Abstract.
The properties of ionic solutions between charged surfaces are often studied within the Poisson-Boltzmann framework, by finding the electrostatic potential profile. For example, the osmotic pressure between two charged planar surfaces can be evaluated by solving coupled equations for the electrostatic potential and osmotic pressure. Such a solution relies on symmetry arguments and is restricted to either equally or oppositely charged surfaces. Here, we provide a different and more efficient scheme to derive the osmotic pressure straightforwardly, without the need to find the electrostatic potential profile. We derive analytical expressions for the osmotic pressure in terms of the inter-surface separation, salt concentration, and arbitrary boundary conditions. Such results should be useful in force measurement setups, where the force is measured between two differently prepared surfaces, or between two surfaces held at a fixed potential difference. The proposed method can be systematically used for generalized Poisson-Boltzmann theories in planar geometries, as is demonstrated for the sterically modified Poisson-Boltzmann theory.
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References
J.N. Israelachvili, Intermolecular and Surface Forces, 3rd edition (Academic Press, New York, 2011)
E.J. Werwey, J.Th.G. Overbeek, Theory of the Stability of Lyophobic Colloids (Elsevier, New York, 1948)
T. Markovich, D. Andelman, R. Podgornik, in Handbook of Lipid Membranes, edited by C. Safinya, J. Rädler (Taylor and Francis) to be published
R.M. Adar, D. Andelman, H. Diamant, Adv. Colloids Interface Sci. 247, 198 (2017)
D. Ben-Yaakov, D. Andelman, D. Harries, R. Podgornik, J. Phys. Chem. B 113, 6001 (2009)
A.C. Maggs, R. Podgornik, Soft Matter 12, 1219 (2016)
D.C. Grahame, Chem. Rev. 41, 441 (1947)
D. Henderson, L. Blum, J. Chem. Phys. 75, 2025 (1981)
D.F. Evans, H. Wennerstrom, The Colloidal Domain, 2nd edition (VCH Publishers, New York, 1999)
D.S. Dean, R. Horgan, Phys. Rev. E 68, 061106 (2003)
A.A. Meier-Koll, C.C. Fleck, H.H. von Grünberg, J. Phys.: Condens. Matter 16, 6041 (2004)
S.A. Safran, Europhys. Lett. 69, 826 (2005)
M. Abramowicz, I.A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965)
V.A. Parsegian, D. Gingell, Biophys. J. 12, 1192 (1972)
A. Lau, P. Pincus, Eur. Phys. J. B 10, 175 (1999)
D. Ben-Yaakov, Y. Burak, D. Andelman, S.A. Safran, EPL 79, 48002 (2007)
D. Ben-Yaakov, D. Andelman, H. Diamant, Phys. Rev. E 87, 022402 (2013)
I. Borukhov, D. Andelman, H. Orland, Phys. Rev. Lett. 79, 435 (1997)
I. Borukhov, D. Andelman, H. Orland, Electrochim. Acta 46, 221 (2000)
M.S. Kilic, M.Z. Bazant, A. Ajdari, Phys. Rev. E 75, 021502 (2007)
K.S. Pitzer, J. Phys. Chem. 77, 268 (1973)
B.W. Ninham, V.A. Parsegian, J. Theor. Biol. 31, 405 (1971)
D. Chan, J.W. Perram, L.R. White, T.W. Healy, J. Chem. Soc. Faraday Trans. I 71, 1046 (1975)
T. Markovich, D. Andelman, R. Podgornik, EPL 113, 26004 (2016)
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This article is dedicated to the memory of Loïc Auvray. An outstanding gentleman of science who introduced us to a wealth of physical phenomena and concepts in polymers, polyelectrolytes, biophysics and charged soft matter systems. His unique kindness and deep understanding of physics will always be remembered.
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Adar, R.M., Andelman, D. Osmotic pressure between arbitrarily charged planar surfaces: A revisited approach. Eur. Phys. J. E 41, 11 (2018). https://doi.org/10.1140/epje/i2018-11620-1
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DOI: https://doi.org/10.1140/epje/i2018-11620-1
Keywords
- Polymers: From Adsorption to Translocation - Topical Issue in Memoriam Loïc Auvray (1956-2016)