The closest approach of water molecules to electrode interfaces

3 The closest approach of water molecules to electrode interfaces 

The interfacial solution layer contains h3 ated ions and dipoles of water molecules. According to the hard sphere model or the mean sphere approximation of aqueous solution, the plane of the center of mass of the excess ionic charge, o,(x), is given at the distance x. from the jellium metal edge in Eqn. 5-31  

This plane of the center of mass of the excess ionic charge o,(x) is the effective excess charge plane on the solution side, which may be compared with the effective image plane on the metal side. In simple cases, the effective excess charge plane coincides with the outer Helmholtz plane (the plane of closest approach of hydrated ions) as shown in Fig. 5-21. 

we discuss the plane of the closest approach (x = of water molecules to the jellium metal edge (x = 0). At the zero charge interface, this plane of closest approach of water molecules is separated by a distance equal to the radius of water molecules from the metal siuface. As the interfadal excess charge increases, the electrostatic pressure (electrostriction pressiue) reduces the distance of Xdip in prop ortion to the square of the interfadal charge, a (= om = - os) the electrostatic force in the compact layer is proportional to om x as. The change in Xitp due to the interfadal charge is then given by Eqn. 5-32  

As shown in Fig. 5-21, the reduction of x p reduces the thickness of the compact layer, the magnitude of which increases as an inverse-parabolic function of the interfacial charge (Fig. 5-22). 

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