SPECIFICITY OF LONDON-EISENSCHITZ-WANG FORCE 31 



same value for any closest pair (I, I), (I, II) or (II, II). This assumption is 

 reasonable for macromolecules I and II which differ only in minor ways in 

 their size, shape, electrical charge etc. This assumption is of course auto- 

 matically satisfied in the above mentioned set-up where only two identical 

 macromolecules are immersed in a homogeneous isotropic medium. 



(b) The interactions are isotropic and additively composed of molecule-pair 

 interactions. The anisotropy is considered later on in this note. 



(c) Entropy of mixing is ignored in order to shorten the calculations. Ac- 

 tually this entropy contribution, which takes account of the fact that there 

 are many more arrangements of the right hand type of Fig. 1 than of the left 

 hand type, is not negligible. 



The total free energy of a given arrangement is the free energy of the iso- 

 lated molecules plus the interaction free energy A^ of each pair. As the inter- 

 action free energy has a strong R dependence, one may ignore all but closest 

 neighbor interactions. If ih i is the number of closest neighbor pairs in which 

 both molecules are of type I, »„ „ the number in which both are of type II, and 

 Wi II the number in which one is of type I and the other of type II, then the 

 total interaction free energy of the arrangement is 



ni lAAi I + nn iiA.4ii „ -f Wi hA^i u 



The total number of all the closest neighbors of all the molecules I is 2»i i -f Wi n 

 and that of the molecules II is 2wii n -|- fii „ . As any closest pair (I, I), (II, II) 

 or (I, II) is assumed to have approximately the same nearest approach R, a 

 rearrangement of the system will (statistically speaking) (d) not change these 

 numbers of closest neighbors. Then, after the system has undergone such a 

 rearrangement, the numbers of closest neighbors will be u'j i = »i i -f 8n, 

 n'l II = Hi II - 25«, w'li II = Wii II -f bn. The resulting free energy change 

 is 5»(A.4i I + A.-f II II — 2Ayli „). A positive bn would mean that there were 

 more like pairs and fewer unlike pairs of molecules after the rearrangement 

 than before. The sign of the "quadruplet free energy difference" A4.4i „ thus 

 determines the sign of the free energy change for any particular rearrangement. 

 If this quantity is negative, the interaction tends to bring like molecules to- 

 gether at the expense of separating unlike ones. 



These considerations can readily be extended to include situations in which 

 several different types of macromolecules are simultaneously present (Yos, 

 1956). The assumptions made are: (a) equality of the volumes of these different, 

 somewhat globular, molecules and sole consideration of nearest neighbor inter- 

 actions, all at the same distance R; (b) isotropy and additivity of interactions; 

 (c) entropy of mixing left aside; (d) number of nearest neighbors per molecule, 

 statistically speaking, the same for every kind of macromolecule. Using a new 

 notation, let iiij denote the total number of molecules of type 7 which are 

 nearest neighbors to molecules of type i. Then N, = ^j Uij = total number 



