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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
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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"
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Polym
ers and C60 fullerenes:
bulk heterojunctions for PV
cellsC
opolymers form
superstructures
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Bond length in conjugated system
s
agreement w
ith molecular orbital sim
ulation ~
Theoretical description of electrical and optical properties
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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)
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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)
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q "quantum num
ber"
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highest occupied molecular orbital
(HO
MO
)low
est unoccupied molecular orbital
estimate of H
OM
O-LU
MO
gap
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