Nuclear Spin Relaxation in Aerogels and Porous Glasses

  • L. Malier
  • J. P. Boilot
  • F. Chaput
  • F. Devreux
Part of the NATO ASI Series book series (NSSB, volume 323)


It has been known for two decades that most of the physical properties are drastically different in amorphous materials as compared to their crystalline counterparts, specially when examined at low temperatures1,2. These specific behaviors have been accounted for by the phenomenological two-level-system (TLS) model3,4 or its more recent generalization through soft modes5. One of the properties specific to the glassy state concerns the nuclear magnetic relaxation, which presents common features over numerous inorganic glasses6,7,8. Though different mechanisms have been debated, all of them require the TLS model to account for the weak température-dépendance of the relaxation. The lack of structural model for these TLS prevents precise estimation of their coupling with the spins and then an absolute evaluation of the relaxation. In the case of electron spin resonance in bio-polymers, relaxation involving fractal-structure vibrations (fractons) have been considered9. Primarily introduced by S.Alexander and R. Orbach10 on a theoretical basis, fractons have been experimentally tracked during these last years, with peculiar attention paid on aerogel dynamics11-14. Aerogels are materials whose fractal structure has been evidenced by small angle scattering15,16 in the reciprocal space and by nuclear spin relaxation in the direct space17. Their density of state, deduced from inelastic light and neutron scattering, presents a weak energy dependance in part of the giga-Hertz range (typically 3 to 100 GHz). Nevertheless, this density cannot be described by a single spectral dimension as initially proposed, and the relevance of scalar or tensorial models is still a subject of debate. Moreover, the characteristic structural length determined from small angle scattering and the one deduced from the dynamics measurements present disrepancies which are not yet understood.


Electron Spin Resonance Relaxation Rate Silica Aerogel Porous Glass Small Angle Scattering 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R.C. Zeller and R.O. Pohl, ‘Thermal conductivities and specific heat of non-crystalline solids’, Phys. Rev. B 4 p2029 (1971).CrossRefGoogle Scholar
  2. 2.
    R.B. Stephens, ‘Low-temperature specific heat and thermal conductivity of non-crystalline dielectric solids’, Phys. Rev. B 8 p2896 (1973).CrossRefGoogle Scholar
  3. 3.
    P.W. Anderson, B.I. Halperin, C.M. Varna, ‘anomalous low-temperature thermal properties of glasses and spin glasses’, Phil. Mag. 25 pl (1972)CrossRefGoogle Scholar
  4. 4.
    W.A. Phillips, ‘Two-level states in glasses’, Rep. Prog. Phys. 50 p 1657 (1987).CrossRefGoogle Scholar
  5. 5.
    Y.M. Galperin, V.G. Karpov, V.I. Kozub, ‘Localized states in glasses’, Adv. in Physics 38 p669 (1989).CrossRefGoogle Scholar
  6. 6.
    J. Szeftel, H. Alloul, ‘Nuclear spin lattice relaxation in the amorphous state: towards an understanding’, J. of Non-Cryst. Solids 29 p 253 (1978), and references therein.CrossRefGoogle Scholar
  7. 7.
    T.L. Reinecke, K.L. Ngai, ‘Low-temperature nuclear spin-lattice relaxation in glasses’, Phys. Rev. B 12 p3476 (1975), and references therein.CrossRefGoogle Scholar
  8. 8.
    S. Estalji, O. Kanert, J. Steinert, H. Jain, K.L. Ngai, ‘Uncommon nuclear-spin relaxation in fluorozirconate glasses at low temperatures’, Phys. Rev. B 43 p7481 (1991).CrossRefGoogle Scholar
  9. 9.
    J.T. Colvin, H.J. Stapleton, ‘Fractal and spectral dimensions of biopolymer chains’, J. Chem. Phys. 82 p4699 (1985).CrossRefGoogle Scholar
  10. 10.
    S. Alexander, R. Orbach, ‘Density of states on fractals: “fractons”’, J. Phys. (Paris) 43 pL–625 (1982).Google Scholar
  11. 11.
    A.M. de Goer, R. Calemczuk, B. Salce, J. Bon, E. Bonjour, R. Maynard, ‘Low-temperature energy excitations and thermal properties of silica aerogels’, Phys. Rev. B 40 p8327 (1989).CrossRefGoogle Scholar
  12. 12.
    A. Bernasconi, T. Sleator, D. Posselt, J.K. Kjems, H.R. Ott, ‘Dynamic properties of silica aerogels as deduced from specific-heat and thermal-conductivity measurements’, Phys. Rev. B 45 pl0363 (1992).CrossRefGoogle Scholar
  13. 13.
    E. Courtens, J. Pelous, J. Phalippou, R. Vacher, T. Woignier, ‘Brillouin scattering measurements of phonon-fracton crossover in silica aerogels’, Phys. Rev. Lett. 58 p128 (1987).CrossRefGoogle Scholar
  14. 14.
    R. Vacher, E.Courtens, G. Coddens, A. Heidemann, Y. Tsujimi, J. Pelous, M. Foret, ‘Crossovers in the density of states of fractal silica aerogels’, Phys. Rev. Lett. 65 p1008 (1990).CrossRefGoogle Scholar
  15. 15.
    R. Vacher, T. Woignier, J. Pelous, E. Courtens, ‘Structure and self-similarity of silica aerogels’, Phys. Rev. B 37 p6500 (1988), and references therein.CrossRefGoogle Scholar
  16. 16.
    F. Chaput, J.P. Boilot, A. Dauger, F. Devreux, A. De Geyer, ‘Self similarity in alumino-silicate aerogels’, J. of Non-Cryst. Solids 116 p133 (1990).CrossRefGoogle Scholar
  17. 17.
    F. Devreux, J.P. Boilot, F. Chaput, B. Sapoval, ‘NMR determination of the fractal dimension in silica aerogels’, Phys. Rev. Lett. 65 p614 (1990)CrossRefGoogle Scholar
  18. 18.
    E.R. Andrew, D.P. Tunstall, ‘Spin-lattice relaxation in imperfect cubic crystals andin non-cubic crystals’, Proc. Phys. Soc. 78 p1 (1961).CrossRefGoogle Scholar
  19. 19.
    R. Orbach, S. Alexander, O. Entin-Wohlman, ‘Relaxation and non-radiative decay in disordered systems: II. 2-fracton inelastic scattering‘, Phys. Rev. B 33 p3935 (1986).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • L. Malier
    • 1
  • J. P. Boilot
    • 1
  • F. Chaput
    • 1
  • F. Devreux
    • 1
  1. 1.Laboratoire de Physique de la Matière CondenséeURA CNRS n°1254 Ecole PolytechniquePalaiseau CedexFrance

Personalised recommendations