1294 THE PIGMENT FACTOR CHAP. 32 



It is not quite certain, however, whether band sharpness and resonance 

 fluorescence are necessary attributes of energy migration of the "fast" type. 

 In the first place, the narrowness of the absorption band is predicated not 

 only on the uncoupHng of electronic excitation from intramolecular vibra- 

 tions, but also on a strict selection of permitted transitions from a broad 

 electronic excitation band. 



The simplest case of energy resonance is that between two atoms, Ai + 

 A2. Their mutual potential energy as a function of distance can be repre- 

 sented by the lower curve in figure 32.8. If one of the two atoms is ex- 

 cited, the resonance between the structures Ai + A2 leads either to attrac- 

 tion or to repulsion, giving rise to two excited electronic levels, Ei and E2. 

 The first absorption line of the separated atoms, hv^, is thus shifted to the 

 red {i. e., to the smaller energy quanta), the amount of the shift being de- 

 termined by equation (32.4). The second absorption hne, leading to the 

 repulsion curve, is shifted to the short-wave side of the original band, and 

 may be a "forbidden" line. 



If this concept is extended from two atoms or molecules to three, four 

 or more resonating systems, the addition of each new link Avill cause an in- 

 crease in the number of levels, until a practically continuous band of energy 

 levels will be formed. (This situation is similar to that in the series Na, 

 Na2 . . . Na metal, with the difference that, in a metal, the multiplicity of 

 levels is due to the exchange of electrons, and not excitons.) Under cer- 

 tain conditions, the probability of transition by light absorption will be 

 high only to the lowest excited states, thus giving a sharp absorption and 

 fluorescence band of the lowest possible frequency {i. e., w4th the maximum 

 possible shift toward the red from the position of the absorption band of a 

 single molecule). 



The sharp selection of the permitted electronic transitions appears to 

 be valid for symmetry conditions prevailing in Scheibe's one-dimensional 

 polymers; but under different symmetry conditions a broader electronic 

 band could possibly arise, to replace, in the resonating system, the vibra- 

 tion-broadened but intrinsically sharp electronic transition in the mono- 

 meric molecule. A closer study is needed also to decide whether the trans- 

 fer of energy from the electronic system to the vibrational degrees of free- 

 dom — including those of the system as a whole, rather than of individual 

 molecules — can be effectively prevented, by rapid fluctuation of electronic 

 excitation, in all two-dimensional or three-dimensional resonating sys- 

 tems, or whether this uncoupHng, too, can be fully effective only under 

 special spatial relationships, such as may exist between the electronic ex- 

 citation and molecular vibrations (or, at least, a certain type of moleculal 

 vibrations) in one-dimensional polymers. 



As to the lack of, or weakness of, fluorescence, this can be caused, in a 



