Interaction between small particles in an electrolyte solution
DOI:
https://doi.org/10.15587/1729-4061.2014.26433Keywords:
Derjaguin-Landau-Verwey-Overbeek theory, Debye-Huckel equation, small particles, energy of interactionAbstract
In studying ion-electrostatic interactions in systems of small particles in electrolyte solutions, the main task is to calculate the energy and forces of interaction that occur between the particles. This problem is closely related to the problem of finding the surface energy of double layers in the interaction of particles in such media. Starting with the works of B.V. Derjaguin, this problem is paid much attention, moreover, it is relevant up to the present time, especially when considering the interaction of small inorganic particles with biological cells or microorganisms. Interaction of diffuse double surface layers, appearing around the particles, is usually calculated based on the method of zones of B.V.Derjaguin. But using this approximation can lead to incorrect results.
The solution of the Debye-Huckel equations for a system of spherical particles with arbitrary radii and surface charges or potentials, located in the electrolyte was constructed in the paper. A general theoretical method for calculating the interaction of the particles in such systems was developed. Practically important two-particle case was considered in detail. From the general relations in the zero approximation, analytical formulas for finding the energy of interaction between two spherical particles with constant charges or potentials were obtained. Known relations of the Derjaguin-Landau-Verwey-Overbeek theory follow from the formulas in the limiting cases.References
- Deryagin, B. V., Churaev, N. V., Muller, V. M. (1985). Poverhnostnye sily. Мoskva: Nauka, 400.
- Bell, G. M., Levine, S., McCartney, J. (1970). Approximate method of determining the Double-layer Free Energy of Interaction between Two Charged Colloidal Spheres. J. Of Colloid and Interface Science, 33 (3), 335–359. doi: 10.1016/0021-9797(70)90228-6
- Verner, E. J. W, Overbeek, J. Th. G. (1948). Theory of the Stability of Lyophobic Cjlloids. Amsterdam: Elsevier.
- Ohshima, H. (1975). Diffuse double layer interaction between two spherical particles with constant surface charge density in an electrolyte solution. Colloid & Polymer Sci., 263, 158-163. doi: 10.1007/bf01775682
- McCartney, L. N., Levine, S. (1969). An improvement on Derjaguin's Expression at Small potentials for the Double Layer Interactions Energy of Two Spherical Colloidal Particles. J. of Colloid an Interface Sci., 30 (3), 345–354. doi: 10.1016/0021-9797(69)90401-9
- Dudnik, V. V. (1992). Neodnorodnost raspredeleniya zaryada vdol kletochnoi membrany kak vozmojnaya prichina izbiratelnoy agregatzii mineralnyh chastitz mikroorganizmami. Kolloidnuy jurnal, 46 (3), 38-43.
- Hsu, J.-P., Lin, S.-H. (2003). Electrical Interaction between Two planar, Parallel Dissimilar Surfaces in a General Electrolytic Solution. Langmuir, 19, 10610–10616.
- Lerman, L. B., Grechko, L. G., Shkoda, N. G., Pokotylo, O. Ya., Chuiko, A. A., Wites, K. W. (2005). Interaction of Nanoparticles with Surface of Biomembranes. NATO ADVANCED RESEARCH WORKSOP. Pure and Applied Surface Chemistry and Nanomaterials for Human Life and Environmental Protection. Book of abstracts. Kyiv, Ukraine, 37.
- Grechko, L. G., Lerman, L. B., Pokotylo, O. Ya., Shkoda, N. G. (2005). Vzaemodiya malyh kulovyh chastynok v elektroliti. Vishyk sytetu. Seriya Fiz.-math. nauky, 3, 483–490.
- Chew, W. C. (1995). Waves and Fields in Inhomogeneous Media. App. D. New York: IEEE Press, 591-596.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2014 Сергей Владимирович Шостак, Наталия Григорьевна Шкода
This work is licensed under a Creative Commons Attribution 4.0 International License.
The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.
A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.
