Solvent Effects on Rate Constants for One-Electron Oxidation of

Charge-Transfer Complexation and Excited-State Interactions in Porphyrin-Silver Nanoparticle Hybrid Structures. Sean Murphy , Libai Huang , and Prasha...
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J. Phys. Chem. 1994,98, 7136-7141

7136

Solvent Effects on Rate Constants for One-Electron Oxidation of Porphyrins S. Marguet,la P. Hapiot,Ib and P. Neta'J' Chemical Kinetics and Thermodynamics Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, and Luboratoire d%lectrochimie M o l h l a i r e de I'Universitl de Paris 7-Denis Diderot, Unit6 Associbe au CNRS No. 438, 75251 Paris Cedex 05, France Received: March 14, 1994.

Absolute rate constants for one-electron oxidation of free base porphyrins (hematoporphyrin-IX, mesoporphyrinIX dimethyl ester) by the trichloromethylperoxyl radical and by the radical cation of N-methylindole have been determined in a variety of solvents by the pulse radiolysis technique. All solvents were air-saturated and contained CC14 as a source for the CC1302*radicals. The rate constants for reactions of these radicals were measured by following the formation of the porphyrin r-radical cation optical absorption a t 700 nm as a function of porphyrin concentration. The rate constants for reaction of CC1302*with the porphyrin were found to vary by an order of magnitude in the different solvents and were correlated with the solvent cohesive energy density. In the second set of experiments, N-methylindole was used in addition to CCl4 so that CC1302*radicals oxidize this solute to its radical cation, which in turn oxidizes the porphyrin. The variations of the rate constants for oxidation of the porphyrin by the N-methylindole radical cation in the different solvents exhibited different trends than those for oxidation by CC1302*radicals. For the reaction of N-methylindole radical cation with mesoporphyrin-IX dimethyl ester, it was possible to measure the oxidation potentials of the two compounds by cyclic voltammetry in seven solvents of widely varying polarities. The rate constants were then correlated with the free energy of the reaction and the solvent reorganization energy according to the Marcus equations.

Introduction Redox reactions involving porphyrins have been the subject of extensive investigation.2 Studies have been carried out with aqueous and several organic solvents, selected mainly on the basis of porphyrin solubility and the electr~chemical)*~ or radiation chemical" propertiesof the solvent. Very few studies have been reported on the oxidation of a given porphyrin in a wide variety of solvents. In the case of metalloporphyrins,solvent effects on their rate of reaction with peroxyl radicals are greatly influenced by the axial ligation of solvent molecules to the metal center. This ligation exerted a strong effect on the reactivity and masked other effects of the solvent^.^ The true solvent effect on the reaction rate may be examined with a free base porphyrin, where intimate ligation of the solvent is not possible. All free base porphyrins are expected to undergo one-electron oxidation to yield r-radical cations. If the oxidation occurs via an outer-sphere electrontransfer mechanism, the variations in rate constants may be correlated with changes in oxidation potentials of the porphyrin and the other reactant as a function of solvent. Various peroxyl radicalshave been shown to oxidize porphyrins by a one-electron-transfermechanism.6~~ We have chosen to use the moderately strong oxidant CC1302*which has been studied frequently because of the important role of this radical in the mechanism of toxicity of CC14.10 The reason for this choice is also that CC1302*radicals can be produced by radiolysis of practically any solvent containing a fraction of C C 4 under air. Among metal-free porphyrins, hematoporphyrin,widely studied as sensitizer in photodynamic therapy,ll was chosen for this work because of its solubility in a wide range of organic solvents. In this study we have measured the rate constant for reaction of CC1302*with hematoporphyrin in 14different solvents covering a wide range of solvent polarity. Further, we have extended the measurementsto the oxidation reactionsof hematoporphyrin with the N-methylindole radical cation, produced by oxidation of N-methylindole with CC13020.12We have correlated the results with a number of solvent parameters. Determination of the

* To whom correspondence should be addressed.

Abstract published in Advunce ACS Abstracts, June 15, 1994.

standard oxidation potentials Eo of mesoporphyrin-IX dimethyl ester and N-methylindole in seven solvents of varying polarity using the cyclicvoltammetry techniquehas allowed us to correlate these thermodynamicand kinetic results according to the Marcus theory.

Experimental Sectionl3 Materials. The porphyrins were obtained from Midcentury Chemical Co., Posen, IL. The following abbreviationsare used for the porphyrins (P): HMP, hematoporphyrin-IX; OEP, octaethylporphyrin; MSPDME, mesoporphyrin-IX dimethyl ester; TSPP, tetrakis(4-sulfonatopheny1)porphyrin. The organic solvents were obtained from Aldrich in their highest available purity. Some of them were further purified as follows. Pyridine, N,N-dimethylformamide(DMF), dimethyl sulfoxide (DMSO), and 2-pyrrolidinonewerevacuum-distilled prior to use. Propylene carbonate and tetramethylene sulfone (sulfolane) were purified by passing through a column of activated neutral alumina (Aldrich). N-Methylindole (MeIn, Aldrich) was vacuum-distilled and kept refrigerated in the dark. Water was purified with a Millipore Super-Q system. Solutions of the porphyrin (10-510-4 mol L-I) were freshly prepared before use, except when the dissolution was slow, and were protected from unnecessary illumination. Radiolytic Studies. Pulse radiolysis experiments were performed with the apparatus described before15 which utilizes 50ns pulses of 2-MeV electronsfrom a Febetron Model 705 pulser. The dose per pulse, determined by KSCN dosimetry,16was varied between 7 and 40 Gy. The irradiation cell was filled with a fresh solution from a syringe before each pulse. All experimentswere carried out at room temperature, 21 f 1 OC. The CC1302*radicals were produced in the various solvent/ CC4 mixtures by reductive dehalogenation of C C 4 to CC4' radicals and subsequent reaction of this radical with oxygen, as described before." Dehalogenationof CC4 is achieved by reaction with solvated electrons and with certain reducing organicradicals. Other organic radicals may be produced in the irradiated solution and may react with oxygen to form peroxyl radicals. Such nonhalogenated peroxyl radicals, however, react much more

This article not subject to U.S.Copyright. Published 1994 by the American Chemical Society

One-Electron Oxidation of Porphyrins slowly9 than CC1302*and in most cases did not interfere with our kinetic measurements. The rate constants for the reaction of CC1302*radicals with the porphyrin were determined by following the rate of formation of the porphyrin *-radical cation (P+) at 700 nm as a function of porphyrin concentration using at least three concentrations that varied by a factor of 4. The secondorder rate constants werederived from plots of k h v s concentration and are generally accurate to f20%. N-Methylindole was also oxidized by CC1302' to yield the radical cation, MeIn*+. The rate of this reaction was determined by following the absorption buildup at 600 nm. Oxidation of the porphyrin by MeIn*+was followed at 700 nm, where P+absorbs stronglywhereas MeIn*+absorbs very weakly. In aqueous solution it was more efficient to produce MeIn'+ by oxidizing MeIn with the azidyl radical, N3*, produced in N2O-saturated solutions containing azide ions.I2 Electrochemical Studies. For cyclic voltammetric measurements, a standard three-electrode configuration was used. The reference electrode was an aqueous saturated calomel electrode and was separated from the bulk of the solution by a bridge filled with the respective solvent and supporting electrolyte. These studies were carried out in solutions containing 0.2 mol L-I tetraethylammonium (or tetrabutylammonium in solvents where the former is not sufficiently soluble) tetrafluoroborate (Fluka, puriss.) as supporting electrolyte. In the case of low scan rate experiments (with MSPDME), the working electrode was a glassy carbon electrode (3-mm diameter), the home-built potentiostat used was equipped with a positive feedback compensation device,18 and the initial concentration of porphyrin was 1 3 X 10-4mol L-I. For high scan rate cyclic voltammetry experiments (with MeIn), the ultramicroelectrode was a gold wire (17-pm diameter sealed in soft glass). The home-built potentiostat, the generator, and the digital oscilloscope were the same as described previ0usly.1~ The initial concentration of MeIn was close to 1 X le3mol L-l. Reversible voltammograms were obtained at low scan rates (0.11.OV s-l) for the first oxidation of MSPDME. For measurements with MeIn, due to the greater instability of its radical cation, reversibility of the first oxidation peak was only observed a t scan rates higher than 3000-10 000 V s-I, depending on the solvent. In all cases, the standard oxidation potentials Eo were taken from the totally or partially reversible voltammograms as the midpoint between the anodic and the cathodic peaks. To circumvent problems caused by liquid junction potentials, the potential of the reference electrode was measured before each set of experiments vs the oxidation potential of the ferrocene/ ferricenium couple. The standard potential for the ferrocene/ ferricenium couple was reported to be independent of the nature of the solvent (EO = 0.405 V vs SCE) and was thus recommended as a reference redox system in studies of solvent effect^.^ Results and Discussion Oxidation of Porphyrins with CCI3Oz' Radicals. The peroxyl radical CC1302*reacts with porphyrins (P) to form the *-radical cations.

We measured the rate constant for reaction 1 for several free base porphyrins in different solvents. The rate constants for H M P in 14 solvents (Table 1) are found to vary between 3 X lo7 and 2 X 108L mol-' s-l. Two other porphyrins, OEP and TSPP, were possible to measure only in a limited number of solvents (Table 2). OEP was soluble only in nonpolar and TSPP only in the more polar solvents. The results are thus insufficient for comparing the reactivities of the three porphyrins in any particular solvent. Only HMP was sufficiently soluble in a wide variety of solvents, and therefore, we use the results with this porphyrin to examine

The Journal of Physical Chemistry, Vol. 98, No. 29, 1994 7137

TABLE 1: Rate Constants for Reaction of CCl3Oz. Radicals with Hematoporphyrin in Various Solvents

solvent (% CC4) k~ (L mol-' S-I)~ bd E~(30)' water/Z-PrOH (9:l) pH 7 (0.1%) (2.2 f 0.4) X l o n d 47.9 63.1 formamide (1%) (1.5 f 0.3) X lo8 39.3 56.6 N-methylacctamide (6%) (5.0 f 1.5) X lo7 29.9 52.0 MeOH (10%) (6.2 f 1.2) X lo7 29.6 55.4 tetramethylene sulfone (5%) (7.9 f 1.7) X lo7 27.4 44.0 propylene carbonate (5%) (6.2 f 1.5) X lo7 27.2 46.6 DMF (10%) (5.3 h 0.9) X lo7 24.8 43.8 DMSO (5%) (1.0 f 0.4) X lo* 24.5 45.1 1-methyl-2-pyrrolidinone(10%) (4.4 0.8) X lo7 23.1 42.2 N,N-dimethylacetamide(10%) (3.0 f 0.5) X lo7 22.1 43.7 pyridine (10%) (4.8 f 0.8) X lo7 21.9 40.5 dioxane (10%) (4.8 f 0.8) X lo7 20.5 36.0 acetone (10%) (3.5 f 1.6) X lo7 20.2 42.2 THF (10%) (3.4 f 0.7) X lo7 18.6 37.4 "There are two major sources of uncertainty in the derived rate constants: the statisticaluncertainty in the first- and second-order fits, which were generally between 2% and 101,though in a few cases they were higher, and errors in the measurements of volumes and weights, which we estimate as 10%. * From ref 28. From ref 29. d Determined for aggregated HMP assuming monomeric concentration. the solvent effect on reaction 1. Before we embark on this correlation, several results deserve comment. In most organic solvents containing CC4, the main oxidizing species produced by irradiation are CC1302* radicals, whose reactions with the porphyrins are observed under our experimental conditions. Nonhalogenated peroxyl radicals may be also produced by irradiation of the solvent, but these generally do not interfere with our measurements because they either decay before reacting with the porphyrin or react much more slowly, Le., on a much longer time scale than that used in our measurements. Only in the case of N-methylformamide were two processes observed that were impossible to separate experimentally. Therefore, we could not obtain a reliable rate constant in this solvent. In DMSO/CCld solutions, two oxidizing radicals are formed, namely, the chlorine atom complex DMSOCl and the peroxyl radical CC1302*,which may oxidize the porphyrin with similar rates.20 The buildup of H M P + absorption at 700 nm exhibits two distinct processes in this solvent mixture. We attribute the fast component to reaction of DMSOCl and the slower component to reaction of CCl302'. This was confirmed by experiments with DMSO/CH2Cl2 solutions, where the fast component remained the same but the slower component was eliminated due to the absence of CC1302*and the much lower reactivity of the other peroxyl radicals formed (CH2C102' and CHC1202'). The slower component in DMSO/CCl4 solutions was also eliminated by the exclusion of 0 2 to prevent formation of CC1302*radicals. Before we compare the rate constants for reaction 1 in organic solvents and in water, we must consider the aggregation of the porphyrin. HMP forms significant amounts of dimers or aggregates in aqueous ~ o l u t i o n . 2 ~It- was ~ ~ found to be only 48% monomeric at 10-5 mol L-1 concentration,23 so that under our experimental conditions (C = 2 X 10-4 to 1 X mol L-l) in aqueous solutions only a small fraction remains monomeric. Conversely, in organic solvents (formamide, alcohols, THF), it was found to be monomeric at 10-4 mol L-I concentrations.22 It has been noted also that the amount of aggregates in aqueous solution is reduced by the addition of organic solvents;22.24 e.g., for 8.3 X 10-5 mol L-1 HMP, the deaggregation process is virtually complete in 30% methanol or formamide.22b These results indicate that the rate constants measured for reaction 1 in the organic solvents are for a monomeric H M P whereas those in aqueous solutions are for aggregated species. If we assume that most of the H M P at 10-4-10-3 mol L-l concentrations in aqueous solutions was in a dimeric form and that the reactivity of a dimer is similar to that of a monomer, we can multiply kob by a factor of ca. 2 to obtain a rate constant in water that can be correlated with

7138 The Journal of Physical Chemistry, Vol. 98, No. 29, 1994

Marguet et al.

TABLE 2 h t e COnstrnQ for Ractlon of CCl302' hdi& rrith Three P d -

in &mol SOIWII~S ~

&I

solvent (% CCL) water (sat.) water/Z-PrOH (9:l)pH 7 (0.1%) formamide (1 %) MeOH (10%) DMSO (10%) Nfl-dimethylacetamide (10%) pyridine (10%) Cc4 PhCN (10%)

OEP

(L mol-' HMP

(1.9X 0.4)

X

108

(3.3 0.5) x 107 (1.4 f 0.6) X lo7

those in organic solvents. The value in Table 1 is the observed rate constant before correction. Another effect to be taken into account when considering the resultsinaqueoussolutionsis theionizationofthecarboxylgroups. In the organic solvents, HMP was dissolved without the addition of base, and thus the two carboxyl groups are present in their neutral form, COOH. In water, on the other hand, HMP is solubleonly when the carboxylgroupsare ionized. The pK, values for the carboxyl groups are ca. 4.5, and the pK3 for protonation on the central nitrogen (W2+ s H3Pt e HzP s HF- s Pz-) is 6.1.25 Therefore, at pH 7 HMP exists predominantly in its HzP form with two COO-groups. The form with ionized carboxyl groups is expected to be slightly more reactive than that with two COOH groups.26 Therefore, to account for the ionization and the aggregation, which have opposing effects, we estimate the rate constant in aqueous solutions as (3 f 1) X lo8 L mol-' s-l and use this value for correlation with the rest of the data in Table 1. The table also lists the values of Hildebrand's solubility 6~192~ and Reichardt's solvent polarity parameter, ET(30):9 for the various solvents. The 6~ parameter was defined27 as the square root of the cohesive energy density and was derived from the latent heat of vaporization for the solvent: 6~ = [(AH" - RT)/ vM]1/2, where AH, is the molar heat of vaporization at zero pressure and VM is the molar volume. 6 ~which ~ , has the units of pressure (used here in units of megapascals),has been calledM the cavity term and was suggested to be a measure of the work necessary to separate the solvent molecules and create a suitably sized cavity for the solute. High values of 6~reflect strongsolventsolvent interactions, typically in the form of hydrogen bonding and dipole interactions. This will result also in strong interaction between the solvent and reactants, particularlythe peroxyl radical, which will influence the reaction rate. The 6~ solvent parameter has been found to give the best correlation with the rate constants for the reactions of CC1302' radicals with trolox and chlorpromazine in different solvents.17 Most other solvent parameters commonly used gave very poor correlations. Therefore,we correlated the rate constantsin Table 1 with 6 ~ .The values of &H given in Table 1 are for the pure solvents; in the correlation we used values corrected for the contributionof the small amount of CC4 (using weight fraction). Most of the solvents used have b~ values between 20 and 30; only formamideand water havesignificantly higher values. Therefore, the plot (Figure la) contains a large number of points at the lower part and only two points at the upper part. Nevertheless, the correlation is quite clear and is of the same quality as that found before for chlorpromazine;the correlation coefficient is R2 = 0.83. Correlation of the rate constants was attempted also with other solvent parameters but was found to be generally poor. Only the solvent polarity parameter &(30), developed by Reichardt based on solvatochromic effects,29 gave a somewhat reasonable correlation (R2 = 0.65) (Figure lb). Combinations of other solvent parameterswith b~ or with E ~ ( 3 0did ) not improve the correlations. The best correlation for the solvent effect on the rate constant for reaction 1 was obtained with the cohesive energy density and

TSPP

(2.2 f 0.3) X (1.5 0.3) X (6.2 f 0.8) X (1.1 f 0.4)X (3.0 f 0.5) X (4.8 f 0.8) X

*

~~~

91)

(8 1) X 108 (6.1 1.0)X 108 (5 A 1) x 107 (1.8 0.5)X lo7 (9 1) x 106 (3.0 1.0) x 107

* *

108 1 6 10' 10'

lo7 lo7

.I

m

c

L

10'

; J

J 20

30

40

50

8, I " " I ' " ' I " " I " ' ' 1

c

I u)

.-

L

10'

;

J 24-

10'

30

40

SO

BO

70

Ed301 Figure 1. Correlation of the rate constants for reaction of CCI30$ with hematoporphyrin in various solvents with the solvent parameters 6~ and ETW.

+

not with the dielectric constant [log k vs 1/c or (c - 1)/(2c l)], despite the fact that reaction 1 involves electron transfer and produces formally charged species. This finding suggests that the critical step in this reaction involves changes in the solvent cavity required for the reaction to proceed, whereas the electrontransfer step within the activated complex in probably very fast. It should be noted also that the products of reaction 1 do not remain as the free ions in most cases. As discussed before,17Jl the hydroperoxide ion protonates to the neutral hydroperoxide CClp02H3zin a process that is concerted with the electron transfer. In low polarity solvents, P+may form ion pairs with C1- (formed by reduction of CC4). Since the solvent dielectric constant is one of the factors that determine the cohesive energy; its effect on reactant polarization and electron transfer may be thus incorporated into the overall effect of 6 ~ .The main effect of 6~ on reaction 1, however, is that of the other factors that contribute to 611,such as hydrogen bonding and van der Waals forces. That the rate constant for reaction 1 increases with increasing solvent cohesion suggests that the reactants form an activated complex whose volume is leas than the sum of those of the reactants, i.e., that the reaction has a negative volume of activation. This, however, could not be verified experimentally in our system. A more quantitative correlation between the rate constants and solvent parameters can be achieved by using the Marcus relation if one can evaluate AGO for the reaction in each solvent. This, however, is not possible for reaction 1 since the reduction

One-Electron Oxidation of Porphyrins

The Journal of Physical Chemistry, Vol. 98, No. 29, 1994 7139

TABLE 3: Rate Constants for Formation of N-Methylindole Radical Cation (kz) and for Its Reaction with Hematoporphyrin (4) in Various Solvents solvent (% CC4) kl (L mol-' s-I) kz (L mol-' s-') water (NaN3, pH 7) (7.0 f 1.2) X 108 water/2-PrOH (1:l) pH 8 (2%) (1.8 f 0.3) X lo9 (1.1 f 0.2) X lo* formamide (1%) (3.5 f 0.9) X lo8 (4.3 f 0.7) X lo7 N-methylformamide(10%) (1.0 f 0.2) X lo9 (6.5 t 1.5) X lo7 2-pyrrolidinone (10%) (1.5 f 0.3) X 108 MeOH (10%) (1.2 0.2) x 109 (1.0 f 0.2) x io* tetramethylene sulfone (5%) (2.4 f 0.4) X lo8 (2.5 f 0.5) X lo7 propylene carbonate (5%) (6.2 f 1.0) X lo8 (4.0 f 0.6) X lo7 (6.6 f 1.1) X 108 DMF (10%) DMSO (10%) (7.2 f 1.2) X lo8 (3.5 f 0.7) X lo7 2-PrOH (10%) (4.1 f 0.6) X lo8 (3.4 f 0.6) X lo7 pyridine (10%) (6.0 f 1.0) X lo8 acetophenone (10%) (5.1 f 1.0) X lo8 2-buianone (10%) (1.5 0.2j x 109 3-pentanone(10%) (9.9 f 2.0) x 108

*

'

potential of CCl3O2*is unknown and cannot be measured by electrochemical Therefore, we attempted to other oxidation reactions of Doruhvrins.. where the oxidation potentials of both reactants may be measurable. The best candidate for this purpose was found to be N-methylindole (MeIn). Formation of the N-Methylindole Radical Cation and Its Reactions with Porphyrins. N-Methylindole can be oxidized by CC1302. and a variety of other radicals12 in different solvents to form the radical cation. *

1

CC1,02'

+ -

+ MeIn

I

CC1,O;

+ MeIn"

(2)

This radical cation may oxidize porphyrins. MeIn"

P

TABLE 4 Rate Constants for Reaction of NMethylindole Radical Cation with Mesoporphyrin-M Dimethyl Ester and Standard One-Electron Oxidation Potentials Determined by Cyclic Voltammetry in Various Solvents oxidation potentials" solvent (5% CC4) k4 (L mol-' s-1) MeIn MSPDME tetramethylene sulfone (5%) (5.6 f 0.8) X 108 0.816 0.438 propylene carbonate (5%) (1.4 f 0.3) X lo9 0.750 0.417 DMF (10%) (1.2 f 0.2) x 109 0.772 0.439 DMSO (10%) (1.3 f 0.3) X lo9 0.785 0.450 acetonitrile(10%) (3.7 0.7) x 109 0.807 0.406 acetone (10%) (3.6 f 0.7) X lo9 0.803 0.424 2-butanone (10%) (3.5 0.7) x 109 0.805 0.428 dichloromethane (3.2 f 0.7) X lo9 0.402 pyridine (10%) (1.6 f 0.3) X lo9 acetophenone (10%) (1.4 f 0.3) X lo9 Standard one-electronoxidation potentials of MeIn and MSPDME, accurate to f0.004 V for MSPDME in most solvents, to f0.008 V for MSPDME in acetone and 2-butanone, to fO.O1O V for MSPDME in DMSO, and to fO.01OV for Me1n;givenvs the potential ofthe ferrocene/ ferriceniumcouple,which is +OM5 V vs SCEand presumably unaffected by solvent.

MeIn + P.+

(3)

Rate constants for reaction 2 in several solvents were obtained from the rate of buildup of the radical cation absorption at 600 nm and are in the range 107-108 L mol-' s-l (Table 3). The highest value, k = 1.1 X 108 L mol-ls-l, obtained in a 1:l water/ 2-PrOH mixture, is identical to that reported previously.'2c Rate constants could not be measured in THF and dioxane because of very weak signals of the MeIn*+absorption. The rate constants for reaction 2 (Table 3) in the various solvents examined are slightly lower than those for reaction 1, but if MeIn is used in a large excess over porphyrin, e.g., >0.01 mol L-l, reaction 2 will predominate and will be complete within 1 1.1s. Therefore, the buildup of P+a t longer time scales can be attributed exclusively to reaction 3, whose rate constant is then determined from the dependence on porphyrin concentration. This measurement is possible also because MeIn*+ absorbs mainly at 600 nm with little absorbance a t 700, where P+formation is monitored. The rateconstants for oxidation of H M P by the N-methylindole radical cation were measured in most cases with solutions that contained 1.6 X le2mol L-l MeIn and 2 X 1eS-2 X 1 V mol L-1 HMP. The solvent also contained a small fraction of CC4 as before, except for the case of aqueous solutions, where oxidation of MeIn was more readily achieved by the azide radical in N2Osaturated solutions containing 0.1 mol L-1 NaN3 and 2 X le3 mol L-I MeIn. The rate constants for reaction 3 in the different solvents (Table 3) vary between 1.5 X 108and 1.8 X lo9L mol-' s-1. This range of k3 is an order of magnitude higher than that of kl (Table l), but there is no correlation between the values of kl and k3. This indicates that the two reactions take place by different mechanisms; reaction 3 is an outer-sphere electron transfer whereas reaction 1 is an inner-sphere reaction that also involves solvent molecules intimately.17.31 The lack of correlation between kl and k3 also implies that there is no correlation between k, and b~ or E ~ ( 3 0 ) . We tested these and other solvent parameter^,^^^^^ including various functions of the dielectric

-

+

constant e [l/e, (e - 1)/(2e l), (l/n2 - 1 / ~ ) but ] found very poor correlations. To correlate the rate constants with the solvent reorganization energy and the free energy of the reaction, we attempted to measure the standard one-electron oxidation potentials of MeIn and H M P in various solvents. The values for MeIn were measurable in a number of solvents (using ultramicroelectrodes and very fast voltage scan rates) whereas those for H M P could not be measured with acceptable accuracy.33 We, therefore, tested several other free base porphyrins and found mesoporphyrin-IX dimethyl ester (MSPDME) to be the most suitable for accurate cyclic voltammetric measurements of the one-electron oxidation potentials. This porphyrin is less soluble than H M P in protic solvents, but this is not a severe disadvantage since the potentials could not be measured in such solvents. The standard one-electron oxidation potentials for MSPDME and for MeIn in several solvents are summarized in Table 4. The rate constants for reaction of MeIn*+ with MSPDME

MeIn'++ MSPDME- MeIn + MSPDME"

(4)

were also measured in the same solvents and are given in Table 4. The two sets of values were correlated with the solvent properties according to the Marcus the0ry.3~ The rate constant for an electron-transfer reaction, such as reaction 4, is determined by the free energy of activation, AG*, and a collision frequency, Z.

The activation-controlled rate constants, k,,,, were calculated from the experimental values, kob (k4 in Table 4), by correcting for the effect of the diffusion-controlled limit, k&ds(Table 9 . 3 6 1 1 -=--kact

kobs

1 kdiff

(6)

Values of AG* were then calculated from eq 5 by taking the commonly used value of Z = 1 X 1011 L mol-' s 4 . 3 4 AG* is related to the free energy of the reaction, AGO, calculated from the difference in standard one-electron oxidation potentials (AGO = -nFAiP) and the reorganization energy, A.

AG* = (AGO

+ Q2/4A

(7)

The work term (Z1Z2e2/Dr12) is zero since reaction 4 involves one uncharged species. We can assume that A is mainly the

7140 The Journal of Physical Chemistry, Vol. 98, No. 29, 1994

TABLE 5 Calculation of f from the Rate Constants for Reaction 4 in Various Solvents solvent tetramethylene sulfone propylene carbonate DMF DMSO acetonitrile acetone 2-butanone

kdap

5.6 X 108 6.7 X 108 3.4 X

IO9

8.33

36.4

1.43

X lo9

8.72

32.1

1.35

1.4X 109 10.52 2.1 x 109 9.53 5.1 X lo9 7.36 4.8 X 109 7.51 4.9 X 109 7.48

32.1 32.3 38.7 36.6 36.4

1.50 1.52 1.24 1.30 1.36

1.4 X 109 2.7 X lo9 2.9 1.2 X 1.3 x 3.7 X 3.6 X 3.5 X

109 7.6 X 109 3.4 x 109 1.4 X 109 1.4 X 109 1.3 X

109 109 10'0 1010 1010

AG'd -AGO* f/lO'f

k,C

a From Table 4. Diffusion-controlled rate constant calculated from the viscosity. C Activation-controlled rate constants calculated from kRp and kdm. Free energy of activation, in W mol-l, calculated from ku. e Free energy of reaction, in W mol-', calculated from the difference in redox potentials in Table 4. /The factor f = (I/zrl + '/2r2 - l/rlz), calculated from AG* and AGO, according to eqs 7 and 8.

TABLE 6 Comparison of Calculated and Experimental Rate Constants for Reaction 4 in Various Solvents tetramethylene sulfone propylene carbonate DMF

DMSO acetonitrile acetone 2-butanone

88.4 92.2 87.8 82.8 100.5 93.2 89.0

4.5 x 1.9 X 2.9 X 4.5 x 2.2 x 3.1 X 4.3 x

109 lo9 lo9 109 109 lo9 109

3.4 x 2.9 X 1.4 X 2.1 x 5.1 x 4.8 X 4.9 x

109 lo9 lo9 109 109 109 109

a Solvent reorganization energy, inkJ mol-', calculated from the average value off= 1.38 X lo7and the solvent dielectric constant and refractive index, according to eq 8. b Rate constants calculated from the reorganization energy according to eqs 7 and 5. From Table 5.

solvent reorganization energy, which is given by

Marguet et al. species. This situation for reaction 4 is clearly different from that indicated for reaction 1, where the peroxyl radical, the porphyrin, and solvent molecules are involved in the electron transfer and form a more condensed transition state. Rate constants for reaction 4 were also measured in CH2C12, pyridine, and acetophenone (Table 4), although the oxidation potentials could not be measured in these solvents. From the above radii factorf= 1.38 X lo7and km for these three solvents, we can estimate the difference in redox potential, 0, to be 0.25, 0.17, and 0.19 V, respectively. By assuming the same extent of agreement between ,.k and k d c as found above, we estimate the errors in the calculated A,?? values to be fO.05 V, approximately 3 times the errors in the measured values. The calculated values of A P for these three solvents are lower than those derived for the other solvents from the measured values in Table 4. The rate constants for oxidation of HMP by MeIn*+ (Table 3) are lower than those of MSPDME (Table 4), probably due to a small difference in the oxidation potentials. For the seven solvents in which the rate constants were measured for both porphyrins, we find that the ratio kdk, = 2.3 j: 0.4, practically constant within the experimental error limits. This ratio may be used to estimate, from the above calculations using the same f factor, that the potential for one-electron oxidation of HMP is ca.90 mV higher than that of MSPDME. Theabovecalculations permit us to estimate redox potentials from the measured rate constants and thus provide us with a method to estimate the potentials in solvents in which these are not measurable.

Acknowledgment. This work was supported by the Division of Chemical Sciences,Office of Basic Energy Sciences,Department of Energy. We thank Drs. Z. B.Alfassi, C. P. Andrieux, and R. E. Huie for helpful discussions. References and Notes

where rl and r2 are the radii of the reactants, r12 is the reaction distance, c is the dielectricconstant, and n is the refractive index.3' The term f = I/2rl */2r2- l / r 1 2should be the same in all solvents. In fact, the calculated values off (Table 5) are nearly constant, within experimental error, and average to (1.38 f 0.1 1) x 107. Another way to test the agreement between the experimental rate constants and the theoretical values is to use the average value off, as a constant for all solvents, to calculate the solvent reorganization energies, A, and from these to calculate the rate constants kWlcaccording to eqs 5 and I. These values of kWlc (Table 6) are found to be similar to the values of k,, (within a factor of 2).3* It should be noted that the value off is calculated from a quadratic equation, and thus two values are obtained. The other value was rejected since it gives values of A smaller than AGO and corresponds to the inverted region, which is unlikely for reaction 4, where the driving force is only of the order of 0.3-0.4 eV. The value off= 1.38 X 107can be used to estimate the reaction radius from the radii of t h e reactants. For planar molecules such as the porphyrins and MeIn, there is a difficulty in calculating the radii rl and r2 to fit to the above theory, which assumes spherical reactants. As suggested before,39 we can treat the reactants as approximate spheres and estimate the radii from the molar volumes. This approximation gives rl = 5.8 A and r2 = 3.1 A for MSPDME and MeIn, respectively. From these values, and f, we calculate r12= 12.2 A, larger than the sum of the individual radii. If we use larger values for the reactants, e.g., the radii of the planar structures, we obtain r12 still larger than the sum of rl and r2. Although this treatment is not exact for planar reactants, these estimates suggest that the electron transfer does not require a very close approach of the reactants to each other and may take place with minimal overlap of the r-clouds of the two reacting

+

(1) (a) NIST. (b) UP7. (2) See, e.&: (a) Felton, R. H. In The Porphyrins; Dolphin, D., Ed.; Academic Press: New York, 1978; Vol. 5, Part C, Chapter 3, p 53. (b) Fuhrhop, J.-H. Struct. Bonding 1974, 18, 1. (3) Davis, D. G. In The Porphyrins; Dolphin, D., Ed.; Academic Press: New York, 1978; Vol. 5, Part C, Chapter 4, p 127. (4) Kadish, K.M.; Cornillon, J. L.; Yao, C. L.; Malinski, T.; Gritzner, G. J. Electroawl. Chem. 1987, 235, 189. (5) Alfassi, Z. B.; Harriman, A.; Mosscri, S.;Neta, P. Int. J. Chem. Kinet. 1986, 18, 1315. (6) Brault, D.; Neta, P. J. Phys. Chem. 1984,88,2857; 1987,91,4156. (7) Huie, R. E.; Brault, D.;Neta, P. Chem.-Biol. Interact. 1987,62,227. ( 8 ) Nahor, G. S.;Neta, P.; Hambright, P.; Robinson, L. R. J. Phys. Chem. 1991,95,4415. Guldi, D. M.; Neta, P.; Hambright, P. J. Chem. Soc., Faraday Trans. 1992,88, 2013. (9) Neta, P.; Huie, R. E.; Ross, A. B. J. Phys. Chem. Ref. Data 1990, 19, 413. (10) Cheeseman, K.H.; Albano, E. F.; Tomaei, A.;Slater, T. F. Emiron. Health Perspect. 1985,64, 8 5 . Brault, D. Emiron. Health Perspect. 1985, 64, 53. (1 1) Dougherty, T. J.; Kaufman, J. E.; Goldfarb, A,; Weishaupt, K. R.; Boyle, D.; Mittleman, A. Cancer Res. 1978, 38, 2628. (12) (a) Shen, X.;Lind, J.; Merenyi, 0. J. Phys. Chem. 1987,91,4403. (b) Merenyi, G.; Lind, J.; Shen. X . J. Phys. Chem. 1988,92,134. (c) Shen, X.;Lind, J.; Eriksen, T. E.; Merenyi, G. J. Chem. Soc.,Perkin Trans 2 1989, 555. (1 3) The mention of commercial equipment or material does not imply recognition or endorsement by the National Institute of Standards and Technology, nor does it imply that the material or equipment identified are necessarily the beat available for the purpose. (14) Since sulfolaneis a solid at room temperature, it was uscd with added 5% CCL in the pulse radiolysis experiments and with added 5% 3-methylsulfolane in the cyclic voltammetry experiments. For the latter case, the solvcntwaspurifiedby theprocedureofhettetal.: Amett,E.M.;Amamath, K.; Harvey, N. 0.;Cheng, J.-P. J . Am. Chem. Soc. 1990, 112, 344. (15) Huie, R. E.;Neta, P. J. Phys. Chem. 1984, 88,5665. (16) Schuler, R. H.; Patterson, L. K.;Janata, E. J. Phys. Chcm. 1980,81, 2088. (17) Alfassi, Z. B.; Huie, R. E.; Neta, P. J. Phys. Chem. 1993,97,7253. (18) Garreau, D.; Saveant, J.-M. J. Electroanal. Chem. 1972, 35, 309. (19) Andrieux, C. P.;Hapiot, P.; Savant, J.-M. C h m . Rev. 1990, 90, 723. (20) Kumar, M.;Neta, P. J. Phys. Chem. 1992,96, 3350. (21) Smith, G. J.; Ghiggino, K.P. J. Photochem. Photobiol. B 1993,19, 49. Smith, G. J.; Ghiggino, K. P.; Bennett, L. E.; Nero, T. L. Photochem.

One-Electron Oxidation of Porphyrins Photobiol. 1989,49,49. Rotomskis, R.; Krammer, B. Proc. SPIE-Inr. Soc. Opt. Eng. 1992,1922,235. Moan, J. Photochem. Phorobiol. 1984,39,445. (22) (a) Andreoni, A,; Cubeddu, R. Chem. Phys. Lett. 1984,108,141. (b) Andreoni, A,; Cubeddu, R.; De Silvestri, S.;Jori,G.; Laporta,P. 2.Naturforch. C 1983, 38, 83. (c) Gallagher, W. A,; Elliott, W. B. Ann. N.Y. Acad. Sci. 1973, 206,463. (23) Turay, J.; Hambright, P.; Datta-Gupta, N. J. Inorg. Nucl. Chem. 1978,40, 1687. (24) Karns, G. A.; Gallagher, W. A,; Elliott, W. B. Bioorg. Chem. 1979, 8, 69. (25) Hambright, P. Inorg. Chem. 1977, 16, 2987. (26) The rate constant for reaction 1 with HMP was found to increase from 2.2 X 108 at pH 7 to 3.4 X lo* at pH 8.4 and to 5.2 X 108 L mol-' s-' at pH 12, despite the fact that HMP has no pK. values above 6.1 and below 14 (and this effect is not due to changes in ionic strength). The reason for this increase is unclear. As the pH is decreased below 7, the rate is expected todecreasedue to protonationof thecarboxylgroupsand thecentral nitrogens, but this could not be verified for HMP because of insufficient solubility at low pH. In MeOH the rate constant increased by a factor of 3 upon addition of 0.06 mol L-l NaOH, partly due to deprotonation of the carboxyl groups and partly in parallel with the above behavior in water. Upon addition of 1% acetic acid in MeOH, the rate decreased by 30% probably due to partial protonation of the central nitrogens. For TSPP in water the rate decreased by a factor of 4 upon changing pH from 7 to 4.2, where all four central nitrogen are protonated. (27) Hildebrand, J. H.; Scott, R. L. Regular Solutions; Prentice-Hall: Englewwd Cliffs, NJ, 1952. The Solubility of Non-Electrolytes, 3rd ed.; Dover: New York, 1964. (28) (a) Barton, A. F. M. Chem. Reo. 1975, 75,731. (b) Barton, A. F. M. In CRC Handbook of Solubilitv Parameters and Other Cohesion Parameters; CRC Press: Boca Raton; FL, 1983.

The Journal of Physical Chemistry, Vol. 98, No. 29, 1994 7141 (29) Reichardt, C. Solvents and Solvent Effects in Organic Chemistry, 2nd ed.;VCH: Weinheim, 1988. (30) (a) Kamlet, J. M.;Carr, P. W.;Taft, R. W.;Abraham, M. H. J. Am. Chem. SOC.1981,103,6062. (b) Abraham, M. H.; Kamlet, J. M.; Taft, R. W. J. Chem. Soc., Perkin Trans. 2 1982, 923. (c) Taft, R. W.; Abraham, M. H.; Doherty, R. M.;Kamlet, M. J. J. Am. Chem. Soc. 1985,107,3105. (d) Abraham, M. H.; Doherty, R. M.; Kamlet, M. J.; Harris, J. M.; Taft, R. W. J. Chem. Soc., Perkin Trans 2 1987, 913. (31) Neta,P.;Huie,R. E.;Maruthamuthu, P.;Steenken,S. J. Phys. Chem. 1989.93, 7654. (32) Protons are generally available from the solvent or as radiolysis products. (33) HMP did not exhibit reversible voltammogram scans probably due to a short lifetime of the radical cation in most solvents. (34) Marcus, R. A. J. Chem. Phys. 1956,24,966; J. Chem. Phys. 1957, 26, 872; Annu. Reo. Phys. Chem. 1964, IS, 155. Marcus, R. A.; Sutin, N. Biochim. Biophys. Acta 1985,811,265. (35) k w was calculated from the viscosity, q, of the solvent mixtures according to & = 8RT/3000q, where q was calculated from the viscosities (from ref 37) of the two solvents in the mixture and their weight fraction. (36) Whenthecorrectionisverylarge,suchasinthecaseoftetramethylene sulfone, the accuracy of this correction is low since k w is an estimated value. 137) Lunm'sHandbookofChemistrv. 13thed.:Dean.J.A..Ed.:McGrawHili: New fork, 1985. Hadbook of &ganic Chemistry, D&n,'J. A,, Ed.; McGraw-Hill: New York,1987. (38) The agreement between k d a n d k.*was worse when an inner-sphere reorganization, Xi, constant in all solvents, was added into the calculation, indicating that Xi is negligible, as expected for reaction 4. (39) Eberson, L. Ado. Phys. Org. Chem. 1982,18,79 (seep 103 and 115 and reference9 therein).