Electrochimica Acta, 1972, Vol. 17, pp. 1803 to 1811. Petsmon
Press. Printed in Northern Ireland
ELECTROCHEMICAL STUDIES OF PHENOTHIAZINEIODINE CHARGE-TRANSFER COMPLEXES* A.
BRAU, J. P. FARGES and F. GuTMANNj’ Laboratoire de Biophysique, Universite de Nice, Part Valrose, 06 Nice, France
Abstract-The conductivity of the freshly prepared yellow adduct of phenothiazine and iodine in acetonitrile is due in about equal parts to 2: 3 and 1: 2 complexes at 20°C. In CH,CN the complexes are completely dissociated_ The equivalent conductivity remains constant, independent of concentration, at 130 mho. cm’/eq which is of the same order as that of strong electrolytes. The mean mobility of the carriers is 6.2 x lo-’ cmO/V.s. Transport numbers were obtained from electrolysis in a Hittorf-type cell as t+ = 0.17 and t- = 083, yielding for the mobilities ,x- = 1-O x lo-* and CL+= 2.1 x 1O-4 cm*/V.s. The anions, identified as I 9-, are thus the majority carriers. It is estimated that the mean radius of the cations is about 2 to 4 times that of a hypothetical benzene ion in the same solvent. Further electrolysis experiments show that the complex formationdissociation equilibria are reversible. Ageing and/or illumination, or addition of water, causes the colour of the adduct to change first to green, then to blue and eventually to violet. A new absorption initially at 650 nm and considered as a charge-transfer band shifts upon ageing to 625 run for the green and to 550 nm for the violet adduct. The conductivity of the complex dissolved in acetonitrile rises with temperature at a rate considerably less than that of the pure solvent, the apparent activation energies being O-003 and O-06 eV respectively; this is considered as indicating the probability of recombination to rise with increasing temperature. The ground state of the complex in acetonitrile solution is shown to be predominantly ionic and its electronic structure to resemble that of the excited state of the isolated complex molecule. R&u&--La conductivito a 20°C du produit d’addition jaune, fralchement prepare, de la phenothiazine et de l’iode dans l’ac&onitrile est dfte en parties $Ipeu p&s &ales aux complexes 2: 3 et 112. Dans CHsCN, les complexes sont complktement dissocies. La conductivite equivalente reste independante de la concentration; sa valeur constante 130 mho . cm*/eq est du meme ordre de grandeur que celle des electrolytes forts. La mobilite moyenne des transporteurs est 6,2 x lo-’ cmg/V.s. Les nombres de transport ont ete obtenus par electrolyse darts une cellule de type Hittorf: leurs valeurs t+ = 0,17 et Z- = 0,83 correspondent aux mobilitb ,x- = 1,O x lo-’ et p+ = 2,l x 1O-4 cmf/V/s. On estime que le rayon Les anions idents&, tels que I,-, sent ainsi les transporteurs ma’oritaires. moyen des cations est d’environ 2 & 4 fois celui d’un ion benzenique hypothttique dans le meme solvant. Des electrolyses ulterieures ont montre que les equilibres de formation-dissociation du complexe sont reversibles. Le vieillissement et/au l’eclairement, ou encore l’addition d’eau, colorent le produit cl’addition d’abord en vert, puis en bleu et eventuellement en violet. Une nouvelle absorption, initiallement a 650 nm et qui est considered comme tme bande de transfert de charge, se d6place par vieillissement, vet-s 625 nm pour le produit vert et 550 nm pour le produit violet. La conductivite du complexe dissous dans l’acetonitrile croit avec la temperature a une vitesse considerablement inferieure & celle du solvant pur, les energies d’activation apparentes &ant respectivement 0,003 et 0,06 eV; ceci indique que la probabilite de recombinaison augmente avec la temperature. L’etat fondamental du complexe dans la solution a&to&rile est cens& btre a predominance ionique et de structure Blectronique analowe ii celle de T&at excite de la mol&cule cumplexe isol&. Zusammenfa~-Die Leitfahigkeit des frisch hergestellten, gelben, Komplexes gel&t in Azetonitril ist in etwa gleichem Masse verbunden mit einer 1: 2 und 2:3 Stoichiometrie, bei 20%. Der Komplex Die Equivalente Leitftiihkeit bleibt konstant und konim Azetonitril ist volbttindig dissoziiert. zentrations-unabhiingig auf einem Wert von 130 Q--l cm*/eq, also der gleichen Griissenordnung wie die eines starken Elektrolyten. Die mittlere Beweglichkeit der Ladungstrager wurde als 6,2 x IO-‘cmp/ V.S. gefunden. Uberftihrungszahlen wurden durchElektrolyseineiner HittorfZellegemessen t+ = OJ7; t- = 0,83 so dass man fI.ir die Beweglichkeiten erhalt p+ = 2,l x lo-’ cm’/V.s, ~1~ = 1,0 x 10 cm8/V.s. Die Anionen, identmert als I,- sind also die Mehrheitstrgger. Der mittlere Radius der Kationen wit-d auf etwa 2 bis 4 mal dem Radius eines hypothetischen Benz01 ions lm gleichen Losungsmittel, Azetonitril, geschltzt. Von weiteren Elektrolyse Experimenten folgt dass die Komplex Formation/Dissociation Gleichgewichte reversibel sind. Altern und/oder Licht oder Zugabe * Manuscript received 6 October 1971. t Present address: Department of Physical Chemistry, 2006, Australia. 1803
University
of Sydney, New
South Wales
1804
A. Bn~u, J. P. FARGIZZ. and F. G~TMANN
von Wasser fihrt zu Farbwechsel: erst grim, dann blau und endlich violett. Eine neue Absorption erscheintanfiinglichbei 650 nm und wird als das Ladungsiibertragungsbandangesehen. Es verschiebt sich mit der Zeit zu 625 nm fIir den griinenund zu 550 nm fiir denvioletten Kornplex. Die Leitf&higkeit der Komplexliisung in Azetonitril steigt mit der Temperatur, aber wesentlichlangsamer als die des reinen Liisungsmittels; die Aktivierungsenergiensind 0,003 turd 0,06 eV. Dies scheint darauf zu deuten dass die Wahrscheinlichkeitder Rekombination mit der Temperatursteigt. Es wird gezeigt dass der Grundzustand des Komplexes im Azetonitrii hauptsiichlichionisch ist und dass dessen elektronischeStruktur dem erregtemNiveau des isoliertenKomplex Molekels iihnelt. 1. INTRODUCTION
CHARGE transfer-complexes between phenothiazine (PH) and iodine were first reported by Matsunagal and subsequently have been studied by Gutmann and Keyser, and by Foster and Fyfe .3 They are of interest since phenothiazine is the parent compound of a large class of substances of considerable physiological import and also because these complexes are in many respects archetypical cases of charge-transfer complexes between a strong donor and a strong acceptor. Matsunagal suggested that the ground state of the complex is dative in the solid state; however, a non-bonding ground state is indicated because the complex dissociates in benzene. Further solid state ir spectra at different temperatures2 again indicate that at least the 2: 3 complex is indeed dative in its ground state. Stoichiometries of 1: 2 as well as of 2 : 3 have been reportede2 2. EXPERIMENTAL
TECHNIQUE
Reagents used were analytical grade purity. Various techniques have been employed to follow the formation of charge-transfer complexes, eg nm$, esr,4 surface tension.5 Nuclear quadrupole resonant+ and spectroscopy,7 especially in the uv and the ir have all been used with some success. Especially in uv spectroscopy, difficulties are often encountered due to the masking of charge-transfer bands by the absorptions of the components. This difficulty does not arise in conductometric titrations, which have been successfully introduced for the study of charge-transfer complexes.8 This method involves the titration of a donor with an acceptor solution or vice versa in a common, inert, but high permittivity solvent, and following the ensuing conductivity changes. The stoichiometry is indicated by a peak in the concentration DSconductivity plot ; the value of the conductivity at the peak is a measure of the concentration in the solvent of the ions forming the complex. It is very difficult to choose a truly inert, high permittivity solvent. Our choice, acetonitrile, has been used in previous work ;2 it tends to exhibit acceptor properties, though these may be neglected in the presence of the far stronger acceptor, viz iodine. The conductivity cell was temperature controlled by pumping water through a mantle surrounding the cell. The electrodes were bright platinum. Cell-resistance values were measured by means of a General Radio bridge type 1650-A operating at 1000 Hz. The cell was standardized against a 0.01 N KC1 solution to permit conversion of conductance values to conductivities. All data refer to 20°C unless stated otherwise. 3. RESULTS
AND
DISCUSSION
3.1 Conductivity titrations The results of two conductimetric titrations2.8 of a 9-9 x lo-4 M solution of phenothiazine with a 10-O x lC@ M solution of iodine in acetonitrile, and vice versa, are shown in Fig. 1.
Electrochemicalstudies of phenothiazine-iodinecharge-transfercomplexes Iodine.
1805
% 3
Phenothiarine.
%
FIG. 1. Conductance titrations of a 9-9 X lo-* M solution of phenothiazine in acetonitrile with a 10-O x lo-* M solution of iodine in the same solvent, and vice verm. The circles refer to addition of iodine and the dots to the converse titration.
A peak occurs at a concentration of 3.4 x 10--4M of phenothiazine and 6.6 x lo-4 M of iodine, corresponding to a stoicbiometry of 2 phenotbiazine: 3 I, with an equal contribution of the 1: 2 complex. Converting to conductivities, and deducting that due to the non-zero conductivity of the acetonitrile itself,* the net contribution to the total conductivity of the ions arising from the charge-transfer complex due to its dissociation in the solvent, is 32-2 mho/cm. Plotting the same data in the differential forms as Aa/Ac vs c, where c is the % concentration of phenothiazine, indicates the presence also of 1: 3, 1: 1 and 3 : 2 stoichiometries, although their contribution to the total conductivity is very small. Since the current at the peak is seen to be about equally due to the I : 2 and to the 2: 3 complex, the actual complex concentration was 2.6 x lOa M. 3.2 Activation
energy
The conductivity of the pre-prepared 1.6 x low4 M complex in CH,CN increases but slightly with increasing temperature. Its activation energy is about 0.0029 eV while that of the conductivity of the solvent, acetonitrile, itself is 0.060 eV, the temperature range being 313-275°K. The latter value is not too different from the activation energy of the viscosity9 of pure CH,CN, viz 0*069 eV. The activation energy of the conductivity of the complex solution is seen to be far below of what would be expected from the effect of the viscosity on the mobility of the ions. It may be that higher temperatures favour recombination, so that the mean lifetime of the carriers drops with rising temperature, thus in part counteracting the rise in mobility to be expected from the viscosity change. Alternatively it is quite possible that the low value of the activation energy might be due to an anomaly similar to that reported by Forster and Langer:lO these authors found conductivity maxima at certain temperatures, working with tetraThus the slope of the conductance vs methylenediamine/aralkyl lithium complexes. temperature curve in the vicinity of the maximum is much reduced, an effect which Forster and Langer ascribe to quadrupoles and higher associates being thermally
1806
A. BRAU, J. P. FARGESand F. GUTMANN
dissociated. An entropy effect, as suggested by Forster means to be ruled out. One would be tempted to associate these very low Grotthus-chain-like charge transport via I 3 (see below), transport mode of H,O+ in aqueous solutions involves an at room temperatures, l1 much in excess of that found in
and Langer,
is also by no
activation energies with a but the qualitatively similar activation energy of 0*09/eV this case.
3.3 Equivaknt conductivity Dilution of the complex in CH,CN solution with CH,CN resulted in the equivalent conductivity remaining constant to f3 per cent at a value of 130 Q-l . cm2/eq within a concentration range of 3 x 1e3 to 10--6M. The complex in acetonitrile thus appears to be completely dissociated. 3.4 Mobility A concentration of the complex of 2-6 x l@ M upon complete dissociation yields a carrier concentration of 3.2 x 101’carriers/cm3, assuming equal contributions to the conduction current from both the 1: 2 and the 2: 3 complexes, yielding a mean stoichiometry of l-05 : 2. We therefore shall simplify matters by assuming the presence only of the I:2 complex. Thus, its concentration of 2-6 x lo”’ M results in 3.2 x 1017carriers/cm.3 From the conductivity equation U = e C niZil(li, I
(1)
where c is the conductivity, ze the charge carried by the i’th carrier species of mobility pi and concentration ni, e being the charge of the electron, the mean ionic mobility p may be calculated as 6-2 x IV cm2p.s at 20°C. The transport numbers were determined from electrolysis in a Hittorf-type cell as t- = 0.83 for the anion, t+ = 0.17 for the cation ,
yielding for the individual ionic mobilities p- = 1-O x 10-s cm2/V.s, p+ = 2.1 x 1o”‘cm~/v.s. The mobility of the majority carrier, viz the anion, is seen to be relatively highapproximately *rd that of the (hydrated) proton in aqueous solutions.ll The mobility values of most organic ions in solution are of the order of lOA to lo+ cm2/v.s; for benzene values between 4-5 and 2.1 x IO-4 cm2/V.s have been quoted.4=12 Correcting for the rise in mobility to be expected from the lesser viscosity of acetonitrile as compared to that of benzenea. cp at 15Oas against O-705 for benzene -and using Walden’s Rule we find for the mobility of a hypothetical benzene ion in CH,CN about 8.5 to 4.2 x 1O-4 cm2/v.s as against our experimental value for ,u+ of about 2-l x 1O-4 cm2/V.s. Thus the mean cation radius is about 2 to 4 times larger than that of the hypothetical benzene ion. The increased carrier size of the complex ion compared to that of a benzene ion therefore appears to be compatible with our suggestion that the carriers in the present
Electrochemicalstudies of phenothiazine-iodine charge-transfercomplexes system are solvated entities of the form I,.PH+.I,,
I,-.PH+.IS-
or I,.PH.I,-
1807
as proposed
below. 3.5 Changes
in the permittivity
of the solvent
A phoreogram of the dilution of the complex in CH,CN solution with Ccl, shown in Fig. 2. Carbon tetrachloride is a solvent of very much lower permittivity
[campbxl
is ;
Kr4M
FIG.2. A 5 x lo-’ M solution of the phenothiazine-iodinecomplex dissolvedin acetonitrite is diluted with carbon tetrachloride.
the slope of the curve is seen to change at about 3 x lo-4 M. This is considered to be due to the formation of larger ionic aggregates caused by the drop in the permittivity of the solvent. The freshly prepared compIex in solution is yellow, changing rapidly to green ad eventually, after several days, to blue-violet. This ageing effect may be speeded up by ikmination and/or by addition of a few vol- *A of water. The latter, in larger concentration, also causes a further about 60 per cent increase in the conductivity. This is illustrated in Fig. 3, which shows conductance values of the pre-prepared complex in
140-
1 a F’IIO.3. A 5
X
10m4M solution of the phenothiazine-iodine complex in acetonitrileis diluted with water.
I
a08
A. BRAU, J. P. FAROES and F. GUI-MANN
CH,CN as a function of water added. The conductance remains substantially constant until about 20 per cent water have been added; it then rises to a peak whence it decreases to approach the very low conductance of “pure” water. It should be emphasized, however, that the acetonitrile used in the present study certainly contained traces of water, and thus further small additions are unlikely to produce any large effects ; in fact it has been suggested by Prue l3 that “over the entire solvent range (permittivity 12 to 38; authors) it is water molecules alone that are in the immediate neighbourhood of the ions.” The pH at 25 per cent water is 2.64 and rises approximately linearly to 3.4 at about 80 per cent water, whence it starts to increase rapidly towards neutrality. The pronounced rise in conductivity upon addition of about 36 per cent water is considered to be due to the further dissociation of the carriers caused by the rise in the permittivity of the medium. The original carriers are probably entities of the form I,PH+.I,, I,.PH+.I,; several other canonical forms are also possible. 3.6 Structures The 2:3 complex has been suggested2 to have a ground-state which then perhaps dissociates thus: Is-.PH+.I,.PH+.I,, I,-.PH+.I,I,-.PH+.I,.PH+I,-
it
Is-.PH+ 12 I,
configuration
of
+ PH+.I,
+ I,-.PH+.I,
+ 2 PH+.
(hl)
The 1: 2 complex can be considered as a resonating structure with the negative charge being shared, uiu the aromatic intermediary, by the two iodine molecules, Is-.PH+.I,-. A collisional dissociation then should give rise to 2 I,.PH+.Iz-
$
I,-.PH+.I,-
+ I,.PH+.I,
2 I,- + I, + PH+.
(a21 WI
In a medium of higher permittivity it is expected that the processes (b) above would be favoured; however even the mere effluxion of time would tend to result in the formation of more and more of the smaller entities if the permittivity of the medium is not too low. The above conjectures are supported by some spectroscopic evidence, since the 1, ion in CH,CN is known l4 to give rise to an absorption line at 335 nm. This line in fact is evident in the spectra of all the PH/I, complexes. It becomes stronger with time and/or with addition of water. However, Kobinata and Nagakura l5 have shown that the equilibrium between the complex and its constituents shifts towards a higher concentration of the complex as the permittivity of the environment rises. Part of the conductivity increase upon addition of water may be due to this effect. Current transport in solid iodine doped with an acceptor has been studied by Kommandeur et aZ,ls who find that the conduction mechanism involves a poly-iodide ion I,- and most likely I,-. They invoke a reaction scheme D + I,-
D+ + I,,
I,- + I,- T;’ I,- + I-.
Electrochemicalstudies of phenothiaziae-iodine charge-transfercomplexes
1809
Previous attempts to prove the existence of I- ions in the solid complex2 were negative ;
this of course does not rule out the existence of I- in CH,CN solution, though it is regarded as unlikely. The relatively high mobility values here reported would also indicate a chargetransport mechanism similar to that of protons-H,O+ ions-in water ;ll such a mechanism has been indeed proposed for the charge transport involving 13ions in an iodine lattice.la Indeed, if iodine is replaced by chloranil as the acceptor the value of the conductivity peak has been showr? to decrease drastically. One can thus conclude that the anion is the (solvated) Is- ion. It is of interest to note that the closely related (solid) N,N’-diphenyI-p-phenylenediamin/I, complex has been shown by Hadekl7 from crystallographical studies to have a 1: 2 stoichiometry with one donor molecule interacting with two acceptor molecules . . . forming “poly-acceptor iodine chains”. The solid structure DAADAADAA would be expected to dissociate in a high permittivity solvent in the manner suggested in schemes (a) above. All ions must be considered to be solvated in a high permittivity medium. 3.7 Electrolysis Prolonged electrolysis in a two-compartment cell with a cellulose separator and gold electrodes 6 cm apart with 280 V applied resulted in the anolyte becoming brown (iodine) while the catholyte became pinkish-violet. The colour changes are reversible upon repeated polarity reversal. While the value of the maximum current in each electrolysis experiment tends to drop approximately exponentially upon repetition, using the same solution, the charge transported stays very nearly constant. Upon cessation of the electrolysis, the anolyte and catholyte slowly recombine by diffusion until the original complex solution is reconstituted. It thus appears that the complex formation/dissociation equilibria are indeed reversible. The discolouration of the anolyte indicates that the anions are iodine ions I,-, molecular iodine being plated out at the anode, in agreement with the reaction schemes proposed above. The polarization voltage measured between the electrodes, after electrolysis, by means of a Cary Electrometer was about l-5 V; it decays slowly with time due to recombination of the ions through the separator. There was no discernible attack on the gold electrodes even after electrolysis prolonged for 6 h. There always remains a small, constant current showing no sign of diminution with time, as observed in the pyridine-iodine system by Wisdom and Forster.24 This current may well be eIectronic, in contradistinction to the timedependent ionic component. 3.8 Energetics A new absorption band appears at about 650 nm = l-92 eV, which tends to shift to lower wavelengths with ageing, becoming also stronger. Thus, in the green complex it appears at 625 nm = 1.99 eV and in the violet adduct at 550 nm = 2.26 eV. There are no absorptions in that region of the components, I, and phenothiazine. These new bands are rather flat and wide and are considered to be the charge-transfer bands of the complex. This is further supported by the report of a charge-transfer band at 665 nm
1810
A. BRAU, J. P. FARC+ESand F. GUTMANN
observed in the phenothiazin+bromanil complex by Kinoshita.la I, is a stronger acceptor thanp-bromanil and thus one would expect the band to appear at somewhat higher energy. The (gas) ionization energy I, of PH is reported”’ to be 7.14 eV and the (gas) electron aflinity A, of I, is given by YomosaaO as 2.19 eV, superseding the earlier value of l-8 eV estimated by Mulliken.21 The energy Isv,, of the charge-transfer band maximum is given by22 E=hv
CT---1 g -AA,-
W,
(2)
where W is the dissociation energy of the charge-transfer excited state. We can also approximate E by E = Ig A, - #a, where 4 is a term determined by the polarization, or the solvation, energy of the environment, which one would expect to be not too far different from W, though the latter quantity refers to an excited state only. Therefore, W = O-9 eV initially, rising with time and/or addition of small quantities of water to 1.07 eV. This is very much below the usual range of hydration energies, as is to be expected. The change itself, from O-9 to l-07 eV, is however much larger than what one would expect from a solely electrostatic interaction and is probably associated with an entropy contribution due to the increased structuring of the medium in the presence of larger amounts of water. A blue shift of the charge-transfer maximum is ascribed by Yomosa20 to an increase in the value of the local field if the potential energy of the ionized ground state of the complex in the local field is larger than its potential energy in the absence of the local field with the ground state and the excited states contributing equally. The local field acting on the complex here is that due to the environmental ions as well as dipoles. It is directed from the acceptor to the donor molecule. Thus, Yomosa defines2* a critical energy of the complex as that value of the potential energy of an isolated complex molecule at which the ionic and non-bonding contributions to the ground state are equal. If now the potential energy of the complex in the presence of a “local field” due to the environment, in which the no longer isolated complex molecule finds itself, exceeds this critical value, a blue shift of hv,, with increase in the value of the local field as well as with increasing permittivity of the environment is predicted. This has indeed been observed in the present case upon addition of water. It then can be concluded that the ground state is predominantly ionic and its electronic structure resembles that of the excited state of the complex in the absence of the local field.21 It is a feature of Yomosa’s theory 2o that the ionic ground state in such a case involves no (or very little) activation energy, as has been observed with this complex. A similar blue shift has been observed Anex and Hill% for the TMPD (N,N,N’,N’tetramethyl-p-phenylenediamine)/chloranil complex upon changing the solvent from cyclohexane to acetonitrile. These authors also conclude that the ground state of that complex is ionic in solution, and it is thought that the results here presented provide unequivocal evidence for such a case. wish to thank the Centre Natl. de la Recherche Scienttique, Paris, as well as the Direction des Recherches et Moyens d’Essai, Paris for Snanciaf support which made this work possible. We are indebted to Dr J. Basso of the Chemistry Dept. of the University of Nice for his assistance with the spectra. One of us (F. G.) wishes to record his appreciation of the hospitality
Acknowledgements-We
EIectrochemicalstudies of phenothiaxine-iodinechargetransfer complexes
1811
receivedfrom the Director of this Laboratory, ProfessorVasilescu, and from his colleaguesand staff, he also wishes to thank the Centre Natl. de la Recherche Scientifique, Paris, the Direction des Recherches et Moyens d’Essai, Paris and the University of Nice for a Visiting Professorship.
:: 3. 4. 5. 6. 7. 8.
REFERENCES Y. MAIXUNAGA,HeIv. phys. Acta 36, 800 (1963). F. G~TMANNand H. KEYZER,J. c/rem.Phys. 46, 1969 (1967). R. FOSTERand C. A. FYFE, Biochim. biophys. Acta 112,460 (1966). K. TSUJIet al. J. them. Phys. 46,2808 (1967); 45,2894 (1966); F. GUTMANN and L. E. LYONS, Orgunic Semiconductors. Wiley, New York (1967); L. I. B~GUSLAVSKII and A. V. VANNIKOV, Organic Semiconductors and Biopolymers. Plenum Press. London, New York (1970). I. BLEI, Archs. Biochem. Biophys. 109, 321 (1965). R. A. BENNETand H. 0. HOOPER,J. them. Phys. 47,4855 (1967). G. BRIEGLEB, Elektron Donator Akzepfor Komplexe. Springer, Berlin (1961); L. J. ANDREWS and R. M. KEEPER,Molecular Complexes in Organic Chemistry. Holden-Day. San Francisco Opt. i Spektroskopya 13, 43 (1962). (1964); N. G. BAKIISHJEV, F. GUTMANN and H. I(E~YzER, Electrochim. Acta 11, 555, 1163 (1966) 12, 1255 (1967); J. ind. Sci. Res. 26, 19 (1967).
9. Handbook of Physics and Chemistry, 51st edn, p. F-37. Chemical Rubber Co., Cbveland, Ohio (1970-71). and A. W. LANGER,Collogues Internationaux du CNRS, Extr. N” 179, Grenoble 10. E. 0. FOR~TER (1968); CNRS, Paris (1970). Modern Electrochemistry, Vol. 1, p. 473. Plenum Press, 11. J. O.‘M. Bocxars and A. K. N. REDDY, New York (1970). Technol. 12. F. G~~MANN, Electrochim. Acta 7,59 (1962); CH. YAMANAKA,P. CHONGand T. S~JI-~A, Reps.
Osaka
Univ. 6, N”
188 (1956).
Ionic Solutions, ed. B. E. CONWAYand R. G. BARRADA~, p. 163. 13. J. E. PRUE,in ChemicaiPhysicsof Wiley, New York (1966)). 14. A. I. Powv and R. F. SWENSEN, J. Am. them. Sot. 77, 3724 (1955). and S. NAGAKURA,J. Am. them. Sac. 88, 3905 (1966). 15. S. KOBINATE and J. Ko MMANDEUR, J. them. Phys. 49, 4069 (1968); J. LUDWIG and J. KOM16. D. BARGEMAN MANDEUR, J. them. Phys. 52,2302 (1970). 17. V. HADEK,J. them. Phys. 49,5202 (1968). 18. V. M. KINOSHITA, Bull. them. Sot. Japan 35,1609 (1962). 19. F. GUTMANNand L. E. LYONS,Organic Semiconductors, p. 693. Wiley, New York (1967). 20. S. YOMOSA,Progr. theor. Phys., Suppl. N” 40,249 (1967). R. S. M ULLIKEN, J. Am. them. Sot. 74, 811 (1952). z’:: J. S. m, J. R. PLAY and H. K. MCCONNELL,J. &em. Phys. 21,66 (1953). 23. B. G. ANEX and E. B. HIJ..L,J. Am. &em. Sot. 88,364S (1966X J. Polym. Sci. C, No 17, 125 (1967). 24. N. E. WISDOMand E. 0. FOR~TER,