Abstract
Many liquids cooled to low temperatures form glasses (amorphous solids) instead of crystals. As the glass transition is approached, molecules become localized and relaxation times increase by many orders of magnitude1. Many features of this ‘slowing down’ are reasonably well described2 by the mode-coupling theory of supercooled liquids3. The ideal form of this theory predicts a dynamical critical temperature T c at which the molecules become permanently trapped in the ‘cage’ formed by their neighbours, and vitrification occurs. Although there is no sharp transition, because molecules do eventually escape their cage, its signature can still be observed in real and simulated liquids. Unlike conventional critical phenomena (such as the behaviour at the liquid–gas critical point), the mode-coupling transition is not accompanied by a diverging static correlation length. But simulation4,5,6,7,8,9,10 and experiment11,12 show that liquids are dynamically heterogeneous, suggesting the possibility of a relevant ‘dynamical’ length scale characterizing the glass transition. Here we use computer simulations to investigate a melt of short, unentangled polymer chains over a range of temperatures for which the mode-coupling theory remains valid. We find that although density fluctuations remain short-ranged, spatial correlations between monomer displacements become long-ranged as T c is approached on cooling. In this way, we identify a growing dynamical correlation length, and a corresponding order parameter, associated with the glass transition. This finding suggests a possible connection between well established concepts in critical phenomena and the dynamics of glass-forming liquids.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 51 print issues and online access
$199.00 per year
only $3.90 per issue
Rent or buy this article
Prices vary by article type
from$1.95
to$39.95
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Ediger, M. D., Angell, C. A. & Nagel, S. R. Supercooled liquids and glasses. J. Phys. Chem. 100, 13200–13212 ( 1996).
Yip, S. & Nelson, P. (eds) Transport Theory. Stat. Phys. 24, 755–1270 ( 1995).
Götze, W. & Sjögren, L. The mode coupling theory of structural relaxations. Transport Theory Stat. Phys. 24, 801–853 (1995).
Hiwatari, Y. & Muranaka, T. Structural heterogeneity in supercooled liquids and glasses. J. Non-Cryst. Solids 235–237 ;, 19–26 (1998).
Perera, D. & Harrowell, P. Atwo-dimensional glass: microstructure and dynamics of a 2D binary mixture. J. Non-Cryst. Solids 235–237;, 314–319 ( 1998).
Onuki, A. & Yamamoto, Y. Kinetic heterogeneities and non-linear rheology of highly supercooled liquids. J. Non-Cryst. Solids 235–237;, 34–40 ( 1998).
Doliwa, B. & Heuer, A. Cage effect, local anisotropies, and dynamic heterogeneities at the glass transition: a computer study of hard spheres. Phys. Rev. Lett. 80, 4915– 4919 (1998).
Kob, W., Donati, C., Plimpton, S. J., Poole, P. H. & Glotzer, S. C. Dynamical heterogeneities in a supercooled Lennard-Jones liquid. Phys. Rev. Lett. 79, 2827–2930 (1997).
Donati, C. et al. String-like clusters and cooperative motion in a model glass-forming liquid. Phys. Rev. Lett. 80, 2338– 2341 (1998).
Donati, C., Glotzer, S. C., Poole, P. H., Kob, W. & Plimpton, S. J. Spatial correlations of mobility and immobility in a glass-forming Lennard-Jones liquid. Phys. Rev. E. (submitted).
Böhmer, R. et al. Nature of the non-exponential primary relaxation in structural glass-formers probed by dynamically selective experiments. J. Non-Cryst. Solids 235–237;, 1–9 (1998).
Cicerone, M. T., Blackburn, F. & Ediger, M. D. Anomalous diffusion of probe molecules in polystyrene: evidence for spatially heterogeneous segmental dynamics. Macromolecules 28, 8224–8232 ( 1995).
Hansen, J. P. & McDonald, I. R. Theory of Simple Liquids (Academic, London, (1986).
Donati, C., Glotzer, S. C. & Poole, P. H. Growing spatial correlations of particle displacements in a simulated liquid on cooling toward the glass transition. Phys. Rev. Lett. (in the press).
Glotzer, S. C., Jan, N., Lookman, T., MacIsaac, A. B. & Poole, P. H. Dynamical heterogeneity in the Ising spin glass. Phys. Rev. E 57, 7350– 7353 (1998).
Stanley, H. E. Introduction to Phase Transitions and Critical Phenomena (Oxford University Press, New York, (1971).
van Blaaderen, A. & Wiltzius, P. Real-space structure of colloidal hard-sphere glasses. Science 270, 1177–1179 (1995).
Leheny, R. L. et al. Structural studies of an organic liquid through the glass transition. J. Chem. Phys. 105, 7783– 7794 (1996).
Bennemann, C., Paul, W., Binder, K. & Dünweg, B. Molecular-dynamics simulations of the thermal glass transition in polymer melts: α-relaxation behavior. Phys. Rev. E 57, 843– 851 (1998).
Bennemann, C., Baschnagel, J. & Paul, W. Molecular-dynamics simulation of a glassy polymer melt: incoherent scattering function. Eur. Phys. J. B (in the press).
Bennemann, C., Paul, W., Baschnagel, J. & Binder, K. Investigating the influence of different thermodynamic paths on the structural relaxation in a glass forming polymer melt. J. Phys. Cond. Mat. (in the press).
Jerome, B. & Commandeur, J. Dynamics of glasses below the glass transition. Nature 386, 589– 592 (1997).
Forrest, J. A., Dalnoki-Veress, K. & Dutcher, J. R. Interface and chain confinement effects on the glass transition temperature of thin polymer films. Phys. Rev. E 56, 5705–5515 (1997).
Wallace, W. E., van Zanten, J. H. & Wu, W. L. Influence of an impenetrable interface on a polymer glass-transition temperature. Phys. Rev. E 52, R3329–R3332 (1995).
Jackson, C. L. & McKenna, G. B. The glass transition of organic liquids confined to small pores. J. Non-Cryst. Solids 131–133;, 221–224 (1991).
Arndt, M., Stannarius, R., Groothues, H. & Kremer, F. Length scale of cooperativity in the dynamic glass transition. Phys. Rev. Lett. 79, 2077–2080 (1997).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bennemann, C., Donati, C., Baschnagel, J. et al. Growing range of correlated motion in a polymer melt on cooling towards the glass transition. Nature 399, 246–249 (1999). https://doi.org/10.1038/20406
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1038/20406
This article is cited by
-
Dynamic molecular ordering in multiphasic nanoconfined ionic liquids detected with time-resolved diffusion NMR
Communications Materials (2023)
-
Surface melting of a colloidal glass
Nature Communications (2022)
-
Glass transition analysis of model metallosupramolecular polyesters bearing pendant pyridine ligands with a controlled ligand–ligand distance
Polymer Journal (2020)
-
Concentrated suspensions of Brownian beads in water: dynamic heterogeneities through a simple experimental technique
Science China Physics, Mechanics & Astronomy (2019)
-
Differential Variance Analysis: a direct method to quantify and visualize dynamic heterogeneities
Scientific Reports (2017)
Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.