772 FLUORKSCENCK OF PIGMENTS IN VITRO CHAF. 23 



last hypothesis is supported by the observation that polar molecules do 

 not affect the absoi-ption spectrum and fluorescence of pheophytin; even 

 more convincing is the fact that a similar difference in behavior occurs 

 between phthalocyanine and its magnesium complex, although these 

 compounds contain no cyclopentanone structure, so that Livingston's 

 interpretation cannot be applied to them. 



5. Influence of Concentration on Yield of Fluorescence. Self- 

 Quenching. Fluorescence of Chlorophyll in Colloids and Adsorbates 



The self-quenching of fluorescence in chlorophyll solutions was studied 

 by Weiss and Weil-Malherbe (1944). They found that with a constant 

 intensity of illumination, the intensity of fluorescence of an ethyl chloro- 

 phyllide solution in ethanol increased with increased concentration, be- 

 tween 1 X 10"^ and 1 X 10^^ mole/1., due to increased absorption. The 

 latter became practically complete above 1 X 10^^ mole/1.; instead of be- 

 coming constant from there on, the fluorescence intensity declined rapidly, 

 dropping at 1 X 10 -^ mole/1, to one sixth of its maximum value. Six 

 points were measured between [Chi] = 2 X 10"* and 1 X 10 --^ mole/1., 

 and found to lie on a hyperbola: 



(23.5) F = C/{l+k[Ch\]) 



where F is fluorescence intensity and k and C are constants. The constant 

 k was evaluated graphically and fc = 2 X 10'^ sec.-^ was found. Making 

 the— unjustified— assumption that the intensity of fluorescence is limited 

 exclusively by self-quenching, one can easily show (c/. equations on page 

 546, Vol. I) that the constant k has the meaning: 



(23.6) k = ke/kf 



where h is the bimolecular rate constant of self-quenching: 



K 



(23.7) Chi + Chi* > Chl2 ( > 2 Chi) 



and kf the monomolecular rate constant of fluorescence • 



(23.8) Chi* > Chi + hu 



The reciprocal, l/kj, is the average life-time of the excited molecule 

 when limited only by fluorescence. According to page 634, k/ ^ 10^ 

 sec.-i; with fc = 2 X 10-^ sec.-\ this gives, according to (23.6): 



(23.9) A-c ^2 X 1012 sec. -1 



This calculation is based on the assumption that reaction (23.7) is the 

 only one that limits the yield of fluorescence. However, equation (23.5) 

 would remain correct, i. e., self-quenching would follow a hyperbolic curve, 



