  The adsorption of DNA or other polyelectrolyte molecules on charged membranes
is a recurrent motif in soft matter and bionanotechnological systems. Two
typical situations encountered are the deposition of single DNA chains onto
substrates for further analysis, e.g., by force microscopy, or the pulling of
polyelectrolytes into membrane nanopores, as in sequencing applications. In
this paper, we present a theoretical analysis of such scenarios based on the
self-consistent field theory approach, which allows us to address the important
effect of charge correlations. We calculate the grand potential of a stiff
polyelectrolyte immersed in an electrolyte in contact with a negatively charged
dielectric membrane. For the sake of conciseness, we neglect conformational
polymer fluctuations and model the molecule as a rigid charged line. At
strongly charged membranes, the adsorbed counterions enhance the screening
ability of the interfacial region. In the presence of highly charged polymers
such as double-stranded DNA molecules close to the membrane, this enhanced
interfacial screening dominates the mean-field level DNA-membrane repulsion and
results in the adsorption of the DNA molecule to the surface. This picture
provides a simple explanation for the recently observed DNA binding onto
similarly charged substrates [G. L.-Caballero et al., Soft Matter 10, 2805
(2014)] and points out charge correlations as a non-negligible ingredient of
polymer-surface interactions.
