Abstract
This Chapter considers principles of the neutron- and x-ray scattering-based porosimetry, which exploits contrast variation and contrast matching method. The coherent scattering from porous solids arises largely from the contrast between the empty and filled pores. A porous medium is exposed to a solvent vapor having the same neutron scattering length density or electron density as the matrix skeleton. The smallest pores are filled with a condensed liquid already at low relative pressure, followed by filling of progressively larger pores. Thus, measured as a function of the relative pressure, SAS probes sub-populations of pores of increasing average size, which is calculated using the Kelvin equation. Illustrative examples are given of how SAS can be used for structural characterization of various types of porous materials including low-dielectric constant polymer films, porous silicas, carbonaceous materials, and Nafion membranes.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Horikawa, T., Do, D.D., Nicholson, D.: Capillary condensation of adsorbates in porous materials. Adv. Colloid Interface Sci. 169, 40 (2011)
Gelb, L.D., Gubbins, K.E., Radhakrishnan, R., Sliwinska-Bartkowiak, M.: Phase separation in confined systems. Rep. Prog. Phys. 62, 1573 (1999)
Rouquerol, F., Rouquerol, J., Sing, K.: Adsorption by Powders & Porous Solids. Academic, London (1999)
Silverstein, M.S., Bauer, B.J., Hedden, R.C., Lee, H.-J., Landes, B.G.: SANS and XRR porosimetry of a polyphenylene low-k dielectric. Macromolecules 39, 2998 (2006)
Hedden, R.C., Lee, H.-J., Soles, C.L., Bauer, B.J.: Characterization of pore structure in a nanoporous low-dielectric-constant thin film by neutron porosimetry and X-ray porosimetry. Langmuir 20, 6658 (2004)
Lee, H.-J., Soles, C.L., Liu, D.-W., Bauer, B.J., Wu, W.-L.: Pore size distributions in low-k dielectric thin films from x-ray porosimetry. J. Polym. Sci. B. 40, 2170 (2002)
Melnichenko, Y.B., Wignall, G.D.: Small-angle neutron scattering in materials science: recent practical applications. J. Appl. Phys. 102, 021101 (2007)
Wu, W.L., Wallace, W.E., Lin, E.K., Lynn, G.W., Glinka, C.J., Ryan, E.T., Ho, H.M.: Properties of nanoporous silica thin films determined by high-resolution x-ray reflectivity and small-angle neutron scattering. J. Appl. Phys. 87, 1193 (2000)
Debye, P., Anderson, H.R., Brumberger, H.: Scattering by an inhomogeneous solid. 2. The correlation function and its application. J. Appl. Phys. 28, 679 (1957)
Hedden, R.C., Lee, H.J., Bauer, B.J.: Characterization of nanoporous low-k thin films by small-angle neutron scattering contrast variation. Langmuir 20, 416 (2004)
Lee, H.-J., Soles, C.L., Liu, D.-W., Bauer, B.J., Lin, E.K., Wu, W.-L., Grill, A.: Structural characterization of porous low-k thin films prepared by different techniques using x-ray porosimetry. J. Appl. Phys. 95, 2355 (2004)
Silverstein, M.S., Shach-Caplan, M., Bauer, B.J., Hedden, R.C., Lee, H.-J., Landes, B.G.: Nanopore formation in a polyphenylene low-k dielectric. Macromolecules 38, 4301 (2005)
Klotz, M., Roussac, V., Rebiscouul, D., Ayral, A., van der Lee, A.: Adsorption-desorption isotherms of nanoporous thin films measured by X-ray reflectometry. Thin Solid Films 495, 214 (2006)
Goh, T.K., Wong, T.K.S.: Investigation of structure, thermal and oxygen plasma stability of mesoporous methylsilsesquioxane films by X-ray reflectivity and small angle scattering. Microelectron. Eng. 75, 330 (2004)
Vogt, B.D., Pai, R.A., Lee, H.-J., Hedden, R.C., Soles, C.L., Wu, W.-L., Lin, E., Bauer, B.J., Watkins, J.J.: Characterization of ordered mesoporous silica films using small-angle neutron scattering and X-ray porosimentry. Chem. Mater. 17, 1398 (2005)
Hoinkis, E.: In situ small angle neutron scattering study of benzene adsorption in the porous SiO2 glass CPG-10-75. Adv .Colloid Interface Sci. 76–77, 39 (1998)
Hoinkis, E.: Small angle neutron scattering study of C6D6 condensation in a mesoporous glass. Langmuir 12, 4299 (1996)
Hohr, A., Neumann, H.-B., Schmidt, P.W., Pfeifer, P., Avnir, D.: Fractal surface and cluster structure of controlled-pore glasses and Vycor porous glass as revealed by small-angle X-ray and neutron scattering. Phys. Rev. B 38, 1462 (1988)
Brown, R.J.C., Evans, M.J.B., Tun, Z.: Neutron scattering study of adsorption in porous MCM-41 silica. Can. J. Phys. 88, 707 (2010)
Hoinkis, E.: Small-angle scattering studies of adsorption and of capillary condensation in porous solids. Part. Part. Syst. Charact. 21, 80 (2004)
Ramsay, J.D.F., Kallus, S., Hoinkis, E.: SANS characterisation of mesoporous silicas having model structures. In: Unger, K.K., Kreysa, G., Baselt, J.P. (eds.) Characterisation of Porous Solids V. Studies in Surface Science and Catalysis, vol. 128, p. 439. (2000)
Smarsly, B., Goltner, C., Antonietti, M., Ruland, W., Hoinkis, E.: SANS investigation of nitrogen sorption in porous silica. J. Phys. Chem. B 105, 831 (2001)
Guenther, G., Prass, J., Paris, O., Schoen, M.: Novel insights into nanopore deformation caused by capillary condensation. Phys. Rev. Lett. 101, 086104 (2008)
Grosman, A., Ortega, C.: Influence of elastic deformation of porous materials in adsorption-desorption process: a thermodynamic approach. Phys. Rev. B 78, 085433 (2008)
Kim, H.Y., Gatica, S.M., Stan, G., Cole, M.W.: Effects of substrate relaxation on adsorption in pores. J. Low Temp. Phys. 156, 1–8 (2009)
Prass, J., Mueter, D., Fratzl, P., Paris, O.: Capillarity-driven deformation of ordered nanoporous silica. Appl. Phys. Lett. 95, 083121 (2009)
Erko, M., Wallacher, D., Brandt, A., Paris, O.: In-situ small-angle neutron scattering study of pore filling and pore emptying in ordered mesoporous silica. J. Appl. Crystallogr. 43, 1 (2010)
Hoinkis, E., Rohl-Kuhn, B.: In situ small-angle neutron scattering study of nitrogen adsorption and condensation in mesoporous silica glass CPG-10-75. J. Colloid Interface Sci. 296, 256 (2006)
Hoinkis, E.: In: Berichte des Hahn-Mainer-Institut Berlin. BENSC Experimental Report, pp. 212–213 (1998)
Hoinkis, E.: In: Berichte des Hahn-Mainer-Institut Berlin. BENSC Experimental Report, pp. 295 (2000)
Hoinkis, E., Rohl-Kuhn, B.: In edited by K. Kaneko and Y. Hanzawa. Proceedings of the Conference on the Fundamentals of adsorption, pp. 601–607. International Adsorption Society; IK International: Chiba-City, Japan (2002)
Schreiber, A., Ketelsen, I., Findenegg, G.H., Hoinkis, E.: In: Studies in Surface and Surface Science and Catalysis. Proceedings of the 7th International Symposium on the Characterization of Porous Solids (COPS-VII), pp. 17–24. Aix-en-Provence, France (2005)
Eschricht, E., Hoinkis, E., Madler, F.: Nitrogen distribution at 77.7 K in mesoporous Gelsil generated via evolutionary minimization with statistical descriptors derived from adsorption and in situ SANS. Langmuir 23, 2145 (2007)
Smarsly, B., Thommes, M., Ravikovitch, P.I., Neimark, A.V.: Characterization of worm-like micro- and mesoporous silicas by small-angle scattering and high-resolution porosimetry. Adsorption 11, 653 (2005)
Mascotto, S., Wallacher, D., Brandt, A., Hauss, T., Thommes, M., Zickler, G.A., Funari, S.S., Timmann, A., Smarsly, B.: Analysis of microporosity in ordered mesoporous hierarchically structures silica by combining physisorption with in situ small-angle scattering (SAXS and SANS). Langmuir 25, 12670 (2009)
Mascotto, S., Wallacher, D., Kuschel, A., Polarz, S., Zickler, G.A., Timmann, A., Smarsley, B.: Adsorption in periodically ordered mesoporous organosilica materials studied by in situ small-angle X-ray scattering and small-angle neutron scattering. Langmuir 26, 6383 (2010)
Sharifi, M., Marschall, R., Wihelm, M., Wallacher, D., Wark, M.: Detection of homogeneous distribution of functional groups in mesoporous silica by small angle neutron scattering and in situ adsorption of nitrogen or water. Langmuir 27, 5516 (2011)
Sharifi, M., Wallacher, D., Wark, M.: Distribution of functional groups in periodic mesoporous organosilica materials studied by small-angle neutron scattering with in situ adsorption of nitrogen. Beilstein J. Nanotechnol. 3, 428 (2012)
Zickler, G.A., Jahnert, S., Wagermaier, W., Funari, S.S., Findenegg, G.H., Paris, O.: Physisorbed films in periodic silica studied by in situ synchrotron small-angle diffraction. Phys. Rev. B 73, 184109 (2006)
Imperor-Clerc, M., Davidson, P., Davidson, A.: Existence of a microporous corona around the mesopores of silica-based SBA-15 materials templated by triblock copolymers. J. Am. Chem. Soc. 122, 11925 (2000)
Jahnert, S., Muter, D., Prass, J., Zickler, G.A., Paris, O., Findenegg, G.H.: Pore structure and fluid sorption in ordered mesoporous silica. I. Experimental study by in situ small-angle x-ray scattering. J. Phys. Chem. C 113, 15201 (2009)
Muter, D., Jahnert, S., Dunlop, J.W., Findenegg, G.H., Paris, O.: Pore structure and fluid sorption in ordered mesoporous silica. II. Modeling. J. Phys. Chem. C 113, 15211 (2009)
Findenegg, G.H., Jahnert, S., Muter, D., Paris, O.: Analysis of pore structure and gas adsorption in periodic mesoporous solids by in situ small-angle X-ray scattering. Colloids. Surf. A. 357, 3 (2010)
Antxustegi, M.M., Hall, P.J., Calo, J.M.: The use of contrast-matching small-angle neutron scattering techniques to monitor closed porosity in carbons. J. Colloids Interface Sci. 202(490) (1998)
Hall, P.J., Ruiz Machado, W., Galan, D.G., Barrientos Barria, E.L., Sherrington, D.C.: Use of contrast matching small-angle neutron scattering to monitor the presence of closed porosity in controlled porosity styrene–divinylbenzene resins. Faraday Trans. 92, 2607 (1996)
Snook, I., Yavorsky, I., Hanley, H.J.M., Lin, M., Mainwaring, D., Rogers, H., Zulli, P.: Characterization of metallurgical chars by small angle neutron scattering. Energy Fuel 16, 1009 (2002)
Hoinkis, E., Allen, A.J.: A small angle neutron scattering study of porous graphitic materials before and after adsorption and condensation of C6D6 within the accessible pores. J. Colloids Interface Sci. 145, 540 (1991)
Mergia, K., Stefanopoulos, K.L., Ordas, N., Garcia-Rosales, C.: A comparative study of the porosity of doped graphites by small-angle neutron scattering, nitrogen adsorption and helium pycnometry. Micropor. Mesopor. Mater. 134, 141 (2010)
Hoinkis, E., Ziehl, M.: A small-angle neutron scattering study of activated carbon fibers. Carbon 41, 2047 (2003)
Mileeva, Z., Ross, D.K., Wilkinson, D., King, S.M., Ryan, T.A., Sharrock, H.: The use of small angle neutron scattering with contrast matching and variable adsorbate partial pressures in the study of porosity in activated carbons. Carbon 50, 5062 (2012)
Gethner, S.: The determination of the void structure of macroporous coals by small-angle neutron scattering: void geometry and structure in Illinois No-6 bituminous coal. J. Appl. Phys. 59, 1068 (1986)
Hall, P.J., Antxustegi, M., Ruiz, W.: Contrast-matching small-angle neutron scattering evidence for the absence of a connected pore system in Pittsburgh No 8 coal. Fuel 77, 1663 (1998)
Antxustegi, M., Hall, P.J., Calo, J.: Development of porosity in Pittsburgh No. 8 coal char as investigated by contrast-matching small-angle neutron scattering and gas adsorption techniques. Energy Fuel 12, 542 (1998)
Hall, P.J., Brown, S.D., Calo, J.M.: The pore structure of the argonne coals as interpreted from contrast matching small angle neutron scattering. Fuel 79, 1327 (2000)
Mitropoulos, A.C., Stefanopoulos, K.L., Kanellopoulos, N.K.: Coal studies by small-angle X-ray scattering. Micropor. Mesopor. Mater. 24, 29 (1998)
Favvas, E.P., Sapalidis, A.A., Stefanopoulos, K.L., Romanos, G.E., Kannellopoulos, N.K., Kargiotis, E.K., Mitropoulos, A.C.: Characterization of carbonate rocks by combination of scattering, porosimetry and permeability techniques. Micropor. Mesopor. Mater. 120, 109 (2009)
Melnichenko, Y.B., He, L., Sakurovs, R., Kholodenko, A.L., Blach, T., Mastalerz, M., Radlinski, A.P., Cheng, G., Mildner, D.F.R.: Accessibility of pores in coal to methane and carbon dioxide. Fuel 91, 200 (2012)
He, L., Chathoth, S.M., Melnichenko, Y.B., Presser, V., McDonough, J., Gogotsi, Y.: Small-angle neutron scattering characterization of the structure of annoporous carbons for energy-related applications. Micropor. Mesopor. Mater. 149, 46 (2012)
Boukhalfa, S., He, L., Melnichenko, Y.B., Yushin, G.: Small-angle neutron scattering for in situ probing of ion adsorption inside micropores. Angew. Chem. Int. Ed. 52, 4618 (2013)
Laszlo, K., Rochas, C., Geissler, E.: Water vapor adsorption and contrast-modified SAXS in microporous polymer-based carbons of different surface chemistry. Adsorption 14, 447 (2008)
Laszlo, K., Czakkel, O., Dobos, G., Lodewyckx, P., Rochas, C., Geissler, E.: Water capor adsorption in highly porous carbons as seen by small and wide angle X-ray scattering. Carbon 48, 1038 (2010)
Kim, M.-H., Glinka, C., Carter, R.N.: In situ vapor sorption apparatus for small-angle neutron scattering and its application. Rev. Sci. Instrum. 76, 113904 (2005)
Kusoglu, A., Modestino, M.A., Hexemer, A., Segalman, R.A., Weber, A.Z.: Subsecond morphological changes in Nafion during water uptake detected by small-angle X-ray scattering. ACS Macro Lett. 1, 33 (2012)
Ramsay, J.D.F.: Surface and pore structure characterization by neutron scattering techniques. Adv. Colloid Interface Sci. 76–77, 13 (1998)
Radlinski, A.P., Busbridge, T.L., MacA Gray, E., Blach, T., Cheng, G., Melnichenko, Y.B., Cookson, D.J., Mastalerz, M., Esterle, J.: Dynamic micromapping of CO2 sorption in coal. Langmuir 25(2385) (2009)
Gray, P.G., Do, D.D.: A graphical method for determining pore and surface diffusivities in adsorption systems. Ind. Eng. Chem. Res. 31, 1176 (1992)
Kallus, S., Hahn, A., Ramsay, J.D.: Gas adsorption in MCM-41 porous silicas dynamic measurements using SANS. Eur. Phys. J. 12, s01 (2003)
Vielstich, W., Lamm, A., Gasteiger, H.A.: Handbook of Fuel Cells: Fundamentals, Technology, Applications. Wiley, New York, NY (2004)
Gebel, G., Lyonnard, S., Mendil-Jakani, H., Morin, A.: The kinetics of water sorption in Nafion membranes: a small-angle neutron scattering study. J. Phys. Condens. Matter 23, 234107 (2011)
Gebel, G., Diat, O.: Neutron and X-ray scattering: suitable tools for studying ionomer membranes. Fuel Cells 5, 261 (2005)
Xu, F., Diat, O., Gebel, G., Morin, A.: Determination of transverse water concentration profile through MEA in a fuel cell using neutron scattering. J. Electrochem. Soc. 154, 1389 (2007)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Melnichenko, Y.B. (2016). Neutron and X-Ray Porosimetry. In: Small-Angle Scattering from Confined and Interfacial Fluids. Springer, Cham. https://doi.org/10.1007/978-3-319-01104-2_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-01104-2_8
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-01103-5
Online ISBN: 978-3-319-01104-2
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)