THE STERN MODEL

Stern model

The ions stuck to the electrode and the remainder scattered in cloud fashion.

                                Neither the Helmholtz nor the Gouy - Chapmann Model is exact representation of the structure.

The Helmholtz model emphasis the rigidity of the ionic environment and the later emphasis into mobility. Stern solved these difficulties by using a combination of the concept of the two model.

* Stern eliminated the point - charge approximation of the Diffuse layer theory. This is done in exactly the same way as to the theory of ion - ion interaction. The ion centres are taken as not coming closest distance and approach of the ions to the electrode.

The solution charge is due to the two contribution :

1) Charge, solution is immobilised close to the electrode in the( OHP) the Helmholtz perrin charge or( qH)

2) The remainders diffusely spread in the solution (the Gouy - Chapmann charge or qG)

So,  qs = qH + qG   ....................... (1)

Potential variation according to this model :-

                       

The total differential capacity c given by me the Helmholtz, and G, capacitance in series (i.e)

    1   =   1   +    1     .............................. (2)

    C      CH       CG

qs = qH + qG. There are therefore two regions of change separation first region is from the electrode to the Helmholtz plane and the region is from this plane of fixed charges into the solution where net charge density is zero.

Whenever changes are separated potential drop results. This implies two potential drops.

The two potential drops are as per stern model are represented as, 

        ψm = ψH + ψG ...................... (3)

Where ψm, ψH and ψG are the potential at the metal at the Helmholtz planes and potential in the solution.

Differentiating equation (3) write ∂qm.

     ∂ψm    =  ∂ψH   +  ∂ψG   

     ∂qm        ∂qm        ∂qm

       =   ∂ψH    +   ∂ψH    ................... (4)

            ∂qm         ∂qd

   ∂qm can be replaced by ∂qd because the total charge on the electrode. Each term in the above equation is the reciprocal of differential capacity. Equation (4) can be written as,

       1     =    1   +   1  

       C        CH      CG

Where, 

C - Total capacity of the interface 

cH - Helmholtz perrin capacity (i.e) The capacity of the region between the metal and the Helmholtz plane charge.

CG - Gouy - Chapmann / Diffuse charge capacity.

               The result is identical to the expression for the total capacity displayed by two capacities in series.  all differential capacity is given by the Helmholtz and Gouy capacities in series.

                      The difficult encountered with the diffuse charge layer theory (i.e) predicted capacity values are higher than those observed in the case of solutions with concentration of about are explained by this model.

Case 1 :

            When the concentration of electrolyte is very large. 

         1    =    1   +    1   

         C         CH     CG

At high concentration, CG is large while CH doesn't charge. 

  1   >>    1       or     1   <<    1  

CH       CG              CG        CH

Hence,           1  ≈    1  

                       C      CH

   (or)

                      C ≈ CH

The total capacity of the two capacitors in series is effectively equal to the smaller capacity when the other one is relatively charge.

At high concentration, most of the solution charge is squeezed into the Helmholtz plane (i.e) very scattered diffusely into solution.

Case 2 :

When the concentration is low under these conditions,

     1  <<    1 

   CH       CG

So,     1    ≈    1    (or)     C ≈ CG

          C         CG

This means that the electrified interface between behaves in a Gouy - Chapmann way with the solution charge scattered under the influence of electric forces and thermal forces.