13052
J. Phys. Chem. 1993, 97, 13052-13060
Counterion Effects in Intramolecular Charge Transfer in Radical Anions Piotr Piotrowiak'Jd and John R. Miller? Chemistry Division, Argonne National Luboratory, Argonne, Illinois 60439, and Department of Chemistry, University of New Orleans, New Orleans, Louisiana 70148 Received: July 1 , 1993; In Final Form: September 28, 1993'
The influence of the presence of an electrolyte in a low-polarity solvent (tetrahydrofuran) on the rate of a weakly exoergic ( 4 0meV) nonadiabatic intramolecular charge shift reaction and on the position of the charge transfer absorption band in a degenerate system has been studied by pulse radiolysis. The investigation focused in particular on the dependence of the effect on the size of the cation of the chemically inert electrolyte. Electrolytes caused dramatic rate reductions of 2-3 orders of magnitude. Unexpectedly, the rate reduction was found to increase with an increasing size of the cation. The recorded spectral blue shifts were as large as 0.5 eV and exhibited the expected tendency: the smaller counterions produced larger spectral shifts, due to a stronger Coulombic interaction. In both cases the effects exceeded the limits predicted by the continuum approach and pointed to the ion-pairing mechanism. The discrepancy between the dependence of the thermal electron transfer and the optically assisted electron transfer on the radius of the counterion could not be easily explained on purely energetic grounds, and the dynamics of the counterion had to be considered. Unfortunately, no agreement between the experimental results and the Eigen model of dissociative diffusion of ion pairs in the zero ionic strength limit could be found. However, a qualitative correlation between the measured rates and thedissociation constants of the used salts, as well as the counterion mobilities was observed.
Introduction Recently there has been an increase of attention focused on the importance of the ionic contribution to the overall energetics and dynamics of medium reorganizationin charge-transfer processes. Both intramolecular192 and interm~lecular~*~ processes are being investigated. This interest is a very natural one for a number of reasons, of which we will mention just a few: In vivo electrontransfer (ET) processes never occur in neat solvents, but rather they take place at the interface of a protein and a physiological solution containing ionic species or within a protein soaked with an aqueous electrolytesolution. Electrolyte or, more specifically, counterion effects are inseparably included in the vast majority of electron-transfer experiments involving inorganic comp1exes;s the choice of counterion is often of fundamental importance in electron transfer mediated synthetic pathways.6 From the practical point of view ionic effects can be utilized to increasethe yields of charge-separated states and to discriminate the forward versus back ET rates.487 The primary points of interest of the investigations are usually the nature of the electrolyte contribution to the reorganization energy, A, its magnitude, and the characteristic relaxation time. There are two limiting pictures of the ionic component of the solvation process, both of which seem to find support in recent literature: (1) The"i0nicatmosphere" asdescribed by the DebyeHiickel-Falkenhagen theory.*+' (2) The ion-pair formation between the species of interest and the inert counterion. In the first one, the solution of an electrolyteis treated as a homogeneous medium with an increased overall dielectric constant, where the magnitude of the new component increases and the relaxation time decreases with the increase of the ionic strength of the salt. This approach is expected to be suitable in the case of strong electrolytes in polar solvents. The second view is likely to be more appropriate for weakly polar solvents, in which the Coulombic interaction between the ions is much larger. In this work we have chosen a well-characterizeddonor-bridge acceptor system, the trans- 1-(4-biphenylyl)-4-(2-naphthyl)cyclo7 Argonne
National Laboratory.
* University of New Orleans. Abstract published in Advance ACS Abstracts, November 15, 1993. 0022-3654f 93f 2091-13052$04.00/0
Figure 1. Donor-acceptor compounds shown with the center-to-center distances: (a) ~rans-l-(4-biphenylyI)-4-(2-naphthyl)cyclohexane (1,4ee-BCN);(b) 6,13-dihydropentaccne (this molecule is not planar, according to PC-MODEL-0 = 144O).
hexane (Figure l), which had been studied in detail in neat solutions in the pastloand used as a probe of the ioniccontribution to the medium reorganization in intramolecular charge shift reactions. In order to independently test the energetics of the ionic solvation, the position of the charge transfer absorption band of the 6,13-dihydropentacene radical anion (Figure lb) has been monitored in the presence of various cations.
Experimental Section Materials. Tetrahydrofuran (Aldrich, 99.9%, HPLC grade) was sonicated with NaK alloy (Aldrich, 56% Na, 44% K) under N2,vacuum distilled to another flask containing fresh NaK, and sonicated again, until stable blue color due to the (e-,Na+) pair was achieved. It was stored in the same flask. The perdeuterated THF (Aldrich, 99.5 atom % D)was purified in a similar manner. The N-methyl-2-pyrrolidinone(BurdickBrJackson, GC and spectrophotometry grade) was vacuum distilled and stored over molecular sieves. Tetraphenylboron sodium (Aldrich, 99.5%, ACS Reagent Grade) was purified by recrystallization from a THF/water mixture. Tetraphenylboronlithium was obtained as a precipitate by mixing saturated THF solutions of tetraphenylboron sodium and lithium chloride (Aldrich, 99+%, ACS Reagent Grade). It was subsequently purified by recrystallization from THF. The tetraphenylboron tetraalkylammonium salts were precipitated by mixing a THF solution of the corresponding tetraalkylammonium bromide (cetyltrimethylammonium bromide, Aldrich, 95%; tetrabutylammonium bromide, Aldrich, 99%; tetraoctylammonium bromide, Fluka, >98%, purum; tetraoctadecylam0 1993 American Chemical Society
Counterion Effects in Intramolecular Charge Transfer monium bromide, Fluka, >98%,purum) and an aqueous solution of tetraphenylboron sodium. The precipitated salts were recrystallized from THF at least twice. The synthesis of trans- 1-(4-biphenylyl)-4-(2-naphthyl)cyclohexane (to be referred to as 1,4-ee-BCN) has been described elsewhere.11 The 6,13-dihydropentacenewas obtained in a high yield via standard Wolf-Kishner reduction of 6,13-pentacenequinone (Aldrich, 99%). Sample Reparation. The sample solutions were prepared by vacuum distillation of THF into a fused silica cell containing preweighted amounts of the donor-acceptor compound and one of the salts. The samples were degassed and sealed off. The amount of the solvent and the concentrations were established by weighing the sample cells. Salt concentrations were kept in the 10-30 mM range, and the model compound concentrations fell in the 0.5-3 mM range, i.e., there was always at least a 10-fold excess of the salt. The correctionsfor the possiblevolume changes of THF upon addition of an electrolyte were not made. Perdeuterated THF and 3 mm path length cells were used for the NIR measurements of charge-transfer bands in the 6- 13dihydropentacene anion in order to achieve sufficient transparency of the sample at long wavelengths.12 Measurements. The kinetic measurements of transient optical absorbance were performed using the 30-ps, 20-MeV linear accelerator pulse as the means of generating excess electrons and a flash lamp as the analyzing light source. A collinear arrangement of the electron beam and analyzing light was employed. The transients were collected using a biplanar photodiode (Hamamatsu, R1328U-03) or silicon photodiodes (PD-10, OptoElectronics Inc. or FOD-100, EG&G), a B&H amplifier, and a Tektronix 7250 ultrafast digitizer. The sequenceof measurements for each studied cation was the following: (i) Measurement of the e-r lifetime in neat THF; transient absorption monitored at 880 nm. (ii) Measurement of the (e-, cation) lifetime in the solution of a given salt; transient absorption monitored at 880 nm. (iii) Measurement of the formation rate of the radical anion of the donor, the acceptor, and the 1.4-ee-BCN as a function of concentration, monitored by the decay of the e-1- band at 880 nm. (iv) Measurement of the lifetimes of the radical anions of the donor and the acceptor, by monitoring the 650-nm band of the biphenyl radical anion and of the 400-nm band of the naphthalene radical anion. (v) Measurement of the decay of the 650-nm band of biphenyl anion in the 1,4-ee-BCN donor-acceptor system. Measurements at three 1,4-ee-BCNconcentrations in the range 0.5-3.0 X l t 3 M were performed for each salt studied in order to provide the intramolecular electron transfer rate. Details of the fitting model that utilizes experimental parameters obtained in the steps outlined above have been described in ref 10. During the measurementsof the charge-transferspectra, longer, 4 ns, electron pulses were applied. Germanium (J 16-18A-R01MHS,EG&G Judson) and InAs (J12-18C-R01M, EG&G Judson) NIR photodetectors were used. The ability of pulse radiolysis to "prepare" as the starting point of the ET reaction the donor site anion with the counterion in its immediate vicinity was very important. It was achieved by practically "delivering" the electron to the model compound in the form of a special ion pair (e-, cation). This particular step may be difficult to reproduce in photoexcited electron-transfer measurements in which the starting point is a neutral molecule or a short-lived charge-separated species. The detailed kinetic scheme is provided in the Appendix. Results and Discussion
1. Thermal Electron-Transfer Results. The influence of the presence of tetraphenylboron (TPB-) salts containing cations of
The Journal of Physical Chemistry, Vol. 97, No. 50, 1993 13053 TABLE I: Intramolecular ET rates in 1,4-ee-BCN in Tetrahydrofuran in the Presence of Various Stable Cations' apparent counterion ratio k m / b ke.r 6 - I ) re(& neat THF 1.6 x 109 1 .oo 0.00 9.8 x 107 neat NMP 6.1 X 1V2 0.27 2.3 x 107 Li+ 1.4 X 1V2 0.42 0.65 7.5 x 1v3 1.2 x 107 Na+ 0.48 1.05 TBA+ 7.5 x l W 1.2 x 106 0.71 4.13 1.9 X lo6 1.2 x 1v3 0.66 4.36 CTMA+ 5.0 X 1W 8.0 X 10' 0.75 5.54 TOA+ 7.6 X 10s 4.8 x 1P 0.76 7.20 TOdA+ a All salts used in this workcontained the sameanion,tetraphenylboron (TPB-). The rates are accurate to *20% Calculated from the Marcus equation.
100
Neat THF. e = 7.58
1
Continwmtheotylhit, e =
1
00
111111111l1111111111llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll
Neat NMP, e = 32.0
lo8 t
:
LI'
w
Na+
C(TM)A'
lo6I t
lo5It
I
I
I
I
I
I
I
0
1
2
3
4
5
6
7
Radius of the cation
[A]
Figure 2. Electron-transfer rates in 1,Cee-BCN in THF solutions of tetraphenylboron salts plotted vs the radius of the cation.
various size on the rate of the intramolecular charge shift reaction in 1,4-ee-BCN was investigated. The cations were Li+, Na+, tetrabutylammonium ((C4H9)4N+ or TBA+), cetyltrimethylammonium (C16H33(CHs)3N+or CTMA+), tetraoctylammonium ((CsH17)4N+ or TOA+), and tetraoctadecylammonium ((CISH37)4N+or TOdA+). Intermediate size cations, such as K+, Cs+, (CH3)4N+, etc., could not be included in this work because of the poor solubility of the corresponding salts in tetrahydrofuran. In all cases studied, dramatic reductions of the intramolecular electron-transfer rate were observed in the presence of approximately 10-30 mM of an inert electrolyte (see Table I and Figure 2). There are two outstanding features of Figure 2. One is the sheer magnitude of the effect; the other is the unexpected dependence on the radius of the cation of the salt: the small alkali metal cations with a high charge density lowered the rate by approximatelya factor of 100,while the bulky, relatively weakly charged tetraalkylammonium cations gave a 10-fold larger decrease of the rate.
Piotrowiak and Miller
13054 The Journal of Physical Chemistry, Vol. 97, No. 50, 1993
TABLE II: Intermolecular ET Rates in THF in the Presence of Various Stable Cations. ET (M-l S-I) naphthalene pyrene counterion acceptor acceptor 5.1 x 109 21.2 x 10'0 neat THF neat NMP 4.8 x 109 6.5 X lo8 1.1 x 1010 Li+ 2.0 x 108 1.0 x 10'0 Na+ TBA+ 5.1 X lo8 7.1 x 109 CTMA+ 6.3 X lo8 7.5 x 109 TOA+ 3.6 X lo8 a The rates are accurate to *15%. k,
for THF, one predicts that the reorganization energy, A,, for our 1,Gee-BCN compound will increase from 0.75 to 0.95 eV if the ET reaction were to proceed in a hypothetical medium with a static dielectric constant approaching infinity. This increase, when used in combination with the driving force of 50 meV and the standard Marcus-Jortner rate equation,14Js (where A, is the solvent reorganization energy, Vis the donor-acceptor electronic coupling, hu is the frequency of the dominant internal mode, set here to 1500cm-l ,and S is the vibronic coupling; all other symbols have their usual meaning)
(r
kET=
)l/2,y2~e*s~
h 2X,kBT
-exP("-0 v!
A,+AG+uhu 4Xsk,T
)
(2) predicts a decrease of the intramolecular electron-transfer rate by a factor of 10. All rate reductions observed experimentally in this work significantly exceed this value. Interestingly, this includes the rate in neat N-methyl-2-pyrrolidinone(NMP), el = 32.0, for which the decrease was 16-fold. One may also evaluate more rigorously the ionic atmosphere contribution to the reorganization energy by using the following expression based on the Debye-Hiickel theory:l6
b-'I
l . O O E + 09
I . O O E + 08
where a = rA + rB and KD is the inverse Debye length I . O O E + 07
(4)
1 . O O R 06
0
0.2
0.4
0.6
0.8
qPBNa
Figure 3. Elcctron-transferrate in 1,4-ee-BCNin THF as a function of
the sodium tetraphenylboron concentration.
The rates of intermolecular, collisional electron transfer between 4-methylbiphenyl donor and either naphthalene or pyrene acceptor in the presence of salts were also measured (Table 11). In all instances the rates were reduced. In the case of the weakly exoergic transfer to naphthalene (AGO zz 50 meV), the decrease was in the range of a factor of 9-29. The effect was attributed to the increase of the activation barrier and possibly to the restricted access by the acceptor to the donor anion in the case of the large organic cations. With pyrene as an acceptor (AGO z 0.52 eV) the rates were lower by a relatively insignificant factor of 1.1-1.6. Since the changes of intermolecular ET rates do not reveal particularly interesting trends they will not be discussed in further detail. 2. Continuum versus Ion-Pairing Interpretation of the Salt Effect. At the first step of the analysis it has to be decided which theoretical approach should be applied to this set of data. It is well-known that in mildly polar solvents ionic association is very common.13 On the other hand, the use of the in principle continuum theory of "ionic atmosphere" is an attractive, more general option. It is possible to establish the upper limit for the continuum contribution to the reorganization energy by using the standard expression for the reorganization energy
where rD and rAare the radii of the donor and the acceptor, RDA is the center-to-center donor-acceptor separation, e, is the static dielectric constant, and Copt is the electronic component of the dielectric constant. By substituting c, in place of c, = 7.58
--
where Z is the ionic strength of the solution. In this case, the additional, largest possible ionic component of the reorganization energy is predicted to be less than 50 meV for any of the solutions studied in this work. Clearly, the magnitude of the observed effects cannot be explained by the nonspecific ionic atmosphere approach. This is not a surprising result, as there is increasing evidence that the ionic atmosphere theory seriously underestimates the electrolyte contribution to the reorganization energy, even in solvents as polar as acetonitrile2 and possibly also water.3 The dependence of the rate reduction on the concentration of the tetraphenylboron sodium (TPBNa) was investigated over a broad range (Figure 3). It was found to be impossible to obtain good kinetic fits to the data using our standard procedures at low salt concentrations of less than approximately 10mM. The reason for this behavior is the complex competition between several processes, primarily between the electron transfer in "free" donoracceptor molecules, the association with the cation of the salt, and electron transfer in "preassociated" molecules. The details are explained in the Appendix. At higher salt concentrations a pseudo-equilibrium starting point for the intramolecular electron transfer is reached, in which more than 90% of the donor states are associated with the cation of the salts prior to the transfer event. While the electron-transfer rate drops dramatically from 1.6 X lo9 s-l in neat THF to 1.2 X lo7 s-l in the presence of 10 mM TPBNa, further 80-fold increase of the salt concentration up to 800 mM causes only a slight decrease of the rate, down to 7.2 X lo6 s-l. This highly nonlinear behavior followed by saturation is a further evidence for the ion-pairing nature of the effect. All measurements discussed in this paper were performed in this "plateau region". While the salt concentrations were not identical in all instances, the rate variations within the plateau are insignificant in comparison with the overall reduction (less than a factor of 2 out of at least 100, i.e., 12%). The high degree of ion pairing could be achieved in part because of the excess of the salt but also, very importantly, thanks to the preferential association due to the bulkiness of the tetraphenylboron (TPB-) anion. The concentration of the salt is on the order
Counterion Effects in Intramolecular Charge Transfer
The Journal of Physical Chemistry, Vol. 97, No. 50, 1993 13055 I
I
I
Abr.
I
I
I
I
I
neat NMP
neal THF
Figure 4. Schematicrepresentation of the thermal and optical intramolecular electron transfer processes in the presence of an inert counterion.
of 1 X l k 2 M while the concentration of the transient ion never exceeds 5 X lo" M. The dissociation constants of the Li+, Na+, andTBA+saltsinTHFare&OX lO-5,8.5 X lks,and4.3 X l k 5 , respectively,17 while the dissociation constant of the (Na+, naphthalene-) ion pair is only 1.0 X lW.13 Further details and the explanation of the need for salt concentrations higher not only than these of the transient species but also than those of the neutral model compound are given in the Appendix. The preferential association also turns out to favor the naphthalene radical anion (the acceptor) over the biphenyl radical anion (the donor). In the case of the sodium cation this preference is translated into additional 50 meV of driving f o r d 3 for the intramolecular ET reaction. This increase should lead to a 2.5fold acceleration of the observed ET rate (in comparison with the same increase of reorganization energy but no change in AGO), a value too small to account for the difference between the Na+ and the organic cations, which are also expected to increase the driving force but, most likely, to a lesser extent. At this point it can be safely concluded that the observed effects have to be attributed to specific ion pairing between donoracceptor molecules with the negative charge residing at the donor site and the cation of the inert salt (Figure 4). The remaining puzzle is the fact that the largest effects occur in the case of the bulky tetraalkylammonium cations, for which the magnitude of the Coulombic interaction is expected to be significantly smaller than for the compact alkali metal cations. Table I contains the calculated "apparent* reorganization energies which increase with the increasing size of the cation. Even if one assumes that the alkali metal cations maintain a solvation sphere in an ion pair, thus reducing the Coulombic attraction (although there exists ample experimental evidence that contact ion pairs are the dominant form at room temperature)13and that there is a sizable entropic contribution to the reorganization free energy of the tetraalkylammonium cations associated with the many possible conformations of the alkyl chains, it becomes apparent that the explanation of the observed trend on purely energetic grounds is difficult, and that the dissociation-association dynamics of the ion pair may be of crucial importance. Since our original intent was to analyze the results in terms of the nonadiabatic electron-transfer theory, according to which the medium influencesthe rate only via the reorganization energy, and which provides the appropriate description of the model compound in neat THF, it was decided that an independent study of the energetics of the system should be performed before the dynamic explanation is invoked. 3. Optically Assisted Electron Transfer. Ion Pairing and CT AbsorptionBands. There are examplesof successfulexperimental utilization18 of the Hush theory19 linking the free energy of activation for the thermal electron transfer to the position of the maximum of the charge transfer absorption band in the same molecular system. More recently measurements of this type are becoming an increasingly popular tool in evaluating the ionic contribution to the overall reorganization energy in fluorescence spectra of photoexcited charge-transfer states.1.2.21 Our intent was to measure the blue shift of the intramolecular CT absorption band in the radical anion of 1,4-ee-BCN as a function of the size of the counterion. Unfortunately, due to the relatively small electronic coupling (approximately 140 cm-l),l0
1
1000
1200
1400
1600
I
I
I
I
1800
2000
2200
2400
Inm1 Figure 5. Charge-transferspectra of the 6,13-dihydropentacene radical anion in solutions of salts in THF and in neat N-methyl-2-pyrrolidinone.
TABLE III: Position of the CT Band in the 613-Dihydropentacene Radical Anion in THF Solutions Containing Stable Cations counterion A- (nm) A. (eV) AA (eV) neat THF neat NMP Na+ TBA+ TOA+
22450 1507 1200 1900 22450
S0.51 0.32 1.03 0.65 50.51
0.00 20.31 20.52 20.14 ?
the charge-transfer band was found to be unmeasurably weak in this compound. Therefore, a more strongly coupled system, 6,13-dihydropentacene, which contains two naphthalene units held rigidly together by two methylene groups, was used as a probe of the magnitude of the Coulombic contribution to the reorganization energy (Figure 1). Since dihydropentacene is a degenerate system, AGO I 0, the position of the maximum of the charge-transferband is exactly equal to the reorganization energy. While the center-to-center distance between the donor and the acceptor is only 7.3 A in dihydropentacene versus 11.8 A in 1,4ee-BCN, it is reasonable to assume that the changes in position of the charge-transfer band as a function of the size of the counterion or medium polarity will exhibit the same trend in both instances. The results of the NIR transient absorption pulse radiolysis measurements on the 6,13-dihydropentaceneradical anion in the presence of 3 cations are presented in Figure 5 and Table 111.The results agree with the intuitive expectation that the smaller alkali metal cations must interact more strongly with the anion of the donor-acceptor system and contribute more to the reorganization energy. The presence of Na+ in solution increases the reorganization energy by 0.52 eV in comparison with neat THF, while the presence of TBA+ increases the energy by only 0.14 eV, Le., the additional contribution to the reorganization energy is in the case of TBA+ approximately 4 times smaller than in the case of Na+, yet the reduction of the thermal electron-transfer rate is 10 times larger. In fact, the blue shift of the charge-transfer band is much larger in neat N-methyl-2-pyrrolidinone(e, = 32) than in the presence of any of the tetraalkylammonium cations. This is a suitable moment to emphasize a very interesting but largely overlooked aspect which has been pointed out by Kuznetsov and Weaver,22namely,the relationshipbetween the reorganization energy and the free energy of activation in the case of ion pairing with inert counterions. In this situationthe potential energy curves of the initial and final states are no longer quadratic, but depending on the size of the ions, they acquire some degree of a Coulombic character (in the gas phase they would be purely Coulombic) and as a result the convenient ratio of A,,/AG* = 4 for AGO 0 d m not hold. In fact, there is no constant ratio between these two
Piotrowiak and Miller
13056 The Journal of Physical Chemistry, Vol. 97, No. 50, 1993
a)
b)
AG
Reaction coordinate
Figure 6. Potential energy surfaces for intramolecularelectron transfer in the presence of ion pairing. (a) The relationshipbetween the reorganization energy, X, and the free energy of activation, AG’, for the purely parabolic and partially Coulombic potential energy surfaces (scaled in such a way that the Coulombic term results in a doubling of the total A). (b) A comparison of a purely parabolicpotential energy surface with a partially Coulombic surface containing a short distance repulsive term.
parameters. In Figure 6 we have illustrated this important fact by plotting “standard” parabolic potential energy curves together with a potential which combines a Coulombic a(l/R) term with a parabolic bR2 term, where R is the reaction coordinate, and a and 6 are arbitrary constants representing the relative contributions of the two terms. Naturally, the Coulombic term, i.e., the attraction within the ion pair dominatesat small displacements from the minimum, while at larger displacements the normal, dipolar solvation takes over. One can see immediately that the ratio of the reorganization energy to the free energy of activation is much smaller than 4:l in the case of the composite potential. This is the only general statement which can be made-that with any ionic contribution to the reorganization energy this ratio will be always less than 4. The potentials in Figure 6 have been scaled approximately to correspond to our (dihydropentacene-, Na+) ion pair, Le., the reorganization energy, b,in the presence of the cation is roughly twice as high as without it (Table 111). The much more than linear increase of the AG* is evident. Therefore, whenever significant association occurs, the position of the charge-transferband cannot be used as a convenient measure of the activation energy for the thermal electron transfer. An increase in X, will be still associated with an increase of AG*,but it will not be proportional to it. The potentials in Figure 6 can be improved by including an exponential term describing the repulsion between the ions at very short distances (Figure 6b). This removes theunrealistically sharp minimum and introduces an avoided region in the center of the well (the region of infinite potential reflects the fact that the ions cannot diffuse through one another but only around one another).23 The effects described above will be reduced, yet qualitatively the argument remains valid. Also of interest is the fact that the changes in the shape of the potentialwellshould be reflectedin theshapeof the CTabsorption band. Since at the equilibrium coordinate, Ro, of the reactant the product curve will be nearly purely parabolic,only the changes in the lower curve have to be considered. In this case the potential energy curve in Figure 6b implies that intramolecular CT spectra in the presence of strongly associated counterions should exhibit a shape with a somewhat flattened maximum and increasedslopes in comparison with the normal, Gaussian shape predicted by the Hush theory. Unfortunately, our spectra contain too few points and are not of sufficient quality to warrant this kind of analysis.
Thus far the fluorescence measurementsin solutionsof electrolytes have not revealed such effects,2however, it has to be remembered that in most cases high-polaritysolvents were used in those studies and that the excited states of the selected probe molecules are far from truly charge-separated systems. 4. Counterion Dynamics. The concept of intramolecular electron exchange in weakly polar solventscontrolled by counterion dynamicsis not a new One can envision that intramolecular electron-transfer reaction in an ion pair necessitates, from the point of view of microscopic reversibility, that the transition state involves a motion of the counterion from its equilibrium position next to the donor state to some intermediate position between the donor and the acceptor. If this motion is significantly slower than the intrinsic nonadiabatic barrier crossing rate determined by the electronic coupling between the donor and the acceptor, then the rate of this motion becomes the rate-determining step. A transition from a nonadiabatic electrontransfer to an adiabatic, nuclear motion controlled process could occur. One can rephrase this statement in a more sophisticated manner using a variation of the van der Zwan and Hynes25 notion of two essentially orthogonal medium modes, one fast and one slow. The fast mode in our case is the normal solvent reorientation mode, while the slow mode is the diffusional motion of the counterion. The final equilibrium state cannot be reached by motion along only one of the modes. As a result, the evolution along the slow modecoordinateonce again becomes the rate-limiting step. From purist’s point of view the existence of two modes in this model is attractive because it allows both for nonadiabaticbarrier crossing (once the system evolved far enough along the slow coordinate) and for medium dynamics control of the experimentallymeasured rate. If indeed the dissociative diffusion of the ion pair containing the counterion and the ion of the donor-acceptor system is the rate-determining step, the observed electron-transferrates should follow the Eigen equation,20 as shown in elegant studies on intermolecular reactions by Chiorbolis and Balzani.26 Since we have conclusively demonstrated above that the observed effects are due to specificion pairing, rather than ionic atmosphereeffects, it will be reasonable to use the Eigen equation in the zero ionic
I
: 10'
=
I
I
I -
Lit
m
Ne'
-
m
.
I
I
I
I
0.2
0.4
0.6
rcrtion
I I 0.8
[nml
Figure 7. Experimental results and the Eigen equation plotted against the counterion radius, 5. The parameters were as follows: rb = 0.50 nm (top curve), a = 0.40 nm (middle curve), 4 = 0.35 nm (bottom curve); temperature T = 298 K, viscosity q = 0.55 cP. strength limit:
where r A and rB are the radii of the ions forming the ion pair, q is the solvent viscosity, D is the dielectric constant, e is the elementary charge, and the remaining symbols have their usual meaning. Alternatively, one can use a simplified, approximate version of the above equation:
Figure 7 shows the plot of eqs 5 and 6 and the experimental data points. The differences between the complete and simplified versions are too small to be visible on the graph. It is apparent that the Eigen equation fails to reproduce the experimentally observed trend of the ET rates. There are several major difficultiesassociated with the selection of proper parameters for the Eigen equation. Even the seemingly simplest ones such as the ionic radii cannot in reality be assigned without ambiguity. For the small alkali metal cations, it is reasonable to use the gas-phase or crystallographic value of the
Figure 8. Illustration of the relative sizes of the ions under study: one of the PC-MODEL local minima of the ion pair consisting of the tetraoctadecylammonium cation (white) and the 1,Ccc-BCN model compound (black) with thenegativechargertsidingat the biphenyl moiety. The sodium cation is shown in upper right for comparison.
radius when the cation is in a tight ion pair; however, when the cation is already at some distance from the anion and when it becomes fully solvated, the Stokes radius should give a more realistic description of its mobility. In the case of Na+ it means a change from 1 to 4 A.I3 The gas-phase radii were used for Na+ and Li+ in this work. A similar dichotomy exists for the soft tetraalkylammonium cations. Their hydrodynamic radii derived from conductivity data vary by more than a factor of 2 from one solvent to another and in all cases are much smaller than the fully extended conformation of the chains or crystallographic data would imply.13J7 PC-MODEL calculations predict that in order to maximize the electrostatic stabilization in ion pairs these cations can adopt a nearly planar conformation by introducing just one 0.9 kcal/mol gauche interaction next to the nitrogen atom in one of the chains.27 On the other hand, it is known that at room temperature the most probable conformation of an 18-carbon chain contains 4 gauche twists, while the 8-carbon chain contains 2 such twists.** Therefore, these ions should be viewed as floppy spaghetti balls which can even wrap themselves around the anion of the donor-acceptor system (Figure 8), rather than as spherical or tetrahedral moieties. The radii the tetraalkylammonium cations used in the plots were obtained from the conductivity data in ethyl methyl ketone. Since the value for tetraoctadecylammonium was not available it was extrapolated as (M[(C,,H,,)*I+I/M[(C,H,,),N+]) 113 times the radius of tetraoctylammonium. As can be seen from Figure 7 the calculated curves are highly sensitive to the size of the anion of the donor-acceptor molecule, and the question what is the relevant radius arises. Normally the obvious choice would be the radius of the donor. In our case this selection will yield a good description of the energetics of the contact ion pair, since the charge is indeed localized either at the donor or at the acceptor. On the other hand the mobility of the entire model compound radical ion, which is much larger than
Piotrowiak and Miller
13058 The Journal of Physical Chemistry, Vol. 97, No. 50, 1993
the donor itself, will be reproduced very poorly. This is not very important when the counterion is much smaller then the model compound, and therefore, it is primarily the counterion which diffuses around the nearly static donor-acceptor system. However, when the size of the counterion exceeds the size of the model compound as in the case of tetraoctadecylammoniumcation,which is nearly three times as heavy as the model compound (although it is the hydrodynamicvolumerather than the mass that matters), the situation reverses. Now it is predominantly the motion of the donor-acceptor molecule in the field of the counterion which determines the ET rate (see Figure 8 as an illustration of the relative sizes of ions under study), and the use of the donor radius will lead to a seriousoverestimateof the rate. One might consider “improving” the Eigen equation by using in the case of these large nonspherical ions two radii: the donor radius in the Coulombic term of the equation and the total radius in the hydrodynamic term. The failure of the Eigen equation to reproducethe experimental results does not come as a complete surprise since even the static properties of ion pairs in THF, such as the associationconstants, are poorly modeled by theory. For instance, the Fuoss equation29
(presented here in the zero ionic strength limit; the meaning of all symbols has been explained previously), which is the ratio of the Debye-Smoluchowski equation30J’ to the Eigen equation predicts that sodium tetraphenylboron (NaTPB) should be dramatically more associated in THF (KA= 2 X lo6) than the tetrabutylammonium tetraphenylboron (TBATPB, K A = 2 X 104). In reality, the dissociation constant of NaTPB is approximately twice as large as this of TBATPB (see the values quoted earlier). It is reasonable to expect that a similar discrepancy between the theory and the relative stability of the ion pairs involving Na+ and TBA+ and the donor radical anion will exist. In fact, the higher dissociation constant of the sodium salt translated into kinetic terms means that ion pairs containing a sodium cation will dissociate faster than the ones containing a tetrabutylammonium cation. Nevertheless, the possibility that the ET rates are controlled by energetics, not dynamics of the motion of the counterion, remains open. It should be also kept in mind that at the relatively high concentrations in solvents of low polarity the bulky tetraalkylammonium salts can form multiple ion aggregates with diffusion and association properties completely different from the single ion. Undoubtedly, such an aggregation can have a profound effect on electron-transferrates measured in the presence of these salts. Unfortunately, at present we have no reliable quantitative data on the clusteringpropertiesof these salts in THF. In general, it would be naive to expect an agreement between theoretical pictures based on the ionic atmosphere concept and designed for submillimolar solutions of perfect electrolytes in highly polar media and our systems. While one intuitively expects that it is easier for an ion to “break loose” from a more shallow potential well and, therefore, have less influence on the electron-transfer rate, it appears that the important factor is not the absolute magnitude of the ionic attraction but its value in comparison with the driving force. Whenever the contribution of a given mode to the reorganization energy is comparable to the driving force, this mode should be viewed as “strongly coupled”, in the Hynes and van der Zwan language.25 Since the driving force in our system is only approximately 50 meV, any slow reorganization mode of this magnitude or larger will have a decisive influenceon the observed rate. This condition appears to be satisfied by all cations studied. In order for the electron transfer to occur, the system has to evolve along the slow mode coordinate, which in this case is the ion diffusion. This evolution could be energeticallycompensated
for by the fast, dipolar mode, but in the present system this would require a large reorganization of the dipolar modes. However, as long as the counterion remains in the vicinity of the donor site, the system is in an unstable nonequilibrium situation, and the electron will be likely to transfer back to the donor before the cation could move away. If the ET rates were controlled by the dynamics of the cations, then we might expect the rates to correlate with their mobilities. Indeed, the ratio of the ET rates in the presence of tetrabutylammonium and tetraoctylammonium counterions is 1.5, while the ratio of the mobilities,” Ao, of these cations is 1.4, however, this correlationdoesnot extend to thealkali metals. Theenergetics of ion pairing continues to be important in controlling the rate of intramolecular electron transfer, but it is not clear whether this control occurs in the usual nonadiabatic sense. Conclusions
The most important accomplishment of this work is the observation of dramatically reduced intramolecular ET rates in the presence of inert counterions and the possibility that the effects correspond to a transition from a fast nonadiabatic intramolecular electron transfer to a counterion migration controlled process. The results underscore the importance of ionic association in determining charge-transfer rates in moderately polar media. No correlation with the reorganization free energies measured from charge-transfer spectra could be established. The tentative conclusion is that the rate of the intramolecular electron transfer is controlled by the new slow reorganization mode-essentially the dissociation/association dynamics of the ion pair consisting of the donor-acceptor anion and the inert cation of the salt. The apparent inability to model the observed behavior within the framework of the well-established theories of ionic solutions is disappointing. On the other hand, the failure of these simple models in the case of a weakly polar and strongly complexing solvent like THF combined with high salt concentrations is not unexpected. The results of the present work point to the need for a further development of molecular level theoretical treatment of ionic solutions.Q33 The counterion control could be observed over such a broad range of cation sizes because the electron-transfer reaction under study was very weakly exoergic. Therefore, even in the case of the relatively weak Coulombicinteraction (large organiccations) the Xionic was on the same order as the driving force and the evolution along the slow coordinate, i.e., the motion of the counterion could become the determining step. It will be very interesting to extend these studies to highly exoergic intramolecular electron-transfer processes, especially these occurring in the “inverted region”. Two general cases can be expected for these reactions: (1) a reaction which is deeply in the “inverted region” in the neat solvent and it remains in the “inverted region” even with the additional reorganization energy contribution due to ion-pair formation with the added electrolyte; (2) the reaction is in the “inverted region” in the neat solvent but it becomes “normal” due to the increase of the reorganization energy in the presence of the electrolyte. In the first case no significant influence of counteriondynamics on the intramolecular ET rate is expected, the reaction will simply proceed faster, as determinedby the new energetics. The dynamics of thecounterion will be important only for the final stabilization of the acceptor state. In the second case the rates will depend in a rather complex way on themobility of thecounterion. All of theabove predictions assume a preassociated pair containing the donor-acceptor ion with the counterion as the starting point. Some of the other areas of counterion effects in electron-transfer reactions which await exploration are the solvent viscosity dependence of these effects, which is expected to be very pronounced, and a careful examination of the shape of intramolecular charge-transfer bands in the presence of strong ion pairing, which should depart from the predictionsof the Hush formalism.
Counterion Effects in Intramolecular Charge Transfer
The Journal of Physical Chemistry, Vol. 97, No. 50, 1993 13059
Acknowledgment. We wish to express our gratitude to the late Professor Gerhard Closs. The present work stems from a long, close collaboration with his group. We thank Dr. Nancy Green, who synthesizedthe original portion of the model compound used in this study. We are grateful to Mr. George Cox and Mr. Donald Ficht for the operation and maintenance of the ANL linear accelerator. P.P. would like to thank Dr. Carol Creutz and Dr. Michael Weaver for useful discussionsand pointing out important references. This work has been supported by the Office of Basic Energy Sciences, Division of Chemical Science, United States Department of Energy, under Contract No. W-31-109-ENG-38. The continuing work in the P.P. laboratory is supported by the Office of Basic Energy Sciences, Division of Chemical Science, United States Department of Energy, Contract No. FG-0592ER 14310. Appendix The Kinetic Scheme. The sequence of events during pulse radiolysis measurements in a solution of an electrolyte is complicated. It involves many competing steps and equilibria (see the Scheme I). Throughout the above paper the tacit assumption that the starting point of the electron-transfer event is the ion pair involving the donor-bridge-acceptor radical anion (with the electronlocalized at the donor site) and the stable cation of the salt has been made. We will show below that indeed it is possible to prepare such a system via pulse radiolysis.
SCHEME I: The Kinetic Scheme Step 1 la lb IC
+ Na+ + (e-, Na+) + TPBe- + D-B-A D-EA e-
-
e- + NaTPB * (e-, Na+)
Step 2 2a 2b 2c 2d
+
-
(e-, Na+) D-EA (Na+, D - E A ) DB-A Na+ + (Na+, D - E A ) D - E A + NaTPB * (Na+, D - E A ) TPBD--EA + D-EA-
+
Step 3 (Na+, D - E A ) 3
+
* (D-EA-,
k z 8 X 10” k = 1 X loll k = 1 X 10”
M-l M-l M-l
k = 5 x 109 M-1 est. k
s-I s-I s-I s-1
= 5 X lo9 M-I s-’
k = 1.6 X lo9 s-l
Na+) k = 1.2 X lo7 s-I
Step 1. The rapidly diffusing thermalized electrons created by the 30-ps pulse from the LINAC can undergo three principal processes: (la) they can form a special “ion pair” with the cation of the inert salt, e.g., Na+, (lb) they can react with a neutral, undissociated molecule of the salt, e.g., sodium tetraphenylborane, and (IC) finally they can react directly with the molecule of the donor-bridge-acceptor compound (only the reaction resulting in the formationof thedonor radical anion is indicatedin the scheme, in the actual data reduction the creation of the radical anion at the acceptor side is also included). The concentration of the solvated electronsand of the resulting radical anions never exceeds 5XlWM. Step 2. The (e-, Na+) pair produced in steps l a and l b is a relatively stable species (kdecoy 1 X 104 s-1) which can be easily identified and monitored by the measurement of its absorbance. The peak is very strongly blue shifted (Amx = 880 nm) from the original band in THF (Amx L 2400 nm). While the blue shifts of the e-1- absorption in the presenceof alkali metal cations in THF were known for quite some time,34 we were also able to measure the shift in the THF solution of tetrabutylammonium tetraphenylboron (Amax = 1500 nm). Interestingly, the equilibrium in the NaTPB solutionappears to be strongly shifted toward the (e-, cation) pair rather than the (TPB-, cation) pair. As it has been mentioned in the text, the dissociation constant of NaTPB in THF is 8.5 X 10-5, while the dissociationconstant of (e-, Na+) is only 5 X 10-6.1 The explanation lies most likely in the large polarizability of &I-, rather than the fact that it is more “compact”
=
than the tetraphenylboron anion. This pair undergoes a further reaction (2a) with the donor-bridgeacceptor molecule forming an ion pair (again, only the reaction leading to the donor radical anion is shown for simplicity, but the data analysis includes the electron capture by the acceptor). The donor-acceptor radical anion can undergo three reactions: (2b) it can associate with the cation of the salt, (2c) it can undergo cation exchange with the neutral molecule of the salt, and (2d) it can also undergo the intramolecular electron-transfer reaction. Step 3. This is the step of interest of this work. The complex of the inert cation with the donor-bridge-acceptor radical anion undergoes an electron-transfer reaction. If one is interested in studyingthe rate of intramolecularelectron transfer in ion pairs (step 3 in Scheme I) rather than the very complex convolution of all the competing steps, it is necessary to assure that the formation of the ion pair containing the donoracceptor radical anion is significantly faster than the processes leading to electron transfer in a free donor-bridge-acceptor molecule. This can be achieved if the combined effective rate of reactions l a and l b is much faster than the rate of reaction IC. Since the investigated solutionscontained approximately (1030) X 10-3 M of the salt, out of which approximately 1 X 10-3 M was dissociated, the overall rate for creation of the cationsolvated electron pair was no less than 2 X lo9s-’, On the other hand, the concentration of the donor-acceptor molecule was in the range 0.5-3 X 10-3 M and the rate of the direct capture of the solvated electron, prior to its association with the cation of the salt, never exceeded 2 X lo8 s-I. Therefore, at least 90% of the original solvated electrons were intercepted by the cation of the salt. This, by default, resulted in the predominant formation of a radical anion of the donor-acceptor system with the counterion in its immediate vicinity. Consequently,the electron transfer in an originally unassociated donor compound accounted for no more than 10% of the overall process and was typically limited to less than 5%. The bimolecular processes 2b and 2c are too slow in comparison with the electron-transfer rate (2d) to play a major role in this sequence, but if they did, they would only further increase the yield of the desired ion pairs. We have shown that a simplified sequence of events, l a + l b 2a 3, which was used implicitly throughout the paper, is a reasonable approximation if a sufficient excess of salt is used. Under these conditions it is appropriate to assume that the vast majority of the thermalized electrons rapidly forms an “ion pair” with a cation of the salt, which subsequently reacts with the donoracceptor molecule yielding a conveniently preset complex of the radical anion with the counterion.
- -
References and Notes (1) Huppert, D.; Ittah, V.; Kosower, E. M. Chem. Phys. Lett. 1989,159, 261-75. (2) Chauman. C. F.: Maroncelli. M. J. Phvs. Chem. 1991, 95. 9095. (3) Chidrboli, C.; Indelli, M. T.;.Rampi Scandola, M. A.; Scandola, F. J . Phys. Chem. 1988,92, 156. (4) Kawanishi, Y.; Kitamura, N.; Tazuke, S . J . Phys. Chem. 1986, 90, 3Ah9-15 -.-_ ._.
( 5 ) Rampi Scandola, M. A.; Scandola, F.; Indelli, A. J. Chem. Soc., Faraday Trans. 1 1985,81, 2967. (6) Loupy, A.; Tchoubar, B.; Astruc, D. Chem. Reo. 1992, 92, 1141. (7) Kawanishi, Y.; Kitamura, N.; Tazuke, S.J. Phys. Chem. 1986,90, 6034. (8) Debye, P.; Falkenhagen, H. Phys. Z . 1928, 29, 121. (9) van der Zwan, G.; Hynes, J. T. Chem. Phys. 1991, 152, 169. (10) Closs, G. L.; Calcaterra, L. T.; Green, N. J.; Penfield, K. W.; Miller, J. R. J. Phys. Chem. 1986, 90, 3673-83. (1 1) Green, N. J. Ph.D. Dissertation Thesis, The University of Chicago, 1986. (12) The NIR absorption of common hydrogen-containing solvents is the result of the C-H stretching mode overtones. Perdeuteration of THF extends the -80% transmittance range from the normal limit of -1650 to -2200 nm with useful windows up to 2900 nm. (13) Szwarc, M. Ions and Ions Pairs in Organic Reactions; Wiley-Interscience: New York, 1972. (14) Marcus, R. A. Discuss. Faraday Soc. 1960,29, 21-31.
13060 The Journal of Physical Chemistry, Vol. 97, No. 50, 1993 (15) Jortner, J. J. Chem. Phys. 1976,64,486&7. (16) Debye, P.; Huckel, E. Phys. Z . 1923, 185. (17) NoMqueow Electrolytes Handbook;Janz, G. J., Tomkins, R. P. T., Eds.; Academic Rw: New York and London, 1972. (18) Penfield, K.W.; Miller, J. R.; Paddon-Row, M.N.; Cotsaris, E.; Oliver, A. M.; Hush, N. S . J . Am. Chem. Soc. 1987,109,5061-5. (19) Hush,N. S . Coord. Chem. Rev. 1985,61,135. (20) Eigen, M.Z.Phys. Chem. 1W, 1, 176. (21) Ittah, V.; Huppert, D. Chem. Phys. Lrrr. 1990,173,496. (22) Kumetsov. A. M.;Phelps, D. K.;Weaver, M.J. Int. J. Chem. Kinet. 1990,22,815. (23) Interestingly, this potential leads to a vibrational mode of an ion pair with a frequency of up to -400 cm-1 for small alkali metal cations (set: Edgell, W. F.; Watts,A. T. J. Am. Chem.Soc. 1966,88,1815)i.e., most likely too low to be of consequence for this work.
Piotrowiak and Miller (24) Furderer, P.; Gerson, F.;Heinzer, J.; Manu, S.;Ohya-Nhhiguchi, H.; Schroeder, A. H. J. Am. Chem. Soc. 1979,101,2275. (25) van der Zwan, G.; Hyner, J. T.J. Chem. Phys. 1983,78,4174. (26) Balzani, V.;Scandola, F.; Orlandi, G.; Sabbatini, N.; Indelli, M.T. J. Am. Chem. Soc. 1981,103,3370-8. (27) Thcse simple calculations do not take the entropy of the system into account. (28) Forbes, M. D. E. Ph.D. Thesis, The University of Chicago, 1988. (29) Fuoss, R. M.J. Am. Chem. Soc. 1958,80,5059. (30) Smoluchowski, M.Z.Phys. Chem. 1917,92,167. (31) Debye, P. Trans. Electrochem. Soc. 1942,82,265. (32) Bcme, B. J. J. Chem. Phys. 1975,62,1154. (33) Wolynes, P. J. Chem. Phys. 1987,86,5133. (34) Bockrath, B.; Dorfman, L. M. J. Phys. Chem. 1973, 77,2618.
