o04 Mr. J. Frenkel on the Surface Electric 



The same intrinsic potential would result from a double- 

 layer consisting of two surfaces with a charge e per sq. cm. 

 at a distance 8 from each other, where 8 is given by the 

 •equation V = 47re6\ or 



8 =4 w 



We shall call it the equivalent double-layer. 



It is clear that similar double-layers must, according to 

 this theory, exist on the surface of all liquid and amorphous 

 solid bodies *, whatever their chemical constitution. The 

 latter will determine but the magnitude and the distribution 

 of electric charges on both sides of the surface. This distri- 

 bution must be calculated upon what we shall call the 

 principle of immobilization of weight-centres, consisting in 

 neglecting the translatory motion of the molecules compared 

 with their relative motion about their own centre of weight. 



In its application to the simple (single-atomic) bodies this 

 principle is reduced to the immobilization of the nuclei. Its 

 fundamental importance may be illustrated by the fact, that 

 if the mass of the hydrogen-line atom, considered in § 2, 

 was concentrated in the electron and not the nucleus, and 

 the latter rotated about the former, then the outer side of 

 the double-layer would be positive and the intrinsic potential 

 negative. Of course, the intrinsic potential may be negative 

 in compound bodies, as we shall presently see. Let each 

 molecule consist of i nuclei of charge +<?i, -f e 2 , . ..H-ft, and 

 k electrons of charge —-e, situated at a distance r 1? r 2 , ...rj, r 

 from the immobile centre of weight of the molecule (it is 

 self-understood that we refer to a simplified model) . Applying 

 the principle of superposition, we may consider each electron 

 and each nucleus as the free end of a doublet, the other end 

 of which is oppositely charged and rigidly fixed in the centre 

 of weight. The mean electric density p x in a plane at 

 distance x from the surface is equal to the algebraic sum of 

 densities corresponding to the separate doublets, and in 



virtue of the equation -=- - = 47r/5 x , the same rule holds for 



the electric force E z and the potential Y x . We shall thus 

 have on the surface of the body a system of i -f 1 layers of 

 thickness 2r lf 2r 2 , ...2r t -, 2r , the smaller being enclosed in 

 the larger. The outermost charge may be both positive and 

 negative, as well as the intrinsic potential. 



§ 4. Returning to metals and remembering that they are 



* The conditions are somewhat altered in the case of crystals. 



