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Carbon slit pore model incorporating surface energetical heterogeneity and geometrical corrugation

Abstract

In our recent paper (Jagiello and Olivier, Carbon 55:70–80, 2013) we considered introducing energetical heterogeneity (EH) and geometrical corrugation (GC) to the pore walls of the standard carbon slit pore model. We treated these two effects independently and we found that each of them provides significant improvement to the carbon model. The present work is a continuation of the previous one, as we include both effects in one comprehensive model. The existing standard slit pore model widely used for the characterization of activated carbons assumes graphite-like energetically uniform pore walls. As a result of this assumption adsorption isotherms calculated by the non-local density functional theory (NLDFT) do not fit accurately the experimental N2 data measured for real activated carbons. Assuming a graphene-based structure for activated carbons and using a two-dimensional-NLDFT treatment of the fluid density in the pores we present energetically heterogeneous and geometrically corrugated (EH–GC) surface model for carbon pores. Some parameters of the model were obtained by fitting the model to the reference adsorption data for non-graphitized carbon black. For testing, we applied the new model to the pore size analysis of porous carbons that had given poor results when analyzed using the standard slit pore model. We obtained an excellent fit of the new model to the experimental data and we found that the typical artifacts of the standard model were eliminated.

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References

  • Evans, R., Tarazona, P.: Theory of condensation in narrow capillaries. Phys. Rev. Lett. 52, 557–560 (1984)

    Article  CAS  Google Scholar 

  • 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. 1 72, 619–636 (1976)

    Article  CAS  Google Scholar 

  • Franklin, R.E.: Crystallite growth in graphitizing and non-graphitizing carbons. Proc. R. Soc. Lond. A 209, 196–218 (1951)

    Article  CAS  Google Scholar 

  • Guo, J., Morris, J.R., Ihm, Y., Contescu, C.I., Gallego, N.C., Duscher, G., Pennycook, S.J., Chisholm, M.F.: Topological defects: origin of nanopores and enhanced adsorption performance in nanoporous carbon. Small 8, 3283–3288 (2012)

    Article  CAS  Google Scholar 

  • Huerta, A., Pizio, O., Bryk, P., Sokołowski, S.: Application of the density functional method to study phase transitions in an associating Lennard-Jones fluid adsorbed in energetically heterogeneous slit-like pores. Mol. Phys. 98, 1859–1869 (2000)

    Article  CAS  Google Scholar 

  • Jagiello, J.: Stable numerical solution of the adsorption integral equation using splines. Langmuir 10, 2778–2785 (1994)

    Article  CAS  Google Scholar 

  • Jagiello, J., Olivier, J.P.: A simple two-dimensional NLDFT model of gas adsorption in finite carbon pores. Application to pore structure analysis. J. Phys. Chem. C 113, 19382–19385 (2009)

    Article  CAS  Google Scholar 

  • Jagiello, J., Olivier, J.P.: 2D-NLDFT adsorption models for carbon slit-shaped pores with surface energetical heterogeneity and geometrical corrugation. Carbon 55, 70–80 (2013)

    Article  CAS  Google Scholar 

  • Jagiello, J., Tolles, D.: Calculation of pore size distribution of activated carbons based on density functional theory (DFT) data. In: Meunier, F. (ed.) Fundamentals of Adsorption—FOA6, pp. 629–634. Elsevier, Paris (1998)

    Google Scholar 

  • Jagiello, J., Ania, C.O., Parra, J.B., Jagiello, L., Pis, J.J.: Using DFT analysis of adsorption data of multiple gases including H2 for the comprehensive characterization of microporous carbons. Carbon 45, 1066–1071 (2007)

    Article  CAS  Google Scholar 

  • Jagiello, J., Kenvin, J., Olivier, J.P., Lupini, A.R., Contescu, C.I.: Using a new finite slit pore model for NLDFT analysis of carbon pore structure. Adsorpt. Sci. Technol. 29, 769–780 (2011)

    Article  CAS  Google Scholar 

  • Konstantakou, M., Samios, S., Steriotis, Th.A., Kainourgiakis, M., Papadopoulos, G.K., Kikkinides, E.S., Stubos, A.K.: Determination of pore size distribution in microporous carbons based on CO2 and H2 sorption data. Stud. Surf. Sci. Catal. 160, 543–550 (2006)

    Article  Google Scholar 

  • Kruk, M., Jaroniec, M., Gadkaree, K.P.: Nitrogen adsorption studies of novel synthetic active carbons. J. Colloid Interface Sci. 192, 250–256 (1997)

    Article  CAS  Google Scholar 

  • Kuchta, B., Firlej, L., Marzec, M., Boulet, P.: Microscopic mechanism of adsorption in cylindrical nanopores with heterogeneous wall structure. Langmuir 24, 4013–4019 (2008)

    Article  CAS  Google Scholar 

  • Lastoskie, C., Gubbins, K.E., Quirke, N.: Pore size distribution analysis of microporous carbons: a density functional theory approach. J. Phys. Chem. 97, 4786–4796 (1993)

    Article  CAS  Google Scholar 

  • López-Ramón, M.V., Jagiello, J., Bandosz, T.J., Seaton, N.A.: Determination of the pore size distribution and network connectivity in microporous solids by adsorption measurements and Monte Carlo simulation. Langmuir 13, 4435–4445 (1997)

    Article  Google Scholar 

  • Lueking, A.D., Kim, H.-Y., Jagiello, J., Bancroft, K., Johnson, J.K., Cole, M.W.: Tests of pore-size distributions deduced from inversion of simulated and real adsorption data. J. Low Temp. Phys. 157, 410–428 (2009)

    Article  CAS  Google Scholar 

  • Marini Bettolo Marconi, U., Van Swol, F.: Microscopic model for hysteresis and phase-equilibria of fluids confined between parallel plates. Phys. Rev. A 39, 4109–4116 (1989)

    Article  Google Scholar 

  • Neimark, A.V., Lin, Y., Ravikovitch, P.I., Thommes, M.: Quenched solid density functional theory and pore size analysis of micro–mesoporous carbons. Carbon 47, 1617–1628 (2009)

    Article  CAS  Google Scholar 

  • Nguyen, T.X., Bhatia, S.K.: Characterization of pore wall heterogeneity in nanoporous carbons using adsorption: the slit pore model revisited. J. Phys. Chem. B 108, 14032–14042 (2004)

    Article  CAS  Google Scholar 

  • Olivier, J.P.: Improving the models used for calculating the size distribution of micropore volume of activated carbons from adsorption data. Carbon 10, 1469–1472 (1998)

    Article  Google Scholar 

  • Olivier, J.P., Conklin, W.B., Von Szombathely, M.: Determination of pore size distribution from density functional theory: a comparison of nitrogen and argon results. Stud. Surf. Sci. Catal. 87, 81–89 (1994)

    Article  CAS  Google Scholar 

  • Pre, P., Huchet, G., Jeulin, D., Rouzaud, J.-N., Sennour, M., Thorel, M.: A new approach to characterize the nanostructure of activated carbons from mathematical morphology applied to high resolution transmission electron microscopy images. Carbon 52, 239–258 (2013)

    Article  CAS  Google Scholar 

  • Ravikovitch, P.I., Vishnyakov, A., Russo, R., Neimark, A.V.: Unified approach to pore size characterization of microporous carbonaceous materials from N2, Ar, and CO2 adsorption isotherms. Langmuir 16, 2311–2320 (2000)

    Article  CAS  Google Scholar 

  • Ravikovitch, P.I., Jagiello, J., Tolles, D., Neimark, A.V.: Improved DFT methods for micropore size characterization of activated carbons: role of pore wall heterogeneity. In: Extended Abstracts, Carbon’01 Conference. American Carbon Society, Lexington (2001)

  • Röcken, P., Somoza, A., Tarazona, P., Findenegg, G.H.: Two-stage capillary condensation in pores with structured walls: a nonlocal density functional study. J. Chem. Phys. 20, 8689–8697 (1998)

    Article  Google Scholar 

  • Rosenfeld, Y.: Free-energy model for the inhomogeneous hard-sphere fluid mixture and density-functional theory of freezing. Phys. Rev. Lett. 63, 980–983 (1989)

    Article  CAS  Google Scholar 

  • Samios, S., Stubos, A.K., Kanellopoulos, N.K., Cracknell, R.F., Papadopoulos, G.K., Nicholson, D.: Determination of micropore size distribution from grand canonical Monte Carlo simulations and experimental CO2 isotherm data. Langmuir 13, 2795–2802 (1997)

    Article  CAS  Google Scholar 

  • Sarkisov, L., Monson, P.A.: Modeling of adsorption and desorption in pores of simple geometry using molecular dynamics. Langmuir 17, 7600–7604 (2001)

    Article  CAS  Google Scholar 

  • Seaton, N.A., Walton, J.P.R.B., Quirke, N.: A new analysis method for the determination of the pore size distribution of porous carbons from nitrogen adsorption measurements. Carbon 27, 853–861 (1989)

    Article  CAS  Google Scholar 

  • Siderius, D.W., Gelb, L.D.: Predicting gas adsorption in complex microporous and mesoporous materials using a new density functional theory of finely discretized lattice fluids. Langmuir 25, 1296–1299 (2009)

    Article  CAS  Google Scholar 

  • Steele, W.A.: The physical interactions of gases with crystalline solids. Gas–solid energies and properties of isolated adsorbed atoms. Surf. Sci. 36, 317–352 (1973)

    Article  CAS  Google Scholar 

  • Tarazona, P.: Free-energy density functional for hard spheres. Phys. Rev. A 31, 2672–2679 (1985)

    Article  CAS  Google Scholar 

  • Tarazona, P., Marini Bettolo Marconi, U., Evans, R.: Phase equilibria of fluid interfaces and confined fluids. Non-local versus local density functionals. Mol. Phys. 60, 573–595 (1987)

    Article  CAS  Google Scholar 

  • Ustinov, E.A., Do, D.D., Fenelonov, V.B.: Pore size distribution analysis of activated carbons: application of density functional theory using nongraphitized carbon black as a reference system. Carbon 44, 653–663 (2006)

    Article  CAS  Google Scholar 

  • Wongkoblap, A., Do, D.D.: The effects of energy sites on adsorption of Lennard-Jones fluids and phase transition in carbon slit pore of finite length. A computer simulation study. J. Colloid Interface Sci. 297, 1–9 (2006)

    Article  CAS  Google Scholar 

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Correspondence to Jacek Jagiello.

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Jagiello, J., Olivier, J.P. Carbon slit pore model incorporating surface energetical heterogeneity and geometrical corrugation. Adsorption 19, 777–783 (2013). https://doi.org/10.1007/s10450-013-9517-4

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  • DOI: https://doi.org/10.1007/s10450-013-9517-4

Keywords

  • Characterization of porous carbons
  • Pore size distribution
  • Non-local density functional theory
  • Modification of the standard carbon slit pore model