SPECIFICITY OF LOXDON-EISENSCHITZ-WANG FORCE 33' 



A more interesting inequality in two variables a and oj has been pointed 

 out by DeBoer (1936) and Hamaker (1937).^ In the simple case of the inter- 

 action of two isotropic oscillators whose frequencies o) are large compared with 

 kT/h, the interaction free energy is 



A.4i II = —%R''^aiaiihoii(hu/{u)i + Wn), (ic) 



as shown by London (1936, 1930, 1942), Eisenschitz and London (1930a, 

 1930b), and Wang (1927). (The quantities a are the static polarizabilities of 

 the oscillators.) Thus 



. , q .„-6, ("iwi — oLii^^ii)" + <ii<iii(a:i — ttii)" . . ,s 



A4.4iii = ~%R h I • < 0> Ud) 



(Apart from a numerical factor, the expression {h times an average of the fre- 

 quencies) in equation (Ic) replaces the kT in equation (la); the relations (Ic) 

 and (Id) are applicable to simple molecules (e.g. the noble gases) whose optical 

 dispersion formulae contain only one important term.) 



If each molecule is adequately represented by a set of oscillators, no essential 

 change occurs in (la), (lb). The sum of the polarizabilities of all the oscillators 

 in molecule I enters instead of the single oscillator polarizability ai , and the 

 same with II; and one obtains again an inequality involving only one inde- 

 pendent term 



A^i Ni+Nii \2 



^Oill — 22 "'II ) 

 i = l l=Ni + l / 



/ numbers the oscillators; the sums contain, strictly speaking, orientation terms. 



The same holds for (Ic), (Id) if all the oscillators have one and the same fre- 

 quency (this becomes also evident from equation (lOd)). Conversely the equa- 

 tion (Id) and its multioscillator generalization becomes of special interest if the 

 oscillators cover a diversified range of frequencies as well as polarizabilities. 



Thus, in the quantum limit case (Ic), (Id) one obtains an inecjuality in- 

 volving a set of negative terms, i.e. a set of inecjualities as was first shown by 

 Hamaker (1937). On the basis of such inequalities, he concluded: "The London- 

 van der Waals force between two particles of the same material imbedded in a 

 fluid is always attractive, provided there is no marked orientation of the fluid 

 molecules. If the particles are of different composition, the resultant force 

 may be a repulsion." It seems, however, to have escaped notice at that time 

 that these inequalities might have something to do with the problem of specific 

 interactions, and the question of how many of the inequalities are efi'ectively 

 independent has still to be studied below. 



The quadruplet free energy difference A4.I i n is thus found to be a negative 

 definite quantity both in the classical and in the quantum limit. If one repre- 



^ We are deeply indebted to H. T. Epstein for having drawn our attention to these 

 papers and to T. Y. Wu for a comment on this inequality. 



