nanofmf: plastik og kvantemekanik thomas garm pedersen inst. for fysik og nanoteknologi aalborg...
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NanoFMF: Plastik og kvantemekanik
Thomas Garm Pedersen
Inst. for Fysik og Nanoteknologi
Aalborg Universitet
Discovery of conducting plastics
Alan Heeger
Alan G. MacDiarmid
Hideki Shirakawa
Nobel Prize in Chemistry 2000
Polyacetylene and Polyethylene
Polyacetylene:
unsaturated
Polyethylene:
saturated
Light emitting plastics at AAU
400 500 600 700 800 9000
1000
2000
3000
Ele
ctro
lum
ines
cenc
e
Wavelength [nm]400 500 600 7000
250
500
750
1000
1250
ITO/LPPP/Ca
Ele
ctro
lum
ines
cenc
e
Wavelength [nm]
Typical polymers
poly(para-phenylene-vinylene)
poly(para-phenylene)
OLED design
Understanding the color
34
8
Energy - frequency:
Frequency - wavelength:
6.63 10 Js (Planck's constant)
3 10 m/s (Speed of light)
E hhc
cE
h
c
Quantum levels
2 2
2
34
30
Energy : , 1, 2,3,......8
6.63 10 Js (Planck's constant)
0.91 10 kg (Electron mass)
n
h nE n
mL
h
m
Small space means large energy!
Geometry and color
Blue (440 nm)
Green (500 nm)
Infrared (2500 nm)
Polymers with rare-earth atoms
Polymer synthesized by AAU
chemistry department
(D. Yu and K. Zhu)
New infrared emitting polymers?
More Info:
http://www.physics.aau.dk/~tgp/oleds_tgp.pdf
Quantum Physics
2 2
2
2 2 2 2 2
2 2 2 2 2
2 2
2 2
Electron waves:
momentum , energy 2 2
2wave function ( ) sin
( ) 4( ) ( )
8 8 2
( )Schrödingers equation: ( )
8
h p hp E
m mx
x A
h d x h hx x
m dx m m
h d xE x
m dx
Standing waves
2 2 2
2 2
34
30
Allowed wavelengths: 2 / , 1, 2,3,....
Energy 2 8
6.63 10 Js (Planck's constant)
0.91 10 kg (Electron mass)
n
L n n
h h nE
m mL
h
m
Waves in atomic chains2 2
2 2
1 1
1
21 1
2 21
21 1
2 2
( )Schrödingers equation: ( )
8( ) ( ) ( ) ( )( ) ( )
,
( ) 2 ( ) ( )( ) 1 ( ) ( )
( ) 2 ( ) ( )(
8
n n n n
n n
n n n
nn n
n n n
h d xE x
m dxx x x xd x d x
dx d dx d
x x xd x d x d x
dx d dx dx d
x x xhE
m d
2 2
2 2 2 2
)
Notation: ( ), ,8 4
n
n n
x
h hx
md md
1 1( )n n n nE
Discrete Schrödinger eq.
Two atoms
1 2 1 1
2 1 2 2
2 2
0
( ) 0
E E
E E
E E
Four atoms
1 2 1 1
2 1 3 2 2
3 2 4 3 3
4 3 4 4
0 0
00
0
0 0
(1 5) / 2, (1 5) / 2
E E
E E
E E
E E
E E
Longer chains
2 4 6 8 10 12 14 16n
-1.5
-1
-0.5
0
0.5
1
1.5
2
ygrenE
Band gap
Alternating chains
Band gap
2 4 6 8 10 12 14 16n
-1.5
-1
-0.5
0
0.5
1
1.5
2
ygrenE