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Theoretical Modeling of Tribochemical Reaction on Pt and Au Contacts: Mechanical Load and Catalysis Yubo Qi, Jing Yang, and Andrew M. Rappe ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.5b12350 • Publication Date (Web): 24 Feb 2016 Downloaded from http://pubs.acs.org on March 1, 2016

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ACS Applied Materials & Interfaces

Theoretical Modeling of Tribochemical Reaction on Pt and Au Contacts: Mechanical Load and Catalysis Yubo Qi, Jing Yang, and Andrew M. Rappe∗ 1

The Makineni Theoretical Laboratories, Department of Chemistry, University of Pennsylvania, Philadelphia, PA 19104-6323 USA E-mail: [email protected]

Phone: 215-898-8313. Fax: 215-573-2112

Abstract

2

3

Micro–electro–mechanical system and nano–electro–mechanical system (MEMS and

4

NEMS) transistors are considered promising for size–reducing and power–maximizing

5

electronic devices. However, the tribopolymer which forms due to the mechanical load

6

to the contacts affects the conductivity dramatically. This is one of the challenging

7

problems that prevent the widespread practical use of these otherwise promising de-

8

vices. Here, we use density functional theory (DFT) to investigate the mechanisms of

9

tribopolymer formation, including normal mechanical load, the catalytic effect, as well

10

as the electrochemical effect of the metal contacts. We select benzene as the background

11

gas, because it is one of the most common and severe hydrocarbon contaminants. Two

12

adsorption cases are considered: one is benzene on the reactive metal surface, Pt(111),

13

and the other is benzene on the noble metal, Au(111). We demonstrate that the for-

14

mation of tribopolymer is induced by both the mechanical load and the catalytic effect

15

of the contact. First, benzene molecules are adsorbed on the Pt surfaces. Then, due ∗

To whom correspondence should be addressed

1

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to the closure of the Pt contacts, stress is applied to the adsorbates, making the C–H

17

bonds more fragile. As the stress increases further, H atoms are pressed close to the Pt

18

substrate and begin to bond with Pt atoms. Thus Pt acts as a catalyst, accelerating

19

the dehydrogenation process. When there is voltage applied across the contacts, the

20

catalytic effect is enhanced by electrochemistry. Finally, due to the loss of H atoms,

21

C atoms become more reactive and link together or pile up to form tribopolymer.

22

By understanding these mechanisms, we provide guidance on designing strategies for

23

suppressing tribopolymer formation.

24

KEYWORDS: tribopolymer, Pt and Au contacts, mechanical load, catalysis, reaction path

25

Introduction

26

Metal oxide semiconductor field effect transistors (MOSFETs) are the fundamental compo-

27

nents in electronic logic devices. Moore’s law predicts that the number of transistors in a

28

defined size electronic device doubles every two years. Effort toward shrinking the MOSFET

29

scale is always ongoing, but a vital challenge is that the leakage current becomes unac-

30

ceptably large as the MOSFET size decreases. 1 Besides, the minimum subthreshold swing

31

S = 60 meV/decade sets a lower limit for energy dissipation in the MOSFET operation. 2,3

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To overcome these problems, microelectromechanical system (MEMS) switches are being

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developed. 4–8 The source and drain electrodes are separated by an air gap, and they can also

34

be connected by an adjustable conductive bar. Such an electronic device has nearly zero

35

leakage current, and the minimum subthreshold swing also breaks the S = 60 meV/decade

36

limitation. However, a prime concern about this approach is the stability of the electrical

37

contact resistance (ECR): a hydrocarbon contaminant forms on the surfaces of the electrodes

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and on the conductive bar after many switching cycles. This tribopolymer may increase the

39

ECR beyond the tolerance of logic applications. 9–13

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The study of the reliability of MEMS devices has been a fast–moving field. 14 In MEMS

41

devices, Pt and Au are two common electrodes in use. The benefits of using Au electrodes 2


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are corrosion retardation, low resistivity, and ease of deposition. 15–17 However, Au is a soft

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metal with low cohesive energy, so surface wear and material transfer are the main drawbacks

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of Au contacts. Also, some contamination can still form after electrical cycling. 9,18 As for

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Pt contacts, previous experiments showed that tribopolymer is more prone to form on Pt

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than on Au. Wabiszewski et al. used atomic force microscopy (AFM) to mimic the Pt/Pt

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electrical contacts. The ECR after cycling was six orders of magnitude higher than before

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. 19 Brand et al. observed considerable amounts of tribopolymer formation on Pt contacts,

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leading to a dramatic increase of ECR. 11,12

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For Pt contacts, the rate of formation and the amount of tribopolymer are related to how

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the MEMS switches are operated. 11,12 Three types of switching-cycle mechanisms are consid-

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ered in their experimental setup: cold switching, hot switching, and mechanical switching.

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In cold switching, voltage is applied after the two contacts are closed, and removed before

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the contacts open. In hot switching, voltage is applied across the device the entire time,

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whether the contacts are closed or open. In mechanical switching, in order to better un-

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derstand the role of electrochemistry relative to other effects, the contacts undergo cycles of

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closing and opening without applying any voltage. When a voltage of 5 V was applied across

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the contacts during the cold–switching cycle, a large amount of tribopolymer was generated.

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However, interestingly, even in mechanical switching, the tribopolymer is still formed, but

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less compared to the cold switching protocol. In this work, we applied a computational com-

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pression experiment to study the effects of mechanical stress and catalysis on tribopolymer

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formation.

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Methodology

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It is believed that the tribopolymer results from the polymerization of hydrocarbon gases

65

from the atmosphere or from packaging. Among them, benzene is the one which causes the

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most severe contamination. 13 Therefore, benzene is selected as the background gas in our

3



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study. In order to investigate tribopolymer formation on Pt contacts in a benzene atmo-

68

sphere, we conducted compression computational experiments with first–principles density

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functional theory (DFT) calculations. Au contacts are also studied as a control system to

70

illustrate the tribopolymer formation mechanism. All calculations are performed with the

71

plane–wave DFT package Quantum–espresso 20 using the generalized gradient approxi-

72

mation (GGA) exchange correlation functional. A plane–wave cutoff energy of Ecut ≈ 680 eV

73

and an 8×8×1 Monkhorst–Pack k–point mesh 21 are used for energy and force calculations.

74

All atoms are represented by norm-conserving pseudopotentials generated by the OPIUM 22

75

code with a plane-wave cutoff, ~2 qc2 /2me ≈ 680 eV. The maximum threshold for atomic force

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convergence is set as 5.0×10−3 eV/Å per atom.

77

A supercell geometry is used with periodically separated metal slabs and two benzene

78

molecules per surface between the slabs to model metal contacts in a benzene atmosphere.

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A four–layer metal slab is used to simulate top and bottom contacts. FIG. 1 shows the

80

initial setup of the supercell structures. The space between the top and bottom contacts

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is 9.3 Å. The vertical distance between the two parallel benzene molecules is selected to be

82

4.1 Å, so that the two benzene molecules have little interaction. In the initial structure, the

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benzene molecules are intact without any deformation. The distance between one benzene

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molecule and its closest metal contact is 2.6 Å. At this distance, the benzene molecule has an

85

attractive adsorption force toward the contact, and no stress is required to press the molecule

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to such a position. After the relaxation, the two benzene molecules are strongly chemisorbed

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on the top and bottom contacts. Once the adsorption system is fully optimized, the value

88

of the distance between each pair of neighboring metal atomic layers, a, is decreased by ∆a.

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Since there are three intervals in the four–layer slabs, the height of the supercell is reduced

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by 3∆a in total in each compression step. At the beginning, the value of ∆a is selected

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as 0.2 Å. Once any significant deformation of the adsorbates is observed, we decrease ∆a

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to 0.02 Å or less, in order to have a subtle observation of the structural changes correlated

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with the height of the supercell. Then, we optimize the compressed system, and after the

4


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relaxation, we repeat this compression and optimization process. Our manual adjustment of

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the supercell is analogous to applying stress to the adsorbed benzene. As the compression

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process goes on, the normal load (stress) increases. The average stress is calculated from the

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energy of the system and the dimension of the supercell

σ=−

1 ∂E S ∂z

(1)

98

where σ is the stress along the z direction of the system, E is the energy of the system, and

99

S is the area of the surface. Since we have optimized the structure to equilibrium, the stress

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in the supercell is approximately uniform and the stress on the molecules is the same as the

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average one.

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Energy barriers are calculated with the nudged elastic band (NEB) method implemented

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in the Quantum–espresso package. The optimization scheme is the quasi–Newton Broy-

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den’s second method. Path optimization stops when the norm of the force orthogonal to the

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path is less than 0.05 eV/Å.

106

Results

107

In Pt–benzene systems, we choose three different registries as shown in FIG. 1. In registry

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(1), there is one carbon atom overlapping between the two benzene molecules from the top

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view. In the second registry, there is no carbon atom overlap. In registry (3), the two

110

benzene molecules have a relatively large overlap.

111

During the relaxation, the compressed electrodes will recover to a new equilibrium struc-

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ture, and hence will expand and squeeze the center vacuum space. The adsorbed molecules

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at the center will sense the stress applied by the two closing contacts. We conduct compres-

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sion computational experiments and observe that for all three different registries, when the

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height of the supercell is reduced to 11.06 Å, chemical reaction occurs: some hydrogen atoms

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dissociate from the adsorbed benzene molecules, making them less saturated. The carbon 5



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(a)

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(b) Top View of three different registries

Benzene molecules are placed at different locations

{ {

Compressed Compressed

{

Not Compressed

{

Compressed

a (1) One C atom overlap 2.6

4.1 (2) No C atom overlap

z

y (3) A large overlap

x

y

z

x

Figure 1: Ball–and–stick model of the initial registries of two benzene molecules. The lattice vectors of the supercell are v1 = (8.117, 0.000, 0.000), v2 = (4.058, 7.029, 0.000) and v3 = (0.000, 0.000, 16.461). (a) Side view of the compression supercell setup with 4–layer Pt (111) slab and two benzene molecules. Compression is initially applied to the metal interlayer spacings, leaving the center vacuum uncompressed (Pt = light grey, C = brown, H = light pink). (b) Top view of three different benzene initial registries on upper and lower Pt slabs. The left panel shows the entire supercell. On the right panel, all benzene molecules sit on the hollow site (three C atoms on top of Pt atoms and three in the Pt 3–fold hollow) of the Pt surfaces with different horizontal intermolecular distances: (1) two carbon directly overlapped, (2) the furthest, no overlap at all, (3) significantly overlapped.

6


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atoms which lose their bonded hydrogen atoms form a C–C bond making a biphenyl–like

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structure, as shown in FIG. 2.

Side View

Top View

(1)

(2)

(3)

Figure 2: Side and top views of the biphenyl–like structure formed after the height of the supercell is reduced to 11.06 Å for the three different registries described in Fig. 1. Each view consists of 2×2×1 supercells. For clarity, in the top view, only the adsorbates and the first layer of Pt atoms beneath are shown.

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In the following part, we take a more detailed look at the formation of the biphenyl–like

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structure. For the structure without any compression, the benzene molecules adsorb on the

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surface and distort to become non–planar. The adsorption is at the hollow site, as it is the

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most favorable position, 23 as shown in FIG. 4 (a). The C–C bonds are around 1.5 Å, which is

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approximately the length of C–C single bond. These indicate the chemisorption of benzene

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on Pt(111) surface. The bonding between C and Pt induces the H atoms to move away from

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the surface, indicating sp3 C character. The C–Pt bond distances are approximately 2.1 Å.

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We should also note that before the compression (no external stress applied), the distance

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between one H atom and its closest Pt atom is approximately 2.7 Å, which is much larger

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than the length of a Pt–H bond (1.7 Å). 24 There is no chemical bond between Pt and H 7



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atoms.

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Taking the first registry as an example, the changes of the structure with the height of

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the supercell c and the resulting σ are shown in FIG. 3. When the stress increases to 24.0

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GPa, it can been seen that one H atom is pushed close to a Pt atom, as shown in FIG. 4.

c = 16.46 0.00 GPa

c = 14.66 = 0.91 GPa

c = 12.26 = 21.8 GPa

c = 12.08 = 24.0 GPa

c = 14.06 = 2.60 GPa

c = 11.78 = 22.9 GPa

c = 13.46 = 8.40 GPa

c = 12.86 = 15.2 GPa

c = 11.66 = 29.4 GPa

c = 11.06 = 47.7 GPa

Figure 3: Ball–and–stick model of the entire compression process of the supercell with benzene on the Pt(111) surface. c is the length of the supercell along the z–direction. σ is the stress of the supercell at each c value. At c = 11.78 Å and σ = 22.9 GPa, the biphenyl–like structure forms.

133

As we compress the system further, a C–H bond breaks, and the H atom is attached

134

to the Pt substrate. The adsorption position of the dissociated H atom is the hollow site,

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which is the most stable one. 25 Two C atoms which lose their H atoms form a C–C bond,

136

and connecting the carbon rings builds a biphenyl–like structure. The adsorbed benzene

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molecules are on the way to more dramatic change: (1) H atoms can fall off due to further

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compression. The detached atoms may form H2 and escape into the atmosphere, which

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indicates that the dehydrogenation is a non–reversible process; (2) C atoms which lose their H

140

atoms become less saturated and more reactive. As these processes continue, more hydrogen

141

atoms may fall off, and reactive C atoms link with others or even pile up, forming a two 8


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(a)

(e)

(b)

120

(c)

Pt-C-H Angle q (°)

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(d)

Reaction occurs

110

100

90

H atom Dissociation

Formation of C-C bond 80

12

14

16

Height of the Supercell (Å)

Figure 4: Ball–and–stick model of detailed benzene bonding geometry and reactivity on Pt (111). (a) Benzene molecule adsorbed at the hollow site. The lengths of the Pt–C bonds are 2.1 Å, and the C–C bonds are 1.54 Å; (b) Part of the structure of the Pt–benzene system with c = 12.08 Å and σ = 24.0 GPa. One H atom is pressed close to a Pt atom; (c) The H atom dissociates from the adsorbed benzene; (d) A biphenyl–like structure forms; (e) The plot of supercell height vs. the Pt–C–H angle. As the compression goes on, the angle is reduced, indicating that the H atoms are pressed toward the Pt contact.

9



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142

dimensional or three dimensional C–rich network. The biphenyl–like linked rings (Fig. 4)

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can be viewed as the primary step of tribopolymer formation.

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To further investigate the dehydrogenation and polymerization processes, we use the

145

NEB 26 method to calculate the energy barrier at different unit cell heights, as shown in Fig.

146

5. Initial structures with different supercell heights provide different stress/mechanical loads.

147

The calculated unit cell height dependence of reaction energies is shown in FIG. 6 (a). For

148

stress below 24.22 GPa, there is a linear relation between stress and reaction barrier, which

149

is consistent with a Brønsted–Evans–Polanyi (BEP) relationship 27–29 as expressed

∆Eact = α∆H = αF · ∆d

(2)

150

where ∆Eact is the change of activation energy Eact , α (0 ≤ α ≤ 1) is a constant which

151

characterizes the position of the transition state, H is the enthalpy of the reaction, F is the

152

applied force, which is proportional to the stress, and ∆d is the distance that the force F

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moves though along the reaction coordinate. As we increase the stress and the dimension of

154

the system shrinks by ∆d, a work W = F · ∆d

(3)

155

is applied to the system. This energy is added to the adsorbates, promoting the reaction, as

156

shown in Fig. 5 (b). If the stress increases further, the energy barrier drops to zero within

157

just a 0.2 GPa period, as in Fig. 6 (a) and (b). This breakdown of the BEP relationship is

158

attributed to the catalysis effect of Pt. Compression not only adds energy to the adsorbates,

159

but also presses hydrogen atoms close to the Pt substrate, changing the reaction pathway.

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Pt, as a catalyst, can weaken the C–H bond and reduce the reaction energy barrier. 30–32 The

161

stronger the Pt–H interaction is, the lower the energy barrier is.

162

The reaction occurs when the stress is 24.42 GPa. In the following part, we demonstrate

163

that the threshold stress can be reduced by including the electrochemical effect. Above 24.22

164

GPa, the relationship of the supercell height and energy barrier deviates from linearity. We 10


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165

deduce that from this point, Pt begins to affect the dehydrogenation as a catalyst. The

166

chemical reaction can be expressed as

C6 H6 → C6 H5 · + H+ + e− .

167

(4)

And the reaction energy change due to applied potential U is 33

∗ ∆Eact = ∆Eact − n · e · U

(5)

168

where e is the electron charge and n is the number of electrons involved in the reaction. At

169

24.22 GPa, the energy barrier is 0.051 eV, and in experiments, the applied voltage (5.0 V)

170

during device switching is larger than 0.051 V. Therefore, due to the electrochemical effect,

171

the H atom can get one electron and leave the benzene as soon as it makes electrical contact

172

with the electrode.

173

The process of adsorbed benzene molecules losing H atoms and linking together by C

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bonds can be summarized as: (1) benzene molecules are adsorbed on the Pt surfaces; (2)

175

due to the closure of the Pt contacts, stress is applied to the adsorbate, flattening it and

176

making C–H bonds easier to break. We emphasize that while the H atoms are not close

177

to the Pt substrate, the fragility of adsorbed benzene mainly results from mechanical load

178

(rather than catalytic effect), and the activation energy–stress relationship obeys the BEP

179

relationship; (3) As the stress increases further, the benzene adsorbates become flat enough

180

and the H atoms begin to be attracted to the Pt atoms. Pt weakens the C–H bond and

181

accelerates the dehydrogenation process, as shown in Fig. 5 (b). This effect can also be

182

enhanced by electrochemistry.

183

In the following section, computational compression experiments of a Au–benzene system

184

are analyzed as a contrast with Pt, highlighting the importance of adsorption and catalysis in

185

polymerization. In FIG. 7, the changes of the Au–benzene structure during the compression

186

are shown. At the outset, benzene molecules are not strongly adsorbed on the contact 11



30

No Polymer Formed Polymer Formed

25 20

Energy (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

15 10 5 0 10

12

14

16

Height of the Supercell (Å)

Figure 5: Energetic behavior of the compression process. The energies are relative energies, with the sum of the energies of a clean Pt slab and two free benzene molecules as zero. (a) Total energy vs. height of the supercell during the compression process. Energies of the structures without polymer formation are shown in red, whereas the black points correspond to the polymerized structures. The subplot shows the detailed stress effect on the polymer 1 evolves to , 2 which is the formation process. With mechanical load applied, structure 3 indicating structure one step before the formation of polymer. The energy drops to , the polymer formation. Continued compression of the cell does not lead to additional new 4 is an expansion step back up to the same supercell volume as . 2 species formation. 5 (b) The energy barrier to form the biphenyl Further expansion changes the structure to ; 1 and 5 are tribopolymer, calculated by NEB method. The supercell configurations at taken as the initial and final structures of the reaction. Schematic model demonstrating the change of the energy barrier is also shown. At the beginning, mechanical load raises the energy levels of the initial, final and transition states (red arrows), making the curve flatter and the reduction of the activation energy. The stress promotes the chemical reaction and the reduce of the energy barrier is proportional to the stress, as expressed in the BEP relationship ∆Eact = αF · ∆d. Then, the height of the barrier drops (blue arrow), due to the catalytic interaction of Pt and H. The three dimensional plot demonstrating the relationship of reaction path, mechanical load and energy barrier is shown in Fig. 6 (b).

12


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(a)

(b) Height (Å) 12.20 12.16

12.11

12.05

Energy (eV)

7.5 7 6.5 6 5.5 5 4.5 4

0.12 8

Energy Barrier (eV)

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6

0.09

4 2

0.06

12 10 8

0.03

0 22

23.2

23

24

Stress (GPa)

25

23.4

6 23.6

23.8

26

Reaction Path

4 24

24.2

Stress (GPa)

24.4

2

Figure 6: (a) Energy barriers for benzene on Pt at different stresses. Above 24.22 GPa, the relationship of energy barrier and stress is no longer linear, demonstrating that the catalysis effect begins to act. The dashed blue line is extrapolated from the linear part. This line and the x–axis intersect at 26 GPa, indicating the estimated polymerization stress without catalysis; (b) The change of reaction paths with applied stress. The reaction barrier decreases sharply as the stress reaches 24.4 GPa.

c = 19.56 = -0.38 GPa

c = 13.56 = 7.33 GPa

c = 17.16 = 0.14 GPa

c = 12.96 = 10.1 GPa

c = 16.56 = 0.65 GPa

c = 12.36 = 12.1 GPa

c = 15.96 = 1.32 GPa

c = 15.36 = 2.40 GPa

c = 14.76 = 3.77 GPa

c = 11.76 = 22.9 GPa

c = 11.16 = 40.2 GPa

c = 10.56 = 54.6 GPa

Figure 7: Ball–and–stick model of the compression of benzene on the Au(111) surface. c is the supercell height along the z–axis, and σ is the stress of the supercell. Different from the benzene on Pt(111) case, no polymer formation is seen during the compression.

13



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187

surfaces, with a -0.1 eV adsorption energy, much weaker than on Pt (-1.9 eV). After normal

188

load is applied, benzene molecules spontaneously glide and avoid each other, due to the lack

189

of strong adsorption or fixed location. As the compression increases, the benzene molecules

190

begin to distort, because of the reduction of free space and applied stress. Different from

191

the benzene on Pt contacts case, there is no C–H bonds broken. Even though the benzene

192

ring is broken at the high stress cases and Au–C bonds are able to form, no polymerization

193

is observed, even when the height of the supercell is reduced to 10.56 Å with stress of 54.6

194

GPa, which is far beyond the requirement of benzene polymerization on Pt contacts (≈ 24

195

GPa).

196

As we know, Au is the noblest metal, possessing a completely filled d–band, and the d–

197

band center is far from the Fermi level. 34 As a result, the bonds that form between Au and

198

adsorbates have anti–bonding orbitals that are partially or mostly filled, indicating that the

199

bonding itself is not stable. Therefore, Au contacts cannot adsorb molecules tightly, so there

200

is nothing to stop intermolecular gliding, and Au does not catalyze the dehydrogenation

201

reaction.

202

If the concentration of benzene is low, the molecules tend to escape from the center

203

space between the two Au contacts, making tribopolymer formation less likely. For the

204

high concentration case, if lots of benzene molecules are trapped in a certain region during

205

the switching, the mechanical load can eventually induce the polymerization. Previous

206

theoretical study demonstrates that benzene molecules can transform to a polymeric phase

207

due solely to pressure, 35 but the required polymerization pressure is relatively high, above

208

80 GPa.

209

The main differences between the Pt and Au cases are the adsorption and dehydrogena-

210

tion. Adsorption is important, because it not only prevents the repulsion and avoidance of

211

molecules, but also breaks the strong and stable delocalized π orbital. For the Au contacts

212

with little adsorption, the delocalized π system is crushed only by the mechanical load, and

213

there is a stricter requirement for this process, such as a higher molecule concentration or

14


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larger mechanical load. However, for the polymerization on Pt case, the strong delocalized

215

π system is broken by the adsorption onto the substrate. Polymerization is induced by the

216

breaking of the C–H bonds, and this process is much easier.

217

For Pt contacts, computational compression experiments demonstrate that polymeriza-

218

tion can occur under stress of 24.22 GPa. Compared with the pure benzene polymerization

219

stress 80 GPa, it is much closer to the experimental situation, for which the stress between

220

contacts is estimated at several GPa. Besides, only uniaxial stress is investigated in this

221

study. Shear may also assist the dehydrogenation, accelerate the polymerization, and hence

222

lower the polymerization threshold stress. Moreover, in the study, a flat Pt surface is as-

223

sumed. Steps and vacancies can also enhance the catalysis effect and reduce the threshold

224

polymerization stress.

225

Conclusion

226

In this study, the mechanism of tribopolymer formation has been studied by computational

227

compression experiments. Benzene molecules adsorb on the surfaces of contacts, and then

228

original chemical bonds can be broken due to mechanical load. Dehydrogenation makes

229

adsorbed benzene molecules less saturated, so they bond with others to form tribopolymer.

230

In a certain stress range, the reaction energy decreases with mechanical load, and the linear

231

relationship between Eact and P follows the BEP relationship. When the stress is large

232

enough to press H atoms close to the Pt substrate, a catalytic effect takes over and the

233

energy barrier decreases to zero more rapidly as stress increases. Our study provides a

234

detailed analysis of the process and mechanism of the initial stage of tribopolymer formation

235

on contacts in MEMS and NEMS.

15



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ACKNOWLEDGMENTS

237

Y.Q. was supported by the U.S. National Science Foundation, under grant DMR1124696.

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J.Y. was supported by the U.S. National Science Foundation, under grant CMMI1334241.

239

A.M.R. was supported by the U.S. Department of Energy, under grant DE–FG02–07ER15920.

240

Computational support was provided by the National Energy Research Scientific Computing

241

Center of the Department of Energy.

242

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Stress

Stress

G id & A oi

Polymerize

C6H6 on Pt

C6H6 on Au

Table of Contents Graphics.

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Mechanical Load and Catalysis - University of Pennsylvania - School

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