Observation of wire bending can give information about shear modulus of the system, A model based on definition of shear modulus is constructed and tested for arbitrary parameters and also for nanowire.

1. Two-dimension curvature of a
wire: A simple model using
shear modulus concept
S. Viridi, M. Abdullah, N. Amalia
28-29 October 2016
Denpasar, Indonesia
1Symposium Nanotechnology 2016

2. Outline
• Introduction
• Model
• Results #1
• Data
• Results #2
• Summary
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2Symposium Nanotechnology 2016

3. Introduction
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Symposium Nanotechnology 2016 3
Stan G, Ciobanu C V, Parthangal P M and Cook R F 2007 Nano Lett. 7 3691

4. Introduction (cont.)
• Eqns (8) & (9)
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Symposium Nanotechnology 2016 4
Stan G, Ciobanu C V, Parthangal P M and Cook R F 2007 Nano Lett. 7 3691
c
c
s E
R
E
t
E
R
+=
NW
NW
c
c
s G
R
G
t
E
R
+=
NW
NW

5. Introduction (cont.)
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Symposium Nanotechnology 2016 5
Chen C Q, Shi Y, Zhang Y S, Zhu J and Yan Y J 2006 Phys. Rev. Lett. 96
075505
















−+−







−+= 4
4
3
3
2
2
0
0 243181
D
r
D
r
D
r
D
r
E
E
EE sssss

6. Model
• Shear
modulus
θ
AF
G
/
=
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Denpasar, Indonesia
6Symposium Nanotechnology 2016

7. Model (cont.)
• Model
∫=
L
l
dlrgF 2
sinθπρ
∫=∆
L
l
dlr
Gr
g 2
2
sinθρ
θ
28-29 October 2016
Denpasar, Indonesia
7Symposium Nanotechnology 2016

8. Model (cont.)
• Discretization
( ) ( ) ( )
( ) ( )
( )∫+=∆+
L
l
dllr
lrlG
l
glll 2
2
sinθ
ρθθ
( ) ( ) ( )lLlxllx θsin∆+=∆+
( ) ( ) ( )lLlylly θcos∆+=∆+
N
L
l =∆
28-29 October 2016
Denpasar, Indonesia
8Symposium Nanotechnology 2016

9. 0
0.2
0.4
0.6
0.8
1
0 0.05 0.1 0.15 0.2
x
y
Results #1
• Arbitrary parameters:
θ0 = 10°, L = 1 m,
M = 2–22 g, D = 2 mm,
G = 2.5×104
–105
N/m2
,
N = 5–80
28-29 October 2016
Denpasar, Indonesia
9Symposium Nanotechnology 2016

10. Results #1 (cont.)
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Symposium Nanotechnology 2016 10
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
x
y
G = 10î 104
G = 5î 104
G = 4î 104
G = 3î 104
G = 2.5î 104
0.5
0.6
0.7
0.8
0.9
1
1E+3 2E+4 4E+4 6E+4 8E+4 1E+5
T
G
( ) ( )2
0
2
0
1
yyxx
L
T NN −+−=

11. Results #1 (cont.)
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Denpasar, Indonesia
Symposium Nanotechnology 2016 11
-1
-0.6
-0.2
0.2
0.6
1
0 0.2 0.4 0.6
x
y
-1
-0.6
-0.2
0.2
0.6
1
0 0.2 0.4 0.6
x
y
-1
-0.6
-0.2
0.2
0.6
1
0 0.2 0.4 0.6
x
y

12. Results #1 (cont.)
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Symposium Nanotechnology 2016 12
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
x
y
M = 2 g M = 8 g
M = 12 g
M = 16 g
M = 20 g
M = 22 g

13. Data
• Nanowire parameters
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14. Data (cont.)
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15. Data (cont.)
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16. Data (cont.)
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17. Data (cont.)
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18. Results #2 (cont.)
• A ‘straight’ nanowire
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0.000000
1.2E-07
1.4E-07
1.6E-07
1.8E-07
65 70 75 80 85 90 95
θN–θ0
G

19. Results #2 (cont.)
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Symposium Nanotechnology 2016 19
( ) 0,12 =+= ννGE

20. Summary
• A simple model of wire bending derived from
definition of shear modulus has been
presented
• It can be used for arbitrary parameters
• It not so successful for the size of nanowire,
since it predicts too higher value than
expected
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Symposium Nanotechnology 2016 20

21. Thank you
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