Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-25T16:37:26.994Z Has data issue: false hasContentIssue false
  • English
  • Français

Length and Time Scales of Entanglement and Confinement Effects Constraining Polymer Chain Dynamics

Published online by Cambridge University Press:  31 January 2011

Rainer Kimmich  and
Nail Fatkullin
Rainer Kimmich
Affiliation:
[email protected], University of Ulm, Ulm, Germany
Nail Fatkullin
Affiliation:
[email protected], Kazan State University, Kazan, Russian Federation
Get access

Abstract

With characteristic time constants for polymer dynamics, namely τs (the segment fluctuation time), τe (the entanglement time), and τR (the longest Rouse relaxation time), the time scales of particular interest (i) t<τs, (ii) τs<t<τe, and (iii) τe<t<τR will be discussed and compared with experimental data. These ranges correspond to the chain-mode length scales (i) l<b, (ii) b<l<d2/b, and (iii) d2/b<l<L, where b is the statistical segment length, d is the dimension of constraints by entanglements and/or confinement, and L is the chain contour length. Based on Langevin-type equations-of-motion coarse-grained predictions for the mean-squared segment displacement and the spin-lattice relaxation dispersion will be outlined for the scenarios “freely-draining”, “entangled”, and “confined”. In the discussion we will juxtapose “local” versus “global” dynamics on the one hand, and “bulk” versus “confined” systems on the other.

Keywords

diffusionnuclear magnetic resonance (NMR)polymer
Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 1227: Symposium JJ – Multiscale Dynamics in Confining Systems , 2009 , 1227-JJ02-01
Copyright
Copyright © Materials Research Society 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1 Mattea, C., Fatkullin, N., Fischer, E., Beginn, U., Anoardo, E., Kroutieva, M., Kimmich, R., Appl. Magn. Reson. 27, 371 (2004).Google Scholar
2 Fatkullin, N., Kimmich, R., Fischer, E., Mattea, C., Beginn, U., Kroutieva, M., New J. Physics 6, 46 (2004).Google Scholar
3 Ardelean, I., Kimmich, R., Ann. Rep. NMR Spectr. 49, 43 (2003)Google Scholar
4 Kimmich, R., Anoardo, E., Progr. NMR Spectr. 44, 257 (2004).Google Scholar
5 Kehr, M., Fatkullin, N., Kimmich, R., J. Chem. Phys. 126, 094903 (2007).Google Scholar
6 Richter, D., Monkenbusch, M., Arbe, A., Comenero, J., Advan. Polym. Sci. 174, 1 (2005).Google Scholar
7 Kargin, V. A., Slonimskii, G. L., J. Fizhimii (USSR) 23, 5 (1949).Google Scholar
8 Rouse, P. E., J. Chem. Phys. 21, 1272 (1953).Google Scholar
9 Doi, M., Edwards, S. F., The Theory of Polymer Dynamics (Oxford Univ. Pr., 1986).Google Scholar
10 Wischnewski, A., Monkenbusch, M., Willner, L., Richter, D., Farago, B., Kali, G., Phys. Rev. Letters 90, 058302 (2003).Google Scholar
11 Kimmich, R., Fatkullin, N., Advan. Polym. Sci. 170, 1 (2004).Google Scholar
12 Kroutieva, M. A., Fatkullin, N. F., Kimmich, R., Polym. Sci. A 47, 1716 (2005).Google Scholar
13 Denissov, A., Kroutieva, M., Fatkullin, N., Kimmich, R., J. Chem. Phys. 116, 5217 (2002).Google Scholar
14 Fischer, E., Beginn, U., Fatkullin, N., Kimmich, R., Macromolecules 37, 3177 (2004).Google Scholar
15 Fatkullin, N., Kausik, R., Kimmich, R., J. Chem. Phys. 126, 094904 (2007).Google Scholar
16 Kausik, R., Mattea, C., Kimmich, R., Fatkullin, N., Eur. Phys. J. 141, 235 (2007).Google Scholar
17 Stapf, S., Kimmich, R., Macromolecules 29, 1638 (1996).Google Scholar
18 Gubaidullin, A., Shakirov, T., Fatkullin, N., Kimmich, R., Solid State NMR 35, 147 (2009).Google Scholar