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Adsorption and catalytic properties of iron coproporphyrin III complex at the octane∣water interface
Bioelectrochemistry and Bioenergetics, 10 (1983) 477-483 A section of J. Electroanal. Chem., and constituting Vol. 155 (1983)
477
Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands
5 5 5 - - A D S O R P T I O N AND CATALYTIC PROPERTIES OF IRON C O P R O P O R P H Y R I N III COMPLEX AT THE OCTANE [ WATER INTERFACE
A.G. VOLKOV, M.A. BIBIKOVA, A.F. M I R O N O V * and L.I. B O G U S L A V S K Y
Institute of Electrochemistry of the Academy of Sciences of the U.S.S.R., * Moscow Institute of Fine Chemical Technology, Leninsky Prospect 31, Moscow, V-71 31 (U.S.S.R.) (Revised manuscript received April 9th 1983)
SUMMARY Adsorption of the iron complex of coproporphyrin III tetramethyl ether at the octane [ water interface has been investigated. It was found that the process is well defined by the Frumkin isotherm. The attraction constant was estimated to be a = 1.3, adsorption energy Gads = --9.3 kcal/mole, the angle between the porphyrin ring and interface - 6 5 °. The electron-transfer reaction at the octane[water interface with a reducing agent in water, an oxidizing agent in octane and with porphyrin as a catalyst was studied. The change of potential drop at the octanelwater interface was found to be proportional to the a m o u n t of adsorbed porphyrin molecules.
INTRODUCTION
An interface of two immiscible liquids is the simplest model for studying the surface characteristics of biomembranes. The process of charge transfer through membranes consists of charge transfer through the interface and diffusion through a membranous layer. The biolelectrochemical reactions accompanied by a special separation of charges can proceed at the interface. This kind of mechanism can be involved in the selective charge transfer through biomembranes. Other processes such as the membrane selectivity mechanism, the generation of the transmembrane potential and others can also be better understood through the study of the mechanisms of ion and electron transfer through interfaces. The redox reactions at the interface of two immiscible liquids with metalloporphyrins as catalysts have been previously studied [1-3]. In the present paper we compare adsorption data with that obtained by the vibrating-electrode method. The iron complex of coproporphyrin tetramethyl ether was used as a catalyst owing to its ability to catalyse a heterogeneous redox reaction and its considerable surface activity.
0302-4598/83/$03.00
© 1983 Elsevier Sequoia S.A.
478 EXPERIMENTAL
The Volta potential was measured by the vibrating electrode method in the chain air
octane CP acceptor
Au
water substrate buffer
water saturated KC1
s.c.e.
(1)
The interfacial tension at the water poctane interface was measured by determining the weight and volume of the drop falling from the end of a capillary tube under its own gravity (4). The surface tension o was obtained from equation (2): o=
V(dl-dz)Fg
(2)
r
where d~ and d z are densities of the liquids studied, V the drop volume, g the acceleration of gravity, F a correction function, found in the Harkins-Brown table and r the capillary radius. An equipment, consisting of a glass capillary, 1 cm 3 syringe, micrometer and a vessel filled by a liquid with lower density used to immerse the capillary, was utilized to measure the interfacial tension. The internal capillary diameter was 0.6-0.8 mm. The drop lifetime necessary to establish adsorption equilibrium [4], was not less than 2 minutes. All solutions were prepared with twice-distilled water. The salts were twice crystallized. Buffer tris-HC1 (trioxymethylaminomethane) was obtained from Sigma Chemical Co. and three times crystallized. Details of the synthesis of the iron coproporphyrin III (CP-complex have been previously reported [5,6]). The experiments were conducted at room temperature (20°C). RESULTS A N D DISCUSSION
Figure l a shows the dependence of interfacial tension a on the logarithm of coproporphyrin (CP) concentration (c) in octane. A gradual reduction of a in the CP concentration range (from 10 .6 to 1.5 × 10 -5 M ) can be observed. The last point in the curve corresponds to the limiting solubility of CP in octane. Using interfacial tension data and the Gibbs adsorption equation r =
1
do
R T d(ln c)
c
do
R T dc
(3)
(where F stands for the superficial concentration) the adsorption CP isotherm at the octane Iwater interface was plotted (Fig. l b). The adsorption equilibrium constant B = 1.2 × l0 s M -1 was evaluated from the slope of the initial section of the isotherm. The concavity of the initial section of the curve, illustrating the dependence of o on c, indicates the attractive nature of the interaction between the particles adsorbed at the interface. The free energy of adsorption Gaas = - 9 . 2 7 kcal/mole was calculated from equation (4) (see Ref. 7): B--~
exp - ~
(4)
479 0.052
----o
G
•
,
0048 0044 0.040 Z
0.036 0.032 0.028
Log [cP] I
i
-lO
I
-9
-8
/
L~ 0
, 2
I
I
I
-7
-6
-5
b
I 4
,[CPII~M 6 8
~ I0
I 12
I 14
1.0 O8 O6 0.4 0.2 i
I
I
I
I
l
2
3
4
5
Fig. I. Adsorption isotherm of CP at the octanelwater interface: (a) dependence of interracial tension on CP concentration; (b) dependence of adsorption on CP concentration; (c) dependence of the extent of the surface coverage on CP concentration in reduced coordinates y = c/co=o. 5 (the solid line is plotted using the Gibbs equation on the basis of experimental data on interracial tension, the dotted line is plotted using the Frumkin isotherm).
If the a m o u n t of C P particles l o c a t e d o n 1 c m 2 of the i n t e r f a c e surface at F = Fma x is k n o w n , the l i m i t i n g a r e a o c c u p i e d b y a C P m o l e c u l e (32.4 .~2) c a n b e c a l c u l a t e d . A c o m p a r i s o n of the l i m i t i n g a r e a w i t h the area of a C P m o l e c u l e [8] of 82 ~2 p e r m i t s
480
evaluation of the angle between the CP molecule plane and the octane]water interface. When the interface surface is completely covered by CP molecules this angle is equal to 65 ° . This value is very near to the values obtained by optical techniques [9,10] for other porphyrins at a membrane]water interface, and in monolayers at the water lair interface. If we consider an adsorption layer as a two-dimensional film, then the dependence shown in Fig. lb can be described by the Frumkin isotherm: 0
BC=l_ 0 e x p ( -
2a0)
(5)
The adsorption equilibrium constant B [7], calculated from equation (5), was 1.1 x 10 -5 M -1 and coincided with the value calculated above. The attraction constant is equal to 1.3, which reveals an attractive interaction between the adsorbed CP molecules. Attention should be called to the close fit between constants B and a for CP and chlorophyll adsorption isotherms at the octane]water interface. Figure lc shows the adsorption isotherm calculated from the Frumkin isotherm. It is seen that only at high surface coverage does the experimental data slightly deviate from the calculated data. Figure 2 shows the dependence of the Volta-potential measured in chain 1 on the CP concentration at the surface (calculated on the basis of experimental data shown in Fig. 1). A deviation from a linear dependence when the projection of a molecule area is less than 100 ,~= shows the interaction between the molecules of the adsorbed particles, leading to a decrease of the effective molecular dipole moment. This deviation, however, is 2.4 times larger than the expected value due to the change of the angle between the porphyrin ring and the interface and may be related to the interaction between the ~r-electron system of porphyrin rings. In the presence of CP and 2-N-methylamino-l,4-naphthoquinone in octane, addition of a reducing agent such as N A D H or ascorbate into the aqueous phase leads to a shift of potential in a negative direction (Fig. 3). This change depends on the concentrations of all the reaction components. According to previous papers
0.16 0,12 ~" O'OIJ 00, i
0
1
n x10-14/cm I
2
z
i
3
Fig. 2. Dependence of the adsorption potential drop on the number of CP particles on the surface.
481 15
> 10
5
[NAOH7 (m,-b I
I
25
50
Fig. 3. Dependence of the Volta-potential, measured in chain 1 on the N A D H concentration in reverse coordinates. Medium: 10 -4 M 2-N-methylamino-l,4-naphthoquinone, 7 x 10 -2 M tris-HC1, 7 X 10 -6 M CP, pH 7.3. The potential is measured against a solution free of NADH.
[1-3,11-13] this effect can be interpreted as a reduction of the acceptor molecules and a substrate oxidation within the electrical double layer in an electron exchange reaction catalysed by CP. The phenomenological theory of a catalytic charge-transfer process through the interface of two immiscible liquids [12] suggests that in the absence of side-reactions the change of Volta-potential in chain 1 upon catalytic charge transfer through the interface can be expressed by the following equation:
z 2[K]o[S]0 / ~ = Ck3( gm +
[S]0 )
(6)
where z is the particle charge, ~-the Faraday constant, C the integral capacitance of the electrical double layer, k z the rate constant for the catalytic reaction, k 3 the rate constant of charge injection into water, [K]0 the initial surface concentration of the catalyst, [S]o the initial substrate concentration and K m the Michaefis constant. This equation can be checked in two different ways described below. First equation (6) can be represented as 1 Km 1 1 m~ -- m~rna'"~x [S]~ "~ AlPma----x
(7)
Using this equation and extrapolating the experimental curve shown in Fig. 3, the Michaelis constant can be determined. From Fig. 3 it is seen that at pH 7.3 K m is equal to 3 x 10 - 4 M. Secondly, Fig. 4 shows that the change of potential drop A~k, due to the electron exchange reaction, is proportional to the number of catalyst molecules located at the interface, which agrees with equation (6). A linear dependence shown in Fig. 4, and characterizing the reactionrate [9,10] may possibly indicate that the orientation of the catalyst in all concentrations studied remains unchanged.
482 1
~
2 (~cm_Z)
3
-005
-0.10
-015
Fig. 4. Dependenceof the Volta-potentialmeasured in chain 1, on the number of CP molecules,adsorbed at the octane]waterinterface. Medium: 10-3 M NADH, 10-4 M 2-N-methylamino-l,4-naphthoquinone, 10-z M tris-HC1, pH 7.3.
The electron-transfer for reaction studied: cP (NADH)H2O + (MnQ)octan e ~ (NAD)HzO + (MNQn2)octane
(8)
occurs in the dark. Illumination by 70 m W / c m 2 light does not effect the potential change. The Volta-potential measured in chain 1 and calculated relative to the background value is not affected by the way in which the reaction starts--by substrate or acceptor. In the absence of one of the following reaction components, i.e. CP, octane, NADH, or naphthoquinone, no change of the Volta-potential was observed. The Volta-potential measured in chain 1 is also independent of the buffer capacity of the solvent (tris concentration range from 10 to 100 mM). This indicates that the change in the potential jump is caused by the electron-transfer reaction. Thus, the physicochemical state of the catalyst molecules at the interface (orientation, interaction between the molecules, adsorption energy, Michaelis constant) may be studied using the adsorption isotherm and measurements of the Volta-potential in chain 1. The experimental results obtained in this work are in a good agreement with a previously proposed model [11,12] of the catalytic charge transfer through the interface of two immiscible liquids.
ACKNOWLEDGEMENTS The authors wish to thank Yu.A. Chizmadzhev and M.I. Gugeshashvili for fruitful discussion of the experimental data.
483 REFERENCES 1 A.G. Volkov, A.F. Mironov and L.I. Boguslavsky, Sov. Electrochem., 12 (1976) 1326. 2 A.G. Volkov, B.T. Lozhkin and L.I. Boguslavsky, Dokl. Biophys. (Proc. Acad. Sci. U.S.S.R.), 220 (1975) 76. 3 L.I. Boguslavsky, A.G. Volkov and M.D. Kandelaki, Bioelectrochem. Bioenerg., 4 (1977) 68. 4 A.W. Adamson, Physical Chemistry of Surfaces, Wiley, New York, London, Sydney, 1976. 5 A.F. Mironov, O.D. Popova, Kh.Kh. Alarkon, V.M. Bairamov and R.P. Evstigneeva, Zh. Organ. Khim., 15 (5) (1979) 1086. 6 A.D. Adler, F.R. Longo, F. Kampas and J. Kim, J. Inorg. Nucl. Chem., 32 (1970) 2443. 7 A.N. Frumkin and B.B. Damaskin in Modern Aspects of Electrochemistry J.O.M. Bockris and B.E. Conway (Editors), Butterworths, London, 1964, p.170. 8 J.L. Hoard in Porphyrins and Metalloporphyrins, K.M. Smith (Editor), Elsevier, Amsterdam, 1975, p. 317. 9 R.J. Cherry, K. Hsu, and D. Chapman, Biochim. Biophys. Acta, 288 (1972) 12. 10 W.D. Belamy, G.L. Gaynes and A.G. Tweet, J. Chem. Phys., 39 (1963), 2528. 11 Yu.I. Kharkats, A.G. Volkov and L.I. Boguslavsky, Dokl. Biophys. (Proc. Acad. Sci. U.S.S.R.), 220 (1975) 17. 12 Yu.I. Kharkats, A.G. Volkov and L.I. Boguslavsky, J. Theor. Biol., 65 (1977) 379. 13 A.G. Volkov, M.I. Gugeshashvily, A.F. Mironov and L.I. Boguslavsky, Bioelectrochem. Bioenerg., 9 (1982) 551.
477
Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands
5 5 5 - - A D S O R P T I O N AND CATALYTIC PROPERTIES OF IRON C O P R O P O R P H Y R I N III COMPLEX AT THE OCTANE [ WATER INTERFACE
A.G. VOLKOV, M.A. BIBIKOVA, A.F. M I R O N O V * and L.I. B O G U S L A V S K Y
Institute of Electrochemistry of the Academy of Sciences of the U.S.S.R., * Moscow Institute of Fine Chemical Technology, Leninsky Prospect 31, Moscow, V-71 31 (U.S.S.R.) (Revised manuscript received April 9th 1983)
SUMMARY Adsorption of the iron complex of coproporphyrin III tetramethyl ether at the octane [ water interface has been investigated. It was found that the process is well defined by the Frumkin isotherm. The attraction constant was estimated to be a = 1.3, adsorption energy Gads = --9.3 kcal/mole, the angle between the porphyrin ring and interface - 6 5 °. The electron-transfer reaction at the octane[water interface with a reducing agent in water, an oxidizing agent in octane and with porphyrin as a catalyst was studied. The change of potential drop at the octanelwater interface was found to be proportional to the a m o u n t of adsorbed porphyrin molecules.
INTRODUCTION
An interface of two immiscible liquids is the simplest model for studying the surface characteristics of biomembranes. The process of charge transfer through membranes consists of charge transfer through the interface and diffusion through a membranous layer. The biolelectrochemical reactions accompanied by a special separation of charges can proceed at the interface. This kind of mechanism can be involved in the selective charge transfer through biomembranes. Other processes such as the membrane selectivity mechanism, the generation of the transmembrane potential and others can also be better understood through the study of the mechanisms of ion and electron transfer through interfaces. The redox reactions at the interface of two immiscible liquids with metalloporphyrins as catalysts have been previously studied [1-3]. In the present paper we compare adsorption data with that obtained by the vibrating-electrode method. The iron complex of coproporphyrin tetramethyl ether was used as a catalyst owing to its ability to catalyse a heterogeneous redox reaction and its considerable surface activity.
0302-4598/83/$03.00
© 1983 Elsevier Sequoia S.A.
478 EXPERIMENTAL
The Volta potential was measured by the vibrating electrode method in the chain air
octane CP acceptor
Au
water substrate buffer
water saturated KC1
s.c.e.
(1)
The interfacial tension at the water poctane interface was measured by determining the weight and volume of the drop falling from the end of a capillary tube under its own gravity (4). The surface tension o was obtained from equation (2): o=
V(dl-dz)Fg
(2)
r
where d~ and d z are densities of the liquids studied, V the drop volume, g the acceleration of gravity, F a correction function, found in the Harkins-Brown table and r the capillary radius. An equipment, consisting of a glass capillary, 1 cm 3 syringe, micrometer and a vessel filled by a liquid with lower density used to immerse the capillary, was utilized to measure the interfacial tension. The internal capillary diameter was 0.6-0.8 mm. The drop lifetime necessary to establish adsorption equilibrium [4], was not less than 2 minutes. All solutions were prepared with twice-distilled water. The salts were twice crystallized. Buffer tris-HC1 (trioxymethylaminomethane) was obtained from Sigma Chemical Co. and three times crystallized. Details of the synthesis of the iron coproporphyrin III (CP-complex have been previously reported [5,6]). The experiments were conducted at room temperature (20°C). RESULTS A N D DISCUSSION
Figure l a shows the dependence of interfacial tension a on the logarithm of coproporphyrin (CP) concentration (c) in octane. A gradual reduction of a in the CP concentration range (from 10 .6 to 1.5 × 10 -5 M ) can be observed. The last point in the curve corresponds to the limiting solubility of CP in octane. Using interfacial tension data and the Gibbs adsorption equation r =
1
do
R T d(ln c)
c
do
R T dc
(3)
(where F stands for the superficial concentration) the adsorption CP isotherm at the octane Iwater interface was plotted (Fig. l b). The adsorption equilibrium constant B = 1.2 × l0 s M -1 was evaluated from the slope of the initial section of the isotherm. The concavity of the initial section of the curve, illustrating the dependence of o on c, indicates the attractive nature of the interaction between the particles adsorbed at the interface. The free energy of adsorption Gaas = - 9 . 2 7 kcal/mole was calculated from equation (4) (see Ref. 7): B--~
exp - ~
(4)
479 0.052
----o
G
•
,
0048 0044 0.040 Z
0.036 0.032 0.028
Log [cP] I
i
-lO
I
-9
-8
/
L~ 0
, 2
I
I
I
-7
-6
-5
b
I 4
,[CPII~M 6 8
~ I0
I 12
I 14
1.0 O8 O6 0.4 0.2 i
I
I
I
I
l
2
3
4
5
Fig. I. Adsorption isotherm of CP at the octanelwater interface: (a) dependence of interracial tension on CP concentration; (b) dependence of adsorption on CP concentration; (c) dependence of the extent of the surface coverage on CP concentration in reduced coordinates y = c/co=o. 5 (the solid line is plotted using the Gibbs equation on the basis of experimental data on interracial tension, the dotted line is plotted using the Frumkin isotherm).
If the a m o u n t of C P particles l o c a t e d o n 1 c m 2 of the i n t e r f a c e surface at F = Fma x is k n o w n , the l i m i t i n g a r e a o c c u p i e d b y a C P m o l e c u l e (32.4 .~2) c a n b e c a l c u l a t e d . A c o m p a r i s o n of the l i m i t i n g a r e a w i t h the area of a C P m o l e c u l e [8] of 82 ~2 p e r m i t s
480
evaluation of the angle between the CP molecule plane and the octane]water interface. When the interface surface is completely covered by CP molecules this angle is equal to 65 ° . This value is very near to the values obtained by optical techniques [9,10] for other porphyrins at a membrane]water interface, and in monolayers at the water lair interface. If we consider an adsorption layer as a two-dimensional film, then the dependence shown in Fig. lb can be described by the Frumkin isotherm: 0
BC=l_ 0 e x p ( -
2a0)
(5)
The adsorption equilibrium constant B [7], calculated from equation (5), was 1.1 x 10 -5 M -1 and coincided with the value calculated above. The attraction constant is equal to 1.3, which reveals an attractive interaction between the adsorbed CP molecules. Attention should be called to the close fit between constants B and a for CP and chlorophyll adsorption isotherms at the octane]water interface. Figure lc shows the adsorption isotherm calculated from the Frumkin isotherm. It is seen that only at high surface coverage does the experimental data slightly deviate from the calculated data. Figure 2 shows the dependence of the Volta-potential measured in chain 1 on the CP concentration at the surface (calculated on the basis of experimental data shown in Fig. 1). A deviation from a linear dependence when the projection of a molecule area is less than 100 ,~= shows the interaction between the molecules of the adsorbed particles, leading to a decrease of the effective molecular dipole moment. This deviation, however, is 2.4 times larger than the expected value due to the change of the angle between the porphyrin ring and the interface and may be related to the interaction between the ~r-electron system of porphyrin rings. In the presence of CP and 2-N-methylamino-l,4-naphthoquinone in octane, addition of a reducing agent such as N A D H or ascorbate into the aqueous phase leads to a shift of potential in a negative direction (Fig. 3). This change depends on the concentrations of all the reaction components. According to previous papers
0.16 0,12 ~" O'OIJ 00, i
0
1
n x10-14/cm I
2
z
i
3
Fig. 2. Dependence of the adsorption potential drop on the number of CP particles on the surface.
481 15
> 10
5
[NAOH7 (m,-b I
I
25
50
Fig. 3. Dependence of the Volta-potential, measured in chain 1 on the N A D H concentration in reverse coordinates. Medium: 10 -4 M 2-N-methylamino-l,4-naphthoquinone, 7 x 10 -2 M tris-HC1, 7 X 10 -6 M CP, pH 7.3. The potential is measured against a solution free of NADH.
[1-3,11-13] this effect can be interpreted as a reduction of the acceptor molecules and a substrate oxidation within the electrical double layer in an electron exchange reaction catalysed by CP. The phenomenological theory of a catalytic charge-transfer process through the interface of two immiscible liquids [12] suggests that in the absence of side-reactions the change of Volta-potential in chain 1 upon catalytic charge transfer through the interface can be expressed by the following equation:
z 2[K]o[S]0 / ~ = Ck3( gm +
[S]0 )
(6)
where z is the particle charge, ~-the Faraday constant, C the integral capacitance of the electrical double layer, k z the rate constant for the catalytic reaction, k 3 the rate constant of charge injection into water, [K]0 the initial surface concentration of the catalyst, [S]o the initial substrate concentration and K m the Michaefis constant. This equation can be checked in two different ways described below. First equation (6) can be represented as 1 Km 1 1 m~ -- m~rna'"~x [S]~ "~ AlPma----x
(7)
Using this equation and extrapolating the experimental curve shown in Fig. 3, the Michaelis constant can be determined. From Fig. 3 it is seen that at pH 7.3 K m is equal to 3 x 10 - 4 M. Secondly, Fig. 4 shows that the change of potential drop A~k, due to the electron exchange reaction, is proportional to the number of catalyst molecules located at the interface, which agrees with equation (6). A linear dependence shown in Fig. 4, and characterizing the reactionrate [9,10] may possibly indicate that the orientation of the catalyst in all concentrations studied remains unchanged.
482 1
~
2 (~cm_Z)
3
-005
-0.10
-015
Fig. 4. Dependenceof the Volta-potentialmeasured in chain 1, on the number of CP molecules,adsorbed at the octane]waterinterface. Medium: 10-3 M NADH, 10-4 M 2-N-methylamino-l,4-naphthoquinone, 10-z M tris-HC1, pH 7.3.
The electron-transfer for reaction studied: cP (NADH)H2O + (MnQ)octan e ~ (NAD)HzO + (MNQn2)octane
(8)
occurs in the dark. Illumination by 70 m W / c m 2 light does not effect the potential change. The Volta-potential measured in chain 1 and calculated relative to the background value is not affected by the way in which the reaction starts--by substrate or acceptor. In the absence of one of the following reaction components, i.e. CP, octane, NADH, or naphthoquinone, no change of the Volta-potential was observed. The Volta-potential measured in chain 1 is also independent of the buffer capacity of the solvent (tris concentration range from 10 to 100 mM). This indicates that the change in the potential jump is caused by the electron-transfer reaction. Thus, the physicochemical state of the catalyst molecules at the interface (orientation, interaction between the molecules, adsorption energy, Michaelis constant) may be studied using the adsorption isotherm and measurements of the Volta-potential in chain 1. The experimental results obtained in this work are in a good agreement with a previously proposed model [11,12] of the catalytic charge transfer through the interface of two immiscible liquids.
ACKNOWLEDGEMENTS The authors wish to thank Yu.A. Chizmadzhev and M.I. Gugeshashvili for fruitful discussion of the experimental data.
483 REFERENCES 1 A.G. Volkov, A.F. Mironov and L.I. Boguslavsky, Sov. Electrochem., 12 (1976) 1326. 2 A.G. Volkov, B.T. Lozhkin and L.I. Boguslavsky, Dokl. Biophys. (Proc. Acad. Sci. U.S.S.R.), 220 (1975) 76. 3 L.I. Boguslavsky, A.G. Volkov and M.D. Kandelaki, Bioelectrochem. Bioenerg., 4 (1977) 68. 4 A.W. Adamson, Physical Chemistry of Surfaces, Wiley, New York, London, Sydney, 1976. 5 A.F. Mironov, O.D. Popova, Kh.Kh. Alarkon, V.M. Bairamov and R.P. Evstigneeva, Zh. Organ. Khim., 15 (5) (1979) 1086. 6 A.D. Adler, F.R. Longo, F. Kampas and J. Kim, J. Inorg. Nucl. Chem., 32 (1970) 2443. 7 A.N. Frumkin and B.B. Damaskin in Modern Aspects of Electrochemistry J.O.M. Bockris and B.E. Conway (Editors), Butterworths, London, 1964, p.170. 8 J.L. Hoard in Porphyrins and Metalloporphyrins, K.M. Smith (Editor), Elsevier, Amsterdam, 1975, p. 317. 9 R.J. Cherry, K. Hsu, and D. Chapman, Biochim. Biophys. Acta, 288 (1972) 12. 10 W.D. Belamy, G.L. Gaynes and A.G. Tweet, J. Chem. Phys., 39 (1963), 2528. 11 Yu.I. Kharkats, A.G. Volkov and L.I. Boguslavsky, Dokl. Biophys. (Proc. Acad. Sci. U.S.S.R.), 220 (1975) 17. 12 Yu.I. Kharkats, A.G. Volkov and L.I. Boguslavsky, J. Theor. Biol., 65 (1977) 379. 13 A.G. Volkov, M.I. Gugeshashvily, A.F. Mironov and L.I. Boguslavsky, Bioelectrochem. Bioenerg., 9 (1982) 551.