Abstract
We present molecular-dynamics simulations for a fully flexible model of polymer melts with different chain length N ranging from short oligomers (N = 4) to values near the entanglement length (N = 64). For these systems we explore the structural relaxation of the supercooled melt near the critical temperature T c of mode-coupling theory (MCT). Coherent and incoherent scattering functions are analyzed in terms of the idealized MCT. For temperatures T > T c we provide evidence for the space-time factorization property of the β relaxation and for the time-temperature superposition principle (TTSP) of the α relaxation, and we also discuss deviations from these predictions for T ≈ T c. For T larger than the smallest temperature where the TTSP holds we perform a quantitative analysis of the dynamics with the asymptotic MCT predictions for the late β regime. Within MCT a key quantity, in addition to T c, is the exponent parameter λ. For the fully flexible polymer models studied we find that λ is independent of N and has a value (λ = 0.735 ) typical of simple glass-forming liquids. On the other hand, the critical temperature increases with chain length toward an asymptotic value T ∞c . This increase can be described by T ∞c − T c(N) ∼ 1/N and may be interpreted in terms of the N dependence of the monomer density ρ, if we assume that the MCT glass transition is ruled by a soft-sphere-like constant coupling parameter Γ c = ρ c T c −1/4, where ρ c is the monomer density at T c. In addition, we also estimate T c from a Hansen-Verlet-like criterion and MCT calculations based on structural input from the simulation. For our polymer model both the Hansen-Verlet criterion and the MCT calculations suggest T c to decrease with increasing chain length, in contrast to the direct analysis of the simulation data.
Graphical abstract
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
W. Götze, L. Sjögren, Rep. Prog. Phys. 55, 241 (1992).
W. Götze, J. Phys.: Condens. Matter 11, A1 (1999).
W. Götze, Complex Dynamics of Glass-Forming Liquids: A Mode-Coupling Theory (Oxford University Press, Oxford, 2009).
A. Cavagna, Phys. Rep. 476, 51 (2009).
L. Berthier, G. Biroli, Rev. Mod. Phys. 83, 587 (2011).
W. Kob, in Slow relaxations and nonequilibrium dynamics in condensed matter, edited by J.L. Barrat, M. Feigelmann, J. Kurchan, J. Dalibard (EDP Sciences/Springer, Les Ulis/Berlin, 2003) pp. 201--269.
J. Baschnagel, F. Varnik, J. Phys.: Condens. Matter 17, R851 (2005).
T. Franosch, M. Fuchs, W. Götze, M.R. Mayr, A.P. Singh, Phys. Rev. E 55, 7153 (1997).
M. Fuchs, W. Götze, M.R. Mayr, Phys. Rev. E 58, 3384 (1998).
W. Götze, L. Sjögren, Transport Theory Stat. Phys. 24, 801 (1995).
M.E. Cates, S. Ramaswamy, Phys. Rev. Lett. 96, 135701 (2006).
P. Meyer, K. Miyazaki, D. Reichman, Phys. Rev. Lett. 97, 095702 (2006).
S.H. Chong, Phys. Rev. E 78, 041501 (2008).
K.S. Schweizer, Curr. Opinion Coll. Interf. Sci. 12, 297 (2007).
A.S. Keys, L.O. Hedges, J.P. Garrahan, S.C. Glotzer, D. Chandler, Phys. Rev. X 1, 021013 (2011).
K.N. Pham, A.M. Puertas, J. Bergenholtz, S.U. Egelhaaf, P.N. Moussaïd, P.N. Pusey, A.B. Schofield, M.E. Cates, M. Fuchs, W.C.K. Poon, Science 269, 104 (2002).
M. Sperl, Phys. Rev. E 68, 031405 (2003).
A.J. Moreno, J. Colmenero, Phys. Rev. E 74, 021409 (2006).
A.J. Moreno, J. Colmenero, J. Chem. Phys. 124, 184906 (2006).
S.H. Chong, M. Fuchs, Phys. Rev. Lett. 88, 185702 (2002).
S.H. Chong, M. Aichele, H. Meyer, M. Fuchs, J. Baschnagel, Phys. Rev. E 76, 051806 (2007).
V. Krakoviack, Phys. Rev. E 75, 031503 (2007).
V. Krakoviack, Phys. Rev. E 79, 061501 (2009).
V. Krakoviack, Phys. Rev. E 84, 050501(R) (2011).
S. Lang, R. Schilling, V. Krakoviack, T. Franosch, Phys. Rev. E 86, 021502 (2012).
M. Fuchs, Adv. Polym. Sci. 236, 55 (2010).
M. Bernabei, A.J. Moreno, J. Colmenero, Phys. Rev. Lett. 101, 255701 (2008).
M. Bernabei, A.J. Moreno, J. Colmenero, J. Chem. Phys. 131, 204502 (2009).
M. Bernabei, A.J. Moreno, E. Zaccarelli, F. Sciortino, J. Colmenero, J. Chem. Phys. 134, 024523 (2011).
W. Paul, D. Bedrov, G.D. Smith, Phys. Rev. E 74, 021501 (2006).
J. Colmenero, A. Narros, F. Alvarez, A. Arbe, A.J. Moreno, J. Phys.: Condens. Matter 19, 205127 (2007).
S. Capponi, A. Arbe, F. Alvarez, J. Colmenero, B. Frick, J.P. Embs, J. Chem. Phys. 131, 204901 (2009).
Y. Khairy, F. Alvarez, A. Arbe, J. Colmenero, Phys. Rev. E 88, 042302 (2013).
C. Bennemann, J. Baschnagel, W. Paul, Eur. Phys. J. B 10, 323 (1999).
M. Aichele, J. Baschnagel, Eur. Phys. J. E 5, 229 (2001).
T. Voigtmann, Europhys. Lett. 96, 36006 (2011).
M. Rubinstein, R.H. Colby, Polymer Physics (Oxford University Press, Oxford, 2003).
M. Doi, S.F. Edwards, The Theory of Polymer Dynamics (Oxford University Press, Oxford, 1986).
B. Schnell, H. Meyer, C. Fond, J. Wittmer, J. Baschnagel, Eur. Phys. J. E 34, 97 (2011).
L. Larini, A. Ottochian, C. De Michele, D. Leporini, Nat. Phys. 4, 42 (2008).
A. Barbieri, D. Prevosto, M. Lucchesi, D. Leporini, J. Phys.: Condens. Matter 16, 6609 (2004).
R.A.L. Vallée, W. Paul, K. Binder, J. Chem. Phys. 132, 034901 (2010).
S. Peter, H. Meyer, J. Baschnagel, J. Polym. Sci. B 44, 2951 (2006).
M. Solar, H. Meyer, C. Gauthier, C. Fond, O. Benzerara, R. Schirrer, J. Baschnagel, Phys. Rev. E 85, 021808 (2012).
R. Everaers, S.K. Sukumaran, G.S. Grest, C. Svaneborg, A. Sivasubramanian, K. Kremer, Science 303, 823 (2004).
S.C. Plimpton, Comput. Phys. 117, 1 (1995).
R. Auhl, R. Everaers, G.S. Grest, K. Kremer, S.J. Plimpton, J. Chem. Phys. 119, 12718 (2003).
W. Götze, J. Phys.: Condens. Matter 2, 8485 (1990).
T.G. Fox, S. Loshaek, J. Polym. Sci. 15, 371 (1955).
K.S. Schweizer, J.G. Curro, Adv. Chem. Phys. 98, 1 (1997).
M. Aichele, S.H. Chong, J. Baschnagel, M. Fuchs, Phys. Rev. E 69, 061801 (2004).
F. Weysser, A.M. Puertas, M. Fuchs, T. Voigtmann, Phys. Rev. E 82, 011504 (2010).
J.P. Hansen, L. Verlet, Phys. Rev. 184, 151 (1969).
M. Fuchs, K.S. Schweizer, J. Phys.: Condens. Matter 14, R239 (2002).
J.P. Wittmer, A. Cavallo, H. Xu, J.E. Zabel, P. Polińska, N. Schulmann, H. Meyer, J. Farago, A. Johner, S.P. Obukhov et al., J. Stat. Phys. 145, 1017 (2011).
P.G. de Gennes, Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca, 1996).
S. Krushev, W. Paul, Phys. Rev. E 67, 021806 (2003).
W. Kob, H.C. Andersen, Phys. Rev. E 51, 4626 (1995).
T. Gleim, W. Kob, Eur. Phys. J. B 13, 83 (2000).
T. Voigtmann, A.M. Puertas, M. Fuchs, Phys. Rev. E 70, 061506 (2004).
F. Weysser, D. Hajnal, Phys. Rev. E 83, 041503 (2011).
J. Horbach, W. Kob, J. Phys.: Condens. Matter 14, 9237 (2002).
J. Horbach, W. Kob, Phys. Rev. E 64, 041503 (2001).
E. Flenner, G. Szamel, Phys. Rev. E 72, 031508 (2005).
G. Foffi, W. Götze, F. Sciortino, P. Tartaglia, T. Voigtmann, Phys. Rev. E 69, 011505 (2004).
X.C. Zeng, D. Kivelson, G. Tarjus, Phys. Rev. E 50, 1711 (1994).
H.Z. Cummins, G. Li, Phys. Rev. E 50, 1720 (1994).
S. Frey, PhD thesis, Université de Strasbourg, Strasbourg (2012) available from http://www.sudoc.fr/165862653.
T. Gleim, W. Kob, K. Binder, Phys. Rev. Lett. 81, 4404 (1998).
L. Berthier, W. Kob, J. Phys.: Condens. Matter 19, 205130 (2007).
F. Sciortino, L. Fabbian, S.H. Chen, P. Tartaglia, Phys. Rev. E 56, 5397 (1997).
S.H. Chong, F. Sciortino, Phys. Rev. E 69, 051202 (2004).
W. Kob, H.C. Andersen, Phys. Rev. E 52, 4134 (1995).
M. Nauroth, W. Kob, Phys. Rev. E 55, 657 (1997).
L. Berthier, G. Tarjus, Phys. Rev. E 82, 031502 (2010).
S. Mossa, R. Di Leonardo, G. Ruocco, M. Sampoli, Phys. Rev. E 62, 612 (2000).
A.E. Likhtman, Polymer Science: A Comprehensive Reference, Vol. 1 (Elsevier, Amsterdam, 2012) chapt. Viscoelasticity and Molecular Rheology, pp. 133--179.
J. Farago, A.N. Semenov, H. Meyer, J.P. Wittmer, A. Johner, J. Baschnagel, Phys. Rev. E 85, 051806 (2012).
J. Farago, H. Meyer, J. Baschnagel, A.N. Semenov, Phys. Rev. E 85, 051807 (2012).
T.G. Fox, P.J. Flory, J. Polym. Sci. 14, 315 (1954).
G.B. McKenna, in Comprehensive Polymer Science, edited by C. Booth, C. Price, Vol. 2 (Pergamon, New York, 1986) pp. 311--362.
J. Hintermeyer, A. Herrmann, R. Kahlau, C. Goiceanu, E.A. Rössler, Macromolecules 41, 9335 (2008).
A.L. Agapov, A.P. Sokolov, Macromolecules 42, 2877 (2009).
J. Dudowicz, K.F. Freed, J.F. Douglas, Adv. Chem. Phys. 137, 125 (2008).
M. Durand, H. Meyer, O. Benzerara, J. Baschnagel, O. Vitrac, J. Chem. Phys. 132, 194902 (2010).
B. Lobe, J. Baschnagel, J. Chem. Phys. 101, 1616 (1994).
T. Voigtmann, Phys. Rev. Lett. 101, 095701 (2008).
N. Gnan, T.B. Schrøder, U.R. Pedersen, N.P. Bailey, J.C. Dyre, J. Chem. Phys. 131, 234504 (2009).
D. Coslovich, C.M. Roland, J. Phys. Chem. B 112, 1329 (2008).
C.M. Roland, S. Hensel-Bielowka, M. Paluch, R. Casalini, Rep. Prog. Phys. 68, 1405 (2005).
L. Berthier, G. Tarjus, Eur. Phys. J. E 34, 96 (2011).
J.P. Hansen, I.R. McDonald, Theory of Simple Liquids (Academic Press, London, 1986). .
C. Bennemann, W. Paul, J. Baschnagel, K. Binder, J. Phys.: Condens. Matter 11, 2179 (1999).
W. Götze, T. Voigtmann, Phys. Rev. E 61, 4133 (2000).
F. Sciortino, P. Tartaglia, J. Phys.: Condens. Matter 11, A261 (1999).
W. Paul, G.D. Smith, Rep. Prog. Phys. 67, 1117 (2004).
F. Sciortino, W. Kob, Phys. Rev. Lett. 86, 648 (2001).
A. Rinaldi, F. Sciortino, P. Tartaglia, Phys. Rev. E 63, 061210 (2001).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Frey, S., Weysser, F., Meyer, H. et al. Simulated glass-forming polymer melts: Dynamic scattering functions, chain length effects, and mode-coupling theory analysis. Eur. Phys. J. E 38, 11 (2015). https://doi.org/10.1140/epje/i2015-15011-x
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1140/epje/i2015-15011-x