Abstract
There has been little, or no, direct testing of theories of gas sorption within particular pores situated amidst a highly inter-connected pore network. The concept of thermodynamically independent pores within networks has also been challenged. In this work, a novel integrated nitrogen sorption and mercury porosimetry technique has been used to deconvolve the condensation and evaporation processes within a specific subset of pores contained within a larger, irregular network. The sizes and geometry of these pores were obtained completely independently of gas sorption, using mercury porosimetry and NMR cryoporometry, respectively. Hence, various theories of capillary condensation, such as the Kelvin equation, the Broeckhoff-de Boer method, Saam-Cole theory, and NLDFT could be directly tested, and the potential influence of any collective network phenomena detected. It was found that, even for a shielded pore, the Cohan equation for a cylindrical meniscus gave rise to the best prediction for the relative pressure of capillary condensation, once the effects of surface chemical heterogeneity on multi-layer build-up had been taken into account. The results were also found to be incompatible with the presence of particular collective adsorption effects, such as advanced condensation.
Similar content being viewed by others
References
Anderson, R.B.: Modifications of the Brunauer, Emmett and Teller equation. J. Am. Chem. Soc. 68, 686–691 (1946)
Androutsopoulos, G.P., Salmas, C.E.: A new model for capillary condensation-evaporation hysteresis based on a random corrugated pore structure concept: Prediction of intrinsic pore size distributions. 1. Model formulation. Ind. Eng. Chem. Res. 39, 3747–3763 (2000)
Avnir, D., Farin, D., Pfeifer, P.: Surface geometric irregularity of particulate materials: The fractal approach. J. Colloid Interface Sci. 103, 112–123 (1985)
Barrett, E.P., Joyner, L.G., Halenda, P.H.: The determination of pore volume and area distributions in porous substances-I. Computations from nitrogen isotherms. J. Am. Chem. Soc. 73, 373–380 (1951)
Beyea, S.D., Caprihan, A., Glass, S.J., DiGiovanni, A.: Nondestructive characterization of nanopore microstructure: Spatially resolved Brunauer-Emmett-Teller isotherms using nuclear magnetic resonance imaging. J. Appl. Phys. 94, 935–941 (2003)
Bras, W.: An SAXS/WAXS beamline at the ESRF and future experiments. J. Macromol. Sci. Phys. B37, 557–565 (1998)
Broekhoff, J.C.P., De Boer, J.H.: Studies on pore systems in catalysts: X. Calculations of pore distributions from the adsorption branch of nitrogen sorption isotherms in the case of open cylindrical pores: B. Applications. J. Catal. 9, 15–27 (1967)
Brunauer, S., Emmett, P.H., Teller, E.: Adsorption of gases in multimolecular layers. J. Am. Chem. Soc. 60, 309–319 (1938)
Brunauer, S., Skalny, J., Bodor, E.E.: Adsorption on nanoporous solids. J. Colloid Interface Sci. 30, 546–552 (1969)
Coasne, B., Grosman, A., Dupont-Pavlovsky, N., Ortega, C., Simon, M.: Adsorption in an ordered and non-interconnected mesoporous material: Single crystal porous silicon. Phys. Chem. Chem. Phys. 3, 1196–1200 (2001)
Cohan, L.H.: Sorption hysteresis and the vapor pressure of concave surfaces. J. Am. Chem. Soc. 60, 433 (1938)
de Boer, J.H.: The shapes of capillaries. In: Everett, D.H., Stone, F.S. (eds.) The Structure and Properties of Porous Solids, pp. 68–94. Butterworths, London (1958)
Eanes, E.D., Posner, A.S.: Small-angle X-ray scattering measurements of surface areas. In: Flood, E.A. (ed.) The Solid-Gas Interface, pp. 975–994. Dekker, New York (1967)
Esparza, J.M., Ojeda, M.L., Campero, A., Dominguez, A., Kornhauser, I., Rojas, F., Vidales, A.M., Lopez, R.H., Zgrablich, G.: N2 sorption scanning behaviour of SBA-15 porous substrates. Colloids Surf. A Physicochem. Eng. Asp. 241, 35–45 (2004)
Findenegg, G.H., Gross, S., Michalski, T.: Multi-layer adsorption and pore condensation in controlled-pore glass: A test of the Saam-Cole theory of mesopore filling. In: Motoyuki, S. (ed.) Proc. IVth Int. Conf. on Fundamentals of Adsorption, Kyoto, pp. 161–168. International Adsorption Society (1992)
Gelb, L.D., Gubbins, K.E.: Pore size distributions in porous glasses: A computer simulation study. Langmuir 15, 305–308 (1999)
Grosse, A.V.: Densities, volumes, expansion coefficients and atomic cell dimensions of metallic mercury for its entire solid and liquid temperature range, i.e. from zero absolute to its critical point (1733 K). J. Inorg. Nucl. Chem. 27, 773–786 (1965)
Halsey, G.D.: Physical adsorption on non-uniform surfaces. J. Chem. Phys. 16, 931 (1948)
Hanzawa, Y., Kaneko, K., Yoshizawa, N., Pekala, R.W., Dresselhaus, M.S.: The pore structure determination of carbon aerogels. Adsorption 4, 187–195 (1998)
Harkins, W.D., Jura, G.: An adsorption method for the determination of the area of a solid without the assumption of a molecular area, and the area occupied by nitrogen molecules on the surfaces of solids. J. Chem. Phys. 11, 431 (1943)
Honig, J.M.: Analysis of multilayer gas adsorption isotherms using the concept of surface heterogeneity. J. Phys. Chem. 57, 349–351 (1953)
Jaroniec, M., Solovyov, L.A.: Improvement of the Kruk-Jaroniec-Sayari method for pore size analysis of ordered silicas with cylindrical mesopores. Langmuir 22, 6757–6760 (2006)
Kikkinides, E.S., Kainourgiakis, M.E., Stubos, A.K.: Origin of hysteresis of gas adsorption in disordered porous media: Lattice gas model versus percolation theory. Langmuir 19, 3338–3344 (2003)
Kloubek, J.: Hysteresis in porosimetry. Powder Technol. 29, 63–73 (1981)
Kresge, C.T., Leonowicz, M.E., Roth, W.J., Vartuli, J.C., Beck, J.S.: Ordered mesoporous molecular sieves synthesised by a liquid-crystal template mechanism. Nature 359, 710–712 (1992)
Kruk, M., Jaroniec, M., Sayari, A.: Application of large pore MCM-41 molecular sieves to improve pore size analysis using nitrogen adsorption measurements. Langmuir 13, 6267–6273 (1997)
Liabastre, A.A., Orr, C.: An evaluation of pore structure by mercury penetration. J. Colloid Interface Sci. 64, 1–18 (1978)
Libby, B., Monson, P.A.: Adsorption/desorption hysteresis in inkbottle pores: A density functional theory and Monte-Carlo simulation study. Langmuir 20, 4289–4294 (2004)
Liley, P.E., Thomson, G.H., Friend, D.G., Daubert, T.E., Buck, E.: Physical and chemical data. In: Perry, R.H., Green, D.W. (eds.) Perry’s Chemical Engineers’ Handbook. McGraw-Hill, Singapore (1998)
Lowell, S., Shields, J.E.: Powder Surface Area and Porosity. Chapman Hall, London (1984)
Lowell, S., Shields, J., Charalambous, G., Manzione, J.: Adsorbate cross-sectional area as a function of the BET C constant. J. Colloid Interface Sci. 86, 191–195 (1982)
Ma, J., Qi, H., Qong, P.: Experimental study of multilayer adsorption on fractal surfaces in porous media. Phys. Rev. E 59, 2049–2059 (1999)
Mahnke, M., Mögel, H.J.: Fractal analysis of physical adsorption on material surfaces. Colloids Surf. A 216, 215–228 (2003)
Matsuhashi, H., Tanaka, T., Arata, K.: Measurement of heat of argon adsorption for the evaluation of relative acid strength of some sulphated metal oxides and H-type zeolites. J. Phys. Chem. B 105, 9669–9671 (2001)
McMillan, W.G.: Multilayer gas adsorption on composite surfaces. J. Chem. Phys. 15, 390–397 (1947)
Murray, K.L., Seaton, N.A., Day, M.A.: Use of mercury intrusion data, combined with nitrogen adsorption measurements, as a probe of pore network connectivity. Langmuir 15, 8155–8160 (1999)
Neimark, A.V., Ravikovitch, P.I.: Capillary condensation in MMS and pore structure characterization. Microporous Mesoporous Mater. 44–45, 697–707 (2001)
Pellenq, R.J.M., Rousseau, B., Levitz, P.E.: A grand-canonical Monte-Carlo study of argon adsorption/condensation in mesoporous silica glasses. Phys. Chem. Chem. Phys. 3, 1207–1212 (2001)
Petrov, O., Furó, I.: Curvature-dependent metastability of the solid phase and the freezing-melting hysteresis in pores. Phys. Rev. E 73, 011608 (2006)
Portsmouth, R.L., Gladden, L.F.: Determination of pore connectivity by mercury porosimetry. Chem. Eng. Sci. 46, 3023–3036 (1991)
Rigby, S.P., Edler, K.J.: The influence of mercury contact angle, surface tension and retraction mechanism on the interpretation of mercury porosimetry data. J. Colloid Interface Sci. 250, 175–190 (2002)
Rigby, S.P., Fletcher, R.S.: Experimental evidence for pore blocking as the mechanism for nitrogen sorption hysteresis in a mesoporous material. J. Phys. Chem. B 108, 4690–4695 (2004a)
Rigby, S.P., Fletcher, R.S.: Interfacing mercury porosimetry with nitrogen sorption. Part. Syst. Charact. 21, 138–148 (2004b)
Rigby, S.P., Gladden, L.F.: Molecular dynamical studies of the mobility of benzene and water on silica surfaces: Correlation with the influence of surface chemistry and morphology. Stud. Surf. Sci. Catal. 122, 183–190 (1999)
Rigby, S.P., Barwick, D., Fletcher, R.S., Riley, S.N.: Interpreting mercury porosimetry data for catalyst supports using semi-empirical alternatives to the Washburn equation. Appl. Catal. A 238, 303–318 (2003)
Rigby, S.P., Fletcher, R.S., Riley, S.N.: Characterisation of porous solids using integrated nitrogen sorption and mercury porosimetry. Chem. Engng Sci. 59, 41–51 (2004)
Rigby, S.P., Evbuomwan, I.O., Watt-Smith, M.J., Edler, K.J., Fletcher, R.S.: Using nano-cast model porous media and integrated gas sorption to improve fundamental understanding and data interpretation in mercury porosimetry. Part. Syst. Charact. 23, 82–93 (2006a)
Rigby, S.P., Watt-Smith, M.J., Chigada, P., Chudek, J.A., Fletcher, R.S., Wood, J., Bakalis, S., Miri, T.: Studies of the entrapment of non-wetting fluid within nanoporous media using a synergistic combination of MRI and micro-computed X-ray tomography. Chem. Eng. Sci. 61, 7579–7592 (2006b)
Rouquerol, F., Rouquerol, J., Sing, K.: Adsorption by Powders and Porous Solids: Principles, Methodology and Applications. Academic Press, London (1999)
Saam, F.W., Cole, M.W.: Excitations and thermodynamics for liquid-helium films. Phys. Rev. B 11, 1086–1105 (1975)
Smarsly, B., Goltner, C., Antonietti, M., Ruland, W., Hoinkis, E.: SANS investigation of nitrogen sorption in porous silica. J. Phys. Chem. B 105, 831–840 (2001)
Schreiber, A., Ketealsen, I., Findenegg, G.H., Hoinkis, E.: Thickness of adsorbed nitrogen films in SBA-15 silica from small angle neutron diffraction. Stud. Surf. Sci. Catal. 160, 17–24 (2006)
Van Brakel, J., Modry, S., Svata, M.: Mercury porosimetry: State of the art. Powder Technol. 29, 1–12 (1981)
Washburn, E.W.: The dynamics of capillary flow. Phys. Rev. 17, 273–283 (1921)
Watt-Smith, M.J., Edler, K.J., Rigby, S.P.: An experimental study of gas adsorption on fractal surfaces. Langmuir 21, 2281–2292 (2005)
Zhao, D., Huo, Q., Feng, J., Chmelka, B.F., Stucky, G.D.: Nonionic triblock and star diblock copolymer and oligomeric surfactant syntheses of highly ordered, hydrothermally stable, mesoporous silica structures. J. Am. Chem. Soc. 120, 6024–6036 (1998)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Rigby, S.P., Chigada, P.I., Perkins, E.L. et al. Fundamental studies of gas sorption within mesopores situated amidst an inter-connected, irregular network. Adsorption 14, 289–307 (2008). https://doi.org/10.1007/s10450-007-9091-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10450-007-9091-8