Solvent effect on the kinetics of the electrooxidation of phenothiazine

SOLVENT EFFECT ON THE KINETICS OF THE ELECTROOXIDATION OF PHENOTHIAZINE M. OPAMO

and A. KAPTURIUEW~CZ

Institute of Physical Chemistry of the Polish Academy of sciences, 01-224 Warszawa, Kasprzaka 44/52, Poland (Received 24 January 1985, in revised form 19 March

1985)

Abstmct4neelectron oxidation of phenothiazine to the corresponding radicalcation was used as a model system to study the solvent effect on the heterogeneous charge-transfer kinetics. The standard rate constant of the studied electrode reaction was found to depend considerably on the nature of the solvent. The experimental kinetic data has been interpreted in terms ofthe dielectric dynamic properties of the solvent. The linear relationships between the standard rate constant and the reciprocal of the longitudinal dielectric relaxation time of a given solvent have been found in the aprotic case as well as for hydrogen-bonded solvents. The difference between both groups of sokents may be explained by the different dielectric relaxation b&&our or by the difference in the reaction site in respect to the electrode surface.

INTRODUCTION The theory of outer-sphere homogeneous and heterogeneous reactions in polar media was developed using both classical and quantum approaches[l-71. The general conclusion of these works is that the observed rate constant, k,,, is related to the overall free energy barrier, AG*, by: k,, =

K~,

A, exp (-AG$fRT)

(1)

where K=, is the electronic transmission coefficient and A, is the nuclear frequency factor. K,! describes the probability with which electron trankfer will occur once the transition state has been formed. A,, has conventionally been assumed to correspond to a collision frequency Z, which is usually taken to be equal to the collision number for gas-phase heterogeneous or homogeneous collisions involving hard spheres[3. S]. However there are intrinsic reasons to prefer different formulation. One is based on an “encounter pre-equilibrium” model whereby the frequency factor is determined by the vibrational activation of a “precursor complex” having a suitable geometric configuration for electron transfer. Such a model has recently received a good deal of attention for homogenous as well as heterogenous processes [9-l 21. The different formulation of A. is proposed in the Levich-Dogonadze theory[5, 61 which also takes into account the properties of the electrode material. It is important to recognize that the above models are based on a distinctly different physical treatment. Indeed distinctly different values of the overall preexpotential factors are obtained from these approaches. The second problem is the estimation of AG*. According to the Marcus treatment[l,B] AGt is the sum of two terms. The first one is the energy of the solvent reorganization &/4 and the second corresponds to inner reorganization energy of reactants &/4. AG* = A,/4 + A,/4

(2)

The value of A, may be estimated on the basis of a simple extension of the Born model. For one-electron electrode processes I, is given as follows[2]: 1, = Ne2/8r&,(r-‘-22d-‘)(&,:

-L-I)

(3)

where + and d are the radii of the reactant and the distance from the electrode respectively, eoprand es are optical and static dielectric constants respectively. copr is usually approximated as equal to ni where nD is the refractive index of a given solvent. Different methods of estimating 1, were also developed A non-spherical model in which the reactant is represented as obiate ellipsoid was proposed by some authors[13, 141. Another refinement in the estimation of I, was introduced by Peover and Powell[l5], who treated species with non-uniformly distributed charge as two or more spheres of different charges. A slightly different treatment along the same lines has been given by Fawcett and Kharkats[lB]. The inner reorganization energy li corresponds to changes in the bond lengths and the bond angles[ 17-j. For organic molecules it is often assumed that & is equal 0.0z-O.10 I,[33. The study of the solvent effect on charge-transfer kinetics can be seen as one of the best methods of examining the theoretical prediction of the rate constant. In the literature some data exist concerning this problem in the homogeneous case as well as for

heterogeneous charge-transfer kinetics. The following types of the electrode reactions have been studied: electroreduction of the simple inorganic ions[ l&20], electroreduction of the organic compounds[21. 223 and both electroreduction and electrooxidation of the transition metal complexesC23, 241. Generally, the experimentally observed solvent effect is greater than the theoretical prediction. The observed discrepancies the cannot be ascribed to the effect of electrode-solution interface; the effect of the solvent on the homogenous charge-transfer kinetics[25-271 is similar to that of the heterogenous ones. Recently it was shown that the dielectric dynamic properties of the solvent may exert a much stronger 1301

M. OPALLO

1302

AND

influence on the rate of heterogeneous charge-transfer than the static properties[22, 241. In the case of both electrooxidation and electroreduction of the transition metal salene complexes[24] and in the case of the electroreduction of nitromesitilene[22] in aprotic solvents it has been found that the shorter the dielectric relaxation time of a given solvent, to the faster is the electrode reaction. Similar conclusion has been also drawn by Weaver and Gennett[28] in the case of the electrode reactions of metallocenes. They used the ‘*encounter preequilibrium model” for the electrode reaction together with theoretical considerations about the influence of the dynamics of polar solvent molecules on the chargetransfer reaction in solutions[29-331 to examine the solvent-dependent rates of the electrochemical processes. They express the heterogenous charge-transfer rate constant, k,, as follows[28]: k, = K~,S~,TL’(~~,/~~~CKT)~~~~X~(-_~/~RT)

(4)

where K~,and Se1are electron tunnelling probability and effective thickness of the “reaction zone”, respectively, rL is the longitudinal dielectric relaxation time defined as: =L = ~o”cQ/~s

(5)

where E, is the high frequency dielectric constant. This expression indicates that the solvent dielectric relaxation can have a marked effect on the reaction rate. The basic mechanism of the effect is simple: the polarization of the surrounding solvent dipoles can lay behind the motion of a charge in its intrinsic reactive step of passage over a chemical potential energy barrier. The solvent is thereby dynamically coupled to the intrinsic activated reaction process. Such non-equilibrium solvation phenomena can lead to a pronounced departure of the electron exchange rate from the classical theory. The purpose of the present investigation was the study of the solvent effect on the heterogeneous charge-transfer kinetics in aprotic and protic solvents. One-electron electrooxidation of the phenothiazine (PNT) to the corresponding cation was chosen as a suitable model system because the mechanism of this reaction is solvent independent ([34] and refs therein).

EXPERIMENTAL Materials The solvents used were: acetonitrile (ACN), acetone (AC), dichlormethane g$Fl,). nitroethane (NE), dunethylsulfoxide dimethylformamide (DMSO), propylene carbonate’( tetrahydrofuran (T’HF), hexamethylphosphoramide (HMPT) and Nmethylformamide. These were dried and purified for electrochemical use in a conventional mannerC35-j. The other solvents: methanol (MeOH), ethanol (EtOH), isopropanol (PrOH-2), n-butanol (BuOH-I) and sulfolane (TMS) were all spectroscopic grade and were used without further purification. Analytical grade NaClO,, KPF, and (C,H,), NCIO., (TBAP), used as the supporting electrolytes, were dried at 120,100 and 60°C respectively in vacuum. Analytical grade ferrocene (Fc) and PNT were used without further purification.

A.

KAFTURKIEWICZ

Apparatus The voltammetric measurements were performed using a measuring system constructed from an EP-20A potentiostat and an EG-20 function generator (both ELPAN, Poland). Cyclic voltammetric curves were recorded on TRP-XY recorder (SEFRAM, France) or on DT-5 16A oscilloscope (KABID, Poland). Measurements were performed in a conventional three-electrode cell. A bright-platinum plate with a surface area of 0.008cm2 was used as the working electrode. The other electrodes were: a mercury pool as a counter electrode and saturated aqueous calomel electrode (with salt bridge) as a reference electrode. The working electrode was polished before each use. The positive feedback technique was used for ceI1 resistance compensation. The uncompensated ohmic drop was smaller than 2 mV. Procedures All measurements were carried out at 25f0.2”C. The solutions were deoxygenated with pure argon presaturated by bubbling~ ihrough the s&ent used. Concentrations of PNT were 0.1-0.5 mM. Diffusion coefficients D and redox potentials E,“, were determined from cyclic voltammetric curves recorded at potential scan rates 5-50mVs-‘. All potentials were redox internal reference system referred to ferrocene/ferricinium using for recalculation our own data from independent experiments. Standard heterogeneous rate constants k, were evaluated from the observed differences in cathodic and anodic peaks potentials AE on the cyclic voltammetric curves according to the relationship given by Nicholson[36]. AE was measured with a precision + 2 mV for a number of different potential scan rates in a range I-50 V s-‘. The errors of evaluation of the electrochemical parameters were estimated as: k, + 20 %, D + 10 % and E& f 5 mV.

RESULTS

AND DISCUSSION

The electrochemical behaviour of PNT in various solvents has been investigated at a platinum electrode using cyclic voltammetry. One-electron oxidation of PNT to the corresponding cation has been observed in all solvents used, as was previously reported in the literature[34]: PNT --em =+PNT+.

(6) The diffusion coefficient of PNT varies with the solvent viscosity, according to the well-known Stokes-Einstein theory. The linear relationship between the estimated D value and the reciprocal of viscosity has been found. This result is compatible with the received mechanism of the electrode process. The values of D correspond to effective radius of PNT molecuIe rp T = 3.9A, which is in good agreement with rpNT expected from the molecular model the value o tp” of PNT.

Solvent effect on the kinetics of the electrooxidation of phenothiine Siandard

potentials

The standard potential of the PNT oxidation, E”,,, t;s Fc, has been found to vary appreciably in different solvents but no effect of the supporting electrolyte concentration has been observed. Evidently the ionpair formation phenomena can be neglected in the present case (cf[34,37]). On the other hand the solvent effect on the E”,,, value can be discussed in terms of donor-acceptor interactions[38]. The approximately linear relationship between E& and the donor number (DN) of a given solvent is observed, a similar result to that noted previously[34]. The changes of E&r with the changes of DN as a measure of the solvent basicity in the Lewis meaning, indicate that the energies of solvation of PNT+ cation are greater than those of the neutral molecule, PNT, but the solvation phenomena are rather weak in the present case. The kineric data in aprotic solvents The rates of the electrode process of PNT have been also measured in all the solvents used. The apparent standard rate constants are nearly independent of the electrolyte concentration. This suggests that the estimated values of k, can be regarded as “true” values of the rate of the electrode process not influenced by the potential drop across the diffuse layer (Frumkin correction), cf[39]. The E”,,, are somewhat positive with respect to the estimated zero charge potentials of platinum electrodes in organic solvents using the ideas of Frumkin[40], cf[41 J. On the other hand, the radius of the PNT molecule is greater than the radius of the solvated anions CIO, or PF,. Thus the reaction site is expected to be outside the outer Helmholtz plane (oHp). This can be the reason why these reaction rates are almost independent of the supporting electrolyte concentration. The values of k, are presented in Table 1 together with the corresponding values of D and E”,,, in the case of aprotic solvents. On the basis of the data presented in Table 1 it is readily apparent that k, varies considerably with the solvent nature. The obtained kinetic data cannot be interpreted in terms of the Marcus theory. No simple correlation between k, and the quantity: E&: -E,~ is observed. Thus the changes of k, with the solvent cannot be explained by the outer shell solvation effects. No simple correlation with DN which should reflect Table

NO. 1 : 4

5 6 7 8 9 10

I. A summary

SOhOt

ACN AC CH2CI,

NE DMF

DMSO PC THF TMS HMPT

of

1303

the inner salvation shell effect could not be also found. On the other hand, the k, values depend on zL of a given solvent. The greater is TVthe smaller is k,. This is presented on the Fig. 1. We tried to interpret our kinetic results in terms of Equation (4). The theoretical values of k, calculated according to above equation are presented in Table 2. Three different values of k, correspond to the different distances of reactant molecule from the electrode: rpNT, 2rsol~+ ‘PNT’ (where rsolv is the radius of the solvent moIecule)_ The last ease d = COcorresponds to where the “image term* in Equation (3) is completely neglected (cf.131). The composite term K& in Equation (4) is taken as 6 x lop9 cm in each solvent; this assumes that the reaction is adiabatic for the closest approach of the reactant to the electrode surfaee[42]. In all three cases the predicted sequence of k, values agrees well with those found experimentally, but the calculated values are in all cases higher than the experimental ones. This can be attributed to neglection of the inner reorganization energy term a,/4 in Equation (4) or to the non-adiabacity of the electrochemical oxidation of PNT: K__,4 1 hence ~,,c5,, Q 6 x 10e9 cm. The first reason seems to be less likely, because the reaction of homogeneous oxidation of PNT is very fast[43], which indicates that li can be neglected in the present ease. Kinetic

data in hydrogen-bonded

solvents

The electrochemical behaviour of PNT has been also investigated in the organic, hydrogen-bonded solvents. One-electron oxidation of PNT to the corresponding cation according to Equation (6) has been observed in aprotic solvents (cf[34]). The estimated electrochemical parameters are summarized in Table 3. The rate of the electrooxidation of PNT is nearly independent of the electrolyte concentration but varies considerably with the solvent. It is readily apparent that the k, values depend on the or of a given solvent as is also presented on Fig. 1. However the interpretation of kinetic data in terms of dielectric relaxation is more complicated. The reason is that in the case of hydrogen-bonded solvents more than one dielectric dispersion region is observed[44]. Taking into consideration only the slowest TV one may observe correlation between this quantity and k, but the

the electrochemicalparameters of the electrooxidation of phenothiazine in aprotic solvents

Electrolyte KPF, KPF, TBAP TBAP KPFG KPFe KPFB NaClO., KPFs KPF,

Electrolyte concentration range W) O.OW.5 0.05-0.3 0.14.5 O.lxl.3 0.05-0.5 o.oE-o.3 0.05-W O.lLa.5 0.14LS O.NI.5

E”,,,

vs Fc

(V) 0.225 0.220 0.150 0.165 0.110 o.a90 0.220 0.140 0.215 0.030

1ObD (cm* s-l) 13.1 17.3 13.0 14.0 10.3 3.4 1.6 9.0 0.2 1.2

k

(ems-‘)

0.44 0.22 0.19 0.19 0.10 0.077 0.068 0.046 0.017 0.014

M. OPAL~O

1304

‘MEOH OS-

non

/ f

/

DMSO

/

G

y&&.$

NMF

I IO-

f 6ACN

f’ *

Of *

AND

P$pF

/ BIJOH-I

B

PrOtl-2

(9 15-

/

W’ THF / /

/

&MS 20

HMPT IO

I I2

II

-1og 7‘

Fig. 1. Standard rate constants k, of the electrooxidation of PNT as a function of reciprocal of Ihe longitudinal dielectric relaxation time zL of given solvent.

A.

KAF-NRK~EWICZ

reaction parison solvents

is faster than it could be expected by comwith experimental data in the case of aprotic assuming the same value of xtldLl for both groups of solvents. The values of k, calculated from Equation (4) are presented in Table 4. The differences between kinetic behaviour of PNT

in both groups of solvents can be caused by many reasons. The first may be that the faster dielectric processes, which may play an important role in hydrogenbonded solvents should be also taken into account. The second may correspond to the polarization diffusion mechanism of the solvent relaxation. According to Van der Zwan and Hynes[45-47] this effect can be intrinsic for the solvent with relatively long TL’ The third one may be the differences in K~,&, values for both groups of the solvents. These may be caused by differences between oHp and the reaction site. This non-coincidence should be expected more in aprotic than hydrogen-bonded solvents. The radius of solvated Clog is greater in alcohols and closer to rpW

Table 2. The values of the longitudinal relaxation times 5L for aprotic solvents. The calculated heterogeneous charge-transfer rate constants k.-lc for the different distance of the reacting molecule from the electrode d kmlc , Solvent

I

ACN AC CHI Cl2 NE

0.526

0.2+

0.493 0.481 0.380

0.3* 0.411 0.8f

163 142 117 129

14.2 12.0 20.9 10.6

2.1 2.4 2.2 5.6

DMF DMSO PC THF TMS HMPT

0.462 0.437 0.48 E 0.372 0.432 0.437

1.37 2.47

42 28

4.1 1.6 1.2 5.3 1.2 0.7

0.9 0.3 0.3 1.6 0.2 0.2

5 6

7 8 9 10

* Radius

of the solvent

l/c.

(cm s-l)

No.

2 :

I/r+

10l=SL (s)

‘PNT

d =

2.6**

18

3.3++ 6.56 8.9li

33 II 7.4

molecule

rsolv calculated

from

d = 2rMlly + rPNT*

the molar

volume

d=a,

V of a given

SOlVCFJC + K. Krishaji and A. Hausingh, J. them. Phys. 41, 827 (1964). * J. H. Calderwood and C. P. Smyth, J. Am. chew. Sot. 78, 1295 (1965). 0 Value ofthe longitudinal relaxation time z,estimated using the Debye equation for TV = 3 QiRT[44]. 11S. Chandra and D. Nath, .I. them. Phys. 51, 5299 (1969). 7 H. Behret, F. Schmithals and J. Barthel. 2. phys. Chem. NF 96, 73 (1975). l * E. A. S. Gavel, J. them. Sot. Faraday Trans. 70. 78 (1974). w J. Crosley, S. W. Tucker and S. Welker, Trans. Fan&y Sot. 62. 576 (1966).

Table

3. A summary

of the electrochemical parameters in hydrogen-bonded

No.

Solvent

Electrolyte

11 12 13 14 15

MeOH EtOH PrOH-2 BuOH-I NMF

NaClO, NaClO, NaCLOd N&IO, KPFs

Electrolyte concentration range (M) o.o?GO. 3 o.o%O.z 0.03-O. I 0.1 o.oz%O. 3

of the electrooxidation solvents

EOPTvr Fe 0.165 0.190 0.170 0.170

0.035

of phenothiazine

fO6D (cm2 s-1)

ks (cm s-‘)

12.8 6.8 4.4 5.2 2.0

0.40 0.22 0.045 0.062 0.20

Solvent

effect on the kinetics of the electrooxidstion

of phenothiazine

1305

Table 4. The values of the longitudinal relaxation times rL for hydrogen-bonded solvents. The calculated heterogeneous charge-transfer rate constants /@c for the different distances of the reacting molecule from the electrode d k,-” No. 11 12 13 14 1s

Solvent MeOH EtOH PrOH-2 BuOH-1 NMF

(ems-‘)

lcPTL 1/n:, - l/E. 0.536 0.500 0.474 0.467 0.484

(s) 3.3+ 15.4+ 54.0$ 35.86 6.1 11

d=r,,

d=2r,,,+rpNT+

9.1 2.6 0.92 1.45 7.5

0.75 0.23 0.085 0.13 0.71

d=

m

0.11 0.041 0.018 0.031 0.14

* Radius of the solvent molecule rsalvcalculated from the molar volume v of a given solvent. + J. A. Saxton, R. A. Bond, G. T. Coats and R. N. Dickinson, J. &em. Phys. 37, 2132 (1962). * H. A. Rizk and I. M. Elanwar, Z. phys. Chem. NF 62, 225 (1968). s H. A. Rizk and N. Youseef, Z. phys. Chem. NF 58, 100 (1968). 11P. Winsor, IV and R. H. Cole, J. phys. Chem. 86. 2486 (1982).

Thus the term K.,&, may be greater because K,, generally depends on the distance of the reactant from the electrode [28]. AU these reasons can be regarded as equally probable. The small number of experimental data and the approximation of the theoretical model do not permit a more detailed discussion of this problem. CONCLUSIONS Our work supports the theoretical considerations about the influence of the polar solvent dynamics on the charge-transfer kinetics in the case of the electrode reactions. The value of the electron-tunneling probability K,~ is needed for more quantitative analysis of this problem. The problem of electron tunnelling across the metal-solution interface should be studied in more detail. Acknowledgements-We thank the late Dr Sci. Barbara Behr from our laboratory for her helpful discussion. This work has been carried within Research Project 03.10.

REFERENCES I.

2. 3. 4. 5. 6. 7. 8. 9. 10.

R. A. Marcus, J. them. Phys. 24, 966 (1956); Ann. Rev. phys. Chem. 29, 21 (1960). N. S. Hush, J. &em. Phys. 28, 962 (1958). J. M. Hale, in Reaction ojMolecules at Electrodes (Edited by N. S. Hush), Chap. 4. Wiley Interscience, New York (1971). I. 0. M. Bockris and S. U. M. Khan, Quantum Electrochemistry. Plenum Press, New York (1979). R. R. Dogonadze. A. M. Kuznersov and T. A. Marsagishvili, Electrochim. Acta 25, I (1980). R. R. Dogonadzc, in Reaction of Molecuks at Electrodes (Edited by N. S. Hush), Chap. 3. Wiley Interscience, New York (1971). J. Ulstrup, Charge Transfer Processes in Condensed Media. Springer Verlag, Berlin (1979). R. A. Marcus, J. phys. Chem. 43, 679 (1965). B. S. Brunschwig, J. Logan, M. D. Newton and N. Sutin, J. Am. them. Sot. 102, 5798 (1980). R. A. Marcus, Int. J. them. Kinet. 13, 865 (1981).

11. J. T. Hupp and M. J. Weaver, J. electroanal. Chem. 152, 1 (1983). 12. T.T.T. Li, M. J. Weaver and C. H. Brubaker, J. Am. them. sot. 104,2381 (1982). I 3. Yu. I. Kharkats, Sov. Eiectrochem. 10, 588 (1974). 14. A. Yamagishi, J. phys. Chem. 80, 1271 (1976). 15. M. E. Peover and J. S. Powell, J. electrounal. Chem 20, 427 (19691. 16. W. k. Fa&ett and Yu. I. Kharkats, 1. efectrounal. Chem. 47, 413 (1973). 17. R. A. Marcus, J. phys. Chem. 67, 853 (1963). 18. A. Bar&ski and W. R. Fawcett, J. electroanal. Chem. 94, 237 (197111 19. i. E‘&&ska, Z. Borkowska and Z. Galus, J. electroanal. Chem. 157, 251 (1983). 20. T. Biegler, E. R. Gonzales and R. Parsons, Coil. Czech. them. commwt. 36,414 (1971). 21. W. R. Fawcett and J. S. Jaworski, J. phys. Chem. 87,2972 ( 1983). 22. A. Kapturkiewin and M. OpaNo, J. electraanal. C&m. 185, 15, (1985). 23. S. Sahami and M. J. Weaver, J. electroonal. Chem. 124,35 (1981). 24. A. Kapturkiewicz and B. Behr, J. electroumal. Chem. 179, 187 (1984). 25. B. A. Kowert, L. Marcoux and A. J. Bard, J. Am. them. Sot. 94, 5538 (1972). 26. S. L. Kelly and K. M. l&dish, fnorq. Chew 23,679 (1984). 27. E. S. Yang. M. S. Chang and A. C. Wahl, J. phys. Chem. 84. 3094 (1980). 28. M. J. Weaver andT. Gennett,Chem. Phys. L&t. 113,213, (1985). 29. D. F. Calef and P. G. Wolynes, J. phys. Gem. 87, 3387 (1983). 30 D. F. Calef and P. G. Wolynes, J. them. Phys. 78, 470 (1983).

31. L. D. Zusman, Chem. Phys. 49, 295 (1980). 32. I. V. Ateksandrov, Chem. Phys. 51,449 (1980). 33. M. Ya. Ovchinnikova, Russ. theor. exp. Chim. 17, 507 11981). 34. b. Pahuszek and M. K. Kalinowski, Electrochim. Acta. 28, 639 (1983). 35. C. K. Mann, in Electroanalytical Chemistry (Edited by A. J. Bard), Vol. 3. Marcel Dekker, New York (1969). 36. R. S. Nicholson, Analyt. Chem. 37, 1351 (1965). 37. S. P. Sorensen and W. H. Bruning, J. Am. them. Sac. 95. 2445 (1973). 38. V. Gutmann,TheDono-Acceptor Approach to Molecular

1306

M. OPA~LO AND A.

Inttvacrions. Plenum Press, New York (1979). 39. P. Delahay, Double Layer and Electrode Kinelics. Wiley Interscience, New York (1965). 40. A. N. Frumkin, Potentialy nulyevovo zaryada, Chaps 7 and 8. Nauka, Moscow (1979). 41. A. Kapturkiewicz and B. Behr, J. elecrroanal. Chem. 163, 189 (1984). 42. J. T. Hupp and M. J. Weaver, J. phys. Chem. 88, 1463 (I 984).

KAFI-LJRKIEWICZ

Aa%. phys. org. Chem. 16, 79 (1983). and P. Bordevijk, Theory of Electric Polarization, Vol. 2. Elsevier, Amsterdam (1978). 45. G. van der Zwan and J. T. Hynes, J. them. Phys. 76,2993 (1982). 46. G. van der Zwan and I. T. Hynes, .I. them. Phys. 78,4114 (1983). 47. G. van der Zwan and J. T. Hynes, Ckem. Phys. L&t. 101, 367 (1983). 43. L. Eberson,

44. C. J. F. Bottcher