J. Phys. Chem. 1993,97, 681 1-6815
6811
Ionic Strength Effects on Electron Transfer in the Inverted Region Hngyun Chen, Sandra L. Mecklenburg, Rich Duesing,! and Thomas J. Meyer' Department of Chemistry, University of North Carolina, Chapel Hill,North Carolina 27599-3290 Received: November 2, 1992; In Final Form: January 26, 1993
Rate constants (k)for the intramolecular electron transfer reaction fuc-[Re1(bpy*-)(C0)3(py-PTZ'+)](PF6) -fuc-[Re1(bpy)(CO)3(py-PTZ)](PF6),which occurs in the inverted region, were measured at 295 K in 1,2dichloroethane solutions at different ionic strengths with [N(n-C4H9)4](PF6) as the added electrolyte (bpy is 2,2'-bipyridine, py-PTZ is 10-(4-picolyl)phenothiazine). The rate constant for electron transfer varies with ionic strength from 1.05 X lo7 s-l (p = 0.0002 m) to 1.65 X lo7 s-l (p = 0.32 m). The variation of k with ionic strength is consistent with an energy gap law dependence for the electron transfer reaction. Based on conductivity measurements at a series of concentrations, the related salt fac-[Re1(bpy)(C0)3(4-Etpy)](PF6) (4-Etpy is 4-ethylpyridine) is nearly completely ion-paired in 1,2-dichloroethane even in the absence of added supporting electrolyte.
In a series of studies based on high-energy intermediates generated by pulse radiolysis or laser excitation, the existence of theinverted region predicted by Marcus has been demonstrated.1" In this region, -AGO > A, where AGO and X are the free energy change and reorganizational energy of the reaction. Both classical and quantum mechanical treatments predict that the rate constant for electron transfer should decrease with increasing -AGO in the inverted regi0n.g-11 The relationship between intramolecular electron transfer in the inverted region and nonradiative decay of excited states has been discussed in the context of energy gap law relationships.5-11J2 Fundamental questions remain about electron transfer in this region which need to be resolved by experimental measurements." These include the role of solvent, temperature, and ionic strength and whether their influencecan beaccommodated within existing theoretical frameworks. In an earlier study rate constants for intramolecular electron transfer were measured in a series of complexes including fac-[Rel(bpy')(CO)p(py-PTZ*+)]+ (Scheme I).5 This reaction lies deeply in the inverted region with X 0.37 eV and AGO -1.76 eV in 0.1 M [N(n-C4H9)4](PFs)-CH2ClCH2Cl (DCE).S In these experiments, the high energy, redox-separated state fu~-[Re~(bpy'-)(CO)~(py-PTZ'+)]+ was generated by d?r'u*(bpy) laser flash excitation at 420 nm followed by intramolecular electron transfer. The initially populated MLCT excited state is rapidly quenchedby intramolecularelectron transfer from -PTZ to Re", k, = 5 X lo9 s-l, and the rate constant for back electron transfer (k) was measured by time-resolved absorption changes after the laser flash.
-
-
In the earlier study it was observed that k was ionic strength dependent.5a Energygap law plots of In kvs AE112 with or without added 0.1 M [N(n-C&)4](PF6) fell on two parallel lines. We report here the results of a detailed study on the effect of ionic i This paper is dedicated to Rich Duesing. Rich obtained his Ph.D. in chemistry from the Universityof North Carolina at Chapel Hill in 1990 and then took a postdoctoral position at Alamos National Laboratory. His tragicdeathinanautomobileaccidentinNovember1991 cut shorta promising scientific career.
0022-3654/93/2097-68 11%04.00/0
strength on the rate constant for this ligand-to-ligand electron transfer reaction.
Experimental Section Materials. High-purity 1,2-dichloroethane (CHzClCH2C1, D C E Burdick and Jackson Laboratories) was used in kinetic and electrochemicalmeasurements. The supporting electrolyte [N(n-C4H9)4](PF.5) (TBAH) was purchased from Aldrich and recrystallized twice from 4: 1 ethanol/water before use. The complexfac-[Re(bpy)(CO)3(py-PTZ)] (PF6) was availablefrom previous studies.5 Electrochemical Measurements. Electrochemical measurements were conducted on a PAR Potentiostat/GalvanostatModel 273 in a single compartment cell. The working electrode was a 10-pmAu microelectrode purchased from Bioanalytical Systems, Inc. A Pt wire auxiliaryelectrodewas wound around the working electrode and a Ag wire reference fitted into a capillary was placed next to it. Samples of solutions in CHzClCHzCl had absorbances of -0.12 at 420 nm (2.0 X 10-4 M). The solutions were deareated by N2 bubbling for -10 min before the first scan and a blanket of N2 was maintained throughout the experiment. The scan was conducted in a single direction, typically from 1000 to -1500 mV with a scan rate of 10 mV/s. The measurements were made on at least two solutions that were prepared independently for each data point and four to seven scans were collected on each sample. The data were transferred to an IBM PC and half-wave potentials (Elp) were determined from the maxima of differentiated current-voltage curves. Because of shift in the potential of the Ag wire pseudoreference, Ella values for the individualcouples changed between scans but the difference between the two, AE!p = E1/2(PTZ+/O)- E,p(bpyO/-), remained nearly constant within experimental error. The values of AE1p obtained from different scans were averaged, and the standard deviation of the set of values was calculated. The results are listed in Table I. Transient Absorption Measurements. Transient absorption measurements were conducted on the nanosecond time scale with 0 1993 American Chemical Society
6812 The Journal of Physical Chemistry, Vol. 97, No. 26, 1993
TABLE I: Ionic Strength Effects on AEl/2 and the Rate ' Constant (k)for Back Electron Transfer in DCE at 295 K [TBAH] (M)b
A E 1 / 2 (mV).
0.0 0.0001 0.0002 0.0005 0.0007 0.0010 0.0050 0.0070 0.010 0.025 0.050 0.100
2047 2028 2014 2003 200 1 1990 1981 1986 1981 1985 1980 1983 1982 1982 1979
0.200 0.300 0.400
k(X10-7,s-1)d 1 .os 1.12 1.16 1.25 1.27 1.30 1.40 1.45 1.47 1.50 1.55 1.62 1.66 1.66 1.65
Me
0.0002 0.0002 0.0003 0.0006 0.0007 0.0010 0.0042 0.0058 0.0082 0.020 0.040 0.080 0.16 0.24 0.32
The solutions had absorbances of -0.12 at 420 nm (2.0 X 1V M). Molar concentration of the added supporting electrolyte [N(nC4H9)d](PF6). A E l / 2 = E1p(PTZ+I0)- Elp(bpf/-). The standard deviations ( I f 7 mV) were calculated from a set of data of at least five different scans on two different samples. d The rate constants for back electron transfer were calculated from the decay curves of the transient absorbance signalsmonitoredat 5 10 nm following 420-nm laser excitation. e The ionic strength, p = 1/2&,2mj, where .q and mi are the charge and the molal concentration of ion i in solution and the summation is over all ions in the solution. Molalities were calculated from molar concentrations and the density of DCE ( p = 1.24 at 25 "C). the use of a laser system that has been described previously.14 Solutions of fac-[Re1(bpy)(C0)3(py-PTZ)](PF6)in DCE with addedTBAH(O.04.4M) andanabsorbanceof -0.12at 420nm were deaerated by bubbling with N2 for 10 min. The solutions were irradiated with 4-ns, 420-nm laser pulses, and colored glass filters and minimal photolysis conditionswere used to limit direct irradiation of PTZ with the white probe light, in order to minimize photodecomposition. The acquired hA vs time decay traces fit well to single exponential decay kinetics. Conductivity Measurements. Conductivity measurementswere performed on solutions offac-[Re1(bpy)(C0)3(4-Etpy)] (PF6) (4Etpy is 4-ethylpyridine) in DCE with equipment and techniques that have been described.I5 A YSI35 conductance meter and YSI glass conductivity cell, with platinum electrodes and a cell constant, K,of 0.104 cm-l were used. The cell was standarized with an aqueous KC1 solution according to the manufacturer's recommended procedure, and soaked in DCE for several hours prior to use. All solutions were permitted to equilibrate to room temperature, 295 f 0.5 K, before measurements were performed. A series of dilutions were prepared with concentrations ranging from 1 X 106to 1.01 X 10-4Minfa~-[ReI(bpy)(C0)~(4-Etpy)](PF6). The conductivities of the solutionswere measured in order of increasing concentration. Theconductivitydata were analyzed according to the procedure of Fuoss,16which was applied in the manner discussed by Ledwith and co-~orkers.~5.l~ A computer program was written to analyze the data iteratively. Concentration and equivalent conductance (A) data were tabulated, and a value for the conductance at infinite dilution, &, was estimated from the intercept of a plot of A vs dc according to the Oswald dilution law for weak electrolytes (eq 1). In eq 1, theequivalent conductancemeasured /Ao
+ Cac/[KD(ao)21
(1)
at concentration c is Ae, and the dissociation constant is KD for the equilibrium shown in eq 2. The Fuoss equation for weak KD
A+/B-
A+//B-
cantact ion pair
solvent-separatedion pair
+A++B-
(2)
free ions
electrolytes, eq 3, can be derived from the Oswald dilution law
Chen et al. and includes additional terms which correct for the activity of the ions in the solvent used and also correct for electrophoresis and the effects of long-range interionic attraction of the ions. These equations give the Debye-Hiickel-Onsager conductance limiting slope and the limiting-law constant for the DebyeHiickel theory of dilute solutions.
In eq 3, F(z) is the correction factor for electrophoresisand ionic effects, calculated by F(z) = (...[l-Z(1-2[1-2]-'/2)-~~2]-1/2...) where z = [(.Ao
+ ~~)(CA~)'/~]/(A,)~/~
a = 159.350/(D25)3/2
and f*,the mean activity coefficient, is given by
-log f; = 28,1c1/2 with
28" = 708.85/(D2,)3/2 For DCE, the dielectric constant at 25 'C, 4 5 , is 10.1, and the viscosity at 25 OC, 925, is 0.0043 poise. Therefore, (Y = 0.04867 (mol/L)-'/2,6 = 104.4 moh-1 cm2mol-V2LV2,and 2@"= 223.046. Values offi2, z, and F(z) were calculated from the conductivity data (Figure la) by using eq 3. A plot of F(z)/A vsfi2c&/F(r) was constructed. Iterative analysisand linear least-squaresfitting allowed for the extraction of KDand &from the data. The value obtained for &was used to recalculate z and F(z) and a new plot was constructed as before. This procedure was repeated until there was less than 0.01% change in the values obtained for KD and &. The results of the final iteration with KD = 6.7 f 1.3 X 106 M and A., = 70 f 14 &I cm-2 are shown in Figure 1. The error in both KD and & is estimated to be f20%. Sources of error include temperaturevariations within the measurement set (f0.5 "C), the precision of the conductance instrument (i2.5 X lo-' W), dilution error (-0.1% per dilution), and the use of a calculated activity coefficient in which the cation and anion were assumed to have equal activity, even though they differ greatly in size. ReSults Electrochemical data and rate constants for back electron transfer (kin Scheme I) in CH2ClCHzCl (DCE) at various ionic strengths ( p ) are listed in Table I. The electrochemical data report the difference in Elp values for the PTZ-based oxidation and bpy-based reduction as A E 1 / 2 = E1/2(2) - El/*(l).
-
Eip(1): [R~'(~PY)(CO)~(P~-PTZ)I+ +e
[Re'(bPY'-)(Co),(PY-pTz)l
-
E1/2(2):[Re'(bpy)(CO)3(py-PTZ*+)]2+ +e
[Re'(bPY)(Co),(PY-~z)I+ A plot of In k vs p1I2 is shown in Figure 2. From these data and those in Table I, there are sizeable decreasesin k and increases in Al21/2+withp over a narrow range of p. Qualitatively similar observationswere made for back electrontransfer infuc-[Re1(4,4'(CH~O)~~PY)(CO)~(PY-PTZ)I+, (4,4'-(CH30bbpy is 4.4'- .dimethoxy:2,2'-bipyridine). Inihis case, the transient absorption
__
Ionic Strength Effects on Electron Transfer
The Journal of Physical Chemistry, Vol. 97, No. 26, 1993 6813
200
1 I
150
16.6
16.5
I
A
IO0
1I
16*7
A
0
0
1
0
0
0
0 oO
16.3
A 16.2
c"
. -. . I
161
0.0
01
I
1
I
0.000
0.005
0.010
I
I
I
I
I
I
0.1
0.2
0.3
0.4
0.5
16.6 I
0.6
1
16.5 0.025
I
t
B I
16.4
8
Y
c -
A
16.3 0.015
0.01 0 0.0
16.2
0.5
1 .o
.
1.5
'
16.1 0.0
Figure 1. (A) Equivalent conductance (A) at 295 Kvs plot from the conductivity data for fac- [Re(bpy)(C0)3(CEtpy)](P&) in DCE, illustrating its behavior as a weak electrolyte. The range of sampleconcentrationsvariedfrom 1.0 X Itsto 0.01 X lk5M. (B)The conductivity data shown in A plotted according to the Fuoss equation. The plot includes points for the lowest five concentrations.
measurements were complicated by the photodecomposition of the complex. Rate constant measurements in a series of solvents revealed that significant ionic strength effects on back electron transfer exist only in solvents of low dielectric constant (CH2C12, CH2ClCH2Cl). In polar solvents such as DMSO, DMF, CH,CN, or benzonitrile, the rate constant for back electron transfer was the same within experimental error in the pure solvent as with added 0.1 M TBAH.18 The conductivity measurements on fa~-[Re(bpy)(C0)~(4Etpy)](PF6) in DCE were conducted in order to ascertain the degree of ion pairing in solution. From the plot of equivalent conductance vs (concentration)1/2in Figure la, the dissociation constant, KD,was calculated to be 6.7 f 1.3 X 1 V M. From the value of KD,at a concentration of 2 X 10-4 M in the absence of added supporting electrolyte, 83% of the complex exists in an ion-paired state in DCE.
From the data in Table I and Figure 2, it is apparent that a measurable ionic strength dependence exists for the rate constant for backelectron transfer (kin Scheme I). From the conductivity measurements on fuc-[Re(bpy)(C0)3(+Etpy)] (PFs), it can be inferred that ion pairing is substantial (83%) in DCE even in solutions of the pure complex at the concentration (2 X 10-4 M) used for the photophysical studies. Sincefac-[ReI(bpy)(CO)s(pyFTZ)](PF6) has the same charge as fac-[Re(bpy)(CO)3(4-
I
0.2
4
Figure 2. (A) The variation of In k with pl/*. (B) The fit of the equation to the experimental data in Table In k = 15.1 i 289 G/(l+ 201 I for p < 0.020 m.
4)
Etpy)] (PF6) and only a slightly larger molecular volume, it seems reasonable to assume that substantial ion pairing exists for the PTZ complex as well. Ionic strength effects are well-documented for bimolecular electron and energy transfer reactions involving diffusion.%J9In many cases the application of the DebyeHiickel theory and standard equations for diffusion have been used successfully to account for the effect of ionic strength variations. The example here is different in that it involves an ionic strength effect on intramolecularelectrontransfer within a cation that is essentially completely ion paired even in the absence of added electrolyte. As illustrated schematically below, rotation around the - C H r
L Discussion
I
0.1
O
link to the PTZ group can bring the center-to-center distance between the bpy'electron transfer donor and the PTz'+ acceptor to -6 A.5 In an earlier paper, AGO for back electron transfer was varied systematically by varying substituents at bpy in the series fac[Re(4,4'-(X)zbpy)(CO)a(py-PTZ)]+(X = COzEt, C(O)NEt2, H, CH3, CH30). In this series it was found that a linear relationship existed between Ink and AE1/@31/2= E1/2(PTZ+IO) -E1/2(4,4-(X)2bpy@/-).saThis result was explained by application
6814
Chen et al.
The Journal of Physical Chemistry, Vol. 97, No. 26, I99‘3
of the quantum mechanical theory of electron transfer and the energy gap law in the form1@-12
ln(k X 1s) = In(
y)+
ln(FC)
“Hab
(4)
The microscopic basis for the energy gap law is the large energy release that accompanies electron transfer. This energy appears in the vibrations and solvent librations. The variation in k with driving force (or energy gap) occurs because vibrational overlap between the excited and ground state vibrational wave functions increases as the energy gap decreases (or as the extent of vibrational distortion increases). A related observation has been made for ion-pairing effects in nonradiative decay of the MLCT excited states of [Os(phen)3]Xzand [Os(4,7-Ph2phen)3]X~(phen is 1,lO-phenanthroline; 4,7Ph2phen is 4,7-diphenyl- 1,lO-phenanthroline; X = PF6-, C104-, C1-, B r , SCN-, BPh4-) in CH2Cl2 where it was found that In k,, varied linearly with the energy gap as estimated by emission energies.22 Of the total decrease that occurs in k, 1/2 occurs from p = 0.0002 to 0.0010 m. Past g = 0.0010 m,there is essentially no further change in A E l / z within experimental error ( f 7 mV), while k continues to decrease until p 0.080 m,past which there is no longer a statistical variation in k with increasing 1.1. The continued decrease in k with p may be a medium effect that exists in addition to the energy gap effect identified a t lower p. Asp increases, for example, the asstmption of a constant solvent reorganizational energy, (A,, = (Av1/2)~/16In 2 k ~ T ) may , be inappropriate because of the formation of higher ion aggregates. In Figure 2b is shown an empirical fit of In k to an ionic strength function suggested by the Debye-Hiickel equation, eq 919,20
-
In the derivation of these equations the following assumptions were made: (1) A series of v(bpy) and v(PTZ) medium frequency, ring stretching modes are the dominant energy acceptors. These modes can be treated as a single, average harmonic oscillator of quantum spacing, h u ~and , an electron-vibrational coupling constant, SM,(2) A series of low-frequency vibrational modes and solvent librational modes also contribute but play a lesser role as energy acceptors. The low-frequency modes can be treated as an average mode of spacing h u and ~ electron-vibrational coupling constant SL.The contribution from the solvent can be treated classically; its contribution to the reorganizational energy is &,, (3) Electron transfer occurs in the weakvibrational coupling limit where-AGO > > S M ~ W (4) M . Thecontribution to theelectron transfer rate constant fromvibrational levels above V M = 0 in the initial state is negligible since h u >> ~ kBT. ( 5 ) There is no change in vibrational frequencies between the initial and final states. In eqs 5 and 6 the free energy change is related to AEllz by AGO = -AE1,2
+ W,
(7)
The work term, wr,is a correction for the electrostatic interaction between the anion bpy’- and cation PTz’+. Expressions are available for calculating the dependence of w, on p for strong electrolytes,9cJ9J0 but they are not relevant to our case where there is essentially complete ion pairing. Of the terms in eq 5, only - ’lAG0I is expected to vary significantly with AGO. If AGO
Ink=-
-
hWM
AEl/2, it is predicted that
YAElf2
(8) hWM and that In k should increase linearly with the energy gap as measured by A E l p There is a region of low ionic strength ( p = 0.0002-0.0042 m) where In k varies linearly with AE1p More importantly, the slope of the plot, d In k/dAE1/2 = -4.2 eV-1, is within experimental error of the slope of the same plot (d In k/dAl?lp = -3.4 eV-l) obtained in the earlier study in which A E 1 / 2 was varied by varying the X substituents in the series [Re(4,4’-(X)zbpy)(C0)3(pyPTZ)]+.5a
-
In k = In k, +
2zlz2Adp
(9) 1 Bd& The data can be satisfactorily fit to the equation In k = 15.1 289 G / 1(+ 201 6) for p < 0.020 m. This equation has been applied successfully in studies of ionic strength effects in bimolecular electron or energy tran~fer.~*19In eq 9, zl and z2 are the charges on the two reactants, d and B are defined in ref 20, and A in ref 23. This is simply an empirical correlation and does not imply the validity of applying Debye-Hiickel theory given the existenceof ion pairing in our case. The strictly empirical nature of the correlation is shown by the fact that the parameters A and B derived from the fit are larger by 2 orders of magnitude than values calculated by using expressions in refs 20 and 23. There are twoadditional points concerningionic strength effects that can be anticipated inother studies. In “chargeshift”reactions where there is no change in charge type and the redox sites are of comparable volumes, there should be no dependence of the energy gap on p. Secondly, the time scale for our kinetic measurements was relatively slow (-5 ns). On still shorter observational time scales it can be anticipated that the dynamics of ion motion (that respond to the electrostatic perturbation caused by photochemical electron transfer) will play an important role in the dynamics of intramolecular electron transfer. Analogous effects involving dynamical solvent motion have been observed in many electron transfer systems.24
+
+
Acknowledgements are made to National Science Foundation for financial support under grant CHE-9022493, to Dr. E. F. Hilinski, Florida State University, for the loan of the cell and conductance meter used in the conductivity measurements, and to Mr. George Coia for assistance in the initial electrochemical measurements.
The existence of the quantitative correlation may be serendipitous. Estimation of formal potentials from the electrochemical measurements is complicated by the distortion of the voltammograms a t low ionic strengths.21 Nonetheless, the variation in In k with p is, at least, qualitatively consistent with a prediction of the energy gap law. Increasing the ioniccontent of the solution stabilizes the anion
