Lecture 2 polymers, w

ave function 28.04.16

A general relationship betw

een disorder, aggregation and charge transport in conjugated polym

ersR

odrigo Noriega, Jonathan R

ivnay, Koen V

andewal, F

elix P. V

. Koch, N

atalie Stingelin, P

aul Sm

itM

ichael F. T

oney & A

lberto Salleo

Nature M

aterials 12, 1038–1044 (2013)

polymers in organic electronics

low bandgap m

aterial

persistence length

persistence length limits

conjugation length

Polym

ers and solvents

interaction parameters (neg. sign =

attractive)

three casesgood solvent

theta solvent ("invisible")

bad solvent

Polym

er mixtures

polymers don't m

ix

condition for phase separation always fulfilled for

long polymers

daily life polymers are "pure"

Polym

ers and C60 fullerenes:

bulk heterojunctions for PV

cellsC

opolymers form

superstructures

Bond length in conjugated system

s

agreement w

ith molecular orbital sim

ulation ~

Theoretical description of electrical and optical properties

exact solution only for hydrogen analoge known

H, C

, ... plenty of room for approxim

ations

Born-O

ppenheimer:

electron and nuclei can be decoupled

further simplification:

include molecular vibrations and change of

"nuclear coordinates" after excitation later

two "sim

ple" concepts from inorganic system

s

I: particles in a box

(cf. Hunklinger)

II: coupled wells

construction of states by Linear com

bination of atomical orbits (LC

AO

)

a simple analytical m

odel for benzene

wave function lim

ited to ring (perimeter)

constant potential within the ring (m

olecule)infinite w

alls

only kinetic energy (= particle in a box)

but here: confined to perimeter

good model for polyarom

atic hydrocarbons (PA

Hs)

q "quantum num

ber"

highest occupied molecular orbital

(HO

MO

)low

est unoccupied molecular orbital

estimate of H

OM

O-LU

MO

gap