figurations in which the majority of dipoles are in the parallel orientation is underestimated. Secondly, the role of the counterions in the diffuse layer which may influence dipole orientation in the inner layer is ignored. Finally, the compressibility of the solvent monolayer has been neglected. The latter contribution is especially important at the extremes of electrode polarization. The results presented in this paper clearly demonstrate the advantages of measuring both the field and temperature dependence of inner-layer properties. Furthermore, they suggest that the classification of solvent behavior in the inner layer introduced by Parsons2 is not entirely correct. One class of interfacial solvent behavior is that shown by strongly associated solvent such as water, formamide, and NMF (class I). The behavior of these systems has been discussed in detail on the basis of cluster models.'0y20822-4The second class of solvents (class 11) display a single maximum on the inner-layer capacity against charge density curve and include cyclic ethers such as PC and sulfolane. The third class involves solvents whose inner-layer-capacity curves are very unlike that for water with at least a minimum on the capacity curve; solvents in this group are the alcohols, aprotic amides such as DMF, acetonitrile, acetone, ethylene glycol, and pyridine. More recent experimental data including those presented here suggest that the division between class I1 and I11 solvents made by Parsons is not correct. If capacity data are available over a sufficiently wide range of charge densities, both a maximum and a minimum are found on the inner-layer capacity against charge density curves for solvents in classes I1 and 111, suggesting that there is no difference in behavior. Thus, a minimum has been found (22) Damaskin, B. B.; Frumkin, A. N. Electrochim. Acta 1974,19,173. (23) Damaskin, B. B. J . Electroanal. Chem. 1977, 75, 359. (24) Fawcett, W. R.; Levine, S.; de Nobriga, R. M.; McDonald, A. C. J. Electroanal. Chem. 1980,111, 163.
on the curve for the Hg/PC interface8 and a maximum on the curve for the Hg/MeOH i n t e r f a ~ e .However, ~ on the basis of the curve of AS, against charge density one can distinguish two types of behavior. For aprotic solvents such as DMF and PC, a single extremum is found on the AS, curve at negative charge densities in the region where Ci is low and changing very slowly. On the other hand, a minimum is observed on the entropy curve for the Hg/ MeOH interface at approximately the same position as that on the capacity curve. However, entropy data should be collected for a wider variety of solvents before a new classification is defined. In conclusion, the analysis of inner-layer properties on the basis of the multistate model is quite helpful in elucidating interfacial solvent behavior. However, in order to use the model in a more detailed fashion, one needs an independent way of determining the most stable orientations a t an uncharged surface and their relative energies of interaction with the atoms of the electrode. One way of achieving this is to use approximate quantum-mechanical methods considering an isolated solvent molecule in a fixed orientation with respect to a conducting substrate.% It might also be possible to determine preferred orientations for interfacial solvent dipoles spectroscopically when the experimental techniques have been developed further. In addition, the experiments described above should be extended to other polarizable metals such as cadmium and gallium. Work in this direction is presently in progress in this laboratory.
Acknowledgment. We thank Prof. H. D. Hurwitz for sending his data for the Hg/PC system and for helpful discussions. The financial support of the National Sciences and Engineering Research Council of Canada is gratefully acknowledged. (25) Hurwitz, H. D., private communication.
An Experimental Test of the Competition Correction for Charge Capture from the Matrix in Intermolecular Electron Tunneling Reactions R. Kurt Huddleston and John R. Miller' Chemlstry Divlsion, Argonne National Laboratory. Argonne, Illinois 60439 (Received: August 16, 1982; In Final Form: March 18, 1983)
Further experimental tests have been made of a previously presented method to correct for competition for charge capture from the matrix in intermolecular electron transfer (ET) reactions in rigid media. The method is based on a two-step tunneling model which takes into account the correlation between matrix charge capture and intermolecular electron transfer. The goal is to obtain reliable intermolecular ET rates as a function of distance from measurements on rigid solutions containingtwo randomly distributed solutes. The method should yield the same rate vs. distance function for different donor solute concentrations. Good agreement was obtained by applying the competition correction to pulse radioloysis data for the reaction of the biphenyl anion with 2-methyl-l,4-naphthoquinone in 2-methyltetrahydrofuran (MTHF) at 77 K for donor:acceptor solute concentration ratios of 2O:l to 2 1 . Worse agreement was obtained for the reaction of the biphenyl anion with phenanthrene in MTHF, in which case the reaction is slow, and its energetics are substantially influenced by solvation. For such slow reactions, accurate measurements of intermolecular ET rates require donor:acceptor solute concentration ratios such that the donor solute captures most of the matrix charges. It was observed that some biphenyl cations are produced by direct ionizations and are stable in frozen MTHF. Introduction We have previously presented' a method to correct experimental data from intermolecular electron transfer (ET) (1) Huddleston, R. K.; Miller, J. R. J . Phys. Chem. 1982, 80,1347. 0022-3654/83/2087-4867$01.50/0
studies rigid media2v3for the effects of the initial matrix charge capture reactions. The intent is to measure the rate (2) M.iller, J. R. Sciences 1975, 189, 221. (3) Kira, A.; Nosaka, Y.; Imamura, M. J.Phys. Chem. 1980,84, 1882.
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constant k(r) for E T between a donor and an acceptor molecule held a t (center to center) distance r. k(r) was f ~ u n d to ~ -depend ~ exponentially on distance k(r) = u exp[-(r - Ro)]/a (1) where the frequency factor, u, and the range parameter, a, are related respectively to the Franck-Condon weighted density of states and the distance dependence of the one-electron exchange matrix element. Ro = 6 A accounts for the finite radii of the donor and acceptor. We wish to accurately determine k(r) as a function of the distance, r, by use of the known distribution of distances obtained when the donors and acceptors are randomly dispersed in a rigid matrix. This is straightforward for reactions of trapped electrons, trapped holes, or excited states. The surviving fraction, P(t),of donors at time t is most simply related to k(r) via the intermediacy of the effective capture radius R(tP
where c is the concentration of acceptor molecules in number per unit volume units. For high accuracy, particularly at high acceptor concentrations, c can be replaced by a slightly larger effective concentration, cg, to account for the fact that two acceptors cannot occupy the same space.6 The E T rate constant for a donor acceptor pair at distance r = R(t)is just k(R)= (gt)-’ where the constant g = 1.9.6 The measurement of k(r) for intermolecular ET by pulse radiolysis is slightly more complicated due to competition during formation of the radical ions we wish to study. Typically, in an intermolecular E T reaction studied by pulse radiolysis, a donor solute D captures charge from the matrix, either trapped electrons (eJ or holes (h+), and transfers it to an acceptor species A. e;(h+) + D D* (3)
-+
D A* (4) D’ + A It is desirable to use a large concentration of D. But since it is not practical to make [D]/[A] = 03, it is also necessary to account for the competing process in which matrix charges are captured directly by the acceptor. e;(h+) + A A’ (5) This competition for charge leads to a nonrandom distribution of acceptor (A) molecules around the donor radical ions D*. The departure from randomness occurs because those D molecules with an A molecule nearby are more likely to be prevented from initially capturing a charge because of competition from reaction 3. We calculated a correction A ( t ) which compensates for competition, restoring the data to the form it would have had if the D molecules captured all the charge and the A molecules were randomly distributed relative to the D* ions. The method is based on an extension of a two-step tunneling model given by T a ~ h i y a . ~ Not surprisingly, the correction A ( t ) is small if [D] 300 "C,the larger acceptor sites seem to be necessary for CT complexation. Primarily this is because of steric reasons, i.e., the size of the acceptor size must be comDarable to the size of the aromatic molecule. For this reason a small aromatic will more probably find a suitable acceptor center than a large one. (4) H. Knoezinger and P. Ratnasamy, Catal. Reu.-Sci. Eng., 17, 31 (1978).
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