Ion strength limit of computed excess functions based on the linearized Poisson-Boltzmann equation

Area of Science:

• Physical Chemistry
• Electrochemistry
• Statistical Mechanics

Background:

• The linearized Poisson-Boltzmann (L-PB) equation is a cornerstone for describing electrostatic interactions in electrolyte solutions.
• The Debye-Hückel (DH) theory, based on L-PB with a single ion size, exhibits limitations at electrolyte concentrations above 0.1 m.
• The SiS (size-in-size) treatment extends DH theory to account for differences in ion sizes.

Purpose of the Study:

• To critically examine the κ-range of validity for the linearized Poisson-Boltzmann equation in both Debye-Hückel and DH-SiS theories.
• To identify the primary reason for the failure of the Debye-Hückel theory at moderate to high electrolyte concentrations.
• To validate the applicability of the DH-SiS treatment across a wider range of electrolyte concentrations.

Main Methods:

• Analysis of the linearized Poisson-Boltzmann equation's validity criteria, moving beyond the traditional 1/κ (Debye reciprocal length) criterion.
• Comparison of experimental mean ionic activity coefficients (γ±) with predictions from DH and DH-SiS theories as a function of molality (m).
• Derivation and application of SiS expressions for extra-electrostatic potential energy, considering distinct ion sizes (a and b).

Main Results:

• The DH-SiS treatment accurately fits experimental mean ionic activity coefficient data up to molalities exceeding 1 m (κ > 0.33 Å⁻¹).
• The linearized Poisson-Boltzmann equation remains valid up to κ ≥ 1.3 Å⁻¹ when a revised criterion based on mean-field potential is employed.
• The failure of the DH theory is attributed to the approximation of equal ion sizes, not the use of the linearized Poisson-Boltzmann equation itself.

Conclusions:

• The linearized Poisson-Boltzmann equation's range of validity is broader than previously assumed, particularly when using an alternative effectiveness criterion.
• The discrepancy between DH theory and experimental data at higher concentrations stems from neglecting ion-size dissimilarity.
• The DH-SiS treatment provides a more accurate description of electrolyte behavior by incorporating differences in ion sizes.