Journal of Fluorescence

, Volume 13, Issue 3, pp 201–219 | Cite as

Effects of the Solvent Refractive Index and Its Dispersion on the Radiative Decay Rate and Extinction Coefficient of a Fluorescent Solute

  • Dmitri Toptygin


It is well known that the probabilities of radiative transitions in a medium differ from those in vacuum. Excitation of a fluorescent molecule and its radiative decay are examples of radiative transitions. The rates of these processes in solution depend on the optical characteristics of the solvent. In this article the radiative decay rate and the extinction coefficient of a fluorescent molecule in solution are expressed in terms of the intrinsic properties of the fluorescent molecule (electronic transition moments) and the optical characteristics of the solvent (refractive index, group velocity of light). It is shown that the group velocity does not enter in the final expressions for the radiative decay rate and the extinction coefficient; this means that the dispersion of the refractive index has no effect on these quantities. The expressions for both the radiative decay rate and the extinction coefficient contain the refractive index of the solvent and the local field correction factor. The latter depends on the cavity model, and, for some cavity models, on the shape of the cavity. Four types of cavity models are discussed; for each model the limits of applicability are examined. Experimental evidence in support of specific cavity models is reviewed.

Radiative decay rate extinction coefficient refractive index local field correction empty cavity model 


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  1. 1.
    J. R. Lakowicz (1999) Principles of Fluorescence Spectroscopy, 2nd ed, Kluwer Academic/Plenum Press, New York.Google Scholar
  2. 2.
    Y. Ooshika (1954) Absorption spectra of dyes in solution. J. Phys. Soc. Japan 9(4), 594–602.Google Scholar
  3. 3.
    N. Mataga, Y. Kaifu, and M. Koizumi (1956) Solvent effects upon fluorescence spectra and the dipolemoments of excited molecules. Bull. Chem. Soc. Japan 29(4), 465–470.Google Scholar
  4. 4.
    E. McRae (1957) Theory of solvent effects on molecular electronic spectra: Frequency shifts. J. Phys. Chem. 61(5), 562–572.Google Scholar
  5. 5.
    Von E. Lippert (1957) Spektroskopische bestimmung des dipol-momentes aromatischer verbindungen im ersten angeregten sin-gulettzustand. Z. Elektrochem. 61(8), 962–975.Google Scholar
  6. 6.
    N. G. Bakhshiev (1961) Universal molecular interactions and their effect on the position of the electronic spectra of molecules in two-component solutions 1: Theory (liquid solutions). Optics Spectrosc. 10 (6), 717–726.Google Scholar
  7. 7.
    F. Perrin (1926) Polarisation de la lumiere de fluorescence: Vie moyenne des molecules dans l'etat excite. J. Phys. Radium Serie 6, 7 (12), 390–401.Google Scholar
  8. 8.
    S. J. Strickler and R. A. Berg (1962) Relationship between absorption intensity and fluorescence lifetime of molecules. J. Chem. Phys. 37(4), 814–822.Google Scholar
  9. 9.
    L. D. Landau and E. M. Lifshitz (1975) The classical theory of fields, 4 th ed, Pergamon Press, New York.Google Scholar
  10. 10.
    G. Herzberg (1950) Molecular Spectra and Molecular Structure: I. Spectra of Diatomic Molecules, 2nd ed, D. Van Nostrand Co., New York.Google Scholar
  11. 11.
    L. D. Landau and E. M. Lifshitz (1977) Quantum Mechanics: Non-Relativistic Theory, 2nd ed, Pergamon Press, New York.Google Scholar
  12. 12.
    V. B. Berestetskii, E. M. Lifshitz, and L. P. Pitaevskii. (1982) Quantum Electrodynamics. 2nd ed. Pergamon Press, New York.Google Scholar
  13. 13.
    L. D. Landau and E. M. Lifshitz (1984) Electrodynamics of Continuous Media, 2nd ed, Pergamon Press, New York.Google Scholar
  14. 14.
    E. Yablonovitch, T. J. Gmitter, and R. Bhat (1988) Inhibited and enhanced spontaneous emission from optically thin AlGaAs/GaAs double heterostructures. Phys. Rev. Lett. 61(22), 2546–2549.Google Scholar
  15. 15.
    R. J. Glauber and M. Lewenstein (1991) Quantum optics of dielectric media. Phys. Rev. A 43(1), 467–491.Google Scholar
  16. 16.
    D. Toptygin, R. S. Savtchenko, N. D. Meadow, S. Roseman, and L. Brand (2002) Effect of the solvent refractive index on the excited-state lifetime of a single tryptophan residue in a protein. J. Phys. Chem. B 106, 3724–3734.Google Scholar
  17. 17.
    A. Einstein (1917) Zur quantentheorie der strahlung. Physik. Z. 18, 121–128.Google Scholar
  18. 18.
    G. Juzeliunas (1995) Molecule-radiation and molecule-molecule processes in condensed media: A microscopic QED theory. Chem. Phys. 198(1–2), 145–158.Google Scholar
  19. 19.
    T. Förster (1951) Fluoreszenz organischer Verbindungen, Vandenhoeck & Ruprecht, Göttingen.Google Scholar
  20. 20.
    H. A. Lorentz (1909) The Theory of Electrons and Its Applications to the Phenomena of Light and Radiant Heat. Leipzig, Teubner.Google Scholar
  21. 21.
    N. Q. Chako (1934) Absorption of light in organic compounds. J. Chem. Phys. 2, 644–653.Google Scholar
  22. 22.
    G. Kortüm (1936). Das optische verhalten gelöster ionen und seine bedeutung für die struktur elektrolytischer lösungen. Z. Physik. Chem. (B) 33(4), 243–264.Google Scholar
  23. 23.
    W. Liptay (1966). Die lösungsmittelabhängigkeit der intensität von elektronenbanden. I. Theorie. Z. Naturforschg. A 21A(10), 1605–1618.Google Scholar
  24. 24.
    S. M. Barnett, B. Huttner, and R. Loudon (1992) Spontaneous emission in absorbing dielectric media. Phys. Rev. Lett. 68(25), 3698–3701.Google Scholar
  25. 25.
    G. L. J. A. Rikken and Y. A. R. R. Kessener (1995) Local field effects and electric and magnetic dipole transitions in dielectrics. Phys. Rev. Lett. 74(6), 880–883.Google Scholar
  26. 26.
    S. M. Barnett, B. Huttner, R. Loudon, and R. Matloob (1996) Decay of excited atoms in absorbing dielectrics. J. Phys. B: At. Mol. Opt. Phys. 29, 3763–3781.Google Scholar
  27. 27.
    F. J. P. Schuurmans, D. T. N. de Lang, G. H. Wegdam, R. Sprik, and A. Lagendijk (1998) Local-field effects on spontaneous emission in a dense supercritical gas. Phys. Rev. Lett. 80(23), 5077–5080.Google Scholar
  28. 28.
    P. de Vries and A. Lagendijk (1998) Resonant scattering and spontaneous smission in dielectrics: Microscopic derivation of localfield effects. Phys. Rev. Lett. 81(7), 1381–1384.Google Scholar
  29. 29.
    S. Scheel, L. Knöll, D.-G. Welsch, and S. M. Barnett (1999) Quantum local-field corrections and spontaneous decay. Phys. Rev. A. 60(2), 1590–1597.Google Scholar
  30. 30.
    M. Fleischhauer (1999) Spontaneous emission and level shifts in absorbing disordered dielectrics and dense atomic gases: A Green's-function approach. Phys. Rev. A 60(3), 2534–2539.Google Scholar
  31. 31.
    S. Scheel, L. Knöll, and D.-G. Welsch (1999) Spontaneous decay of an excited atom in an absorbing dielectric. Phys. Rev. A. 60(5), 4094–4104.Google Scholar
  32. 32.
    F. J. P. Schuurmans, P. de Vries, and A. Lagendijk (2000) Localfield effects on spontaneous emission of impurity atoms in homogeneous dielectrics. Phys. Lett. A 264(1), 472–477.Google Scholar
  33. 33.
    F. J. P. Schuurmans and A. Lagendijk (2000) Luminescence of Eu(fod)3 in a homologic series of simple alcohols. J. Chem. Phys. 113(8), 3310–3314.Google Scholar
  34. 34.
    M. S. Tomas (2001) Local-field corrections to the decay rate of excited molecules in absorbing cavities: The Onsager model. Phys. Rev. A 63(5), 053811–1–053811–11.Google Scholar
  35. 35.
    V. M. Agranovich and M. D. Galanin (1982) Electronic Excitation Energy Transfer in Condensed Matter, North-Holland, Amsterdam.Google Scholar
  36. 36.
    T. Shibuya (1983) A dielectric model for the solvent effect on the intensity of light-absorption. J. Chem. Phys. 78(8), 5175–5182.Google Scholar
  37. 37.
    T. Shibuya (1983) The refractive-index correction to the radiative rate constant. Chem. Phys. Lett. 103(1), 46–48.Google Scholar
  38. 38.
    C. Q. Cao, W. Long, and H. Cao (1997) The local field correction factor for spontaneous emission. Phys. Lett. A 232, 15–24.Google Scholar
  39. 39.
    E. V. Tkalya (2001) Spontaneous multipole radiation in a condensed medium. J. Exper. Theoret. Phys. 92(1), 71–79.Google Scholar
  40. 40.
    E. V. Tkalya (2002) Spontaneous electric multipole emission in a condensed medium and toroidal moments. Phys. Rev. A 65, 022504–1–022504–5.Google Scholar
  41. 41.
    T. B. Jones (1995) Electromechanics of Particles, Cambridge, New York.Google Scholar
  42. 42.
    S. Hirayama, H. Yasuda, M. Okamoto, and F. Tanaka (1991) Effect of pressure on the natural radiative lifetimes of anthracene derivatives in solution. J. Phys. Chem. 95(8), 2971–2975.Google Scholar
  43. 43.
    Y.-P. Sun and M. A. Fox (1993) Fluorescence of 9–cyanoanthracene in supercritical ethane: A very unusual dependence of fluorescence lifetime on solvent refractive index. J. Phys. Chem. 97(2), 282–283.Google Scholar
  44. 44.
    J. Saltiel, A. S. Waller, D. F. Sears, and C. Z. Garrett (1993) Fluorescence quantum yields of trans-stilbene-d0 and-d2 in n-hexane and n-tetradecane: Medium and deuterium isotope effects on decay process. J. Phys. Chem. 97(11), 2516–2522.Google Scholar
  45. 45.
    J. K. Rice, E. D. Niemeyer, and F. V. Bright (1996) Solute-fluid coupling and energy dissipation in supercritical fluids: 9–cyanoanthracene in C2H6, CO2, and CF3H. J. Phys. Chem. 100(20), 8499–8507.Google Scholar
  46. 46.
    S. Hirayama, K. Shobatake, and K. Tabayashi (1985) Lack of a heavy-atom effect on fluorescence lifetimes of 9–cyanoanthracene-rare gas clusters in a supersonic free jet. Chem. Phys. Lett. 121(3), 228–232.Google Scholar
  47. 47.
    D. Toptygin and L. Brand (1993) Fluorescence decay of DPH in lipid membranes: Influence of the external refractive index. Biophys. Chem. 48(2), 205–220.Google Scholar
  48. 48.
    D. Toptygin and L. Brand (1995) Determination of DPH order parameters in unoriented vesicles. J. Fluoresc. 5(1), 39–50.Google Scholar
  49. 49.
    M. M. G. Krishna and N. Periasamy (1998) Fluorescence of organic dyes in lipid membranes: Site of solubilization and effects of viscosity and refractive index on lifetimes. J. Fluoresc. 8(1), 81–91.Google Scholar
  50. 50.
    M. M. G. Krishna and N. Periasamy (1998) Orientational distribution of linear dye molecules in bilayer membrances. Chem. Phys. Lett. 298(4–6), 359–367.Google Scholar
  51. 51.
    E. P. Petrov, J. V. Kruchenok, and A. N. Rubinov (1999) Effect of the external refractive index on fluorescence kinetics of pery-lene in human erythrocyte ghosts. J. Fluoresc. 9(2), 111–121.Google Scholar
  52. 52.
    P. Lavallard, M. Rosenbauer, and T. Gacoin (1996) Influence of surrounding dielectrics on the spontaneous emission of sulforho-damine B molecules. Phys. Rev. A 54(6), 5450–5453.Google Scholar
  53. 53.
    G. Lamouche, P. Lavallard, and T. Gacoin (1998). Spontaneous emission of dye molecules as a function of the surrounding dielectric medium. J. Luminesc. 76–77, 662–665.Google Scholar
  54. 54.
    G. Lamouche, P. Lavallard, and T. Gacoin (1999) Optical properties of dye molecules as a function of the surrounding dielectric medium. Phys. Rev. A 59(6), 4668–4674.Google Scholar
  55. 55.
    K. H. Drexhage (1970) Influence of a dielectric interface on fluor-escence decay time. J. Lumines. 1,2, 693–701.Google Scholar

Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • Dmitri Toptygin
    • 1
  1. 1.Department of BiologyJohns Hopkins UniversityBaltimore, Maryland

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