  We probe the electrostatic cost associated with the approach phase of DNA
translocation events. Within an analytical theory at the Debye-Huckel level, we
calculate the electrostatic free energy of a rigid DNA molecule interacting
with a dielectric membrane. For carbon or silicon based low permittivity
neutral membranes, the DNA molecule experiences a repulsive energy barrier
between 10 kBT and 100 kBT. In the case of engineered membranes with high
dielectric permittivity, the membrane surface attracts the DNA with an energy
of the same magnitude. Both the repulsive and attractive interactions result
from image-charge effects and their magnitude survive even for the thinnest
graphene-based membranes of size d~6 A. For weakly charged membranes, the
electrostatic free energy is always attractive at large separation distances
but switches to repulsive close to the membrane surface. We also characterise
the polymer length dependence of the interaction energy. For specific values of
the membrane charge density, low permittivity membranes repel short polymers
but attract long polymers. Our results can be used to control the strong
electrostatic free energy of DNA-membrane interactions prior to translocation
events by chemical engineering of the relevant system parameters.
