Band theory of some polymers derived from polyparaphenylene

~

Solid State Communications, Printed in Great Britain.

Vol.47,No.12,

pp.965-968,

0038-1098/83 $3.00 + .00 Pergamon Press Ltd.

1983.

BAND THEORY OF SOME POLYMERS DERIVED FROM POLYPARAPHENYLENE M. Dugay and C. Fabre Laboratnire d'Electronique et R~sonance Magn~tique, E.R.A. 90 du C.N.R.S., Universit~ Clermont II, 24 avenue des Landais, B.P. 45, F 63170 AUBIERE (Received

15 March

de

1983 by A. Blandin)

We report the results of calculations dealing with a series of polymers related to polyparaphenylene . In order to investigate the possible effects of linking aromatic rings with segments having conjugated bonds and/or heteroatoms, semi-empirical calculations have been performed from a Pariser-Pazr-Pople hamiltonian . It is shown that, within this simple methodology, reliable informations can be get concerning the ability of a polymer to form a conducting system upon doping .

conducting system . To answer this question we must first recall that the so-called doping process has nothing to do with the doping of classical inorganic semiconductors 8 . In the case of electro-active polymers the (somewhat inappropriate) word doping stands for a complex chemical process which brings additional charges through a charge transfer inducing drastic geometrical changes 9. The appearance of localized states in the gap is governed by these geometrical changes and will not be discussed in this note . We shall restrict ourselves to the capability of the polymer to be "doped" (i.e. to the possible occurrence of a change-transfer) and shall wonder whether the created carriers (if any) are mobile. The parameters determining these properties are : (a) the ionization potential (IP) which indicates whether an acceptor doping agent is able to oxidize the polymer . (b) the energy gap (Eg) of which the main interest is not to determine the conductivity of the undoped polymer but to provide (when substracted to IP) the electron-affinity, thus giving the capability to be doped by a donator agent . (c) the width (BW) of the highest occupied energy band which roughly indicates the degree of delocalization of the carriers in that band .

THE PRESENT NOTE is concerned by the study of a few organic materials exhibiting a high electrical conductivity . These compounds, named electroactive polymers, consist of macromolecules which do not have any remarkable property by themselves but generate highly conducting systems upon doping by appropriate agents . Among electro-active polymers, the most widely studied has been, up to now, polyacetylene . Its formula is simply ~ CH }n and we shall use throughout this article the shortened notation PA in place of the whole name polyacetylene . The strong interest for PA originates from very fascinating theoretical properties . PA is very unique in possessing (under its all-trans form) a completely degenerate groundstate . This degeneracy leads to soliton excitations I and related phenomena 2 . Concerning its practical potentialities, PA is also a very interesting system : rechargeable batteries 3, photovoltalc cells and Schottky barriers 4 are its main domains of applications . However, unless until a very recent date5, PA could not be processed and handled as conventional polymers and there were sometimes some problems concerning the stability of the prepared materials (they were in particuliar damaged by oxygen) . This is the reason why the last few years have seen an intensive quest for "processible" materials . Some advances have been made with polyparaphenylene (an array of aromatic rings linked in the para position) thereafter referred to as PPP . Despite relatively less good electrical properties than that of PA, PPP also generates highly conducting systems . They can be obtained as thin films 6 . Moreover, PPP offers the opportunity of proceeding via a very promising technique of solid-state polymerization : AsF 5 doping of oligomer single crystals leads directly to highly conducting complexes under a relatively tractable form 7 . It is very tempting to try to obtain new materials offering the same advantages as PPP with improved physical properties . To do so, we have attempted to link the aromatic rings by segments having conjugated bonds and/or heteroatoms . The present note is intended to report the results of theoretical investigations performed to know whether a given PPP derivative could form a

To determine semi-empirically IP, Eg, BW, we have used the framework of the Pariser-ParrPople hamiltonian, which is one of the simplest methods to get reliable informations upon large quantum systems . Assuming total o-~ separability, n-electrons only are dealt with, in terms of zero-differential everlap . This procedure has been abundantly justified by Lowdin I0 . Within such a framework we are left for ~ electrons with the following hamiltonian 11 + H= i,o Z ~i niq + i#j Z ~ij ~ Z Yii ni÷ ni+ aio a.JO + i

1

+ ~ i~j Yij nit O#T

965

n.

(I)

966

BAND THEORY OF SOME POLYMERS DERIVED FROM P O L Y P A R A R H E N Y L E N E

ai~ (resp. ai~) creates (resp. annihilates) an electron with spin ~ in a ~-orbital of a t o m i ; ni~ ; di and 8ij are (respectively) diagonal and off-diagonal elements of the hamiltonian containing kinetic energy and core attractions ; Yij represents Coulomb repulsion . From (]) the energy levels are found by solving the Fock matrix equation w i t h i n a very classical self-conslstent field procedure ]2 . Here the elements of the Fock matrix are obtained with the aid of the following expressions |3 :

=a~.ai~

[F..(~)]

11

=

Z {H!~ )

-(P) (p) e ikpa} - rii Yii

ij

P + 2

Z P ! ? ) " (p) . Jl Yij Pl

(2)

[Fij(~)] = Z {H!~ ) - P!~)} e ikpa 1J

1J

(3)

P

a is the lattice spacing, P~)- an element of the charge and bond-order matrl~ within the pth cell, y(~) is the coulomb integral b e t w e e n the i th orbital in the origin cell and the jth orbital in the pth cell . It has been obtained from the empirical relationship to electron-affinities and ionization potentials of atoms i and j given by Mataga and Nishimoto 14 . As for H-matrix, it is defined as follows .

H!? )= - I. - Z Z. y!?)11

l

j

Z

13

i

Z Z. y!~)

p~o j

i

1]

(4)

Z. is the effective charge on nucleus i, Z. 1 . . 1 the lonlzatlon potential of the concerned ~ orbital . H!~ ) = K . S!~ ) {I. + I.} 1J

1J

1

j

(5)

S ~ij ) is the overlap between the i th orbital in the origin cell and the jth orbital in the pth cell and K is an adjustable parameter . As previously stated, the above formalism has been applied to investigate the possible effects on Eg, BW and IP of the linkage of the aromatic rings of PPP by different segments . Oesides PPP itself three derivatives are presented : polyparaphenylene-vinylene ~C6H4-CH=CH~ n or PPV, polyparaphenylene-azomethine ~C6H4-CH=N % or PPCN and poly-azophenylene ~C6H4-N=N~ n or PPN . The four polymers have the geometries shown on figures I to 4 . These geometries are assumed from data available either on the poly-mer itself (PPP case |5) or on the first oligomers (PPV 16 and ppN;7 cases) . For PPCN a plausible geometry has been inferred from a compilation of most common Schiff bases |8 In order to check the reliable (or non-reliable) character of our computations, we have applied the same treatment to trans PA . Thus we can compare our results for Eg and BW to existing results of other calculations in the same field as well as to existing experimental data . As for IP, it is quite out of question to obtain any accurate value . What we should want to achieve is only a reliable estimation of the

Vol.

47, No. 12

energy of the highest occupied molecular orbital . We speculate that, if the methodology is able to provide a correct classification of the energies of highest occupied orbitals of different polymers, it should provide a correct scale for their ionization potentials . In the course of our calculations, ionization potentials are chosen -||.24 eV for C and -14.51 eV for N . Electron affinities are respectively 1.25 and -.6 eV . All atomic orbitals are of Slater type with exponents 1.625 for C and 1.695 for N . The coefficient K in equation (5) is taken from an adjustment made for benzene molecule . Our numerical results are gathered in table l . We shall see that they compare favourably both with other calculations in the same field and experiments . Polymer ?PP (planar)

Eg 4

1

BW

IP

[3.2]

2.6

[3.9] 7.5

[5.5]

PPV PPCN PPN

2.35 [2.5] 2.7 1.7

|.9 ! 1.2

[2.8] 7.3 6.8 6.7

[5.1]

PA

1.85 [ 1 . 4 ~

5.2

[6.5

[4.7]

6.5

Table I - Eg, BW, IP within our seml-empirical calculations . IP column contains only energies of highest occupied orbitals and should be shifted downward . In brackets results of VEH calculations (see text) . Units are eV . Before going on, an important point must be stressed . The true geometry of PPP is not planar but twisted . The twisting of the rings (by a amount of 22.7 °) with respect to each other ]9 results from a compromise between solid-state packing and conjugation which favour planar structure and repulsion of orthohydrogen atoms which favours non-planar structure . In the course of our calculations we have always assumed a planar geometry . Thus our model appears very crude and somewhat unrealistic . Its crudeness is associated with the fact that, dealing with n-electrons only, we are quite unable to account for effects caused by the u-skeleton . Concerning its unrealistic aspect and the importante of deviations from planarity let us recall that an analysis of the effect had been made within preliminary systematical comparative studies on some electro-active polymers20 . BW and Eg vary smally while IP is almost unaffected by the change from 0 ° to 22.7 ° in the twist angle . In a first approach, we have the feeling that the results obtained for PPP are enough for a c o m p a r i s o n w i t h other polymers and investigation of the linkage of the rings. N o w we come back to the comparison of our results to experiments and other computations . Recently a new methodology has been developed to obtain one-electron energies within a completely no-empirical scheme : the v a l e n c e - e f fective hamiltonian technique (abreviated as VEH) 2! . Extended to polymers 22 it has been proved a very useful tool for calculating elec-

VoW. 47, No. 12

BAND THEORY OF SOME POLYMERS DERIVED FROM POLYPARAPHENYLENE

I . 402~

I

967

1.56A

:

1.50A

i~39~,,

i~i~/,:~ 2

, ,

O l

Fig. 1 : Poly Paraphenylene

(PPP)

e i1.46A

Fig. 3 : P o l y P a r a p h e n y l e n e

i. 457~

1.415~

~.39~j I

I

.

.

.

.

Azclnethine (PPCN)

1.2

'

.

Fig. 2 : Poly Paraphenylene Vinylene

(PPV)

tronic structures : the results are of ab-initio double-zeta quality . In comparison to the VEH-determined Eg and BW of ppp23, ppv20 and PPN 24, our results are quite acceptable . On the experimental point of view, the available energy gaps are 3.5 eV for ppp7, 1.8 eV for PA 25 and 2.8 eV for PPCN 26 . Our results do agree with these values . Concerning now the energies of the highest occupied orbitals and the proposed scale for IP's we find that PPN and PPCN are expected to lie between PPP and PA, closer to PA . Thus they should be potential candidates for doping by electron acceptors . It is well established that the IP of PPP is higher than that of PA (by .8 eV) and that it is the reason why PPP can only be doped by very strong acceptors such as AsF 5 . As for PA, it is dopable by weaker acceptors, such as iodine. Experiments have been deviced to test the behaviour of PPN and PPCN upon attempts of doping . PPN is destroyed by AsF5, owing probably the too high chemical reactivity of the -N=Ngroups . Upon 12-doping an increase of electrical conductivity by at least 6 orders of magnitude is observed 27 • The definitive evidence for the occurrence of a charge-transfer is provided by Raman scattering studies on the doped system : there does exist I~ species 28 . Experiments on PPCN are only at their very beginning . An important increase of conductivity has been noticed ; the test for the existence of 17 has not yet been made . Thus our very crude results are strengthened by experiments . As expected, PPN can be iodine-doped . The complex resulting from this doping has still a low conductivity 27 . This indication could be considered as corroborating the relatively narrow BW found by calculations for this compound . To sum up, it seems that the aim of finding, through a very simple theoretical model, a tool to predicate the possible behaviour of a candidate electro-active polymer has been achieved . Within the framework of the Pariser-Parr-Pople methodology, a parametrization has been possible

I

: 1.415A

Fig.

4 : PolyAzophenylene

/

r

(PIN)

to reach an acceptable estimation of energy gaps and a correct scale for the ionization potentials, key quantities to expect an aptitude (or nonaptitude) for doping .

REFERENCES 1. 2.

3.

4. 5.

6. 7.

8. 9. 10. l]. 12.

13.

J.A. Pople and S.H. Walmsley, Mol. Phys. 5, ]5 (1962) . W.P. Su, J.R. Schrieffer and A.J. Heeger, Phys. Rev. Lett. 42, 1698 (1978); Phys. Rev. B 22 , 2209 (1980) . P.J. Nigrey, A.G. Mc Diarmid and A.J. Heege~ Mol. Cryst. Liq. Cryst. 83, 309 (1982) and references therein . J. Kacnicki, S. Boue and E. Van der Donckt, Mol. Cryst. Liq. Cryst. 83, 319 (1982) . G.L. Baker and F.S. Bates, Proceedings of the ]982 Les Arcs (France), Conference on the Physics and Chemistry of Conducting Polymers, in press . B. Tieke, C. Bubeck and C. Lieser, Proceedings of the 1982 Les Arcs Conference . L.W. Shacklette, H. Eckhardt, R.R. Chance, G.G. Miller, D.M. Ivory and R.H. Baughman, J. Chem. Phys. 73, 1098 (1980) . E.J. Mele and M.J. Rice, Phys. Rev. B 23, 5397 (]981) . J.L. Br~das, R.R. Chance and R. Silbey, Phys. Rev. B 26, 5843 (1982) . P.O. L~wdin, Sv. Kem. Tidskr. 67, 380 (1955) . J. Linderberg and Y. ~hrn, J. Chem. Phys. 49, 716 (1968) . J. Ladik in Electronic Structure of Polymers and Molecular Crystals, J.M. Andre and J. Ladik Editors (Plenum, New York 1975) . S. Suhai, J. Phys. (London) C 9, 3073 (1976)

14. 15.

.

N. Mataga and K. Nishimoto, J. Phys. Chem. 13, ]40 (1957) . L.W. Shacklette, R.R. Chance, D.M. Ivory, G.G. Miller and R.H. Baughman, Synthetic Metals ~, 307 (]979) .

968 16. 17, 18.

19. 20.

21. 22.

BAND THEORY OF SOME POLYMERS R.M. Robertson and I. Woodward, Proc. Roy. Soc. A 162, 568 (1937) . C.J. Brown, Acta Cryst. 2__I, 146 (1966) . H.B. B~rgi, J.D. Dunitz and C. Zust, Acta Cryst. B 24, 463 (]963) ; H.B. Burgi and J.D. Dunitz, J. Chem. Soc. Comm. 472 (1969); G. Manecke, W.E. Wille and C. Koom, Makromol. Chem. ]60, III (1972) . Y. Delugeard, J. Desuche and J.L. Baudour, Acta Cryst. B 32, 702 (1976) . R.R. Chance, R.H. Baughman, J.L. Br~das, H. Eckhardt, R.L. Elsenbaumer, J.E. Froemer, L.W. Shacklette and R. Silbey, Mol. Crysto Liq. Cryst. 83, 217 (]982) . G. Nicolas and Ph. Durand, J. Chem. Phys. 70, 2020 (1979) ; 72, 453 (]980) . J.M. Andre, L.A. Burke, J. Delhalle, G. Nicolas and Ph. Durand, Int. J. Quant. Chem. S 13, 283 (1979) .

DERIVED FROM POLYPARAPHENYLENE 23.

24. 25.

26. 27.

28.

Vol. 47, Nor 12

J.L. Br~das, R.R. Chance, Ro Silbey, G. Nicolas and Ph. Durand, J. Chem. Phys. 77, 371 (1982) . J.L. Br~das and B. Th~mans (private communication) . C.R. Fincher, D.L. Peebles, A.J. Heeger, M.A. Druy, Y. Matsumara, A.G. Mc Diarmid, S. Shirakawa and S. Ikeda, Solid State Comm. 27, 489 (]978) . B. Millaud and C. Strazielle, Polymer 20, 563 (]979) . F. Barbarin, G. Berthet, J.P. Blanc, M. Dugay, C. Fabre, J.P. Germain and H. Robert, Proceedings of the ]982 Les Arcs Conference on the Physics and Chemistry of Conducting Polymers, in press . C. Fabre and S. Lefrant (unpublished results) .