Differential Capacitance of Entire Double-Layer

The thickness of the Helmholtz layer has a fixed value. Therefore, its differential capacitance should be constant and not change with its potential drop. The differential capacitance of the Helmholtz layer is in the range of 18 to 100 pF.cm and depends on the electrolyte concentration, type of solution solvent, and status of the electrode surface. Combining Equations (2.4) and (2.16) will produce the differential capacitance of the entire double-layer  

In capacitors, the differential capacitance of the Helmholtz layer can be expressed as 

Differential capacitance as function of potential drop across diffuse layer at three electrolyte concentrations calculated according to Equation (2.9) by assuming = 28 pRcm, e = 40, s = 8.854 X 10 F.m, z = 1,25°C and 1.0 atm. 

In addition. Equation (2.19) demonstrates that the dielectric constant has the same weight as that of the electrol5de concentration, meaning that the differential capacitance of the diffuse layer is also proportional to the square root of the dielectric constant. Therefore, using different electrolyte solutions such as aqueous, non-aqueous, and ion liquid solutions can produce different capacitances of the double-layer. 

5 Potential Drop Distribution within Electric Double-Layer 

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