- #1

greisen

- 76

- 0

The problem is going from the Poisson-Boltzmann equation

[tex]\nabla (e(r)*\nabla \phi(r)) - \kappa^2(kT/q)*sinh(q*\phi(r)/kT) = -4*\pi \rho(r)[/tex]

The equation is than rewritten in terms of a reduced potential u

[tex]\nabla (e(r)*\nabla u(r)) - \kappa^2 sinh(u(r)) = -4\pi*\rho(r)[/tex]

The reduced potential is defined as [tex]u(r) = q*\phi / (kT)[/tex] - I can see that term q/kT is multiplied on the right side but nothing changes on the left side?

Have I totally misunderstood the equation and the approximation of the PBE?

Any help or advice appreciated. Thanks in advance.

best regards

[tex]\nabla (e(r)*\nabla \phi(r)) - \kappa^2(kT/q)*sinh(q*\phi(r)/kT) = -4*\pi \rho(r)[/tex]

The equation is than rewritten in terms of a reduced potential u

[tex]\nabla (e(r)*\nabla u(r)) - \kappa^2 sinh(u(r)) = -4\pi*\rho(r)[/tex]

The reduced potential is defined as [tex]u(r) = q*\phi / (kT)[/tex] - I can see that term q/kT is multiplied on the right side but nothing changes on the left side?

Have I totally misunderstood the equation and the approximation of the PBE?

Any help or advice appreciated. Thanks in advance.

best regards

Last edited by a moderator: