, Volume 19, Issue 1, pp 121–129 | Cite as

Multilayer adsorption equilibrium model for gas adsorption on solids



Adaptation of the ENSIC model to physisorption of nitrogen or argon on a solid surface first led to a 3 parameters model called multilayer adsorption equilibrium model (MAE model). One of these parameters is related to the formation of a multilayer of adsorbate on the solid surface. Exploitation of data from the literature pointed out that this parameter does not depend on the nature of the solid surface and an average value was calculated in the case of N2 and Ar. As a consequence, the MAE model can be considered as a 2 parameters model. Linearization of the model was established allowing an easy determination of surface areas of macroporous and some mesoporous solids. Fitting of isotherms of meso and macroporous solids has led to promising results compared to the ones obtained with the BET model. Moreover, adaptation of this model to microporous solids can also be used for an uncomplicated determination of porous volume and external surface. Results obtained from data of the literature were close to those obtained with the t-plot model.


Adsorption isotherm Surface area Pore volume Mesoporous solid Microporous solid 


  1. Amati, D., Kovats, E.S.: Nitrogen adsorption isotherms on organic and ionic model surfaces. Langmuir 3, 687–695 (1987) CrossRefGoogle Scholar
  2. Anglin, E.J., Lingyun, C., Freeman, W.R., Sailor, M.J.: Porous silicon in drug delivery devices and materials. Adv. Drug Deliv. Rev. 60, 1266–1277 (2008) CrossRefGoogle Scholar
  3. Anu Prathap, M.U., Srivastava, R.: Synthesis of nanoporous metal oxides through the self-assembly of phloroglucinol–formaldehyde resol and tri-block copolymer. J. Colloid Interface Sci. 358, 399–408 (2011) CrossRefGoogle Scholar
  4. Astarita, G., Joshi, S.: Sample-dimension effects in the sorption of solvents in polymers—a mathematical model. J. Membr. Sci. 4, 165–182 (1978) CrossRefGoogle Scholar
  5. Bartoszek, M., Eckelt, R., Jäger, C., Kosslick, H., Pawlik, A., Schulz, A.: Mesoporous silica-aluminas derived from precipitation: a study of the acidity, textural properties and catalytic performance. J. Mater. Sci. 44, 6629–6636 (2009) CrossRefGoogle Scholar
  6. Blanco, J.F., Sublet, J., Nguyen, Q.T., Schaetzel, P.: Formation and morphology studies of different polysulfones-based membranes made by wet phase inversion process. J. Membr. Sci. 283, 27–37 (2006) CrossRefGoogle Scholar
  7. Brunauer, S.: The Adsorption of Gases and Vapors. University Press, Oxford (1945) Google Scholar
  8. Brunauer, S., Emmett, P.H.: Adsorption of gases in multimolecular layers. J. Am. Chem. Soc. 60, 309–319 (1938) CrossRefGoogle Scholar
  9. de Boer, J.H., Lippens, B.C., Linsen, B.G., Broekhoff, J.C.P., van den Heuvel, A., Osinga, T.J.: The t-curve of multimolecular N2 adsorption. J. Colloid Interface Sci. 21, 405–414 (1966) CrossRefGoogle Scholar
  10. Dimitrov, L., Mihaylov, M., Hadjiivanov, K., Mavrodinova, V.: Catalytic properties and acidity of ZSM-12 zeolite with different textures. Microporous Mesoporous Mater. 143, 291–301 (2011) CrossRefGoogle Scholar
  11. Emmett, P.H., Brunauer, S.: The use of low temperature van der Waals adsorption isotherms in determining the surface area of iron-synthetic ammonia catalysts. J. Am. Chem. Soc. 59, 1553–1564 (1937) CrossRefGoogle Scholar
  12. Everett, D.H.: In: Unger, K.K., Rouquerol, J., Sing, K.S.W., Kral, H. (eds.) Characterisation of Porous Solids, pp. 1–22. Elsevier, Amsterdam (1998) Google Scholar
  13. Favre, E., Clément, R., Nguyen, Q.T., Schaetzel, P., Néel, J.: Sorption of organic solvents into dense silicone membranes. J. Chem. Soc. Faraday Trans. 89, 4339–4353 (1993) CrossRefGoogle Scholar
  14. Favre, E., Nguyen, Q.T., Clément, R., Schaetzel, P., Néel, J.: The engaged species induced clustering (ENSIC) model: a unified mechanistic approach of sorption phenomena in polymers. J. Membr. Sci. 117, 227–236 (1996) CrossRefGoogle Scholar
  15. Flory, P.J.: Principles of Polymer Chemistry. Cornell University Press, Ithaca (1953) Google Scholar
  16. Frackowiak, E.: Supercapacitors based on carbon materials and ionic liquids. J. Braz. Chem. Soc. 17, 1074–1082 (2006) CrossRefGoogle Scholar
  17. Gregg, S.J., Sing, K.S.W.: Adsorption, Surface Area and Porosity, 2nd edn. Academic Press, London (1982) Google Scholar
  18. Guzmán-Castillo, M.L., Armendáriz-Herrera, H., Pérez-Romo, P., Hernández-Beltrán, F., Ibarra, S., Valente, J.S., Fripiat, J.J.: Y zeolite depolymerization–recrystallization: simultaneous formation of hierarchical porosity and Na dislodging. Microporous Mesoporous Mater. 143, 375–382 (2011) CrossRefGoogle Scholar
  19. Halsey, G.D.: Physical adsorption on non-uniform surfaces. J. Chem. Phys. 16, 931–937 (1948) CrossRefGoogle Scholar
  20. Hill, T.L.: Theory of physical adsorption. Adv. Catal. 4, 211–258 (1952) CrossRefGoogle Scholar
  21. Izquierdo-Barba, I., Sánchez-Salcedo, S., Colilla, M., José Feito, M., Ramírez-Santillán, C., Portolés, M.T., Vallet-Regí, M.: Inhibition of bacterial adhesion on biocompatible zwitterionic SBA-15 mesoporous materials. Acta Biomater. 7, 2977–2985 (2011) CrossRefGoogle Scholar
  22. Jelinek, L., Kovhts, E.: True surface areas from nitrogen adsorption experiments. Langmuir 10, 4225–4231 (1994) CrossRefGoogle Scholar
  23. Jura, G., Harkins, W.D.: Surfaces of solids. XI. Determination of the decrease (π) of free surface energy of a solid by an adsorbed film. J. Am. Chem. Soc. 66, 1356–1373 (1944) CrossRefGoogle Scholar
  24. Keller, N., Pham-Huu, C., Ledoux, M.J., Estournes, C., Ehret, G.: Preparation and characterization of SiC microtubes. Appl. Catal. A, Gen. 187, 255–268 (1999) CrossRefGoogle Scholar
  25. Lecloux, A., Pirard, J.P.: The importance of standard isotherms in the analysis of adsorption isotherms for determining the porous texture of solids. J. Colloid Interface Sci. 70, 265–281 (1979) CrossRefGoogle Scholar
  26. Leite, E., Naydenova, I., Mintova, S., Leclercq, L., Toal, V.: Photopolymerisable nanocomposites for holographic recording and sensor application. Appl. Opt. 49, 3652–3660 (2010) CrossRefGoogle Scholar
  27. Leofanti, G., Padovan, M., Tozzola, G., Venturelli, B.: Surface area and pore texture of catalysts. Catal. Today 41, 207–219 (1998) CrossRefGoogle Scholar
  28. Lippens, B.C., DeBoer, J.H.: Studies on pore systems in catalysts: V. The t method. J. Catal. 4, 319–323 (1965) CrossRefGoogle Scholar
  29. Marinovic, S., Vukovic, Z., Nastasovic, A., Milutinovic-Nikolic, A., Jovanovic, D.: Poly(glycidyl methacrylate-co-ethylene glycol dimethacrylate)/clay composites. Mater. Chem. Phys. 128, 291–297 (2011) CrossRefGoogle Scholar
  30. McClellan, A.L., Hainsberger, H.F.: Cross-sectional areas of molecules adsorbed on solid surfaces. J. Colloid Interface Sci. 23, 577–599 (1967) CrossRefGoogle Scholar
  31. Méndez, M.O.A., Lisbôa, A.C.L., Coutinho, A.R., Otani, C.: Activated petroleum coke for natural gas storage. J. Braz. Chem. Soc. 17, 1144–1150 (2006) CrossRefGoogle Scholar
  32. Mikhail, R.S., Brunauer, S.: Surface area measurements by nitrogen and argon adsorption. J. Colloid Interface Sci. 52, 572–577 (1975) CrossRefGoogle Scholar
  33. Moore, W.R., Shuttleworth, R.: Thermodynamic properties of solutions of cellulose acetate and cellulose nitrate. J. Polym. Sci., Part A, Gen. Pap. 1, 733–749 (1963) CrossRefGoogle Scholar
  34. Passe-Coutrin, N., Altenor, S., Cossement, D., Jean-Marius, C., Gaspard, S.: Comparison of parameters calculated from the BET and Freundlich isotherms obtained by nitrogen adsorption on activated carbons: a new method for calculating the specific surface area. Microporous Mesoporous Mater. 111, 517–522 (2008) CrossRefGoogle Scholar
  35. Payne, D.A., Sing, K.S.W., Turk, D.H.: Comparison of argon and nitrogen adsorption isotherms on porous and nonporous hydroxylated silica. J. Colloid Interface Sci. 43, 287–293 (1973) CrossRefGoogle Scholar
  36. Pomonis, P.J., Petrakis, D.E., Ladavos, A.K., Kolonia, K.M., Pantazis, C.C., Giannakas, A.E., Leontiou, A.A.: The I-point method for estimating the surface area of solid catalysts and the variation of C-term of the BET equation. Catal. Commun. 6, 93–96 (2005) CrossRefGoogle Scholar
  37. Ramila, A., Munoz, B., Perez-Pariente, J., Vallet-Reg, M.: Mesoporous MCM-41 as drug host system. J. Sol-Gel Sci. Technol. 26, 1199–1202 (2003) CrossRefGoogle Scholar
  38. Ramsay, J.D.F.: In: Unger, K.K., Rouquerol, J., Sing, K.S.W., Kral, H. (eds.) Characterisation of Porous Solids, pp. 23–37. Elsevier, Amsterdam (1998) Google Scholar
  39. Robinson, J.P., Tarleton, E.S., Millington, C.R., Nijmeijer, A.: Nanofiltration of organic solvents. Membr. Technol. 2004, 5–12 (2004) CrossRefGoogle Scholar
  40. Rodrigues, A.E.: Permeable packings and perfusion chromatography in protein separation. J. Chromatogr. B 699, 47–61 (1997) CrossRefGoogle Scholar
  41. Rodrigues, A.E., LeVan, M.D., Tondeur, D.: Adsorption, Science and Technology. Kluwer, Boston (1989) CrossRefGoogle Scholar
  42. Ruzicka, J., Kudlacek, L.: A study of the surface structure of cellulose by means of the argon adsorption isotherm. Vysokomol. Soyed. 6, 577–586 (1964) Google Scholar
  43. Scherdel, C., Reichenauer, G., Wiener, M.: Relationship between pore volumes and surface areas derived from the evaluation of N2 sorption data by DR-, BET- and t-plot. Microporous Mesoporous Mater. 132, 572–575 (2010) CrossRefGoogle Scholar
  44. Selles-Perez, M.J., Martin-Martinez, J.M.: Application of the αs method to adsorption isotherms of argon and n-butane. Carbon 30(1), 41–46 (1992) CrossRefGoogle Scholar
  45. Sergio, M., Musso, M., Medina, J., Diano, W.: Aluminum-pillaring of a montmorillonitic clay: textural properties as a function of the starting mineral particle size. AZojomo (2006). doi:10.2240/azojomo0179
  46. Serwicka, E.M.: Surface area and porosity, X-ray diffraction and chemical analyses. Catal. Today 56, 335–346 (2000) CrossRefGoogle Scholar
  47. Sing, K.S.W., Williams, R.T.: Empirical procedures for the analysis of physisorption isotherms. Adsorp. Sci. Technol. 23, 839–853 (2005) CrossRefGoogle Scholar
  48. Sing, K.S.W., Everett, D.H., Haul, R.A.W., Moscou, L., Pierotti, R.A., Rouquerol, J., Siemieniewska, T.: Reporting physisorption data for gas/solid systems with special reference to the determination of surface area and porosity. Pure Appl. Chem. 57, 603–619 (1985) CrossRefGoogle Scholar
  49. Storck, S., Bretinger, H., Maier, W.F.: Characterization of micro- and mesoporous solids by physisorption methods and pore-size analysis. Appl. Catal. A, Gen. 174, 137–146 (1998) CrossRefGoogle Scholar
  50. Thielmann, F., Butler, D.A., Williams, D.R.: Characterization of porous materials by finite concentration inverse gas chromatography. Colloids Surf. A, Physicochem. Eng. Asp. 187, 267–272 (2001) CrossRefGoogle Scholar
  51. Trammell, S.A., Melde, B.J., Zabetakis, D., Deschamps, J.R., Dinderman, M.A., Johnson, B.J., Kusterbeck, A.W.: Electrochemical detection of TNT with in-line pre-concentration using imprinted diethylbenzene-bridged periodic mesoporous organosilicas. Sens. Actuators B, Chem. 155, 737–744 (2011) CrossRefGoogle Scholar
  52. Whalley, W.R., Watts, C.W., Hilhorst, M.A., Bird, N.R.A., Balendonck, J., Longstaff, D.J.: The design of porous material sensors to measure the matric potential of water in soil. Eur. J. Soil Sci. 52, 511–519 (2001) CrossRefGoogle Scholar
  53. Witoon, T., Chareonpanich, M., Limtrakul, J.: Effect of hierarchical meso-macroporous silica supports on Fischer-Tropsch synthesis using cobalt catalyst. Fuel Process. Technol. 92, 1498–1505 (2011) CrossRefGoogle Scholar
  54. Yan, X., Liu, G., Dickey, M., Willson, C.G.: Preparation of porous polymer membranes using nano- or micro-pillar arrays as templates. Polymer 45, 8469–8474 (2004) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Laboratoire Catalyse et Spectrochimie, ENSICAENUniversité de Caen, CNRSCaenFrance

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