electronic structure of organic polymers with aNON degenerate ground state:

there can be NO soliton

because the resonance forms do NOT possess the same energy:

Edefect = E radical + n ∆E

in cis (CH)x, the radicals migrate to a chain end and remain immobile

c) Band Structure Evolution upon Doping

trans-polyacetylene

Moses et al, Phys. Rev. B 25, 7652 (1982)

between ~1% and ~7%:spinless conductivity: electrons are NOT the charge carriers

evolution of optical absorption upon doping in trans-polyacetylene

evidence for a transition ~5% doping

Pauli susceptibility shoots upsmooth evolution in the optical absorption datadisappearance of the π π* transition

evolution of electronic structure upon doping in trans-polyacetylene

separation between + and · (in number of sites)

formation of a polaron in trans-polyacetylene

Phys. Rev. B 26, 5843 (1982)

polaron: binding energy 0.7 eV - 0.65 eV = 0.05 eV

0.3 eV

0.3 eV

soliton geometry and charge distribution

Phys. Rev. B 28, 6927(1983)

polaron geometry and charge distribution

Phys. Rev. B 28, 6927(1983)

energetics of two polarons vs. two solitons:

in the case of two adjacent polarons:

pairing of the spin (radical) parts of the two polaronsleads to two charged solitons

Phys. Rev. B 26, 5843 (1982)

band structure evolution upon doping of trans-(CH)x

1) lattice of polarons& charged solitons

2) lattice of charged solitons

3) formation of a soliton band

upon application of an external electric field, the charged solitons could become mobile and carry a currentthis is consistent with spinless conductivity between ~0.2%

and 7%

4) closure of the Peierls gap

Pauli susceptibility appears above 7%: the charge carriers are electrons

conjugated polymers with a NON degenerate ground state:

polypyrrole

polythiophene

polyparaphenylene