Understanding graphene nano-ribbon manipulation

Andrea Benassi !

TU Dresden, Institute for materials science — Chair of Material Science and Nanotechnology

50 nm100 nm

A variety of quasi 1D carbon based nano-structuresInterpreting, understanding

and improving nano-manipulation experiments

Learning some physics:!!✤ basics of nano-friction and superlubricity

✤ basic nano-mechanical properties of nano-bio structures

200 𝜇m

650 C 400 C

Nature 466 470 (2010)

Nat. Nanotechnol. 8 912 (2013)

PNAS 111 3968–3972 (2014)

Nat

. Mat

eria

ls 14

583

(201

5)

N=7 GNR on Au(111)

A simple extension of the Frenkel-Kontorova model The idea is to use a minimalistic model catching only the necessary physical ingredients: ✤ proper substrate geometry and 2D periodicity ✤ proper GNR geometry, 2D periodicity ✤ introduce long and short edges ✤ correctly account for the GNR elastic properties

C-C bonds with REBO II potentials

rigid Au substrate

Au-C interaction with plane LJ potential

Nat. Mater. 9 634 (2010) Phys.Rev.B 61 16084 (2000)

H atoms not explicitly simulated

a viscous damping is included to account for the energy dissipation through the Au substrate !

The driving can be uniformly applied to all the C atoms or at the edge only

`

Structural properties on the (111) surface

GNR along the [1,-2,1] direction

GNR along the [-1,0,1] direction

roughness map

potential map

roughness map

potential map

meV-4.72 -3.24

+0.070-0.15 A

meV

A +0.014-0.016

-4.16 -3.05

0

meV

A

meV

A

2.97 nm

8.04 nm

b

a

3 nm

Slow

sca

n di

rect

ion lateral

move

ment

1-2 nm up to 50 nm in length typically found aligned to the [0,1,-1] direction

Phys

.Rev

.Let

t. 69

156

4 (1

992)

Structural properties on the (111) surface

GNR along the [1,-2,1] direction

GNR along the [-1,0,1] direction

roughness map

potential map

roughness map

potential map

meV-4.72 -3.24

+0.070-0.15 A

meV

A +0.014-0.016

-4.16 -3.05

0

meV

A

meV

A

2.97 nm

8.04 nm

b

a

3 nm

Slow

sca

n di

rect

ion lateral

move

ment

consistent with patterns and corrugations measured on graphene flakes Phys.Rev.B 85 205406 (2012)

Structural properties on the (111) surface

GNR along the [1,-2,1] direction

GNR along the [-1,0,1] direction

roughness map

potential map

roughness map

potential map

meV-4.72 -3.24

+0.070-0.15 A

meV

A +0.014-0.016

-4.16 -3.05

0

meV

A

meV

A

2.97 nm

8.04 nm

consistent with patterns and corrugations measured on graphene flakes Phys.Rev.B 85 205406 (2012)

b

a

3 nm

Slow

sca

n di

rect

ion lateral

move

ment

Measuring static friction force

The method to estimate the static friction force is described in Science 319, 1066 (2008) !The surface reconstruction makes the static friction force length and position dependent:

The manipulation of too long GNR is impeded by nearby ribbons…

The manipulation of too short GNR is impeded by rotations…

b

ca

Au tipscan

Δf (

Hz)

X (nm)

Z (n

m)

-9

-12

before

after1 2 30

1 2 30

0.5

0.0

10 nm

Δf (

Hz)

-11.

33.

4

GNR

X (nm)

Fx (p

N)

-50

-100

0.8 1.0 1.2

d

X (nm)

d

Fstat

e

0 5 10 15 200

20

40

60

80

GNR length (nm)

|Fst

at| (

pN)

totalper unit length

10 nm

1 nm

Static friction vs. GNR length: a proof of superlubricityformal proof of superlubricity: the friction force per unit length must go to zero with increasing GNR length.

egde effects are responsible for the force modulation on the unreconstructed surface

Moire pattern periodicity 2.97 nm

!

Force oscillation periodicity 22.3 nm

b

ca

Au tipscan

Δf (

Hz)

X (nm)

Z (n

m)

-9

-12

before

after1 2 30

1 2 30

0.5

0.0

10 nm

Δf (

Hz)

-11.

33.

4

GNR

X (nm)

Fx (p

N)

-50

-100

0.8 1.0 1.2

d

X (nm)

d

Fstat

e

0 5 10 15 200

20

40

60

80

GNR length (nm)

|Fst

at| (

pN)

totalper unit length

`

`

Dynamic friction: a dragging experiment

✤ a clear periodicity exists of 1.4 A for small Z and becomes 2.8 A al Z > 2 nm.

!✤ large scale modulation

✤ form small Z the forward and backward scans behave exactly in the same way

!✤ for large Z only the GNR edge remains attached to the Au surface and the forward and backward scans are drastically different

` `

`

`

`

`

Z = 1 nm

What about the force? Is there a real stick-slip?

The role of surface reconstruction

✤ On the unreconstructed Au (111) the periodicity of the stick-slip is more complex with 3 inequivalent jumps !

✤ The surface reconstruction eliminates an intermediate energy barrier leaving 2 almost equivalent jumps of amplitude 1.4 A !

✤ As Z increases the system undergoes a single slip event recovering the 2.8 A periodicity

✤ The surface reconstruction produces a modulation of the frequency shift depending on the GNR position.

0 1 2 3 4

102030

50

X (nm)

forc

e (p

N)

0

40

Fx(Z)Fz(Z)Fz(Z+ΔZ)

-1.0

-0.5

0.0

0.5

1.0

Δf (

Hz)

0 5 10 15 20 25

- 1.5- 1.0- 0.5

0.00.51.0

X (nm)

Δf (

Hz)

- 1.5- 1.0- 0.5

0.00.51.0

Δf (

Hz)

- 1.5- 1.0- 0.5

0.00.51.0

Δf (

Hz)

scan 1

scan 2

scan 3

12 3 1 1 3 1 3 3

12 3 1

33

3 31

33

HCPscan 1

scan 3

surface layer middle layer inner layer C atom

FCC

a

b

c

d

e

f

g

scan 2

�f / dFz(x, z)

dz

The role of elasticity

0 2 4 6 8 10X (nm)

- 1.5- 1.0- 0.5

0.00.51.01.5

Δf (

Hz)

Z=2nm

- 1.5- 1.0- 0.5

0.00.51.01.5

Δf (

Hz)

Z=3nm

- 1.5- 1.0- 0.5

0.00.51.01.5

Δf (

Hz)

Z=4nm

Z=5nm

- 1.5- 1.0- 0.5

0.00.51.01.5

Δf (

Hz)

a

b

c

d

`

`

`

`

The bending of the suspended piece of GNR determines whether the forward and backward signals are in phase or in anti-phase

At large Z the model fails as only the GNR edge is touching the Au surface and the role of H atoms might become dominant

A closer look to the stick-slip motion

0 1 2 3 4

102030

50

X (nm)

forc

e (p

N)

0

40

Fx(Z)Fz(Z)Fz(Z+ΔZ)

-1.0

-0.5

0.0

0.5

1.0

Δf (

Hz)

0 5 10 15 20 25

- 1.5- 1.0- 0.5

0.00.51.0

X (nm)

Δf (

Hz)

- 1.5- 1.0- 0.5

0.00.51.0

Δf (

Hz)

- 1.5- 1.0- 0.5

0.00.51.0

Δf (

Hz)

scan 1

scan 2

scan 3

12 3 1 1 3 1 3 3

12 3 1

33

3 31

33

HCPscan 1

scan 3

surface layer middle layer inner layer C atom

FCC

a

b

c

d

e

f

g

scan 2

The short edge atoms are the last to detach before the slip takes place. !

The stick-slip dynamics can change significantly upon changing the sliding direction

zig-zag path

railroad effect

Again on the surface reconstruction

0 1 2 3 4

102030

50

X (nm)

forc

e (p

N)

0

40

Fx(Z)Fz(Z)Fz(Z+ΔZ)

-1.0

-0.5

0.0

0.5

1.0

Δf (

Hz)

0 5 10 15 20 25

- 1.5- 1.0- 0.5

0.00.51.0

X (nm)

Δf (

Hz)

- 1.5- 1.0- 0.5

0.00.51.0

Δf (

Hz)

- 1.5- 1.0- 0.5

0.00.51.0

Δf (

Hz)

scan 1

scan 2

scan 3

12 3 1 1 3 1 3 3

12 3 1

33

3 31

33

HCPscan 1

scan 3

surface layer middle layer inner layer C atom

FCC

a

b

c

d

e

f

g

scan 2

0 1 2 3 4

102030

50

X (nm)

forc

e (p

N)

0

40

Fx(Z)Fz(Z)Fz(Z+ΔZ)

-1.0

-0.5

0.0

0.5

1.0

Δf (

Hz)

0 5 10 15 20 25

- 1.5- 1.0- 0.5

0.00.51.0

X (nm)

Δf (

Hz)

- 1.5- 1.0- 0.5

0.00.51.0

Δf (

Hz)

- 1.5- 1.0- 0.5

0.00.51.0

Δf (

Hz)

scan 1

scan 2

scan 3

12 3 1 1 3 1 3 3

12 3 1

33

3 31

33

HCPscan 1

scan 3

surface layer middle layer inner layer C atom

FCC

a

b

c

d

e

f

g

scan 2

the bridging regions have a pinning effect on the GNR short edges… !

… but they are less effective on the inner GNR atoms

Acknowledgments

Fundings:

GNR preparation and characterization

Modeling and simulation

AFM and STM manipulation

E. Meyer S. Kawai

E. Gnecco R. Guerra

Hypatia HPC cluster

R. Fasel and coworkers…

Thank you for your attention!

More information at: https://sites.google.com/site/benassia/