IXTERMOLECULAK FORCES AXD IXTERACTIOX ENERGY 227 



between them occurs so rapidly that the movements are synchronized 

 but as the separation becomes greater, a point is reached where the elec- 

 trodynamic effects cannot pass between the atoms sufficiently rapidly 

 and retardation of the mutual interaction occurs. This factor may be in- 

 cluded as a correction factor in the London expressions: 



V = f<FL (6-44) 



where 9?^ is the usual London interaction energy and / is the retardation 

 correction. At short distances, /= 1, but as the separation increases / 

 becomes proportional to Ijd. From plots of /made by Casimir and Polder, 

 it may be seen that it equals about 0.5 when the separation is one-fifth 

 the appropriate wavelength and about 0.25 when the separation is one-half 

 the wavelength. At distances near or greater than the critical wavelength, 

 (f thus varies as lid'' for two interacting spheres, rather than as Ijd^. It 

 is interesting that the importance of retardation has been experimentally 

 demonstrated recently by Derjaguin et al. (1956), direct measurements of the 

 molecular forces between solids separated by narrow gaps (around 1000 A) 

 following the Casimir-Polder law rather than the London law. In the 

 usual enzyme interactions, the distances are, of course, small enough 

 so that retardation is probably unimportant, but there are biological 

 situations, some perhaps connected with enzymes and the control of their 

 activity, in which retardation effects might be significant. The technical 

 advances through which such intermolecular forces can be measured di- 

 rectly make it likely that in the future it will be possible to determine 

 dispersion interactions of importance to enzymologists and place the theo- 

 retical treatments on a firmer basis. 



Experimental values for the dispersion energy are almost confined to 

 situations in which the interacting molecules are identical and little accurate 

 data are available for reactions between unlike molecules. For the latter 

 one may use the expressions given above or recourse may be made to re- 

 lations between the interaction constants for each substance. If the poten- 

 tial energy due to dispersion forces between two unlike molecules is given by : 



-D12 



cp = - ^^ (6-45) 



the constant B^.^ can be related to B^^ and B.o, the interaction constants 

 for each substance, by making various assumptions. Equation 6-41 taken 

 in connection with: 



B„ = '"-'^f ■'*''■'■ (6.46) 



4 



3a,'\/ Z,{hv,h ,. ..,, 



-D22 = -. (6-47) 



