We consider an osmotic equilibrium between bulk solutions of polyelectrolyte bounded by semi-permeable membranes and separated by a thin film of salt-free liquid. Although the membranes are neutral, the counter-ions of the polyelectrolyte molecules permeate into the gap and lead to a steric charge separation. This gives rise to a distance-dependent membrane potential, which translates into a repulsive electrostatic disjoining pressure. From the solution of the nonlinear Poisson–Boltzmann equation, we obtain the distribution of the potential and of ions. We then derive an explicit formula for the pressure exerted on the membranes and show that it deviates from the classical van't Hoff expression for the osmotic pressure. This difference is interpreted in terms of a repulsive electrostatic disjoining pressure originating from the overlap of counterion clouds inside the gap. We also develop a simplified theory based on a linearized Poisson–Boltzmann approach. A comparison with simulation of a primitive model for the electrolyte is provided and does confirm the validity of the theoretical predictions. Beyond the fundamental result that the neutral surfaces can repel, this mechanism not only helps to control the adhesion and long-range interactions of living cells, bacteria, and vesicles, but also allows us to argue that electrostatic interactions should play enormous role in determining behavior and functions of systems bounded by semi-permeable membranes.
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21 January 2012
Research Article|
January 17 2012
Electrostatic interaction of neutral semi-permeable membranes
Olga I. Vinogradova;
Olga I. Vinogradova
a)
1A. N. Frumkin Institute of Physical Chemistry and Electrochemistry,
Russian Academy of Sciences
, 31 Leninsky Prospect, 119991 Moscow, Russia
2Faculty of Physics,
M. V. Lomonosov Moscow State University
, 119991 Moscow, Russia
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Lyderic Bocquet;
Lyderic Bocquet
3LPMCN, University Lyon 1 and UMR CNRS 5586,
University of Lyon
, 69622 Villeurbanne, France
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Artem N. Bogdanov;
Artem N. Bogdanov
1A. N. Frumkin Institute of Physical Chemistry and Electrochemistry,
Russian Academy of Sciences
, 31 Leninsky Prospect, 119991 Moscow, Russia
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Roumen Tsekov;
Roumen Tsekov
4Faculty of Chemistry,
University of Sofia
, 1164 Sofia, Bulgaria
5DWI,
RWTH Aachen
, Forckenbeckstr. 50, 52056 Aachen, Germany
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Vladimir Lobaskin
Vladimir Lobaskin
6School of Physics and Complex and Adaptive Systems Laboratory,
University College Dublin
, Belfield, Dublin 4, Ireland
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a)
Electronic mail: oivinograd@yahoo.com.
J. Chem. Phys. 136, 034902 (2012)
Article history
Received:
November 01 2011
Accepted:
December 20 2011
Citation
Olga I. Vinogradova, Lyderic Bocquet, Artem N. Bogdanov, Roumen Tsekov, Vladimir Lobaskin; Electrostatic interaction of neutral semi-permeable membranes. J. Chem. Phys. 21 January 2012; 136 (3): 034902. https://doi.org/10.1063/1.3676246
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