Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Isotherms of individual pores by gas adsorption crystallography


Accurate measurements and assessments of gas adsorption isotherms are important to characterize porous materials and develop their applications. Although these isotherms provide knowledge of the overall gas uptake within a material, they do not directly give critical information concerning the adsorption behaviour of adsorbates in each individual pore, especially in porous materials in which multiple types of pore are present. Here we show how gas adsorption isotherms can be accurately decomposed into multiple sub-isotherms that correspond to each type of pore within a material. Specifically, two metal–organic frameworks, PCN-224 and ZIF-412, which contain two and three different types of pore, respectively, were used to generate isotherms of individual pores by combining gas adsorption measurements with in situ X-ray diffraction. This isotherm decomposition approach gives access to information about the gas uptake capacity, surface area and accessible pore volume of each individual pore, as well as the impact of pore geometry on the uptake and distribution of different adsorbates within the pores.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Ar adsorption behaviour in the individual pores of PCN-224.
Fig. 2: Ar adsorption behaviour in the individual pores of ZIF-412.
Fig. 3: Decomposition of Ar adsorption isotherms of MOFs into sub-isotherms of individual pores.
Fig. 4: Adsorption behaviour of different adsorbates in individual pores of MOFs.
Fig. 5: Correlation between pore geometry and the adsorption behaviour of different adsorbates.

Data availability

The data that support the findings in this study are available within the article and its Supplementary Information and/or from the corresponding authors on reasonable request.

Code availability

The program VESTA was coded by K.M. and is available free of charge via public domain at


  1. 1.

    Allison, S.A. & Barrer, R.M. Sorption in the β -phases of transition metal(II) tetra-(4-methylpyridine)thiocyanates and related compounds. J. Chem. Soc. A Inorg. Phys. Theor. 0, 1717–1723 (1969).

    CAS  Article  Google Scholar 

  2. 2.

    Li, H., Eddaoudi, M., Gory, T. L. & Yaghi, O. M. Establishing microporosity in open metal–organic frameworks: gas adsorption isotherm for Zn(BDC) (BDC = 1,4-benzenedicarboxylate). J. Am. Chem. Soc. 120, 8571–8572 (1998).

    CAS  Article  Google Scholar 

  3. 3.

    Furukawa, H., Cordova, K. E., O’Keeffe, M. & Yaghi, O. M. The chemistry and applications of metal–organic frameworks. Science 341, 1230444 (2013).

    Article  Google Scholar 

  4. 4.

    Kitagawa, S., Kitaura, R. & Noro, S. Functional porous coordination polymers. Angew. Chem. Int. Ed. 43, 2334–2375 (2004).

    CAS  Article  Google Scholar 

  5. 5.

    Rosi, N. L. et al. Hydrogen storage in microporous metal–organic frameworks. Science 300, 1127–1129 (2003).

    CAS  Article  Google Scholar 

  6. 6.

    Makal, T. A., Li, J., Lu, W. & Zhou, H. Methane storage in advanced porous materials. Chem. Soc. Rev. 41, 7761–7779 (2012).

    CAS  Article  Google Scholar 

  7. 7.

    Nugent, P. et al. Porous materials with optimal adsorption thermodynamics and kinetics for CO2 separation. Nature 495, 80–84 (2013).

    CAS  Article  Google Scholar 

  8. 8.

    Sumida, K. et al. Carbon dioxide capture in metal–organic frameworks. Chem. Rev. 112, 724–781 (2012).

    CAS  Article  Google Scholar 

  9. 9.

    Muroyama, N. et al. Argon adsorption on MCM-41 mesoporous crystal studied by in situ synchrotron powder X-ray diffraction. J. Phys. Chem. C 112, 10803–10813 (2008).

    CAS  Article  Google Scholar 

  10. 10.

    Jafta, C. J. et al. Correlating pore size and shape to local disorder in microporous carbon: a combined small angle neutron and X-ray scattering study. Carbon 123, 440–447 (2017).

    CAS  Article  Google Scholar 

  11. 11.

    Rowsell, J. L. C., Spencer, E. C., Eckert, J., Howard, J. A. K. & Yaghi, O. M. Gas adsorption sites in a large-pore metal–organic framework. Science 309, 1350–1354 (2005).

    CAS  Article  Google Scholar 

  12. 12.

    Yan, Y. et al. Metal−organic polyhedral frameworks: high H2 adsorption capacities and neutron powder diffraction studies. J. Am. Chem. Soc. 132, 4092–4094 (2010).

    CAS  Article  Google Scholar 

  13. 13.

    Olds, D. et al. Capturing the details of N2 adsorption in zeolite X using stroboscopic isotope contrasted neutron total scattering. Chem. Mater. 30, 296–302 (2018).

    CAS  Article  Google Scholar 

  14. 14.

    Yoshimoto, M. et al. Mesoscopic investigation of an ‘Immiscible’ cyclohexane and water micro-mixture in carbon micropores by contrast variation small-angle neutron scattering. Chem. Lett. 47, 336–339 (2018).

    CAS  Article  Google Scholar 

  15. 15.

    Giacobbe, C., Lavigna, E., Maspero, A. & Galli, S. Elucidating the CO2 adsorption mechanism in the triangular channels of the bis(pyrazolate) MOF Fe2 (BPEB)3 by in situ synchrotron X-ray diffraction and molecular dynamics simulations. J. Mater. Chem. A 5, 16964–16975 (2017).

    CAS  Article  Google Scholar 

  16. 16.

    Miller, S. R. et al. Single crystal X-ray diffraction studies of carbon dioxide and fuel-related gases adsorbed on the small pore scandium terephthalate metal organic framework, Sc2(O2CC6H4CO2)3. Langmuir 25, 3618–3626 (2009).

    CAS  Article  Google Scholar 

  17. 17.

    Li, L. et al. Efficient separation of ethylene from acetylene/ethylene mixtures by a flexible-robust metal–organic framework. J. Mater. Chem. A 5, 18984–18988 (2017).

    CAS  Article  Google Scholar 

  18. 18.

    Carrington, E. J., Vitórica-Yrezábal, I. J. & Brammer, L. Crystallographic studies of gas adsorption in metal–organic frameworks. Acta Cryst. B 70, 404–422 (2014).

    CAS  Article  Google Scholar 

  19. 19.

    Ghosh, S. K., Bureekaew, S. & Kitagawa, S. A dynamic, isocyanurate-functionalized porous coordination polymer. Angew. Chem. Int. Ed. 47, 3403–3406 (2008).

    CAS  Article  Google Scholar 

  20. 20.

    Krause, S. et al. A pressure-amplifying framework material with negative gas adsorption transitions. Nature 532, 348–352 (2016).

    CAS  Article  Google Scholar 

  21. 21.

    Cho, H. S. et al. Extra adsorption and adsorbate superlattice formation in metal–organic frameworks. Nature 527, 503–507 (2015).

    Article  Google Scholar 

  22. 22.

    Feng, D. et al. Construction of ultrastable porphyrin Zr metal–organic frameworks through linker elimination. J. Am. Chem. Soc. 135, 17105–17110 (2013).

    CAS  Article  Google Scholar 

  23. 23.

    Yang, J. et al. Principles of designing extra-large pore openings and pores in zeolitic imidazolate frameworks. J. Am. Chem. Soc. 139, 6448–6455 (2017).

    CAS  Article  Google Scholar 

  24. 24.

    Yuan, D., Zhao, D., Sun, D. & Zhou, H. An isoreticular series of metal–organic frameworks with dendritic hexacarboxylate ligands and exceptionally high gas-uptake capacity. Angew. Chem. Int. Ed. 49, 5357–5361 (2010).

    CAS  Article  Google Scholar 

  25. 25.

    Koh, K., Wong-Foy, A. G. & Matzger, A. J. A porous coordination copolymer with over 5000 m2/g BET surface area. J. Am. Chem. Soc. 131, 4184–4185 (2009).

    CAS  Article  Google Scholar 

  26. 26.

    Farha, O. K. et al. De novo synthesis of a metal–organic framework material featuring ultrahigh surface area and gas storage capacities. Nat. Chem. 2, 944–948 (2010).

    CAS  Article  Google Scholar 

  27. 27.

    Liu, H. et al. A porous zirconium-based metal–organic framework with the potential for the separation of butene isomers. Chem. Eur. J. 22, 14988–14997 (2016).

    CAS  Article  Google Scholar 

  28. 28.

    Li, P. et al. Toward design rules for enzyme immobilization in hierarchical mesoporous metal–organic frameworks. Chem 1, 154–169 (2016).

    CAS  Article  Google Scholar 

  29. 29.

    Liang, C. et al. Engineering of pore geometry for ultrahigh capacity methane storage in mesoporous metal–organic frameworks. J. Am. Chem. Soc. 139, 13300–13303 (2017).

    CAS  Article  Google Scholar 

  30. 30.

    Thommes, M. et al. Physisorption of gases, with special reference to the evaluation of surface area and pore size distribution. Pure Appl. Chem. 87, 1051–1069 (2015).

    CAS  Article  Google Scholar 

  31. 31.

    Collins, D. M. Electron density images from imperfect data by iterative entropy maximization. Nature 298, 49–51 (1982).

    CAS  Article  Google Scholar 

  32. 32.

    Momma, K., Ikeda, T., Belik, A. A. & Izumi, F. Dysnomia, a computer program for maximum-entropy method (MEM) analysis and its performance in the MEM-based pattern fitting. Powder Diffr. 28, 184–193 (2013).

    CAS  Article  Google Scholar 

  33. 33.

    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).

    CAS  Article  Google Scholar 

  34. 34.

    Ravikovitch, P. I. & Neimark, A. V. Density functional theory model of adsorption on amorphous and microporous silica materials. Langmuir 22, 11171–11179 (2006).

    CAS  Article  Google Scholar 

  35. 35.

    Evans, R., Marconi, U. M. B. & Tarazona, P. Capillary condensation and adsorption in cylindrical and slit-like pores. J. Chem. Soc. Faraday Trans. II 82, 1763–1787 (1986).

    Article  Google Scholar 

  36. 36.

    Rouquerol, J. et al. Recommendations for the characterization of porous solids. Pure Appl. Chem. 66, 1739–1758 (1994).

    CAS  Article  Google Scholar 

  37. 37.

    Brunauer, S., Emmett, P. H. & Teller, E. Adsorption of gases in multimolecular layers. J. Am. Chem. Soc. 60, 309–319 (1938).

    CAS  Article  Google Scholar 

  38. 38.

    Barrett, E. P., Joyner, L. G. & Halenda, P. P. The determination of pore volume and area distributions in porous substances. I. Computations from nitrogen isotherms. J. Am. Chem. Soc. 73, 373–380 (1951).

    CAS  Article  Google Scholar 

  39. 39.

    Walton, K. S. & Snurr, R. Q. Applicability of the BET method for determining surface areas of microporous metal−organic frameworks. J. Am. Chem. Soc. 129, 8552–8556 (2007).

    CAS  Article  Google Scholar 

  40. 40.

    Deng, H. et al. Large-pore pore openings in a series of metal–organic frameworks. Science 336, 1018–1023 (2012).

    CAS  Article  Google Scholar 

  41. 41.

    Peng, Y. et al. Methane storage in metal–organic frameworks: current records, surprise findings, and challenges. J. Am. Chem. Soc. 135, 11887–11894 (2013).

    CAS  Article  Google Scholar 

  42. 42.

    Gandara, F., Furukawa, H., Lee, S. & Yaghi, O. M. High methane storage capacity in aluminum metal–organic frameworks. J. Am. Chem. Soc. 136, 5271–5274 (2014).

    CAS  Article  Google Scholar 

  43. 43.

    Mason, J. A. et al. Methane storage in flexible metal–organic frameworks with intrinsic thermal management. Nature 527, 357–361 (2015).

    CAS  Article  Google Scholar 

  44. 44.

    Alezi, D. et al. MOF crystal chemistry paving the way to gas storage needs: aluminum-based soc-MOF for CH4, O2, and CO2 storage. J. Am. Chem. Soc. 137, 13308–13318 (2015).

    CAS  Article  Google Scholar 

  45. 45.

    Rouquerol, F., Rouquerol, J. & Sing, K. Adsorption by Powders and Porous Solid: Principle, Methodology, and Applications (Academic, San Diego, 1999).

    Google Scholar 

  46. 46.

    Qajar, A., Daigle, H. & Prodinovic, M. The effect of pore geometry on adsorption equilibrium in shale formations and coal-beds: lattice density functional theory study. Fuel 163, 205–213 (2016).

    CAS  Article  Google Scholar 

  47. 47.

    Marra, G. L. et al. Cation location in dehydrated Na−Rb−Y zeolite: an XRD and IR study. J. Phys. Chem. B 101, 10653–10660 (1997).

    CAS  Article  Google Scholar 

  48. 48.

    Petříček, V., Dušek, M. & Palatinus, L. Crystallographic computing system JANA2006: general features. Z. Kristallogr. 229, 345–352 (2014).

    Google Scholar 

  49. 49.

    Momma, K. & Izumi, K. VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data. J. Appl. Crystallogr. 44, 1272–1276 (2011).

    CAS  Article  Google Scholar 

Download references


We acknowledge financial support from BK21+ program, the Center for Hybrid Interface Materials (2013M3A6B1078884) and the National Research Foundation of Korea (2017M2A2A6A01070673) (H.S.C., J.K.K. and O.T.), CEM, SPST of ShanghaiTech University (no. EM02161943) (H.S.C. and O.T.), Foreign 1000 Talents Plan, China (O.T.), King Abdulaziz City for Science and Technology, Riyadh, Saudi Arabia (O.M.Y.), National Natural Science Foundation of China (no. 21471118, 91545205 and 91622103) and National Key Basic Research Program of China (no. 2014CB239203) (X.G. and H.D.), NSFC 21522105 (Y.B.Z.) and an Advanced European Research Grant (ERC, no. 321140) (H.S.C. and B.M.W.). We also thank R. Flaig for proofreading the manuscript, and X. Cai for providing the three-dimensional structure illustration of each individual cage.

Author information




O.T. and O.M.Y. conceived the idea. O.T., O.M.Y. and H.D. led the project. H.S.C. performed the in situ XRD experiments and analysis. J.Y., X.G., Y.-B.Z. and H.D. prepared the samples, and K.M. coded the computer program VESTA. O.T, H.S.C. and J.K.K. contributed to set up the experimental system. H.S.C., J.Y., X.G., H.D., O.M.Y. and O.T. prepared the first version of the manuscript and all the authors contributed to the final version.

Corresponding authors

Correspondence to Hexiang Deng or Omar M. Yaghi or Osamu Terasaki.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary data, discussion and methods, Supplementary Figs. 1–52 and Supplementary references 1–11.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Cho, H.S., Yang, J., Gong, X. et al. Isotherms of individual pores by gas adsorption crystallography. Nat. Chem. 11, 562–570 (2019).

Download citation

Further reading


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing