Reaction between Diiodide Anion Radicals in Ionic Liquids - The

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Reaction between Diiodide Anion Radicals in Ionic Liquids† Kenji Takahashi,* Shingo Sakai, Hiroaki Tezuka, and Yusuke Hiejima DiVision of Material Science, Graduate School of Natural Science and Technology, Kanazawa UniVersity, Kanazawa 920-1192, Japan

Yosuke Katsumura Department of Nuclear Engineering and Management, School of Engineering, The UniVersity of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan

Masayoshi Watanabe Department of Chemistry and Biotechnology, Yokohama National UniVersity, 79-5 Tokiwadai, Yokohama 240-8501, Japan ReceiVed: October 30, 2006; In Final Form: December 21, 2006

Photodetachment of electrons from iodide ions produced diiodide anion radicals in ionic liquids containing ammonium, pyrrolidinium, and piperidinium cations. The rates of reaction between diiodide anion radicals in molecular solvents such as H2O, methanol, and ethanol could be estimated by the Debye-Smoluchowski equation, which accounts for electrostatic interactions using dielectric constants for the molecular solvents. In contrast, the rates of reaction between diiodide anion radicals in the ionic liquids were close to the diffusionlimited rates for the neutral molecules, suggesting that electrostatic repulsion between the diiodide anion radicals is weakened by Coulombic shielding in the ionic liquids.

Introduction Because of their unique properties and potential for practical applications, ionic liquids have generated considerable research interest in recent years. One application of ionic liquids is in electrochemical devices, such as electric double-layer capacitors,1 lithium batteries,2 fuel cells,3 and dye-sensitized solar cells (DSSCs).4,5 In DSSCs, a photo-oxidized dye molecule must be reduced by a redox couple. The I-/I3- redox couple has been used for this purpose and plays an important role in charge transfer in DSSCs. The diffusion of ions in ionic liquids is generally slow because of the high viscosity of ionic liquids, and this is a disadvantage when an ionic liquid is used as an electrolyte. Recently, using an ultramicroelectrode technique, one of us reported that, in the I-/I3- redox couple system, a Grotthuss-like charge exchange might contribute to charge transfer in 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide.6,7 It is considered that the charge exchange reaction occurs by the following process:7

I- + I3- f I-‚‚‚I2‚‚‚I- f I3- + ITo have this type of charge exchange take place, I- and I3must be in close proximity. However, the close approach of Iand I3- is hindered in a molecular solvent because of Coulombic repulsion between the two ions. On the other hand, the ions of an ionic liquid may weaken the electrostatic repulsion by Coulombic shielding, allowing I- and I3- to approach each other quite easily. Here, we examine the reaction between diiodide †

Part of the special issue “Physical Chemistry of Ionic Liquids”. * Corresponding author. E-mail: [email protected].

anion radicals (I2-). We expected that if Coulombic shielding weakens the electrostatic repulsion between I2- anion radicals, the diiodide anion radicals would approach each other easily, and reaction would proceed readily. Recently, Zistler et al. suggested a similar possibility in a study of the non-Stokesian transport of triiodide in ionic liquids.8 Previously, the effect of Coulombic shielding on reaction rate has been studied as a kinetic salt effect.9 Previous theories for both diffusion-controlled reactions and activation-controlled reactions are based on the Debye-Hu¨ckel theory. Hence the applicable range of ion concentration is limited to about 0.01 mol/L. In contrast, the concentrations of ionic liquids may be in the range of about 2 to 5 mol/L. Therefore ionic reactions under such high ionic strength conditions are of interest. Several studies of the solvation dynamics10-15 and reaction kinetics16-24 in ionic liquids have been reported. However, only a few studies of ionic reactions in ionic liquids have been carried out. In molecular solvents, the kinetic salt effect on ionic reactions has been studied extensively.25,26 For instance, Schmidt and Bartels examined the ionic strength effect on the recombination of hydrated electrons and suggested the importance of the salt effect not only on the electrostatic interaction but also on the diffusion constant of ionssnamely, that the diffusion rate of the hydrated electron is reduced by the additional friction from the ionic atmosphere.27 Here we examine the reaction between I2- anion radicals, where the Coulombic repulsion between the reactants plays an important role. The reaction kinetics of I2- is also important in DSSCs with an I-/I3- redox system.28-31 In the present study, I2- was produced by using 248-nm laser pulses to photodetach electrons from I- ions, and the reaction between I2- anion radicals was monitored by transient absorption spectroscopy. We discuss the reaction rate on the basis of the DebyeSmoluchowski equation.

10.1021/jp0671087 CCC: $37.00 © 2007 American Chemical Society Published on Web 02/01/2007

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TABLE 1: Ionic Liquids Used in the Experiments and Their Full and Abbreviated Names TMPA-TFSI P13-TFSI P14-TFSI PP13-TFSI DEME-TFSI DEME-BF4

N,N,N-trimethyl-N-propylammonium bis(trifluoromethylsulfonyl)imide N-methyl-N-propylpyrrolidinium bis(trifluoromethylsulfonyl)imide N-butyl-N-methylpyrrolidinium bis(trifluoromethylsulfonyl)imide N-methyl-N-propylpiperidinium bis(trifluoromethylsulfonyl)imide N,N-diethyl-N-methyl-N-(2methoxyethyl)ammonium bis(trifluoromethylsulfonyl)imide N,N-diethyl-N-methyl-N-(2methoxyethyl)ammonium tetrafluoroborate

Experiments All ionic liquids except DEME-TFSI and DEME-BF4 were purchased from Kanto Chemical CO., Inc. (Table 1). The DEME ionic liquids were kindly donated by Nisshinbo Industries Inc. Ionic liquid samples containing KI were first prepared in 30mL sample bottles and dried under vacuum at 60 °C. The concentrations of KI were adjusted to 0.4-0.8 mM. For the kinetics measurements, aliquots of the dried KI-containing samples were placed in screw-capped, 1-cm quartz cuvettes and dried again under vacuum at 60 °C prior to measurement. Care was taken to dry the ionic liquid because water impurity may accelerate the diffusion of ions.32 Water content was measured by Karl Fischer titration (Mettler Toledo, DL31). The concentrations of water were about 17 to 1000 ppm. The viscosity of the ionic liquid was measured with a viscometer (Brookfield, DV-II+Pro, CP-40). Nanosecond transient absorption was measured with a 248nm excimer laser (Lamda Physik, Lextra 100).33 A 300-W xenon arc lamp was used as an analyzing light source, and the excitation pulse was perpendicular to the analyzing light. The excitation pulse irradiated the sample in the cuvette through a 10 × 6 mm rectangular mask, while the analyzing light passed through 2-mm pinholes. Wide band-pass filters (40 nm, Optoline) were used to select the analyzing wavelength, and a system consisting of a 100-mm monochromator (JASCO) and a photomultiplier tube (Hamamatsu, R928) was used for spectral measurement. The kinetics was normally measured at 700 and 830 nm because, around these wavelengths, the S/N ratio was better than that in the near-UV region. Transient signals were collected with a fast silicon photodiode (New Focus 1801, 125 MHz, 3-ns rise time) and recorded on a 500-MHz oscilloscope (Tektronix, DPO 7054). Cline et al. have reported that many photodiodes exhibit a “long tail” following a fast impulse excitation, which comes from factors such as inhomogeneity in the electric field and deep traps in the semiconductor material.34 We checked the secondary-response distortion in the transient signals from the 1801 photodiode at several wavelengths (400-830 nm) of analyzing light, using an EG&G FND100 silicon photodiode as a reference detector.34 There was no unusual response from the detector. All experiments were carried out at room temperature. Results and Discussion The I2- species is formed by the 248-nm laser photolysis of iodide through the following reactions:35

I- + hν f I + es k2

I + I- 98 I2 k3

I2 + I2 98 I3 + I

(1) (2) (3)

As discussed later, we found that photodetachment of electrons from I- ions produces solvated electrons (es-) in ionic liquids as well as in molecular solvents. After photodetachment, iodine atoms react with I- to form diiodide anion radicals. In aqueous

solution, the transient absorption maxima of I2- are located around 400 and 720 nm.36 The extinction coefficients of I2- in aqueous solution at 385 and 725 nm are 10 000 and 2560 M-1 cm-1, respectively.36 Figure 1 shows the absorption spectrum of I2- in TMPA-TFSI together with a previously measured spectrum of I2- in aqueous solution.36 We obtained the spectra of I2- in other ionic liquids and found that the peak positions and peak widths of I2- are quite similar to those in water. In a recent study in which the quantum efficiencies for producing hydrated electrons by photodetachment of electrons from I- ions were determined, Sauer et al. found that there was no spectral change in I2- in the presence of NaClO4.37 These results suggest that the spectra of I2- are quite insensitive to the salinity of the solvent. Theoretical calculations38 also support these experimental results. Both of the absorption bands (400 and 720 nm) are intramolecular in origin; neither the absorption spectrum nor the oscillator strength of I2- is expected to change with ionic strength.38 In the following discussion, we assume that the extinction coefficient of I2- in ionic liquids can be approximated to that measured in water. Figure 2 shows examples of transient absorption signals at 700 nm in molecular solvents and ionic liquids. The aqueous sample was bubbled with N2O (scavenger of hydrated electrons) to minimize the contribution from the absorption of hydrated electrons, whereas the alcohol samples were used under the airsaturated condition. The reaction kinetics was normally examined at three different initial I2- concentrations by changing the laser pulse intensity. These initial concentrations were between 5 and 30 µM. The decay signals were fitted well with secondorder kinetics, and values of 2k3/ were extracted. The rate constants were calculated by using the extinction coefficient of I2- in water (2400 M-1 cm-1 at 700 nm) (Table 2). The reaction rates are averages of 4-6 measurements. The error in day-today measurements was on the order of 10%. The viscosities and dielectric constants of the molecular solvents are also included in Table 2. The reaction between I2- anion radicals in molecular solvents is considered to be diffusion-controlled,36 and as discussed later, the reaction rates in water and alcohols can be predicted well by the Debye-Smoluchowski equation. In Figure 3a, the transient signal measured at 700 nm in the ionic liquid PP13-TFSI is plotted against the logarithm of time. The transient signal includes two components: one component builds up very fast and decays within a few hundred nanoseconds, and the other component builds up within a few microseconds and decays within a few milliseconds. The former signal, which disappeared in the presence of the electron scavengers O2, SF6, and N2O, can be attributed to the formation and decay of solvated electrons. The latter signal can be attributed to the formation and decay of I2-. The decay signal of I2- is well separated from that of the solvated electrons (Figure 3a). Hence the decay kinetics for all of the samples was well fitted with second-order kinetics (Figure 3b). The straight-line correlation between the reciprocal of the absorbance and time in Figure 3b indicates that I2- decayed with second-order kinetics in the ionic liquid PP13-TFSI. Similar transient signals were obtained for the other ionic liquids examined.

Diiodide Anion Radicals in Ionic Liquids

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Figure 1. Transient absorption spectra of I2- in TMPA-TFSI (filled circles) and I2- in water36 (open triangles).

Figure 2. Examples of absorbance traces of I2- in molecular solvents and ionic liquids.

As mentioned earlier, reaction 3 is considered to be diffusioncontrolled in molecular solvents. In molecular solvents, the diffusion-controlled rate for an ionic reaction can be calculated by the Debye-Smoluchowski equation:39

kdiff ) 4πRabDabf() f() )

rc/Rab exp(rc/Rab) - 1

rc )

ZaZbe2 4π0kBT

(4) (5)

(6)

where Rab is the reaction distance of closest approach, Dab is the relative diffusion coefficient of reactants, f() is the so-called Debye correction factor, e is the charge on the ions, kB is Boltzmann’s constant, 0 is the permittivity of free space,  is the dielectric constant, and T is the absolute temperature. If the diffusion coefficient can be expressed by a simple hydrodynamic modelsthat is, the Stokes-Einstein equation, Da ) kBT/(6πηRa), the diffusion-limited rate constant of eq 4 may be written as follows:

kdiff ) 8000RTf()/3η

(7)

where η is viscosity (in Pa‚s) and R is the gas constant (8.3144 J K-1 mol-1). A limitation in applying the Stokes-Einstein equation for estimating the diffusion-limited reaction rate will be discussed later. The Debye correction factors f() for H2O, MeOH, and EtOH were calculated from the dielectric constants

of the solvents and are listed in Table 2. The reaction distance of closest approach Rab (0.63 nm) was calculated from the molar volume of I2-.40 The Debye correction factor for aqueous solution was calculated to be 0.52, whereas the values for methanol and ethanol were calculated to be 0.18 and 0.091, respectively, indicating that the Coulombic repulsion between the I2- radical anions in the alcohol solvents is greater than that in water. These calculated Debye correction factors predict that the reaction between I2- anion radicals in the alcohol solvents is much slower than that in water. As indicated in Table 2, the reaction rates in MeOH and EtOH are slower by a factor of 1/5 than the rate in water. The decay rate constants k3 for reaction 3 (Table 2) in the molecular solvents and the ionic liquids are plotted in Figure 4 as a function of the reciprocal of viscosity. The solid line in Figure 4 is the plot for the diffusion-limited rate constants calculated from eq 7 with f() ) 1; that is, the calculations for reaction between neutral molecules (denoted k0). Except for PP13-TFSI and DEME-BF4, the reaction rate constants for the ionic liquids are very close to the solid line. The k3/k0 ratios for the ionic liquids (except PP13-TFSI and DEME-BF4) are almost unity (Table 2), indicating that the Debye factors f() for the ionic liquids are close to unity and that the electrostatic repulsion between the diiodide anion radicals is unimportant. In contrast, the k3/k0 ratios for H2O, MeOH, and EtOH are 0.37, 0.064, and 0.086, respectively, reflecting the importance of electrostatic repulsion between the diiodide anion radicals. The present experimental results for the ionic liquids suggest the following possibilities: (1) The dielectric constants of the ionic liquids are very high; hence the Debye factors for the ionic liquids are close to unity. (2) The electrostatic interactions between the diiodide anion radicals are effectively screened by the ions of the ionic liquids. Therefore the diiodide anion radicals can approach each other without any Coulombic repulsions. As discussed later, the former possibility may be unlikely, though the dielectric constants of the ionic liquids used in the present study are not known. The available data for dielectric constants of ionic liquids is limited,41 and the reported values are around 10 for the ionic liquids with imidazolium cations. These values are too small to explain the present results. The coincidence of the experimental rate constants of I2- in the ionic liquids with those calculated based on the viscosity (eq 7 with f() ) 1) was unexpected. In previous pulse radiolysis experiments on the reaction of butylpyridinyl radical with duroquinone,22 the experimental reaction rates deviated significantly from calculated values based on viscosities with the simple hydrodynamic assumption. In that work,22 the experimental rates were almost an order of magnitude higher than the values estimated from the viscosities of the ionic liquids. Skrzypczak and Neta suggested that this difference was due to the voids that exist in ionic liquids and the possibility that reacting species diffuse through movement of small groups of ions, whereas viscosity is related to simultaneous movement of all ions.22 Furthermore, Maroncelli et al. have pointed out the limitation of the continuum approximation of solvents and the importance of considering the molecularity of solvents in solvation dynamics.42 The reason the simple hydrodynamic model can predict the present results for the reaction between I2- anion radicals could be due to the relatively simple molecular shape of the diiodide anion radicals. However, for the reaction of I2- in PP13-TFSI and DEME-BF4, the agreement between the measured reaction rate and the calculated rate was not good. These results could reflect a limitation of the Stokes-Einstein

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TABLE 2: Solvent Properties and Rate Constants for Reaction between I2- Anion Radicals no. 1 2 3 4 5 6 7 8 9 10 11 12 13

solvent H2O MeOH EtOH 40% Glye 60% Glye 70% Glye 80% Glye TMPA-TFSI P13-TFSI P14-TFSI PP13-TFSI DEME-TFSI DEME-BF4

ηa 0.89 0.55 1.01 3.1 8.6 17 43



k0b

78.4 32.7 24.6 68 61 56 51

69 55 69 135 63 300

k3c 9

7.4 × 10 1.2 × 1010 6.1 × 109 2.1 × 109 7.7 × 108 3.8 × 108 1.5 × 108

(2.8 ( 0.2) × 10 (7.7 ( 0.5) × 108 (5.3 ( 0.7) × 108 (9.1 ( 0.8) × 108 (3.0 ( 0.2) × 108 (1.7 ( 0.3) × 108 (6.8 ( 0.9) × 107

9.6 × 107 1.2 × 108 9.6 × 107 4.9 × 107 1.0 × 107 2.2 × 107

(1.1 ( 0.2) × 108 (1.3 ( 0.2) × 108 (9.1 ( 0.5) × 107 (6.6 ( 0.4) × 107 (1.2 ( 0.5) × 108 (4.0 ( 0.7) × 107

9

f()d

k3/k0

0.52 0.18 0.091 0.47 0.43 0.39 0.35

0.37 0.064 0.086 0.43 0.37 0.44 0.45 1.15 1.08 0.95 1.35 1.14 1.82

a Viscosity, in mPa‚s. b Calculated diffusion-limited rate constant with f() ) 1, in M-1 s-1. c Experimental rate constant for reaction 3, in M-1 s-1. d Debye correction factor. e Glycerol-H2O mixture.

Figure 3. (a) Transient absorbance in PP13-TFSI at 700 nm plotted against logarithm of time. (b) Plot of reciprocal of OD measured in PP13-TFSI at 700 nm versus time. A straight-line correlation between the reciprocal of OD and time indicates that the decay signal is fitted well with second-order kinetics.

Figure 4. Plots of rate constants for reaction between I2- anion radicals in molecular solvents and ionic liquids as a function of the inverse of viscosity: (0) H2O, (2) alcohols, (O) glycerol-H2O mixtures, (b) ionic liquids. The numbers correspond to the numbers in Table 2. The filled square is data for reaction between Br2- anion radicals in an ionic liquid.21 The line plots the calculated diffusion-limited rate constants for reaction between neutral molecules (eq 7, f() ) 1).

approximation and indicate the importance of considering the molecularity of ionic liquids. To examine both the applicability of the Debye-Smoluchowski equation to the reaction between I2- anion radicals and the effect of the presence of solvent charges on the reaction between I2- anion radicals in highly viscous media such as ionic

liquids, we measured the rates of reaction between the diiodide anion radicals in glycerol-H2O mixtures. The viscosities of the glycerol-H2O mixtures were measured with a viscometer, and the dielectric constants of the mixtures were calculated from ref 43. The measured reaction rates (Figure 4) were nearly equal to the values predicted from the Debye-Smoluchowski equation, where the Debye correction factors were 0.39 and 0.35 for 70 and 80 wt % glycerol-H2O solution (the viscosities were 17 and 43 mPa‚s) and the k3/k0 ratios were 0.44 and 0.45, respectively. Hence the reaction between I2- anion radicals under viscous conditions is predicted fairly well by the DebyeSmoluchowski equation. However, there are some disagreements between the calculated trends and the experimental values. The Debye factors for the glycerol-H2O solutions decreased with glycerol concentration, whereas the k0/k3 ratio increased slightly with glycerol concentration. This discrepancy could be due to the microstructure of the glycerol-H2O solution and may indicate a limitation of the Stokes-Einstein equation in estimating the diffusion coefficient of ions in a mixed solvent. Solvent structure in a mixed solution affects reaction kinetics, and reaction rates are affected by solution composition.44 Moreover, glycerol possesses a non-Debye dielectric response.45 Hence deviation between the calculation and the experimental rate very likely depends on the concentration of glycerol. It may be possible to calculate the Debye correction factors for ionic liquids if the static dielectric constants for the ionic liquids are known. Unfortunately, the dielectric constants of the ionic liquids used in the present study are not known. The available data for dielectric constants of ionic liquids with imidazolium cations is limited. Wakai et al. carried out a microwave dielectric spectroscopic study of a series of ionic liquids with imidazolium cations and obtained static dielectric constants of the ionic liquids.41 The reported dielectric constants were, for instance, 12.8, 11.7, 11.4, and 8.9 for Emim-BF4, Bmim-BF4, Bmim-PF6, and Hmim-PF6, respectively, where Emim is ethylmethylimidazolium, Bmim is butylmethylimidazolium, and Hmim is hexylmethylimidazolium. Therefore, the Debye correction factors for those ionic liquids would be 5.5 × 10-3, 3.1 × 10-3, 2.6 × 10-3, and 3.4 × 10-4, and these values indicate that the reaction between I2- anion radicals in these ionic liquids would be much slower than reaction between neutral molecules. If we assume that the dielectric constants for the ionic liquids used in the present study are similar to those of ionic liquids with imidazolium cations, the same values of the Debye correction factors are expected, and the reaction between diiodide anion radicals would be prevented to a significant extent. However, as the experimental data show, this is not the case, and thus Coulombic repulsion is being effectively

Diiodide Anion Radicals in Ionic Liquids screened in the ionic liquids. In a previous pulse radiolysis study,21 the reaction between Br2- anion radicals was examined in an ionic liquid, methyltributylammonium bis(trifluoromethylsulfonyl)imide (viscosity is 470 mPa‚s at 25 °C). The reported reaction rate for Br2- is 1.5 × 107 M-1 s-1, which is plotted in Figure 4. As can be seen from Figure 4, the reaction between Br2- anion radicals can be predicted by the Debye-Smoluchowski equation with f() ) 1, suggesting that the electrostatic interaction between Br2- anion radicals may be unimportant, as in the reaction between I2- anion radicals. Recently, the mean spherical approximation was applied to the kinetic salt effect under high-salt concentrations.46,47 In that work, no electrostatic interaction was assumed in the diffusion-limited ionic reaction since the charges on the reactants would be totally screened by ions of the salts. Considering the present and previous21,46,47 results, we emphasize that it is the screening effect that is important in the reaction between charged particles in ionic liquids. In the present work, we have studied a reaction between like charged ions in ionic liquids. We are planning to study a reaction between oppositely charged ions in ionic liquids. Conclusions We have studied the reaction between I2- anion radicals in molecular solvents, highly viscous glycerol-H2O mixtures, and ionic liquids. I2- was produced by using 248-nm laser pulses to photodetach electrons from I- ions. The rates of reaction between I2- anion radicals in the molecular solvents can be predicted by the Debye-Smoluchowski equation even under highly viscous conditions, where electrostatic interactions between I2- anion radicals were considered using the dielectric constant of those solvents. On the other hand, the rates of reaction between I2- anion radicals in ionic liquids are close to the diffusion-limited rate for neutral molecules, suggesting that the Coulombic repulsion between I2- anion radicals is well screened by the ions of the ionic liquids. Acknowledgment. This work was supported by a Grantin-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan. References and Notes (1) Nanjundiah, C.; McDevitt, S. F.; Koch, V. R. J. Electrochem. Soc. 1997, 144, 3392-3397. (2) MacFarlane, D. R.; Meakin, P.; Sun, J.; Amini, N.; Forsyth, M. J. Phys. Chem. B 1999, 103, 4164-4170. (3) Noda, A.; Susan, M. A. B. H.; Kudo, K.; Mitsushima, S.; Hayamizu, K.; Watanabe, M. J. Phys. Chem. B 2003, 107, 4023-4033. (4) Papageorgiou, N.; Athanassov, Y.; Armand, M.; Bonhote, P.; Pettersson, H.; Azam, A.; Gra¨tzel, M. J. Electrochem. Soc. 1996, 143, 30993108. (5) Wang, P.; Zakeeruddin, S. M.; Moser, J. E.; Humphry-Baker, R.; Gra¨tzel, M. J. Am Chem. Soc. 2004, 126, 7164-7165. (6) Kawano, R.; Watanabe, M. Chem. Commun. 2003, 330-331. (7) Kawano, R.; Watanabe, M. Chem. Commun. 2005, 2107-2109. (8) Zistler, M.; Wachter, P.; Wasserscheid, P.; Gerhard, D.; Hinsch, A.; Sastrawan, R.; Gores, H. J. Electrochim. Acta 2006, 52, 161-169. (9) Moelwyn-Hughes, E. A. The Kinetics of Reactions in Solution, 2nd ed.; Clarendon Press: London, 1947; p 90.

J. Phys. Chem. B, Vol. 111, No. 18, 2007 4811 (10) Ingram, J. A.; Moog, R. S.; Ito, N.; Biswas, R.; Maroncelli, M. J. Phys. Chem. B 2003, 107, 5926-5932. (11) Kamakar, R.; Samanta, A. J. Phys. Chem. A 2002, 106, 66706675. (12) Wishart, J. F.; Lall-Ramnarine, S. I.; Raju, R.; Scumpia, A.; Bellevue, S.; Ragbir, R.; Engel, R. Radiat. Phys. Chem. 2005, 72, 99104. (13) Shirota, H.; Fuston, A. M.; Wishart, J. F.; Castner, E. W., Jr. J. Chem. Phys. 2005, 122, 184512. (14) Arzhantsev, S.; Jin, H.; Ito, N.; Maroncelli, M. Chem. Phys. Lett. 2006, 417, 524-529. (15) Ito, N.; Huang, W.; Richert, R. J. Phys. Chem. B 2006, 110, 43714377. (16) Gordon, C. M.; McLean, A. J. Chem. Commun. 2000, 1395-1396. (17) Behar, D.; Gonzalez, C.; Neta, P. J. Phys. Chem. A 2001, 105, 7607-7614. (18) Behar, D.; Neta, P.; Schltheisz, C. J. Phys. Chem. A 2002, 106, 3139-3147. (19) Grodkowski, J.; Neta, P. J. Phys. Chem. A 2002, 106, 5468-5473. (20) Grodkowski, J.; Neta, P. J. Phys. Chem. A 2002, 106, 9030-9035. (21) Grodkowski, J.; Neta, P. J. Phys. Chem. A 2002, 106, 1113011134. (22) Skrzypczak, A.; Neta, P. J. Phys. Chem. A 2003, 107, 7800-7803. (23) Wishart, J. F.; Neta, P. J. Phys. Chem. B 2003, 107, 7261-7267. (24) Grodkowski, J.; Neta, P.; Wishart, J. F. J. Phys. Chem. A 2003, 107, 9794-9799. (25) Jonah, C. D.; Miller, J. R.; Hart, E. J.; Matheson, M. S. J. Phys. Chem. 1975, 79, 2705-2711. (26) Hickel, B. J. Phys. Chem. 1978, 82, 1005-1010. (27) Schmidt, K. H.; Bartels, D. M. Chem. Phys. 1995, 190, 145-152. (28) Huang, S. Y.; Schlichtho¨rl, G.; Nozik, A. J.; Gra¨tzel, M.; Frank, A. J. J. Phys. Chem. B 1997, 101, 2576-2582. (29) Pelet, S.; Moser, J. E.; Gra¨tzel, M. J. Phys. Chem. B 2000, 104, 1791-1795. (30) Nogueira, A. F.; De Paoli, M. A.; Montanari, I.; Monkhouse, R.; Nelson, J.; Durrant, J. R. J. Phys. Chem. B 2001, 105, 7517-7524. (31) Bauer, C.; Boschloo, G.; Mukhtar, E.; Hagfeldt, A. J. Phys. Chem. B. 2002, 106, 12693-12704. (32) Shroder, U.; Wadhawan, D. W.; Compton, R. G.; Marken, F.; Suarez, P. A. Z.; Consorti, C. S.; de Souza, R. F.; Dupont, J. New J. Chem. 2000, 24, 1009-1015. (33) Zuo, Z.; Katsumura, Y.; Ueda, K.; Ishigure, K. J. Chem. Soc., Faraday Trans. 1997, 93, 533-536. (34) Cline, J. A.; Jonah, C. D.; Bartels, D. M. ReV. Sci. Instrum. 2002, 73, 3908-3915. (35) Blandamar, M. J.; Fox, M. F. Chem. ReV. 1970, 70, 59-93. (36) Elliot, A. J.; Sopchyshyn, F. C. Int. J. Chem. Kinet. 1984, 16, 12471256. (37) Sauer, M. C., Jr.; Shkrob, I. A.; Lian, R.; Crowell, R. A.; Bartels, D. M.; Chen, X.; Suffern, D.; Bradfort, S. E. J. Phys. Chem. A 2004, 108, 10414-10425. (38) Tasker, P. W.; Balint-Kurti, G. G.; Dixon, R. N. Mol. Phys. 1976, 32, 1651-1660. (39) Debye, P. Trans. Electrochem. Soc. 1942, 82, 265-272. (40) Borsarelli, C. D.; Bertolotti, S. G.; Previtali, C. M. Photochem. Photobiol. Sci. 2003, 2, 791-795. (41) Wakai, C.; Oleinikova, A.; Ott, M.; Weinga¨rtner, H. J. Phys. Chem. B 2005, 109, 17028-17030. (42) For example: (a) Maroncelli, M.; Fleming, G. R. J. Chem. Phys. 1987, 86, 6221-6239. (b) Papazyan, A.; Maroncelli, M. J. Chem. Phys. 1995, 102, 2888-2919. (c) Ito, N.; Arzhantsev, S.; Heitz, M.; Maroncelli, M. J. Phys. Chem. B 2004, 108, 5771-5777. (43) Åkerlo¨f, G. J. Am. Chem. Soc. 1932, 54, 4125-4139. (44) Maham, Y.; Freeman, G. R. Can. J. Chem. 1988, 66, 1706-1711. (45) DeToma, R. P.; Easter, J. H.; Brand, L. J. Am Chem. Soc. 1976, 98, 5001-5007. (46) Simonin, J. P.; Hendrawan, H. Phys. Chem. Chem. Phys. 2001, 3, 4286-4295. (47) Simonin, J. P.; Billard, I.; Hendrawan, H.; Bernard, O.; Lu¨tzenkirchen, K.; Se´mon, L. Phys. Chem. Chem. Phys. 2003, 5, 520-527.