# Debye length

Keyword picked by Kelly Miller

The Debye length is the scale over which mobile charge carriers screen out electric fields in plasmas and other conductors.

In the context of a charged surface in an electrolytic solution, the thickness of the double layer that forms at the charged surface is called the Debye Length ($\kappa^{-1}$)

It is also known as the shielding distance as it represents the distance over which the charged surface is shielded from the bulk.

Adsorbed ions determine the surface potential which is referred to as the zeta potential ($\zeta$)

The potential in the solution is a function of the surface potential and the distance from the charged surface and can be expressed as:

Potential = $\zeta exp(-\kappa x)$

Figure 1:

Reference: AP225 Course Lecture notes: (Topic 7 Charged interfaces)

When there is a charged surface in an electrolytic solution, there must be a balancing counter charge in the liquid. The charges will not be uniformly distributed throughout the liquid phase but, will be concentrated near the charged surface.

Figure 2:

A double layer is formed in the liquid to neutralize the charged surface and this creates a potential between the surface and any point in the mass of the suspending liquid. This charged surface and the resulting charge distribution in the solution is known as the electrical double layer (EDL). The magnitude of the potential is related to the surface charge and the thickness of the double layer. The potential drops off exponentially through the diffuse layer:

Potential = $\zeta exp(-\kappa x)$

The thickness of the double layer is called the Debye length ($\kappa ^-1$)

Where

and

I is referred to as the ionic strength. The Debye length is proportional to the reciprocal of the ionic strength. The larger the concentration of ions, the more they "shield" the charged surface and the thinner the Debye length is. This is represented in figure 1 above by the dotted green line. As the ionic strength increases, the potential drops off faster and the effects of the charged surface are negated quicker (as a function of distance). Nonaqueous solutions tend to have lower ionic strengths and therefore smaller $\kappa$ and therefore larger Debye length.