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