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Density dependence of the Stokes shift and solvent reorganization energy in supercritical fluids
Radiation Physics and Chemistry 55 (1999) 579±581
www.elsevier.com/locate/radphyschem
Density dependence of the Stokes shift and solvent reorganization energy in supercritical ¯uids Kenji Takahashi a,*, Katsutoshi Fujii a, Sadashi Sawamura a, Charles D. Jonah b a
Division of Quantum Energy Engineering, Hokkaido University, Sapporo 060, Japan b Chemistry Division, Argonne National Laboratory, Argonne, IL 60439, USA
Abstract The Stokes shifts of coumarin 153 (C153) in CF3H, CO2 and C2H6 have been measured at several reduced densities (0.3±1.8). For C153 in CF3H, the shifts increase with a decrease in reduced density and show a maximum value at a reduced density of 0.5. In non-polar solvents, the shifts are not dramatically altered as a function of reduced density but slightly increase with a decrease in the reduced density. # 1999 Elsevier Science Ltd. All rights reserved.
1. Introduction In electron transfer reactions, as has been well discussed previously, both solvation dynamics and energetics play important roles (Marcus and Sutin, 1985). For example, in the Marcus-type description of the electron transfer reaction, the electron transfer rate can be expressed as a function of the free energy change and the solvent reorganization energy (Er). We have recently shown the possibility that the solvent reorganization energy, Er, in supercritical ethane strongly depends on the pressure or density of ¯uid (Takahashi and Jonah, 1997). While the values of Er calculated are unphysically large, relatively large values of Er have also been reported in experimental studies of chargetransfer in liquid non-polar solvents (e.g. Gould et al., 1993). In those studies, unfortunately, one needs a lot of parameters and assumptions to calculate Er , and the assumptions lead to uncertainty in the calculated
* Corresponding author. Fax: +81-11-706-6675. E-mail address: [email protected] (K. Takahashi)
energy. On the other hand, the reorganization of the solvent around the newly formed ion or excited molecule gives rise to the well-known Stokes shift in the spectrum. The value of Er is directly related to the Stokes shift. Hence the measurements of the Stokes shift in polar and non-polar supercritical ¯uids (SCFs) can give a new information about the energetics of solvation. One of advantages of using SCFs is that we can control solvent properties (dielectric constant, refractive index) by making only small changes in the pressure and thus can examine eects of the solvent properties on the solvation energetics without changing the solvent itself. However few studies have been carried out for pressure dependence of the Stokes shifts in SCFs. It is known that an interesting feature of SCFs is in the clustering of solvent molecules around a solute molecule. Such local density augmentation must have remarkable eects on the energetics and the dynamics of solvation in SCFs.
2. Experimental The measurements of absorption and ¯uorescence
0969-806X/99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 9 - 8 0 6 X ( 9 9 ) 0 0 2 4 9 - 2
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K. Takahashi et al. / Radiation Physics and Chemistry 55 (1999) 579±581
Fig. 1. Absorption and ¯uorescence spectra of C153 in CF3H at several densities. The density increases with the direction of the arrow.
spectra have been carried out using almost the same apparatus as the previous work (Takahashi et al., 1998) except for a new high pressure optical cell. A new optical high pressure cell (Takagi Co., Ltd) has been designed to be able to measure ¯uorescence spectra as well as absorption spectra. The absorption and ¯uorescence spectra were measured using Hitachi U3200 and JASCO FP-750, respectively. As a probe molecule C153 was chosen because, as reported by Lewis and Maroncelli, C153 is a nearly ideal solvation probe (Lewis and Maroncelli, 1998). The critical temperature, pressure and density for CF3H, CO2 and C2H6 are, respectively, 298.98, 304.2 and 305.3 K, 4.82, 7.38 and 4.88 MPa, and 526, 468 and 204.5 kg mÿ3. 3. Results and discussion In Fig. 1 the density dependence of ¯uorescence and absorption spectra in CF3H are shown. As the density increases, the ¯uorescence spectra shift to the red. For absorption spectra, the spectra narrow with a decrease in the density, while for the ¯uorescence spectra, the spectra broaden. Furthermore, the absorption spectra do not change shape, only the width and peak position shift; however, the shape of ¯uorescence spectra ¯atten at low densities. This is quite interesting and shows a dramatic change of solvation environment about C153, especially a dierence between solvation of the ground
and excited states. We can extract a lot of information about solvation from these spectral changes, however, in this article, we limit our discussion to energetics of solvation in SCFs, namely the solvent reorganization energy (the Stokes shift). In Fig. 2, the Stokes shifts for C153 in SC CF3H, CO2 and C2H6 are shown as a function of the reduced density (density normalized by the critical density of a ¯uid). The shifts shown in the ®gure are relative values to the shift measured in c-hexane. As expected, the shifts in CF3H are larger than the shifts in CO2 and C2H6. For CF3H, the maximum shift occurs at a reduced density of 0.5 and decreases at higher and lower densities. For CO2 and C2H6, although the shifts do not dramatically change as a function of the reduced density, the shifts decrease with density. The experimental results do not correspond with predictions of the classical continuum theory such as the Onsager's reaction ®eld theory (e.g. Ooshika, 1954). In the theory the Stokes shift is proportional to the reaction ®eld factor F(e, n ), where F(e,n )=(e ÿ 1)/(2e+1)(n 2 ÿ 1)/(2n 2+1) where e is the static dielectric constant and n is the refractive index. Fig. 2 shows the density dependence of F(e,n ) for CF3H calculated using the bulk dielectric and refractive index of CF3H. The calculated F(e,n ) monotonically increases with the density and is quite dierent from the experimental results. In a previous paper, we suggested that the local density around a solute in SCFs would be greater than the
K. Takahashi et al. / Radiation Physics and Chemistry 55 (1999) 579±581
581
Fig. 2. Density dependence of Stokes shift: CF3H, Tr=1.03 (.); CF3H, Tr=1.15 (R); CO2, Tr=1.03 (r); C2H6, Tr=1.03 (W), where Tr is a temperature normalized by the critical temperature. The solid line shows the reaction ®eld factor (see text). A solid line with circle symbol is a reaction ®eld factor calculated using local ¯uid properties for CF3H.
bulk density (Takahashi et al., 1998). Because the density dependence of Er would be related to the density dependence of the local electrostatic properties rather than the bulk properties, the local properties would give some insights to Er. In Fig. 2 the values of F(e,n )local, where F(e,n )local=(elocal ÿ 1)/(2elocal+1)(n 2local ÿ 1)/(2n 2local+1), as a function of density are shown. These were calculated using the local dielectric constant elocal and the local refractive index nlocal, are shown. In the calculation the density dependence of these local properties are assumed as the same as our previous work on 4-aminobenzophenone in CF3H. The calculated F(e,n )local show a similar density dependence to the experimental shifts in the reduced density of 0.3±0.8. However, in the high density regions, the density dependence of the calculated F(e,n )local and the experimental shifts are quite dierent. To explain the decrease in the Stokes shifts at higher density region, the density dependence of local density augmentation around C153 at both the ground and excited states has to be considered. The magnitudes of solvent reorganization energy, compared to c-hexane, are E0.01 eV for C2H6, and between 0.02 and 0.05 eV for CO2. In CF3H, the solvent reorganization energies relative to c-hexane are 0.12±0.16 eV. This suggest that electron transfer rate
will be remarkably altered by small pressure changes (50±140 bar). To understand dynamics of solvation in SCFs, time resolved studies, such as pulse radiolysis and laser ¯ash photolysis, will be required. References Gould, I.R., Noukakis, D., Goodman, J.L., Young, R.H., Farid, S., 1993. A quantitative relationship between radiative and nonradiative electron transfer in radical-ion pairs. J. Am. Chem. Soc. 115, 3830. Lewis, J.E., Maroncelli, M., 1998. On the (uninteresting) dependence of the absorption and emission transition moments of coumarin 153 on solvent. Chem. Phys. Lett. 282, 197. Marcus, R.A., Sutin, N., 1985. Electron transfers in chemistry and biology. Biochimica et Biophysica Acta 811, 265. Ooshika, Y., 1954. Absorption spectra of dyes in solution. J. Phys. Soc. Jpn. 9, 594. Takahashi, K., Jonah, C.D., 1997. The measurement of an electron transfer reaction in a non-polar supercritical ¯uid. Chem. Phys. Lett. 264, 297. Takahashi, K., Abe, K., Sawamura, S., Jonah, C.D., 1998. Spectroscopic study of 4-aminobenzophenone in supercritical CF3H and CO2: local density and Onsager's reaction cavity radius. Chem. Phys. Lett. 282, 361.
www.elsevier.com/locate/radphyschem
Density dependence of the Stokes shift and solvent reorganization energy in supercritical ¯uids Kenji Takahashi a,*, Katsutoshi Fujii a, Sadashi Sawamura a, Charles D. Jonah b a
Division of Quantum Energy Engineering, Hokkaido University, Sapporo 060, Japan b Chemistry Division, Argonne National Laboratory, Argonne, IL 60439, USA
Abstract The Stokes shifts of coumarin 153 (C153) in CF3H, CO2 and C2H6 have been measured at several reduced densities (0.3±1.8). For C153 in CF3H, the shifts increase with a decrease in reduced density and show a maximum value at a reduced density of 0.5. In non-polar solvents, the shifts are not dramatically altered as a function of reduced density but slightly increase with a decrease in the reduced density. # 1999 Elsevier Science Ltd. All rights reserved.
1. Introduction In electron transfer reactions, as has been well discussed previously, both solvation dynamics and energetics play important roles (Marcus and Sutin, 1985). For example, in the Marcus-type description of the electron transfer reaction, the electron transfer rate can be expressed as a function of the free energy change and the solvent reorganization energy (Er). We have recently shown the possibility that the solvent reorganization energy, Er, in supercritical ethane strongly depends on the pressure or density of ¯uid (Takahashi and Jonah, 1997). While the values of Er calculated are unphysically large, relatively large values of Er have also been reported in experimental studies of chargetransfer in liquid non-polar solvents (e.g. Gould et al., 1993). In those studies, unfortunately, one needs a lot of parameters and assumptions to calculate Er , and the assumptions lead to uncertainty in the calculated
* Corresponding author. Fax: +81-11-706-6675. E-mail address: [email protected] (K. Takahashi)
energy. On the other hand, the reorganization of the solvent around the newly formed ion or excited molecule gives rise to the well-known Stokes shift in the spectrum. The value of Er is directly related to the Stokes shift. Hence the measurements of the Stokes shift in polar and non-polar supercritical ¯uids (SCFs) can give a new information about the energetics of solvation. One of advantages of using SCFs is that we can control solvent properties (dielectric constant, refractive index) by making only small changes in the pressure and thus can examine eects of the solvent properties on the solvation energetics without changing the solvent itself. However few studies have been carried out for pressure dependence of the Stokes shifts in SCFs. It is known that an interesting feature of SCFs is in the clustering of solvent molecules around a solute molecule. Such local density augmentation must have remarkable eects on the energetics and the dynamics of solvation in SCFs.
2. Experimental The measurements of absorption and ¯uorescence
0969-806X/99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 9 - 8 0 6 X ( 9 9 ) 0 0 2 4 9 - 2
580
K. Takahashi et al. / Radiation Physics and Chemistry 55 (1999) 579±581
Fig. 1. Absorption and ¯uorescence spectra of C153 in CF3H at several densities. The density increases with the direction of the arrow.
spectra have been carried out using almost the same apparatus as the previous work (Takahashi et al., 1998) except for a new high pressure optical cell. A new optical high pressure cell (Takagi Co., Ltd) has been designed to be able to measure ¯uorescence spectra as well as absorption spectra. The absorption and ¯uorescence spectra were measured using Hitachi U3200 and JASCO FP-750, respectively. As a probe molecule C153 was chosen because, as reported by Lewis and Maroncelli, C153 is a nearly ideal solvation probe (Lewis and Maroncelli, 1998). The critical temperature, pressure and density for CF3H, CO2 and C2H6 are, respectively, 298.98, 304.2 and 305.3 K, 4.82, 7.38 and 4.88 MPa, and 526, 468 and 204.5 kg mÿ3. 3. Results and discussion In Fig. 1 the density dependence of ¯uorescence and absorption spectra in CF3H are shown. As the density increases, the ¯uorescence spectra shift to the red. For absorption spectra, the spectra narrow with a decrease in the density, while for the ¯uorescence spectra, the spectra broaden. Furthermore, the absorption spectra do not change shape, only the width and peak position shift; however, the shape of ¯uorescence spectra ¯atten at low densities. This is quite interesting and shows a dramatic change of solvation environment about C153, especially a dierence between solvation of the ground
and excited states. We can extract a lot of information about solvation from these spectral changes, however, in this article, we limit our discussion to energetics of solvation in SCFs, namely the solvent reorganization energy (the Stokes shift). In Fig. 2, the Stokes shifts for C153 in SC CF3H, CO2 and C2H6 are shown as a function of the reduced density (density normalized by the critical density of a ¯uid). The shifts shown in the ®gure are relative values to the shift measured in c-hexane. As expected, the shifts in CF3H are larger than the shifts in CO2 and C2H6. For CF3H, the maximum shift occurs at a reduced density of 0.5 and decreases at higher and lower densities. For CO2 and C2H6, although the shifts do not dramatically change as a function of the reduced density, the shifts decrease with density. The experimental results do not correspond with predictions of the classical continuum theory such as the Onsager's reaction ®eld theory (e.g. Ooshika, 1954). In the theory the Stokes shift is proportional to the reaction ®eld factor F(e, n ), where F(e,n )=(e ÿ 1)/(2e+1)(n 2 ÿ 1)/(2n 2+1) where e is the static dielectric constant and n is the refractive index. Fig. 2 shows the density dependence of F(e,n ) for CF3H calculated using the bulk dielectric and refractive index of CF3H. The calculated F(e,n ) monotonically increases with the density and is quite dierent from the experimental results. In a previous paper, we suggested that the local density around a solute in SCFs would be greater than the
K. Takahashi et al. / Radiation Physics and Chemistry 55 (1999) 579±581
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Fig. 2. Density dependence of Stokes shift: CF3H, Tr=1.03 (.); CF3H, Tr=1.15 (R); CO2, Tr=1.03 (r); C2H6, Tr=1.03 (W), where Tr is a temperature normalized by the critical temperature. The solid line shows the reaction ®eld factor (see text). A solid line with circle symbol is a reaction ®eld factor calculated using local ¯uid properties for CF3H.
bulk density (Takahashi et al., 1998). Because the density dependence of Er would be related to the density dependence of the local electrostatic properties rather than the bulk properties, the local properties would give some insights to Er. In Fig. 2 the values of F(e,n )local, where F(e,n )local=(elocal ÿ 1)/(2elocal+1)(n 2local ÿ 1)/(2n 2local+1), as a function of density are shown. These were calculated using the local dielectric constant elocal and the local refractive index nlocal, are shown. In the calculation the density dependence of these local properties are assumed as the same as our previous work on 4-aminobenzophenone in CF3H. The calculated F(e,n )local show a similar density dependence to the experimental shifts in the reduced density of 0.3±0.8. However, in the high density regions, the density dependence of the calculated F(e,n )local and the experimental shifts are quite dierent. To explain the decrease in the Stokes shifts at higher density region, the density dependence of local density augmentation around C153 at both the ground and excited states has to be considered. The magnitudes of solvent reorganization energy, compared to c-hexane, are E0.01 eV for C2H6, and between 0.02 and 0.05 eV for CO2. In CF3H, the solvent reorganization energies relative to c-hexane are 0.12±0.16 eV. This suggest that electron transfer rate
will be remarkably altered by small pressure changes (50±140 bar). To understand dynamics of solvation in SCFs, time resolved studies, such as pulse radiolysis and laser ¯ash photolysis, will be required. References Gould, I.R., Noukakis, D., Goodman, J.L., Young, R.H., Farid, S., 1993. A quantitative relationship between radiative and nonradiative electron transfer in radical-ion pairs. J. Am. Chem. Soc. 115, 3830. Lewis, J.E., Maroncelli, M., 1998. On the (uninteresting) dependence of the absorption and emission transition moments of coumarin 153 on solvent. Chem. Phys. Lett. 282, 197. Marcus, R.A., Sutin, N., 1985. Electron transfers in chemistry and biology. Biochimica et Biophysica Acta 811, 265. Ooshika, Y., 1954. Absorption spectra of dyes in solution. J. Phys. Soc. Jpn. 9, 594. Takahashi, K., Jonah, C.D., 1997. The measurement of an electron transfer reaction in a non-polar supercritical ¯uid. Chem. Phys. Lett. 264, 297. Takahashi, K., Abe, K., Sawamura, S., Jonah, C.D., 1998. Spectroscopic study of 4-aminobenzophenone in supercritical CF3H and CO2: local density and Onsager's reaction cavity radius. Chem. Phys. Lett. 282, 361.