Quantum Theory of Polymers3° Electronic structure of conducting and 

semi­conducting polymers

Jean­Marie André

EC ­ Socrates ­ Erasmusprogramme

FUNDP, NamurUniversity of Warsaw

Metal Semiconductor

π-band structure of Polyacetylene (PA)Polyene

In the middle of the 1960's, experimental data were not available on polyenes.

Some date are available on related compounds

7,7'dehydro-β-carotene 1964 1.400-1.450 Å 15,15' dehydro-β-carotene 1964 1.351-1.427 Å β-carotene 1964, 1.350-1.520 Å crotonic acid β-ionylidene 1959 1.346-1452 Å Vitamine A 1963 1.353-1.442 Å

Infinite polyene (PPP) 1967 1.363-1.429 Å(STO-3G) 1982 1.33 -1.48 Å

Status of bond alternation in polyenesin the 1960’s

1910 Insulator A new sulphide of nitrogenF.P. BurtJ. Chem. Soc., 1121 (1910)

The sulfur nitrides (SN)2 and (SN)x

M. Goehring and D. VoigtNaturwissenschaften, 40, 482 (1953

History of the Electronic Behaviour of (SN)x (Polysulfurnitride)

1964 Semiconductor

Spectra and the semiconductivity of the (SN)x polymerD. Chapman et al.Trans. Faraday Soc., 60, 294 (1964)

1973 Metal

Polysulfurnitride, a one-dimensional chain with a metallic ground stateV.V. Walatka, M.M. Labes, and J.H. PerlsteinPhys. Rev. Lett., 31, 1139 (1973)

1975 Superconductor

Superconductivity in polysulfurnitride (SN)x

R.L. Greene, G.B. Street, and L.J. SuterPhys. Rev. Lett., 34, 557 (1975)

Ethylene C2H4 H-(CH=CH)-H -103,7 °C - 169 °

C

Butadiene C4H6 H-(CH=CH)-(CH=CH)-H - 4,4 °C - 108,9

°C

Hexatriene C6H8 H-(CH=CH)-(CH=CH)-(CH=CH)-H 78 °C - 12 °C

PolyenesPolyacetylenes

1° Increase of conductivity with temperature

1° Increase of conductivity with temperature

2° Dramatic increase of conductivity upon doping No accompanying increase in Curie spin susceptibility

3° Red shifted new electronic transition

1° Increase of conductivity with temperature

2° Dramatic increase of conductivity upon doping No accompanying increase in Curie spin susceptibility

3° Red shifted new electronic transition

!!! For the first time:Correlation between

molecular geometry and electronic properties

H 2 C=CH−CH=CH n−CH=CH2¿ N−CH=CH n−CH=N«N=CH−CH=CH n−N¿

¿

MetalZero Gap

SemiconductorGap < 2 eV

InsulatorGap > 2 eV

k=β 2

β 1

Regular geometryMetal

Alternant geometrySemiconductor

Fukui’s principleFrontier orbitals and geometry

1947 : A. Pullman et R. Daudel (théor. )1961 : Srinivasan (exp. )

⇒ tendency of bond alternation to decay upon doping⇒ band gap not completely removed

J.M. André, J.L. Brédas, B. Thémans (1982)

Trans-Polyacetylene (bond lengths in Å)

1.4081.329C=C

1.4181.485C-C

Lithium-

Doped

Undoped

Cis-(Transoïd)-Polyacetylene (bond lengths in Å)

J.M. André, J.L. Brédas, B. Thémans (1982)

1.4021.325C=C

1.4151.482C-C

(Li) doped

undoped

V=a Dr 4b Dr 2c ,    

µ Dr 4−Dr 2

F=−¶ V¶ Dr

µ Dr 3−Dr

Basis of Soliton TheoryPeierls-like Distortion

⇑⇓

Phase A

Phase B

Basis of Soliton TheoryCoulson-Rushbrooke Theorem

The π-molecular orbitals of non-zero binding energy (ε 0) appears in ≠pair (conjugate molecular orbitals) with opposite energies.

C.A. Coulson and G.S. Rushbrooke, Proc. Cambridge, Phil.Soc. 36, 193 (1940)

Basis of Soliton TheoryCoulson-Rushbrooke Theorem

The π-molecular orbitals of non-zero binding energy (ε 0) appears ≠in pair (conjugate molecular orbitals) with opposite energies.

C.A. Coulson and G.S. Rushbrooke, Proc. Cambridge, Phil.Soc. 36, 193 (1940)

Polyacetylenes with even number of carbon atoms

Polyacetylenes with odd number of carbon atoms

PA+ Oxidative p-doping Conduction without spin

PA- Reductive n-doping Conduction without spin

[CH ]n3 x2

I 2 [CH ]nxx I 3

−

[CH ]nx Na [CH ]nx−x Na

−e− e−

!!! If mobile, conductivity without spin

!!! Red shift upon doping

Undoped PA Doped PA

Mol. Phys. 5, 15 (1962)

The existence of misfits should by no means be limited to odd polyenes. One can conceive of a series of such misfits, at regular distances, in a large even polyene.

Such unpaired electrons may be detectable by electron spin resonance. The defect is able to travel through the molecule since its motion depends only on a small displacement of one carbon atom. This is illustrated in

Figure 3. (p.19)

A strong concentrations of spins – one per 5000 atoms at room temperature has been observed by ESR in extremely long even conjugated polymers [M. Nechstein, J. Polymer Sci. C1, 1367-1376 (1963)]

¶ 2 u

¶ t 2−

¶ 2 u

¶ x 2=u3−uφ4 Equation:

J. Scott RusselReports on wavesProc. Roy. Soc. Edinburgh, 319-320 (1844)

Soliton = Waves

that retain their size and shape

but do not spread or disperse

J. Scott RusselReports on wavesProc. Roy. Soc. Edinburgh, 319-320 (1844)

I was observing the motion of a boat which was rapidly drawn along a narrow channel by a pair of horses, when the boat suddenly stopped - not so the mass of water in the channel which it had put in motion; it accumulated round the prow of the vessel in a state of violent agitation, then suddenly leaving it behind, rolled forward with great velocity, assuming the form of a large solitary elevation, a rounded, smooth and well-defined heap of water, which continued its course along the channel apparently without change of form or diminution of speed. I followed it on horseback, and overlook it still rolling on at a rate of some eight or nine miles an hour preserving its original figure some thirty feet long and a foot to a foot and half in height. Its height gradually diminished, and after a chase of one or two miles I lost it in the windings of the channel. Such, in the month of August 1834 was my first chance interview with that singular and beautiful phenomenon …

SSH ResultsSoliton formation energy: 0.42 eVWidth parameter: 7 unit cells

14 bondsMotion barrier: 0.002 eV

Net effect: Moving domain wall down to temperatures 20 - 40 K≈

!!! Process controlled by activation energy!!! Conductivity increases with temperature

Pople-Walmsley

Su-Schrieffer-Heeger (SSH)

ECC«  Effective Conjugate Coordinate  »

Examples of Conducting Polymers

Practical Applications

Conductive plastics used in, or being developed industrially for:- anti-static substances for photographic films- shields for computer screens against electromagnetic radiation- "smart" windows that can exclude sunlight

Semi-conductive polymers recently developed in:- light-emitting diodes (LEDs)- solar cells- displays in mobile telephone and mini-format televisions screens

Applications ⇒ Plastic Electronics

Polyanilineconductorelectromagnetic shielding of electronic circuitscorrosion inhibitor

Poly(ethylendioxythiophene) – PEDOTantistatic coating material on photographic emulsionshole injecting electrode material in PLED

Poly(phenylene vinylidene)active layer in electroluminescent displays (GSM)

Poly(dialkylfluorene)emissive layer in full-colour video matrix displays

Poly(thiophene)field-effect transistor

Poly(pyrrole)microwave-absorbing "stealth" (radar-invisible) screen coatingsactive thin layer of sensing devices

Role of quantum chemistry:Evaluate the various parameters

⇒ Energy levels⇒ Rate constants

Electronic band structures available for

PolyacetylenePolyparaphenylene

Polyparaphenylene vinylidenePolypyrrole

PolythiophenePolyaniline

…

J.L. Brédas, JMAFUNDP, UMH, UofA,GeorgiaTech,…

Importance of the relative position of the important levels. Driving force = redox potential

eLUMOD −eHOMO

A

Alan MacDiarmid:

Research on conductive polymers has also fueled the rapid development of molecular electronics. In the future scientists may be able to produce transistors and other electronic components consisting of individual molecules, dramatically increasing the speed and reducing the size of computers: a computer corresponding to the laptops we now carry around suddenly fits inside a wristwatch.