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Adobe.Photoshop.CC.2019.×64.RePack.KpoJIuK setup free
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.Surface-assisted molecular breathing of the polymer surface.
Interaction forces between a polarized polyelectrolyte and a polyelectrolyte-coated substrate are studied in the framework of a mean-field continuum theory of the Poisson-Boltzmann type. The substrate is modeled as a planar, infinitely extended, charged and perfectly conducting plate. This plate is charged as a whole and not as a collection of charged atoms. A nonlinear Poisson-Boltzmann equation for the concentration of monomeric counterions in the gap is solved analytically. A matching condition between the solution in the gap and the bulk concentrations leads to an equation for the surface potential which is the main result of this Letter. The solution shows that the surface potential generated by the substrate varies along its surface and has different values at the surface and at the center of the substrate. These two values are related by an approximate exponential law. It is shown that the values at the surface and in the bulk coincide when the interactions between charged monomers at the surface are described by a force expressed as a sum of two square-well potentials, one of which corresponds to the direct Coulomb interaction and the other to an indirect interaction via the counterions. The latter interaction can be considered as arising from the counterion induced image dipoles at the edges of the semi-infinite surface of the counterions (an approximation related to the Debye-Hückel approximation). Comparison with recent experiments on poly(allylamine hydrochloride) adsorption onto oppositely charged, polystyrene-divinylbenzene microarrays reveals that

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