J. Phys. Chem. 1984, 88, 1065-1068
number M and ( T2-l(M)) the averaged width as defined in ref 7, the condition
Cw2k(M)1-’- [Tzk’(M)l-’l
k,k’
(Tz-I(M))
(3)
applies in our spin system. With the r subscript indicating the different groups of equivalent nuclei, the following equation holds: ( T2-I[Wr)= ( T2-’(Ma,Ma,My,Ma,M,,MN)) =
C(T99%) or AnalaR grade except for Laboratory reagent acrylamide (>98.5%), 3,4-dimethylphenol, and 9,lO-anthraquinone (>98%). Diethylaniline was redistilled under Nz, and benzaldehyde was purified chromatographically. The fluorescence was measured in a conventional fluorimeter with a R-928 (Hamamatsu) photomultiplier and a Brookdeal-Ortec photon-counting system (PC-5). The ZnOEP was excited in its 533-nm absorption band. The fluorescence lifetimes were measured on a S L M phase fluorimeter at 18- and 30-MHz modulations.
Results The fluorescence lifetimes of ZnOEP in the presence of oxygen in toluene and in acetonitrile were found to be 1.9 and 2.1 ns, respectively. The standard deviation was 0.15 ns. Lifetimes were obtained from both phase shift and intensity demodulation. The difference in the values obtained by the two methods was found to lie within the above error range. These lifetimes of ZnOEP in the absence of quenchers were used to calculate the quenching rate constants, k,, from the Stern-Volmer quenching constants. The latter were generally obtained by steady-state measurements. In some cases the quenching constants were also determined by lifetime measurements. Because of the inherently short lifetime of ZnOEP*, these measurements yield k, values that are less accurate (f30%) than those from steady-state measurements. Within the estimated error range, the k, values from lifetime measurements agreed with the steady-state results. The quenching rate constants in the polar solvent acetonitrile and in the nearly apolar toluene for a number of electron acceptors and electron donors together with their polarograpic half-wave reduction and oxidation potentials, respectively, are presented in Table I. The values obtained from lifetime measurements are given in parentheses. In all cases studied the fluorescence spectrum of ZnOEP did not change in the presence of the quencher. Even in the apolar toluene no new emission band indicative of an excited-state complex was observed. The number of electron acceptors and donors used in the quenching experiments was severely limited by two factors: (a) the solubility of the solutes in at least one of the solvents usedacetonitrile and/or toluene; (b) the requirement that specific interactions and complex formation in the ground state between ZnOEP and the quenching substance do not take place. Particularly in the nonpolar solvent toluene, the absorption spectra showed that with many known electron donors and acceptors ZnOEP formed ground-state complexes. Some potential quenchers that caused changes in the ZnOEP absorption spectrum were benzophenone in acetonitrile and in toluene, phenylenediamine and a-naphthylamine in toluene, and fumaric and maleic acid in acetonitrile. In some cases in which no ground-state complex is observed, the Stern-Volmer quenching plots did not obey the usual linear relation (for example, indole gave an upward curvature). This might be due to preexisting weak molecular interactions not revealed by the absorption spectrum. Quenchers that showed such specific interactions were not used in this study. The quenching substances in Table I are ordered according to their decreasing polarographic half-wave reduction potentials. It is seen that good electron acceptors, the quinones (EY; > -1.0 V with respect to the standard calomel electrode (SCE)), quench the ZnOEP fluorescence with a rate that is, or is almost, diffusion controlled. The quenching rate decreases by a factor of more than 30 for substances with reduction potentials of EYA = -2.0 V with respect to the SCE. Discussion It has been experimentally found that the difference between the first polarographic half-wave oxidation potential and the first reduction potential of ZnOEP, Eb(,z - E Y i = 0.63 V - (-1.61 V) = 6, nearly equals the lowest excitation energy of the molecule, moo = 2.15 eV. In simple molecular orbital language, this might be taken to mean that the energy needed to transfer an electron from one porphyrin molecule to another; Le., the standard free energy for the reactions 2P P+ + P is given by the difference
-
Barboy and Feitelson TABLE I: Quenching of ZnOEP Fluorescence by Electron Acceptors and Donors in Acetonitrile and in Toluene; Half-Wave Potentiala and Quenching Rate Constants kqb
E& acceptor 1. p-benzoquinone
2. 1,4-naphthoquinone 3. duroquinone 4. 9,10-anthraquinone 5. benzaldehyde ZnOEP 6. benzoic acid 7. acrylamide 8. naphthalene
10-9~~~
in
CH,CN -0.48 -0.82 -0.84 -0.98 -1.58' -1.61' -1.94' -1.94 -2.63
donor
13. 14. 15. 16.
phenylenediamine o-aminophenol a-naphthylamine 3,4-dimethylphenol ZnOEP N,N-diethylanilined a-naphthol 1,4-hydroquinone phenol
toluene
18 (23) 20 16
22 (17) 17 10 20 1.0
1.6 (1.8) 0.7 0.57 20.01
in CH,CN Ell2
9. 10. 11. 12.
CH,CN
ox
+0.6 i-0.4' +0.62 +O.5lc +0.63' +0.76 +1.14 +1.16 +1.47
10-9kq -
CH,CN
toluene
10 3.5 2.5 1.8 0.7 1.3 1.7 0.33
0.6
a Half-wave potentials against the SCE in acetonitrile were k , values taken from ref 13 except where indicated otherwise. in parentheses are from lifetime measurements. Estimated error is r30%. Reference 7. Benzaldehyde in 1 : l benzene:MeOH, ref 1 3 ; benzoic acid in 75% dioxane, ref 13;o-aminophenol in aqueous buffer, ref 1 4 ; 3,4-dimethylphenol in 1 :1 2-propano1:acac buffer, ref 15; ZnOEP in Me,SO, ref 6.
'
between the highest occupied (HOMO) and the lowest unoccupied molecular orbital (LUMO) of the porphyrin.6 In fact, the near is probably due to the mutual cancellation equality of 6 and moo of effects since such an approach neglects conformational entropy changes, solvation energies, and charge interaction^.^ On the other hand, it has been found experimentally that in polar solvents the fluorescence quenching of excited electron donors, D*, in the presence of acceptors, A, or of excited electron acceptors, A*, in presence of donors, D, is often accompanied by the formation of the corresponding ions D+ and A-. The standard free energy for the transfer of an electron in these systems D* A a D*-.A (encounter cage) s D+-A- (solvated ion pair)
+
-
at the distance where this transfer takes place can be described by AGO = E(D/D+) - E(A-/A) - AEoo- e2/trDA
(1)
where E(D/D+) and E(A-/A) are the oxidation potential of the donor and the reduction potential of the acceptor, respectively.',* They are approximated by the corresponding polarographic is the lowest electronic half-wave potentials Eb(: and EYA. moo excitation energy of the donor or acceptor, and t is the dielectric constant of the solution. The last term in eq 1 represents the stabilization due to the Coulomb interaction of the solvated D+ and A- ions formed at the distance of electron transfer. It has been found by Weller and co-workers, for a variety of donoracceptor pairs in polar solvents, that as long as the value of AGO is less than e-0.4 eV (-10 kcal/mol), the electron-transfer rate is determined by the rate of diffusion and takes place with a rate constant of k N 2 X 1OloM-' s-*. For more positive AGO values (5) Felton, R. H. "The Porphyrins"; Academic Press: New York, 1978; Vol. V, pp 53-1 15. (6) Fuhrhop, J. H.; Kadish, K. M.; Davis, G. W. J . Am. Chem. SOC.1973,
95, 5140-5147. (7) Rehm, D.; Weller, A. Ber. Bunsenges. Phys. Chem. 1969, 73, 834-839. (8) Knibbe, H.; Rehm, D.;Weller, A. Ber. Bunsenges. Phys. Chem. 1968, 72, 257-263.
The Journal of Physical Chemistry, Vol. 88, No. 6, 1984 1067
Reactions of Zinc Octaethylporphyrin it was found that the above rate constants decrease. Below k, = lo8 M-' s-l a linear dependence of log k, on AGO was observed. Such a behavior can quite generally be expected for reactions that do not involve complex molecular bond rearrangements. Proton transfer is an example of such a process. More relevant to the present discussion is the transfer of charge in the excited singlet state of molecules whose valence electrons are located in extended ?r or peripheral nonbonding orbitals. If for such a donoracceptor system the equilibrium strongly favors the transfer of charge, Le., AGO < 0, and no chemical-bond breakage is involved, one can expect that the process will proceed with no appreciable activation energy and that electron transfer will take place on every encounter. In the range of positive AGO values, a free energy of activation, which at least equals AGO, will be experienced. In this range of slowed-down charge transfers other processes that quench the excited state might compete with the transfer of electric charge. In polar solvents, porphyrins, such as ZnOEP, in the excited triplet state are known to interact with similar molecules in their ground state. By the transfer of an electron, a positive and a negative ion are formed in the process.' If such a process were also to take place between excited singlet and ground-state molecules of ZnOEP, it follows from eq 1 that, because of the near equality of Ea: - E Y i = 6 (2.24 eV for ZnOEP) and the excitation energy AEoo(2.15 eV), the free energy change for the reaction 'ZnOEP*
+ ZnOEP
-
ZnOEP'
+ ZnOEP-
would be determined by the Coulomb interaction at the distance of charge transfer; Le., AGO 0.09 - eZ/ErDA(ev). Mauzerallg has shown that for various metal porphyrins, electron transfer probably takes place over relatively large distances by a tunneling mechanism. The average charge separation for tunneling in the singlet state is estimated at a ring to ring distance of 5 8 or a molecular center to center distance of about 10 8. This would yield a value of AGO E 0.01-0.05 eV for the above charge-transfer reaction in the polar solvent acetonitrile. It is proposed here that the fluorescence quenching of ZnOEP by electron acceptors or donors other than porphyrins in polar solvents also takes place by electron transfer from or to the excited 'ZnOEP*. Such a quenching mechanism is indicated by the dependence of the quenching rate constant kq on AGO, the standard free energy change for electron transfer as calculated from the reduction or oxidation potentials of the quenchers (eq 1). Our data in Table I show that in CH3CN various quinones, which are good electron acceptors, and phenylendiamine, an electron donor, all quench the ZnOEP fluorescence with a rate constant in the k, = (1.5 f 0.5) X 1O1OM-' s-l range as can be expected if their EYA or Ea: values, respectively, are inserted in eq 1 (see Figure 1). We used a dielectric constant o f t = 37 and an average ZnOEP to donor (or acceptor) distance for electron transfer of rDA= 7 8.This yields a Coulomb stabilization term of e2/trDA 0.06 eV. It seems, therefore, that for processes in which the electrochemical considerations predict a zero free energy of activation for the electron-transfer step, fluorescence quenching takes place upon every donor-acceptor encounter. When electron acceptors with reduction potentials similar to or more negative than and electron donors with oxidation potentials similar to or more positive than the corresponding Ell2 values for ZnOEP are used, a decrease in the quenching rate constant is observed as must be expected if the electron-transfer reaction has a free energy of activation. Because of the short lifetime of ZnOEP, the decrease in the quenching rate constant in our experiments could not be measured in the range in which a linear dependence of log k, on AGO has been found in other systems.' However, even so, the scatter in data points is larger than warranted by the experimental error. Moreover, in many cases the decrease in log k, is much smaller than can be expected from the above electrochemical considerations. The broken line in Figure (9) Mauzerall, D. 'The Porphyrins"; Academic Press: New York, 1978; Vol. V, pp 29-52.
9.5 CI
1
-," 9.08.5-
8.0 -
IO
-0 5
00 AG"(eV)
05
IO
Figure 1. Dependence of rate constant k, for ZnOEP fluorescence quenching by electron acceptors (A, A) and donors (0,0 ) . The open symbols refer to acetonitrile and the filled-in symbols to toluene solutions. AGO was calculated from eq 1 with eZ/trDA= 0.06 eV. The numbers relate to the quenchers listed in Table I. Arrows indicate that the value of AGO is expected to be larger in acetonitrile than in the aqueous mixtures in which Ell2 was determined.
1 roughly indicates the decrease in log k, with AGO for the quenching by electron transfer as found by Rehm and Weller.7 It seems that in the range where our rate constants decrease to values of k IO9 M-I s-l or less, other quenching processes are more rapid than the transfer of an electron. The quenching rate constants measured then represent the fastest deactivation pathway of ZnOEP and would be specific for each quencher molecule. This, for example, seems to occur with the hydroxylated aromatics 14, 15, and 16 in Figure 1. In such cases the rate constants need not, of course, follow the dependence expected for the transfer of an electronic charge. The accuracy of the AGO values in Figure 1 is limited by the uncertainty in the quantities E(D/D+) and E(A-/A) (eq 1). The polarographic half-wave potentials were in most cases determined in acetonitrile as solvent. However, the concentration and the kind of supporting electrolyte used seem to affect the value of Ell2 obtained. Moreover, even under the same experimental conditions, different Ell2 values are often reported for the same substance (see, for example, data for benzoquinone12). Fluorescence quenching by electron donors or acceptors in nonpolar solvents often proceeds via intermediary excited dimers-heteroexcimers or exciplexes-with their own characteristic emission.s~10Similar to the formation of solvated ion pairs in polar solution, the quenching by heteroexcimer formation A* D P A*-D (encounter cage) P (AD) * (heteroexcimer)
+
-
is also accompanied by the transfer of an electronic charge. The exciplex finally reverts to the initial ground-state molecules.8J0J1 For electron donor-acceptor pairs that yield a significantly negative AGO value in eq 1, it has been found that the rate of heteroexcimer formation is diffusion limited." That no change in the fluorescence spectrum of ZnOEP and hence no exciplex fluorescence was observed in any of the molecular systems in Table I does not mean that a short-lived nonfluorescent complex is not involved as an intermediary in the quenching process.'0 Indications also exist that even in apolar solvents electron transfer within the photochemical cage yields a small amount of free ions in solution.' In any case we cannot estimate with any confidence the free energy change of the quenching process in nonpolar solvents like toluene. Strictly speaking, eq 1 might not be applicable if the electrontransfer step in the reaction chain does not result in (almost) separated ionic species but in a heteroexcimer of partial (10) Mataga, N.; Ottolenghi, M. 'Photophysical Aspects of Exciplexes in Molecular Association"; Foster, R., Ed.; Academic Press: New York, 1979; Vol. 2. (1 1) Chuang, T. J.; Eisenthal, K.B. J. Chem. Phys. 1975,62,2213-2222.
1068
J. Phys. Chem. 1984,88, 1068-1076
charge-transfer character. Even if that equation does constitute a good approximation to AGO for the quenching process, data for oxidation and reduction potentials are not available in toluene. As a rule, reduction potentials become more negative and oxidation potentials more positive with a decrease in solvent polarity;'* i.e., the transfer of charge becomes more difficult. On the other hand, the Coulomb stabilization, eZ/crDAin eq 1, will also increase in nonpolar solvents. Though the two effects cancel each other to some extent, still one cannot predict the free energy change for the quenching process in toluene on the basis of its value in a polar solvent. Nevertheless, for lack of the correct AGO values, log k , in toluene in Figure 1 was plotted against AGO as calculated for acetonitrile. In view of this crude representation the similarity in the quenchihg rate constants in the two solvents is quite remarkable. For quenchers with very negative AGO values for electron transfer, i.e. good electron donors, in acetonitrile, it stands to reason that also in toluene the free energy change for the process will still remain negative. The data points ought perhaps be shifted along the AGO axis but would still remain in the AGO < 0 range. The measured reaction rates in toluene in these cases show that the process here too is encounter limited. A mechanism invoking charge transfer to account for the fluorescence quenching of ZnOEP by electron donors and acceptors in both polar and nonpolar solvents agrees well with the obserations of Ballard and Mauzerall,' who found by conductometric measurements that the rate of the ZnOEP triplet-ZnOEP ground-state reaction yielding positive and negative ions is very similar to those in CH3CN and (12) Peover, M. "Electroanalytical Chemistry"; Bard, A. J., Ed.; Marcel Dekker: New York Vol. 2. ChaDter IIC. (13)."Techniques of Electroorganic Synthesis" Part 11; Weinberg, N. L., Ed.; W h y : New York, 1975; Vol. 5, appendix. (14) Meites, L.; Zusman, P. "Electrochemical Data"; Wiley: New York, London, 1973; Part I, Vol. A. (15) Suatori, J. C.; Snyder, R. E. Anal. Chem. 1961, 33, 1894-1897.
in toluene. Of course, the free ion yields differ vastly in the two solvents. It is even more astonishing that when the electrochemically determined AGO values (eq 1) in acetonitrile become positive and when they might have a quite different value in toluene, the quenching constants for ZnOEP in the two solvents still resemble each other. The similar position of the break in the log k, vs. AGO curve leads us to assume that the contribution to the true AGO values due to electron transfer in toluene and in acetonitrile are not very different. The log k, values in the two solvents in the range where log k, < 1O'O indicate that the quenching mechanisms, which might differ for different quenching substances, are apparently similar for a given quencher in the two solvents. This is brought out by the data for substances 14, 15, and 16 in Figure 1. In conclusion, we feel it is very likely that as long as the electrochemicallydetermined AGO value is negative, the quenching of ZnOEP fluorescence in both polar and apolar media takes place via electron transfer. For quenching substances with redox potentials such that AGO > 0 for the transfer of an electron, other quenching routes might become more efficient. However, in such cases the rate-determining step in the reaction between ZnOEP and the quencher seems to be the same in both the polar acetonitrile and the apolar toluene. Acknowledgment. This research has been sponsored in part by the U S . Army through its Research and Standardization Group (Europe). Registry No. ZnOEP,17632-18-7; CHjCN, 75-05-8;toluene, 10888-3;p-benzoquinone, 106-51-4; 1,4-naphthoquinone, 130-15-4; duroquinone, 527-17-3;9,10-anthraquinone,84-65-1; benzaldehyde, 100-52-7; benzoic acid, 65-85-0;acrylamide, 79-06-1;naphthalene, 91-20-3;phenylenediamine, 25265-76-3; o-aminophenol, 95-55-6;a-naphthylamine, 134-32-7; 3,4-dimethylphenol, 95-65-8; N,N-diethylaniline, 91-66-7; a-naphthol, 90-15-3; 1,4-hydroquinone, 123-31-9;phenol, 108-95-2.
Kinetlcs of Multicomponent Transport by Structured Flow In Polymer Solutions. 5. Ternary Diffusion in the System Poly(vinylpyrro1idone)-Dextran-H,O W. D. Cornper,* G . J. Checkley, and B. N. Preston Biochemistry Department, Monash University, Clayton, 3168, Victoria, Australia (Received: April 26, 1983; In Final Form: July 18, 1983)
The etiological events associated with the formation of structured flows in dextran-poly(vinylpyrro1idone) systems have been investigated. The numerical values of all four diffusion coefficients in the model ternary system have been calculated from thermodynamic (osmotic) and binary or tracer transport experiments. Utilizing this information and the known mathematical solutions to the system of flow equations has led to the calculation of the spatial density distribution as a function of time. These calculations demonstrate a direct correlation between the polymer concentrations required for the formation of a density inversion at the boundary and the onset of structured flows. Previous theoretical treatments of the stability of these solutions have also been analyzed.
Introduction It has been previously shown that ternary systems consisting of a uniform concentration of dextran (regarded as a pseudosolvent) with an imposed concentration gradient of poly(viny1pyrrolidone) (PVP) exhibit two striking features which are as follows: (i) the transport of either radioactively labeled dextran or PVP in the system is extremely rapid as compared to its difand (ii) this rapid fusional transport in the binary (1) B. N. Preston, T. C. Laurent, W. D. Comper, and G . J. Checkley, Nature (London),287,499 (1980). (2) T. C. Laurent, B. N. Preston, W. D. Comper, G. J. Checkley, K. Edsman, and L.-0. Sundelof, J . Phys. Chem., 87,648 (1983).
0022-3654/84/2088-lO68$01.50/0
polymer transport is accompanied by the formation of visible, coherent structures (structured flows) in the solution as seen by labeling either of the polymers with blue dye.'s4 The onset of rapid transport and structured flow formation has been equated with the critical concentration of the dextran-solvent at which transient network formation occur^.^ (3) B. N. Preston, W. D. Comper, T. C. Laurent, G. J. Checkley, and R. G. Kitchen, J . Phys. Chem., 87,655 (1983). (4) W. D. Comper, B. N. Preston, T. C. Laurent, G . J. Checkley, and W. H.Murphy, J . Phys. Chem., 87, 667 (1983). ( 5 ) B. N. Preston, W. D. Comper, G . J. Checkley, and R. G . Kitchen, J . Phys. Chem., 87,662 (1983).
0 1984 American Chemical Society
