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The Casimir-Polder force between atoms or nanoparticles and graphene-coateddielectric substrates is investigated in the region of large separations.Graphene coating with any value of the energy gap and chemical potential isdescribed in the framework of the Dirac model using the formalism of thepolarization tensor. It is shown that the Casimir-Polder force from agraphene-coated substrate reaches the limit of large separations atapproximately 5.6 $\mu$m distance between an atom or a nanoparticle andgraphene coating independently of the values of the energy gap and chemicalpotential. According to our results, however, the classical limit, where theCasimir-Polder force no longer depends on the Planck constant and the speed oflight, may be attained at much larger separations depending on the values ofthe energy gap and chemical potential. In addition, we have found a simpleanalytic expression for the Casimir-Polder force from a graphene-coatedsubstrate at large separations and determined the region of its applicability.It is demonstrated that the asymptotic results for the large-separationCasimir-Polder force from a graphene-coated substrate are in better agreementwith the results of numerical computations for the graphene sheets with largerchemical potential and smaller energy gap. Possible applications of theobtained results in nanotechnology and bioelectronics are discussed.

Large-Separation Behavior of the Casimir-Polder Force from Real Graphene Sheet Deposited on a Dielectric Substrate