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Static and dynamic electrolyte effects on excited large dipole solvation: high dielectric constant solvents
Volume 173, number 5,6
CHEMICAL PHYSICS LETTERS
19 October 1990
Static and dynamic electrolyte effects on excited large dipole solvation: high dielectric constant solvents V. Ittah and D. Huppert Raymond and Beverly Sackler, Faculty of Exact Sciences, School ojChemistry,
Tel-Aviv University, Ramat Aviv 69978, Israel
Received 4 June 1990;in final form I3 August 1990
We report on an increase in the steady-state fluorescence Stokes shift of coumarin 153when LiCI04 is added to polar solvents. A new relaxation process is observedin the presence of the electrolyte which is related to the ionic atmosphererelaxationaround
the largedipole created in the excitedstate.
1. Introduction
Recently, a new aspect of solvation dynamics of molecules which exhibit intramolecular electron transfer in their first excited state has been investigated [ 1,2 1. Time-resolved fluorescence as well as steady-state fluorescence techniques were employed to study the dynamics and energetics of “salt effect” on solvation. The probe molecule used was coumarin 15 3 (Cul53) with LiC104as a salt. It has been observed that in electrolytes solutions in solvents whose dielectric constant is low (diethyl ether, c,= 4.2; ethyl acetate, ~,=6; tetrahydrofuran (THF), es= 7.4) a new mode of solvation appears. The solvation salt effect was explained in terms of translational motions of the ionic species in solution. According to Bjerrum [ 31 and Fuoss and Kraus [4] electrolyte solutions in low dielectric constant solvents include mostly ion pairs even at comparatively low concentrations ( 10s4 M). The relaxation of the fluorescence Stokes shift of coumarin due to the presence of ions in solution was explained by us using the Debye-Falkenhagen theory (DF) [ 51 describing the relaxation of the ionic atmosphere around a central ion. The DF theory predicts that the ionic atmosphere relaxation time T will be proportional to rae,lA0C,
(1)
where t, is the dielectric constant, no is the equiva496
lent conductance at infinite dilution and C is the ion concentration. This equation refers to ion-ion interaction, while in low dielectric solvents, the interactions are mainly between the probe molecule (large dipole) and ion pairs (dipoles). In electrolyte solutions in low dielectric constant solvents we found that the relaxation rate measured by the Stokes shift was proportional to c,/A,C as predicted by the DF theory (eq. (1)). In this Letter we report on a study of the ionic relaxation around excited Cu 153 in two polar solvents with high dielectric constant containing LiClO,; propylene carbonate (PC), 5 = 65.1, and acetonitrile, ~~~37.5. The salt in PC using the Bjerrum criterion was calculated to be in the form of ions only, even in the highest salt concentration measured (0.6 M). Thus, such a solution represents the case of the iondipole interaction. In acetonitrile both ions and ionpairs exist in comparable amounts, and so ion-dipole as well as dipole-dipole interactions have to be considered, In this study we shall focus on the dynamics of the ionic relaxation and on the steady-state fluorescence band shift in solutions of different salt concentrations.
2. Experimental Transient fluorescence was detected using time correlated single-photon counting (TCSPC). As a
0009-2614/90/$ 03.50 0 1990 - Elsevier Science Publishers B.V. (North-Holland)
CHEMICAL PHYSICS LETTERS
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sample excitation source we used a cw mode-locked Nd/YAG-pumped dye laser (Coherent Nd/YAG Antares and a 702 dye laser) providing high repetition rate of short pulses ( 1 ps fwhm). The (TCSPC) detection system is based on a Hamamatsu, 1564U-05photomultiplier, Tennelec 864 TAC and 454 discriminator. An IBM personal computer was used as a multichannel analyzer, and for data storage and processing. The overall instrumental response at full width at half maximum was about 100 ps. Measurements were taken at 20 or 50 ns full scale. Steady-state fluorescence spectra were taken using a Perkin-Elmer spectrofluorimeter MPF-4. Coumarin 153 (Eastman Kodak), lithium perchlorate (Fluka), propylene carbonate (Fluka) and acetonitrile (Merck) were used without further purification.
3. Results and discussion 3.1. Conductance of LiCKI in propylene carbonate and acetonitrile Following Bjerrum [ 3 1, Fuoss and Kraus [ 41 introduced an ion-pair dissociation equilibrium constant K, i.e. for A- t B+=AB. From the equilibrium constant, the fraction of ions y= [A-] /Ccan be obtained. Calculations were done for acetonitrile in different concentrations and are presented in table 1. The ion fractions decrease from = 0.7 to 0.5 in the concentration range 0.06-o. 19 M. For PC, the calculations predict that no ion pairs are supposed to be formed even in the highest concentration used, i.e. 0.6 M LiClO+ These estimates Table 1 Ion fraction in LiClO,-acetonitrile solutions ‘I Concentration of salt (M)
Y= [A-l/C
0.06 0.09 0.13 0.19
0.729 0.664 0.604 0.537
*) The ion fraction was calculated according to Fuoss and Kraus [ 41, the ion pair radius was taken a’s5 A.The ion pair dissociation equilibrium constant was calculated to be &1.18x 10-l.
I9 October 1990
are supported by conductance measurements. The conductance of LiC104 in PC obeys the existence Kohlrausch law A=Ao -AC’/’ _
(2)
A is the equivalent conductance in cm2/R, A, is the equivalent conductance at infinite dilution, C is the salt concentration. The Kohlrausch law is expected to exist in solutions where the dissolved electrolyte forms 100% free ions. The coefficient A in eq. (2) can be estimated according to Debye Hiickel Onsager theory [ 6,7]. When ion pairs are formed the conductance decreases and the dependence on salt concentration is stronger than a square root behavior. In the case of acetonitrile there is a large decrease in the conductance at low concentration, pointing to the fact the ion pairing occurs. The equivalent conductance at infinite dilution can he estimated to be z 160 cm2/S2 in accordance with previous results [ 8,9 1. The conductance data confirms the existence of a large fraction of free ions in these solvents, this is in contrast to our previous study where ion pairs presence was dominant in the solution. 3.2. Steady-statefluorescence Steady-state fluorescence spectra of PC and acetonitrile solutions which include LiC104 at various concentrations are shown in fig. 1. In low dielectric constant solvents, the fluorescence band maximum of Cu 153 shifts to the red on adding salt and the maximum position converges at high concentrations to x 530 nm [ 1,2]. This phenomenon exists in PC and acetonitrile as well as in water, E,= 78.5, we have found J,,,,= 550 nm, with or without salt. In our previous paper we dealt with low dielectric constant solvents and correlated the salt concentration-dependent spectral shift of Cu153 with the increase in the solvent reorganization energy, (3) where hD is the change in the electric displacement, C,= l/c: - l/c:. t: is the contribution of the solvent to the static dielectric constant and e; is the total static dielectric constant of the electrolyte solution. The increase in e: as a function of salt concentra497
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153
coumorin
450
500
550
tion is attributed to the increase in salt ion-pair concentration (from the calculated concentration of ion pairs the dipole moment of an ion pair is x 10 D while that of ethyl acetate is 1.7 D) [ 10,111. In the current study where ion pairing is less significant, a comparison between the spectral energy shift and the Debye-Hiickel (DH) theory [ 61 is made. DH introduced the case of a central ion surrounded by an ionic atmosphere. The potential at the central ion due to its atmosphere can be derived from the Poisson equation. From the Debye-Htickel theory the potential energy CJof a single out ion +e whose finite diameter is a with respect to its surrounding is
I
I
600
650
where 1/K is a characteristic length of the ionic atmosphere in which the charge density is reduced to l/e of its value at the origin. At very large concentrations, we obtain an asymptotic value for the potential energy which is independent of the salt concentration,
700
k(nml
)
I
I
I
I23
400
I
I
coumorin
153 LX104
ocetoniirile
500
600
U= -e2/t,a
7
x(nm) Fig. 1.(a) Steady-state emission spectra of coumarin 153 in PC: (I)nosalt;(2)0.18MLiCIO,:(3)0.6MLiCIO,.(b)Steadystate emission spe4h-a of coumarin 1.53 in acetonitrile: (1) no salt; (2) 0.06 M LiClO,; (3) 0.2 M LiClO,.
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_
(5)
In our case, instead of a central ion, a coumarin molecule approximated as a dipole is turned on by a photon excitation to its lowest excited electronic state. However, as a crude approximation, we compare the spectral energy shift to the Debye-Hiickel expression U, eq. (4). For the calculation the radius of the central ion was estimated to be 3-5 A. Our main purpose here is to correlate the calculated ionic atmosphere energy at the probe of eq. (4) with the experimental steady-state band shift. As will be shown in section 3.3 the ionic relaxation process is relatively slow and the relaxation time is comparable to the radiative lifetime of the coumarin. The observed steady-state fluorescence band shift due to the presence of the ions in solution does not assume its full value since the molecules relax to the ground state while the relaxation of the ionic atmosphere is not yet accomplished. In our previous study [ 1,2] we develop a procedure to estimate the steady-state fluorescence band position for a totally relaxed ionic atmosphere. In table 2, the relevant data for the corrected steady-state fluorescence of LiClO, in PC and ace-
19 October 1990
CHEMICAL PHYSICS LETTERS
Volume 173, number 5,6 Table 2 Salt effect on steady-state fluorescence Stokes shift Solvent
PC
acetonitrile
LiClO, concentration (M)
&9x (cm-’ )
Amaxa) (cm-‘)
l/ICb’ (A)
u C’ (cm-‘)
a=5A
a=3A
0 0.18 0.6
19268 19157 18797
-524 - 1014
6.52 3.57
-153 -205
-185 -268
0 0.06 0.19
19305 19120 I8868
-524 - 769
8.85 4.85
-221 -310
-258 -389
I) Corrected spectral shift, see text. b, Ionic atmosphere radius. =) Energy shift according to Debye and Hiickel theory, [ I 11, eq. (4)
tonitrile is given. Only a qualitative agreement is obtained between the experimental energy shii A,, and the calculated potential energy at an ionic probe molecule due to the existence of an ionic atmosphere. The explanation to the deviations might be a result of the fact that the DH theory was derived for spherical ions with Coulombic forces. It does not apply to the case of dipole-ion or dipole-dipole interactions. Specific interactions of the ions with either the coumarin or with the other ions as well as solvent-ion interaction effects are not included. Dielectric saturation in the close vicinity of the ions decreases the effective short range dielectric constant, and hence increases the potential energy. This phenomenon might explain that the experimental solvation energy is larger than the calculated one. With all the above limitations in mind a qualitative trend of the increase in the ionic atmosphere energy difference when adding salt comes out of this model, as well as the upper limit of this energy, which appears in our spectrum as a convergence of the spectra at higher concentrations_ The maximum value of the band shift for PC is calculated from eq. (5 ) to be 535 nm. The experimental A,, shows a shift to 547 mm, closer to the shift in water. For acetonitrile, the calculated value 547 nm, cannot be achieved experimentally because of salt solubility limitations. 3.3. Time-resolved measurements In the case of Cu 153 the Stokes shift dynamics is quantitatively described by C(t), the normalized
spectral shift correlation function, C(t)=
h-(t) - Vf(m) h(O) - Vf(o3) ’
(6)
where vf( t), vf(oo) and yf(0) are the fluorescence frequencies at time t, 00 and 0. The C(t) function was both experimentally and theoretically related to the longitudinal relaxation time tL [ 12-22 1, (7)
where em and cJ are the dielectric constants at high and low frequencies, respectively, and ?D is the dielectric relaxation time. Barbara and co-workers [ 15] suggested a useful time saving procedure to find a single characteristic wavelength where the fluorescence decay profile represents the relaxation of the C(t) function. In Cul53 the characteristic wavelength was found to be at 460 nm. Plots of the time-resolved fluorescence curves of Cu153 at 460 nm in PC and acetonitrile solutions with different concentrations of LiC104 are given in fig. 2. Data analysis with a three-exponential fitting procedure was performed. The shortest relaxation component, TV,corresponds to the solvent orientational relaxation, the next one, 72, is attributed to the salt effect relaxation and the last one is related to the radiative decay of the relaxed upper polar state to the ground state. The first relaxation is very fast (a few picosecond) and could not be time resolved with our experimen499
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CHEMICAL PHYSICS LETTERS
19 October 1990
ACETONITRILE
- LiClO4
Fig. 2. (a) Time-resolved luminescence of coumarin 153 in PC containing LiClO, at 460 nm. The fluorescence intensity is on a log scale. Salt concentrations (from top to bottom) are: no salt, 0.06 M, 0.3 M, 0.6 M. (b) Time-resolved luminescence of coumarin 153 in acetonitrile containing LiClO, at 460 nm. The fluorescence intensity is on a log scale. Salt concentrations (from top to bottom) are: no salt,0.06M,0.09M,0.13M,0.2M. Table 3 Coumarin 153, ionic relaxation time LiClO, concentration (M)
Viscosity 20°C (cP)
Relaxation time (ns)
PC (c,=65.1)
0 0.06 0.18 0.3 0.6
2.78 2.9 a’ 3.02 ” 3.25 a’ 4.55
37.1 12.3 7.7 5.9
4.44 1.54 1.00 0.70
acetonitrile (c,=37.5)
0 0.06 0.09 0.13 0.2
0.39 0.4 n’ 0.41 ‘) 0.41 a) 0.42
11.75 7.7 6.05 4.4
0.62 0.46 0.33 0.23
Solvent
7m
b’
(ns)
‘) Extrapolated. ‘) Calculated using eq. (9) with the measured conductance results.
tal system. Although the solvent orientational relaxation component cannot be resolved in time, the apparent amplitude of this component in the fluorescence curves is w 0.05. If one deconvolute the apparatus time response then the amplitude of the short life time component increases to x0.4. The third component r3, the radiative decay, was measured at longer wavelengths (650 nm). The radiative decay time measured at 650 nm was found to be 5.7 ns for pure PC and 5.3 ns for 0.6 M LiC104 in PC, showing a very small quenching effect. For acetonitrile the radiative decay time was 5.4 500
ns in pure solvent and 5.3 ns in 0.2 M LiC104 solution. In order to get the net ionic relaxation rate from the second simulated component r~‘, the radiative rate ~7’ was subtracted,
The ionic relaxation time, 72, at various salt concentrations in PC and acetonitrile are given in table 3. Included also are viscosity measurements taken at 20°C. We have compared the salt-induced relaxation phenomenon and the Debye-Falkenhagen (DF)
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CHEMICAL PHYSICS LETTERS
theory [ 5 1. The DF theory for frequency dependence electrolyte solution conductivity [9] estimates the relaxation time for the ionic atmosphere to appear or disappear. The ionic atmosphere relaxation time ?DFis given by z: 25 15.3x Io-s TDF= Z:n_ +Z?A+ kTqrC2 ’
(9)
where, for 1: 1 electrolyte (LiClO.+) q=O.5, and l/x is the ionic atmosphere radius. Calculations according to the above equation, taking into account the results of the conductance measurement described before, reveals that the measured ionic relaxation r2 is longer than zDFby a factor of x 5 for PC and by a factor of x 18 in acetonitrile. The same trend was found also for lower dielectric solvents [ 1,21. Those results are also given in table 3. Plots of log( ~~2)and 10g(TDF)versus log (c,q/C) are given in fig. 3. The best correspondence between ‘IDFand the experimental results r, for PC hinting is that when the salt in a solution is completely ionized (ion pairs do not exist in PC) its resemblance to DF theory is more pronounced. Acetonitrile as mentioned before is partially in the form of ion pairs and the correspondence to DF theory is worse. However, both solvents, as well as the low dielectric solvents studied before, show a linear dependence on the EJ/C quantity which is introduced in the DF theory. The large difference in the actual relaxation rate shows that the use of DF theory is inadequate for the quantitative description of the ionic relaxation in solvation dynamics of large dipoles like Cul53 used in this study.
4. Conclusions Steady-state fluorescence emission, as well as dynamic measurements of Cu15 3 in electrolyte solutions of solvents with high dielectric constant reveals the existence of a new relaxation in accordance with previous results for low dielectric constant solvents. This relaxation is attributed to the ionic atmosphere rearrangement around the central Cul53 dipole suddenly increased due to an electronic excitation by a photon. The ionic species motion is basically translational and includes free ions as well as ion pairs, both ex-
I
1.0-b
I
I
I
,
c
vr c T
,“.,“I/< ACETONITRILE
r, 0.4tf ol 2
L1C104
0.2-
I
I
18
20
I
I
22
I
I
24
Fig. 3. (a) Plot of log of the observed electrolyte relaxation rate (I) and the calculated rate (---) versus q/C on log-log scale in PC. It includes also (---) the DF calculations (eq. (9)) with I&,= 32.9 cm’/R. (b) Plot of the observed electrolyte relaxation rate (m) and the calculated rate (- --) versus t,q/C, on a log-log scale, in acetonitrile.
isting in electrolyte solution of solvents with high dielectric constant, while in the case of low dielectric solvents only ion pairs exist. According to the Debye-Falkenhagen relaxation theory (eq. ( 1) ), the relaxation time was found to depend linearly on the following quantities: the dielectric constant, the viscosity (or the inverse of the conductance) and the inverse of the concentration. This relation was found experimentally for high dielectric solvents as well as for low ones [ 1,2]. How501
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ever, the exact calculations show a difference of a factor of 5-50 between the experimental ionic relaxation and DF theory predictions. Using the Debye-Hiickel theory, we have qualitatively correlated the experimental steady-stale fluorescence band shift with the potential energy due to the ionic atmosphere at the coumarin origin. At high salt concentrations, the theory also predicts the convergence of the red-band-shift to a certain limit as was found experimentally.
Acknowledgement We are grateful to Professor E.M. Kosower and Professor Y. Klafter for discussions and suggestions. This work is supported in part by the James Franck Binational German-Israel Program in Laser Matter Interaction.
References [ 1] D. Huppert, V. Ittahand E.M. Kosower, Chem. Phys. Letters 159 (1989) 267.
[ 21 D. Huppert and V. Ittah, in: Perspectives in photosynthesis, eds. J. Jortner and B. Pullman (Kluwer, Dordrecht, 1990) pp. 301-316. [ 31 N. Bjerrum, Kgl. Danske Vidensk. Selskab. Skr. 7 (1926) [4] k.M. Fuoss and C.A. Kraus, J. Am. Chem. Sot. 55 (1933) 1019,2387. [5] P. Debye and H. Falkenhagen, Physik. Z. 29 (1928) 121, 401. [6] P. Debye and E. Hiickel, Physik. Z. 24 (1923) 185. [ 71 L. Onsager, Physik. Z. 28 ( 1927) 277.
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[ 81 R.A. Robinson and R.H. Stokes, in: Electrolyte solutions (Butterworths, London, 1959). [ 91 L.M. Mukhejee and D.P. Boden, J. Phys. Chem. 73 ( 1969) 3965; J. Padova, in: Modem aspects of electrochemistry, Vol. 7, eds. B.E. Conway and J.O’M. Bockris (Plenum Press, New York, 1974) ch. 1; F. Accassina, G. Pistoria and S. Schiavo, Ric. Sei. 36 ( 1966) 560. [ IO]J.C. Lestrade, J.P. Badialli and H. Chachet, Dielectric and related molecular processes, Vol. 2 (Chem. Sot., London, 1975) ch. 3. [ I 1] T. Sigvartsen, B. Gestblom, E. Noreland and J. Songstad, Acta Chim. Stand. 43 (1989) 103. [ 121M. Maroncelli and G.R. Fleming, J. Chem. Phys. 86 ( 1987) 6221; 89 (1988) 875; B. Bagchi, Ann. Rev. Phys. Chem. 40 ( 1989) 115. [ 131F. Heisel and J.A. Miehe, Chem. Phys. Letters 128 ( 1986) 323. [ 141E.M. Kosower and D. Huppert, Chem. Phys. Letters 96 (1983) 433. [ 151V. Nagarajan, A.M. Brearley, T.J. Kang and P.F. Barbara, J. Phys. Chem. 91 (1987) 6452; M.A. Kahlor, W. Jazeba, T.J. King and P.F. Barbara, J. Chem. Phys. 90 (1989) 151. [ 161S.G. Su and J.D. Simon, J. Phys. Chem. 93 (1989) 753. [ 171P.G. Wolynes, J. Chem. Phys. 86 (1987) 5133. [ 181J. Rips,J. Klafter and J. Jortner, J. Chem. Phys. 88 ( 1988) 3246. [ 191H. Sumi and R.A. Marcus, J. Chem. Phys. 84 ( 1986) 4894. [20] Y.J. Yan, M. Sparaghone and S. Mukamel, J. Chem. Phys. 87 (1987) 5840. [21] M.D. Newton and H.L. Friedman, J. Chem. Phys. 88 ( 1988) 4460. [22] A.I. Burshtein and G. Kofman, Chem. Phys. 40 (1979) 289; 8.1. Yakobson and A.I. Burshtein, Chem. Phys. 49 ( 1980) 385; A.I. Burshtein, I.V. Khudyakov and B.I. Yakobson, Progr. React. Kinetics 13 (1984) 221.
CHEMICAL PHYSICS LETTERS
19 October 1990
Static and dynamic electrolyte effects on excited large dipole solvation: high dielectric constant solvents V. Ittah and D. Huppert Raymond and Beverly Sackler, Faculty of Exact Sciences, School ojChemistry,
Tel-Aviv University, Ramat Aviv 69978, Israel
Received 4 June 1990;in final form I3 August 1990
We report on an increase in the steady-state fluorescence Stokes shift of coumarin 153when LiCI04 is added to polar solvents. A new relaxation process is observedin the presence of the electrolyte which is related to the ionic atmosphererelaxationaround
the largedipole created in the excitedstate.
1. Introduction
Recently, a new aspect of solvation dynamics of molecules which exhibit intramolecular electron transfer in their first excited state has been investigated [ 1,2 1. Time-resolved fluorescence as well as steady-state fluorescence techniques were employed to study the dynamics and energetics of “salt effect” on solvation. The probe molecule used was coumarin 15 3 (Cul53) with LiC104as a salt. It has been observed that in electrolytes solutions in solvents whose dielectric constant is low (diethyl ether, c,= 4.2; ethyl acetate, ~,=6; tetrahydrofuran (THF), es= 7.4) a new mode of solvation appears. The solvation salt effect was explained in terms of translational motions of the ionic species in solution. According to Bjerrum [ 31 and Fuoss and Kraus [4] electrolyte solutions in low dielectric constant solvents include mostly ion pairs even at comparatively low concentrations ( 10s4 M). The relaxation of the fluorescence Stokes shift of coumarin due to the presence of ions in solution was explained by us using the Debye-Falkenhagen theory (DF) [ 51 describing the relaxation of the ionic atmosphere around a central ion. The DF theory predicts that the ionic atmosphere relaxation time T will be proportional to rae,lA0C,
(1)
where t, is the dielectric constant, no is the equiva496
lent conductance at infinite dilution and C is the ion concentration. This equation refers to ion-ion interaction, while in low dielectric solvents, the interactions are mainly between the probe molecule (large dipole) and ion pairs (dipoles). In electrolyte solutions in low dielectric constant solvents we found that the relaxation rate measured by the Stokes shift was proportional to c,/A,C as predicted by the DF theory (eq. (1)). In this Letter we report on a study of the ionic relaxation around excited Cu 153 in two polar solvents with high dielectric constant containing LiClO,; propylene carbonate (PC), 5 = 65.1, and acetonitrile, ~~~37.5. The salt in PC using the Bjerrum criterion was calculated to be in the form of ions only, even in the highest salt concentration measured (0.6 M). Thus, such a solution represents the case of the iondipole interaction. In acetonitrile both ions and ionpairs exist in comparable amounts, and so ion-dipole as well as dipole-dipole interactions have to be considered, In this study we shall focus on the dynamics of the ionic relaxation and on the steady-state fluorescence band shift in solutions of different salt concentrations.
2. Experimental Transient fluorescence was detected using time correlated single-photon counting (TCSPC). As a
0009-2614/90/$ 03.50 0 1990 - Elsevier Science Publishers B.V. (North-Holland)
CHEMICAL PHYSICS LETTERS
Volume 173, number $6
sample excitation source we used a cw mode-locked Nd/YAG-pumped dye laser (Coherent Nd/YAG Antares and a 702 dye laser) providing high repetition rate of short pulses ( 1 ps fwhm). The (TCSPC) detection system is based on a Hamamatsu, 1564U-05photomultiplier, Tennelec 864 TAC and 454 discriminator. An IBM personal computer was used as a multichannel analyzer, and for data storage and processing. The overall instrumental response at full width at half maximum was about 100 ps. Measurements were taken at 20 or 50 ns full scale. Steady-state fluorescence spectra were taken using a Perkin-Elmer spectrofluorimeter MPF-4. Coumarin 153 (Eastman Kodak), lithium perchlorate (Fluka), propylene carbonate (Fluka) and acetonitrile (Merck) were used without further purification.
3. Results and discussion 3.1. Conductance of LiCKI in propylene carbonate and acetonitrile Following Bjerrum [ 3 1, Fuoss and Kraus [ 41 introduced an ion-pair dissociation equilibrium constant K, i.e. for A- t B+=AB. From the equilibrium constant, the fraction of ions y= [A-] /Ccan be obtained. Calculations were done for acetonitrile in different concentrations and are presented in table 1. The ion fractions decrease from = 0.7 to 0.5 in the concentration range 0.06-o. 19 M. For PC, the calculations predict that no ion pairs are supposed to be formed even in the highest concentration used, i.e. 0.6 M LiClO+ These estimates Table 1 Ion fraction in LiClO,-acetonitrile solutions ‘I Concentration of salt (M)
Y= [A-l/C
0.06 0.09 0.13 0.19
0.729 0.664 0.604 0.537
*) The ion fraction was calculated according to Fuoss and Kraus [ 41, the ion pair radius was taken a’s5 A.The ion pair dissociation equilibrium constant was calculated to be &1.18x 10-l.
I9 October 1990
are supported by conductance measurements. The conductance of LiC104 in PC obeys the existence Kohlrausch law A=Ao -AC’/’ _
(2)
A is the equivalent conductance in cm2/R, A, is the equivalent conductance at infinite dilution, C is the salt concentration. The Kohlrausch law is expected to exist in solutions where the dissolved electrolyte forms 100% free ions. The coefficient A in eq. (2) can be estimated according to Debye Hiickel Onsager theory [ 6,7]. When ion pairs are formed the conductance decreases and the dependence on salt concentration is stronger than a square root behavior. In the case of acetonitrile there is a large decrease in the conductance at low concentration, pointing to the fact the ion pairing occurs. The equivalent conductance at infinite dilution can he estimated to be z 160 cm2/S2 in accordance with previous results [ 8,9 1. The conductance data confirms the existence of a large fraction of free ions in these solvents, this is in contrast to our previous study where ion pairs presence was dominant in the solution. 3.2. Steady-statefluorescence Steady-state fluorescence spectra of PC and acetonitrile solutions which include LiC104 at various concentrations are shown in fig. 1. In low dielectric constant solvents, the fluorescence band maximum of Cu 153 shifts to the red on adding salt and the maximum position converges at high concentrations to x 530 nm [ 1,2]. This phenomenon exists in PC and acetonitrile as well as in water, E,= 78.5, we have found J,,,,= 550 nm, with or without salt. In our previous paper we dealt with low dielectric constant solvents and correlated the salt concentration-dependent spectral shift of Cu153 with the increase in the solvent reorganization energy, (3) where hD is the change in the electric displacement, C,= l/c: - l/c:. t: is the contribution of the solvent to the static dielectric constant and e; is the total static dielectric constant of the electrolyte solution. The increase in e: as a function of salt concentra497
Volume 173, number $6
a
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CHEMICAL PHYSICS LETTERS
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153
coumorin
450
500
550
tion is attributed to the increase in salt ion-pair concentration (from the calculated concentration of ion pairs the dipole moment of an ion pair is x 10 D while that of ethyl acetate is 1.7 D) [ 10,111. In the current study where ion pairing is less significant, a comparison between the spectral energy shift and the Debye-Hiickel (DH) theory [ 61 is made. DH introduced the case of a central ion surrounded by an ionic atmosphere. The potential at the central ion due to its atmosphere can be derived from the Poisson equation. From the Debye-Htickel theory the potential energy CJof a single out ion +e whose finite diameter is a with respect to its surrounding is
I
I
600
650
where 1/K is a characteristic length of the ionic atmosphere in which the charge density is reduced to l/e of its value at the origin. At very large concentrations, we obtain an asymptotic value for the potential energy which is independent of the salt concentration,
700
k(nml
)
I
I
I
I23
400
I
I
coumorin
153 LX104
ocetoniirile
500
600
U= -e2/t,a
7
x(nm) Fig. 1.(a) Steady-state emission spectra of coumarin 153 in PC: (I)nosalt;(2)0.18MLiCIO,:(3)0.6MLiCIO,.(b)Steadystate emission spe4h-a of coumarin 1.53 in acetonitrile: (1) no salt; (2) 0.06 M LiClO,; (3) 0.2 M LiClO,.
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_
(5)
In our case, instead of a central ion, a coumarin molecule approximated as a dipole is turned on by a photon excitation to its lowest excited electronic state. However, as a crude approximation, we compare the spectral energy shift to the Debye-Hiickel expression U, eq. (4). For the calculation the radius of the central ion was estimated to be 3-5 A. Our main purpose here is to correlate the calculated ionic atmosphere energy at the probe of eq. (4) with the experimental steady-state band shift. As will be shown in section 3.3 the ionic relaxation process is relatively slow and the relaxation time is comparable to the radiative lifetime of the coumarin. The observed steady-state fluorescence band shift due to the presence of the ions in solution does not assume its full value since the molecules relax to the ground state while the relaxation of the ionic atmosphere is not yet accomplished. In our previous study [ 1,2] we develop a procedure to estimate the steady-state fluorescence band position for a totally relaxed ionic atmosphere. In table 2, the relevant data for the corrected steady-state fluorescence of LiClO, in PC and ace-
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Volume 173, number 5,6 Table 2 Salt effect on steady-state fluorescence Stokes shift Solvent
PC
acetonitrile
LiClO, concentration (M)
&9x (cm-’ )
Amaxa) (cm-‘)
l/ICb’ (A)
u C’ (cm-‘)
a=5A
a=3A
0 0.18 0.6
19268 19157 18797
-524 - 1014
6.52 3.57
-153 -205
-185 -268
0 0.06 0.19
19305 19120 I8868
-524 - 769
8.85 4.85
-221 -310
-258 -389
I) Corrected spectral shift, see text. b, Ionic atmosphere radius. =) Energy shift according to Debye and Hiickel theory, [ I 11, eq. (4)
tonitrile is given. Only a qualitative agreement is obtained between the experimental energy shii A,, and the calculated potential energy at an ionic probe molecule due to the existence of an ionic atmosphere. The explanation to the deviations might be a result of the fact that the DH theory was derived for spherical ions with Coulombic forces. It does not apply to the case of dipole-ion or dipole-dipole interactions. Specific interactions of the ions with either the coumarin or with the other ions as well as solvent-ion interaction effects are not included. Dielectric saturation in the close vicinity of the ions decreases the effective short range dielectric constant, and hence increases the potential energy. This phenomenon might explain that the experimental solvation energy is larger than the calculated one. With all the above limitations in mind a qualitative trend of the increase in the ionic atmosphere energy difference when adding salt comes out of this model, as well as the upper limit of this energy, which appears in our spectrum as a convergence of the spectra at higher concentrations_ The maximum value of the band shift for PC is calculated from eq. (5 ) to be 535 nm. The experimental A,, shows a shift to 547 mm, closer to the shift in water. For acetonitrile, the calculated value 547 nm, cannot be achieved experimentally because of salt solubility limitations. 3.3. Time-resolved measurements In the case of Cu 153 the Stokes shift dynamics is quantitatively described by C(t), the normalized
spectral shift correlation function, C(t)=
h-(t) - Vf(m) h(O) - Vf(o3) ’
(6)
where vf( t), vf(oo) and yf(0) are the fluorescence frequencies at time t, 00 and 0. The C(t) function was both experimentally and theoretically related to the longitudinal relaxation time tL [ 12-22 1, (7)
where em and cJ are the dielectric constants at high and low frequencies, respectively, and ?D is the dielectric relaxation time. Barbara and co-workers [ 15] suggested a useful time saving procedure to find a single characteristic wavelength where the fluorescence decay profile represents the relaxation of the C(t) function. In Cul53 the characteristic wavelength was found to be at 460 nm. Plots of the time-resolved fluorescence curves of Cu153 at 460 nm in PC and acetonitrile solutions with different concentrations of LiC104 are given in fig. 2. Data analysis with a three-exponential fitting procedure was performed. The shortest relaxation component, TV,corresponds to the solvent orientational relaxation, the next one, 72, is attributed to the salt effect relaxation and the last one is related to the radiative decay of the relaxed upper polar state to the ground state. The first relaxation is very fast (a few picosecond) and could not be time resolved with our experimen499
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ACETONITRILE
- LiClO4
Fig. 2. (a) Time-resolved luminescence of coumarin 153 in PC containing LiClO, at 460 nm. The fluorescence intensity is on a log scale. Salt concentrations (from top to bottom) are: no salt, 0.06 M, 0.3 M, 0.6 M. (b) Time-resolved luminescence of coumarin 153 in acetonitrile containing LiClO, at 460 nm. The fluorescence intensity is on a log scale. Salt concentrations (from top to bottom) are: no salt,0.06M,0.09M,0.13M,0.2M. Table 3 Coumarin 153, ionic relaxation time LiClO, concentration (M)
Viscosity 20°C (cP)
Relaxation time (ns)
PC (c,=65.1)
0 0.06 0.18 0.3 0.6
2.78 2.9 a’ 3.02 ” 3.25 a’ 4.55
37.1 12.3 7.7 5.9
4.44 1.54 1.00 0.70
acetonitrile (c,=37.5)
0 0.06 0.09 0.13 0.2
0.39 0.4 n’ 0.41 ‘) 0.41 a) 0.42
11.75 7.7 6.05 4.4
0.62 0.46 0.33 0.23
Solvent
7m
b’
(ns)
‘) Extrapolated. ‘) Calculated using eq. (9) with the measured conductance results.
tal system. Although the solvent orientational relaxation component cannot be resolved in time, the apparent amplitude of this component in the fluorescence curves is w 0.05. If one deconvolute the apparatus time response then the amplitude of the short life time component increases to x0.4. The third component r3, the radiative decay, was measured at longer wavelengths (650 nm). The radiative decay time measured at 650 nm was found to be 5.7 ns for pure PC and 5.3 ns for 0.6 M LiC104 in PC, showing a very small quenching effect. For acetonitrile the radiative decay time was 5.4 500
ns in pure solvent and 5.3 ns in 0.2 M LiC104 solution. In order to get the net ionic relaxation rate from the second simulated component r~‘, the radiative rate ~7’ was subtracted,
The ionic relaxation time, 72, at various salt concentrations in PC and acetonitrile are given in table 3. Included also are viscosity measurements taken at 20°C. We have compared the salt-induced relaxation phenomenon and the Debye-Falkenhagen (DF)
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CHEMICAL PHYSICS LETTERS
theory [ 5 1. The DF theory for frequency dependence electrolyte solution conductivity [9] estimates the relaxation time for the ionic atmosphere to appear or disappear. The ionic atmosphere relaxation time ?DFis given by z: 25 15.3x Io-s TDF= Z:n_ +Z?A+ kTqrC2 ’
(9)
where, for 1: 1 electrolyte (LiClO.+) q=O.5, and l/x is the ionic atmosphere radius. Calculations according to the above equation, taking into account the results of the conductance measurement described before, reveals that the measured ionic relaxation r2 is longer than zDFby a factor of x 5 for PC and by a factor of x 18 in acetonitrile. The same trend was found also for lower dielectric solvents [ 1,21. Those results are also given in table 3. Plots of log( ~~2)and 10g(TDF)versus log (c,q/C) are given in fig. 3. The best correspondence between ‘IDFand the experimental results r, for PC hinting is that when the salt in a solution is completely ionized (ion pairs do not exist in PC) its resemblance to DF theory is more pronounced. Acetonitrile as mentioned before is partially in the form of ion pairs and the correspondence to DF theory is worse. However, both solvents, as well as the low dielectric solvents studied before, show a linear dependence on the EJ/C quantity which is introduced in the DF theory. The large difference in the actual relaxation rate shows that the use of DF theory is inadequate for the quantitative description of the ionic relaxation in solvation dynamics of large dipoles like Cul53 used in this study.
4. Conclusions Steady-state fluorescence emission, as well as dynamic measurements of Cu15 3 in electrolyte solutions of solvents with high dielectric constant reveals the existence of a new relaxation in accordance with previous results for low dielectric constant solvents. This relaxation is attributed to the ionic atmosphere rearrangement around the central Cul53 dipole suddenly increased due to an electronic excitation by a photon. The ionic species motion is basically translational and includes free ions as well as ion pairs, both ex-
I
1.0-b
I
I
I
,
c
vr c T
,“.,“I/< ACETONITRILE
r, 0.4tf ol 2
L1C104
0.2-
I
I
18
20
I
I
22
I
I
24
Fig. 3. (a) Plot of log of the observed electrolyte relaxation rate (I) and the calculated rate (---) versus q/C on log-log scale in PC. It includes also (---) the DF calculations (eq. (9)) with I&,= 32.9 cm’/R. (b) Plot of the observed electrolyte relaxation rate (m) and the calculated rate (- --) versus t,q/C, on a log-log scale, in acetonitrile.
isting in electrolyte solution of solvents with high dielectric constant, while in the case of low dielectric solvents only ion pairs exist. According to the Debye-Falkenhagen relaxation theory (eq. ( 1) ), the relaxation time was found to depend linearly on the following quantities: the dielectric constant, the viscosity (or the inverse of the conductance) and the inverse of the concentration. This relation was found experimentally for high dielectric solvents as well as for low ones [ 1,2]. How501
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ever, the exact calculations show a difference of a factor of 5-50 between the experimental ionic relaxation and DF theory predictions. Using the Debye-Hiickel theory, we have qualitatively correlated the experimental steady-stale fluorescence band shift with the potential energy due to the ionic atmosphere at the coumarin origin. At high salt concentrations, the theory also predicts the convergence of the red-band-shift to a certain limit as was found experimentally.
Acknowledgement We are grateful to Professor E.M. Kosower and Professor Y. Klafter for discussions and suggestions. This work is supported in part by the James Franck Binational German-Israel Program in Laser Matter Interaction.
References [ 1] D. Huppert, V. Ittahand E.M. Kosower, Chem. Phys. Letters 159 (1989) 267.
[ 21 D. Huppert and V. Ittah, in: Perspectives in photosynthesis, eds. J. Jortner and B. Pullman (Kluwer, Dordrecht, 1990) pp. 301-316. [ 31 N. Bjerrum, Kgl. Danske Vidensk. Selskab. Skr. 7 (1926) [4] k.M. Fuoss and C.A. Kraus, J. Am. Chem. Sot. 55 (1933) 1019,2387. [5] P. Debye and H. Falkenhagen, Physik. Z. 29 (1928) 121, 401. [6] P. Debye and E. Hiickel, Physik. Z. 24 (1923) 185. [ 71 L. Onsager, Physik. Z. 28 ( 1927) 277.
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[ 81 R.A. Robinson and R.H. Stokes, in: Electrolyte solutions (Butterworths, London, 1959). [ 91 L.M. Mukhejee and D.P. Boden, J. Phys. Chem. 73 ( 1969) 3965; J. Padova, in: Modem aspects of electrochemistry, Vol. 7, eds. B.E. Conway and J.O’M. Bockris (Plenum Press, New York, 1974) ch. 1; F. Accassina, G. Pistoria and S. Schiavo, Ric. Sei. 36 ( 1966) 560. [ IO]J.C. Lestrade, J.P. Badialli and H. Chachet, Dielectric and related molecular processes, Vol. 2 (Chem. Sot., London, 1975) ch. 3. [ I 1] T. Sigvartsen, B. Gestblom, E. Noreland and J. Songstad, Acta Chim. Stand. 43 (1989) 103. [ 121M. Maroncelli and G.R. Fleming, J. Chem. Phys. 86 ( 1987) 6221; 89 (1988) 875; B. Bagchi, Ann. Rev. Phys. Chem. 40 ( 1989) 115. [ 131F. Heisel and J.A. Miehe, Chem. Phys. Letters 128 ( 1986) 323. [ 141E.M. Kosower and D. Huppert, Chem. Phys. Letters 96 (1983) 433. [ 151V. Nagarajan, A.M. Brearley, T.J. Kang and P.F. Barbara, J. Phys. Chem. 91 (1987) 6452; M.A. Kahlor, W. Jazeba, T.J. King and P.F. Barbara, J. Chem. Phys. 90 (1989) 151. [ 161S.G. Su and J.D. Simon, J. Phys. Chem. 93 (1989) 753. [ 171P.G. Wolynes, J. Chem. Phys. 86 (1987) 5133. [ 181J. Rips,J. Klafter and J. Jortner, J. Chem. Phys. 88 ( 1988) 3246. [ 191H. Sumi and R.A. Marcus, J. Chem. Phys. 84 ( 1986) 4894. [20] Y.J. Yan, M. Sparaghone and S. Mukamel, J. Chem. Phys. 87 (1987) 5840. [21] M.D. Newton and H.L. Friedman, J. Chem. Phys. 88 ( 1988) 4460. [22] A.I. Burshtein and G. Kofman, Chem. Phys. 40 (1979) 289; 8.1. Yakobson and A.I. Burshtein, Chem. Phys. 49 ( 1980) 385; A.I. Burshtein, I.V. Khudyakov and B.I. Yakobson, Progr. React. Kinetics 13 (1984) 221.