| Autor: |
Eric S. Reiner, Clayton J. Radke |
| Rok vydání: |
1993 |
| Předmět: |
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| Zdroj: |
Advances in Colloid and Interface Science. 47:59-147 |
| ISSN: |
0001-8686 |
| DOI: |
10.1016/0001-8686(93)80014-3 |
| Popis: |
The variational approach of Reiner and Radke (1990) is employed to investigate the effect of surface charge regulation upon the double layer interaction free energy Ve of pairs of colloidal particles immersed in an electrolyte. A model for dissociating surface groups that permits the consideration of an arbitrary number ofion-complexation reactions is introduced. The variational method is then used to derive (in the Poisson-Boltzmann approximation) the configurational free energy functional Ω of an ensemble of particles bearing such groups. The Debye-Huckel (DH) linearization process is applied to this functional, and ensuing consistency issues are examined. The DH free energy is extremized for a configuration of two interacting flat plates, and Derjaguin's (1934 and 1939) method is used to obtain an approximate analytical form for Ve for two different-sized spherical particles bearing different surface groups. This second problem is next considered from the perspective ofLevine's (1934, 1939b) exact multipole expansion of the electrostatic potential surrounding two axisymmetric particles. It is shown that the linear superposition approximation (LSA) for Ve developed by Levine (1939c) and Verwey and Overbeek (1948) emerges rigorously from this formulation in the limit of large interparticle separations. The interaction free energy from Levine's expansion is calculated te a six digit accuracy for identical spheres over the range of regulated behavior from fixed surface charge density qs to fixed surface potential ψs for surface-surface separation h to Debye length λ ratios from 0 to 2 and ratios of the particle radius a to λ of 0.1, 1, and 10. These results are compared to those obtained from Derjaguin's method and the linear superposition approximation. Derjaguin's method is only quantitatively accurate (in error by less than 10%) for the largest value of a/λ and becomes progressively less so as the boundary is changed from perfectly regulating (constant ψs) to unregulated (constant qs). Agreement of the LSA with the exact Ve is good over a wide range of parameters, but worsens for large a/λ and small h/λ. Appendices present extensions of our approach to surfaces bearing more than one type of complexing group and to the consideration of Stern layer formation at the particle-electrolyte boundary in the context of a standard model for metal oxide-aqueous interfaces. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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