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Excited-state solvent dynamics and fluorescence quenching of solutions
Journal of Luminescence 87}89 (2000) 592}594
Excited-state solvent dynamics and #uorescence quenching of solutions Vladimir S. Pavlovich* Institute of Molecular and Atomic Physics, 70 F. Scaryna Prospect, Minsk 220072, Belarus
Abstract In terms of the histons, new quasi-particles, the #uorescence quenching controlled by solvent relaxation is considered for polar compounds in polar solutions. The relations for the nonradiative rate are presented for wide temperature region. At high temperature the contribution of motion of l- and j-histons into the Marcus reorganization energy is found with the help of Onsager model for dipole}dipole interactions. An example of the hole forming in #uorescence spectrum as a result of resonance S PXL conversion is presented. 2000 Elsevier Science B.V. All rights reserved. Keywords: Solvent dynamics; Fluorescence quenching; New quasi-particles; Histons
1. Introduction Following Marcus theory [1,2] for high temperatures in polar solutions the electron transfer (ET) rate k is expressed by 2p k" <(4pjk ¹)\ exp(!E /k ¹),
(1)
where < is the electronic coupling, j is the solvent reorganization energy. The activation energy is given as E "(j#*G3)/4j,
(2)
where *G3 is the standard free-energy change. The dynamic solvent e!ects on the outer-sphere ET rate was studied by Rips and Jortner [3]. They derived the next relation for solvent-controlled ET rate k : * k k* " . (3) 1#(4p/ )(<q* /j) This result corresponds to Eq. (1) with the new frequency factor, which includes the longitudinal relaxation time q . * In this paper we present mainly the theoretical results demonstrating the role of solvent dynamics in #uores-
* Fax: #375-172-84-00-30. E-mail address: [email protected] (V.S. Pavlovich)
cence quenching of polar compounds in polar solutions. Since the nonradiative conversion in polar compounds arises between the charge-separated states and is attended with intramolecular charge transfer, obtained rate constants are compared with those of Marcus (1) and Rips}Jortner (3).
2. Model and general equations Let us consider the ensemble of clusters the nucleuses of which are the #uorescent probe molecules and the solvation shells consist of the solvent molecules. The #uctuations of the dipole}dipole interactions of a probe with nearby solvent molecules in each cluster lead to inhomogeneous broadening of the electronic levels of polar molecules in polar solutions. For every electronic state of a probe molecule there is a band (zone) of quasicontinuous orientational sublevels [4}6]. As shown with full details in Ref. [6], the photo-induced nonequilibrium solvent dynamics in this ensemble can be examined as the motion of a quasi-particle called a histon. For description of collective librations and cooperative jump reorientations of solvent molecules the concept of l- and j-histons are also introduced [6], respectively. From this standpoint the orientational sublevels at the bands (Fig. 1) arise as a result of the motion of l- and j-histons under action of chance forces. Thus, one can say about
0022-2313/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 2 3 1 3 ( 9 9 ) 0 0 3 0 5 - 1
V.S. Pavlovich / Journal of Luminescence 87}89 (2000) 592}594
593
Eqs. (4) and (5) it follows that (2p< exp(!E /k ¹), k "
("=H "k ¹ E "(= !=H )/2"=H ",
(6)
where E is the activation energy of quenching. Comparing Eqs. (2) and (6) we see that "=H" can be identi"ed with j. Thus the contribution of l- and j-histons into the Marcus solvent reorganization energy j*( equals "=H "/2 and is given by j*( "2m a\(e!1)/(2e#1), Fig. 1. Band structure of electronic levels of polar probe in polar solutions. Nonradiative transition S PX is the internal con L version, when X "S , or the intersystem crossing, when L L X "T . L L
the existence of a mixed lj-continuum of histonic sublevels for every electronic state. The transitions between lj-sublevels of di!erent electronic states obey the selection rules determined in Refs. [4}6]. Radiative transitions between band lj-levels have di!erent frequencies u. Taking into account these facts and the resonance nature of nonradiative transitions it is possible to explain the reasons for the hole forming in #uorescence spectrum and the dependence of #uorescence quantum yield not only from the temperature but the viscosity of solvent as well. According to the golden rule of quantum mechanics the nonradiative rate k for the conversion between ljsublevels of S and XL states (Fig. 1) may be written as 2p k " <o oL .
(4)
At high temperatures, when the solvent relaxation time q is signi"cantly shorter than the #uorescence lifetime q , the thermal equilibration takes place in S state and the distribution of clusters throughout the available energy = of lj-sublevels is oH (= )"C exp[!(= !=H )/2d ].
where m is the dipole moment of probe molecule in S state, a is the Onsager radius, e is the static dielectric permittivity of solvent. Since the l- and j-histons are the new quasi- particles it must be emphasized that j*( is the contribution into Marcus reorganization energy from two independent kinds of solvent motion, namely: (i) collective librations and (ii) cooperative jump reorientations (for details see Ref. [6]). The rate k can be presented in an equivalent form by the application of u-distribution:
(2p< (u !uH) k " exp ! ,
D 2D
(7)
where uH is the ensemble-averaged frequency and D is the variance of the frequency u for electronic S PS transitions: e!1 D"4 \k ¹(m !m )a\ , 2e#1 m is the dipole moment of probe molecule in S state. At low temperatures, when q
(5)
Taking into account that the motion of l- and j-histons are appreciably independent (see Ref. [6]) and using the Onsager treatment for dipole}dipole interactions [7], the relations for the ensemble-averaged orientational energy =H and for the variance d may be found. From the resonance condition for S PXL conversion u "u , knowing the value *E16 (Fig. 1), and using the general selection rule [4}6], we have the possibility to obtain a rather cumbersome expression for = , which is not presented here. Because C "(2pd)\ , d " !k ¹=H , o "oH (= ), and oL is taken as unity, from
Fig. 2. Solvent relaxation R and hole "lling F. Nonequilibrium u-distributions 1 is transformed to equilibrium 2 with maximum uH under relaxation and the Stokes shift *u takes place. 1
594
V.S. Pavlovich / Journal of Luminescence 87}89 (2000) 592}594
Fig. 3. Steady-state #uorescence spectra of 4-monomethylamino-N-methylphthalimide in isobutanol at temperatures 137, 142, 145 and 158 K (1}4).
An example of the hole forming in #uorescence spectrum is presented in Fig. 3. With heating, when q is comparable with q , the role of solvent dynamics in #uorescence quenching is illustrated in Fig. 2. There are two signi"cant processes for quenching: (i) the "lling of hole F caused by solvent relaxation R and (ii) the thermal varying of population at hole frequency u . In terms of histons the nonequilibrium solvent dynamics is described in Ref. [6]. At intermediate temperature region the full correlation function includes ultrafast Gaussian and slow Debye contributions [6]. Here we take into account only Debye exponential component with relaxation time q . A semiempirical relation for S PX conversion rate k can be obtained by entering a transmission coe$cient into Eq. (7). After some assumptions and calculations we can write
(2p<q (u !u2 ) k " exp ! ,
D(q #q) 2D
(8)
where q is the radiative #uorescence lifetime, u2 "uH#*u1 q /(q #q), *u1 is the Stokes shift of steady-state #uorescence spectrum under heating. One can see that in Rips}Jortner Eq. (3) and in our Eq. (8) the transmission coe$cients have only the structural similarity. To this we can add that the solvent relaxation time q does not agree with the longitudinal relaxation time q* , because in solvation shells of clusters, q crucially depends on electric "eld produced by polar excited-state probe molecule [8]. Fluorescence quenching controlled by solvent relaxation is observed for phthalimides in alcohols at 77}300 K [9,10]. It is believed that our theoretical results will be useful for interpretation of the data on #uorescence quantum yield and decay time determined for the solvents of di!ering polarity at wide temperature region.
References [1] R.A. Marcus, in: H. Gerischer, J.J. Katz (Eds.), Lightinduced Charge Separation in Biology and Chemistry, Verlag Chemie, Berlin, 1979, p. 15. [2] R.A. Marcus, N. Sutin, Biochem. Biophys. 811 (1985) 265. [3] I. Rips, J. Jortner, J. Chem. Phys. 87 (1987) 2090. [4] V.S. Pavlovich, Weszi Akad. Nauk BSSR, Ser, Fiz.-Mater. Nauk (Minsk) 6 (1987) 55. [5] V.S. Pavlovich, Zh. Prikl. Spektrosk. (Minsk) 64 (1997) 209. [6] V.S. Pavlovich, J. Fluoresc. 7 (1997) 321. [7] L. Onsager, J. Am. Chem. Soc. 58 (1936) 1486. [8] V.S. Pavlovich, S.V. Zablotskii, L.Sh. Afanasiadi, Khim. Phys. (Moscow) 10 (1991) 110. [9] V.S. Pavlovich, S.V. Zablotskii, L.G. Pikulik, Dokl. Akad. Nauk BSSR (Minsk) 31 (1987) 707. [10] V.S. Pavlovich, S.V. Zablotskii, L.G. Pikulik, Zh. Prikl. Spektrosk.(Minsk) 58 (1993) 76.
Excited-state solvent dynamics and #uorescence quenching of solutions Vladimir S. Pavlovich* Institute of Molecular and Atomic Physics, 70 F. Scaryna Prospect, Minsk 220072, Belarus
Abstract In terms of the histons, new quasi-particles, the #uorescence quenching controlled by solvent relaxation is considered for polar compounds in polar solutions. The relations for the nonradiative rate are presented for wide temperature region. At high temperature the contribution of motion of l- and j-histons into the Marcus reorganization energy is found with the help of Onsager model for dipole}dipole interactions. An example of the hole forming in #uorescence spectrum as a result of resonance S PXL conversion is presented. 2000 Elsevier Science B.V. All rights reserved. Keywords: Solvent dynamics; Fluorescence quenching; New quasi-particles; Histons
1. Introduction Following Marcus theory [1,2] for high temperatures in polar solutions the electron transfer (ET) rate k is expressed by 2p k" <(4pjk ¹)\ exp(!E /k ¹),
(1)
where < is the electronic coupling, j is the solvent reorganization energy. The activation energy is given as E "(j#*G3)/4j,
(2)
where *G3 is the standard free-energy change. The dynamic solvent e!ects on the outer-sphere ET rate was studied by Rips and Jortner [3]. They derived the next relation for solvent-controlled ET rate k : * k k* " . (3) 1#(4p/ )(<q* /j) This result corresponds to Eq. (1) with the new frequency factor, which includes the longitudinal relaxation time q . * In this paper we present mainly the theoretical results demonstrating the role of solvent dynamics in #uores-
* Fax: #375-172-84-00-30. E-mail address: [email protected] (V.S. Pavlovich)
cence quenching of polar compounds in polar solutions. Since the nonradiative conversion in polar compounds arises between the charge-separated states and is attended with intramolecular charge transfer, obtained rate constants are compared with those of Marcus (1) and Rips}Jortner (3).
2. Model and general equations Let us consider the ensemble of clusters the nucleuses of which are the #uorescent probe molecules and the solvation shells consist of the solvent molecules. The #uctuations of the dipole}dipole interactions of a probe with nearby solvent molecules in each cluster lead to inhomogeneous broadening of the electronic levels of polar molecules in polar solutions. For every electronic state of a probe molecule there is a band (zone) of quasicontinuous orientational sublevels [4}6]. As shown with full details in Ref. [6], the photo-induced nonequilibrium solvent dynamics in this ensemble can be examined as the motion of a quasi-particle called a histon. For description of collective librations and cooperative jump reorientations of solvent molecules the concept of l- and j-histons are also introduced [6], respectively. From this standpoint the orientational sublevels at the bands (Fig. 1) arise as a result of the motion of l- and j-histons under action of chance forces. Thus, one can say about
0022-2313/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 2 3 1 3 ( 9 9 ) 0 0 3 0 5 - 1
V.S. Pavlovich / Journal of Luminescence 87}89 (2000) 592}594
593
Eqs. (4) and (5) it follows that (2p< exp(!E /k ¹), k "
("=H "k ¹ E "(= !=H )/2"=H ",
(6)
where E is the activation energy of quenching. Comparing Eqs. (2) and (6) we see that "=H" can be identi"ed with j. Thus the contribution of l- and j-histons into the Marcus solvent reorganization energy j*( equals "=H "/2 and is given by j*( "2m a\(e!1)/(2e#1), Fig. 1. Band structure of electronic levels of polar probe in polar solutions. Nonradiative transition S PX is the internal con L version, when X "S , or the intersystem crossing, when L L X "T . L L
the existence of a mixed lj-continuum of histonic sublevels for every electronic state. The transitions between lj-sublevels of di!erent electronic states obey the selection rules determined in Refs. [4}6]. Radiative transitions between band lj-levels have di!erent frequencies u. Taking into account these facts and the resonance nature of nonradiative transitions it is possible to explain the reasons for the hole forming in #uorescence spectrum and the dependence of #uorescence quantum yield not only from the temperature but the viscosity of solvent as well. According to the golden rule of quantum mechanics the nonradiative rate k for the conversion between ljsublevels of S and XL states (Fig. 1) may be written as 2p k " <o oL .
(4)
At high temperatures, when the solvent relaxation time q is signi"cantly shorter than the #uorescence lifetime q , the thermal equilibration takes place in S state and the distribution of clusters throughout the available energy = of lj-sublevels is oH (= )"C exp[!(= !=H )/2d ].
where m is the dipole moment of probe molecule in S state, a is the Onsager radius, e is the static dielectric permittivity of solvent. Since the l- and j-histons are the new quasi- particles it must be emphasized that j*( is the contribution into Marcus reorganization energy from two independent kinds of solvent motion, namely: (i) collective librations and (ii) cooperative jump reorientations (for details see Ref. [6]). The rate k can be presented in an equivalent form by the application of u-distribution:
(2p< (u !uH) k " exp ! ,
D 2D
(7)
where uH is the ensemble-averaged frequency and D is the variance of the frequency u for electronic S PS transitions: e!1 D"4 \k ¹(m !m )a\ , 2e#1 m is the dipole moment of probe molecule in S state. At low temperatures, when q
(5)
Taking into account that the motion of l- and j-histons are appreciably independent (see Ref. [6]) and using the Onsager treatment for dipole}dipole interactions [7], the relations for the ensemble-averaged orientational energy =H and for the variance d may be found. From the resonance condition for S PXL conversion u "u , knowing the value *E16 (Fig. 1), and using the general selection rule [4}6], we have the possibility to obtain a rather cumbersome expression for = , which is not presented here. Because C "(2pd)\ , d " !k ¹=H , o "oH (= ), and oL is taken as unity, from
Fig. 2. Solvent relaxation R and hole "lling F. Nonequilibrium u-distributions 1 is transformed to equilibrium 2 with maximum uH under relaxation and the Stokes shift *u takes place. 1
594
V.S. Pavlovich / Journal of Luminescence 87}89 (2000) 592}594
Fig. 3. Steady-state #uorescence spectra of 4-monomethylamino-N-methylphthalimide in isobutanol at temperatures 137, 142, 145 and 158 K (1}4).
An example of the hole forming in #uorescence spectrum is presented in Fig. 3. With heating, when q is comparable with q , the role of solvent dynamics in #uorescence quenching is illustrated in Fig. 2. There are two signi"cant processes for quenching: (i) the "lling of hole F caused by solvent relaxation R and (ii) the thermal varying of population at hole frequency u . In terms of histons the nonequilibrium solvent dynamics is described in Ref. [6]. At intermediate temperature region the full correlation function includes ultrafast Gaussian and slow Debye contributions [6]. Here we take into account only Debye exponential component with relaxation time q . A semiempirical relation for S PX conversion rate k can be obtained by entering a transmission coe$cient into Eq. (7). After some assumptions and calculations we can write
(2p<q (u !u2 ) k " exp ! ,
D(q #q) 2D
(8)
where q is the radiative #uorescence lifetime, u2 "uH#*u1 q /(q #q), *u1 is the Stokes shift of steady-state #uorescence spectrum under heating. One can see that in Rips}Jortner Eq. (3) and in our Eq. (8) the transmission coe$cients have only the structural similarity. To this we can add that the solvent relaxation time q does not agree with the longitudinal relaxation time q* , because in solvation shells of clusters, q crucially depends on electric "eld produced by polar excited-state probe molecule [8]. Fluorescence quenching controlled by solvent relaxation is observed for phthalimides in alcohols at 77}300 K [9,10]. It is believed that our theoretical results will be useful for interpretation of the data on #uorescence quantum yield and decay time determined for the solvents of di!ering polarity at wide temperature region.
References [1] R.A. Marcus, in: H. Gerischer, J.J. Katz (Eds.), Lightinduced Charge Separation in Biology and Chemistry, Verlag Chemie, Berlin, 1979, p. 15. [2] R.A. Marcus, N. Sutin, Biochem. Biophys. 811 (1985) 265. [3] I. Rips, J. Jortner, J. Chem. Phys. 87 (1987) 2090. [4] V.S. Pavlovich, Weszi Akad. Nauk BSSR, Ser, Fiz.-Mater. Nauk (Minsk) 6 (1987) 55. [5] V.S. Pavlovich, Zh. Prikl. Spektrosk. (Minsk) 64 (1997) 209. [6] V.S. Pavlovich, J. Fluoresc. 7 (1997) 321. [7] L. Onsager, J. Am. Chem. Soc. 58 (1936) 1486. [8] V.S. Pavlovich, S.V. Zablotskii, L.Sh. Afanasiadi, Khim. Phys. (Moscow) 10 (1991) 110. [9] V.S. Pavlovich, S.V. Zablotskii, L.G. Pikulik, Dokl. Akad. Nauk BSSR (Minsk) 31 (1987) 707. [10] V.S. Pavlovich, S.V. Zablotskii, L.G. Pikulik, Zh. Prikl. Spektrosk.(Minsk) 58 (1993) 76.