Debye Length

Topics

• Poisson-Boltzmann Equation

${\lambda }_D=\sqrt{\frac{D{\epsilon }_0{k}_{B}T}{2z^2{e}^2{c}_{\infty }}}$

• Is the distance at which in a model of charge screening that assumes exponential decay with respect to distance from the charge object of positive/negative ion concentrations surrounding the charge object, the charge density returns back to what it is at infinity
• $D$ is the dielectric constant of the medium
• $z$ is the $\frac{Q}{e}$ for each ion, or the charge number of the ion
• $c_{\infty }$ is the concentration of the positive and negative ions at infinity relative to the charged object
• $e$ is the elementary charge

${\lambda }_D=\sqrt{\frac{3D{\epsilon }_0{k}_{B}T}{z^2{e}^2{c}_{\infty }}}$

• Assumes uniform positive/negative ion charge density with respect to distance until a sudden cutoff