Computer Simulations in Condensed Matter Systems: From Materials to Chemical Biology Volume 2
This extensive and comprehensive collection of lectures by world-leading experts in the field introduces and reviews all relevant computer simulation methods and their applications in condensed matter systems. Volume 1, published as LNP 703 (ISB
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Kurt Kremer
K. Kremer: Polymer Dynamics: Long Time Simulations and Topological Constraints, Lect. Notes Phys. 704, 341–378 (2006) c Springer-Verlag Berlin Heidelberg 2006 DOI 10.1007/3-540-35284-8 14
342
K. Kremer
1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343
2
Polymer Dynamics and Network Elasticity . . . . . . . . . . . . . . . . 345
3
Theoretical Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348
3.1 3.2
Unentangled Chains – Rouse Regime . . . . . . . . . . . . . . . . . . . . . . . . . . 348 Entangled Chains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350
4
Simulation Models, Equilibrated Melts . . . . . . . . . . . . . . . . . . . . 354
4.1
Preparing an Equilibrated Melt, Specific Systems . . . . . . . . . . . . . . . . 356
5
Entanglement Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360
5.1 5.2 5.3
“Visual” Inspection of Melts and Networks . . . . . . . . . . . . . . . . . . . . . 360 Analysis of Chain Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362 Structure and Property Relations: Specific Polymers . . . . . . . . . . . . . 366
6
Primitive Path Analysis: PPA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369
7
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374
8
Annotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374
Polymer Dynamics: Long Time Simulations and Topological Constraints
343
Simulations are very versatile tools to study the relaxation and dynamics of polymer melts and networks. The fact that polymer chains cannot pass through each other poses special difficulties for analytic theories, while on the other hand many experiments are dominated by this fact. The contribution discusses some basic concepts and conditions and ways to study such problems by computer simulations.
1 Introduction This book deals with several aspects of soft matter science, which includes classical polymer physics problems as well as a variety of topics in biophysics, such as membranes or proteins. In all these cases we have to study and understand the properties of rather large molecules, which in the case of proteins and especially polymers can contain many thousands of atoms. In this context classical synthetic polymers are a prototypical class of systems, as their molecular structure in most cases is simpler than those of typical biopolymers. In the simplest case a polymer is a long chain molecule of identical repeat units (beads or monomers). Of course modern polymer chemistry goes well beyond that simple scheme. On the other hand many characteristic problems to treat such systems by computer simulations can be illustrated best for simple pol
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