SURFACES OF MOLECULES 223 



Debye (9) has shown that in general because of thermal agitation a 

 dipole (or quadrupole) molecule in a gas or liquid is changing its orienta- 

 tion so fast that we nuist not regard the force produced by a dipole as a 

 steady force, but a rapidly fluctuating force, and under these conditions 

 many of the elTects produced 1)\- the force are proportional to E- or the 

 mean square field. The effective force can thus vary inversely as the sixth 

 power of the distance from the dipole. 



NON-POLAR MOLECULES 



If tlie molecule is a quadrupole the instantaneous force in any given 

 direction will var\- inversely as the^ fourth power of the distance, and tints 

 the efifective fiuctuating force will vary inversely as tlie eighth power of 

 the distance. With more symmetrical molecules the forces will \'ar\- in- 

 versely with still higher powers of the distance. 



Under the influence of forces of the kinds we have been considering 

 the various types of molecules in liquids respond in different ways, l^ositive 

 ions tend to concentrate around negative ions in the manner considered by 

 the Debve-Hiickel theory (8). Dipole molecules tend to be orientated 1)\ 

 the fiekl in tlie neighborhood of the ion. Thermal agitation tends to ])revent 

 this orientation, so that only when the dipole molecule is very close to the 

 ion is the orientation of the molecule complete. 



The dipole molecule, orientated in a field, tends to move in the direc- 

 tion towards which the field is of greater intensity. The change in potential 

 energy is niE, where E represents the change in field strength and in is the 

 efifective dipole moment (average moment ) in the direction of the field. 



A field insufficient to orientate the dipoles completely gives an effective 

 dipole moment in, which according to Debye (10) is 



);/ = li- F/^kT 



where F is the electric force tending to produce the orientation. Since the 

 energy available for producing motion of translation in a dipole is pro- 

 portional to inF, we see that at large distances dipoles attract one another 

 in proportion to F- and therefore in inverse proportion to the sixth ]:iower 

 of the distance. If, however, we consider a fixed dipole (for example one 

 attached to a large organic molecule) acting en another dipole at a very 

 short distance so that the latter is orientated by the field of the former, 

 then the force of attraction will var\' inversely as the fourth power of 

 the distance. 



An electric field of intensity F, acting on a non-polar molecule, causes 

 a deformation, or polarization, of the molecule so that it acquires a dipole 

 moment m given by 



m = a F 



