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Multicomponents of Spin–Spin Relaxation, Anisotropy of the Echo Decay, and Nanoporous Sample Structure

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Abstract

We have experimentally and theoretically investigated multicomponent 1H nuclear magnetic resonance (NMR) echo decays in a-Si:H films containing anisotropic nanopores, in which randomly moving hydrogen molecules are entrapped. The experimental results are interpreted within the framework of the previously developed theory, in which a nanoporous material is represented as a set of nanopores containing liquid or gas, and the relaxation rate is determined by the dipole–dipole spin interaction, considering the restricted motion of molecules inside the pores. Previously, such characteristics of a nanostructure as the average volume of pores and their orientation distribution were determined from the angular dependences of the spin–spin and spin–lattice relaxation times. We propose a new approach to the analysis of the NMR signal, the main advantage of which is the possibility of obtaining nanostructure parameters from a single decay of the echo signal. In this case, there is no need to analyze the anisotropy of the relaxation time T2, the determination of which is a rather complicated problem in multicomponent decays. Despite multicomponent signals, the fitting parameter associated with the size and shape of nanopores is determined quite accurately. This made it possible to determine the size and shape of nanopores in a-Si:H films, herewith our estimates are in good agreement with the results obtained by other methods. The fitting of the decays also provides information about the nanostructure of the sample, such as the standard deviations of the angular distribution of pores and the polar and azimuthal angles of the average direction of the pore axes relative to the sample axis, with reasonable accuracy. The approach makes it possible to quantitatively determine the parameters of the non-spherical nanoporous structure from NMR data in a non-destructive manner.

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Availability of data and materials

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

References

  1. A. Abragam, The Principles of Nuclear Magnetism, (Oxford Clarendon Press, 1961)

  2. P. T. Callaghan, Principles of Nuclear Magnetic Resonance Microscopy, (Oxford Clarendon Press, 1991)

  3. M. Mehring, Principles of High Resolution NMR in Solids, 2nd edn. (Springer, Berlin, 1983)

    Book  Google Scholar 

  4. B. Blumich, NMR Imaging of Materials, (Oxford Clarendon Press, 2000)

  5. E. Breitmaier, Structure Elucidation by NMR in Organic Chemistry: A Practical Guide, (John Wiley&Sons Ltd., 2002)

  6. R.S. Macomber, A Complete Introduction to Modern NMR Spectroscopy (Wiley, Chichester, 1998)

    Google Scholar 

  7. K. H. Hausser, H. R. Kalbitzer, NMR in Medicine and Biology: Structure Determination, Tomography, In Vivo Spectroscopy (Physics in Life Sciences), (Springer-Verlag Berlin Heidelberg, 1991)

  8. Y. **a, K. Momot, Biophysics and biochemistry of cartilage by NMR and MRI (The Royal Society of Chemistry, Cambridge UK, 2016)

    Book  Google Scholar 

  9. A.M. Panich, NMR study of the F-H...F hydrogen bond. Relation between hydrogen atom position and F-H...F bond length. Chem. Phys. 196, 511–519 (1995)

    Article  Google Scholar 

  10. M. Thommes, C. Schlumberger, Characterization of nanoporous materials. Annu. Rev. Chem. Biomol. Eng. 12, 137–162 (2021)

    Article  Google Scholar 

  11. B. Mohebbi, J. Claussen, B. Blümich, Fast and robust quantification of liquid inside thin fibrous porous materials with single-sided NMR. Magn Resonance Imaging. 56, 131–137 (2019). https://doi.org/10.1016/J.Mri.2018.09.022

    Article  Google Scholar 

  12. A.M. Panich, Nuclear magnetic resonance study of fluorine–graphite intercalation compounds and graphite fluorides. Synth. Met. 100, 169–185 (1999)

    Article  Google Scholar 

  13. A.M. Panich, I.A. Belitskii, N.K. Moroz, S.P. Gabuda, V.A. Drebushchak, Y.V. Seretkin, Ionic and molecular diffusion and order-disorder phase transition in the thallium form of natrolite. Zh. Strukt. Khimii 31, 67–73 (1990)

    Google Scholar 

  14. G.B. Furman, S.D. Goren, V.M. Meerovich, V.L. Sokolovsky, Anisotropy of spin–spin and spin–lattice relaxation times in liquids entrapped in nanocavities: application to MRI study of biological systems. JMR 263, 71–78 (2016)

    Google Scholar 

  15. G.B. Furman, S.D. Goren, V.M. Meerovich, V.L. Sokolovsky, Correlation of transverse relaxation time with structure of biological tissue. JMR 270, 7–11 (2016)

    Google Scholar 

  16. G.B. Furman, S.D. Goren, V.M. Meerovich, V.L. Sokolovsky, Dipole-dipole interactions in liquids entrapped in confined space. J. Mol. Liq. 272, 468–473 (2018)

    Article  Google Scholar 

  17. G. Furman, V. Meerovich, V. Sokolovsky, Y. **a, Spin locking in liquid entrapped in nanocavities: application to study connective tissues. J. Magn. Reson. 299, 66–73 (2019)

    Article  ADS  Google Scholar 

  18. G. Furman, V. Meerovich, V. Sokolovsky, Y. **a, Spin-lattice relaxation in liquid entrapped in a nanocavity. J. Magn. Reson. 311, 106669 (2020)

    Article  Google Scholar 

  19. G. Furman, S. Goren, V. Meerovich, A. Panich, V. Sokolovsky, Y. **a, Anisotropy of transverse and longitudinal relaxations in liquids entrapped in nano- and micro-cavities of a plant stem. J. Magn. Reson. 331, 107051 (2021)

    Article  Google Scholar 

  20. G. Furman, V. Meerovich, V. Sokolovsky, Y. **a, S. Salem, T. Shavit, T. Blumenfeld-Katzir, N. Ben-Eliezer, Determining the internal orientation, degree of ordering, and volume of elongated nanocavities by NMR: application to studies of plant stem. J. Magn. Reson. 341, 107258 (2022)

    Article  Google Scholar 

  21. A. Panich, G. Furman, V. Sokolovsky, Y. **a, P. Roca i Cabarrocas, Anisotropic spin–lattice and spin–spin relaxations in hydrogen molecules trapped in non-spherical nanocavities. Appl. Magn. Resonance 54, 371–381 (2023). https://doi.org/10.1007/s00723-022-01515-6

    Article  Google Scholar 

  22. G. Furman, A. Panich, V. Sokolovsky, Y. **a, Nanostructure of hydrogenated amorphous silicon (a-Si:H) films studied by nuclear magnetic resonance. J. Magn. Resonance 350, 107434 (2023). https://doi.org/10.1016/j.jmr.2023.107434

    Article  Google Scholar 

  23. Y. **a, Magic-angle effect in magnetic resonance imaging of articular cartilage. Invest. Radiol. 35, 602 (2000)

    Article  Google Scholar 

  24. Y. **a, Relaxation anisotropy in cartilage by NMR microscopy (μMRI) at 14-μm resolution. Magn. Reson. Med. 39, 941–949 (1998)

    Article  Google Scholar 

  25. S.K. Zheng, Y. **a, Multi-components of T2 relaxation in ex vivo cartilage and tendon. J. Magn. Reson. 198, 188 (2009)

    Article  ADS  Google Scholar 

  26. D.A. Reiter, P.-C. Lin, K.W. Fishbein, R.G. Spencer, Multicomponent T2 relaxation analysis in cartilage. Magn. Reson. Med. 61, 803 (2009)

    Article  Google Scholar 

  27. E.B. Fel’dman, G.B. Furman, S.D. Goren, Spin locking and spin–lattice relaxation in a liquid entrapped in nanosized cavities. Soft Matter 8, 9200 (2012)

    Article  ADS  Google Scholar 

  28. E.B. Fel’dman, M.G. Rudavets, Nonergodic nuclear depolarization in nanocavities. J. Exp. Theor. Phys. 98, 207–219 (2004). https://doi.org/10.1134/1.1675888

    Article  ADS  Google Scholar 

  29. D.L. Williamson, Nanostructure of a-Si: H and related materials by small-angle x-ray scattering. Mat. Res. Soc. Symp. Proc. 377, 251–262 (1995)

    Article  Google Scholar 

  30. X. Xu, J. Yang, S. Guha, Hydrogen dilution effects on a-Si: H and a-SiGe: H materials properties and solar cell performance. J. Non-Crystal. Solids 198–200, 60–64 (1996)

    Article  ADS  Google Scholar 

  31. A.H. Mahan, Y. Xu, W. Beyer, J.D. Perkins, M. Vanecek, L.M. Gedvilas, B.P. Nelson, Structural properties of hot wire a-Si: H films deposited at rates in excess of 100 Å/s. J. Appl. Phys. 90, 5038–5047 (2001)

    Article  ADS  Google Scholar 

  32. Y.J. Chabal, C.K.N. Patel, Molecular hydrogen in a-Si: H. Rev. Mod. Phys. 59, 835 (1987)

    Article  ADS  Google Scholar 

  33. J. Baugh, A. Kleinhammes, D. Han, Q. Wang, Y. Wu, Confinement effect on dipole-dipole interactions in nanofluids. Science 294, 1505–1507 (2001)

    Article  ADS  Google Scholar 

  34. P. Roca i Cabarrocas, J.B. Chévrier, J. Huc, A. Lloret, J.Y. Parey, J.P.M. Schmitt, A fully automated hot-wall multiplasma-monochamber reactor for thin film deposition. J. Vac. Sci. Technol. A 9, 2331 (1991)

    Article  Google Scholar 

  35. E. Gericke, J. Melskens, R. Wendt, M. Wollgarten, A. Hoell, K. Lips, Quantification of nanoscale density fluctuations in hydrogenated amorphous silicon. Phys. Rev. Lett. 125, 185501 (2020)

    Article  ADS  Google Scholar 

  36. D.L. Young, P. Stradins, Y. Xu, L.M. Gedvilas, E. Iwaniczko, Y. Yan, H.M. Branz, Q. Wang, Nanostructure evolution in hydrogenated amorphous silicon during hydrogen effusion and crystallization. Appl. Phys. Lett. 90, 081923 (2007)

    Article  ADS  Google Scholar 

  37. W.E. Carlos, P.C. Taylor, Molecular hydrogen in a-Si:H. Phys. Rev. B 25, 1435–1438 (1982)

    Article  ADS  Google Scholar 

  38. S. Meiboom, D. Gill, Modified spin-echo method for measuring nuclear relaxation times. Rev. Sci. Instrum. 29, 688–691 (1958)

    Article  ADS  Google Scholar 

  39. J. Baugh, D. Han, A. Kleinhammes, C. Liu, Y. Wu, Q. Wang, Microstructure and dynamics of hydrogen in a-Si: H detected by nuclear magnetic resonance. J. Non-Cryst. Solids 266–269, 185–189 (2000)

    Article  ADS  Google Scholar 

  40. E.W. Hansen, A. Kjekshus, J.O. Odden, On the hydrogen in hydrogen-containing amorphous silicon. J. Non-Cryst. Solids 353, 2734–2743 (2007)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We gratefully thank Prof. Pere Roca i Cabarrocas for helpful discussions and for providing a-Si:H films. This research was supported by a grant from the United States - Israel Binational Science Foundation (BSF), Jerusalem, Israel (No. 2019033), and by a grant from the National Institutes of Health in the United States (AR 069047).

Funding

This research was supported by a grant from the United States - Israel Binational Science Foundation (BSF), Jerusalem, Israel (No. 2019033), and by a grant from the National Institutes of Health in the United States (AR 069047).

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Authors and Affiliations

  1. Physics Department, Ben Gurion University of the Negev, Beer Sheva, Israel

    Theodore Aptekarev, Gregory Furman, Vladimir Sokolovsky & Alexander Panich

  2. Physics Department, Oakland University, Rochester, MI, US

    Yang **a

Authors
  1. Theodore Aptekarev
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  2. Gregory Furman
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  3. Vladimir Sokolovsky
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  4. Alexander Panich
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  5. Yang **a
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Contributions

All the authors contributed to the concept and design of the study. AP carried out experiments. TA, GF, VS, and YX performed data processing, composed the computer program, and took part in the calculations. All the authors read and approved the final version of the manuscript.

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Correspondence to Gregory Furman.

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Aptekarev, T., Furman, G., Sokolovsky, V. et al. Multicomponents of Spin–Spin Relaxation, Anisotropy of the Echo Decay, and Nanoporous Sample Structure. Appl Magn Reson 54, 1481–1492 (2023). https://doi.org/10.1007/s00723-023-01553-8

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