Debye-Hiickel reciprocal thickness

Equation (1.9) is the linearized Poisson-Boltzmann equation and k in Eq. (1.10) is the Debye-Htickel parameter. This linearization is called the Debye-Hiickel approximation and Eq. (1.9) is called the Debye-Hiickel equation. The reciprocal of k (i.e., 1/k), which is called the Debye length, corresponds to the thickness of the double layer. Note that nf in Eqs. (1.5) and (1.10) is given in units of m . If one uses the units of M (mol/L), then must be replaced by IQQQNAn, Na being Avogadro s number. 

Debye Length A parameter in the Debye—Hiickel theory of electrolyte solutions, k-1. For aqueous solutions at 25 °C, k = 3.288y7 in reciprocal nanometers, where I is the ionic strength of the solution. The Debye length is also used in the DLVO theory, where it is referred to as the electric double-layer thickness. See also Electric Double-Layer Thickness. 

The last equality pertains to any solvent and any temperature. For aqueous solutions at 25°C A/mor kg = 0.510 z z. The quantity in the denominator equals k, the reciprocal of the thickness of the ionic atmosphere in the Debye-Hiickel theory [2]. This thickness is to be construed as pertaining to the distance beyond the distance of closest approach of the ions, a, to the periphery of the ionic atmosphere. Therefore, BF may be replaced by B aF, where, according to the theory ... 

Although the importance of the ionic strength was first realized from empirical considerations, it is now known to play an important part in the theory of electrolytes. It will be observed that equation (12) on page 83, which gives the reciprocal of the thickness of the ionic atmosphere according to the theory of Debye and Hiickel, contains the quantity where n is the number of ions of the zth kind in unit volume... 

---