SPECIFICITY OF LONDON-EISENSCHITZ-WANG FORCE 29 



On the other hand, if the interacting molecules are not in direct contact, but 

 are still fairly close, the London force might constitute an important specific 

 interaction. In this case identical structures, rather than complementary ones 

 would tend to aggregate. The London interaction would be sharply specific in 

 the case of macromolecules whose representative oscillators had sufficiently 

 large polarizabilities and frequencies covering a wide range. 



One can form a model for use in discussing biological London interactions 

 by considering somewhat globular, compact, rigid macromolecules or molecule 

 complexes endowed with an electric charge and imbedded in an ionic medium. 

 Such macromolecules are surrounded by ionic atmospheres. Their electro- 

 static interaction is highly dependent on the ionic composition of the medium 

 (Debye and Hueckel, 1923; Onsager, 1933; Kallmann and Willstaetter, 1932; 

 Vinograd, 1935; De Boer, 1936; Hamaker, 1937; idem, 1938; idem, 1948; idem, 

 1952; Verwey and Overbeek, 1946; Overbeek, 1952; idem, 1948; idem, 1954; 

 Levine, 1946; idem, 1948; Derjaguin, 1939; idem, 1940a; idem, 1940b; idem, 

 1940c; idem, 1954; Derjaguin and Landau, 1941; Harned and Owen, 1950; 

 Klotz, 1953; Prigogine and Bellemans, 1953). The interplay between this 

 Debye-Hueckel-Onsager force and the London-Eisenschitz-Wang force deter- 

 mines whether or not the macromolecules associate. At smaller separations be- 

 tween the macromolecules a similar compensation of their charges is effected 

 by ions inserted between the macromolecules. 



Free Energy of Rearrangement 



Let En denote the energies of the levels of a pair of molecules, and let their 

 partition function and Helmholtz free energy be 



Z = Eexp i-EjkT) 



n 



A = -kTlnZ 



If a temperature bath permits the molecule-pair to occupy its levels according 

 to a Boltzmann distribution, the attractive force between the pair becomes 



5 = E (dEjdR) exp i-EjkT)/Z = {dA/dR)T 



n 



Instead of the force one may simply calculate the difference between the 

 Helmholtz free energies at finite separation and at infinite separation, 



A/1 = -kT{\nZ - InZJ 



The problem of specificity might be approached by asking the question: 

 How does the interaction free energy A of an identical pair I, I differ from that 

 of a pair I, II where II differs in a variety of minor ways from I? Calling I, II 

 a detuned pair I, I, this procedure may be termed a "detuning approach". 



