1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Poisson_boltzmann equation

  1. Mar 21, 2007 #1
    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
    Last edited by a moderator: Mar 21, 2007
  2. jcsd
  3. Mar 22, 2007 #2
    I think I have it here; the electrostatic potential \phi can be written as the reduced potential u. If one again assumes that q*u / kT << 1 than the hyperbolic function can be approximated as
    sinh(q*u/kT) \approx q*u/kT
    which than reduces to the equation.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook