Skip to main content

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Horikawa, T., Do, D.D., Nicholson, D.: Capillary condensation of adsorbates in porous materials. Adv. Colloid Interface Sci. 169, 40 (2011)

    Article  Google Scholar 

  2. Gelb, L.D., Gubbins, K.E., Radhakrishnan, R., Sliwinska-Bartkowiak, M.: Phase separation in confined systems. Rep. Prog. Phys. 62, 1573 (1999)

    Article  Google Scholar 

  3. Rouquerol, F., Rouquerol, J., Sing, K.: Adsorption by Powders & Porous Solids. Academic, London (1999)

    Google Scholar 

  4. 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)

    Article  Google Scholar 

  5. 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)

    Article  Google Scholar 

  6. 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)

    Article  Google Scholar 

  7. Melnichenko, Y.B., Wignall, G.D.: Small-angle neutron scattering in materials science: recent practical applications. J. Appl. Phys. 102, 021101 (2007)

    Article  Google Scholar 

  8. 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)

    Article  Google Scholar 

  9. 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)

    Article  Google Scholar 

  10. 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)

    Article  Google Scholar 

  11. 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)

    Article  Google Scholar 

  12. 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)

    Article  Google Scholar 

  13. 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)

    Article  Google Scholar 

  14. 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)

    Article  Google Scholar 

  15. 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)

    Article  Google Scholar 

  16. 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)

    Article  Google Scholar 

  17. Hoinkis, E.: Small angle neutron scattering study of C6D6 condensation in a mesoporous glass. Langmuir 12, 4299 (1996)

    Article  Google Scholar 

  18. 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)

    Article  Google Scholar 

  19. 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)

    Article  Google Scholar 

  20. Hoinkis, E.: Small-angle scattering studies of adsorption and of capillary condensation in porous solids. Part. Part. Syst. Charact. 21, 80 (2004)

    Article  Google Scholar 

  21. 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)

    Google Scholar 

  22. 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)

    Article  Google Scholar 

  23. Guenther, G., Prass, J., Paris, O., Schoen, M.: Novel insights into nanopore deformation caused by capillary condensation. Phys. Rev. Lett. 101, 086104 (2008)

    Article  Google Scholar 

  24. Grosman, A., Ortega, C.: Influence of elastic deformation of porous materials in adsorption-desorption process: a thermodynamic approach. Phys. Rev. B 78, 085433 (2008)

    Article  Google Scholar 

  25. 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)

    Article  Google Scholar 

  26. Prass, J., Mueter, D., Fratzl, P., Paris, O.: Capillarity-driven deformation of ordered nanoporous silica. Appl. Phys. Lett. 95, 083121 (2009)

    Article  Google Scholar 

  27. 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)

    Article  Google Scholar 

  28. 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)

    Article  Google Scholar 

  29. Hoinkis, E.: In: Berichte des Hahn-Mainer-Institut Berlin. BENSC Experimental Report, pp. 212–213 (1998)

    Google Scholar 

  30. Hoinkis, E.: In: Berichte des Hahn-Mainer-Institut Berlin. BENSC Experimental Report, pp. 295 (2000)

    Google Scholar 

  31. 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)

    Google Scholar 

  32. 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)

    Google Scholar 

  33. 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)

    Article  Google Scholar 

  34. 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)

    Article  Google Scholar 

  35. 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)

    Article  Google Scholar 

  36. 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)

    Article  Google Scholar 

  37. 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)

    Article  Google Scholar 

  38. 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)

    Article  Google Scholar 

  39. 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)

    Article  Google Scholar 

  40. 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)

    Article  Google Scholar 

  41. 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)

    Article  Google Scholar 

  42. 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)

    Article  Google Scholar 

  43. 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)

    Article  Google Scholar 

  44. 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)

    Google Scholar 

  45. 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)

    Article  Google Scholar 

  46. 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)

    Article  Google Scholar 

  47. 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)

    Article  Google Scholar 

  48. 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)

    Article  Google Scholar 

  49. Hoinkis, E., Ziehl, M.: A small-angle neutron scattering study of activated carbon fibers. Carbon 41, 2047 (2003)

    Article  Google Scholar 

  50. 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)

    Article  Google Scholar 

  51. 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)

    Article  Google Scholar 

  52. 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)

    Article  Google Scholar 

  53. 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)

    Article  Google Scholar 

  54. 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)

    Article  Google Scholar 

  55. Mitropoulos, A.C., Stefanopoulos, K.L., Kanellopoulos, N.K.: Coal studies by small-angle X-ray scattering. Micropor. Mesopor. Mater. 24, 29 (1998)

    Article  Google Scholar 

  56. 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)

    Article  Google Scholar 

  57. 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)

    Article  Google Scholar 

  58. 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)

    Article  Google Scholar 

  59. 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)

    Article  Google Scholar 

  60. 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)

    Article  Google Scholar 

  61. 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)

    Article  Google Scholar 

  62. 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)

    Article  Google Scholar 

  63. 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)

    Article  Google Scholar 

  64. Ramsay, J.D.F.: Surface and pore structure characterization by neutron scattering techniques. Adv. Colloid Interface Sci. 76–77, 13 (1998)

    Article  Google Scholar 

  65. 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)

    Google Scholar 

  66. 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)

    Article  Google Scholar 

  67. Kallus, S., Hahn, A., Ramsay, J.D.: Gas adsorption in MCM-41 porous silicas dynamic measurements using SANS. Eur. Phys. J. 12, s01 (2003)

    Google Scholar 

  68. Vielstich, W., Lamm, A., Gasteiger, H.A.: Handbook of Fuel Cells: Fundamentals, Technology, Applications. Wiley, New York, NY (2004)

    Google Scholar 

  69. 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)

    Article  Google Scholar 

  70. Gebel, G., Diat, O.: Neutron and X-ray scattering: suitable tools for studying ionomer membranes. Fuel Cells 5, 261 (2005)

    Article  Google Scholar 

  71. 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)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints 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

Publish with us

Policies and ethics