1286 THE PIGMENT FACTOR CHAP. 32 



gested that concentration quenching of fluorescence is generally due to 

 remote energy transfer. This is certainly not true as a general rule, since 

 in many dyestuffs (such as methylene blue) self-quenching is due pre- 

 dominantly to the formation of nonfluorescent dimers at the higher con- 

 centrations. Furthermore, at concentrations as high as 10"^ mole/hter, 

 quenching (and depolarization) by actual kinetic encounters is unlikely to 

 be entirely negligible even in a medium as viscous as glycerol. 



In methylene blue and similar dyestuffs, the self-quenching occurs at concentra- 

 tions at which dimer formation is revealed by changes in the absorption spectrum. In 

 other dyestuffs, however, quenching occurs when the equilibrium concentration of di- 

 meric molecules is too small to permit the assumption that only the Ught quanta directly 

 absorbed by such molecules are lost for fluorescence. The concentration quenching 

 can nevertheless be attributed to dimer formation, by means of either or both of the 

 following two hypotheses : first, that short-lived, nonfluorescent dimers can be formed 

 in encounters of excited and normal pigment molecules; and second, that the excitation 

 can "seek out" the few dimeric molecules present in equilibrium, by making numerous 

 jumps from molecule to molecule during the excitation period (Forster's hypothesis). 

 According to Franck and Livingston (1949), migration of excitation energy could lead 

 to quenching also by another mechanism, not requiring dimers: the perambulating 

 quantum could be dissipated whenever in its travel it visits a molecule containing an 

 abnormally high amount of vibrational energy, since, in such a molecule, electronic exci- 

 tation may produce a configuration permitting conversion of the electronic energy into 

 vibrations of the ground state (for an objection to this hypothesis, see Forster 1951, p. 

 252). 



A mathematical theory of quenching by energy migration was developed also by 

 Vavilov (1942, 1944, 1950), who postulated that each transfer of electronic energy from 

 molecule to molecule involves a certain probability of its loss, without specifying the 

 mechanism of this dissipation. 



Perrin (1932) calculated, using a classical harmonic oscillator as a model 

 of pigment molecules, that the probability of energy transfer from the orig- 

 inally excited to a second, resonating oscillator, becomes equal to the prob- 

 abihty of re-emission of energy by the primary absorber, when the distance 

 between the two oscillators is of the order of X/27, corresponding to about 

 100 myu for visible light. Neither the concentration quenching nor the de- 

 polarization occur at such extreme dilutions. Forster (1946) ascribed this 

 to lack of exact resonance (assumed in Perrin's calculations) . The resonance 

 is not exact for two reasons: the displacement of the fluorescence band 

 relative to the absorption band, and the finite width of both bands. Forster 

 made a rough calculation, taking into account two requirements : (a) that 

 the frequencies of the two interacting oscillators must be within the region 

 where the fluorescence band and the absorption band overlap, and (6) that 

 these frequencies must differ by not more than E/h (where E is the inter- 

 action energy). The result of this calculation is that the "critical distance" 

 {i. e., the intermolecular distance at which the probabilities of re-emission 



