210 THE PHYSICS OF VIRUSES 



attraction is necessary. Two types of attractive processes exist, 

 and probably both play a part in virus synthesis. 



Van der Waals Forces Between Macromolecules 



The forces between neutral molecules which give rise to 

 liquefaction of even spherical molecules like helium, and which 

 are known generally as Van der Waals forces, have been ex- 

 plained by London (1930, 1937). According to quantum me- 

 chanics, an electron associated with a positive nucleus to form 

 an atom does not occupy a smoothly regular orbit, but has a 

 chance of occupying many different positions with respect to the 

 nucleus. Thus, although the average location of the electron 

 may be such that no net-time-averaged dipole moment exists, 

 there may be very large instantaneous dipole moments, and a 

 mean-square dipole moment may have a considerable value. 



Now each ephemeral dipole produces an electric field around 

 it, distorts nearby atoms, and produces induced dipoles in them. 

 These induced dipoles now interact with the originating transient 

 dipole and cause an attraction. There are thus two factors to 

 consider — first, the size of the transient electric field due to the 

 random position of the electron in the first atom, and second, 

 the readiness of the second atom to change its configuration to 

 produce a dipole and so become attracted. Once the originating 

 and induced dipoles have assigned values, the mutual potential 

 energy due to their interaction (which is attractive) is easy to 

 com])ute. The electric field due to a dipole varies as l/7i^ so 

 the induced dipole will have a strength dependent on this, and 

 the attractive potential between two dipoles also depends on 

 1/R^, so that the over-all attractive potential depends on l/h'^. 



The magnitude of the constant of proportionality dei)ends on 

 the polarizability,* 0:2, of the second atom and the polarizability, 

 ai, of the first. In addition, if the frequency for an electronic 

 transition from a state L to a state K, of energies F^ and E^ is 

 Vkh so that 



hvKL = El — Ek 



* Polariziihility is the induced dipole moment per unit applied electric field. 



