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Interaction between like-charged surfaces in water: does mean-field (Poisson Boltzmann) always apply for monovalent counterions?

Abstract : Charged interfaces in water are widespread in industry and biology. The interactions of two like-charged interfaces, colloid/water/colloid[1, 2] or cell(vesicle)/water/cell(vesicle)[3] for example, received continuous attention since the start of the 20th. century[4]. It was early realized that several type of "interactions" are at work besides electrostatics, like van der Waals interactions, in the celebrated DLVO theory[4], or short range hydration forces (defined from neutral interfaces). In practice, for want of better options, those interactions are usually added up. The standard treatment of the electrostatic part uses the continuous Poisson-Boltzmann (P-B) theory, which is a mean-field theory. There are many, potentially important, corrections to the standard P-B treatment: non-electrostatic counterion-surface interactions, discreteness of the surface charge (both noted early[5]), non-uniform dielec-tric constant, correlations between counterions. * The paper by Schlaich et al. combines chemically realistic Molecular Dynamics (MD) simulations and analytical theory (with the additional input of Monte Carlo (MC) for pure electrostatics) to address all these points and essentially solve the problem (for polar surfaces). It offers much more than suggested by the, unavoidably reductive, title. This comment presents some of Schlaich et al.'s results in relation to a posterior experimental paper on deposited bilayers[6] and a much older one on biliquid foams[7]. In continuous theories, the strength of electrostatics for a given solvent characterized by the Bjerrum length l B = e 2 /(4π 0 k B T) decreases with increasing dielectric constant , 0 being the permittivity of vacuum. Electrostatics of an isolated pair of elementary charges separated by more than l B is overcome by thermal noise. The P-B theory adds a second length * Reading, for exemple, the book by Verwey and Overbeek[4], it is clear that the community knew about the weaknesses of the Poisson-Boltzmann treatment for electrostatics, already by that time. But the success of DLVO steadily reported since, at least for monovalent counterions, is striking. At this point it is fair to say that in most experimental setups the conditions of the experiments are not easy to control and the parameters not always known with precision, or even fitted.
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Albert Johner. Interaction between like-charged surfaces in water: does mean-field (Poisson Boltzmann) always apply for monovalent counterions?. Journal Club for Condensed Matter Physics, 2020, 35, pp.551 - 560. ⟨10.36471/JCCM_September_2020_01⟩. ⟨hal-03008698⟩

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