44 YOS, BADE AND JEHLE 



polarizabilities and to the intermolecular separation R which in turn depends 

 on the ionic constitution of the medium. 



The ''range" of the interaction may be defined as that distance Ro at which 

 the rearrangement free energy A4.4i n = —kT. If the oscillator frequencies 

 would only reach from the ultraviolet to the infrared and not all the way 

 down to the classical region, one could simply write 



Ro = {H)Hh^/2kTyi\a)KAiA, „/A.4i i)^ (16) 



where a is the polarizability per oscillator, and Co is an average value of the 

 oscillator frequencies of I. Ro is proportional to N' and therefore proportional 

 to the radius of a spherical macromolecule. The range is thus to be judged in 

 relation to the radii of the molecules involved. 



There is a relevant connection between the concept of "range i?o" and the 

 concept of "degree of specificity at separation R": If I, II happens to be an 

 "average pair" of molecules types whose squared distance in the Ws space (at 

 a particular separation R) is about equal to the average squared distance for all 

 molecule pairs (at the same separation R) taken from that manifold of mole- 

 cules, then Ro could also be characterized by remarking that the degree of 

 specificity for this manifold would start to fall well below unity when the separa- 

 tion R is raised to the value Ro . 



In the actual biologically interesting cases the most important polarizabilities 

 are in the ultraviolet and in the classical regions. The formula (16) which uses 

 an 'average' oscillator frequency cannot be properly applied to that case and it 

 will therefore be advisable to give a crude estimate of the magnitude of the 

 rearrangement free energy A4A1 n on the basis of equation (lOd). 



The ultraviolet contributions to the polarizabilities are evidently contribu- 

 tions from electrons in the valence shells, and the classical contributions are due 

 to fluctuations of the proton distribution over the surfaces of the molecules, 

 of the type investigated by Kirkwood and Shumaker (1952). If one lumps all 

 the ultraviolet polarizabilities together and assigns to them an average fre- 

 quency which might correspond to Si ^ 78 (14a) and if, on the other hand, one 

 lumps all the classical polarizabilities together, corresponding to a.n si ^ 

 (14a), one has a situation like that illustrated in Fig. 3. In such a procedure 

 which disregards all further details of the distribution of polarizabilities over 

 the frequency spectrum, (lOd) can appro.ximately be split into an ultraviolet 

 contribution (denoted by / = UV), and a classical one (/ = CI) which only 



contributes to the term 5 = 0. 



/+00 

 [1 + (V-^uv)']"' ds 

 -00 



+ E «ci - S «ci]"} (17) 



I II ^ ' 



= 2kT R^*^ {{r/l) sijv [2 «uv — £ «uv]" + [£ «ci — S «^ci]'} 



I II I II 



