Diffuse layer near a plate

Next we investigate some solutions of the equations embodied in the Gouy-Chapman model. For a flat interface and a 2-z S5unmetrical electrolyte e.g. KCI,the Poisson- 

The expression (e j,A T/2c z ni,) / represents the Debye screening length, symbolized by. The solution of equation 2.53 gives 

Where ip. represents the potential at the surface. r 1). Hence the potential and space charge are non-zero in a region of thickness adjacent to the interface. 

The exact solution of the non linearized Poisson-Boltzmaim equation 2.52 can be obtained explicitly under an analytical form, this property being closely related to the one dimensional character of the present problem. By multiplying both sides by (Hi/dj. one obtains exact differentials which, after integrating twice and applying the boundary conditions yields 

From equation 2.55 we recover the Debye-Hiickel approximation for 4 j/4 1. The factor accounts for the numerical accuracy of the Debye-Huckel formula for dimensionless potentials somewhat larger than unity. For large positive surface potentials I j 1, and a 0, 

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