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Hopping dynamics and diffusion of atoms, molecules, and ions in nanoporous solids by exchange NMR spectroscopy

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Abstract

Molecular diffusion in nanoporous materials can be understood as series of dynamic hopping or exchange motions of molecules between different discrete sites. Exchange NMR offers the spectral resolution to distinguish between these different sites, based on isotropic and anisotropic NMR interactions that manifest differences in the local chemical or structural environments of molecules at different sites or their local orientations. Such interactions facilitate the observation of distinct adsorption environments and provide insights on the number and distributions of distinct types of environments and the geometries and motional correlation times of local hopping events between different sites. The temporal range accessible by exchange NMR is governed by the time required for the observation of the NMR signal (< 1 ms) and the return of the nuclear magnetic polarization to thermal equilibrium (typically several seconds). Over such timescales, this permits slow molecular exchange processes between local environments to be probed in great quantitative detail. The resulting insights on dynamic exchange or hopping of atoms, molecules, or ions in nanoporous solids provide a basis for understanding processes that occur over longer length and time scale, which ultimately account for their macroscopic diffusion properties.

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Abbreviations

B :

Magnetic-flux density, in Tesla or kg s−2 A−1

\(R^{EIS}\) :

Ratio of integrated centerband and sideband peak areas

B 0 :

Stationary main magnetic-flux density in z-direction, Tesla

\({R}_{\rm {fe}}\) :

\({R}^{EIS}\)In the full exchange limit

\({C}_{n}\) :

nth order autocorrelation function

\(S\left(\omega \right)\) :

Spectral intensity

D :

Diffusion coefficient, in m2 s−1

T 1 :

Longitudinal (spin–lattice) relaxation time, s

\({E}_{a}\) :

Activation energy, Joules mol−1

T 2 :

Transverse (spin–spin) relaxation time, s

\({E}^{*}\) :

Transition state energy, Joules mol−1

t n :

Time domain in the nth dimension, s

\({F}_{n}\) :

Free energy associated with n xenon atoms in a cage, J mol−1

t :

Time, s

f n :

Frequency domain in the nth dimension, rad s−1

T :

Absolute temperature, K

\(\Delta F\) :

Separation energy, Joules

\({\tau }_{n}\) :

Correlation time of exchange process n, s

\({k}_{0}\) :

Pre-exponential factor associated with an mth-order exchange process, molm s−1

\({t}_{\rm {mix}}\) :

Mixing time, s

\({k}_{\rm {n}}\) :

Rate coefficient associated with an mth-order exchange process n, molm s−1

\({\nu }_{\rm {MAS}}\) :

Magic angle spinning frequency, Hz

\({k}_{\rm {B}}\) :

Boltzmann’s constant, J K−1

\({\nu }_{\rm {aniso}}\) :

Frequency of the anisotropic NMR interaction, Hz

\({k}_{\rm {eff}}\) :

Effective rate coefficient with an mth-order exchange process, molm s−1

\({\omega }_{n}\) :

Angular frequency of the nth component, rad s−1

\({k}_{\rm {micr}}\) :

Microscopic rate coefficient with an mth-order exchange process, molm s−1

\({\omega }^{(n)}\) :

Angular frequency associated with a cage containing n atoms

\({k}_{\rm {SD}}\) :

Spin diffusion rate coefficient, s−1

\({\varvec{\Pi}}\) :

Magnetization exchange matrix

L :

Characteristic length, m

\({\Pi }_{n,m}\) :

Magnetization exchange matrix element

\(\mathbf{M}\) :

Normalized spectral intensity matrix at time

\(\lambda\) :

Decay rate, s−1

\({M}_{n,m}\) :

Normalized spectral intensity matrix element

\({\omega }_{0}\) :

Larmor frequency, rad s−1

\(P\left(n\right)\) :

Probability for a cage to have an occupancy of n atoms

\(\theta , \phi\) :

Polar angles, radians

\({P}_{n}\) :

nth-order Legendre polynomial

\(\eta\) :

Asymmetry parameter in the Haeberlen convention

\(\mathbf{R}\) :

Atomic (e.g., Xe) exchange matrix

\(\delta\) :

Reduced chemical shift anisotropy in the Haeberlen convention, Hz MHz−1 (ppm)

\({R}_{n,m}\) :

Atomic exchange matrix element

\({\delta }_{iso}\) :

Isotropic chemical shift, Hz MHz−1 (ppm)

References

  1. Hartley, G.S., Crank, J.: Some fundamental definitions and concepts in diffusion processes. Trans. Faraday Soc. 45, 801–818 (1949). https://doi.org/10.1039/tf9494500801

    Article  CAS  Google Scholar 

  2. Karger, J., Ruthven, D.M.: On the comparison between macroscopic and n.m.r. measurements of intracrystalline diffusion in zeolites. Zeolites 9(4), 267–281 (1989). https://doi.org/10.1016/0144-2449(89)90071-7

    Article  CAS  Google Scholar 

  3. Trautz, M.: Das Gesetz Der Reaktionsgeschwindigkeit Und Der Gleichgewichte in Gasen. Bestätigung Der Additivität von C v -3/2R. Neue Bestimmung Der Integrationskonstanten Und Der Moleküldurchmesser. Zeitschrift für Anorg. und Allg. Chemie 96(1), 1–28 (1916). https://doi.org/10.1002/zaac.19160960102

  4. Eliason, M.A., Hirschfelder, J.O.: General collision theory treatment for the rate of bimolecular, gas phase reactions. J. Chem. Phys. 30(6), 1426–1436 (1959). https://doi.org/10.1063/1.1730216

    Article  CAS  Google Scholar 

  5. Pechukas, P.: Statistical Approximations in Collision Theory. In: Dynamics of Molecular Collisions, pp. 269–322. Springer US: Boston, MA (1976) https://doi.org/10.1007/978-1-4757-0644-4_6

  6. Jeener, J., Meier, B.H., Bachmann, P., Ernst, R.R.: Investigation of exchange processes by two-dimensional nmr spectroscopy. J. Chem. Phys. 71(11), 4546–4553 (1979). https://doi.org/10.1063/1.438208

    Article  CAS  Google Scholar 

  7. Spiess, H.W., Schmidt-Rohr, K.: Multidimensional Solid-State NMR and Polymers. Academic Press (1994). https://doi.org/10.1016/C2009-0-21335-3

  8. Hentschel, D., Sillescu, H., Spiess, H.W.: Deuteron n.m.r. study of chain motion in solid polyethylene. Polymer (Guildf). 25(8), 1078–1086 (1984). https://doi.org/10.1016/0032-3861(84)90342-2

    Article  CAS  Google Scholar 

  9. Larsen, R.G., Shore, J., Schmidt-Rohr, K., Emsley, L., Long, H., Pines, A., Janicke, M., Chmelka, B.F.: NMR study of xenon dynamics and energetics in Na-A zeolite. Chem. Phys. Lett. 214(2), 220–226 (1993). https://doi.org/10.1016/0009-2614(93)90085-F

    Article  CAS  Google Scholar 

  10. Schaefer, D.J., Favre, D.E., Wilhelm, M., Weigel, S.J., Chmelka, B.F.: Site-hopping dynamics of benzene adsorbed on Ca-LSX zeolite studied by solid-state exchange 13C NMR. J. Am. Chem. Soc. 119(39), 9252–9267 (1997). https://doi.org/10.1021/ja971563m

    Article  CAS  Google Scholar 

  11. Auerbach, S.M., Metiu, H.I.: Diffusion in zeolites via cage-to-cage kinetics: modeling benzene diffusion in Na-Y. J. Chem. Phys. 105(9), 3753–3760 (1996). https://doi.org/10.1063/1.472195

    Article  CAS  Google Scholar 

  12. McCormick, A.V., Chmelka, B.F.: Xenon adsorption in Na-A zeolite cavities. Mol. Phys. 73(3), 603–617 (1991). https://doi.org/10.1080/00268979100101411

    Article  CAS  Google Scholar 

  13. Chmelka, B.F., Raftery, D., McCormick, A.V., De Menorval, L.C., Levine, R.D., Pines, A.: Measurement of Xenon Distribution Statistics in Na-A Zeolite Cavities. Phys. Rev. Lett. 66(5), 580–583 (1991). https://doi.org/10.1103/PhysRevLett.66.580

    Article  CAS  PubMed  Google Scholar 

  14. Moudrakovski, I.L., Ratcliffe, C.I., Ripmeester, J.A.: Application Of 129Xe 2D-EXSY NMR to intra- and interparticle exchange in zeolites. Appl. Magn. Reson. 8(3–4), 385–399 (1995). https://doi.org/10.1007/BF03162653

    Article  CAS  Google Scholar 

  15. Liu, Y., Zhang, W., Liu, Z., Xu, S., Wang, Y., Xie, Z., Han, X., Bao, X.: Direct observation of the mesopores in ZSM-5 zeolites with hierarchical porous structures by laser-hyperpolarized 129Xe NMR. J. Phys. Chem. C 112(39), 15375–15381 (2008). https://doi.org/10.1021/jp802813x

    Article  CAS  Google Scholar 

  16. Sears, D.N., Demko, B.A., Ooms, K.J., Wasylishen, R.E., Huang, Y.: Formation of porous aluminophosphate frameworks monitored by hyperpolarized 129Xe NMR spectroscopy. Chem. Mater. 17(22), 5481–5488 (2005). https://doi.org/10.1021/cm0513132

    Article  CAS  Google Scholar 

  17. Giovine, R., Volkringer, C., Springuel-Huet, M.-A., Nossov, A., Blanc, F., Julien, Trébosc, T., Loiseau, T., Amoureux, J.-P., Lafon, O., Pourpoint, F.: Study of Xenon Mobility in the Two Forms of MIL-53(Al) Using Solid-State NMR Spectroscopy (2017). https://doi.org/10.1021/acs.jpcc.7b06006

  18. Ooms, K.J., Wasylishen, R.E.: 129Xe NMR study of xenon in iso-reticular metal-organic frameworks. Microporous Mesoporous Mater. 103(1–3), 341–351 (2007). https://doi.org/10.1016/j.micromeso.2007.01.054

    Article  CAS  Google Scholar 

  19. McCusker, L.B., Olson, D.H., Baerlocher, C.: Atlas of Zeolite Framework Types. Elsevier (2007). https://doi.org/10.1016/B978-0-444-53064-6.X5186-X

  20. Breck, D.W.: Zeolite Molecular Sieves - Structure, Chemistry, and Use. John Wiley & Sons (1974)

  21. Vitale, G., Bull, L.M., Morris, R.E., Cheetham, A.K., Toby, B.H., Coe, C.G., MacDougall, J.E.: Combined neutron and X-Ray powder diffraction study of zeolite Ca LSX and a 2H NMR study of its complex with benzene. J. Phys. Chem. 99(43), 16087–16092 (1995). https://doi.org/10.1021/j100043a058

    Article  CAS  Google Scholar 

  22. Lechert, H., Wittern, K.-P.: Nuclear magnetic resonance studies of the arrangement of benzene molecules in the cavities of the zeolite NaX. Berichte der Bunsengesellschaft für Phys. Chemie 82(10), 1054–1060 (1978). https://doi.org/10.1002/bbpc.19780821007

    Article  CAS  Google Scholar 

  23. Burmeister, R., Schwarz, H., Boddenberg, B.: The determination of translational intracrystalline diffusion constants of molecules in faujasite-type zeolites with the aid of deuteron-nmr-spectroscopy. Berichte der Bunsengesellschaft für Phys. Chemie 93(11), 1309–1313 (1989). https://doi.org/10.1002/bbpc.19890931133

    Article  CAS  Google Scholar 

  24. De Mallmann, A., Barthomeuf, D.: Changes with dealumination of the state of benzene adsorbed on faujasites. J. Chem. Soc. 6, 476–477 (1986). https://doi.org/10.1039/C39860000476

    Article  Google Scholar 

  25. Freeman, J.J., Unland, M.L.: Laser raman study of benzene adsorption on alkali metal X and Y zeolites. J. Catal. 54(2), 183–196 (1978). https://doi.org/10.1016/0021-9517(78)90041-6

    Article  CAS  Google Scholar 

  26. Ernst, R., Bodenhausen, G., Wokaun, A.: Principles of Nuclear Magnetic Resonance in One and Two Dimensions. Clarendon Press, Oxford, UK (1987)

  27. Schmidt, C., Wefing, S., Blümich, B., Spiess, H.W.: Dynamics of molecular reorientations: direct determination of rotational angles from two-dimensional NMR of powders. Chem. Phys. Lett. 130(1–2), 84–90 (1986). https://doi.org/10.1016/0009-2614(86)80431-6

    Article  CAS  Google Scholar 

  28. Schmidt, C., Blümich, B., Spiess, H.W.: deuteron two-dimensional exchange NMR in solids. J. Magn. Reson. 79(2), 269–290 (1988). https://doi.org/10.1016/0022-2364(88)90219-3

    Article  CAS  Google Scholar 

  29. Gédéon, A., Favre, D.E., Reichert, D., MacNeil, J., Chmelka, B.F.: Distributions of site-hopping geometries and rates for benzene adsorbed on Ag-Y zeolite. J. Phys. Chem. A 103(34), 6691–6703 (1999). https://doi.org/10.1021/jp990953n

    Article  CAS  Google Scholar 

  30. Wilhelm, M., Firouzi, A., Favre, D.E., Bull, L.M., Schaefer, D.J., Chmelka, B.F.: Dynamics of benzene adsorbed on Ca-LSX zeolite studied by solid-state two-dimensional exchange 13C NMR. J. Am. Chem. Soc. 117(10), 2923–2924 (1995). https://doi.org/10.1021/ja00115a026

    Article  CAS  Google Scholar 

  31. Favre, D.E., Schaefer, D.J., Chmelka, B.F.: Direct determination of motional correlation times by 1D MAS and 2D exchange NMR techniques. J. Magn. Reson. 134(2), 261–279 (1998). https://doi.org/10.1006/jmre.1998.1506

    Article  CAS  PubMed  Google Scholar 

  32. Favre, D.E., Schaefer, D.J., Auerbach, S.M., Chmelka, B.F.: Direct measurement of intercage hopping in strongly adsorbing guest-zeolite systems. Phys. Rev. Lett. 81(26), 5852–5855 (1998). https://doi.org/10.1103/PhysRevLett.81.5852

    Article  CAS  Google Scholar 

  33. Dixon, W.T., Schaefer, J., Sefcik, M.D., Stejskal, E.O., McKay, R.A.: Total suppression of sidebands in CPMAS C-13 NMR. J. Magn. Reson. 49(2), 341–345 (1982). https://doi.org/10.1016/0022-2364(82)90199-8

    Article  CAS  Google Scholar 

  34. Luzgin, M.V., Freude, D., Haase, J., Stepanov, A.G.: Methane Interaction with Zn2+-Exchanged Zeolite H-ZSM-5: study of adsorption and mobility by one- and two-dimensional variable-temperature 1H solid-state NMR. J. Phys. Chem. C 119(25), 14255–14261 (2015). https://doi.org/10.1021/acs.jpcc.5b04028

    Article  CAS  Google Scholar 

  35. Xu, Z., Stebbins, J.F.: Cation dynamics and diffusion in lithium orthosilicate: two-dimensional lithium-6 NMR. Science 270(5240), 1332–1334 (1995). https://doi.org/10.1126/science.270.5240.1332

    Article  CAS  Google Scholar 

  36. Wilkening, M., Romanova, E.E., Nakhal, S., Weber, D., Lerch, M., Heitjans, P.: Time-resolved and site-specific insights into migration pathways of Li+ in α-Li3VF6 by 6Li 2D exchange MAS NMR. J. Phys. Chem. C 114(44), 19083–19088 (2010). https://doi.org/10.1021/jp103433h

    Article  CAS  Google Scholar 

  37. Davis, L.J.M., Heinmaa, I., Goward, G.R.: Study of lithium dynamics in monoclinic Li3Fe2(PO4)3 using 6Li VT and 2D exchange MAS NMR spectroscopy †. Chem. Mater. 22(3), 769–775 (2010). https://doi.org/10.1021/cm901402u

    Article  CAS  Google Scholar 

  38. Bottke, P., Freude, D., Wilkening, M.: Ultraslow Li exchange processes in diamagnetic Li2ZrO3 as monitored by EXSY NMR. J. Phys. Chem. C 117(16), 8114–8119 (2013). https://doi.org/10.1021/jp401350u

    Article  CAS  Google Scholar 

  39. Gschwind, F., Rodriguez-Garcia, G., Sandbeck, D.J.S., Gross, A., Weil, M., Fichtner, M., Hörmann, N.: Fluoride ion batteries: theoretical performance, safety, toxicity, and a combinatorial screening of new electrodes. J. Fluorine Chem. (2016). https://doi.org/10.1016/j.jfluchem.2015.12.002

    Article  Google Scholar 

  40. Wang, F., Grey, C.P.: A 1- and 2-D 19F MAS NMR study of fluoride-ion mobility in α PbF2. J. Am. Chem. Soc. 120(5), 970–980 (1998). https://doi.org/10.1021/ja972312g

    Article  CAS  Google Scholar 

  41. Lunghammer, S., Düvel, A., Posch, P., Kunert, B., Resel, R., Wilkening, H.M.R.: Self-diffusion and ionic exchange in mechanosynthesized, nanocrystalline solid solutions of PbF2 and CaF2 –19F 2D NMR visualizes the flourine hopping preferences. Solid State Ion 343, 115067 (2019). https://doi.org/10.1016/j.ssi.2019.115067

    Article  CAS  Google Scholar 

  42. Düvel, A.: Ionic conductivity and structure of M1–x Pbx F2 (M = Ca, Sr, Ba) solid solutions prepared by ball milling. Dalt. Trans. 48(3), 859–871 (2019). https://doi.org/10.1039/c8dt03759k

    Article  CAS  Google Scholar 

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  1. Department of Chemical Engineering, University of California, Santa Barbara, CA, 93106, USA

    Philipp Selter, Michael B. Schmithorst & Bradley F. Chmelka

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Selter, P., Schmithorst, M.B. & Chmelka, B.F. Hopping dynamics and diffusion of atoms, molecules, and ions in nanoporous solids by exchange NMR spectroscopy. Adsorption 27, 857–874 (2021). https://doi.org/10.1007/s10450-021-00318-8

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