Abstract
On cooling toward the glass transition temperature, glass-forming liquids display long periods of localized motion interrupted by fast “jumps” in the single-particle trajectories. Several theoretical models based on these single-particle jumps have been proposed, most prominently the continuous-time random walk (CTRW). The central assumption of the CTRW is that jumps are renewal events, i.e. that the internal clock of a particle can be reset upon a jump. In this paper, I present an easy-to-implement method to test whether jumps detected in a supercooled liquid or glass are renewal events or not. The test was applied to molecular dynamics simulations of a short-chain polymer melt, demonstrating that the jumps can in fact be treated as renewal events. The test further revealed that additional relaxation processes are present which are not accounted for in the CTRW picture, highlighting the limitations of this approach. The notion of renewal events in glass-forming systems could be a very important building block for the interpretation of aging and the glass transition. Furthermore, it could have practical implications for the study of non-equilibrium dynamics in glasses as well as mechanical rejuvenation.
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H. Scholze, Glass -- Nature, Structure, and Properties (Springer-Verlag, New York, 1991).
L. Berthier, G. Biroli, Rev. Mod. Phys. 83, 587 (2011).
M.D. Ediger, P. Harrowell, J. Chem. Phys. 137, 080901 (2012).
G. Biroli, J.P. Garrahan, J. Chem. Phys. 138, 12A301 (2013).
E.J. Donth, The Glass Transition (Springer-Verlag, Berlin-Heidelberg, 2001).
K. Binder, W. Kob, Glassy Materials and Disordered Solids (World Scientific, Singapore, 2005).
W. Götze, Complex Dynamics of Glass-Forming Liquids: A Mode-Coupling Theory (Oxford University Press, Oxford, 2009).
L.C.E. Struik, Physical Aging in Amorphous Polymers and Other Materials (Elsevier, Amsterdam, 1978).
W. Götze, J. Phys.: Condens. Matter 11, A1 (1999).
S.C. Glotzer, J. Non-Cryst. Solids 274, 342 (2000).
M. Aichele, Y. Gebremichael, F.W. Starr, J. Baschnagel, S.C. Glotzer, J. Chem. Phys. 119, 5290 (2003) publisher's note: J. Chem. Phys. 120.
Y. Jung, J.P. Garrahan, D. Chandler, J. Chem. Phys. 123, 084509 (2005).
L.O. Hedges, L. Maibaum, D. Chandler, J.P. Garrahan, J. Chem. Phys. 127, 211101 (2007).
H. Sillescu, J. Non-Cryst. Solids 243, 81 (1999).
M.D. Ediger, Annu. Rev. Phys. Chem. 51, 99 (2000).
R. Richert, J. Phys.: Condens. Matter 14, R703 (2002).
L. Berthier, G. Biroli, J.P. Bouchaud, L. Cipelletti, W. van Saarloos, Dynamical Heterogeneities in Glasses, Colloids and Granular Media (Oxford University Press, Oxford, 2011).
H. Miyagawa, Y. Hiwatari, B. Bernu, J.P. Hansen, J. Chem. Phys. 88, 3879 (1988).
K. Vollmayr-Lee, J. Chem. Phys. 121, 4781 (2004).
L. Berthier, D. Chandler, J.P. Garrahan, Europhys. Lett. 69, 320 (2005).
M. Warren, J. Rottler, EPL 88, 58005 (2009).
J.W. Ahn, B. Falahee, C. Del Piccolo, M. Vogel, D. Bingemann, J. Chem. Phys. 138, 12A527 (2013).
K. Vollmayr-Lee, R. Bjorkquist, L.M. Chambers, Phys. Rev. Lett. 110, 017801 (2013).
E.W. Montroll, G.H. Weiss, J. Math. Phys. 6, 167 (1965).
J.P. Bouchaud, A. Georges, Phys. Rep. 195, 127 (1990).
R. Metzler, J. Klafter, Phys. Rep. 339, 1 (2000).
R. Metzler, J. Klafter, J. Phys. A: Math. Gen. 37, R161 (2004).
J. Klafter, I.M. Sokolov, First Steps in Random Walks (Oxford University Press, Oxford, 2011).
T. Odagaki, Phys. Rev. B 38, 9044 (1988).
T. Odagaki, Y. Hiwatari, Phys. Rev. A 41, 929 (1990).
G. Wahnström, Phys. Rev. A 44, 3752 (1991).
T. Odagaki, Phys. Rev. Lett. 75, 3701 (1995).
C. Monthus, J.P. Bouchaud, J. Phys. A: Math. Gen. 29, 3847 (1996).
P. Chaudhuri, L. Berthier, W. Kob, Phys. Rev. Lett. 99, 060604 (2007).
P. Chaudhuri, Y. Gao, L. Berthier, M. Kilfoil, W. Kob, J. Phys.: Condens. Matter 20, 244126 (2008).
E. Barkai, Y.C. Cheng, J. Chem. Phys. 118, 6167 (2003).
J.H.P. Schulz, E. Barkai, R. Metzler, Phys. Rev. X 4, 011028 (2014).
T.B. Schrøder, S. Sastry, J.C. Dyre, S.C. Glotzer, J. Chem. Phys. 112, 9834 (2000).
P.G. Debenedetti, F.H. Stillinger, Nature 410, 259 (2001).
A. Heuer, J. Phys.: Condens. Matter 20, 373101 (2008).
O. Rubner, A. Heuer, Phys. Rev. E 78, 011504 (2008).
C.F.E. Schroer, A. Heuer, Phys. Rev. Lett. 110, 067801 (2013).
M. Warren, J. Rottler, Phys. Rev. Lett. 110, 025501 (2013).
C. de Michele, D. Leporini, Phys. Rev. E 63, 036701 (2001).
M. Warren, J. Rottler, J. Chem. Phys. 133, 164513 (2010).
M. Warren, J. Rottler, Phys. Rev. Lett. 104, 205501 (2010).
A. Smessaert, J. Rottler, Phys. Rev. E 88, 022314 (2013).
J. Helfferich, F. Ziebert, S. Frey, H. Meyer, J. Farago, A. Blumen, J. Baschnagel, Phys. Rev. E 89, 042603 (2014).
J. Helfferich, F. Ziebert, S. Frey, H. Meyer, J. Farago, A. Blumen, J. Baschnagel, Phys. Rev. E 89, 042604 (2014).
R. Pastore, A. Coniglio, M.P. Ciamarra, Soft Matter 10, 5724 (2014).
W. Feller, An Introduction to Probability Theory and Its Applications, Vol. I (Wiley, New York, 1968).
W. Feller, An Introduction to Probability Theory and Its Applications Vol. II (Wiley, New York, 1966).
S. Peter, H. Meyer, J. Baschnagel, Eur. Phys. J. E 28, 147 (2009).
B. Schnell, H. Meyer, C. Fond, J.P. Wittmer, J. Baschnagel, Eur. Phys. J. E 34, 97 (2011).
M. Solar, H. Meyer, C. Gauthier, C. Fond, O. Benzerara, R. Schirrer, J. Baschnagel, Phys. Rev. E 85, 021808 (2012).
S. Peter, H. Meyer, J. Baschnagel, J. Polym. Sci. Part B Polym. Phys. 44, 2951 (2006).
S. Plimpton, J. Comput. Phys. 117, 1 (1995).
S. Frey, PhD Thesis, Université de Strasbourg, Strasbourg (2012) (available from http://www.sudoc.fr/165862653).
J. Baschnagel, F. Varnik, J. Phys.: Condens. Matter 17, R851 (2005).
B.L. Holian, A.F. Voter, R. Ravelo, Phys. Rev. E 52, 2338 (1995).
D. Frenkel, B. Smit, Understanding Molecular Simulation, 2nd edition (Academic Press, London, 2002).
S. Melchionna, G. Ciccotti, B.L. Holian, Mol. Phys. 78, 533 (1993).
W. Kob, J.L. Barrat, Eur. Phys. J. B 13, 319 (2000).
G.B. McKenna, J. Phys.: Condens. Matter 15, S737 (2003).
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Helfferich, J. Renewal events in glass-forming liquids. Eur. Phys. J. E 37, 73 (2014). https://doi.org/10.1140/epje/i2014-14073-6
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DOI: https://doi.org/10.1140/epje/i2014-14073-6