Accurate Analytic Formulas for the Double-Layer Interaction between Spheres

• Published in: Journal of colloid and interface science 1995-04, Vol.171 (1), p.46-54
• Main Authors: Sader, John E., Carnie, Steven L., Chan, Derek Y.C.
• Format: Article
• Language: English
• Subjects: Chemistry; Colloidal state and disperse state; Exact sciences and technology; General and physical chemistry; Physical and chemical studies. Granulometry. Electrokinetic phenomena
• ISSN: 0021-9797; 1095-7103
• DOI: 10.1006/jcis.1995.1149

Very simple but accurate analytic formulas are presented for the electrical double-layer force and interaction free energy between two spherical colloidal particles, valid up to the moderate-to high-potential regime. These formulas represent a remarkable improvement on previous analytic and semianalytic formulas for the interaction, while maintaining an excellent degree of analytic simplicity. Furthermore, a detailed derivation of the interaction free energy between two dissimilar spheres in the linear Debye-Huckel approximation is presented that is valid for all κh, where κ is the Debye screening parameter and h is the distance of closest approach between the spheres. In doing so, it is demonstrated that the well-known Hogg-Healy-Fuersteneau (HHF) formula, which is valid only in the small κh regime, may be trivially modified to extend its range of applicability to all κh.