Abstract
Here we use classical applied mathematical modeling to determine surface binding energies between both single-strand and double-strand DNA molecules interacting with a graphene sheet. We adopt basic mechanical principles to exploit the 6-12 Lennard-Jones potential function and the continuum approximation, which assumes that intermolecular interactions can be approximated by average atomic line or surface densities. The minimum binding energy occurs when the single-strand DNA molecule is centred 20.2 angstrom from the surface of the graphene and the double-strand DNA molecule is centred 20.3 angstrom from the surface, noting that these close values apply for the case when the axis of the helix is perpendicular to the surface of graphene. For the case when the axis of the helix is parallel to the surface, the minimum binding energy occurs when the axis of the single-strand molecule is 8.3 angstrom from the surface, and the double-strand molecule has axis 13.3 angstrom from the surface. For arbitrary tilted axis, we determine the optimal angles Omega of the axis of the helix, which give the minimum values of the binding energies, and we observe that the optimal angles tend to occur in the intervals Omega is an element of (pi/4, pi/2) and Omega is an element of (pi/7, pi/5) for the single and double-strand DNA molecules, respectively.