Energy behaviour for DNA translocation through graphene nanopores

• We determine the optimal pore size in graphene for single and double strand DNA analytically.
• The results are nearly identical to experimental observations.
• The model can simplify the complexity of molecular crossing graphene nanopores.
• Our results can be offered new applications in the atomic surface processes.

Nanoparticles have considerable promise for many applications in electronics, energy storage, bioscience and biotechnologies. Here we use applied mathematical modelling to exploit the basic principles of mechanics and the 6–12 Lennard-Jones potential function together with the continuum approach, which assumes that a discrete atomic structure can be replaced by an average constant atomic surface density of atoms that is assumed to be smeared over each molecule. We identify a circular hole in a graphene sheet as a nanopore and we consider the molecular interaction energy for both single-strand and double-strand DNA molecules assumed to move through the circular hole in a graphene sheet to determine the radius b   of the hole that gives the minimum energy. By minimizing the interaction energy, we observe that the single-strand DNA and double-strand DNA molecules penetrate through a graphene nanopore when the pore radii b>b> 7.8 Å and b>b> 12.7 Å, respectively. Our results can be adopted to offer new applications in the atomic surface processes and electronic sensing.