Geodesic
Separation of methane-helium mixture by porous graphite
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 45 (2017), pp. 80-87

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In this paper, the permeability of a double layer formed by parallel-laid sheets of sparse graphene is studied theoretically. The performed analysis is based on the Pöschl–Teller intermolecular interaction potential which better describes both the vicinity of the equilibrium position and the distant interactions. The mathematical pores are created by the removal of two consecutive carbon cycles out of the hexagonal structure (twelve atoms of carbon are removed). The pores are uniformly distributed over the graphene sheet and separated from each other by rectilinear hexagonal tapes. The resulting sparse graphene has an average density equal to fourteen atoms per one square nanometer of the sheet area. Despite the essential heterogeneity of the obtained $\mathrm{2D}$ graphene structure, the equivalent uniform layer method developed by the authors is proposed for calculating the permeability of the sparse graphene sheets. This method is based on the Maxwell velocity distribution of the molecules. It allows one to take into account all possible slant-directed blows of molecules on an ultrathin layer. Using this method, the permeability of both monocarbonic layer and, then, double graphene layer were investigated. It is revealed that the permeability of a two-layered membrane increases more than twice in comparison with a one-layer case when the sparse graphene sheets naturally approach each other.
Keywords: molecular dynamics, a Pöschl–Teller potential, the method of equivalent uniform layer, permeability of a double layer. 
A. M. Bubenchikov; M. A. Bubenchikov; E. A. Tarasov; O. V. Usenko; A. S. Chelnokova. Separation of methane-helium mixture by porous graphite. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 45 (2017), pp. 80-87. http://geodesic.mathdoc.fr/item/VTGU_2017_45_a6/
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     author = {A. M. Bubenchikov and M. A. Bubenchikov and E. A. Tarasov and O. V. Usenko and A. S. Chelnokova},
     title = {Separation of methane-helium mixture by porous graphite},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {80--87},
     year = {2017},
     number = {45},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2017_45_a6/}
}
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