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Dynamic Correlation Under Isochronal Conditions

  • C. M. Roland
  • D. Fragiadakis
Chapter
Part of the Advances in Dielectrics book series (ADVDIELECT)

Abstract

Results of various methods of evaluating the dynamic correlation volume in glassforming liquids and polymers are summarized. Most studies indicate that this correlation volume depends only on the α-relaxation time; that is, at state points associated with the same value of τ α , the extent of the correlation among local motions is equivalent. Nonlinear dielectric spectroscopy was used to measure the third-order susceptibility. Its amplitude, a measure of the dynamic correlation volume, is constant for isochronal state points, which supports the interpretation of the magnitude of the nonlinear susceptibility in terms of dynamic correlation. More broadly, it serves to establish that for non-associated materials, the cooperativity of molecular motions is connected to their timescale.

Notes

Acknowledgements

This work was supported by the Office of Naval Research.

References

  1. 1.
    B. Frick, C. Alba-Simionesco, K.H. Andersen, L. Willner, Influence of density and temperature on the microscopic structure and the segmental relaxation of polybutadiene. Phys. Rev. E 67, 051801 (2003)CrossRefGoogle Scholar
  2. 2.
    A. Cailliaux, C. Alba-Simionesco, B. Frick, L. Willner, I. Goncharenko, Phys. Rev. E 67, 010802 (2003)CrossRefGoogle Scholar
  3. 3.
    R. Bohmer, Nanoscale heterogeneity of glass-forming liquids: experimental advances. Cur. Opin. Sol. State Mat. Sci. 3, 378–385 (1998)CrossRefGoogle Scholar
  4. 4.
    H. Sillescu, Heterogeneity at the glass transition: a review. J. Non-Cryst. Solids 243, 81–108 (1999)CrossRefGoogle Scholar
  5. 5.
    M.D. Ediger, Spatially heterogeneous dynamics in supercooled liquids. Ann. Rev. Phys. Chem. 51, 99–128 (2000)CrossRefGoogle Scholar
  6. 6.
    H. Sillescu, R. Bohmer, G. Diezemann, G. Hinze, Heterogeneity at the glass transition: what do we know? J. Non-Cryst. Sol. 307–310, 16–23 (2002)CrossRefGoogle Scholar
  7. 7.
    R. Richert, N. Israeloff, C. Alba‐Simionesco, F. Ladieu, D. L’Hote, Experimental approaches to heterogeneous dynamics in Dynamical Heterogeneities in Glasses, Colloids, and Granular Media, ed. by L. Berthier, G. Biroli, J.-P. Bouchaud, L. Cipelletti, W. van Saarloos (Oxford University Press, Oxford, 2011)CrossRefGoogle Scholar
  8. 8.
    K. Kim, S. Saito, Multiple length and time scales of dynamic heterogeneities in model glass-forming liquids: a systematic analysis of multi-point and multi-time correlations. J. Chem. Phys. 138, 12A506 (2013)CrossRefPubMedGoogle Scholar
  9. 9.
    C.M. Roland, D. Fragiadakis, D. Coslovich, S. Capaccioli, K.L. Ngai, Correlation of nonexponentiality with dynamic heterogeneity from four-point dynamic susceptibility χ4(t) and its approximation χT(t). J. Chem. Phys. 133, 124507 (2010)CrossRefPubMedGoogle Scholar
  10. 10.
    R. Böhmer, K.L. Ngai, C.A. Angell, D.J. Plazek, Nonexponential relaxations in strong and fragile glass formers. J. Chem. Phys. 99, 4201–4209 (1993)CrossRefGoogle Scholar
  11. 11.
    K. Niss, C. Dalle-Ferrier, G. Tarjus, C. Alba-Simionesco, On the correlation between fragility and stretching in glass-forming liquids. J. Phys. Cond. Mat. 19, 076102 (2007)CrossRefGoogle Scholar
  12. 12.
    E.R. Weeks, J.C. Crocker, A.C. Levitt, A. Schofield, D.A. Weitz, Three-dimensional direct imaging of structural relaxation near the colloidal glass transition. Science 287, 627–631 (2000)CrossRefPubMedPubMedCentralGoogle Scholar
  13. 13.
    O. Dauchot, G. Marty, G. Biroli, Dynamical heterogeneity close to the jamming transition in a sheared granular material. Phys. Rev. Lett. 95, 265701 (2005)CrossRefPubMedGoogle Scholar
  14. 14.
    G. Adam, J.H. Gibbs, On the temperature dependence of cooperative relaxation properties in glass-forming liquids. J. Chem. Phys. 43, 139–146 (1965)CrossRefGoogle Scholar
  15. 15.
    K.S. Schweizer, E.J. Saltzman, Activated hopping, barrier fluctuations, and heterogeneity in glassy suspensions and liquids. J. Phys. Chem. B 108, 19729–19741 (2004)CrossRefGoogle Scholar
  16. 16.
    J.P. Garrahan, D. Chandler, Dynamics on the way to forming glass: bubbles in space-time. Ann. Rev. Phys. Chem. 61, 191–217 (2010)CrossRefGoogle Scholar
  17. 17.
    V. Lubchenko, P.G. Wolynes, Theory of structural glasses and supercooled liquids. Ann. Rev. Phys. Chem. 58, 235–266 (2007)CrossRefGoogle Scholar
  18. 18.
    A. Heuer, Exploring the potential energy landscape of glass-forming systems: from inherent structures via metabasins to macroscopic transport. J. Phys. Con. Mat. 20, 373101 (2008)CrossRefGoogle Scholar
  19. 19.
    F. Rittig, A. Huwe, G. Fleischer, J. Kärger, F. Kremer, Molecular dynamics of glass-forming liquids in confining geometries. Phys. Chem. Chem. Phys. 1, 519–523 (1999)CrossRefGoogle Scholar
  20. 20.
    G. Dosseh, C. Le Quellec, N. Brodie-Lindner, C. Alba-Simionesco, W. Haeussler, P. Levitz, Fluid–wall interactions effects on the dynamical properties of confined orthoterphenyl. J. Non-Cryst. Sol. 352, 4964–4968 (2006)CrossRefGoogle Scholar
  21. 21.
    J. Koppensteiner, W. Schranz, M.A. Carpenter, Revealing the pure confinement effect in glass-forming liquids by dynamic mechanical analysis. Phys. Rev. B 81, 024202 (2010)CrossRefGoogle Scholar
  22. 22.
    C.L. Jackson, G.B. McKenna, The glass transition of organic liquids confined to small pores. J. Non-Cryst. Sol. 131–133, 221–224 (1991)CrossRefGoogle Scholar
  23. 23.
    Y.B. Melnichenko, J. Schuller, R. Richert, B. Ewen, C.K. Loong, Dynamics of hydrogen bonded liquids confined to mesopores—a dielectric and neutron spectroscopy study. J. Chem. Phys. 103, 2016–2024 (1995)CrossRefGoogle Scholar
  24. 24.
    F. Kremer, A. Huwe, M. Arndt, P. Behrens, W. Schwieger, How many molecules form a liquid? J. Phys. Cond. Mat. 11, A175–A188 (1999)CrossRefGoogle Scholar
  25. 25.
    A. Schonhals, H. Goering, C. Schick, B. Frick, R. Zorn, Glassy dynamics of polymers confined to nanoporous glasses revealed by relaxational and scattering experiments. Eur. Phys. J. E 12, 173–178 (2003)CrossRefPubMedGoogle Scholar
  26. 26.
    A. Schonhals, H. Goering, C. Schick, B. Frick, M. Mayorova, R. Zorn, Segmental dynamics of poly(methyl phenyl siloxane) confined to nanoporous glasses. Eur. Phys. J. Spec. Topics. 141, 255–259 (2007)CrossRefGoogle Scholar
  27. 27.
    J.P. Bouchaud, G. Biroli, On the Adam-Gibbs-Kirkpatrick-Thirumalai-Wolynes scenario for the viscosity increase in glasses. J. Chem. Phys. 121, 7347–7354 (2004)CrossRefPubMedGoogle Scholar
  28. 28.
    G. Biroli, J.-P. Bouchaud, A. Cavagna, T.S. Grigera, P. Verrocchio, Thermodynamic signature of growing amorphous order in glass-forming liquids. Nat. Phys. 4, 771–775 (2008)CrossRefGoogle Scholar
  29. 29.
    S. Yaida, L. Berthier, P. Charbonneau, G. Tarjus, Point-to-set lengths, local structure, and glassiness. Phys. Rev. E 94, 032605 (2016)CrossRefPubMedGoogle Scholar
  30. 30.
    W. Kob, S. Roldán-Vargas, L. Berthier, Non-monotonic temperature evolution of dynamic correlations in glass-forming liquids. Nat. Phys. 8, 164 (2012)CrossRefGoogle Scholar
  31. 31.
    G.M. Hocky, L. Berthier, W. Kob, D.R. Reichman, Static point-to-set correlations in glass-forming liquids. Phys. Rev. E 85, 011102 (2012)CrossRefGoogle Scholar
  32. 32.
    K. Hima Nagamanasa, S. Gokhale, A.K. Sood, R. Ganapathy, Direct measurements of growing amorphous order and non-monotonic dynamic correlations in a colloidal glass-former. Nat. Phys. 11, 403 (2015)CrossRefGoogle Scholar
  33. 33.
    S, Gokhale, K. Hima Nagamanasa, R. Ganapathy, A. K. Sood, Growing dynamic facilitation on approaching the random pinning colloidal glass transition. Nat. Commun. 5, 4685 (2014)Google Scholar
  34. 34.
    B. Mei, Y. Lu, L. An, H. Li, L. Wang, Nonmonotonic dynamic correlations in quasi-tow-dimensional confined glass-forming liquids. Phys. Rev. E 95, 050601(R) (2017)CrossRefGoogle Scholar
  35. 35.
    A. Schonhals, E. Schlosser, Relationship between segmental and chain dynamics in polymer melts as studied by dielectric spectroscopy. Phys. Scr. T49, 233–236 (1993)CrossRefGoogle Scholar
  36. 36.
    C. Gainaru, W. Hiller, R. Bohmer, A dielectric study of oligo- and poly(propylene glycol). Macromolecules 43, 1907–1914 (2010)CrossRefGoogle Scholar
  37. 37.
    D. Fragiadakis, R. Casalini, R.B. Bogoslovov, C.G. Robertson, C.M. Roland, Dynamic heterogeneity and density scaling in 1,4-polyisoprene. Macromolecules 44, 1149–1155 (2011)CrossRefGoogle Scholar
  38. 38.
    U. Tracht, M. Wilhelm, A. Heuer, H. Feng, K. Schmidt-Rohr, H.W. Spiess, Length scale of dynamic heterogeneities at the glass transition determined by multidimensional nuclear magnetic resonance. Phys. Rev. Lett. 81, 2727–2730 (1998)CrossRefGoogle Scholar
  39. 39.
    S.A. Reinsberg, X.H. Qiu, M. Wilhelm, H.W. Spiess, M.D. Ediger, Length scale of dynamic heterogeneity in supercooled glycerol near Tg. J. Chem. Phys. 114, 7299–7302 (2001)CrossRefGoogle Scholar
  40. 40.
    S.A. Reinsberg, A. Heuer, B. Doliwa, H. Zimmermann, H.W. Spiess, Comparative study of the NMR length scale of dynamic heterogeneities of three different glass formers. J. Non-Cryst. Solid 307–310, 208–214 (2002)CrossRefGoogle Scholar
  41. 41.
    X.H. Qiu, M.D. Ediger, Length scale of dynamic heterogeneity in supercooled d-sorbitol: comparison to model predictions. J. Phys. Chem. B 107, 459–464 (2003)CrossRefGoogle Scholar
  42. 42.
    E. Donth, The size of cooperatively rearranging regions at the glass transition. J. Non-Cryst. Sol. 53, 325–330 (1982)CrossRefGoogle Scholar
  43. 43.
    K. Schroter, Characteristic length of glass transition heterogeneity from calorimetry. J Non-Cryst. Sol. 352, 3249–3254 (2006)CrossRefGoogle Scholar
  44. 44.
    A. Saiter, L. Delbreilh, H. Couderc, K. Arabeche, A. Schönhals, J.-M. Saiter, Temperature dependence of the characteristic length scale for glassy dynamics: Combination of dielectric and specific heat spectroscopy. Phys. Rev. E 81, 041805 (2010)CrossRefGoogle Scholar
  45. 45.
    E. Hempel, G. Hempel, A. Hensel, C. Schick, E. Donth, Characteristic length of dynamic glass transition near tg for a wide assortment of glass-forming substances. J. Phys. Chem. B 104, 2460–2466 (2000)CrossRefGoogle Scholar
  46. 46.
    C. Dasgupta, A.V. Indrani, S. Ramaswamy, M.K. Phani, Is there a growing correlation length near the glass transition? Europhys. Lett. 15, 307–312 (1991)CrossRefGoogle Scholar
  47. 47.
    L. Berthier, G. Biroli, Theoretical perspective on the glass transition and amorphous materials. Rev. Mod. Phys. 83, 587–645 (2011)CrossRefGoogle Scholar
  48. 48.
    L. Berthier, G. Biroli, J.-P. Bouchaud, L. Cipelletti, D. El Masri, D. L’Hote, F. Ladieu, M. Pierno, Direct experimental evidence of a growing length scale accompanying the glass transition. Science 310, 1797–1800 (2005)CrossRefPubMedGoogle Scholar
  49. 49.
    C. Dalle-Ferrier, C. Thibierge, C. Alba-Simionesco, L. Berthier, G. Biroli, J.P. Bouchaud, F. Ladieu, D. L’Hote, G. Tarjus, Spatial correlations in the dynamics of glassforming liquids: experimental determination of their temperature dependence. Phys. Rev. E 76, 041510 (2007)CrossRefGoogle Scholar
  50. 50.
    L. Berthier, G. Biroli, J.-P. Bouchaud, L. Cipelletti, D. El Masri, D. L’Hôte, F. Ladieu, M. Pierno, Direct experimental evidence of a growing length scale accompanying the glass transition. Science 310, 1797–1800 (2005)CrossRefPubMedGoogle Scholar
  51. 51.
    L. Berthier, G. Biroli, J.-P. Bouchaud, W. Kob, K. Miyazaki, D.R. Reichman, Spontaneous and induced dynamic fluctuations in glass formers. 1. General results and dependence on ensemble and dynamics. J. Chem. Phys. 126, 184503 (2007)CrossRefPubMedGoogle Scholar
  52. 52.
    S. Capaccioli, G. Ruocco, F. Zamponi, Dynamically correlated regions and configurational entropy in supercooled liquids. J. Phys. Chem. B 112, 10652–10658 (2008)CrossRefPubMedGoogle Scholar
  53. 53.
    E. Flenner, G. Szamel, Dynamic heterogeneities above and below the mode-coupling temperature: evidence of a dynamic crossover. J. Chem. Phys. 138, 12A523 (2013)CrossRefPubMedGoogle Scholar
  54. 54.
    K. Koperwas, A. Grzybowski, K. Grzybowska, Z. Wojnarowska, A.P. Sokolov, M. Paluch, Effect of temperature and density fluctuations on the spatially heterogeneous dynamics of glass-forming van der Waals liquids under high pressure. Phys. Rev. Lett. 111, 125701 (2013)CrossRefPubMedGoogle Scholar
  55. 55.
    R. Casalini, L. Zhu, E. Baer, C.M. Roland, Segmental dynamics and the correlation length in nanoconfined PMMA. Polymer 88, 133–136 (2016)CrossRefGoogle Scholar
  56. 56.
    T.S. Ingebrigtsen, J.R. Errington, T.M. Truskett, J.C. Dyre, Predicting how nanoconfinement changes the relaxation time of a supercooled liquid. Phys. Rev. Lett. 111, 235901 (2013)CrossRefPubMedGoogle Scholar
  57. 57.
    D. Fragiadakis, R. Casalini, C.M. Roland, Density scaling and dynamic correlations in viscous liquids. J. Phys. Chem. B 113, 13134–13147 (2009)CrossRefPubMedGoogle Scholar
  58. 58.
    C. Alba-Simionesco, C. Dalle-Ferrier, G. Tarjus, Effect of pressure on the number of dynamically correlated molecules when approaching the glass transition. AIP Conf. Proc. 1518, 527–535 (2013)CrossRefGoogle Scholar
  59. 59.
    R. Casalini, D. Fragiadakis, C.M. Roland, Dynamic correlation length scales under isochronal conditions. J. Chem. Phys. 142, 064504 (2015)CrossRefPubMedGoogle Scholar
  60. 60.
    J.-P. Bouchaud, G. Biroli, Nonlinear susceptibility in glassy systems: a probe for cooperative dynamical length scales. Phys. Rev. B 72, 064204 (2005)CrossRefGoogle Scholar
  61. 61.
    C. Crauste-Thibierge, C. Brun, F. Ladieu, D. L’Hôte, G. Biroli, J.-P. Bouchaud, Evidence of growing spatial correlations at the glass transition from nonlinear response experiments. Phys. Rev. Lett. 104, 165703 (2010)CrossRefPubMedGoogle Scholar
  62. 62.
    Th Bauer, P. Lunkenheimer, A. Loidl, Cooperativity and the freezing of molecular motion at the glass transition. Phys. Rev. Lett. 111, 225702 (2013)CrossRefPubMedGoogle Scholar
  63. 63.
    M. Michl, Th Bauer, P. Lunkenheimer, A. Loidl, Nonlinear dielectric spectroscopy in a fragile plastic crystal. J. Chem. Phys. 144, 114506 (2016)CrossRefPubMedGoogle Scholar
  64. 64.
    S. Albert, Th Bauer, M. Michl, G. Biroli, J.-P. Bouchaud, A. Loidl, P. Lunkenheimer, R. Tourbot, C. Wiertel-Gasquet, F. Ladieu, Fifth-order susceptibility unveils growth of thermodynamic amorphous order in glass-formers. Science 352, 1308 (2016)CrossRefPubMedGoogle Scholar
  65. 65.
    G. Diezemann, Higher-order correlation functions and nonlinear response functions in a Gaussian trap model. J. Chem. Phys. 138, 12A505 (2013)CrossRefPubMedGoogle Scholar
  66. 66.
    C. Brun, C. Crauste-Thibierge, F. Ladieu, D. L’Hôte, Third harmonics nonlinear susceptibility in supercooled liquids: a comparison to the box model. J. Chem. Phys. 134, 194507 (2011)CrossRefPubMedGoogle Scholar
  67. 67.
    P. Kim, A.R. Young-Gonzales, R. Richert, Dynamics of glass-forming liquids. XX. Third harmonic experiments of non-linear dielectric effects versus a phenomenological model. J. Chem. Phys. 145, 064510 (2016)CrossRefGoogle Scholar
  68. 68.
    R. Richert, Nonlinear dielectric signatures of entropy changes in liquids subject to time dependent electric fields. J. Chem. Phys. 144, 114501 (2016)CrossRefPubMedGoogle Scholar
  69. 69.
    P. Gadige, S. Albert, M. Michl, Th Bauer, P. Lunkenheimer, A. Loidl, R. Tourbot, C. Wiertel-Gasquet, G. Biroli, J.-P. Bouchaud, F. Ladieu, Unifying different interpretations of the nonlinear response in glass-forming liquids. Phys. Rev. E 96, 032611 (2017)CrossRefPubMedGoogle Scholar
  70. 70.
    C. Brun, F. Ladieu, D. L’Hôte, M. Tarzia, G. Biroli, J.-P. Bouchaud, Nonlinear dielectric susceptibilities: accurate determination of the growing correlation volume in a supercooled liquid. Phys. Rev. B 84, 104204 (2011)CrossRefGoogle Scholar
  71. 71.
    Dynamical Heterogeneities in Glasses, Colloids and Granular Materials, ed. by L. Berthier, G. Biroli, J.-P. Bouchaud, L. Cipelletti, W. van Saarloos (Oxford University Press, Oxford, 2011)Google Scholar
  72. 72.
    C.M. Roland, R. Casalini, R. Bergman, J. Mattsson, Role of hydrogen bonds in the supercooled dynamics of glass-forming liquids at high pressures. Phys. Rev. B 77, 012201 (2008)CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Naval Research Laboratory, Chemistry DivisionWashingtonUSA

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