Helmholtz model of the double layer

The appropriate model of the interface for e.g. Pt/LiCFaSOa-PEO depends on the concentration of charged species in the PEO. When the salt PEO ratio is less than 1 10 the Debye length will also be less than the size of a mobile charge. In this case again the Helmholtz model of the double layer will be appropriate. 

Fig. 3.5 The Helmholtz model of the double layer, (a) Rigid arrangement of ions (b) Variation of the electrostatic potential, 0, with distance x, from the electrode (c) Variation of Cd with applied potential.

Davis developed an equation similar to the Vanselow equation from statistical thermodynamics. Electrostatic forces between colloid surfaces and adsorbed cations were calculated for various surface configurations of charge sites. These sites were assumed to be neutralized by individual adsorbed ions. Hence, the model resembles most closely the Helmholtz model of the double layer with the charge of cations on the surface assumed to be just equal to the number of colloid charges. The resultant equation is... 

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