
Nernst Potential
Storyboard 
If a potential is applied to a membrane this will lead to a polarization in which the positive charges move to the negative plate and the negative charges to the positive plate. The difference in concentration however leads to a diffusion that tempts to match the distribution. Nernst's potential is the limit potential over which the applied potential exceeds the tendency to diffuse by polarizing the membrane. For potentials smaller than Nernst's potential, diffusion tends to depolarize the membrane.
ID:(820, 0)

Ohm's law with Conductivity
Equation 
If a potential difference
so with
y
with what
j =- \kappa \displaystyle\frac{ dV }{ dx } |
ID:(3877, 0)

Conductivity
Equation 
In the case of ion conduction, conductivity must include the sign of the charge, which is entered with the number of charges
\kappa =\displaystyle\frac{ z }{ \mid z \mid } \mu_e c |
where
ID:(3876, 0)

Current density
Equation 
The flow density
j =\displaystyle\frac{ I }{ S } |
ID:(3221, 0)

Nernst Current
Equation 
The electron current is the
that is
equation/druyd>
ID:(3222, 0)

Fick's Law for Charged Particles
Equation 
The diffusion leads to the difference in concentrations
j =- D \displaystyle\frac{ dc }{ dx } |
where
ID:(3878, 0)

Diffusion Constant for Charged Particles
Equation 
The diffusion constant
D =\displaystyle\frac{ \mu_e R T }{\mid z \mid F } |
ID:(3879, 0)

Concentration of Charges
Equation 
If there is more than one type of ion, the actual concentration of the ions must be estimated, that is, add the concentrations weighted by the number of charges they have
c_m=\sum_i\mid z_i\mid c_i |
where
ID:(3883, 0)

Concentration of Charges (1)
Equation 
In case of a type of load
c_m =\mid z_1 \mid c_1 |
where
ID:(3884, 0)

Concentration of Charges (2)
Equation 
In case of two types of charges
c_m = \mid z_1\mid c_1 + \mid z_2\mid c_2 |
where
ID:(3885, 0)

Concentration of Charges (3)
Equation 
In case of three types of charges
c_m = \mid z_1\mid c_1 + \mid z_2\mid c_2 + \mid z_3\mid c_3 |
where
ID:(3886, 0)

Equilibrium Condition
Equation 
The equilibrium condition occurs when the flow due to the potential difference is equal to the flow due to the diffusion. That is why you have to
for what you have
dV =\displaystyle\frac{ R T }{ z F }\displaystyle\frac{ dc }{ c } |
ID:(3880, 0)

Nernst Potential
Equation 
If the potential difference is integrated, the relationship of the potential difference corresponding to the limit in which the electric field is compensated with the Diffusion can be established:
V_m =-\displaystyle\frac{ R T }{ F }\ln\displaystyle\frac{ c_1 }{ c_2 } |
where
ID:(3881, 0)