48 YOS, BADE AND JEHLE 



dominating; and the calculation of London forces between the two macromole- 

 cules will be very complicated. At larger separation when the centers of the 

 macromolecules might be more than a macromolecular diameter apart, the 

 London force can be better evaluated and in this case the London force is of 

 great importance. Such separations are usually maintained by the balance be- 

 tween the attractive London force with the repulsive electrostatic force of the 

 two macromolecules. If they are identical, they have equal electrical charges 

 which, however, are somewhat compensated by gegen ions furnished from the 

 surrounding medium. Depending on the circumstances, slow charge fluctua- 

 tions may be compensated too, but oscillator moments change too rapidly to 

 be compensated. 



When one asks for preferences in association of identical versus non-identical 

 molecules imbedded in a liquid medium, one has to consider a differential effect 

 of interaction free energy described in Fig. 1 and designated by "rearrangement 

 free energy A4.4i n". This quantity turns out to be negative under pretty 

 general conditions. The inequality (lb) and Hamaker's inequality (Id) clearly 

 show this fact. In order to handle the general case and in order to be able to 

 define degree of specificity and assess its value, the partition function and free 

 energy are calculated. Provided the polarizability distribution in the macro- 

 molecules is strong and diversified enough (both as regards the frequency and 

 spatial distribution), specificity may result due to the multi-dimensionality of 

 the macromolecular oscillators. (The finer details of the polarizability distribu- 

 tion are irrelevant, that is evident from Fig. 3.) 



Orientation effects play a significant role too. Specific London interaction 

 implies (as was outlined before equation (12)), that identical macromolecules 

 which are nearest neighbors orient themselves in parallel in the z direction 

 (the z axes are chosen to be directed along the line connecting the nearest neigh- 

 bors under consideration), anti-parallel in the x and y directions (.v and y axes 

 are in the planes perpendicular to that line). 



Biological Implications 



The object of this paper is not to present a solution to a biophysical problem 

 or to some problems of crystallization, but only to define the simplest kind of 

 model in which London forces play a central role and to work out, by straight- 

 forward quantum and statistical mechanics, the conditions under which it shows 

 specificity. Further research will be required to determine the kinds of macro- 

 molecules which are capable of exhibiting highly specific London interactions 

 and the conditions, as regards ionic atmospheres and polarizabilities under 

 which this capability can manifest itself. At the present time these physico- 

 chemical data necessary for a correct evaluation of the role of the London force 



