The cooperative free volume rate model for segmental dynamics: Application to glass-forming liquids and connections with the density scaling approach

  • Ronald P. White
  • Jane E. G. LipsonEmail author
Regular Article
Part of the following topical collections:
  1. Dielectric Spectroscopy Applied to Soft Matter


In this paper, we apply the cooperative free volume (CFV) rate model for pressure-dependent dynamics of glass-forming liquids and polymer melts. We analyze segmental relaxation times, \( \tau\) , as a function of temperature (T and free volume ( \( V_{\rm free}\) , and make substantive comparisons with the density scaling approach. \( V_{\rm free}\) , the difference between the total volume (V and the volume at close-packing, is predicted independently of the dynamics for any temperature and pressure using the locally correlated lattice (LCL) equation-of-state (EOS) analysis of characteristic thermodynamic data. We discuss the underlying physical motivation in the CFV and density scaling models, and show that their key, respective, material parameters are connected, where the CFV b parameter and the density scaling \( \gamma\) parameter each characterize the relative sensitivity of dynamics to changes in T , vs. changes in V . We find \( \gamma\approx 1/[b(V_{{{\rm free}}}/V)_{@T_{\rm g}}]\) , where \( (V_{{{\rm free}}}/V)_{@T_{\rm g}}\) is the value predicted by the LCL EOS at the ambient \( T_{\rm g}\) . In comparing the predictive power of the two models we highlight the CFV advantage in yielding a universal linear collapse of relaxation data using a minimal set of parameters, compared to the same parameter space yielding a changing functional form in the density scaling approach. Further, we demonstrate that in the low data limit, where there is not enough data to characterize the density scaling model, the CFV model may still be successfully applied, and we even use it to predict the correct \( \gamma\) parameter.

Graphical abstract


Topical issue: Dielectric Spectroscopy Applied to Soft Matter 


  1. 1.
    R.P. White, J.E.G. Lipson, Macromolecules 51, 7924 (2018)ADSCrossRefGoogle Scholar
  2. 2.
    R.P. White, J.E.G. Lipson, J. Chem. Phys. 147, 184503 (2017)ADSCrossRefGoogle Scholar
  3. 3.
    R.P. White, J.E.G. Lipson, Macromolecules 51, 4896 (2018)ADSCrossRefGoogle Scholar
  4. 4.
    C. Roland, S. Hensel-Bielowka, M. Paluch, R. Casalini, Rep. Prog. Phys. 68, 1405 (2005)ADSCrossRefGoogle Scholar
  5. 5.
    G. Floudas, M. Paluch, A. Grzybowski, K. Ngai, Molecular Dynamics of Glass-Forming Systems - Effects of Pressure (Springer, Berlin, 2011)Google Scholar
  6. 6.
    A. Grzybowski, M. Paluch, in The Scaling of Relaxation Processes, edited by F. Kremer, A. Loidl (Springer International Publishing, Cham, 2018) pp. 77--119Google Scholar
  7. 7.
    L. Bohling, T.S. Ingebrigtsen, A. Grzybowski, M. Paluch, J.C. Dyre, T.B. Schroder, New J. Phys. 14, 113035 (2012)ADSCrossRefGoogle Scholar
  8. 8.
    J.C. Dyre, J. Phys. Chem. B 118, 10007 (2014)CrossRefGoogle Scholar
  9. 9.
    N. Gnan, T.B. Schroder, U.R. Pedersen, N.P. Bailey, J.C. Dyre, J. Chem. Phys. 131, 234504 (2009)ADSCrossRefGoogle Scholar
  10. 10.
    D. Fragiadakis, C.M. Roland, J. Chem. Phys. 134, 044504 (2011)ADSCrossRefGoogle Scholar
  11. 11.
    R. Casalini, U. Mohanty, C.M. Roland, J. Chem. Phys. 125, 014505 (2006)ADSCrossRefGoogle Scholar
  12. 12.
    R. Casalini, C.M. Roland, J. Non-Cryst. Solids 353, 3936 (2007)ADSCrossRefGoogle Scholar
  13. 13.
    A.K. Doolittle, J. Appl. Phys. 22, 1471 (1951)ADSCrossRefGoogle Scholar
  14. 14.
    M.L. Williams, R.F. Landel, J.D. Ferry, J. Am. Chem. Soc. 77, 3701 (1955)CrossRefGoogle Scholar
  15. 15.
    J.D. Ferry, Viscoelastic Properties of Polymers, second edition (Wiley, New York, 1970)Google Scholar
  16. 16.
    M.H. Cohen, D. Turnbull, J. Chem. Phys. 31, 1164 (1959)ADSCrossRefGoogle Scholar
  17. 17.
    R.P. White, J.E.G. Lipson, Macromolecules 49, 3987 (2016)ADSCrossRefGoogle Scholar
  18. 18.
    R.P. White, J.E.G. Lipson, ACS Macro Lett. 6, 529 (2017)CrossRefGoogle Scholar
  19. 19.
    A. Debot, R.P. White, J.E.G. Lipson, S. Napolitano, ACS Macro Lett. 8, 41 (2019)CrossRefGoogle Scholar
  20. 20.
    W. Hoover, M. Ross, Contemp. Phys. 12, 339 (1971)ADSCrossRefGoogle Scholar
  21. 21.
    Y. Hiwatari, H. Matsuda, T. Ogawa, N. Ogita, A. Ueda, Prog. Theor. Phys. 52, 1105 (1974)ADSCrossRefGoogle Scholar
  22. 22.
    U.R. Pedersen, N.P. Bailey, T.B. Schroder, J.C. Dyre, Phys. Rev. Lett. 100, 015701 (2008)ADSCrossRefGoogle Scholar
  23. 23.
    U.R. Pedersen, T.B. Schroder, J.C. Dyre, Phys. Rev. Lett. 105, 157801 (2010)ADSCrossRefGoogle Scholar
  24. 24.
    D. Coslovich, C.M. Roland, J. Chem. Phys. 131, 151103 (2009)ADSCrossRefGoogle Scholar
  25. 25.
    D. Coslovich, C.M. Roland, J. Phys. Chem. B 112, 1329 (2008)CrossRefGoogle Scholar
  26. 26.
    D. Coslovich, C.M. Roland, J. Chem. Phys. 130, 014508 (2009)ADSCrossRefGoogle Scholar
  27. 27.
    I. Avramov, J. Non-Cryst. Solids 262, 258 (2000)ADSCrossRefGoogle Scholar
  28. 28.
    J.E.G. Lipson, R.P. White, J. Chem. Eng. Data 59, 3289 (2014)CrossRefGoogle Scholar
  29. 29.
    G. Adam, J.H. Gibbs, J. Chem. Phys. 43, 139 (1965)ADSCrossRefGoogle Scholar
  30. 30.
    R. Casalini, C.M. Roland, Phys. Rev. Lett. 113, 085701 (2014)ADSCrossRefGoogle Scholar
  31. 31.
    K. Koperwas, A. Grzybowski, S.N. Tripathy, E. Masiewicz, M. Paluch, Sci. Rep. 5, 17782 (2015)ADSCrossRefGoogle Scholar
  32. 32.
    M. Goldstein, J. Phys. Chem. 77, 667 (1973)CrossRefGoogle Scholar
  33. 33.
    C. Roland, R. Casalini, Macromolecules 36, 1361 (2003)ADSCrossRefGoogle Scholar
  34. 34.
    M. Paluch, S. Haracz, A. Grzybowski, M. Mierzwa, J. Pionteck, A. Rivera-Calzada, C. Leon, J. Phys. Chem. Lett. 1, 987 (2010)CrossRefGoogle Scholar
  35. 35.
    M. Naoki, H. Endou, K. Matsumoto, J. Phys. Chem. 91, 4169 (1987)CrossRefGoogle Scholar
  36. 36.
    P. Zoller, D. Walsh, Standard Pressure-Volume-Temperature Data for Polymers (Technomic Pub Co., Lancaster, PA, 1995)Google Scholar
  37. 37.
    W. Heinrich, B. Stoll, Colloid Polym. Sci. 263, 873 (1985)CrossRefGoogle Scholar
  38. 38.
    R. Casalini, C. Roland, J. Chem. Phys. 119, 4052 (2003)ADSCrossRefGoogle Scholar
  39. 39.
    T. Ougizawa, G.T. Dee, D.J. Walsh, Macromolecules 24, 3834 (1991)ADSCrossRefGoogle Scholar
  40. 40.
    M. Paluch, C. Roland, S. Pawlus, J. Chem. Phys. 116, 10932 (2002)ADSCrossRefGoogle Scholar
  41. 41.
    M. Paluch, R. Casalini, A. Patkowski, T. Pakula, C. Roland, Phys. Rev. E 68, 031802 (2003)ADSCrossRefGoogle Scholar
  42. 42.
    M. Paluch, S. Pawlus, C. Roland, Macromolecules 35, 7338 (2002)ADSCrossRefGoogle Scholar
  43. 43.
    P. Panagos, G. Floudas, J. Non-Cryst. Solids 407, 184 (2015)ADSCrossRefGoogle Scholar
  44. 44.
    A. Panagopoulou, S. Napolitano, Phys. Rev. Lett. 119, 097801 (2017)ADSCrossRefGoogle Scholar
  45. 45.
    S. Hensel-Bielowka, J. Ziolo, M. Paluch, C. Roland, J. Chem. Phys. 117, 2317 (2002)ADSCrossRefGoogle Scholar
  46. 46.
    M. Paluch, C. Roland, R. Casalini, G. Meier, A. Patkowski, J. Chem. Phys. 118, 4578 (2003)ADSCrossRefGoogle Scholar
  47. 47.
    R. Casalini, M. Paluch, C. Roland, Phys. Rev. E 67, 031505 (2003)ADSCrossRefGoogle Scholar
  48. 48.
    R. Casalini, M. Paluch, C.M. Roland, J. Phys.: Condens. Matter 15, S859 (2003)ADSGoogle Scholar
  49. 49.
    M. Paluch, R. Casalini, A. Best, A. Patkowski, J. Chem. Phys. 117, 7624 (2002)ADSCrossRefGoogle Scholar
  50. 50.
    M. Naoki, S. Koeda, J. Phys. Chem. 93, 948 (1989)CrossRefGoogle Scholar
  51. 51.
    A. Rivera-Calzada, K. Kaminski, C. Leon, M. Much, J. Phys. Chem. B 112, 3110 (2008)CrossRefGoogle Scholar

Copyright information

© EDP Sciences, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of ChemistryDartmouth CollegeHanoverUSA

Personalised recommendations