  The van der Waals interaction between a lipid membrane and a substrate
covered by a graphene sheet is investigated using the Lifshitz theory. The
reflection coefficients are obtained for a layered planar system submerged in
water. The dielectric response properties of the involved materials are also
specified and discussed. Our calculations show that a graphene covered
substrate can repel the biological membrane in water. This is attributed to the
significant changes in the response properties of the system due to the
monolayer graphene. It is also found that the van der Waals interaction is
mostly dominated by the presence of graphene, while the role of the particular
substrate is secondary.
