Surface Charge and Debye Layer Capacitance

The Debye layer acts as a capacitor since it contains electric charges due to the potential difference C between the surface and the bulk. One way to obtain the capacitance of the Debye layer is by integrating the charge density p ix) along thex-direction from the surface atx = 0 

Using the Poisson equation and the potential distribution, 0 (equations (6.65) and (6.66)), 

The resulting which is the charge per area A that is contained in the liquid in the direction perpendicular to any small area A on the surface, can be written as 

The basic definition of capacitance is that it is equal to the amount of charge, Q, stored in between two plates for a potential difference or voltage, V, across the two plates 

From this linear relation (equation (6.67)) between charge per area and applied potential difference, we can immediately read off the capacitance per area C of the Debye layer in thermal equilibrium as 

---