FACTORS LIMITING THE YIELD 761 



which is significantly different from 1 if f is not < T/n, i. e., if the duration 

 of the thermal fluctuation is not much shorter than that of electronic ex- 

 citation of a single molecule. The former can be postulated to last for a 

 period of a few molecular vibrations, thus t ^ 10 -^^ sec. The total period 

 of electronic excitation is T ^ 10 -« sec. (for example, in alcoholic chloro- 

 phyll solution, the natural life-time of excitation is ^5 X 10-^ sec; the 

 actual life-time must be ten times shorter, as indicated by a fluorescence 

 yield of about 10%). Under these conditions, for t to be not much shorter 

 than T/n, the number n must be higher than 10^ i.e., excitation energy 

 must be exchanged more than ten thousand times before its dissipation 

 (staying < 10-^^ gee. at each molecule visited). The role of thermally 

 excited ("hot") monomeric dyestuff molecules in the concentration quench- 

 ing of fluorescence thus is predicated on this minimum length of energy 

 exchange chains, and on the possibility of internal conversion occurring 

 during the extremely short sojourn of the electronic energy in the hot mole- 

 cule. It may be suggested that conversion requires (at least) a period of a 

 single molecular vibration (^10-^^ sec). This would restrict quenching 

 by hot molecules (in the case of chlorophyll) to exchange chains not shorter 

 than 10^ and not longer than 10^ molecules. 



In addition to the various physical mechanisms of self-quenching which 

 were considered so far, two chemical mechanisms also are feasible, analogous 

 to the two chemical mechanisms of quenching by foreign substances, dis- 

 cussed in section (c). They are: an oxidation-reduction reaction between 

 the excited and a normal molecule (photodismutation) : 



(23.3) Chi* + Chi > oChl + rChl 



and formation of nonfluorescent dimers by two normal molecules: 



(23.4) Chi + Chi , Chl2 



Dimerization of dyestuff molecules is favored by the fact that marked 

 resonance attraction must occur not only between an excited and a normal 

 molecule (as discussed above), but also between two molecules in the non- 

 excited state. (This application of London's theory of intermolecular 

 forces to pigment molecules was suggested by Rabinowitch and Epstein 

 1941.) The tendency of dyestuff molecules to dimerize (or polymerize) 

 in solution may be attributed to such resonance phenomena. In many 

 cases— perhaps the majority of those observed so far—self-quenching of 

 fluorescence appears to be due to "permanent" dimerizations (or polymeri- 

 zations) rather than to reaction (23.3) or dimerization after excitation. 

 The dechne in yield of fluorescence with increasing concentration is in this 

 case a direct measure of the degree of association. Like the unstable dimers 

 formed in light, the stable dimeric molecules formed in the dark can be 



