chemicallytechFine Chemical TechnologiesТонкие химические технологии2410-65932686-7575MIREA – Russian Technological University (RTU MIREA).chemicallytech-424Research ArticleTHEORETICAL BASIS OF CHEMICAL TECHNOLOGYТЕОРЕТИЧЕСКИЕ ОСНОВЫ ХИМИЧЕСКОЙ ТЕХНОЛОГИИSimple diffusion model of cage effectПростая диффузионная модель клеточного эффектаФинкельштейнЕ. И.FinkelshteynE. I.

кафедра Биотехнологии и бионанотехнологии, профессор

evgfink@yandex.ruМИТХТ им. М.В. Ломоносова, 119571, Москва, пр-т Вернадского, д. 86РоссияM.V. Lomonosov Moscow State University of Fine Chemical Technologies, 86, Vernadskogo pr., Moscow 119571Russian Federation201428122014966974Copyright © Finkelshteyn E.I., 20142014Финкельштейн Е.И.Finkelshteyn E.I.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.finechem-mirea.ru/jour/article/view/424

On the assumption of the initial Gaussian distribution of the inter-radical distances the dependence of the radical combination probability in a solvent cage on the viscosity and temperature was derived. The dependence describes the published data correctly and may be used for the initial inter-radical distances estimation in different radical pairs.

В представлении о гауссовом распределении начальных расстояний между партнёрами радикальных пар получена зависимость вероятности рекомбинации радикалов в клетке растворителя от вязкости и температуры, правильно описывающая опубликованные данные и позволяющая оценить начальные расстояния в различных радикальных парах.

клеточный эффектвязкостьрекомбинациямежрадикальные расстоянияcage effectviscosityradical recombinationinter-radical distances in cage.ReferencesFranck J., Rabinowitsch E. Some remarks about free radicals and the photochemistry of solutions // Trans. Furaday Soc. 1934. V. 30. Р. 120-130.Franck J., Rabinowitsch E. Some remarks about free radicals and the photochemistry of solutions // Trans. Furaday Soc. 1934. V. 30. Р. 120-130.North A.M. The collision theory of chemical reactions in liquids. London: Methuen, 1964. 145 p.North A.M. The collision theory of chemical reactions in liquids. London: Methuen, 1964. 145 p.Koenig T., Fischer H. «Cage» Effects // Free radicals / Ed. J.K. Kochi. N Y: J. Wiley & Sons, Inc. 1973. V. 1. Р. 157-189.Koenig T., Fischer H. «Cage» Effects // Free radicals / Ed. J.K. Kochi. N Y: J. Wiley & Sons, Inc. 1973. V. 1. Р. 157-189.Lorand J.P. The Cage Effect // Progress in Inorganic Chemistry. V. 17. / Ed. J.O. Edwards. N Y: J. Wiley & Sons, 1972. Р. 208-325.Lorand J.P. The Cage Effect // Progress in Inorganic Chemistry. V. 17. / Ed. J.O. Edwards. N Y: J. Wiley & Sons, 1972. Р. 208-325.Денисов Е.Т. Механизмы гомолитического распада молекул в жидкой фазе // Итоги науки и техники. Серия: Кинетика и катализ. 1981. Т. 9. С. 49-82.Денисов Е.Т. Механизмы гомолитического распада молекул в жидкой фазе // Итоги науки и техники. Серия: Кинетика и катализ. 1981. Т. 9. С. 49-82.Багдасарьян Х.С. Кинетика рекомбинации радикалов и ион-радикалов в жидкой фазе // Успехи химии. 1984. Т. 53. № 7. С. 1073-1100.Багдасарьян Х.С. Кинетика рекомбинации радикалов и ион-радикалов в жидкой фазе // Успехи химии. 1984. Т. 53. № 7. С. 1073-1100.Багдасарьян Х.С. Кинетика рекомбинаций в жидкой среде. М.: Наука, 1989. 95 с.Багдасарьян Х.С. Кинетика рекомбинаций в жидкой среде. М.: Наука, 1989. 95 с.Denisov E.T., Denisova T.G., Pokidova T.S. Handbook of free radical initiators. Hoboken: Wiley-Interscience, 2003. 879 p.Denisov E.T., Denisova T.G., Pokidova T.S. Handbook of free radical initiators. Hoboken: Wiley-Interscience, 2003. 879 p.Denisov E.T., Afanas’ev I.B. Oxidation and antioxidants in organic chemistry and biology. Boka Raton, London, New York: Taylor & Francis Group, 2005. 981 p.Denisov E.T., Afanas’ev I.B. Oxidation and antioxidants in organic chemistry and biology. Boka Raton, London, New York: Taylor & Francis Group, 2005. 981 p.Khudyakov I.V., Zharikov A.A., Burshtein A.I. Cage effect dynamics // J. Chem. Phys. 2010. V. 132. № 1. Р. 014104-1- 014104-6.Khudyakov I.V., Zharikov A.A., Burshtein A.I. Cage effect dynamics // J. Chem. Phys. 2010. V. 132. № 1. Р. 014104-1- 014104-6.Khudyakov I.V., Turro N.J. Cage effect dynamics under photolysis of photoinitiators // De- signed Monomers and Polymers. 2010. V. 13. Р. 487-496.Khudyakov I.V., Turro N.J. Cage effect dynamics under photolysis of photoinitiators // De- signed Monomers and Polymers. 2010. V. 13. Р. 487-496.Lyon R.K. The cage effect in solution and gas phase with application to the determination of rate constants // J. Amer. Chem. Soc. 1964. V. 85. № 10. Р. 1907-1913.Lyon R.K. The cage effect in solution and gas phase with application to the determination of rate constants // J. Amer. Chem. Soc. 1964. V. 85. № 10. Р. 1907-1913.Khudyakov I.V., Kiryukhin Yu.I., Yasmenko A.I. Kinetiks of geminate recombinaton of aromatic free radicals // Chem. Phys. Letters. 1980. V. 74. № 3. Р. 462-466.Khudyakov I.V., Kiryukhin Yu.I., Yasmenko A.I. Kinetiks of geminate recombinaton of aromatic free radicals // Chem. Phys. Letters. 1980. V. 74. № 3. Р. 462-466.Fricke H. Track effect in iochemistry of aqueous solutions // Ann. New York Acad. Sci. 1955. V. 59. Р. 567-573.Fricke H. Track effect in iochemistry of aqueous solutions // Ann. New York Acad. Sci. 1955. V. 59. Р. 567-573.Франк-Каменецкий Л.А. Диффузия и теплопередача в химической кинетике. М.: Наука, 1987. 490 с.Франк-Каменецкий Л.А. Диффузия и теплопередача в химической кинетике. М.: Наука, 1987. 490 с.Noyes R.M. Effects of diffusion rates on chemical kinetics // Progress in Reaction Kinetics / Ed. G. Porter. N Y: Pergamon Press, 1961. V. 1. Р. 129-157.Noyes R.M. Effects of diffusion rates on chemical kinetics // Progress in Reaction Kinetics / Ed. G. Porter. N Y: Pergamon Press, 1961. V. 1. Р. 129-157.Dobis 0., Pearson J. M., Szwarc M. Studies of cage reactions. I. The need for refined models. Combination of CF3 radicals // J. Amer. Chem. Soс. 1968. V. 90. № 2. Р. 278-282.Dobis 0., Pearson J. M., Szwarc M. Studies of cage reactions. I. The need for refined models. Combination of CF3 radicals // J. Amer. Chem. Soс. 1968. V. 90. № 2. Р. 278-282.Niki E., Kamiya Y. Cage reactions of tert-butoxy radicals. Effects of solvent and viscosity // J. Amer. Chem. Soc. 1974. V. 96. № 7. Р. 2129-2133.Niki E., Kamiya Y. Cage reactions of tert-butoxy radicals. Effects of solvent and viscosity // J. Amer. Chem. Soc. 1974. V. 96. № 7. Р. 2129-2133.Kiefer H., Traylor T.G. Cage reactions of t-butoxy radicals. Effects of viscosity and of in-terventing molecules // J. Amer. Chem. Soc. 1967. V. 89. № 25. Р. 6667-6671.Kiefer H., Traylor T.G. Cage reactions of t-butoxy radicals. Effects of viscosity and of in-terventing molecules // J. Amer. Chem. Soc. 1967. V. 89. № 25. Р. 6667-6671.Neuman R.C., Jr., Bussey R.J. High pressure studies. V. Activation volumes for activation and diffusion of geminate t-butoxy radicals // J. Amer. Chem. Soc. 1970. V. 92. № 8. Р. 2440-2444.Neuman R.C., Jr., Bussey R.J. High pressure studies. V. Activation volumes for activation and diffusion of geminate t-butoxy radicals // J. Amer. Chem. Soc. 1970. V. 92. № 8. Р. 2440-2444.Lorand J.P., Wallace R.W. Radicals and scavengers. IV. Cage effects in the decomposition of tert-butyl peresters which generate the stable radicals triphenylmethyl and 1,l- diphenylneopentyl // J. Amer. Chem. Soc. 1974. V. 96. № 5. Р. 1402-1407.Lorand J.P., Wallace R.W. Radicals and scavengers. IV. Cage effects in the decomposition of tert-butyl peresters which generate the stable radicals triphenylmethyl and 1,l- diphenylneopentyl // J. Amer. Chem. Soc. 1974. V. 96. № 5. Р. 1402-1407.Chakravorty K., Pearson J. M., Szwarc M. Studies of cage reactions. II. Combination of CH3 radicals and of CH3, and CF3 into CF3CH3 // J. Amer. Chem. Soc. 1968. V. 90. № 2. Р. 283-285.Chakravorty K., Pearson J. M., Szwarc M. Studies of cage reactions. II. Combination of CH3 radicals and of CH3, and CF3 into CF3CH3 // J. Amer. Chem. Soc. 1968. V. 90. № 2. Р. 283-285.Kodama S. Studies of the cage effect of solvent. IV. Dependence of the cage combination of methyl radicals on solvent and on temperature // Bull. Chem. Soc. Japan. 1962. V. 35. № 5. Р. 827-832.Kodama S. Studies of the cage effect of solvent. IV. Dependence of the cage combination of methyl radicals on solvent and on temperature // Bull. Chem. Soc. Japan. 1962. V. 35. № 5. Р. 827-832.Kodama S. Studies of the cage effect of solvent. I. Photolysis of azomethane in n-hexane // Bull. Chem. Soc. Japan. 1962. V. 35. № 4. Р. 652-657.Kodama S. Studies of the cage effect of solvent. I. Photolysis of azomethane in n-hexane // Bull. Chem. Soc. Japan. 1962. V. 35. № 4. Р. 652-657.Kodama S. Studies of the cage effect of solvent. II. Photolysis of azoethane in various solvents // Bull. Chem. Soc. Japan. 1962. V. 35. № 4. P. 658-662.Kodama S. Studies of the cage effect of solvent. II. Photolysis of azoethane in various solvents // Bull. Chem. Soc. Japan. 1962. V. 35. № 4. P. 658-662.Stefani A.P., Thrower G.F., Jordan C.F. Solvent effects in electroneutral reactions. 11. diffusion-controlled reactions of ethyl and trifluoromethyl radicals // J. Phys. Chem. 1969. V. 73. № 5. Р. 1257-1261.Stefani A.P., Thrower G.F., Jordan C.F. Solvent effects in electroneutral reactions. 11. diffusion-controlled reactions of ethyl and trifluoromethyl radicals // J. Phys. Chem. 1969. V. 73. № 5. Р. 1257-1261.Oelkers A.B., Scatena L.F., Tyler D.R. Femtosecond pump-probe transient absorption study of the photolysis of [Cp¢Mo(CO)3]2 (Cp¢=h5-C5H4CH3): Role of translational and rotational diffusion in the radical cage effect // J. Phys. Chem. A. 2007. V. 111. № 25. Р. 5353-5360.Oelkers A.B., Scatena L.F., Tyler D.R. Femtosecond pump-probe transient absorption study of the photolysis of [Cp¢Mo(CO)3]2 (Cp¢=h5-C5H4CH3): Role of translational and rotational diffusion in the radical cage effect // J. Phys. Chem. A. 2007. V. 111. № 25. Р. 5353-5360.Male J.L., Lindfors B.E., Covert K.J., Tyler D.R. The Effect of Radical Size and Mass on the Cage Recombination Efficiency of Photochemically Generated Radical Cage Pairs // J. Amer. Chem. Soc. 1998. V. 120. № 50. Р. 13176-13186.Male J.L., Lindfors B.E., Covert K.J., Tyler D.R. The Effect of Radical Size and Mass on the Cage Recombination Efficiency of Photochemically Generated Radical Cage Pairs // J. Amer. Chem. Soc. 1998. V. 120. № 50. Р. 13176-13186.Braden D.A., Parrack E.E., Tyler D.R. Solvent cage effects. I. Effect of radical mass and size on radical cage pair recombination efficiency. II. Is geminate recombination of polar radicals sensitive to solvent polarity? // Coord. Chem. Rev. 2001. V. 211. Р. 279-294.Braden D.A., Parrack E.E., Tyler D.R. Solvent cage effects. I. Effect of radical mass and size on radical cage pair recombination efficiency. II. Is geminate recombination of polar radicals sensitive to solvent polarity? // Coord. Chem. Rev. 2001. V. 211. Р. 279-294.

The authors declare that there are no conflicts of interest present.