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Application of electron-transfer theory to excited-state redox processes
VoIume
CHEMICAL
61, number 3
APPLICATION
PHYSICS
OF ELECTRON-TRANSFER
1 March 1979
LEJTERS
THEORY TO EXCITEDSTATE
REDOX PROCESSES
Carl R. BOCK, Joseph A_ CONNOR, Adolph0 R_ GUTIERREZ *, Thomas J. MEYER, Dabid G. WHITTEN. B. P&trick SULLIVAN and Jeffrey K. NAGLE Deparrrnenr of Chctnisrr_v, 73e (Ir*ir-ersiry of L\‘ortft Carolina. Chapel Hitt, Kortir Carolina Z 7514. IX4 Rtxx&&
5 September
1978
@uenchiq
mte corutmts have been obtained for oxidative electron transfer quenching of Ru(bpy)z+* by a series of and bipq ridinium quenchers and reductive qucnchinz by d series of somatic amines. The results are cwsistent r the sum of r&ox-pioduct-separtion and back-electron-transfer to gixe Ru(bp))z*_
nitroaromxic
From the results of their kinetic studies on the quenching of fiuorescznce from a series of aromatic e.xcited states_ Rehm .md Weller were able to investi.@e the free energy dependence of electron-transfer ate constants over 3 wide range in AC values [ I] _ The theoretica dependence is given by 2lG2* = f X( I l %&/X)2
,
(1)
where “CT3 is the free energy of activation fcr electron transfer within an association compfcx of the rertctrtnts, X2, is the corresponding free energy ch.mge, and ;\f4 is the vIbrationa barrier to eIectron transfer [3]_ l \% includes coraributions both from inner- and outersphere coordination vibrdtionai changes_ Rehm and WcIler noted that in their data there was no evidence for the fall-off in rate predicted by eq. (1) in the abnormal or inverted free-energy region where - >G > h_ They also suggested that eq_ (I) did not ztdequately fit their data in the norma free energy region. and suggesred the empirical relationshi_? AG& = ; AGa; + [(f aG,3)’
f f A] 111 *
(‘I)
x\hich did_ We hare reported rate constants for quenching of the charge-transfer excited state Ru(bpy)T* (bpy is ’
Pr~znt addrL%r IBM Research Laboratory. Cahfornia 95 193. USA.
San Jose.
2,2’-bipyridyl) by a series of nitroaromatin [3] _From the kinetic data we were able to estimate the formal potential for the excited state couple Ru(bpy)F’12tx_ We hae extended the quenching studies to a series of osidative bipyridinium ion quenchers like hfe-N _N-h;fe’+ (P2+; eq_ (3)) and to a series of reductive amine quenchers Iike hle, N -21 (R2NAr; eq. (4)). Ru(bpy$*
+ 6”
+ Ru(bpy)p+P*
Ru(bpy)p*
+ R,NAr
-+ Ru(bpy)g
, + R2NAr+
(3 -
(4)
In both cases. at least partial electron-transfer quenching is known to occur since the expected redox products are observed following flash photolysis [4-7]_ The resuhs are shown in tig- I as pIots of RTInkk ve:sus aGz3 _The “\ values were obtained in CH,CN(I=O.I M; 22 22”) using the Stern-Volmer technique and are corrected for diffusion31 effects l. AGz, values were caIcuIated from redox potentials for l
“& values acre calcuhted
from experimental kq values using the equation l/kq = l/k6 + i/kD (8 J_ The diffusion-limited rate ranstant. Phich \ias caicubted from the DebyeSmoIuchorxkiequation [9J. waskD = 2.1 X 10’“hl-’ s-r for the neutral amine and nitroaromatic quenchers- and X-D = 6.1 X IO9 hi-’ For the dipyridinium quenchers. For certain of the dipyridinium quenchers where energy and eIectron transfer quenching are knolrn to be competitive, i e. the kq values \iere corrected for the energy transfer component_
s-t
Volume 61. number 3
CHEMICAL
1 March 1979
PHYSICS LETTERS
different behavior for the different sets of quenchers. In the figure hnes of slope==OS are shown drawn through the points for oxidatrve quenching by the bipyridinium ions (Pz*) and for reductive quenching by the amines (R,NAr). Lines of slope = 0.5 and slope = I -are shown drawn through the points for oxidative quenching by the nitroaromatics (ArNO& In fact, the curious behavior shown in fig. 1 and probably the results obtained by Rehm and Weller as well can be explained using electron transfer theory by taking into clccount processes which occur following the electron transfer quenching step. A kinetic scheme for chemicatly activated quenching
using reductive the equation RUBY -a2
aGz3.v
01)
h.2
Id
RttB’+ 3
Fig_ I. Plots ofRTIn 26(V) tenus AG~_~(V) for eiectrontransfer quenchm~ of Ru(bp)>Sf* b) nitro.zrom&ic (~-~O~C~H~h’0.p-~‘tf~C6ffJNOr?, etc.) 13.51, .mune (p-~fe~KC~HjNBie~_ pJfe~NC~H4.\fe, etc.) [ iOj axi bipyndinium (Sfe-N N-ffe”+. trans-%.it’JfeNCs H&H= CHCSH+N.\~~‘*, etc_) [6I quenchers in occtonitrlle (I= 0-I \f, 22 t 2°C).
the coupIes involved using the equations reductive quenching: AG&V)
= - fE(RuB$+*/*)
- E(Ox/Red)]
(51 + Wp- ii’=.
oxidative quenching:
(6)
where Wr and ?Vp are the eIectrostatic work terms for bringing together the reactants and products, respectively. Wp and Wr in acetonitrile at 22” can be calculated by
W(kcaljmole)
= (9_1OZ,Zn/d)
“12
+ Dz
hv r j l/-e
\ a-r
(1 i- 0_4Sd11~“)-1,
where ZA and ZB rue the ion charges, d the internuclear separation in the association compiex, and I the ionic strength_ The excited state potent%& are E(Ruf3~~=*) = -O_SI e0.07 V and E(RuB;+) = 0.77% 0.07 V in the medium used for the quenching studies(CH3CN,I=0.1 h-l, [N(c~H~)~](c~o~)) [3,10]. The data in fig. 1 are strikin!: in that they suggest
quenching
*
RuB$f,
as the example,
D$
RUB;,
is shown in
D”
(7)
32
-
: k30
x-1 &_
+ D
RuB;+D*
A kinetic analysis of the scbtme
k7
RUB;+, D.
in eq. (7) gives
where X-,, is the eiectron transfer quenching rate constant ,md Ki’,, the equilibrium constant for formation of the association cornpIes. The term k;o/(Xr;u fk,,) is a partitioning factor which arises because followmg the quenching step there is n competition between back electron transfer to give the excited state Q;-,) and net quenching (Jzzo)_ Net quenching can occur either by sepamtion of the redox products Q1) or by electron tmnsfer to give the ground state (&)_ If X-3n% k-32, back electron transfer to give the excited state is slow, R30/(k30+ ks2) = 1, snd eq. (8) becomes k; = k23h712_
@I
The electron
transfer quenching rate constant is ghen by .$s = u2s esp (- AG&/RT) where vzs is the frequency factor for electron transfer. Since aG:s is given by eq. (I), eq. (Sa) becomes, kk = vrjKllexp
[-$
h(l+
or in logarithmic
form,
M723jX)zlfZTf
,
(9)
VoIume6 1, number 3
CHEMCAL
PHYSICS LETTJZRS
If IAGz31 (c D, eq_ [sfa) simplifies to give RTIn “; = RTIn k;(O) - $ AGzs -
(IO1
In eq_(10)it is assumed that the reorgauizational parameter Xand the product z&CE2
remain essential.ly
constant for a structuraIIy reIated series of quenchers. k&$3) is then the chemiczJIy activated quenching rate constant for rt hypothetical quencher where AG23=0. Eq- (10) correctly predicts the slope = 0-S dependence found for the amine quenchers_ The dependence predicted by eq.. (9s) (using h= 11 k&/mole) fits the amine quenching data reasonably welt for the points where -AC& is large and the assumption that I&(;331 <2X no longer holds_ The quadratic dependence exphins why the flattening out in RTJnkh occurs at Iarge negative v&~es of AGs_ TJlere is a second Jimiting case for the partitioning factor k,,/(k3o * k-&_ &suming that net quenching is stower than back-electron tmnsfer to give the excited state (&o < k3;z) gives #%$= K@t’,
x’J&~
=R,,K,k,,
.
Of)
This situation holds when the rate of electron osciJJation bacii and forth between the excited state and quencher is rapid compared to the rate of net quenching_ TJze competitive reactions invo!ved are shown in the equation
d%*(RuBy),
n’fR,NAr)
Since Kz3 = esp (-AC&T), eq_ ( 11) becomes RTln$
* d%“(RuBf),
n1 (R$Ar+)
in fogarithmic form,
= RTlo kJOK12 - AGz3 _
03)
Eq_ (13) succe=fuJly predfcts the slope = I behavior found in fig- i which occurs only for those nitroaromatic quenchers where AC,, is positive. The difference in behavior found for the different
quenchers can be expIained on energetic grounds and the explanation has important implications for related processe.ssuch sg e~ectroc~e~ru~nes~nce yields. (;_I, the charge separation step, should be independent of AC- k~. the mte constant for electron transfer to give the ground state should also be relatively independent of21G. This reaction, which is h&hJy favored for
aU cases (-AC = I .2-2.5 V), falls in the inverted or abnormti free-energy region and the av&lable experimental evidence suggests that there should be at best a weak dependence ofki on AG. Since k30 = ill f kz, ksO is relativeiy independent of AC,,. However, back-electron transfer to give the excited state is in the normal free-energy region and there is a dependence on AC since RTln k,, is given by
(14) where AG,, = - AGz3 _ From the dsts in fJg. I, the sJope =l behzviior is observed only for those points where AGsz< -0.2 V. For these points, the free energy change. AG32t is relatively favorable and back-electron transfer to give the excited state is more rapid than electron transfer to give the ground state -(k32S k3& -4sAGS5 becomes more positive, k3z fa until ksr C=kSO. fn this intermediafe region the equation
holds. As AC,, i?creases further thtt &ctrOn-traW&?r quenching step becomes rate determining since kzO B k,, and RThk~ varies as 4 AG?,. The siope =O.S beh&or is observed untif the con&tion IAG,,I e 2h uo longer holds_ For the points where iAG& is of the same order of magnitude as 1, the quadratic dependence predicted by eq_ (9) is appropriate and correctly predicts the flattening in the nitroaromatic and amine quenching data in fig. 1 at Iarge, negative A& values. From the data in fig_ 1 *k&(O), the chemicaiIy activated efectron transfer rate constants where AGzs = 0, can be &c&ted for the three types of quenchers_ They are the vaIues of RTJn k; where AC,, = Cl_The vafues, wvhich are of considerable fundamental significance since they are similar to setfexchange rate constants, are S-4 X IO~M-~ s-1 for the bipyridinium quenching reactions, 53 X lOgM_Is-1 for the amine reactions, and 7.8 X LO9M-l s--l fosthe nirroarornatic reactions. It should be noted that these values are for chemically activated etectron transfer and that experimental vaIues for the amine and nitroaromatic quenchers would be slightly lower because of diffusional effects.
Volume 61, number 3
CHEMICAL PHYSICS LEITERS
~c~owiedge~ent is given to the National Science Foundation under Grants CHE77-03423 and CHE14405 for SUppOrt of t&s research.
References [I 1 D. Rehm and A. Weffer, Ber. Bunsenges. Physik- Chem. 73 (1969) 834; israel J. Chem. 8 (1970) 259. [5] NS. Hush, -f-e Faraday Sot. 57 (1961) 5.57; R-A- Marcus. J. Chem. Phys. 24 (1956) 966; 43 f196.5) 679; R-A. hfarcus and N. Sutin, Inorg. Chem. 14 (1975) 2f3, ancf references therein. I3 J C-R. Bock, D-G_ Whitten and TJ. Meyer, J_ Am. Chem. Sac. 97 (1975) 2909-
1 bfarch 1979
t4J C-R- Bock D-G. WhWen and T-J_ Bfeyer, J.
Am. Chem. Sot. 96 (19745 4710; 97 (19755 7909: R-C. Young. D-G_ W&ten &d T-i. Bfeyer, 3. Am. C&em. sac. 97 (1975) 4781; 98 (1976) 286. [S 1 A-R- Gutierrez, ph. D. Disscrrtation. The University of North Carohna (1975). [6l CR. Bock, Ph. D. Dissertation, The Unhcrsity of North Carolina (1174). 171 C-P. Anderson, D J. Salmon, R.C. Young- and T.J. Meyer, J. Am. Chem. Sot. 99 (1977) 1950; %f_Maestri and M Gratzel, Ber. Bunsen~es_ Ph>s9. f&em_ 8 f(l977) 504. [8] R.Sf. Noyes, Progr- Reaction Kinetics f (19611 129. 191 P. Debye, Trans. Faraday Sot. 82 (1942) 265. [IO] C-R. Bock, J.A.CORRO~,A-R. Gt~tienez. T-J. Xforer, D.G. Whitten, B-P. Sol&an and JX. N&e, sub&ted for publication.
525
CHEMICAL
61, number 3
APPLICATION
PHYSICS
OF ELECTRON-TRANSFER
1 March 1979
LEJTERS
THEORY TO EXCITEDSTATE
REDOX PROCESSES
Carl R. BOCK, Joseph A_ CONNOR, Adolph0 R_ GUTIERREZ *, Thomas J. MEYER, Dabid G. WHITTEN. B. P&trick SULLIVAN and Jeffrey K. NAGLE Deparrrnenr of Chctnisrr_v, 73e (Ir*ir-ersiry of L\‘ortft Carolina. Chapel Hitt, Kortir Carolina Z 7514. IX4 Rtxx&&
5 September
1978
@uenchiq
mte corutmts have been obtained for oxidative electron transfer quenching of Ru(bpy)z+* by a series of and bipq ridinium quenchers and reductive qucnchinz by d series of somatic amines. The results are cwsistent r
nitroaromxic
From the results of their kinetic studies on the quenching of fiuorescznce from a series of aromatic e.xcited states_ Rehm .md Weller were able to investi.@e the free energy dependence of electron-transfer ate constants over 3 wide range in AC values [ I] _ The theoretica dependence is given by 2lG2* = f X( I l %&/X)2
,
(1)
where “CT3 is the free energy of activation fcr electron transfer within an association compfcx of the rertctrtnts, X2, is the corresponding free energy ch.mge, and ;\f4 is the vIbrationa barrier to eIectron transfer [3]_ l \% includes coraributions both from inner- and outersphere coordination vibrdtionai changes_ Rehm and WcIler noted that in their data there was no evidence for the fall-off in rate predicted by eq. (1) in the abnormal or inverted free-energy region where - >G > h_ They also suggested that eq_ (I) did not ztdequately fit their data in the norma free energy region. and suggesred the empirical relationshi_? AG& = ; AGa; + [(f aG,3)’
f f A] 111 *
(‘I)
x\hich did_ We hare reported rate constants for quenching of the charge-transfer excited state Ru(bpy)T* (bpy is ’
Pr~znt addrL%r IBM Research Laboratory. Cahfornia 95 193. USA.
San Jose.
2,2’-bipyridyl) by a series of nitroaromatin [3] _From the kinetic data we were able to estimate the formal potential for the excited state couple Ru(bpy)F’12tx_ We hae extended the quenching studies to a series of osidative bipyridinium ion quenchers like hfe-N _N-h;fe’+ (P2+; eq_ (3)) and to a series of reductive amine quenchers Iike hle, N -21 (R2NAr; eq. (4)). Ru(bpy$*
+ 6”
+ Ru(bpy)p+P*
Ru(bpy)p*
+ R,NAr
-+ Ru(bpy)g
, + R2NAr+
(3 -
(4)
In both cases. at least partial electron-transfer quenching is known to occur since the expected redox products are observed following flash photolysis [4-7]_ The resuhs are shown in tig- I as pIots of RTInkk ve:sus aGz3 _The “\ values were obtained in CH,CN(I=O.I M; 22 22”) using the Stern-Volmer technique and are corrected for diffusion31 effects l. AGz, values were caIcuIated from redox potentials for l
“& values acre calcuhted
from experimental kq values using the equation l/kq = l/k6 + i/kD (8 J_ The diffusion-limited rate ranstant. Phich \ias caicubted from the DebyeSmoIuchorxkiequation [9J. waskD = 2.1 X 10’“hl-’ s-r for the neutral amine and nitroaromatic quenchers- and X-D = 6.1 X IO9 hi-’ For the dipyridinium quenchers. For certain of the dipyridinium quenchers where energy and eIectron transfer quenching are knolrn to be competitive, i e. the kq values \iere corrected for the energy transfer component_
s-t
Volume 61. number 3
CHEMICAL
1 March 1979
PHYSICS LETTERS
different behavior for the different sets of quenchers. In the figure hnes of slope==OS are shown drawn through the points for oxidatrve quenching by the bipyridinium ions (Pz*) and for reductive quenching by the amines (R,NAr). Lines of slope = 0.5 and slope = I -are shown drawn through the points for oxidative quenching by the nitroaromatics (ArNO& In fact, the curious behavior shown in fig. 1 and probably the results obtained by Rehm and Weller as well can be explained using electron transfer theory by taking into clccount processes which occur following the electron transfer quenching step. A kinetic scheme for chemicatly activated quenching
using reductive the equation RUBY -a2
aGz3.v
01)
h.2
Id
RttB’+ 3
Fig_ I. Plots ofRTIn 26(V) tenus AG~_~(V) for eiectrontransfer quenchm~ of Ru(bp)>Sf* b) nitro.zrom&ic (~-~O~C~H~h’0.p-~‘tf~C6ffJNOr?, etc.) 13.51, .mune (p-~fe~KC~HjNBie~_ pJfe~NC~H4.\fe, etc.) [ iOj axi bipyndinium (Sfe-N N-ffe”+. trans-%.it’JfeNCs H&H= CHCSH+N.\~~‘*, etc_) [6I quenchers in occtonitrlle (I= 0-I \f, 22 t 2°C).
the coupIes involved using the equations reductive quenching: AG&V)
= - fE(RuB$+*/*)
- E(Ox/Red)]
(51 + Wp- ii’=.
oxidative quenching:
(6)
where Wr and ?Vp are the eIectrostatic work terms for bringing together the reactants and products, respectively. Wp and Wr in acetonitrile at 22” can be calculated by
W(kcaljmole)
= (9_1OZ,Zn/d)
“12
+ Dz
hv r j l/-e
\ a-r
(1 i- 0_4Sd11~“)-1,
where ZA and ZB rue the ion charges, d the internuclear separation in the association compiex, and I the ionic strength_ The excited state potent%& are E(Ruf3~~=*) = -O_SI e0.07 V and E(RuB;+) = 0.77% 0.07 V in the medium used for the quenching studies(CH3CN,I=0.1 h-l, [N(c~H~)~](c~o~)) [3,10]. The data in fig. 1 are strikin!: in that they suggest
quenching
*
RuB$f,
as the example,
D$
RUB;,
is shown in
D”
(7)
32
-
: k30
x-1 &_
+ D
RuB;+D*
A kinetic analysis of the scbtme
k7
RUB;+, D.
in eq. (7) gives
where X-,, is the eiectron transfer quenching rate constant ,md Ki’,, the equilibrium constant for formation of the association cornpIes. The term k;o/(Xr;u fk,,) is a partitioning factor which arises because followmg the quenching step there is n competition between back electron transfer to give the excited state Q;-,) and net quenching (Jzzo)_ Net quenching can occur either by sepamtion of the redox products Q1) or by electron tmnsfer to give the ground state (&)_ If X-3n% k-32, back electron transfer to give the excited state is slow, R30/(k30+ ks2) = 1, snd eq. (8) becomes k; = k23h712_
@I
The electron
transfer quenching rate constant is ghen by .$s = u2s esp (- AG&/RT) where vzs is the frequency factor for electron transfer. Since aG:s is given by eq. (I), eq. (Sa) becomes, kk = vrjKllexp
[-$
h(l+
or in logarithmic
form,
M723jX)zlfZTf
,
(9)
VoIume6 1, number 3
CHEMCAL
PHYSICS LETTJZRS
If IAGz31 (c D, eq_ [sfa) simplifies to give RTIn “; = RTIn k;(O) - $ AGzs -
(IO1
In eq_(10)it is assumed that the reorgauizational parameter Xand the product z&CE2
remain essential.ly
constant for a structuraIIy reIated series of quenchers. k&$3) is then the chemiczJIy activated quenching rate constant for rt hypothetical quencher where AG23=0. Eq- (10) correctly predicts the slope = 0-S dependence found for the amine quenchers_ The dependence predicted by eq.. (9s) (using h= 11 k&/mole) fits the amine quenching data reasonably welt for the points where -AC& is large and the assumption that I&(;331 <2X no longer holds_ The quadratic dependence exphins why the flattening out in RTJnkh occurs at Iarge negative v&~es of AGs_ TJlere is a second Jimiting case for the partitioning factor k,,/(k3o * k-&_ &suming that net quenching is stower than back-electron tmnsfer to give the excited state (&o < k3;z) gives #%$= K@t’,
x’J&~
=R,,K,k,,
.
Of)
This situation holds when the rate of electron osciJJation bacii and forth between the excited state and quencher is rapid compared to the rate of net quenching_ TJze competitive reactions invo!ved are shown in the equation
d%*(RuBy),
n’fR,NAr)
Since Kz3 = esp (-AC&T), eq_ ( 11) becomes RTln$
* d%“(RuBf),
n1 (R$Ar+)
in fogarithmic form,
= RTlo kJOK12 - AGz3 _
03)
Eq_ (13) succe=fuJly predfcts the slope = I behavior found in fig- i which occurs only for those nitroaromatic quenchers where AC,, is positive. The difference in behavior found for the different
quenchers can be expIained on energetic grounds and the explanation has important implications for related processe.ssuch sg e~ectroc~e~ru~nes~nce yields. (;_I, the charge separation step, should be independent of AC- k~. the mte constant for electron transfer to give the ground state should also be relatively independent of21G. This reaction, which is h&hJy favored for
aU cases (-AC = I .2-2.5 V), falls in the inverted or abnormti free-energy region and the av&lable experimental evidence suggests that there should be at best a weak dependence ofki on AG. Since k30 = ill f kz, ksO is relativeiy independent of AC,,. However, back-electron transfer to give the excited state is in the normal free-energy region and there is a dependence on AC since RTln k,, is given by
(14) where AG,, = - AGz3 _ From the dsts in fJg. I, the sJope =l behzviior is observed only for those points where AGsz< -0.2 V. For these points, the free energy change. AG32t is relatively favorable and back-electron transfer to give the excited state is more rapid than electron transfer to give the ground state -(k32S k3& -4sAGS5 becomes more positive, k3z fa until ksr C=kSO. fn this intermediafe region the equation
holds. As AC,, i?creases further thtt &ctrOn-traW&?r quenching step becomes rate determining since kzO B k,, and RThk~ varies as 4 AG?,. The siope =O.S beh&or is observed untif the con&tion IAG,,I e 2h uo longer holds_ For the points where iAG& is of the same order of magnitude as 1, the quadratic dependence predicted by eq_ (9) is appropriate and correctly predicts the flattening in the nitroaromatic and amine quenching data in fig. 1 at Iarge, negative A& values. From the data in fig_ 1 *k&(O), the chemicaiIy activated efectron transfer rate constants where AGzs = 0, can be &c&ted for the three types of quenchers_ They are the vaIues of RTJn k; where AC,, = Cl_The vafues, wvhich are of considerable fundamental significance since they are similar to setfexchange rate constants, are S-4 X IO~M-~ s-1 for the bipyridinium quenching reactions, 53 X lOgM_Is-1 for the amine reactions, and 7.8 X LO9M-l s--l fosthe nirroarornatic reactions. It should be noted that these values are for chemically activated etectron transfer and that experimental vaIues for the amine and nitroaromatic quenchers would be slightly lower because of diffusional effects.
Volume 61, number 3
CHEMICAL PHYSICS LEITERS
~c~owiedge~ent is given to the National Science Foundation under Grants CHE77-03423 and CHE14405 for SUppOrt of t&s research.
References [I 1 D. Rehm and A. Weffer, Ber. Bunsenges. Physik- Chem. 73 (1969) 834; israel J. Chem. 8 (1970) 259. [5] NS. Hush, -f-e Faraday Sot. 57 (1961) 5.57; R-A- Marcus. J. Chem. Phys. 24 (1956) 966; 43 f196.5) 679; R-A. hfarcus and N. Sutin, Inorg. Chem. 14 (1975) 2f3, ancf references therein. I3 J C-R. Bock, D-G_ Whitten and TJ. Meyer, J_ Am. Chem. Sac. 97 (1975) 2909-
1 bfarch 1979
t4J C-R- Bock D-G. WhWen and T-J_ Bfeyer, J.
Am. Chem. Sot. 96 (19745 4710; 97 (19755 7909: R-C. Young. D-G_ W&ten &d T-i. Bfeyer, 3. Am. C&em. sac. 97 (1975) 4781; 98 (1976) 286. [S 1 A-R- Gutierrez, ph. D. Disscrrtation. The University of North Carohna (1975). [6l CR. Bock, Ph. D. Dissertation, The Unhcrsity of North Carolina (1174). 171 C-P. Anderson, D J. Salmon, R.C. Young- and T.J. Meyer, J. Am. Chem. Sot. 99 (1977) 1950; %f_Maestri and M Gratzel, Ber. Bunsen~es_ Ph>s9. f&em_ 8 f(l977) 504. [8] R.Sf. Noyes, Progr- Reaction Kinetics f (19611 129. 191 P. Debye, Trans. Faraday Sot. 82 (1942) 265. [IO] C-R. Bock, J.A.CORRO~,A-R. Gt~tienez. T-J. Xforer, D.G. Whitten, B-P. Sol&an and JX. N&e, sub&ted for publication.
525