760 FLUORESCENCE OF PIGMENTS IN VITRO CHAP. 23 



energy traps are provided by monomers which are in the state of excep- 

 tionally strong thermal agitation. (This hypothesis explains also the de- 

 cline in the intensity of fluorescence, usually observed with rising tempera- 

 ture.) Accelerated dissipation of electronic energy in "hot" molecules is 

 plausible, since in order to convert electronic energy into vibrational energy, 

 a configuration of the nuclei must be reached in which the electronic sys- 

 tem has the same energy in the excited and in the normal state ("crossing 

 point of two potential curves" in the diatomic model). This configuration 

 usually can be achieved only by combination of electronic excitation with 

 vibrations of appropriate kind; the excited molecule must wait until an 

 accidental fluctuation of thermal agitation supplies the critical degree of 

 freedom with the amount of vibrational energy required to make internal 

 conversion possible. The higher the temperature, the shorter will be this 

 waiting period, and the greater the probability of internal conversion oc- 

 curring during the electronic excitation period, and competing successfully 

 with fluorescence. 



One may ask: how can resonance migration of excitation energy assist 

 this mechanism of dissipation? Does it make any difference whether the 

 excitation stays with one molecule and awaits there the thermal fluctua- 

 tion that will permit it to be dissipated, or whether it visits a thousand 

 molecules during the same total life-time, spending a correspondingly short 

 time with each of them? We said elsewhere in this book that a man cannot 

 change his life expectancy by sleeping every night in a different bed! 

 Whether this analogy applies here or not depends on the relative duration 

 of a thermal fluctuation and electronic excitation. If the fluctuation is 

 short-lived, in comparison not only with the total duration of electronic 

 excitation, but also with the time during which the excitation remains 

 with a single host molecule, then migration can have no effect — the chance 

 of being hit by lighting is the same whether one spends the thunderstorm 

 under a single tree or shifts every minute from one to another (identical) 

 tree. If, however, the state of abnormal thermal agitation lasts long com- 

 pared to electronic excitation of a single molecule, then resonance exchange 

 will increase the chances of the two meeting in one molecule. (If one house 

 in a hundred in a town is quarantined for smallpox, then a visitor who 

 comes to town will be much safer if he stays the whole time in the first 

 house he has entered than if he visits a hundred houses, spending a corre- 

 spondingly short time in each of them.) 



In mathematical form, the probability of two independent events, one 

 lasting T sec. (electronic excitation) and another t sec. (thermal fluctuation) 

 overlapping each other in a single molecule, is changed, by subdividing T 

 into n periods of T/n sec. each, by the factor: 



(nt/T) + 1 



