38 RADIATION BIOLOGY 



in which co is the original concentration of quenching agent. This equa- 

 tion, also due to Smoluchowski (1918), is a fair first approximation but 

 fails, as does the Stern-Volmer mechanism, at high D and high co- Cor- 

 rections for these and electrostatic effects have been given by Montroll 

 (1946), Umberger and LaMer (1945), and Grand et al. (1951), so that it 

 is now possible to relate rate constants for quenching to those for dif- 

 fusion in a variety of cases. Some examples of diffusion-limited reactions 

 thus treated are the quenching of uranin fluorescence by aniline and of 

 riboflavin fluorescence by potassium iodide (Grand et al, 1951). The 

 effective quenching radii determined in this way are usually less than 

 the combined kinetic-theory radii of the participants. Collision cross 

 sections calculated from simple collision theory, on the other hand, are 

 frequently much larger (Baxter, 1930; Boechner, 1930). The mean life- 

 times can be determined with high precision and are satisfactorily in 

 agreement with lifetimes determined by depolarization of fluorescence. 

 Fluorescence produced by an initially polarized incident light beam is 

 polarized if the viscosity of the solvent hinders rotation of the excited 

 molecule until emission can take place (see, for instance, Perrin, 1926; 

 Pringsheim and Wavilow, 1926; Lewschin, 1924). A study of depolari- 

 zation versus viscosity yields the mean lifetime of excitation. 



Diffusion-limited processes afford scant information on energy exchange 

 between molecules. Quenching-rate constants determined when the 

 interaction of participants is rate-limiting are more helpful. In solution 

 reactions, viscosity has little effect on rate, but chemical properties do 

 affect it. Quenching reactions of this type alone are of interest in this 

 discussion of energy transfer. However, we must include for complete- 

 ness a third interpretation of the quenching constant ka, different from 

 the first two discussed and of minor significance since such cases occur 

 rarely if at all. In this last case the quencher enters and escapes from 

 the vicinity of the excited molecule several times during the lifetime of 

 excitation. The constant k-, is a conventional bimolecular rate constant 

 and can be expressed in the usual form, given by Eq. (1-12). The reac- 

 tion, which is independent of viscosity, proceeds hke any reaction with a 

 positive free energy of activation. 



4-3. ENERGY TRANSFER BETWEEN ELECTRONIC DEGREES 



OF FREEDOM 



The simplest example of a process in which electronic excitation energy 

 is transferred directly as such to cause electronic excitation of the quench- 

 ing molecule is the collision of two atoms in the gas phase. Mercury 

 atoms excited at 2537.5 A to the e^P? state fluoresce with unit quantum 

 yield at low pressures. At higher pressures, collisions of the second kind 

 with other atoms quench the fluorescence. Carlo (1922) and Carlo and 

 Franck (1923) noticed that thallium atoms were efficient in the quench- 



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