changing the endgroups also helps to change the mechanical properties relevant to f riction and lubrication.27, 28 SAMs can also be used as build ing blocks in heterostructures as templates to initiate the growth of the adlayer. Further layers might be attached to the material using these SAMs.5 They have also been used to start polymerization by chemically anchorin g the adlayer. An exampl e might be ZrO2 in nanocrystalline ceramics.29, 30 They could form a link between organic and inorganic matter which makes them ideal for interfacing biological materials. The could be used for filtering and analytical purposes in bio technology.31 SAMs of alkanethiol molecules on a Au(111) surface that present tri -(propylene sulfoxide) groups prevent the non-specific adsorption of protein that is confirmed by surfa ce plasmon resonance (SPR) spectroscopy.31 Another example would be the transducer technology, various forms of chemical, optical, piezoelectric sensors have been made using SAMs.32 X -ray photoelectron spectroscopy (XPS) results show that it is possible to detect small organic molecules such as C2Cl4 by alkanethiol

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15 molecules on a Au(111) surface.32 Tailoring the chain groups leads to det ection of gaseous analytes.33, 34 These systems also serve as test beds for investigations of properties of possible new generation molecular -electronic devices. The alkanethiol SAM presents a classical metal insulator metal (MIM) tunnel junction when fabricated between metal contacts due to their large HOMOLUMO gap (HOMO: highest occupied molecular orbital; LUMO: lowest unoccupied molecular orbital) of approximately 8 eV.3537 From Experiment to T heory To simula te the SAMs, various models and approximations have been used. Researchers have focused on various aspects such as the headgroup bonding structure or the thermal behavior of the chains.5 Pioneering simulations of SAMs were preformed by the Klein group .38, 39 They used a structureless model pot ential with united -atom approximation. Since then, various force fields have been used to describe the behavior of these monolayers. Most of the simulations have yielded the ( 0 structure with a tilt angle of about 28 degrees.2 These simulations also reported the thermal behavior and the disordering (melting) transition.3941 Bhatia and Garrison42 did molecula r dynamics studies in which the sulfur groups were left mobil e on the Au(111) surface. Again, they used the united -atom model to de scribe the molecular potentials. T hey obse rved the change in tilt angles and the phase transition in the monolayers. Beardmore43 developed an empirical potential funct ion by fitting parameters of the Au -S interaction to quantum calculations. Overview of Research P rojects Classical molecular dynamic simulations were used with quantum mechanical calculations to simulate the behavior of these systems and their applications in molecular electronics.

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16 First Project: Simulations of Azobenzene Containing Alkanethiol SAMs on the Au(111) Surface In our first project, we simulated alkanethiol monolayers with an azobenzene molecule on the Au(111) surface. We characterized a phase tr ansition by looking at the change in tilt angles, heat capacity and the diffusion constant of the host molecules. We obser ved a phase transition at about 350 K which agrees well with the experimental results. The results of these simulations were published in Journal of Physical Chemistry C.45 Second Project: Molecu lar Dynamics Simulations of Au Penetration T hrough Alkanethiol Molecules on the Au(111) S urface In the second project, the dynamics of Au atoms on alkanethiol monolayers was described using classical molecular dynamics in conjunction with first principle s quantum mechanical calcula tions. The interaction between the Au atoms and the monolayer was adjusted on the basis of the quantum calculations. The Au ato ms were observed to penetrate into t he monolayer at room temperature, as in experiments. There was no Au penetration at 50K, which is also in agreement with the experiments. This work has been accepted for publication in the Journal of Physical Chemistry C. Third Project: Dynamics of Silver C lusters on Alkanethiol Molecules on the Au(111) S urface In the third project, silve r clusters of various sizes were placed on top of the alkanethiol monolayers and their diffusion, dynamics and sinter ing processes were analyzed This work has been accepte d for publication in Physical Review B.

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17 CHAPTER 2 METHOD Molecular Dynamics Molecular dynamics is a virtual experiment that represents an interface between laboratory experiments and theory. It is a form of computer simulation in which the atoms and the molecules are allowed to interact under the laws of physics for a period of time. The molecular dynamics simulates the way large systems behave under various conditions Since the 1970s, t he method of molecular dynamics has become popular and has been used in physics, chemistry and biology. MD is used to model X -ray crystallo graphy and NMR results to determine protein structures. It is also possible to use the MD in order to describe atomi c level phenomena and to design new nanotechnological devices. In an MD simulation the main parameters are: the potentials to be used, the thermostat, the integration algorithm and the boundary conditions. Potentials Used The Universal F orce F ield (UFF)44 is used to describe the bonding parameters of organic molecules in our simulations. This force field is based on the element, its hybridization and its connectivity. It is possible to generate the force field parameters for the entire periodic table using various combination rules. Five -character mnemonic labels are used to describe the atoms. The first two characters are used to denote the chemical symbol. The chemical symbol is descri bed by the first two characters. An underscore is used in the second column if the symbol has one letter. For example hydrogen atom is described as H_ and rhodium as Rh. The next column represents the hybridization or the geometry. (1=linear, 2=trigonal, R =resonant, 3=tetrahedral, 4=square planar 5= trigonal bypyramidial, 6=octahedr al) C_3 is used to describe tetrahedral carbon atom.

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18 The potential energy of a molecule is described as the combination of bond stretching ( R E ), bond angle be nding ( E ), dihedral angle torsion ( E ) and nonbonding interactions ( vdw E ). vdw E E E R E E (2 -1) T o describe the bond stretching, UFF44 uses either the harmon i c oscillator function or the M orse function 2 2 1 ij r r ij k r E H armonic oscillator (2 -2) 2 1 ij r r e ij D r E Morse function (2 -3) ij k is the force constant in units of (kcal/mol)/2, ij r is the natural bond length in ij D is the bond dissociation energy (kcal/mol) and 2 1 2 ij D ij k (2 -4 ) The second term is the valence angle potential. The valence angle (bending) potential describes th e bond bending terms between specified atoms. In this type of force field the angle bend term is described as the harmonic cosine function :44 2 0 cos cos2 ijk k ijk U (2 -5) where ijk is the angle between three atoms and 0 is the equilibrium angle. The third term in the potenti al is the torsional term, which can be written as follows :44

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19 ijkn m A ijkn U cos 1 (2 -6) where m is the multiplicity and is the phase angle. The last term is t he van der Waals term. T o descr ibe these interactions a Lennard -Jones type expression is used :44 12 6 2 x ij x x ij x vdw E (2 -7) In this expression, j x i x ij x 2 1 where i x is the atomic van der Waals radius and ij D is the potential well depth defined as 2 1 j D i D ij D The UFF is commonly used to simulate organic molecules such as alkanethiols,45 benzenethiols ,46 and it gives a generally accurate description of organic molecules. The metal metal bonding interactions are described with the Sutton Chen potenti al.47 This type of potential describe s metals very well. This potential combines the long-range interactions (van der Waals terms as the tail) and the short -range interactio ns. The analytical form of the potential is :47 n ij r a ij r ij V (2 -8) m ij r a ij p (2 -9) i p c i p F (2 -10)

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20 w ith parameters c m n a , The term is an energy term, a is a term used to describe the length and m and n are integers such that n is greater than m The typical values of m are between 6 and 8 and for n bet ween 9 and 12 and c is a dim ensionless parameter.47 This type of potential has been used to describe the metal clusters in various scientific papers.4850 Thermostat In our simulations the Berendsen thermostat51 was used to keep the tem perature constant. In this type of thermostat, the system is coupled to an external heat bath which is fixed at a desired temperature. This bath acts as a source of thermal energy and supplies or removes heat from the system. The rate of change of temperature is proportional to the difference in temperature between the bath and the system and the vel ocities are scaled at each step,51 t T bath T dt t dT 1 (2 -11) In this equation, is a coupli ng parameter that defines how strongly the bath and the system are coupled together. In this type of thermostat, there is an exponential decay of the system towards the desired temperature.51 If the coupling factor is large, then the coupl ing will be weak. If this factor is small, the coupling will be strong. The change in temperature between the successive time steps is: t T bath T t T (2 -12) The scaling factor for the velocities is: 1 1 2 t T bath T t (2 -13)

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21 Verlet Leapfrog Algorithm With continuous potential s, the motions of all particles are coupled together, giving ri se to a many body problem that can not be solved analytically. Instead the e quations of motion are integrated using a finite difference method .52 In this method, continuous potential models are used to generate molecu lar dynamics trajectories that are pairwise addi tive. The idea is to break the integration into many small stages, each separated in a fixed time t The total force on each particle is the vector sum of its interactions with other particles. By looking at the force, it is possible to determine the acceleration of particles and the n these are combined with the position and velocities at time t and then the velocities and positions are calculated at a time t t During each time step, the force is assumed to b e constant. The next step determine s the forces at a time t t2 .52 Several algorithms can be used to integrate the equations of motion. These algorithms are based on the assumption that the positions a nd the dynamic properties can be approximated as Taylor series expansion: ... 4 24 1 3 6 1 2 2 1 t c t t b t t a t t tv t r t tR (2 -14) ... 3 6 1 2 2 1 tc t t b t t ta t v t t V (2 -15) ... 2 2 1 t c t t tb t a t a (2 -16) ... t tc t b t t b (2 -17) In these equations, v is the velocity, a is the acceleration and b is the third derivative.52 One of the most common methods for integrating the equations of motion is the Ver let algorithm.53 This algorithm uses the positions at time t and the positions from the previous step. t t R to calcu late new positions at t t .53

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22 ... 2 2 1 t a t t tv t r t t r (2 -18) ... 2 2 1 t a t t tv t r t t r (2 -19) If these two equations are added and if the difference in positions at times t t and t t are divided by t2 the velocity is : t t t r t t r t v 2 (2 -20) In our simulations the leap-frog algorithm is used.53, 54 This type of algorithm uses these equations: t t tv t r t t r 2 1 (2 -21) t ta t t v t t v 2 1 2 1 (2 -22) In this algorithm, the velocitie s t t v 2 1 are calculated from the velocities at time t t2 1 using the accelerations at time t The velocities are: t t v t t v t v 2 1 2 1 ( 2 1 (2 -23) The velocities leap frog over the positions to give their values at t t2 1 The positions leap over the velocities to give the values at tt and so on. The advantage of this algorithm is that ther e is no need to calculate the differences of large numbers.53, 54 Periodic Boundary Conditions Periodic boundary conditions are used to simulate a n infinitely tiled system that has one or more macromolecules in a bath of an explicit solvent When the simul ations are performed in a vacuum environment, the molecules will fly away unless there is a restraining force. Another

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23 option wo uld be to use reflective walls, but this introduces unwanted forces into the system which causes additional complication When we apply periodic boundary conditions, we define a unit cell to give an infinite description of the system. When a molecule passes through one of the faces of the unit cell, it reappears on the other side of the unit cell with the same velocity. There are various types of periodic boundary conditions such as the cubic boundary condition, orthorhombic boundary condition, slab boundary condition and the parallelepiped boundary condition. The choice of a periodic boundary condition is important. If the pe riodic box is too small then the molecule interact s with its own tail which will lead to unphysical dynamics. The idea is that a particle will interact with the closest image of the remaining particles in the system. This is called the minimum image condition. In our molecular dynamics simulations we applied an orthorhombic periodic boundary condition with dimensions of 80 12 43 91 44 x x to give an infinitely tiled description of our systems. Density Functional Theory Density functional theory (D FT) is used to investigate the electronic structure of the ground state of molecules and atoms. This method is used widely in computational physics and chemistry. DFT has also been a useful tool f or solid -state calculations and is currently a leading metho d for electronic structure calculations. However, it is difficult to describe intermole cular interactions, such as van der Waals forces, charge transfer excitations, transition st ates, potential energy surfaces, and band gaps in semiconductors usin g DFT. T he main idea behind DFT is to replace the many -body electronic wavefunction with the electronic density. In this theory, there are three spatial variables for each of the N electrons and the many body wavefunction depends on 3N variables.

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24 Hohenberg -Kohn T heorems DFT is based on the Hohenberg-Kohn Theorems.55 According to these theorems, there is a one -to one mapping between the ground state electron density and the ground state wavefunction of a manyparticle system. These theorems also state that the ground state density minimizes the total electronic energy of the sy stem. These theorems are true o nly for the ground state in the absence of external field s .56 Formalism of DFT The KohnSham equations are a set of eigenvalue equations within density functional theory (DFT).57 DFT reduces a many body problem for the N particle wavefunction N Ns r s r ;....; ,1 1 to one in terms of the charge density r p using the Hohenberg-Koh n theorems.55 The wavefunction has 4N variables and the charge density has 3 variables. It is possible to write the total energy as a functional of the charge density: p XC E p H V dr r p r ext V p T p E (2 -24) where T is the kinetic energy of the system and ext V is the external potential acting on the system. The term VH, 2 2 drdr r r r p r p e H V (2 -25) is the Hartree energy and th e xc E is the exchange correlation energy. It is difficult to obtain the exchange energy exactly, and so it is approximated. The kinetic energy is usually formulated in terms of charge density. It is possible to formulate the charge density as the sum of squares of orthonormal wave functions s r i :

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25 N i s s r i r p 2 (2 -26) which as solutions to the Schr dinger equation for N electrons in an effective potential r eff V s r i i s r i r eff s r i m 2 2 2 (2 -27) The effective potential is: p p xc E dr r r r p e r ext V r eff (2 -28) Combi ning these equations, we get the KohnSham orbital equations that are solved iteratively until a self -consistency is reached. The total energy of the system is: dr r p r p p xc E p XC E p H V N i i E (2 -29) In DFT calcul ations, the idea is to find single particle solutions to the KohnSham equation: i i i effV 2 (2 -30) The single particle orbitals can be represented in any complete basis set. In VASP,57, 58 the basis s ets are plane waves that can be written in the following form: r k G i e G G k c r k ). ( (2 -31) The Gs are reciprocal lattice vectors and k is a symmetry label in the First Brillouin zone. We used the VASP58, 59 code to perform our quantum mechanical calculations. VASP is a complex package to perform quantum mechanical calculations using pseudopotentials. Pseudopotentials are used to replace the effects of the motion s of core electrons in an atom a nd its nucleus with an effective potential, or pseudopotential. Instead of a C oulombic potential term

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26 for the core electrons there will be a modified effective potential term which is the pseudopotential. In our simulations we used the projector augmented wave method (PAW)60 and the PW9161 exchange correlatio n functional. In all cal culations with a cutoff energy of 300 eV was used. In the VASP code, the cut -off energy for a plane wave basis set is given in eV. All plane waves with a kinetic energy smaller tha t cut E cut E k G 2 2 ) ( (2 -32) The choice of cutoff energy depends on the elements in the system. The energy decreases to the ground sta te energy as cut E increases. We used 4x4x1 kpoint Monkhorst -Pack62 grid. A Monkhorst -Pack grid is a method to choose a set of k points for sampling the Brillouin zone. It is a rectangular grid of points of dimensions z y XM M M spaced evenly throughout the Brillouin zone. As we increase the size of the dimensions of the grid, we get a finer and a more accurate sampling of the zone. In our simulations, Methfessel Paxton63 smearing is used due to the presence of Au metal in our systems. Density of States The density of states (DOS) is a property that shows how closely packed the energy levels are in a quantum mechanical system. The symbols N n p g are used to describe the density of states, where ) ( E g is a function of the internal energy E The expression dE E g ) ( represents the number of states between the energy E and the energy dE E DOS refers to electron, photon and phonon energy le vels in a crystalline solid and is widely used in condensed matte r physics. A DOS of zero means the electr ons can not be excited to that energy.

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27 In the VASP58, 59 code, it is possible to calculate the DOS in units of number of states/unit cell The density of states (DOS) n is determined by the difference of the integrated DOS between two points 1 i ii N N n (2 -33) wher e is the distance between two pins (energy difference between two grid points) and i N is the integrated D OS, d i n Ni (2 -34) VASP58, 59 also gives the projected DOS on different orbitals (s,p,d) for each individual atom in the system. It is possible to sum the PDOS and get the total DOS for one component of the entire system The int egration of the total DOS up to the Fermi energy level EF gives the total number of electrons in the system. It is also possible to calculate the number of electrons for each component of the system (integration up to EF) after summing the P DOS for all the atoms comprising this component. These techniques are helpful in charge analysis.

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28 CHAPTER 3 MOLECULAR DYNAMICS SIMULATIONS OF ALKANETHIOL MONOLAYERS WITH AZOBENZENE MOLECULES ON THE AU (111) SURF ACE Introduction The concept of using molecules as components in electronic circuits was proposed theoretically in the early 1970s.64 The first experimental confirmation of this idea was achieved nearly 20 years later. Following the measurement of the conducta nce of a single molecule by the Reed group,65 a variety of molecules has now been proposed a s candidates for molecular devices.6672 Prominent among these are azobenzene and its derivatives. One feature that makes azobenze ne appealing as a molecular device is its photochemistry. Molecules in this family can be transformed between their cis and trans isomers via optical excitation. This makes them potential candidates as optical switches, or other nanooptomechanical devices.73, 74 Recent theoretical work indicates that the conductance of the two co nformations differs by a factor of 100.75 This raises the possibility that azobenzene derivatives can be used as the ON and OFF states of a singlemolecule, light -driven switch. Experimental studies in several groups have confirmed this idea, via direct measurement of conductance with a scanning tunneling microscopy (STM) tip.76, 77 For azobenzene, or any other molecule, to be useful as a device, it must be attached in some way to the solid state, ideally to metallic leads. As a first step towards this goal, candidate molecules can be studied in self -assembled monolayers (SAMs), which help to stabilize them and constrain their geometry. Indeed, SAMs are proving to be essential components of emerging bottom -up technology.7880 Understanding the properties of these monolayers, and how these properties are altered by the addition of guest molecules is critical to progress in the field. Many polymer/organic molecule assemblies have been investigated recently, due to their vast range of applications as protective coatings, in surface chemistry, and as bio -sensors.2, 5, 81 In

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29 particular, SAMs of alkanethiol on the Au(111) surface are structurally simple, thermodynamically stable, and have well -defined order. As a result, their structure and growth have been studied extensively since their discovery in the early 1980s.1, 8287 Monolayers on surfaces can be used as host matrices to support guest molecules for studies of the properties of the guest molecules, or to stabilize metallic nano -crystals.88 Such systems provide a fertile test bed for investigating the properties of molecular electronics devices. In the laboratory, molecules are often assembled as monola yers on a solid surface or inserted into alkanethiol SAMs and studied using scanning tunneling microscopy (STM).89, 90 In the former case, the STM tip is usually in contact with several molecules during the measurement. In the latter, the interaction between the host alkanethiol molecules and the guest molecule can influence the packing structure of the monolayer. In general, the structure of a monolayer mixed with guest molecules will have large local disorder, even if the monolayer itself is highly ordered. Since conductance is sensitive to the contact between the STM tip and the molecules of interest, a clear physical picture of the structure, thermodynamics and dynamics of the system is essential. Simulations are especially valuable in this regard, since i nformation concerning the microscopic details of a heterogeneous structure is often difficult to obtain directly in experiments. One example of the diverse phenomena associated with SAMs, which must be incorporated into the design of potential molecu lar devices, is the phase transition of the quasi two-dimensional system as a function of temperature. Beginning with the first experimental evidence91 for this transition, substantial ef fort has been devoted to preparing true twodimensional systems and to properly characterizing the transition. On the theory side, molecular dynamics simulations have played a significant role since the 1960s. Systems such as SAMs of chain-shaped polymers or peptides are much more complex than ideal, monoatomic 2D systems, which leads to exotic

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30 behavior and rich physics during phase transitions. For a pure alkanethiol monolayer on a gold surface, which is the reference system for our work, a number of groups have reported investigations of the structure and characteristics of the phase transition. In addition to STM,92 experimental techn iques such as low -energy atom diffraction93 (LEAD), grazing incidence x-ray diffraction (GIXD),94 and atomic force microscopy (AFM)95 have been used to investigate the s tructure of alkanethiol molecules on the Au(111) substrate. These studies have reported tilt angles of the alkanethiol chains, temperature effects, and the coverage and the chain length dependence of the properties of the monolayers. A general revi ew on properties and issues of SAMs has been reported by Ulman.2 Pioneering theoretical molecular dynamics (MD) simulations were provided by Kleins gr oup,38, 39 in which the surface was modeled with a structureless model potential. Zhang and Beck96 used a consistent valence force field to describe the molecular systems. Leng et al .46 and L. Zhang et al .97calculated properties of the monolayer using a similar model. In papers by Bhatia and Garrison,41, 42 a united -atom model was used to describe the molecular potentials and an MD/MC corrected effective medium (MD/MC CEM ) potential was used to describe the Au surface. Beardmore43 develo ped an empirical potential function by fitting parameters of the AuS interaction to quantum calculations. Finally, Fisher et al .98 reported structural results using a hybrid quantum mechanical and molecular mechanical (QM /MM) method. Inspired by the developments in the above mentioned scientific pursuits, we have performed molecular dynamics simulations to study pure and azobenzene -containing alkanethiol monolayers on the Au(111) surface. We address such issues as the structure of the monolayer and its temperature dependence, as well as the caloric curve, heat capacity, phases and phase transitions of the quasi -two dimensional systems. Our focus is a comparison of the pure and mixed

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31 systems, as well as on local distort ions of the alkanethiol monolayer when guest molecules are introduced. Our aim in this is to provide detailed information for future applications of azobenzene and similar systems as molecular devices. The chapter is organized as follows: Section II descri bes the system and the MD models; Section III presents results; and Section IV contains a summary. Systems, Simulation Model, and Computational Details This work begins by the design of models for three monolayers. These include systems comprising a pure dodecanethiol layer, a dodecanethiol monolayer containing a trans -azobenze molecule, and a dodecanethiol monolayer containing a cis -azobenzene molecule. Note that the species we refer to as azobenzene (See Fig. 3. 1) have been chemically substituted with a terminal CH2S group, to form the S Au bonds to the surface, and a terminal CH2SH group on the end directed away from the surface. The proper name of this molecule is (bis -[4 methanethiol phenyl] diazene, but we will refer to it as azobenzene for s implicity. Similarly, although all of the results in this paper were obtained for dodecanethiol, a 12-carbon alkanethiol, we will refer to this system as simply alkanethiol. The monolayers are placed on the (111) surface of 6 and 9layer Au slabs. In the lateral direction, each layer of the surface contains 18x15=270 atoms, with a size of 44.9 by 43.2 For the homogeneous system, ninety dodecanethiol molecules are included to simulate 100% coverage of the surface. Periodic boundary conditions a re used in all three directions. A 20 vacuum is inserted between two adjacent slabs in the z-direction to model the (111) surface. The MD unit box has the shape of a hexagonal ( 3 3 )R30 lattice in the x and y directions. All-atom potential functions are used with a D reiding force field99 to describe the intra -and inter molecular interactions for all molecules in the three systems. We have performed substantial tests of various potentials, in cluding the parameters used by Jung et al .100 to describe

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32 benzenethiolate and benzyl mercaptide on Au(111) in MD simulations We found, thoug h, as illustrated below, that for this work the potentials developed by Sellers, et al.8 were the most convenient and accurate. The two -body Lennard-Jones potentials for AuS were developed from a simple Au S harmonic function.8 The parameters were = 0.3 eV and = 2 We chose the Universal Force Field (UFF)44 to describe the van der Waals interactions, and modeled the interactions between Au atoms by the SuttonChen Potential .47, 101 In previous approaches, the interface between the Au surface and monolayer included: (i) Two -body LennardJones potentials for S and Au; (ii) Three body truncated harmonic potentials for C, S and Au; and (i ii) van der Waal s interactions between Au atoms and C, H and S. Details of the potentials used in our simulations are discussed below. Before embedding the cis and trans azobenzene i nto the alkanethiol monolayer, energy minimization was performed with the Dreiding force field. We found that the trans structure is about 0.7 eV lower than the energy of the cis structure, which is close to the value of 0.6 eV determined by highlevel q uantum calculations75 and experiments.102 The pure monolayer was also optimized before dynamical simulation. The heterogeneous systems were prepared by removing three (for the trans -azobenzene) or four (for the cis -azobenzene) dodecanethiol molecules from the pure system, and inserting an azobenzene molecule in the resulting cavity. At each temperature, we ran MD for 400 ps with a 2.0 fs time step before recording statistical information. The Beren dsen thermostat51 was used to control the temperature. The systems were held at constant numbe r, volume, and temperature (NVT ensemble). After relaxation at 0 K, all three systems were heated from 50 K to 800 K with an interval of 50 K. After equilibration, the MD runs continued for 240 ps, and structures were saved every 200-400 steps. To eliminate possible complications caused by cis to trans -transitions of the azobenzene during

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33 high temperature simulations, the C -N=NC dihedral angles were fixed at temperatures higher than 400 K. Results Tests of Molecule -Surface Potentials, 0 K S tructures The first simulation performed energy minimization using potential parameters from the work of Jung et al .100Figure 2 depicts the optimized s tructure at 0 K. With this potential, we found that the first three layers reconstructed. In the initial structure, the S atoms in the dodecanethiols are surrounded by three Au atoms in the first layer (Fig.2a), but in the reconstructed structure, each S a tom has six nearest neighbor Au atoms (Fig.2b). In addition, some of the Au atoms in the second layer move upward from their initial positions (Fig. 2c). This reconstruction would be expected to have a dramatic effect on the structure and energetics of the monolayer. The question, though, is whether the reconstruction is real, or an artifact of the potentials. To understand the effects on the structure due to the three -body potential, we calculated the energy of a single dodecanethiol molecule at a dis tance from the surface of 5 to 2 in steps of 0.2 At each step, a single point energy (static energy) was obtained. We found that the adsorption energy of the optimal structure is about 3.91 eV (90 kcal/mol) at the lowest -energy point (1.8 above the first surface layer). As the system relaxes, this binding energy would be expected to increase to a value considerably higher than the experimental value of 1.3 eV/molecule for this monolayer.5 A new set of two-body potential parameters was tested to reduce the binding energy to 1/3 of its original value. Once again, however, surfac e reconstruction occurred. We conclude from these tests that the two -body potential does not cause the reconstruction. We next examined the role of the 3body potential in the surface reconstruction. The 3body potential, which is a truncated harmonic potential, depends on three Au-S C angles, as shown

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34 in Fig. 3a. Before optimization, the three AuS C angles are set to 1 = 2 = 114 and 3 = 173o (due to the all trans structure assumed for dodecanethiol). This structure is nearly 3.0 eV higher than the energy of the equilibrium structure. Consequently, the force generated by this strong potential energy pushes the Au atoms away from the slab, and causes the surface to reconstruct. When the strength of the 3-body potential is adjusted a variety of interface structures are formed. Fig. 3 3b shows a structure in which an S atom of an alkanethiol has been moved from its initial hcp hollow site to a bridge fcc site to reduc e the overall 3 body energy. To investigate the suspicious surface reconstruction and AuAu elongation further, studies of a smaller model system were performed using density functional theory (DFT).57 The calculations used the Vienna Atomic Simulation Package (VASP),58, 59 with the projector augmented wave method (PAW)60 and the Perdew, Burke and Ernzerhof (PBE)103 exchange correlation functional. We considered a monolayer of CH3S on the Au(111) surface. The unit cell chosen was five layers thick in the z -direction and contained 3 Au ato ms per layer, for a total of 15 Au atoms. Three different initial configurations of CH3S on the Au(111) surface were modeled. One corresponds to the CH3S on the fcc hollow site, the second is on the hcp hollow site, and the third is the reconstructed structure. After ionic relaxation using DFT, we found that the energy of the configuration in which the molecules are on the fcc site is 0.1 eV lower than that on the hcp site, which is in good agreement with previous quantum calculations.104 In contrast, the reconstructed structure is unstable, and the system reverts to the non-reconstructed geometry (Fig. 4) when optimized. The results of these quantum calculations p rovide strong evidence that the reconstructed surface is an artifact due to imperfect potential functions

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35 To provide further detail about the AuAu elongation, additional (DFT)57 calculations were performed using a ( 3 3 )R30 surface unit cell. The slab included 5 atomic layers of Au and the bottom 2 layer s were frozen during ionic relaxation. We used the theoretical value of 4.17 for the Au fcc lattice constant. The vacuum thickness was at least 15 and the kinetic energy cutoff was 400 eV. We chose a 4x4x1 k-point mesh with Methfessel -Paxton smearin g63 of 0.4 eV were used. The total energy was converged to 2.0 meV/atom with respect to kpoint mesh and vacuum thickness. The absolute value of the force on each atom was reduced below 0.02 eV/A at t he end of ionic relaxation. We found that the elongation of the inplane Au Au distance for the fcc site upon the methyl thiol ate adsorption was more than 8% (from 2.95 to 3.20 ). Gronbeck and Andreo ni105 used a larger surface unit cell of (5x5), corresponding to low coverage, which led to a larger relaxation. The purpose of this DFT calculations was not to search thoroughly for all possible surface reconstructions induced by methyl thiol ate adsorption, but to verify whether or not the particular surface reconstruction observed in MD simulations was physical. For this reason, the DFT calculations were performed for the same unit cell of ( 3 3 )R30, used in the MD calculations. If a larger surface unit cell w ere used, other surface reconstructions might be observed, as shown recently by Mazzarello, et al.106 After analyzing these potentials and their effects on surface c onstruction, we removed the three -body term obtained from Sellers, et al.8 The gold atoms were held rigid in the production MD simulations. Consequently, the only interaction between the gold surface and the monolayers was the t wo -body L -J potential obtained from Sellers, et al.,8 as described above. With these potential parameters, the optimal binding is found to be on an off -center hcp -bridge site, which

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36 agrees with the results of Fisher, et al. usin g a hybrid quantum -classical model.98 Figure 5a depicts the energy landscape, as calculated with the empirical potentials, as the molecule moves from site to site on the surface. The various sites on the surface are illust rated in Fig. 5b. Note that the diffusion barrier between the hcp sites and the fcc sites is quite low, which indicates that the dodecanethiol molecules will diffuse rapidly upon thermal excitation. Similar barrier heights have been calculated previously.43 Phase T ransitions To study the effects of temperature on the structure and thermodynamics of the monolayers, dynamics simulations were performed within the canonical NVT ensemble. Temperature control was achieved using the Berendsen51 thermostat for equilibrium states and dynamics. Starting from optimized zero temperature structures, the three systems were investigated from 50 K to 800 K at intervals of 50 K. After equilibration, statistical data were recorded every 200400 steps and averaged over 240 ps. The heterogeneous systems were created initially by removing three alkanethiol molecules from the pure monolayer, and replacing them with a cis or t rans -azobenzene. We discovered, however, that the cis molecule isomerized to the trans at temperatures above 100 K. This is probably because the cis isomer occupies more space in the plane of the surface than the trans -, and hence has greater interact ions with the alkanethiol units. To provide additional space, and to reduce the interaction strength, we removed a fourth alkanethiol for the cis isomer simulations. In this case, the cis azobenzene remains stable to thermal isomerizaton at temperatures up to 400 K (note that in the gas phase, cis -azobenzene isomerizes thermally at room temperature). At temperatures above 400 K, we fixed the dihedral angles to prevent isomerization of the cis isomer.

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37 Caloric Curves and Heat C apacity. Figure 6 depicts caloric curves (upper panels) and heat capacity Cv (lower panels) for all three systems. The heat capacity is calculated from the energy fluctuations as, CV H2 H 2kBT2 (3 1) where H the Hamiltonian, kB is the Boltzmann constant, and T is the temperature. Strong peaks are seen around 350 K in the CV curves, indicating a phase transition. Experiments107 indicate that the phase transition occurs at about 500 C (325 K), and thus our calculations are in good agreement with the experiments. Molecular O rientation As the temperature increases, molecules in the s ystems display increased thermal motion. This causes changes in physical properties of the monolayer such as structure and dynamics. Figure 7 presents snapshots from the dynamics to illustrate the structures of the three systems at 50 K, a temperature bel ow the phase transition, and at 350 K, the temperature of the phase transition. One striking feature that can be observed in the figure is the relative orientation of the molecules. At room temperature the dodecanethiol molecules are tilted with similar tilt angles. In the systems with the azobenzene molecules, the dodecanethiol molecules near the azobenzene molecule are disordered only slightly compared to the pure system, and the azobenzene molecule tilts in the same direction as the alkanethiol monolayer (a more quantitative analysis is presented below). At temperatures above the transition temperature, all molecules are oriented normal to the surface including the azobenzene. To obtain statistical information on the tilt angle, we collected structure s along the trajectory and averaged over 240 ps. The tilt angle is defined in Fig. 3 8a. At room temperature,

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38 the experimental value108 of the tilt angle is 33.7 0.8 degrees. Our simulations predict an average tilt angle of 35.0 5.0 degrees. The distributions of tilt angles are presented in Fig. 3 8b for the pure, cis -containing, and trans -containing monolayers at three differen t temperatures. At low temperature (top), all distributions display small deviations from the mean. However, in the heterogeneous systems, the distribution is slightly broader. The results for the thermal behavior indicate that the presence of even a singl e azobenzene molecule introduces considerable local disorder. This is due, in part, to the density of the monolayer. For the pure system with full coverage, the molecule number density is 1/21.6 2; for the trans -containing monolayer, it decreases to 1/22. 0 2; and for cis -containing monolayer it decreases to 1/22.3 2 The lower density evidently provides more space for the molecule to move and tilt. Note that entropy is proportional to the volume, in general, so these results are not unexpected. As discus sed above, the cis -isomer would be expected to cause more local disorder than the trans isomer. Note, too, that even with a fourth alkanethiol removed, the distribution of tilt angles is nearly as broad for the cis case as it is for the trans -. Figure 3 -8 b illustrates that the melting begins at 350 K (middle) and is nearly complete by 375 K (bottom), at which point almost all of the molecules are vertical. Radial Distribution F unctions (RDF) Figure 3 -9a depicts S -S RDFs for all three systems at three temperatures. As a reference, we consider only the S atoms of the alkanethiol molecules. At low temperature (top), the peaks are quite sharp. Due to the stronger thermal motion at 350 K (middle), the peak s in the RDF curves broaden. At temperatures above the phase transition (bottom), additional broadening is observed. Figure 3 9b displays a snapshot of the positions of the S atoms on the surface at 50 K (top) and 400 K (bottom). Considerable disorder in the structure is evident at the higher temperature.

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39 Surface D iffusion The dynamical property of surface diffusion provides additional information concerning the physical phase of the monolayers. We have computed the mean square displacement (MSD), R ( t) R ( 0 ) 2 and the diffusion coefficient, D = for S atoms on the Au(111) surface as a function of temperature. At low temperature, all three systems are in a solid like state, with a MSD that is nearly flat (Fig 3 10a). As the temperature increases, the S atoms begin to move from their original locations, and finite (non -zero) slopes are observed. The diffusion constants, which are proportional to the slope of the mean square displacement, are presented in Fig. 3 -10b. Above the phase transition, the diffusion constants increase rapidly as the temperature increases. The systems change from solid like states to liquid like states. For the two heterogeneous systems, we find that the guest azobenzene molecule enhances the rate of di ffusion slightly. Local D isorder. To quantify the local disorder, which is difficult to achieve in the laboratory, we compute the tilt angle and height of the molecules in the monolayer as a function of distance from the guest azobenzene molecule. For the pure monolayer the center alkanthiol was considered as the reference. Figure 3 -11a shows the tilt angles of the molecules as a function of the distance from the guest azobenzene molecule. Figure 3 11b shows the height of the molecules as a function of the distance from the reference azobenzene molecule and the Fig. 3 -11c shows a histogram of the height of the molecules at different temperatures. Clear indications of local disorder caused by the guest molecules are evident, although the differences between the cis and trans azobenzene are small Conclusions In this chapter we investigated a homogeneous alkanethiol monolayer and two heterogeneous systems consisting of an alkanethiol monolayer with a cis and trans azobenzene

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40 on the Au(111) surface, us ing classical molecular dynamics. We found, in agreement with experiment, that at a temperature of about 350 K, the three systems undergo a phase transition from an ordered, tilted structure to a vertical, liquidlike structure. We presented a thorough ana lysis of temperature dependent properties such as energy, heat capacity, molecular orientation, radial distribution functions, diffusion, and local disorder. The variations in the properties indicate that the phase transition is first order for these quasi two dimensional systems. The global properties of the system, such as the nature of the phase transition, diffusion constants, radial distributions, and the transition temperature are not affected strongly by the guest molecules with the ratio of azobenze ne to alkanethiol molecules (1:87 or 1:86) used in the simulations. The local structure of the monolayer, however, is influenced by both the cis and trans azobenzene as indicated by quantities such as the molecular height, and fluctuations in the tilt an gle. Further investigations of coverage dependence, monolayers of pure cis and trans -azobenzene, and the effects of surface phonons are underway.

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41 A B Figure 31 A zobenzene molecule A) Trans azobenzene, B) cis azobenzene

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42 Figure 32 Surface structures A ) Top view and side view of the initial Au(111) surface (top 3 layers) including the positions of the S atoms on the alkanethiol molecules. Atoms in yellow are S, while blue, magenta, and green indicate the first, second and th ird layers of Au, respectively, B) Top view of the reconstructed Au(111) surface (top 3 layers) includ ing the S atoms from azobenzene, C) Side view of the reconstructed structure; S atoms are in yellow, the first layer of gold is blue, the second layer is pink, and the third layer is green. B A C

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43 A B Figure 33. Au -S C angles A) Schematic showing the three Au S C angles discussed in the text, B) Adjustment of the 3-body potential parameters produces a variety of interface structures. The center of the left triangle is an hcp hollow site, and the center of the right triangle is an fcc hollow site. The S atom (yellow) is on a bridge fcc site. S 2 3 C 1

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44 A B C D E F Figure 34. CH3S monolayer on the Au(111) surface (4x4 unit cell). A) and B) CH3S on fcc hollow site s (top view and side view), C) and D) CH3S on hcp hollow sites, E) and F) CH3S on the reconstructed surface.

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45 A -1 0 1 2 3 4 5 6 7 toptop_hcp hcphcp_bribri bri_fcc fcc fcc_top B Figure 35. Different atomic sites and energy curve A) Relative binding energy of one dodecanethiol molecule on the Au(111) surface alon g a selected diffusion path, B) Schematic of the surface, indicating the various surface sites. top bri hcp fcc Relative Binding Energy (kcal/mol) Positions

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46 -10000 -8000 -6000 -4000 -2000 0 2000 4000 6000 8000 10000 0 200 400 600 800 T (K) T (K) Figure 3-6. Caloric curves. From left to right, are alkanethiol monolayers with the cis -containing monolayer, the trans -containing monolayer and the pure monolayer. Top: Total energy versus temperature; Bottom: Heat capacity versus temperature. Total Energy (kcal/mol ) Cv (kcal/mol K ) -10000 -8000 -6000 -4000 -2000 0 2000 4000 6000 8000 10000 0 200 400 600 800 -10000 -8000 -6000 -4000 -2000 0 2000 4000 6000 8000 10000 0 200 400 600 800 0 1 2 3 4 5 6 0 200 400 600 800 0 1 2 3 4 5 6 0 200 400 600 800 0 1 2 3 4 5 6 0 200 400 600 800

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47 Figure 37. Equilibrium configuration of the pure alkanethiol monolayer. The cis -containing monolayer and the trans -containing monolayer, are on the left and righ t, respectively. Top: Panels A), B) and C) illustrate the structure at a temperature b elow the phas e transition (50 K); Bottom: D), E) and F) illustrate the structure at the phase transition temperature (350). A C D E F B

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48 Figure 38. Tilt angle A) Definition of the tilt angle, B) Total distribution of tilt angles. From left to right are the cis -containing monolayer, the trans -containing monolayer, and the pure monolayer; from top to bottom, 50 K, 350 K, and 375 K. A

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49 Figure 38 Continue

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50 A Distance between S and S atom () Figure 39 Radial Distribution functions A) Radial distribution functions of S atoms in alkanethiol molecules. From left to right are the cis -containing monolayer, the trans containing monolayer and the pure monolayer at (top to bottom) 50 K, 350 K, and 375 K, respectively, B) Snapshots of the posi tions of the S atoms on the surface at 50 K (top) and 400 K (bottom). Radial Distribut ions 0 20 40 60 80 100 120 140 160 180 200 0 2.5 5 7.5 10 12.5 15 0 20 40 60 80 100 120 140 160 180 200 0 2.5 5 7.5 10 12.5 15 0 20 40 60 80 100 120 140 160 180 200 0 2.5 5 7.5 10 12.5 15 0 20 40 60 80 100 120 140 160 180 200 0 2.5 5 7.5 10 12.5 15 0 20 40 60 80 100 120 140 160 180 200 0 2.5 5 7.5 10 12.5 15 0 20 40 60 80 100 120 140 160 180 200 0 2.5 5 7.5 10 12.5 15 0 20 40 60 80 100 120 140 160 180 200 0 2.5 5 7.5 10 12.5 15 0 20 40 60 80 100 120 140 160 180 200 0 2.5 5 7.5 10 12.5 15 0 20 40 60 80 100 120 140 160 180 200 0 2.5 5 7.5 10 12.5 15

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51 B Figure 39 Continue

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52 A Time (ps) B T (K) Figure 310. Diffusion process. A) Mean square displacement (MSD) of sulfur atoms as a function of temperature (50K to 800K). Left to right are the cis -containing monolayer, the trans containing monolayer a nd the pure monolayer, B) Diffusion coeffici ent (D ) versus temperature (T) 0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014 0.0016 0 100 200 300 400 500 600 700 800 cis trans pure D ( 2 /ps) MSD ( 2 ) 0 0.5 1 1.5 2 2.5 3 3.5 0 40 80 120 160 200 240 0 0.5 1 1.5 2 2.5 3 3.5 0 40 80 120 160 200 240 0 0.5 1 1.5 2 2.5 3 3.5 0 40 80 120 160 200 240

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53 Figure 311. Angle Distributions and guest molecule relation. A) Tilt angle of the host alkanethiol molecules as a function of the distance from a guest molecule. From left to right are the cis -containing, the trans -containing and the pure monolayer, at temperature of 50 K, 350 K, and 375 K, from top to bottom.. The distance is measured between two S atoms attached to the surface. For the pure monolayer, the center alkanethiol molecule serves as the reference, B) Heig ht of the molecules, from the surface to the terminal atom, as a function of distance from a guest molecule. From left to right are the cis -containing, the trans -containing and the pure monolayer at (top to bottom) 50K, 350K, and 375K, C) Distributions of molecular height during the simulations. From left to right are the cis -containing, the trans -containing and the pure monolayer at (top to bottom) 50 K, 350 K, and 375 K.

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54 B Distance () Figure 311. Continue 12 13 14 15 16 0 5 10 15 20 25 30 12 13 14 15 16 5 10 15 20 25 12 13 14 15 16 0 5 10 15 20 25 30 12 13 14 15 16 17 18 0 5 10 15 20 25 30 12 13 14 15 16 17 18 5 10 15 20 25 12 13 14 15 16 17 18 0 5 10 15 20 25 30 12 13 14 15 16 17 18 19 0 5 10 15 20 25 30 12 13 14 15 16 17 18 19 5 10 15 20 25 12 13 14 15 16 17 18 19 0 5 10 15 20 25 30 Height ()

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55 C Height () Figure 311. Continue Number of molecules 0 10 20 30 40 50 60 70 11.5 12.5 13.5 14.5 15.5 16.5 0 10 20 30 40 50 60 70 11.5 12.5 13.5 14.5 15.5 16.5 0 10 20 30 40 50 60 70 11.5 12.5 13.5 14.5 15.5 16.5 0 5 10 15 20 25 30 35 40 45 14.5 15 15.5 16 16.5 17 0 5 10 15 20 25 30 35 40 45 14.5 15 15.5 16 16.5 17 0 5 10 15 20 25 30 35 40 45 14.5 15 15.5 16 16.5 17 0 10 20 30 40 50 60 16 16.5 17 17.5 18 18.5 0 10 20 30 40 50 60 16 16.5 17 17.5 18 18.5 0 10 20 30 40 50 60 16 16.5 17 17.5 18 18.5

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56 CHAPTER 4 MOLECULAR DYNAMICS S IMULATIONS OF AU PEN ETRATION THROUGH ALKANETHIOL MONOLAYE RS ON THE AU (111) S URFACE Introduction Due to their wide range of applications as protective coatings, in surface chemistry, and as bio -sensors,109, 110 many polymer/organic molecule assemblies have been investigated recently.2, 81 One prototypical is alkanethiol self -assembled monolayers (SAMs) on the A u(111) surface. This family of molecular assemblies is easy to prepare, structurally simple and has well -defined order. Since their discovery in the early 1980s, these systems have been studied extensively.1, 87 These systems also serve as test beds for investigations of properties of possible new generation molecular -electronic devices. The alkanethiol SAM presents a classical metal insulator metal (MIM) tunnel junction when fabricated between metal contacts due to their large HOMO LUMO gap (HOMO: highest occ upied molecular orbital; LUMO: lowest unoccupied molecular orbital) of approximately 8 eV.3537 Considerable experimental work has now been performed to investigate the structure and characteristics of alkanethiol monolayers including scanning -tunneling microscopy (STM),92 low energy atom diffraction (LEAD),93 gazing incidence X -ray diffraction (GIXD)94 and atomic force microscopy (AFM).95 These studies have reported detailed structural information about such monolayers including the tilt angles of the alkanethiol chains, temperature effects, and the coverage and the chain length dependence of the properties of the monolayers. Recent experiments aim at using an Au/SAM/Au layered structure as a molecular junction.111114 One way to prepare an Au/SAM/Au structure is using a vapor deposition technique to deposit Au onto alkanethiol SAMs that are formed on the Au(111) surface.111, 112 One difficulty with this techniq ue is the possibility that the gold atoms can penetrate through the SAMs at room temperature.112, 115, 116 Scanning tunneling microscope measurements have shown significant

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57 penetration of Au atoms through CH3 terminated SAMs.116, 117 Molecular motion at room temperature causes vacancies that Au atoms can use penetrate through the alkanethiol SAMs.112, 118 Experimentally, Zhu and co-workers prepared self -assembled alkanethiol monolayers by adsorption of alkanethiolates on the Au(111) surface and then deposited Au atoms on these monolayers.112 They applied different surface characterization techniques such as time of flight secondary ion mass spectrometry (ToF SIMS)111, 118, 119 and AFM.112 By analyzing the ToF SIMs spectra, they identified three dist inct sets of peaks in the spectra, Au+, (CnHm )+ and AuS(CH2)16 +. No Au(CnHm)+ peaks were observed, which indicates that the Au ad -atoms do not remain in between the layers, or on top of the layers. Even after large amounts of Au was deposited, no changes in the spectra were observed, indicating that Au atoms penetrate extensively i nto alkanethiol SAMs and form metallic layers on the Au/S interface.112 In addition to mass spectra, conductance probe AFM (CPAFM) indicated the presence of metallic filaments inside SAMs.112 Using the tip as the conductance probe enabled detection of the presence of such buried filaments. These filaments can form conduction pathways via tunneling from the tip.112 Experiments also indicate that it is possible to reduce the mobility of the Au ad -atoms by decreasing the temperature. Reed and co -workers cooled the SAMs to liquid-nitrogen temperature and observed that the Au atoms did not penetrat e the SAMs.111 Theoretical work based on molecular dynamics simulations (MD) have also done to study the structure, dynamical and thermodynamic properties of alkanethiol SAM on Au surface41, 42, 120, 121 as well as impurity molecules in the pure SAMs.45 These calculations focus on the alkanethiol SAMs, in which molecules interact mainly by weak van der Waals forces. To date, there is no

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58 theoretical investigation that studies deposition of metal ad-atoms which is extremely important to fabricating metal molecule metal junctions. Inspired by the experimental results and the need of understanding the motion of ad-atoms, we have investigated the penetration of Au atoms into alkanethiol monolayers using molecular dynamics simulations. In particular, we performed molecular dynamics simulations starting with placing Au atoms on top of alkanthiol S AMs, which has been thoroughly characterized in our previous investigation.45 Varying numbers of Au atoms (varying concentration) at a nu mber of randomly selected ini tial configurations have been simulated at room temperature and low temperature (50 K). To describe the monolayer Au atom interaction properly, we performed quantum mechanical calculations to calibrate the MD potential parameters. In addition, we have also investigated the electronic structure of the system, and charge transfer between the monolayer and the Au(111) surface. The rest of the chapter is organized as follows: Section II describes the computational details, section III are results from the simulations, and we discuss and conclude our investigations at the end. Computational Details Our model system consists of an alkanethiol (dodecanethiol) monolayer on a Au(111) surface. The gold surface is modeled using a six atomic layers slab. In the lateral direction, each layer of surface contains 18x15=270 atoms; with a size of 44.9 x 43.2 90 alkanethiol molecules have been placed on the surface to simulate 100% coverage. Periodic boundary conditions have been used in all three directions. But a 20 vacuum has been inserted between two adjacent slabs in the z -direction (perpend icular to the surface) to model a Au(111) surface. The MD unit box had the shape of a hexagonal ( 3 3 )R30 lattice in the x and ydirections.

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59 To describe the intra molecular interactions, we have applied the Dreiding force field.99 The AuS interaction were obtained from Sellers,8 as in our previous publication.45 The Universal Force Field (UFF)44 was used to describe the van der Waals interactions, and the interactions between the Au atoms were modeled with the SuttonChen potential.47, 101 Most of our MD simulations were preformed at 300 K, with a few test cases at 50 K. The Berendsen thermostat51 has been used for temperature control. Systems that consist gold substrates and alkanethiol monolayers in our studies have been equilibrated (400 ps) before adding extra Au atoms. Typically, we let MD simulation runs go on for about 1.0 ns before collecting final statistical information. Various initi al configurations of Au ad-atoms on top of the alkanethiol SAMs have been used to test the sensitivity of the results to the initial conditions and to improve statistics. To improve the reliability of our MD simulations, quantum mechanical calculations bas ed density functional theory (DFT)57 have been performed. The purpose of these DFT calculations is to investigate the binding energy of Au on alkanethiol SAMs, which is critical to the quality of the force field used for MD simulations, and to analyze the electronic structure of the molecule metal interface. The DFT calculations have been performed using the (VASP)58, 59 program with the projector augmented wave method (PAW)60 and generalized gradient approximation (GGA); specifically the PW9161 exchange functional. For quantum modeling, we have used a slab of 5 atomic layer s for surface calculations. A vacuum of thickness of 15 between two neighboring slabs have been inserted in the z -direction. An energy-cutoff of 300 eV, a 4x4x1 kpoint Monkhorst -Pack62 mesh, and a Methfessel -Paxton smearing63 of 0.2 eV, have been used. The systems have been relaxed until the force on each atom is below 0.02 ev/A.

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60 Results Binding E nergy of Au on A lkanethiol SAMs As a fist step we have tested the UFF to determine whether or not this potential is adequate to describe the interactions of the Au ad-atoms with the alkanethiol SAM. We have found that the classical UFF force field gives a binding energy of -0.7 kcal/mole between an ad -atom and the alkanethiol Au(111) surface. In contrast, the DFT calculations give a binding energy of -7.0 kcal/mole, which is a factor of ten greater in magnitude. This difference suggests that modifications of empirical potential are necessary. Our first test of the UFF has involved calculations of the Au-alkanethiol potential as a function of the distance of the Au atom above the surface. Figure 4 1 shows configurations of a system composed of four alkanethiol molecules per unit cell connected to a slab of 60 Au atoms (5 layers, 12 atoms in each layer with the bottom two layers fixed). One Au adatom has been placed at various heights within the mono layer. The optimizations have been performed with the z coordinate constrained, except for the initial and final configurations, in which full relaxation has been allowed. Note that the constraint does not apply to the x and the y directions. Similar calcu lations have been performed for two systems. In the first one (Figure 4 1), the alkanethiol species are tilted by 350, and in the second, the alkanethiols are vertical (Figure 4 -2), corresponding to low temperature and high temperature, respectively .45 In the z -direction, the ad Au atom was constrained in positions ranging from 18 to 3 above the slab. When the z component was allowed to relax, the ad-atom penetrated the monolayer to the top of the Au/S interface. Figure 4 3 shows the binding energy of the Au ad-atom as a function of z. Fig. 4 3a shows the results of the DFT calculations, and Fig. 4 3b shows the results with the Aumonolayer potential scaled by a factor of 10. Clearly, the agreement between the DFT results i s much better

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61 with the scaled UFF parameters. This provides the rationale for scaling the UFF parameters in the dynamics calculations, as described below. In addition to this, we calculated the binding energy of the vertical and the tilted alkanethiol molecules on the Au(111) surface. Binding energy of one vertical alkanethiol turned out to be 34.1 kcal/mol and the binding energy of one tilted alkanethiol i s -29.9 kcal/mol. Molecular Dynamics To examine the extent to which gold ad-atoms penetrate the alkanethiol SAMs, and how this penetration depends on surface coverage and temperature, we performed detailed molecular dynamics simulations of the entire ad -a tom plus SAM plus gold slab system. Our first tests used the unmodified UFF parameters to describe the interaction between the Au ad-atoms and the monolayer. We found that with this force field we could not reproduce event the qualitative aspects of the experimental results. Rather than interacting with the SAM, the gold atoms simply flew away. Based on our comparisons of the potentials with DFT (see Fig. 4 3), we repeated the calculations with the relevant UFF potential parameters scaled by factors of 5 and 10. To do this, we simply scaled the potential well depth values (e in the formula) in the UFF. The 12 6] and here we scaled only the Au C and AuH interactions and did not modify the Au -S parameters. Only Au ad-atom and molecule interaction has been scaled. In the first set of simulations, 9 gold atoms were placed Au at random configurations on top of alkanethiol SAMs (i.e. 9 Au atoms/90 molecule). The simulations were run with the UFF parameters sc aled by a factor of 5. The results showed that most of the Au atoms were clustered on top of the monolayer. Some atoms left the surface and a small number penetrated the monolayer (see Fig. 4). Next, we scaled the UFF parameters by a factor of 10 and repea ted the simulations. In this case, the results showed that most Au atoms penetrate the monolayer (see Fig. 5). Histograms

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62 of the z values of the gold ad-atoms (averaged over five different initial conditions are show in Fig. 4 6a, in which the potential is scaled by a factor of 10, and Fig. 4 6b, in which the potential is scaled by a factor of 5. In the histograms the topmost gold layer has a z value of -3 and the bottom layer has a z value of -15 The peak at -15 is an artifact due to periodic boundary conditions (atoms leave the surface and they appear at the bottom layer). Figure 4 -6a shows large peaks near 0 which indicates that most of the atoms penetrate the alkanethiol monolayers and form films at the Au/S interface. In figure 4 -6b, in contrast, most of the Au ad -atoms cluster on top of alkanethiol monolayers, as show by the peaks near 1520 Note that that the results in Fig. 4 6a, which are consistent with those seen in the experiments, are also consistent with the predictions of the D FT calculations (see Fig. 4 3) To test the effects of initial coverage, we repeated the simulations with 18 Au ad -atoms on the alkanethiol SAMs. The same procedures were followed and similar results were obtained. The histograms of the average z values of the Au ad-atoms can be seen in Fig. 4 7. As in Fig. 4 6, when the UFF parameters are scaled by a factor of 5, clustering occurs on top of monolayers, resulting in peaks near 15 and 20 When the parameters are scaled by a factor of 10, the Au ad atoms pen etrate into the alkanethiol molecules and form buried layers on the Au/S interface, as evidenced by the large peak at 0 As seen in the experiment,112 the main result of increasing the initial covera ge is to create additional buried layers. Density of States and Charge Transfer The molecular dynamics simulations, in agreement with experiment, provide strong evidence that Au ad-atoms have a high propensity to penetrate the alkanethiol monolayer and interact strongly with the surface. To investigate the nature of this interaction, we have performed density of states (DOS) and projected DOS (PDOS) calculation to examine the changes in electronic structure, and to analyze the mechanism of charge transf er within the system. The DOS and PDOS

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63 of the two systems, one without and one with a gold ad-atom, are shown in Fig 4 8, and Fig 4 -9, respectively, and the DOS and PDOS of the pure Au surface are shown in Fig 4 10 for comparison. The figures show that while d orbitals dominate the DO S below -1 eV (measured from EF) in pure Au surface, s p and d-orbitals have approximately equal contributions to the DOS near EF (-1 to 1 eV). The tilted and vertical molecule systems produce very similar DOS and PDOS, m eaning that the tilting angle of the thiol molecule has little influence on the electronic structure of the surface. From Fig. 4 8 and 4 -9, we also see that a single ad -atom modifies the DOS/PDOS only moderately, the Fermi level is shifted by ~0.25 eV in both the tilted and vertical cases. In both systems with and without ad-atom, the PDOS on the Au surface is almost identical to that for the pure Au surface. However, a more careful separation of PDOS (Fig. 4 11) shows that the electronic structure for the topmost layer of Au surface actually changes drastically, especially around 2.0 eV to 3.0 eV below EF; while other layers that is not directly bonded with the molecules are not substantially affected. This clearly shows the screening effect of a metallic substrate, and thus the modification is limited very close to the surface. To analyze the nature of the charge transfer, the PDOS is integrated of various regions of the system. The DOS data shows that the charge transfer to both tilted and vertical molecu les from the gold surface is ~1.4 electron. Table 4 1. Charge transfer (per molecule) from the Au surface and charge transfer to alkanethiol molecules System 1(e) 2(e) V ert ical mol ecule on the surface -0.36 +0.36 Tilt molecule on the surface -0.35 +0.35 V ert ical mol ecule and the Au ad-atom on the surface -0.12 +0.41 T ilt molecule and the Au ad-atom on the surface -0.13 +0.39 1 charge transfer from the Au surface 2 charge transf er to the alkanethiol molecules

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64 Once an ad -atom is attac hed to the surface, the Au ad-atom transfers ~1.1 electrons to the molecule, which reduces the charge transfer from the Au surface to ~0.5 electrons The PDOS analysis, which shows that the ad-atom i nduces a shift of the Fermi level, agrees with the charge transfer data. The data also show that the detailed structure (tilted or vertical) does not alter the charge transfer substantially, which is also consistent with the PDOS analysis. Conclusions In this chapter we analyzed the penetration of Au ad -atoms through alkanethiol SAMS using computational methods. Quantum mechanical calculations were performed to modify the classical potential parameters. When the potentials were changed to mat c h the exper imental interaction energies, we found that the ad -atoms penetrate the SAM readily and form buried layers at the Au/S interface. The coverage and temperature dependence observed in the simulations are in good agreement with the experimental results. In par ticular, we found that, there is extensive penetration of Au atoms in the molecules at 300 K. At 50 K, there is no Au penetration inside the monolayer during simulations (trajectories are 20 times as long as the cases of 300 K, i.e. 20 ns). When the Au co verage was increased, the Au ad -atoms continued to penetrate the monolayer and formed buried layers beneath the SAM. To match the experimental results, the UFF interactions between the Au ad-atoms and the monolayer were scaled by a factor of ten. These res ults are a warning to the community that universal force fields may require modifications in systems outside of the range in which they were calibrated. Calculations of the DOS and PDOS revealed detailed information about the electronic structure and ch arge transfer between the alkanethiol monolayer and the Au(111) surface. We expect that these results will be important for the design of new generation molecular -electronic devices. We believe our calculations will inspire new research in constructing new Au/SAM/Au sandwich structures. For the specific system investigated in this work, for example, it is clear that producing layered structures using the methods suggested

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65 experimentally will require passivating the SAM in some way to prevent penetration by the Au adatoms.

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66 Figure 41. Snaphots of a system with four tilted alkanethiol molecules attached to a model of the Au(111) surface with an Au ad-atom after relaxation wi th DFT. A) 18 above the surface, B) 9 above the surface and C) interacting with the Au/S interface. Figure 42. Snaphots of a system with four vertical alkanethiol molecules attached to a model of the Au(111) surface with an Au ad-at om after relaxation with DFT. A)18 above the surface, B) 9 above the surface and C) interacting with the Au/S interface. A B C A B C

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67 Height () A Height () B Figure 43. Binding energy of the Au ad-atom with respect to the distance above the the Au/S interface. A) DFT and B) the modified UFF as described in the text. Results are presented for both the tilted monolayer and the vertical monolayer. 6 7 8 9 0 4 8 12 16 20 tilted vertical 6 7 8 9 0 4 8 12 16 20 vertical tilted Binding Energy (kcal/mol) Binding Energy (kcal/mol)

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68 Figure 44. Snapshots from the molecular dynamics simulations for 9 atoms placed on the alkanethiol SAMs. A) in i tial configuration, B) snapshot after 1ns of simulation with the UFF parame ters scaled by a factor of 5, C) initial configuration for 18 Au atoms p laced on the alkanthiol SAMs, D) snapshot after 1ns simulation, UFF parameters are scaled by a factor of 5. A B C D

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69 Figure 45. Snapshots from the molecular dynamics simulations for 9 atoms pl aced on the alkanethiol SAMs. A) in i tial configu ration, B) snapshot after 1ns of simulation with the UFF paramet ers scaled by a factor of 10, C) initial configuration for 18 Au atoms p laced on the alkanthiol SAMs, D) snapshot after 1ns simulation, UFF parameters are scaled by a factor of 10. A B

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70 Zvalue () A Zvalue () B Figure 46. Average histograms of z, the distance of the Au ad -atom above the su rface, for 9 atoms on the SAMs. A) the UFF scaled by a factor of 10 and B ) the UFF scaled by a factor of 5. 9 atoms UFF*10 0 10 20 30 40 50 0 5 10 15 20 25 30 35 9 atom UFF*5 0 10 20 30 40 50 60 0 5 10 15 20 25 30 35 Number of atoms Number of atoms .. + .. +

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71 Zvalue () A) Zvalue () B) Figure 47. Average histograms of z, the distance of the Au ad -atom above the surface, for 18 atoms on the SAMs A) the UF F scaled by 10 and B) the UFF scaled by 5. 18 atom UFF*10 0 20 40 60 80 100 0 5 10 15 20 25 30 35 18 atom UFF*5 0 20 40 60 80 100 0 5 10 15 20 25 30 35 Number of atoms Number of atoms .. + .. +

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72 A B Figure 48 DOS and PDOS for th e system without the Au ad-atom. A) Vertical molecules on Au surface, total DOS, projected DOS on Au, projected DOS on Au dorbital an d the total DOS on molecules, B) Tilted molecules on Au surface, total DOS, projected DOS on Au, projected DOS on Au dorbital and the total DOS on molecules.

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73 A B Figure 49. DOS and PDOS of the system with the Au ad-atom A) Vertical molecules and the Au ad -atom on Au surface, total DOS, projected DOS on Au, projected DOS on Au dorbital an d the total DOS on molecules, B) Tilted molecules and the Au ad -atom on Au surface, total DOS, pro jected DOS on Au, projected DOS on Au dorbital and the total DOS on molecules.

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74 Figure 410. Pure Au surface, S, P and D projected DOS and the total DOS.

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75 Figure 411. Renormalized PDOS for the topmost layer in the upper panel and the rest of the surface in the lower panel.

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76 CHAPTER 5 DYNAMICS OF SILVER C LUSTERS ON ALKANETHIOL MONOLAYE RS ON AU(111) SURFACE Introduction Intense investigation of metal organic interfaces ov er the past decade has revealed a vast range of applications in nano molecular electronics80, 122124 and as e lectrochemical and optical bio sensors.109, 125 128Diffusion of nanoparticles at such interfaces is of fundamen tal importance in the making of functional nano -structures. Unlike diffusion in solid surfaces, which has been studied,129131 the motion of particles on organic molecular surfaces has yet to be explored and offers new possibilities for observing complex phenomena. Metal clusters, especially metals Au and Ag are the most popular candidates for constructing twodimensional quantum dot arrays.132136 Small metal clusters have interesting spectroscopic properties that are different from those of the ir bulk counterparts and they can also be used to immobilize large molecules such as proteins.137, 138 A great expectation is emerging that one can utilize special features of nano -structured matter in future technology. Growing nano-size clusters on surfaces can be traced back to t he early 1990s. There have been two basic experimental techniques, one that involves size -selected clusters pre formed in a chamber and beamed down at the surfaces; and a second that employs self -assembly methods in which clusters form on the surface.132, 139 Theoretical investigations in the early to mid 1990s attempted to understand the control mechanisms of the deposition process.140, 141 Since the mid 1990s, studies of nanostructured entities have attracted immense attention and much effort has been made to create structures with characteristic sizes in the range 1 100 nm. One motivation for investigating metal clusters on organic surfaces is to control the interface of metal organic metal junctions. In contrast to generating nanodot arrays, the idea is to force metal atoms to coalesce in a controlled way. Because of the strong cohesive energy between

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77 metal and inorganic materials (silicon etc.), metal clusters on surfaces must be passivated by organic molecules or separated by an inactive matrix. For gold and silver clusters, molecules with thiol groups are often used to passivate the cluster surfaces.133135 A natural alternative is to passivate the bulk surface instead of clusters. Self -assembled monolayers (SAMs) of alkanethiol on Au(111) surfaces are particulary widely used in surface studies because they are structurally simple, thermodynamically stable, and have well -defined order.45, 84, 142, 143 Previous studies found that atomic diffusion through organic layers prevents the for mation of a quality junction.144 Controlled deposition or growth of unpassivated metal clusters over organic surfaces would provide a novel way of creating nano particle arrays or growth of metal organic metal junctions. For this purpose, understanding diffusion of atoms and nano-clusters on organic assemblies is of essential importance. We therefore choose this system for study. In a recent paper, we presented an extensive investigation of the dynamics and thermodynamics of alkanethiol monolayers45 and the properties of such monolayers in the presenc e of guest molecules. In this work, using a similar molecular dynamics simulation method, we focus on the dynamics of silver clusters Agn, with n=55, 147 and 1289, deposited on alkanethiol monolayers self -assembled on Au(111) surfaces. Clusters with 55 and 147 atoms, known as magic number clusters, are complete -shell Mackay icosahedra and have high stability. For the 1289 atom cluster, structure relaxation leads to the formation of facets and the loss of high symmetry, but the detailed structure of the clus ter is not an important factor in the physics we present in this chapter. Computational Details Metal metal interactions follow the Sutton Chen47 potential, the nonbonding VDW interactions are described with the Universal Force Field (UFF),44 and the Au-S interaction are of a LJ form obtaine d from the previous work of Sellers,8 as also in our previous work.45 The intra -

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78 molecular interactions for the alkanethiol molecules are described with the Dreiding force field.99 The MD unit box has the shape of a hexagonal oR x 30 3 3 lattice in the x and y directions. In the lateral direction each layer consisted of 18x15=270 atoms, with a size of 44.91 by 43.2 The gold atoms were held fixed during the simulations. Ninety alkanethiol molecules were placed on the surface, for 100 % coverage. Periodic boundary conditions were used in all three directions. A 20 vacuum was inserted between two adjacent slabs in the z direction to model the (111) surface. To follow the di ffusion of bigger clusters (147, 1289 atom) we used a surface four times larger. The clusters (n=55, 147, 1289) were placed on dodecanethiol SAMs (the closest distance between Ag and alkanethiol atoms was about 3 ). The systems were relaxed at 0K during a 10ns (4ns equilibration time) simulation. The binding energies of these clusters were -4.7 kcal/mole for the smallest one, -5 kcal/mole for the mid-size one and -14 kcal/mole for the largest cluster. After the relaxation, simulations were performed at 150K to investigate the diffusion and sintering; the NVT Brendsen51 thermostat was used to mainta in a constant temperature. This temperature was chosen because at higher temperatures all but the largest cluster are unbound and fly away from the surface. For the smallest cluster we obtained 130ns of simulation time (in all simulations the first 10ns si mulation contains 4 ns of equilibration time). For the midsize cluster the total simulation time was 80 ns, and for the largest cluster, the total simulation time was 70 ns. As an additional test, we placed four 55 atom clusters on a surface a factor of four larger and ran simulations at 150K. In this case, the four clusters eventually collided with one another and formed one large cluster. Figure 5 1 shows a snapshot of a typical simulation configuration, including the gold substrate, the alkanethiol SAM and a 55 atom cluster.

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79 Results Figure 5 2 shows the x -y surface projection of the trajectory of the cluster center of mass for three clusters. The 55-atom cluster trajectory, which lasts 130ns, is composed of three separate segments, between which the cluster briefly leaves the surface. The 147-atom cluster tr ajectory covers 80ns, and the 1289-atom cluster trajectory lasts 70ns. The trajectories display, in a general sense, a wandering random walk, but the nature and the scale of the wandering is very different from the smallest to the largest cluster, differ ences that we quantify in the following analysis. All components of velocity are Gaussian distributed to high accuracy for all three clusters, with 2 d x -y variance consistent with the expected m kT /2 Measured variances are slightly aniso tropic, broader in one direction and narrower in another. The anisotropy is greatest for n=1289, where the excess is 2.3%, only a 2.1very different for different size clusters. Figure 5 -3 shows the spectra l densities of x and y components of the velocity, normalized by the velocity variance. The spectrum of the 55-atom cluster spectrum is almost scale free, similar to the characteristic behavior of Brownian motion, for which, as an integral of uncorrelate d kicks, the velocity has a n 2 f spectrum. The spectrum of the 147-atom cluster shows hints of a characteristic scale. The 1289 -atom cluster has distinct peaks that are at different frequencies for x and y components. Inserts show the correlation function ) ( t c of the vector velocity, 2 1 2 1 2 1 2 1/ t t t t c All correlations drop sharply, with a time constant of order 0.1 ns or smaller. For the 55-atom cluster the correlation falls off roughly as the exponential of a frac tional power, / exp t with 15 0 67 0 and 047 0 ns. The correlations of the 147and 1289 -atom clusters also show oscillations at multiple frequencies.

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80 Figure 5 4 shows the rms displacement 2 1 2t R for two points on a trajectory separated by time difference t averaged over a trajectory. At small times, the motions of clusters of all sizes are nearly ballistic, t R with m kT /2 (for 01 .0 t ns, t R with 95 055 89 0147 95 01289 ). For n=55 the late time trajectory has t R with a superdiffusive value 65 055 This scaling applies not only to the rms R ; the entire distribution scales roughly self -similarly. Unlike the power law distribution, the distributions we find for R at a fixed time separation fall off exponentially. For the 1289-atom cluster and for 1 0 t ns the cluster sticks in place; t R grows almost not at all, approximately logarithmically, with many oscillations apparent. The n =147 cluster presents an immediate behavior, approximately Brownian, with 43 055 Figure 5 5 shows the distribution of fractional departures from isotropy in the velocity direction as a function of orientation. Several of the tallest spike s in the distribution for n=55 represent extended times when the cluster is not strongly in contact with the surface. Writing N N f as a series in m sin and m cos we find no statistically significant anisotropy for n=55 or n=147, but for n=1289 there is a significant (5.75peaked along the axis o5 98 and o5 81 This is approximately the direction in which the trajectory is extended in Figure 5 -2. The curve in the figure includes this m=2 mode plus a marginally significant m=4 mode that makes the contrast between highest and lowest probabilities about 8.8%. Conclusions Based on these quantitative st atistics and on visualizations of the evolution, we have developed on the following picture. All clusters display a nearly ballistic motion for time intervals

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81 shorter than a few hundred picoseconds. For longer times, longer than about one nanosecond, the l ightest cluster continues to move freely over the alkanethiol layer, sliding or rolling over the ends of alkanethiol strands in a motion resemb ling the activity known as crowd surfing at a concert or sporting event, but with a slightly impeded motion as the alkanethiol strands tug at the surface of the cluster. The motion of the heaviest cluster is much more substantially impeded, resembling that of a tethered balloon buffeted by guts of wind. The frequency spectra reflect this, with a featureless, directio nally isotropic spectrum for n=55 cluster, but with pronounced peaks at characteristic scales, different for the x and y components of the motion, for the n=1289 cluster. The behavior of the n=147 cluster lies in between all of these considerations. From the smallest to the largest cluster, the low frequency power components decrease substantially from one to the next. In conclusion, we have developed a theoretical understanding of nano-size particle motion on organic assemblies based on large -scale simu lations that include a huge numbers of freedom. Unlike motions on solid surfaces, nano-silver particles on organic surfaces can display size dependent, nonBrownian motions. Our analysis of the transition from super -diffusive motion to localized vibration can apply to a wide range of particle motion on organic surfaces with different sizes.

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82 Figure 51 Typical cluster/alkanethiol SAM/gold surface configuration for the n=55 cluster. The x direction is oriented left right in the picture, the y-direction is out of the page, and z direction is vertical.

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83 Figure 52. Projected xy trajectories o f cluster center of mass for Ag clusters with n=55,147 and 1289 atoms (counterclockwise from top left). For n=1289, darker colors are later in time.

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84 Figure 5 3. Velocity frequency spectra P(f), normalized by velocity variance, as a function of frequency f. Each panel shows the spectrum for both x and ycomponents, which are indistinguishable except for n=1289. Spectra are smoothed over a moving window of 2 0 points; remaining statistical uncertainties are reflected in the center of the curves. Inserts show the (vector) velocity correlation as a function of time separation t over times from 0 to 1ns.

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85 Figure 54. Root mean square displacement 2 1 2t R averaged over a trajectory as a function of time t for n=55, n=147 and n=1289 (top to bottom). Dashed lines show the ballistic limit t R for thermal velocity m kT /2 ; for small times the motion is nearly ballistic.

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86 Figure 55. Velocity anisotropy: histogram of fractional deviation from isotropy for velocity as a function of direction for n=55, n=147 and n=1289 (top to bottom). Deviations are small, and with similar numbers of points all bins have similar uncertai nities, reflected in bin -to bin scatter.

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87 CHAPTER 6 CON CLUSIONS In the first project, using classical molecular dynamics, we investigated a homogeneous alkanethiol monolayer and two heterogeneous systems consisting of an alkanethiol monolayer with cis and trans azobenzene molecules on the Au(111) surface. We found that at a temperature of 350K all three systems undergo a phase transition from an ordered tilted structure to a ver tical, liquid like structure. A through analysis of temperature dependent properties such as energy, heat capacity, molecular orientation, radial distribution functions, diffusi on and local disorder was presented. The results indica te that the phase transition is first -order for these 2-D systems. The global properties of the system, such as the nature of the phase transition, diffusion constants, radial distributions and the transition temperature are not strongly affected by the guest molecules. In the second project, penetration of Au ad-atoms through alkanethiol SAMS were analyzed Classical potential para meters were calibrated by quantum me chanical calculations. We found that Au ad-atoms penetrate the alkanethiol monolayers and form buried layers on the Au/S interface. Our results were in agreement with experiments. At 30 0K, we observed ex tensive penetration of Au atoms through the monolayers At 50K, there was no penetration of Au atoms into the monolayer As the coverage was increased, formation of layers on the Au/S interface was observed. To achieve agreement with expe riments, we scaled the (UFF) parameters by a factor of ten. We also performed DOS and PDOS ca lculations to analyze the charge transfer between the alkanethiol monolayer and the Au(111) surface. In the third project, we fou nd that when Ag clusters are pla ced on top of alkanethiol monolay ers, all clusters show ballistic motion for time intervals shorter than a few hundred picoseconds. If the time interval is longer than 1 ns, the lightest cluster continues to move freely over the alkanethiol layer, sliding and rolling over the surface. This motion is similar to crowd

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88 surfing in a concert or sports event. For the largest cluster, the motion was impeded a nd it resembled the motion of a tethered balloon. The behavior of the cluster that consists of 147 atoms w as intermediate between the two limits These results were confirmed by frequency spectra. As we move from the smallest to the largest cluster, the low frequency power component decreases substantially from one to the next.

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97 BIOGRAPHICAL SKETCH Sabri Alkis was bor n in Turkey in the year 1981. He went to high school in Bursa Fen Lisesi. He got a B S in chemistry from Bilkent Univ ersity in 2004. He developed alkaline fuel cells under th e direction of Dr. Borovsky. In the summer 2003, he attended a summer research pr ogramme in Max Plan ck Institute for Coll oids and d id research with Dr. Colfen. He started graduate school at the Universit y of Florida and he specialized in computational nanotechnology under the direction of Dr. Krause and Dr. Cheng. He received a Ph.D i n chemistry in the year 2009.