, Volume 24, Issue 1, pp 1–9 | Cite as

Development of averaged solid–fluid potential energies for layers and solids of various geometries and dimensionality

  • Lumeng Liu
  • Yonghong Zeng
  • D. D. Do
  • D. Nicholson
  • Junjie Liu


The solid–fluid (SF) interaction energy describes the affinity between one adsorbate molecule and a solid. Its quantification is an essential input for the simulation of the adsorption isotherm, the isosteric heat and details of the microscopic structure of the adsorbate. A good approximation to the SF energy can be obtained by direct summation of all effective pairwise interaction energies (LJ plus electrostatic) between an adsorbate molecule and all the atoms in the solid. To repeat this summation for each new configuration in a simulation is very time-consuming. One resolution is to construct database tables of the solid–fluid potentials, which leads to massive databases if the grid separation used is very small. For solids that have simple geometries an alternative is to determine the approximate solid–fluid potential by ignoring the discrete atomic structure of the solid. This level of approximation is adequate for many simulations of engineering interest where fine details, for example in the first adsorbate layer, are not necessary. In this paper, we report comprehensive derivations of solid–fluid potentials for a wide range of solids, in layered structures with constant surface atom density or solid structures with constant atom density, and various curvatures and dimensions. These solids are common in engineering applications and the derived analytical solutions will be of value to scientists and engineers. We take a finite solid as an example of the application of the SF potential equations developed in this paper, and show the spatial variation of the solid–fluid potential energy in the neighbourhood of the edges of the solid, which is found to be remarkably different from the usual 1D potential energy equation commonly used in the adsorption literature.


Solid-fluid potential Simulation Adsorption Integration 



This project is supported by the Australian Research Council (DP16013540), and the scholarship from China Scholarship Council (CSC) for Lumeng Liu in spending his tenure at the University of Queensland.

Supplementary material

10450_2017_9921_MOESM1_ESM.docx (1.9 mb)
Supplementary material 1 (DOCX 1936 KB)


  1. Asai, M., Ohba, T., Iwanaga, T., Kanoh, H., Endo, M., Campos-Delgado, J., Terrones, M., Nakai, K., Kaneko, K.: Marked adsorption irreversibility of graphitic nanoribbons for CO2 and H2O. J. Am. Chem. Soc. 133(38), 14880–14883 (2011)CrossRefGoogle Scholar
  2. Bojan, M.J., Steele, W.A.: Computer simulation of physisorption on a heterogeneous surface. Surf. Sci. 199(3), 395–402 (1988)CrossRefGoogle Scholar
  3. Chandrakumar, K., Srinivasu, K., Ghosh, S.K.: Nanoscale curvature-induced hydrogen adsorption in alkali metal doped carbon nanomaterials. J. Phys. Chem. C 112(40), 15670–15679 (2008)CrossRefGoogle Scholar
  4. Cong, S., Sugahara, T., Wei, T., Jiu, J., Hirose, Y., Nagao, S., Suganuma, K.: Diverse adsorption/desorption abilities originating from the nanostructural morphology of VOC gas sensing devices based on molybdenum trioxide nanorod arrays. Adv. Mater. Interfaces 3(14), 1600252 (2016)CrossRefGoogle Scholar
  5. Crowell, A., Steele, R.: Interaction potentials of simple nonpolar molecules with graphite. J. Chem. Phys. 34(4), 1347–1349 (1961)CrossRefGoogle Scholar
  6. Everett, D.H., Powl, J.C.: Adsorption in slit-like and cylindrical micropores in the henry’s law region. A model for the microporosity of carbons. J. Chem. Soc. Faraday Trans. 72, 619–636 (1976)CrossRefGoogle Scholar
  7. Goler, S., Coletti, C., Tozzini, V., Piazza, V., Mashoff, T., Beltram, F., Pellegrini, V., Heun, S.: Influence of graphene curvature on hydrogen adsorption: toward hydrogen storage devices. J. Phys. Chem. C 117(22), 11506–11513 (2013)CrossRefGoogle Scholar
  8. Gor, G.Y., Rasmussen, C.J., Neimark, A.V.: Capillary condensation hysteresis in overlapping spherical pores: a Monte Carlo simulation study. Langmuir 28(33), 12100–12107 (2012)CrossRefGoogle Scholar
  9. Gotovac, S., Honda, H., Hattori, Y., Takahashi, K., Kanoh, H., Kaneko, K.: Effect of nanoscale curvature of single-walled carbon nanotubes on adsorption of polycyclic aromatic hydrocarbons. Nano Lett. 7(3), 583–587 (2007)CrossRefGoogle Scholar
  10. Nguyen, P.T., Do, D., Nicholson, D.: On the cavitation and pore blocking in cylindrical pores with simple connectivity. J. Phys. Chem. B 115(42), 12160–12172 (2011)CrossRefGoogle Scholar
  11. Nika, D., Pokatilov, E., Askerov, A., Balandin, A.: Phonon thermal conduction in graphene: role of Umklapp and edge roughness scattering. Phys. Rev. B 79(15), 155413 (2009)CrossRefGoogle Scholar
  12. Ohba, T.: Significant curvature effects of partially charged carbon nanotubes on electrolyte behavior investigated using Monte Carlo simulations. PCCP 18(21), 14543–14548 (2016)CrossRefGoogle Scholar
  13. Ohba, T., Kanoh, H.: Intensive edge effects of nanographenes in molecular adsorptions. J. Phys. Chem. Lett. 3(4), 511–516 (2012)CrossRefGoogle Scholar
  14. Radovic, L.R., Bockrath, B.: On the chemical nature of graphene edges: origin of stability and potential for magnetism in carbon materials. J. Am. Chem. Soc. 127(16), 5917–5927 (2005)CrossRefGoogle Scholar
  15. Rasmussen, C.J., Gor, G.Y., Neimark, A.V.: Monte Carlo simulation of cavitation in pores with nonwetting defects. Langmuir 28(10), 4702–4711 (2012)CrossRefGoogle Scholar
  16. Shen, A., Zou, Y., Wang, Q., Dryfe, R.A., Huang, X., Dou, S., Dai, L., Wang, S.: Oxygen reduction reaction in a droplet on graphite: direct evidence that the edge is more active than the basal plane. Angew. Chem. 126(40), 10980–10984 (2014)CrossRefGoogle Scholar
  17. Son, Y.-W., Cohen, M.L., Louie, S.G.: Half-metallic graphene nanoribbons. Nature 444(7117), 347–349 (2006)CrossRefGoogle Scholar
  18. Steele, W.A.: The physical interaction of gases with crystalline solids: I. Gas–solid energies and properties of isolated adsorbed atoms. Surf. Sci. 36(1), 317–352 (1973)CrossRefGoogle Scholar
  19. Steele, W.A.: The Interaction of Gases with Solid Surfaces. Pergamon, London (1974)Google Scholar
  20. Tjatjopoulos, G.J., Feke, D.L., Mann, J.A. Jr.: Molecule-micropore interaction potentials. J. Phys. Chem. 92(13), 4006–4007 (1988)CrossRefGoogle Scholar
  21. Villarreal, E., Li, G.G., Zhang, Q., Fu, X., Wang, H.: Nanoscale surface curvature effects on ligand–nanoparticle interactions: a plasmon-enhanced spectroscopic study of thiolated ligand adsorption, desorption, and exchange on gold nanoparticles. Nano Lett. 17(7), 4443–4452 (2017)CrossRefGoogle Scholar
  22. Von Goeler, F., Muthukumar, M.: Adsorption of polyelectrolytes onto curved surfaces. J. Chem. Phys. 100(10), 7796–7803 (1994)CrossRefGoogle Scholar
  23. Vrabec, J., Stoll, J., Hasse, H.: A set of molecular models for symmetric quadrupolar fluids. J. Phys. Chem. B. 105(48), 12126–12133 (2001)CrossRefGoogle Scholar
  24. Wongkoblap, A., Do, D.D., Nicholson, D.: Explanation of the unusual peak of calorimetric heat in the adsorption of nitrogen, argon and methane on graphitized thermal carbon black. PCCP 10(8), 1106–1113 (2008)CrossRefGoogle Scholar
  25. Wu, C.-M., Baltrusaitis, J., Gillan, E.G., Grassian, V.H.: Sulfur dioxide adsorption on ZnO nanoparticles and nanorods. J. Phys. Chem. C. 115(20), 10164–10172 (2011)CrossRefGoogle Scholar
  26. Young, D., Crowell, A.: Physical Adsorption of Gases. Butterworths, London (1962)Google Scholar
  27. Zeng, Y., Horio, K., Horikawa, T., Nakai, K., Do, D.D., Nicholson, D.: On the evolution of the heat spike in the isosteric heat versus loading for argon adsorption on graphite-A new molecular model for graphite and reconciliation between experiment and computer simulation. Carbon. 122, 622–634 (2017)CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.School of Chemical EngineeringUniversity of QueenslandSt. LuciaAustralia
  2. 2.School of Environmental Science and EngineeringTianjin UniversityTianjinChina

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