IX. ELECTROPHORESIS 273 



elect rokinetic potential, considered both layers of the electrical double 

 layer to be planar layers of charges existing at a fixed distance apart 

 in the region of and parallel to the surface of the particle. Guoy 

 (1910), and later Debye (1924), orhphasized the necessity of consider- 

 ing the outer layer as an atmosphere of ions in which the density of 

 charge decreases from a large value near the surface to zero at a point 

 beyond the maximum distance that a counterion can reach kineti- 

 cally, while still being attracted electrostatically by the fixed charges 

 on the surface. The effective thickness of the double layer is there- 

 fore to be considered as the distance of separation of the fixed charge 

 on the surface (including any charge elements within the layer of 

 fluid that is immovable with respect to the actual particle surface) 

 and the electrical center of gravity of the charged elements consti- 

 tuting the diffuse outer layer. The distance from the particle sur- 

 face at which the change in potential with distance becomes zero will 

 be a function of the density of population of ions in the body of the 

 liquid, this distance decreasing in proportion to the ionic strength of 

 the solution bathing the particle surface. The effective thickness of 

 the double layer, charge density on the particle remaining constant, 

 will decrease similarly with increase in the ionic strength. On the 

 basis of this definition of the thickness of the double layer, the equa- 

 tions of Helmholtz may still be used in the interpretation of the 

 phenomena. The thickness of the double layer and the magnitude 

 of the electrokinetic potential, however, cannot be regarded as fixed 

 and invariable at constant charge density but must be expected to 

 vary as a function of the ionic strength of the solution with which the 

 particle is in contact. 



The displacement per unit time interval that one layer of the 

 electrical double layer in the region of the interface will experience 

 with respect to the other when an externallj^ applied electric field is 

 imposed on the system in a direction parallel to the planes of the 

 double layer will be a function of the forces, electrical and frictional, 

 acting upon the system. When the volume element containing one 

 layer of the double layer is not capable of displacement in space, 

 while that containing the other layer is displaceable, all relative move- 

 ment observable will occur as a spacial displacement of the latter. 

 For example, if the double layer is one existing in the region of the 

 interface of a solid ca])illaiy filled with fluid and an external potential 

 is applied through the fluid in a dii-ection parallel to the lumen of the 

 capillary, all relative movement of the two layers of the double layer 



