Novel surface diffusion characteristics for a robust pentacene derivative on Au(1 1 1) surfaces

Accepted Manuscript Novel Surface Diffusion Characteristics for a Robust Pentacene Derivative on Au(111) Surfaces Ryan A. Miller, Amanda Larson, Karsten Pohl PII: DOI: Reference:

S0009-2614(17)30339-1 http://dx.doi.org/10.1016/j.cplett.2017.04.018 CPLETT 34706

To appear in:

Chemical Physics Letters

Received Date: Accepted Date:

4 December 2016 5 April 2017

Please cite this article as: R.A. Miller, A. Larson, K. Pohl, Novel Surface Diffusion Characteristics for a Robust Pentacene Derivative on Au(111) Surfaces, Chemical Physics Letters (2017), doi: http://dx.doi.org/10.1016/j.cplett. 2017.04.018

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Novel Surface Diffusion Characteristics for a Robust Pentacene Derivative on Au(111) Surfaces Ryan A. Miller1,a,∗, Amanda Larsona,2 , Karsten Pohla,3 a Department

of Physics and Materials Science Program, University of New Hampshire, 9 Library Way, Durham, NH 03824

Abstract Molecular dynamics simulations have been performed in both the ab initio and classical mechanics frameworks of 5,6,7-trithiapentacene-13-one (TTPO) molecules on flat Au(111) surfaces. Results show new surface diffusion characteristics including a strong preference for the molecule to align its long axis parallel to the sixfold Au(111) symmetry directions and subsequently diffuse along these close-packed directions, and a calculated activation energy for diffusion of 0.142 eV, about four times larger than that for pure pentacene on Au. The temperature-dependent diffusion coefficients were calculated to help quantify the molecular mobility during the experimentally observed process of forming self-assembled monolayers on gold electrodes. Keywords: Molecular dynamics, Surface diffusion, Organic photovoltaics, Pentacene derivatives, Au(111)

1. Introduction In the field of tailoring p-n junctions of organic photovoltaic (OPV) devices, pentacene is a well-studied donor molecule [1, 2, 3, 4, 5, 6, 7]. Pentacene’s assembly and subsequent dynamics as it forms self-assembled monolayers (SAM) ∗ Corresponding

author [email protected]. P: (909) 664-4780. 2 E: [email protected]. Current address: Tufts University, Department of Chemistry, Medford, MA. 3 E: [email protected]. P: (603) 862-4197. 1 E:

Preprint submitted to Chemical Physics Letters

April 3, 2017

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on metal surfaces have been studied to a great extent. It is a flat, planar molecule consisting of five adjacent benzene rings, making it symmetric about its long and short axes. This planarity and symmetry leads to a flat adsorption on Au(111) surfaces with the molecules forming ordered substructures [2]. Furthermore, molecular simulations have shown that pentacene molecules are

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mobile on Au(111) surfaces at room temperature due to their relatively low diffusion activation energy of 0.041 eV (calculated), and at low temperatures there is a relatively anisotropic diffusion along the Au(111) substrate symmetry directions [1]. While pure pentacene itself serves as an effective donor molecule, it has criti-

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cal drawbacks including photooxidation, which limits its charge-carrying ability. To mitigate these effects, a new class of pentacene derivatives with substituents at the 6 and 13 positions (the top and bottom of the molecule’s short axis) have emerged that aim to tailor the base molecule towards more effective electrical and structural properties [8]. Among these derivatives is 5,6,7-trithiapentacene-

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13-one (TTPO) [9]. As a small-molecule organic semiconductor, TTPO has several beneficial qualities including good solubility, very high thermal stability up to 450◦ C, parallel-displaced, head-to-tail crystallization which melts around 350◦ C without decomposition, and variable-temperature transistor behavior with increased charge-carrying ability at increased temperature [9]. Scanning

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Tunneling Microscopy (STM) studies have shown that TTPO can be thermally evaporated to produce very uniform thin films with a unique configuration of individual TTPO molecules on Au(111) surfaces [10], notably that its assembly on gold is angled, whereas pentacene lies flat [11]. Therefore, studying the unique structure and dynamics of TTPO on gold surfaces will provide new insight and

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understanding of this class of molecule-substrate systems. Room temperature STM studies of the self-assembly of TTPO into wellordered molecular monolayers on Au also revealed a very high mobility of TTPO molecules during the nucleation of the SAM [10], despite the presumed strong interaction of TTPO’s thiol bridge with the Au surface. Because scanning probe

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techniques have time resolution on the order of seconds, molecular dynamics 2

(MD) simulations have been employed to gain a better understanding of the surface diffusion characteristics of this important system. In addition to being able to describe the system down to the atomic level, timescales down to picoseconds and below can be probed to analyze molecular dynamics behavior. 40

By exploring molecular TTPO surface diffusion on Au(111) via MD simulations, we were able to determine important parameters characteristic to molecular surface diffusion such as activation energy barriers and diffusion coefficients. We found new surface diffusion characteristics including a strong preference for the molecule to align its long axis parallel to the sixfold Au(111) symmetry di-

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rections and subsequently diffuse along these close-packed directions, and an activation energy for diffusion of 0.142 eV.

2. Methodology 2.1. Simulation Details To study for the first time the surface diffusion characteristics of TTPO, MD 50

simulations were performed in two frameworks. Quantum-mechanical based (ab initio) simulations fully relax the coupled electronic wavefunctions selfconsistently at each timestep while evolving the atomic configurations in the molecules and are therefore considered to be the most accurate form of molecular simulation. However, these are extremely time consuming and only very

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small timescales can be sampled for a reasonably large system. In contrast, molecular mechanics (MM) simulations approximate each pairwise atomic interaction with a closed-form analytic expression and therefore run orders of magnitude faster. Though they introduce approximation into the simulation, MM simulations can be used to successfully model large-scale molecular behav-

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ior that would otherwise be computationally infeasible with ab initio approaches [6, 7, 12, 13, 14, 15] The ab initio simulations were run with the Quantum ESPRESSO (QE) package [16]. Specifically, the Car-Parrinello (CP) [17] technique was employed within QE along with Vanderbilt Ultrasoft Pseudopotentials to simulate core

3

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electron behavior. Periodic boundary conditions were employed in the x, y, and z directions. Kinetic energy cutoffs of 30.0 Ry and 400.0 Ry were used for the wavefunctions and charge densities, respectively. The MM simulations were performed using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) software package [18]. The gold sub-

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strate was simulated with the embedded-atom model (EAM) [19]. The TTPO molecules were constructed using an all-atom method with the following energy terms: harmonic bonds, harmonic angular energy, and dihedral torsional energy. A Lennard-Jones potential was used to simulate long-range molecular interaction, and a Morse potential to represent the Au-S, Au-C, and Au-H interactions.

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The Au-S interaction requires particular attention since it is a partially covalent, partially ionic bond, and the pairwise potential must be tailored to take this into account. The Morse potential has modeled this behavior successfully before [20, 12, 21, 22] and was used in this study with the form shown in Equation 1: Emorse = D0 [e−2α(~x−~x0 ) − 2e−α(~x−~x0 ) ]

(1)

Table 1 displays all non-Coulombic parameters of the pairwise and bonded/non80

bonded parameters used in this study. The AMBER94 [23] and GAFF [24] force field databases were used to find interaction parameters for many common atomic interactions, indicated in Table 1. All LAMMPS simulations were performed with periodic boundary conditions in the x,y directions and a fixed boundary in the z direction.

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Table 1: Interaction Parameters for LAMMPS Simulations

Interaction Interaction Type Value Reference Au-Au EAM N/A N/A Au-S Morse D0 = 0.138, α = 1.38, r0 = 2.903 [12] Au-C Morse D0 = 0.0096, α = 1.013, r0 = 4.104 [13] Au-H Morse D0 = 0.0031, α = 1.166, r0 = 4.006 [13] Au-O LJ  = 0.00392, σ = 2.946 [25]* C-C LJ  = 0.00372, σ = 3.399 [23] H-H LJ  = 0.00065, σ = 2.599 [23] O-O LJ  = 0.00910, σ = 2.959 [23] S-S LJ  = 0.0108, σ = 3.563 [23] C=O Bond Kbond = 24.72, r0 = 1.229 [23] C-C Bond Kbond = 12.579, r0 = 1.55 [24] C-H Bond Kbond = 15.914, r0 = 1.08 [23] C=S Bond Kbond = 10.563, r0 = 1.79 [23] S-S Bond Kbond = 7.198, r0 = 2.038 [24] C=C Bond Kbond = 20.340, r0 = 1.400 [23] C-S Bond Kbond = 14.262, r0 = 1.675 [24] H-C-C Angle Kθ = 1.51, θ0 = 120 [23] C-C-C Angle Kθ = 2.73, θ0 = 120 [23] S-C-C Angle Kθ = 2.69, θ0 = 120 [24] O-C-C Angle Kθ = 3.11, θ0 = 120 [24] H-C-C-C Dihedral KD = 0.157, d = −1, n = 2 [23] H-C-C-H Dihedral KD = 0.157, d = −1, n = 2 [23] C-C-C-C Dihedral KD = 0.157, d = −1, n = 2 [23] O-C-C-C Dihedral KD = 0.130, d = −1, n = 2 [24] S-C-C-C Dihedral KD = 0.157, d = −1, n = 2 [24] ∗−Computed manually from Au-Au and O-O parameters from mixing rules. All energies are in eV, angles in degrees, and distances in ˚ A.

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TTPO is an inherently dipolar molecule, with a dipole moment extending from the central sulfur atom (positively charged) to the oxygen atom (negatively charged). To capture the effect of atomic charges on the molecular trajectories, a Coulombic potential of the form

EC =

Cqi qj r

was used, where C is an energy conversion constant (set to 1 here), and  is 90

the dielectric constant (set to 1.0). The partial charges on the TTPO molecule were assigned based on the Natural Bond Order population analysis performed

5

in [26] and are shown in Figure 1.

Figure 1: Partial charge distribution of a TTPO molecule, in units of e. Reprinted with permission from [26]. Copyright 2014 American Chemical Society.

For all simulations a Nos´e-Hoover (NH) [27, 28] thermostat was used to control the temperature of the substrate and diffusing TTPO molecules. This method 95

essentially couples the system to a fictitious heat bath (through an extra degree of freedom in the system’s Hamiltonian) that will act as a friction term to either dampen or accelerate atomic motion in a way that simulates the user-defined ambient temperature. 2.2. Physical Model

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STM images in Ref. [10] suggest low-coverage TTPO molecules to be highly mobile on a flat, pristine surface, and there to be little to no organization in assembled substructures. To overcome the poor time resolution of STM we employed simulations to study the diffusion of thermally-deposited TTPO molecules and their cluster nucleation on Au(111). Ab initio calculations were

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employed to study the diffusion along close-packed directions, indicated by the red lines in Figure 5(b). The Density Functional Theory (DFT) simulations consisted of a one-layer slab of 60 fixed gold substrate atoms and two TTPO molecules deposited on top. The cell was equilibrated to a temperature of 300 K via the NH thermostat and ran for 5 ps with a timestep of 0.25 fs. The TTPO

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molecules were placed at a non-equilibrium position close to the surface initially to ensure they would stay adsorbed to the surface. As stated previously, classical simulations allow for much larger unit cells to be explored. Thus, the majority of the simulations in this study were run 6

in this framework, with the ab initio simulations providing additional support. 115

Simulations to investigate close-packed direction diffusion were run with fivelayer gold slabs, with the top three layers now allowed to move in the three Cartesian directions. Four TTPO molecules were placed far from each other to minimize intermolecular interaction. The unit cell contained 10,512 atoms and ran for over 400 ps. The simulations to calculate diffusion coefficients and

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activation energies were run with a three-layer gold slab, where the top layer was allowed to relax, and 48 TTPO molecules placed in random orientations at appropriate adsorption distances. The initial tilt angles (the angle between the short axis of the molecule and the horizontal plane of the gold surface) and initial facing direction were randomized. The initial setup of the system used

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to calculate diffusion coefficients is depicted in Figure 2.

Figure 2: Initial setup for the diffusion coefficient simulations. The direction each molecule was facing and the tilt angle (between the axis formed by the oxygen atom (red) and central sulfur atom (yellow), and the surface plane) were randomized for each molecule. The molecules were placed close to the surface so they would properly adsorb.

Simulations were run at temperatures of T=200 K, 260 K, 280 K, 320 K, 340 K, 360 K, 420 K, 500 K, and 600 K. All LAMMPS simulations were performed with a timestep of 250 fs and a damping constant for the NH thermostat of 12.493 ps.

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2.3. Activation Energy for Diffusion Surface diffusion is, in part, a thermally activated process. At low temperatures, molecule-substrate interactions dominate the intramolecular thermal vibrations, causing molecules to remain stationary. However, increasing the temperature (the introduced thermal energy ∼ kB T ), provides the adsorbed

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species with sufficient energy to overcome the diffusion barrier and be able to explore adjacent adsorption sites. The temperature dependence of kinetic processes give insight to the energetics involved in diffusive processes. One method of analyzing diffusion characteristics is by fitting mean-squared displacement (MSD) data to an Arrhenius model. The energy landscape of a

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smooth surface like a wide, flat Au terrace can be thought of as a series of potential wells, shown in Figure 3. In practice, this is an obvious oversimplification: the exterior shell of valence electrons on a gold surface do not represent spherical cavities, but consist of a complex map of orbitals in which electrons are most likely to be found. However, by reducing the idea of diffusion to this “hill

145

and valley” model, valuable insight can be gained into the kinetics of TTPO diffusion through classical MD simulations.

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(a)

(b) Figure 3: Two representations of the Au(111) surface. (a) An idealized version of the periodic potential energy landscape along the surface. The crests (“peaks”) are areas of higher potential energy, and the troughs (“valleys”) are regions of lower potential energy. (b) Two different configurations of adatoms on a metal surface. When the adatom is directly over a surface atom, it is a high-energy configuration and is unstable, since the adatom would prefer to lower its potential energy to a configuration like the stable position shown. Figure inspired by [29].

Surface diffusion is a more complex process for an extended molecule like TTPO. A hierarchy of interactions are governing the adsorption/ diffusion kinetics of the TTPO-Au system: the (relatively) weak Van der Waals attraction 150

from the pentacene backbone and oxygen atom to the gold surface atoms, and the strong S-Au partially-covalent bond. However, the molecule will still seek to minimize its potential energy by seeking local energy minima along the surface. Since the molecules are on a periodic lattice of gold atoms (and therefore a repeating “hill and valley” potential energy landscape as shown in Figure 3),

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it is reasonable to suspect that they will transition from one local minimum

9

site on the surface to an adjacent site. An activation energy barrier exists for this thermally activated process to occur, the details of which can be extracted from the Arrhenius Equation. This is an equation that models the temperature dependence of a kinetic constant in a chemical reaction. In the present case, 160

it can be used to extract the activation energy for diffusion by considering the diffusion coefficients from the models described above. The Arrhenius Equation to be used here is D(T ) = D0 e−Ea /kB T

(2)

where D is the diffusion coefficient, D0 is a pre-exponential factor, and Ea is the activation energy barrier for diffusion. By plotting the logarithm of D vs. 165

1/kB T , the slope will be equal to −Ea . By analyzing the precise dependence of D on T, one can get a better understanding of the energetics of TTPO surface diffusion on gold.

3. Results 3.1. Diffusion Along Close-Packed Directions 170

Two simulations were run with the specifications explained previously, one in the DFT framework and one in the classical regime of LAMMPS. The results for the DFT simulation are summarized in Figure 4.

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(a) 1 ps

(b) 3.75 ps

(c) 5.25 ps Figure 4: A small DFT simulation showing a clear preference for alignment of the sulfur bridge along a close-packed direction. (a) During the first ps after initial placement, the molecules lowered themselves to the surface and raised their temperatures to 300K, but remained very close to the initial configuration. (b) Until 3.75 ps the top molecule rotated 60◦ clockwise to align its sulfur bridge along a close-packed direction. (c) During the 5th ps the top molecule moved about one lattice site along the direction of the blue arrow, which is the plane associated with the close-packed symmetry direction. The bottom molecule can be seen aligning along this symmetry direction as well.

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Even during a short run of 5.25 ps, there is a clear preference for the molecule to align its sulfur bridge along a close-packed symmetry direction and then sub175

sequently begin to diffuse along this direction, with the sulfur atoms remaining aligned in this orientation. This is indicative of the substrate surface anisotropy helping to direct the diffusion of the TTPO molecules, making the surface diffusion process less random and therefore easier to predict. The DFT simulation unit cell above was restricted to a representation of the

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Au substrate by one layer of 60 Au atoms per unit cell to handle the computational demand. Therefore, it might not seem surprising that the sulfur bridge aligned itself with a symmetry direction since the surface atoms were not transferring thermal energy to the molecules, and the most stable configuration of the sulfur atoms is given by the highest bonding coordination (similar to Figure

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3(b)). The same effect was seen with a MM simulation with five substrate layers, the top three of which were free to relax and thus transferring more energy to the TTPO molecules. The results of the MM simulation are shown in Figure 5.

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(a) 397.5 ps

(b) 407.5 ps

Figure 5: LAMMPS simulation at 300K showing an isolated TTPO molecule traveling along a close-packed symmetry direction. The molecule traveled approximately two lattice sites (twice as far as in the above DFT simulation) while maintaining its alignment along the symmetry direction. The blue arrow in (b) indicates the direction of motion along the symmetry plane, and the red lines show the sixfold symmetry for reference.

Naturally, the molecule did not maintain perfect alignment along this direc190

tion when the temperature effects were included (as can be seen by the slight twist about an axis normal to the surface in Figure 5(a)). The thermal motion of the system causes the molecule to be less stable even at local minimum sites, and the alignment along close-packed directions becomes less predictable. The thiol bridge would remain aligned parallel to the symmetry direction and dif-

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fuse in this orientation only for a few lattice sites before twisting and changing directions. Sometimes molecules would diffuse via a completely different process, such as hopping over the gold atoms. Despite the chaotic behavior, the molecules tended to show a definite preference for wanting to align their sulfur atoms along these symmetry directions. This is consistent with the relative

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strengths of the S-Au interaction and the pentacene backbone-Au interaction. The S-Au interaction energy has been characterized to be 1.95 eV (calculated) [30], while the benzene-Au interaction has been calculated to be between 0.776 13

eV and 0.850 eV for different, flat adsorption orientations on the Au(111) surfaces [13]. The benzene interaction with the Au surface is much weaker, and 205

since the pentacene backbone of TTPO is comprised of five adjacent benzene rings, the interaction of this backbone with the surface is much weaker than the (more localized) S-Au bond. Therefore, this latter interaction will dominate the surface mobility. The anisotropic diffusion is determined by the sulfur atoms seeking their lowest-energy configuration by aligning themselves along

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the six-fold symmetric “trough” directions shown in Figure 3(a) (compare to red lines in lower right corner of Figure 5(b)), and using these directions as a low-energy avenue to diffuse. There were multiple cases of mobility along these directions, even at room temperature. This result was seen in both the DFT and classical frameworks and shows that while the diffusion process does not

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obey one definite mode, the anisotropy of the substrate defines the mobility of TTPO diffusion on Au(111). 3.2. Activation Energy for Diffusion Larger simulations described previously were run to determine diffusion coefficients and activation energies. While the lengths of the simulations varied, the

220

calculations were stable through 30,000,000 timesteps (7.5 ns). At the higher temperatures (360 K, 420 K, 500 K, 600 K), the computations grew unstable after a few million timesteps and the simulation stopped. However, the trajectories persisted for several million timesteps at the appropriate temperature with MSD data that are in line with the more stable simulations. After initial

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energy minimization, the system was heated to a temperature T, and MSD data were transferred every 10,000 timesteps for the center of mass of each molecule, then the MSDs for each molecule were averaged at each timestep to obtain the average MSD for that timestep. The data for the linear MSD fits and the corresponding diffusion coefficients

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are shown in Table 2. Since surface diffusion occurs primarily in the xy-plane and dz 2 ≈ 0, it is a better approximation to set the MSD slope proportional to 4Dt, where D is the diffusion coefficient instead of 6Dt (as in three dimensional 14

diffusion). Table 2: Diffusion Coefficients for TTPO on Flat Surface

T(K) 200 260 280 320 340 360 420 500 600

2

Slope (˚ A /fs) 1.198 × 10−5 2.07 × 10−5 4.815 × 10−5 6.064 × 10−5 0.000359 0.000248 0.000622 0.00037 0.0033

2

y-intercept (˚ A ) 282.3 261.4 330.6 370.2 264.6 207.4 -253.2 311.9 -1287

Diffusion Coefficient (cm2 /s) 2.995 × 10−7 5.175 × 10−7 1.204 × 10−6 1.516 × 10−6 8.975 × 10−6 6.2 × 10−6 1.555 × 10−5 9.25 × 10−6 8.25 × 10−5

From Equation 2, the natural logarithm of the diffusion coefficients can be 235

plotted against 1/kB T to yield the activation energy associated with TTPO diffusion on a flat gold surface. This Arrhenius Plot is shown in Figure 6. Arrhenius Plot, Flat Terrace -10 lnD vs. 1/kT Linear Fit

ln(D)

-11 -12 -13 -14 -15 20

25

30

35

40

45

50

55

1/k B T

Figure 6: Arrhenius plot for a flat, smooth, three-layer gold slab. The parameters for the fit (with 95% confidence bounds in parentheses) are: slope = -0.142 (-0.1919, -0.092) eV, y-intercept = -7.462 (-9.304, -5.619).

From this plot, the pre-exponential factor D0 is 0.000574 cm2 /s, and the activation energy for diffusion Ea is equal to 0.142 eV. The diffusion barrier came out to about four times larger than that reported for pentacene in [1], where 240

it was found that pure pentacene faces a diffusion barrier of 0.041 eV in the x and y directions (calculated from DFT-based simulations). The value obtained 15

here for TTPO diffusion is completely consistent with our understanding that the S-Au interaction in TTPO is much stronger than the interaction of pure pentacene with the Au surface. Also, by inspection of the data in Figure 6, it is 245

clear that the mechanisms by which TTPO moves across a gold surface are not trivial. For a simple monatomic, non-interacting (with other adatoms) particle on a surface, the data would better trace out a straight line on an Arrhenius plot with little deviation. The activation energy would then likely correspond to a hopping from a local minimum in an interstitial site to an adjacent site, or

250

a similar simple diffusion scheme. However, TTPO is a relatively large molecule with a complicated interaction profile with the substrate and with other adsorbed molecules. While the plot does not provide the exact methods in which TTPO moves, it provides an estimate for the energies involved with TTPO diffusion. For example, compared with room temperature (≈ 0.025 eV), the ac-

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tivation energy calculated here is about an order of magnitude higher. However, TTPO has been seen via STM to diffuse at room temperature [10]. Therefore, other factors are surely involved. This is likely a combination of the substrate supplying energy to a molecule (so that it has sufficient energy to jump sites), and lateral effects from the substrate and other molecules (a “pulling” from the

260

other molecules and laterally-positioned substrate atoms). Hence, while surely affected greatly by thermal effects, it is not purely thermally-activated diffusion.

4. Conclusions This work investigated for the first time the underlying surface diffusion characteristics of the pentacene derivative TTPO on Au(111) surfaces through 265

molecular dynamics simulations in the ab initio and molecular mechanics frameworks. This work complements our earlier experimental and computational work [10] on the self-assembly of TTPO on flat, wide Au(111) terraces into well-ordered monolayers. The main conclusions of our study are the following: First, the DFT cal-

270

culations gave the first insight into a preferential direction of alignment and

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diffusion for TTPO molecules. The molecule clearly aligned its sulfur bridge along one of the sixfold symmetry directions of the Au(111) surface and then moved along that direction, indicating that the atomic coordination of the gold surface determines the mobility of the molecules. This DFT result is in perfect 275

agreement with what was seen on a much larger and more energetic system in the MM model at elevated temperatures. However, the molecule clearly does not diffuse exclusively via this mode, but it was observed to repeatedly try to align its sulfur bridge along one of the close-packed directions. These key results provide some new understanding towards the mechanisms in which novel

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TTPO diffuses on a Au(111) surface, and can eventually help to understand how larger-scale TTPO substructures may form into ordered monolayers on the gold substrate. Moreover, diffusion coefficients were calculated for several temperatures of 48 TTPO molecules on a flat Au terrace, and are shown in Table 2. By plotting

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the diffusion coefficients versus inverse temperature, an activation energy for diffusion of 0.142 eV was found for TTPO on flat gold, which is half an order of magnitude higher than that reported for pentacene in [1]. This is consistent with the much higher binding energy of the sulfur bridge with the gold surface compared to the (relatively weak) pure pentacene interaction with the surface.

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Diffusion mode analysis would need to be performed to explore the actual methods in which TTPO diffuses to see what modes of diffusion contribute to this activation energy, but the value found in this study indicates that the energies involved in the diffusion modes are consistent with previously-studied similar systems.

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5. Acknowledgments This study was partially supported by the Nanoscale Science and Engineering Center for High-rate Nanomanufacturing (NSF EEC-0425826) and by NSF DMR-1006863. The computations were performed on Trillian, a Cray XE6m200 supercomputer provided to the University of New Hampshire through NSF

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MRI grant PHY-1229408. The authors thank the Trillian staff for their support throughout the project. The authors also thank Dr. Harish Vashisth for insightful discussions.

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Article Highlights • • • •

Molecular dynamics simulations were performed in the classical and ab initio frameworks Anisotropic diffusion was observed along six-fold substrate symmetry directions Diffusion coefficients for various sampled temperatures were calculated The temperature-dependent diffusion coefficients yielded an activation energy of 0.142 eV