4254
J. Phys. Chem. 1994,98, 4254-4260
Interaction between Electrolyte and Charge-Transfer States: Evidence for Complex Formation Richard J. LaVallee+&and Matthew B. Zmmt' Department of Chemistry, Brown University, Providence, Rhode Island 02912 Received: November 23, 1993; In Final Form: February 7, 1994'
The effects of tetraalkylammonium salts on intramolecular charge-transfer absorption and emission spectra in solution are measured. Addition of tetrabutylammonium hexafluorophosphate (TBAPF6) to methylene chloride solutions of the donor-spacer-acceptor compound 2 reduces the intensity of the charge-transfer emission band and red shifts the emission maximum. The band maximum (cm-l) and width of the lowest-energy, chargetransfer absorption transition in 1 increase upon addition of salts. The observed shift and broadening are strongly dependent on the structure of the salt cation, being larger for tributylmethylammonium (TBMPF6) than for tetrabutylammonium (TBAPF6) salts, but are independent of the salt anion. The dependence of the absorption band shape of 1 on salt concentration is simulated using a model that includes (1) an equilibrium between monomeric and dimeric (aggregated) salt molecules and (2) an equilibrium between uncomplexed 1 and 1complexed to monomeric salt molecules. The charge-transfer absorption spectra of the complex between 1 and TBMPF6 and between 1 and TBAPFa are determined and are used to obtain estimates of the association constants for complex formation. The relevance of complex formation, between neutral charge-transfer states and added salts, to ongoing studies of electrolyte perturbation of reaction kinetics is discussed.
I. Introduction
SCHEME 1
Electron-transfer (ET) processes occupy a central position in modern investigations of reaction mechanisms' and dynamics.2 Considerableeffort has been directed toward understanding the dependence of electron-transfer kinetics on structural features of the reactants and on interactions of the reactants with the surrounding medium.3 Theoretical' and experimental5studies have elucidated strong dependences of transfer rate constants on the free energy change attending reaction. For ET reactions in fluid solution, the latter quantity is often approximated using electrochemicallydetermined reduction and oxidation potentials? With the exception of smallcorrectionsfor differences in diffusion constants,' these potentials may be directly related to the free energy difference between the redox partners. As electrochemical measurements are usually performed in the presence of electrolyte, the lowest-energyand predominantform of charged redox species may involve significant interactions with the added salt. This is particularly true in weakly polar and nonpolar organic solvents, in which ion pair and higher aggregate formation are well documented.* These ion-electrolyte interactions are generally absent in the electron-transferreaction under investigation; thus, electrochemical measurements may not provide an accurate determination of the associatedtransfer thermodynamicsin lowpolarity solvents, leading to errors in detailed analyses. From an alternative perspective, it is of interest to understand the coupling between electrolyte and electron-transfer processes. In analogy to solvent effects on electron-transfer reactions,' interactions between the electron donor or acceptor and the electrolyte will alter the free energy and activation barrier accompanying ET in solution. Electrolyte-induced changes in ET kinetics or in associated charge-transfer (CT) spectra provide evidence of these interactions and, in principle, can be used to characterize and quantify the interactions. A number of recent studies have probed the kinetic9 and spectroscopic10perturbations resulting from interactions with electrolytes. In this paper we report and analyze the effects of tetraalkylammonium electrolytes on the spectroscopy of photoinduced,
* To whom correspondence should be addressed. Current address: Departmentof Chemistry,UniversityofGeorgia, Athens, GA 30601. t 1992 Summer NSF REU participant. @Abstractpublished in Advance ACS Abstracts. March 15, 1994. 0022-3654/94/2098-4254$04.50/0
Ph
0.
1
2
intramolecular charge separation and charge recombination reactions in methylene chloride. The ET systems investigated include Reichardt's dye" 1 and a semirigid naphthalene donorheptacyclotetradecane spacer-dicyanoethylene acceptor molecule 2 (Scheme 1). The CT absorption spectrum in the former compound is the source of the well-known solvent polarity parameter ET(3O).'l The existence of charge separation in the ground state of 1 leads to equilibration of probbelectrolyte interactionsprior to the measurement,thus enablingquantitative evaluation of the resulting spectroscopic changes. The absence of strongattractive interactions betweenelectrolyteandthe ground state of 2 necessitates electrolyte redistribution following formationoftheCTstate, whichcomplicatesanalysisoftheCTemission spectra.
E. Experimental Section Absorption spectra were recorded on a Perkin-Elmer Lambda
3B UV-vis spectrometer. The band-pass of the spectrometer is approximately 1 nm. Spectra were taken versus a reference sample of neat methylene chloride. Fluorescence spectra were collectedin a right angle geometry on a SPEX Fluorolog-2 F111XI spectrofluorometer system. Spectra were corrected for lamp intensity variation using a quantum counter reference assembly (SPEX 1910A). Spectra were also corrected for the detector and monochromator response using calibration factors determined with the SPEX 1908MOD standard lamp and MgO scattering block. A HOYA L37 filter inserted prior to the detection optics minimized scattered excitation and Raman signals. Methylene chloride was distilled from CaHz immediately prior to sample 0 1994 American Chemical Society
Interaction between Electrolyte and CT States 300000 A
."8 P '3 WH
l4r
250000
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The Journal of Physical Chemistry, Vol. 98, No. 16, 1994 4255
-
12
-
+ 550nmTBABr .-e500 nm TEAPFs
10
-
--+--- 800 nm TBAPFe -+- 850 nm TBAF'FR
550 nm TBAPFe
8 -
11
50000
1
I
1 ''W ____
___..--------+---------*..--- _______._ ~
01 0
"
10
"
"
20
30 [Salt] /
"
40
"
50
'
60
mM
Figure 2. Stem-Volmer plots of the CT emission intensity from 2detected at various wavelengths. The solid line connects the data for TBABr. The broken lines connect the data for TBAPF6.
III. Results A. Additive Effects on 2: Naphthalene Local Emission. The naphthalene locally excited-state (Np LE) emission from 2 in CH2C12 exhibited maxima at 327 and 336 nm (Figure 1) and a lifetime on the order of 0.6-0.7 ns. The presence of additives inducedonly minor perturbations in thespectrum. Concentrations of acetonitrile as high as 230 mM reduced the emission intensity by less than 3%. The emission intensity decreased by 12% in the presence of 50 mM tetrabutylammonium hexafluorophosphate, TBAPF6. In 56 and 122 mM tetrabutylammonium bromide (TBABr) solutions, the emission intensity was reduced by 10% and 16% respectively. None of these additives induced a shift in the emission maxima by more than 1 nm.
B. Additive Effects on 2 CbargeTransfer Emission. The charge-transfer (CT) state emission from 2 in CHzClz consisted of a structureless band, centered at 524 nm, with a full width at half-maximum of 185 nm. In dry CHzC12, the rise time of the CT state luminescence was less than 1 ns and the decay lifetime was 13 ns.13 Addition of acetonitrile changed the emission spectrum slightly. In the presence of 230 mM acetonitrile, the CT emission intensity was reduced by -20% and the maximum shifted to 527 nm. Addition of TBAPF6 or TBABr changed the spectrum much more dramatically. In the presence of 55 mM TBABr more than 90% of the CT emission was quenched. SternVolmer plots of the emission intensity at a single wavelength were nearly linear, with a slope of 190 M-l at all wavelengths across the CT band (Figure 2). A 50 mM TBAPFa solution quenched more than 80% of the CT emission and shifted the band maximum to 541 nm (Figure 1). In contrast to the bromide salt, Stern-Volmer plots of emission intensity for TBAPF6clearly exhibited downward curvature, with the curvature increasing as the detection wavelength was shifted toward the red edge of the CT band (Figure 2). The CT state emission decay was accelerated by the presence of electrolyte. TBAPFs (50 mM) reduced the l / e time of the decay, measured at 525 nm, from 13 to -2 ns.13 The decays did not obey single- or double-exponential kinetics at TBAPFs concentrations above 10 mM. The rise time of the emission intensity was slightly longer on the red edge (625nm) of the band relative to the blue edge (525nm), although this effect was difficult to quantify as a result of weak emission in the presence of electrolyte and reduced detector sensitivity at longer wavelengths. C. Additive Effects on 1: Charge-Transfer Absorption. The maximum in the long-wavelength CT absorption band of 1in dry CHzClz is reported to occur at 702.5 nm.14J5 The presence of 130 mM acetonitrile shifted the maximum in the CT absorption band slightly, to 699 nm. In contrast, tetraalkylammonium salts induced much larger changes in the CT absorption spectrum (Figure 3). For concentrations up to 25 mM TBAPF6, there was an approximately linear blue shift of the absorption maximum to 686 nm (Figure 4). Higher concentrations of TBAPF6 generated larger blue shifts of the absorption maximum, but with smaller shifts per additional unit concentration of salt. Thus, the band maximum in 175 mM TBAPF6 appeared at 672 nm. The full width at half-maximum (fwhm) of the CT absorption band exhibited a similar TBAPF6concentration dependence, increasing by 200 cm-l between 0 and 25 mM TBAPF6 and by 100 cm-1 between 25 and 150 mM TBAPF6. Concentrations of up to 150 mM TBABr produced nearly identical shifts and shapes of the CT absorption band as did comparable concentrations of TBAPF6. However, addition of tributylmethyl hexafluorophosphate, TBMPF6, produced much larger blue shifts of the absorption maximum (Figures 3 and 4).
Lavallee and Zimmt
The Journal of Physical Chemistry, Vol. 98, No. 16, 1994
4256
Iv. Analyses
0.0 I 500
700
600
800
Wavelength (nm) 1.0
0.9 0.8 0.7
0.6 0.5
A. CT Absorption: Two-State Model. The predominant speciespresent in solutionsof tetraalkylammonium salts in weakly polar organic solvents, such as CH2C12, varies with the salt concentration.6 At micromolar concentrations, the free ions predominate. In the millimolar range, the salts occur as ion pairs. At larger salt concentrations, the ion pairs form higher-order aggregates. The observations that concentrations of tetraalkylammoniumsalts between 0 and 25 mM induced the largest change per unit concentration in the position and width of the CT band in 1 suggests that the predominant interaction involves 1 and monomeric, ion-paired salt molecules. Therefore, the following model was used to analyze the salt effects. 1 forms a complex, 1 4 ,with addedsalt. TheCTabsorptionspectrumofthecomplex is blue-shifted with respect to that of 1 (vide infra). The association constant for this complex formation is K.. Added salt is present as monomer,S,as salt dimer, SS,or in the complex, 14. The equilibrium constant for salt dimerization is K2. The concentration of 1 used in these experiments was less than 0.2 mM, a factor of 20 less than the lowest salt concentration. Thus, the total added salt concentration, [%I, may be approximated as
0.4
0.3
and the ratio of complexed to uncomplexed 1 is
0.2
0.1 0.0
500
700
600
800
Wavelength (nm)
Figure 3. (a, top) Comparison of experimentalspectra of 1plus TBAPF6 and the corresponding spectra calculated using the largest two eigenvectm. The two-component,simulated spectra are shown for TBAPF6 concentrationsofOmM (diamonds),7.8 mM (filledcircles),and 82mM (shaded squares). The solid lines passing through the points are the experimental spectra. For clarity, only these three spectra are shown. All spectra have been normalized to constant height. (b, bottom) Comparison of experimental spectra of 1 plus TBMPF6 and the corresponding spectra calculated using the largest two eigenvectors. The two-component, simulated spectra are shown for TBMPF6 concentrations of 0 mM (diamonds),7.3 mM (filledcircles), 29.1 mM (shadedsquares),and 117 mM (pluses). The solid lines passing through the points are the experimentalspectra. All spectra havebeennormalizedtocomtant height. 1000 900 -
800
-
700
-
. 1 I
I
1 .
500 600
i
i
piGLl 1 with TBAPFs
1001
A
0
20
40
60
80 [Salt],
100
120 140 160 180
/mM
Figure 4. Plot of the blue shift of the absorption band maximum from CHZC12solutionscontaining 1as a function of the total salt concentration. Squares indicate the data for TBMPF6; triangles indicate the data for TBAPF6.
At 25 mM TBMPF6, the absorption maximum appeared at 673 nm; at 210 mM TBMPF6, the maximum was further shifted to 655nm. Thus,aswasobservedwithTBAPF6,the bandmaximum shift was larger between 0 and 25 mM TBMPF6 than between 25 and 200 mM. Similarly, the fwhm of the absorption band increased by 450 cm-l between 0 and 30 mM TBMPF6 and remained relatively constant up to 120 mM TBMPF6.
In order to evaluate the equilibrium constants and to test this model, the absorption spectrum of the complex, 14, must be determined. B. CT Absorption: 1 4Complex Spectrum. The absorption spectra of the 1-TBAPF6 and the 1-TBMPF6 complexes are shown in Figure 5 . These spectra were obtained in two ways. In the f m t approach, the spectrumof 1in pureCHzC12was multiplied by a scaling factor and subtracted from the experimentalspectrum with the highest salt concentration. The value of the scaling factor was interatively determined subject to the following constraints: (1) the difference spectrum (14) approach zero absorption at wavelengths corresponding to the red edge of the spectrum of 1, (2) the spectrum contain a single maximum, and (3) thedifferencespectrum have positivevaluesat all wavelengths. This procedure generated a narrow range of candidate spectra for 1 4 with both TBAPF6 and TBMPF6. Most significantly, the experimental spectra obtained at all salt concentrations, with each salt, were successfullyregenerated using linear combinations of the 1 and 1 4 spectra. In the second approach, principal component analysis with self-modeling*6was performed on the series of spectra obtained from 1in the presence of either TBAPF6 or TBMPF6. Spectral matrices were generated and analyzed using the experimental absorption spectra at 1-nm intervals from 550 to 850 nm. For each salt, the five eigenvectors(v1-V~)with the largest eigenvalues (k1-X~)and the corresponding spectral weighting coefficients for each salt concentration were visualized. For both salts, b and A5 were 4-5 orders of magnitude smaller than Ai. The corresponding eigenvectors, V,and V,,clearly contained only spectral noise and, thus, were ignored. A3 was 3 orders of magnitude smaller than A2 for TBAPF6 and 2 orders of magnitude smaller than A2 for TBMPF6. For both salts, V3 was nonrandom, suggesting that a third component might be contributing to the experimental spectra. However, there was excellent agreement between the experimental spectra and the spectra simulated using only VIand V2 (Figure 3). Furthermore, the spectra simulated using V1-V3 were not noticeably different from those derived using VI and V2; Le., the contributions (spectral weighting coefficients) of V3 to the experimental spectra were not visibly
Interaction between Electrolyte and CT States 1.1
1.0
0.9
The Journal of Physical Chemistry, Vol. 98, No. 16, 1994 4257
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0.6 0.5 0.4 -
0.8
2 1
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/
I /
0.1 0.0 0.2
0.00 0.02 0.04 0.06 0.08 0.10 0.12
1
[Salt]
kK
1.0
0.9
0.8 0.7 0.6 0.5 0.4
0.3 0.2 0.1
0.0 12
13
14
15
16
17
18
19
kK
Figwe 5. (a, top) Comparison of the experimentally derived chargetransfer absorption spectra of 1(squares) and of the complex 1-TBAPF6 (trianglcs) with the best fit spectra calculated using the semiclassical model (dashed line, 1; solid line, 1-TBAPF6). See Table 2 for the parameters used to calculated the spectra. (b, bottom) Comparison of the experimentally derived charge-transfer absorption spectra of 1 (squares)and of the complex l-TBMPF6 (circles)with the best fit spectra calculated using the semiclassical model (dashed line, 1; solid line,
l-TBMPF6). SeeTable2 fortheparametersused tocalculatethespcctra.
r
0.03
,
I
Experimental Points
1
1
0.01 0.00 -0.01
4
-0.02
u"
-0*03
I .*
I
\\
\
-0.04
0.0640
Normalization Line
I
Y 1i
4
0.0645
0.0650
0.18
0.18
Figure 7. Plots of the ratio of complexed (14) to uncomplexed 1 as a function of added salt. The diamondsare the experimentallydetermined ratios for TBAPF6; the dot-dash line is the most accurate simulation, which is obtained using the model described in the text with Kz = 75.6 M-I and K, = 40.4 M-I. The squarcs are the experimentally determined ratios for TBMPF6; the solid line is the most accurate simulation, which is obtained using K2 = 75.6 M-I and K, = 101 M-l.
1.1
11
0.14
/M
0.0655
0.0660
0.0665
0.0670
Coefficient of Vector-1
Figure 6. Normalization line for the coefficients of eigenvectors 1 and 2, obtained from the two-component with self-modelinganalysis'" of the spectra from 1with TBAPF6. The experimentalpoints are indicated by squares. The coefficients of the pure 1-TBAPF6 spectrum are indicated by a circle. See text for the manner in which this point was determined.
significant. Thus, the principal component normalization line was calculated using only VI and V2 (Figure 6). The spectra of the pure components 1and 1 4 can be obtained by moving along the normalization line, in opposite directions, until the resulting simulated spectra contained a negative value. Saltiel has pointed out that this constraint leads to wide regions of acceptable pure component simulation coefficients and significant uncertainties in the pure component spectra.'" Saltiel further noted that a unique definition of the pure component can
be better obtained by using as many additional constraints as possible to determine the pure component spectra. As the pure component spectrum of 1 is part of our experimental data set, there is no ambiguity in its determination. In order to further constrain the pure component spectrum corresponding to 1 4 , simulated spectra along the relevant portion of the normalization line were fit using a semiclassical single quantized mode model for CT absorption (vide infra).I7 The calculated spectrum from the normalization line that was best fit using the semiclassical model was used as 1 4 (Figure 5). The spectra of 1 4 obtained using the above two methods were essentially identical for both salts. C. CT Absorption: 1 4 Complex Association Constants. The ratio of complexed, 1 4 , to uncomplexed 1was evaluated at each salt concentration by fitting the experimental spectra as linear combinations of the pure component spectra. It was assumed that the oscillator strength of the longest-wavelength CT band,'* determined as the integral over the entire CT band plotted versus wavenumbers, was identical for 1and 1 4 . As the edges of the CT bands were obscured, the oscillator strength calculations were performed using the best fit spectra obtained with the semiclassical CT absorption band model. The fwhm of the pure component spectra increased in the order 1 < l-TBAPF6 S 1-TBMPF6; thus, the extinctioncoefficient at the CT absorption band maxima was largest for 1 and smallest for 1-TBMPF6. The relative contribution of 1 4 and 1 in each spectrum was determined by a nonlinear least-squares analysis of the data between 550 and 850 nm. The [ 141/ [ 11ratios for both salts are shown in Figures 7. The concentration dependence of the [14]/[1] ratio for TBAPFs was simulated using the two-component model described above. The minimum value of K2, the salt dimerization equilibrium constant, required to reproduce the downward curvature in the plot was -25 M-l. Thevalue of K,, the l-salt association constant, required to obtain an adequate fit of the data was well determined given a specific value of K2. However, a broad range of (K2,Ka) pairs provided reasonable fits to the data (Table 1). Thus, it was not possible to precisely determine K2 and K, for TBAPF6 or TBMPF6. However, for any fixed value of Kz, K,,(TBMPF6) was 2.5 time larger than K,(TBAPF6) (Table 1). D. CI' Absorption: Line Shape Analysis. The CT absorption line shapes of 1 and 1 s were analyzed using a standard, semiclassical model for charge-transfer absorption.17a The Franck-Condon factors were calculated using the photon energy, the free energy difference between the ground and excited state (AGO),and a classical, low-frequency reorganization energy (&) along with a single, quantized, high-frequency mode (hw) and
4258 The Journal of Physical Chemistry, Vol. 98, No. 16, 1994
TABLE 1: Values of l S a l t Association Constants (&) Determined by Fitting the Plots of [l-Sy[l] vs Salt Concentration for Assumed Val- of the Salt Dimerization Equilibrium Constant (&) K2 (M-') K. (1-TBAPF6) (M-') K, (1-TBMPF6) (M-') 263 40 52 75.6b 95
25.0 32 35 40.4b 45
62 78 87 101 112
Minimum value of K2 that adequately reproduces the plot curvature. Values of K2 and K, (1-TBAPF6) that provide the best fit of the data.
TABLE 2
Parameters of the CT Absorption Band Analysis AGO (ev) As (eV). XV (eWb ho (cm-9'
1
1.38
0.35
0.09
1860
1-TBAPF6 1.57 0.23 0.14 1400 1.55 0.28 0.14 1460 I-TBMPFs a Low-frequency reorganization energy (often called solvent reorganization energy). Quantized mode (high frequency) reorganization energy. C Average quantized mode frequency. reorganization energy (h). The Franck-Condon factor at each wavelength was multiplied by the transition energy and by the transition dipole matrix squared. The former introduces a Y dependence and the latter a v-2 dependence,)b resulting in an overall v-l contribution to the line shape. Table 2 lists the values of AGO, &, A,, and hw used to simulate the spectra of 1, 1-TBAPF6, and 1-TBMPF6. V. Discussion
From the outset, a continuum explanation for the salt effects must be considered. Addition of tetraalkylammonium salts to CH2C12 increases the solution polarity as measured by the bulk dielectric constant.*' The salt-induced red shift and decrease in emission intensity from the excited CT state of 2 as well as the induced blue shift in the CT absorption spectrum of 1 are qualitatively consistent with the effects that increasing solvent polarity produce on charge-transfer transitions.lg However,upon closer inspection, a number of the results are inconsistent with explanations based on changes in the bulk dielectric properties but require specificinteraction between thesalt and chromophore. For example, if the principal means by which salt perturbed the CT transitions involved changes in the homogeneousdielectric constant, only one type of excited CT State would be expected. The wavelength dependences of the Stern-Volmer plots and of the CT emission time dependence for 2 with added TBAPF6 demonstrate the presence of more than one species of CT excited state when salt is present. The weak quenching of the NP LE state emission in 2 by TBAPF6indicates that there is no significant complexation between the ground state of 2 and salt. The slopes of the Stern-Volmer plots for 2 with TBAPF6, in the limit of zero concentration, and for TBABr yield quenching rate constants of -1.5 X 10'0 M-1 s-1, close to the diffusion-controlled limit in CH2Clz. Once the CT state is formed, encounters with TBAPF6 molecules result in the formation of a CT-salt complex that is stabilized by Coulombic interactions between the salt ion pair and the CT state. The resulting emission is red-shifted relative to the uncomplexed CT emission. The complex's emission quantum yield is reduced as the result of faster nonradiativecharge recombinationthrough a reduced energy gap to theground state.19b The red shift and diminished quantum yield from the complex are responsible for the wavelength-dependentCT quenching.The curvature in the Stern-Volmer plot for TBAPF6 suggests that aggregates of salt molecules, which become significant above 10 mM, are less effective than salt molecules at stabilizing the CT state.20 Comparable arguments may be presented against a continuum explanation for the salt effects on the charge-transfer absorption
Lavallee and Zimmt band in 1. Although the bulk dielectric constants (e) of CHzCl2 solutionsincrease upon addition of salt, the experimental c values for concentrations of up to 100 mM tetraalkylammonium perchlorates are nearly independent of the number of carbons in the alkylammonium ion.**f If salt-induced changes in the bulk dielectric constant were responsible for the variations in the CT bandwidthsand band maxima, similar concentrationdependences would be expected upon addition of TBAPF6 and TBMPF6. Contrary to this expectation, the observed spectralchanges (Figure 4) are clearly sensitive to the molecular structure of the salt, thus supportingexplanationsinvolving formation of a complexbetween salt and 1. There is literature precedent for complex formation between ion-paired salts and CT states. Blackboum and Huppl" reported that the absorption line shape and transition energy for the intervalencechargetransfer band in acetylenebridged biferrocene (BP) monocations are modified by higher-order aggregation in CH2C12. Evidence was presented for aggregation of BPX- ion pairs at chromophore concentrations above 1 mM or between BPX- ion pairs and added TBAPF6 (5-200 mM). Lowery et al.lobreached a similar conclusion from studies of the intervalence band in the parent biferrocenium cation in CH2C12. In the forementionedbiferrocenium-X- systems,the CT transitions were more strongly perturbed by formation of the monomeric ion pairs from the free ions than by aggregation.2l Nontheless, both studies demonstrated that complex formation between charge-separated ground states and ion pairs occurs and alters the associated CT spectra. Charge separation in the ground state of 1 is substantial, producing an effective dipole moment of 15 D.22 The CT absorption substantially reduces the extent of charge separation, resulting in a 6-D dipole moment in the excited state.2' Arguing on the basis of Coulombic interactions alone, the free energy of complex formation will be larger for salt with the ground state of 1than with the excited state, resulting in a hypsochromicshift of the complex's CT absorption band. The extent to which the experimental absorption band maximum shifts at any specific salt concentration is determined by the fraction of complexed 1 and the difference between the absorption band maxima of free and complexed 1. Both quantities depend on the free energy of complex formation between salt and 1's ground state (AGO,), There are at least two ways to estimate AGO. from the data. Most directly, it can be determined from the magnitude of the association constant, K,. Using the two-equilibrium model presented above, it was not possible to obtain a unique value for this quantity, although the minimum value of K,,26.5 M-1 (K2 = 25 M-l), for TBAPF6 yields AGO. = -2 kcal/mol. With the assumption that K2, the salt dimerization equilibrium constant, is the same for TBAPF6 and TBMPF6,23AGO, for formation of the 1-TBMPF6 complex is 0.55 kcal/mol more exoergic than for the 1-TBAPF6 complex. The CT absorption bands from 1 and the I S complex may also be analyzed to obtain an estimate of AGO,. To the extent that the respective CT band shapes, corrected for the dependence of extinction coefficient on transition energy, are similar, the energy difference between the band maxima of 1 4 and 1 is approximately equal to the difference in the free energies of complex formation for the salt with the ground state and the excited stateof 1. As mentioned previously,the latter freeenergy is presumably significantly smalkr in magnitude. Thus, the energy shift of the band maxima provides an estimate of the ground-state complexationfree energy. With these assumptions, AGO, for 1-TBAPF6 formation is -2.92 f .26 kcal/mol and for 1-TBMPF6 formation is -3.46 f .27 kcal/mol. These free energy changes are 1 kcal/mol more exoergicthan the values obtained from the analyses of the minimum equilibrium constants. The difference in AGO, for TBMPF6 and TBAPF6, -0.54 f0.28 kcal/ mol, is similar to the estimate from the equilibrium constants.2'
-
Interaction between Electrolyte and CT States Thus, despite only a slightly larger blue shift in the 1 4 CT spectrum for TBMPF6 compared to TBAPF6, the more favorable free energy of complex formation with the former salt generates a larger fraction of bound dye and a larger apparent absorption blue shift at every salt concentration. The absorptionstudies provide no structural informationabout the 1 4complex. The spectral shapes are clearly more sensitive to the structure of the cation (TBAPF6 vs TBMPF6) than to the structure of the anion (TBABr vs TBAPF6). Coulombic interactions favor placement of the ammonium ion proximate to the phenoxide ring and the salt anion (X-)near the pyridiniumgroup. Minimized structures for 1 show that access to the phenoxide ring, and in particular the oxygen, is much less sterically encumbered than access to the pyridinium. Large 1-X- separations would be expected to reduce both the magnitude of this pair’s Coulombic interaction and the sensitivity to anion structure (separation radius). In light of recent studies on interpenetrated ion pairs,9w the phenoxide-ammonium separationcould be small, resulting in a large, favorable interaction. The observed sensitivity to the ammonium ion structure certainly has a steric origin, although it is not clear whether the greater steric bulk of TBA+ compared to TBM+ simply increases the interaction distance or weakens a hydrogen-bonding-like interaction between the ammonium a C-H’s and the phenoxide ring. It is interesting to compare the results described above with an extensive study of electrolyte effects on the absorptionspectra and steady-state and time-resolved emission spectra from a series of polar, solvatochromic dyes reported by Chapman and Maroncelli.* Most significantly, these authors concluded that discrete ion-dye complexes are formed in solution. They simulated both the steady-state and time-dependentobservables for the dye Cu102, in the presence of 0-2 M NaC104 in CHICN, using a model incorporating sequential associations of Cu 102 with salt cations. Two-state models, with only one cation-dye complex, were unable to reproduce the steady-state and timeresolved observables. Although this contrasts with our analysis of salt effects on 1, both in the number of distinct complexes formed and in the identity of the complexing agent (ion vs ion pair), the differences can be rationalized in terms of a greater number of accessible interaction sites on Cu102, the smaller size of Na+ relative to tetraalkylammonium ions, the polarity of the solvent, and a 10-fold greater salt concentrationrange investigated by Chapman and Maroncelli.” These authorsalsonotedincreased spectral shifts with smaller cation radius and a large increase in the cation-dye association constant in the electronic state with the greater dipole moment, in agreement with our conclusions. The effects of salt on the absorption band shape were somewhat different for Cu102 and 1. Whereas Chapman and Maroncelli observed that Na+-induced spectral broadening was less than 20% of the Na+-induced spectral shift (Table IV,ref 9e), we observed that spectral broadening (25-30 mM added salt) was nearly 75% as large as the spectral shift.26a Furthermore, when the experimental spectra from 1 and salt were simulated and scaled to give constant integrated area, isosbestic points were observed at 673 and 681 nm for TBMPF6 and TBAPF6, respectively.26b No isosbestic point wasobserved for Cu102upon addition of salt.9c Overall,considering the significant differences in the dyes, solvent, and electrolytes employed, the two studies provide concurring evidence for specific salt-dye interactions in solution. From these discussions, it appears that the two-state model provides an adequate framework within which to interpret the data. There are, however, aspects of these results which appear to be at odds with previously reported results. For example, in their analyses of ion-pairing effects on intervalence transitions, Blackbourn and Hupplw noted that the observed bandwidth reached a maximum when the ion-paired and free ion chromophores were present at equal concentrations. The fwhm of
The Journal of Physical Chemistry, Vol. 98, No. 16, 1994 4259 the spectra from 1with TBAPF6 increased throughout the range of concentrationsused, albeit much less significantlyat the higher concentrations. The fwhm of the spectra with added TBMPF6 increased at Iow salt concentrations and plateaued at the higher concentrations. The conclusions from the spectral analyses were that 45% (TBAPF6) and 71% (TBMPF6) of 1was complexed at the highest salt concentration studied. For neither salt was there evidence of a narrowing in the spectra at the highest concentrations, in apparent contradiction with the observations of Blackbourn and Hupp. However, spectral analyses indicated that the 1-TBAPF6 and 1-TBMPF6 CT absorption spectra were -5% and lO%broader,respectively,than thespectrumof 1. Numerical simulationswith the pure component spectra and with Gaussian spectra demonstrated that a difference of 10% in the fwhm’s of the pure component spectra shifted the composition of the widest spectrumto a 60:40 mixture,with moreof the broader component. Furthermore, the widths of the 5050 and 70:30 mixtures were indistinguishablefrom the width of the 6040 mixture within the uncertanties appropriate to our experiment. Thus, although spectral narrowing cannot be advanced in support of complex formation for salt and 1, its absence can be rationalized. A second point of concern is that K2 obtained from this work may be too large. The minimum acceptable and best fit values are 25 and 75 M-l, respactively. Estimates of aggregation equilibriumconstants for TBAClO4 in CHzCl2, ranging from 1.5 M-1 at 0.068 M& to 15 M-l at 0.2 MM TBAClO4, have been obtained from the concentration-dependent slopes of dielectric constant versus concentrationplots. The similaritiesin the effects seen for 1 with TBABr or TBAPF6 argue against a significant dependence of aggregation constants on the anion structure.2’ There is considerableuncertainty in the magnitude and the exact nature of the association constants obtained from the dielectric constant measurements. Thus, agreement of the association constants, determined by the different methods, to within 1 order of magnitude may be sufficient. Further studies will be required to better quantify salt-salt and salt4ye aggregation processes. A third point to be a d d r d is whether the semiclassicalmodel employed to simulate the CT absorption spectra adequately represents the interactions between salt and 1. The dynamics in electroiyte solutions have been discussed9+928 in terms of the Debye-Falkenhagen theory.29 A model for CT absorptionbands in the presence of electrolytes, which incorporates elements of the Debye-Falkenhagen theory, has also been deve1oped.w Infrared studies of alkali salts in weakly polar solventshave shown that the alkali ion vibrational frequency (100400 cm-I) is a function of the solvent and the anion.” To the extent that a l-cationvibration couples to the electron transfer in the complexes, the low- and high-frequency modes included in the semiclassical model should provide an adequate, if highly averaged, means to include the contributions of these vibrationsto the CT spectrum. The decrease of the best fit, quantized mode frequency in the CT spectra of the complexes relative to 1 (see Table 2) and the corresponding increase in the vibrational reorganizationenergies may reflect contributionsof the l-ion vibrational reorganization. However, as the spectra of the 1 4complex exhibit no structure and, furthermore, are not directly observed, the results from this investigation should not be interpreted as providing a definitive answer to this point. The evidence for associationof salt with dyes with highly polar ground states may have ramifications in dynamical studies of ion solvation. Recently, Thompson et al.ZBbreported the formation of ground-state complexes between alkali cations and l-aminofluorene in acetonitrile. The authors concluded that the excitedstate dynamics of preformed complexes differed from those of the uncomplexed dye. No evidence was obtained for similar complexes between the dye and tetrabutylammonium ions. In a previous study281 using 3-aminofluorene, 1 was employed to determine the solvent polarity of acetonitrilesalt mixtures. The
Lavallee and Zimmt
4260 The Journal of Physical Chemistry, Vol. 98, No. 16, 1994
observed dynamical behaviors of 3-aminofluorene in different salt solutions, with identical solvent polarities as determined by themaximumin thespectrumof 1 plus thesalt, werequitedistinct. The possibility that ground-state complexes may have formed between salt and 1 potentially complicates the interpretation of the solvent polarity measurement. It is clearly necessary to quantify contributions from multiple ground- and excited-state species when interpreting spectroscopic and dynamical results from studies of electrolytes with charged and neutral probes.*
Acknowledgment. We are grateful to the National Science Foundation for support of this work and for providing funds to support the REU program at Brown. We also thank Professor Dwight Sweigart for initial samples of the salts and Dr. John R. Miller for informative discussions.
References and Notes (1) (a) Eberson, L. E. Electron Transfer ReuctionsinOrgonlcChemlsrry; Springer-Verlag: Berlin, 1987, (b) In Phoroinduced Electron Trunsfer, Part C;Fox, M. A., Chanon, M., Eds.; Elsevier: Amsterdam, 1988. (c) Bordwell, F. G.; Harrehn, J. A., Jr. J. Am. Chem. Soc. 1987,109,8112. (2) (a) Johnson, A. E.; Lcvinger, N. E.; Jarzeba, W.; Schlief, R. E.; Kliner, D. A. V.; Barbara,P. F. Chem. Phys. 1993,176,555. (b) Wiedcrrecht, G. P.; Watanabe, S.;Wasielewski, M. R. Chem. Phys. 1993,176,601. (c) Maroncelli, M.; MacInnis, J.; Fleming, G. R. Science 1989, 213, 1674. (3) (a) In Phoroinduced Elecrron Transfer,Parts A and B Fox, M. A., Chanon, M., Eds.; Elsevier: Amsterdam, 1988. (b) Gould, I. R.; N O W , D.; Gomez-Jahn, L.; Young, R. H.; Goodman, J. L.; Farid, S . Chem. Phys. 1993, 176, 439. (4) (a) Marcus, R. A. Can. J. Chem. 1%9,37,155. (b) Kestner, N. R.; Logan, J.; Jortner, J. J. Phys. Chem. 1974, 78, 2148. (5) (a) Closs, G. L.; Miller, J. R. Science 1988, 210,440. (b) Gould, I. R.; Young, R. H.; Moody, R.E.; Farid, S.J. Phys. Chem. 1991,95,2068.
(12) Zeng, Y.; Zimmt, M. B. J. Phys. Chem. 1992,96,8395. (13) The CT state lifetime is affected by the oxygen concentration. The lifetimes in the text reflect measurements in air-saturated solutions. (14) Laurence, C.; Nicolet, P.; Reichardt, C. 8311. Soc. Chim. Fr. 1987, 1001. (IS) For the experiments deacribcd herein, the CT absorption maximum in different samples of "dry" CHlCll varied between 701 and 703 nm. For each set of experiments, the experimental CT maximum,ldctcnnined at zero additiveconctntrati~forthetrial,wasusedtocalculatespodralshifts (Figure 4). (16) (a) Lawton, W. H.; Sylvestre, E. A. TechnomefricsI971,13,617. (b) Osten, D. W.; Kowalski, B. R. Anul. Chcm. 1984,56,991. (c) Sun,Y.-P.; Seam,D., Jr.; Saltiel, J. Anul. Chem.1987, 59, 2515. (17) (a) Marcus, R. A. J . Phys. Chem. 1989,93,3078. fb) Kjaer, A. M.; Ubtrup, J. J. Am. Chem. Soc. 1987,109, 1934. (c) Walker, G. C.; A k a n , E.; Johnson, A. E.; Levinger, N. E.; Barbara, P. F. J. Phys. Chem. 1992,96, 3728. (18) There are two CT transitionsin 1 which shift similarly upon addition of electrolyte. Only the behavior of the longer wavelength band was characterized. (19) (a) Reichardt, C. Solvents undSolwnt Eflecrs inOrgunic Chemistry, 2nd ed.; VCH Weinhcim, 1988; Chapter 7. (b) Caspar, J. V.; Meyer, T. J. J. Phys. Chem. 1983,87,952. (20) The absence of both curvature and wavelength dependence in the Stem-Volmer plot for 2 with TBABr may indicate chemical quenching by
Br.
(21) InCHZCl2,ionpair fo~tionwasnear~quantitativeatcon~~tions of 1 mM.lw (22) (a) Schwe' A.; Reichardt, C. Z. Nutw orsch. 1966, 21A, 1373. (b) Liptay, W.; Sclkser, H.-J.; Dumbacher, B.; unig, S.Z . Naturforsch. 1968,23A, 1613. (23) The dependence of the dielectric constant on salt concentration is nearly the same for tetraalkylammonium perchlorates with alkyl chain lengths from 2 to 6 carb0ns.W This suggests that the aggregation behavior of these salts k not a strong function of the alkyl chain length. (24) Errors originating fromdifferenceain thelieahapescan be eliminated by use of the AGO values from the CT fits. In contrast to the precision with which the CT maximum can be determined, the AGO values are obtained by (~)Gaines,G.L.III;O'Ncil,M.P.;Svec,W.A.;Nirmczyk,M.P.;Wasidewsld, extfapolation to a region where the spectral data are least amrate. Using M. R. J. Am. Chem. Soc. 1991,113,719. this data and the approximations described in the text, AGO. of complex (6) Rehm, D.; Weller, A. Isr. J. Chem. 1970,8, 259. formation is -4.4 f 1.3 kcal/mol for TBAPF6 and -3.9 1.5 kcal/mol for (7) Rieger, P. Electrochemistry,2nd ed.;Chapmanand Hall: New York, TBMPF6. 1994; Chapter 4.9. (25) (a) &he, G. Angew. Chem. 1992,104,742. (b) Ses aim: Angew. (8) (a) Fuose, R. M.; Kraus, C. A. J. Am. Chem. Soc. 1933,55,476, Chem., Int. Ed. Engl. 1992, 31, 731. 1019,2387. (b) Beronius, P.; Lindback, T. Acru Chem. Scund. A 1978,32, (26) (a) Chapman and Maroncellis observe comparable broadening and 423. (c) Staples, T. L.; Szwarc, M. J. Am. Chem. Soc. 1970,92,5022. (d) shifts in the aborption spectrum of Cul02 in dH$N upon addition of 1 M Sigvartscn, T.; Gestblom, B.; Noreland, E.; Songstad, J. Actu Chem. Scund. TBA+. (b) Isosbestic points were not observed in the experimental spectra. 1989,43, 103. (e) Gestblom, B.; Songstad, J. Acru Chem. Scund. E 1987, We attribute this to concentration-dependent bleaching of 1 due to traces of 41, 396. (f) Gestblom, B.; Svorstel. I.; Songstad, J. J. Phys. Chem. 1986, acidic impurities in the salts. 90,4684. (8) Svomtel. I.; Songstad, J. Acra Chem. Scund. E 1985,39,639. (27) Based on effective radii, a change from Clod- to PF6- should not (9) (a) Y a k , T.; Sankarmman, S.;Kochi, J. K. J. Phys. Chem. 1991, produce a bigger change in aggregation constants than from PF6- to B r . As 95, 4177. (b) Zou, C.; Miem, J. B.; Ballew, R. M.; Dlott, D. D.; Schuster, TBABr and TBAPF6 have nearly identical effects on the CT spectra, we 0. J. Am. Chem. Soc. 1991, 113, 7823. (c) Vining, W. J.; Caspar, J. V.; expect that TBAPFsandTBAClO4 would havesimilar effects. Unfortunately, Mever. T. J. J. Phvs. Chem. 1985.89.1095. (d) Bart. E.: H u m r t . D. Chem. the latter salt bleached the CT bands of 1. This probably resulted from Phis. irrr. 1992,'195, 37. (e) Ckpman, C.'F.; Maronce& M. J. Phys. inadequate removal of acidic contaminants. Chem. 1991,95,9095. (28) (a) Thompson, P. A.; Simon, J. D. J. Chem. Phyf. 1992,97,4792. (10) (a) Wamer, L. W.; Hoq, M. F.; Myser, T. K.; Henderson, W. W.; (b) Thompson, P. A,; Broudy, A. E.; Simon, J. D. J. Am. Chem. Soc. 1993, Sheperd, R. E. Inorg. Chem. 1986,25,1911. (b) Lowery, M. D.;Hammack, 115, 1925. W.S.: Drickamer. H. G.: Hendricbn. D. N. J . Am. Chem. Soc. 1987,109, (29) Debye, P.; Falkenhagen, H. Phys. 2.1928,29, 121. 8019. (c) Blackbourn, R. L.; Hupp, J. T. Chem. Phys. k r r . 1988,.150,399. (30) Piotrowiak, P.; Miller, J. R. J. Phys. Chem. 1993, 97, 13052. (d) Blackbourn, R. L.; Hupp, J. T. J. Phys. Chem. 1990,91, 1788. (31) Edgell, W. F. In Ions and Ion Pairs in Orgunic Reactions, Vol. 1; (1 1) Dimroth, K.; Reichardt, C.; Siepmann, T.; BohlmaM, F. Liebigs Szwarc, M., EM.;Wiley-Interscience: New York, 1972; Chapter 4. Ann. Chem. 1963, 661, 1 .
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