Topology and Geometry in Polymer Science

Witt De Sumners

ISBN 10: 0387985808 / ISBN 13: 9780387985800

Editore: Humana, 1998

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nach der Bestellung gedruckt Neuware - Printed after ordering - This IMA Volume in Mathematics and its Applications TOPOLOGY AND GEOMETRY IN POLYMER SCIENCE is based on the proceedings of a very successful one-week workshop with the same title. This workshop was an integral part of the 1995-1996 IMA program on 'Mathematical Methods in Materials Science.' We would like to thank Stuart G. Whittington, De Witt Sumners, and Timothy Lodge for their excellent work as organizers of the meeting and for editing the proceedings. We also take this opportunity to thank the National Science Foun dation (NSF), the Army Research Office (ARO) and the Office of Naval Research (ONR), whose financial support made the workshop possible. A vner Friedman Robert Gulliver v PREFACE This book is the product of a workshop on Topology and Geometry of Polymers, held at the IMA in June 1996. The workshop brought together topologists, combinatorialists, theoretical physicists and polymer scientists, who share an interest in characterizing and predicting the microscopic en tanglement properties of polymers, and their effect on macroscopic physical properties.

Codice articolo 9780387985800

Dati bibliografici

• Titolo: Topology and Geometry in Polymer Science
• Editore: Humana
• Data di pubblicazione: 1998
• Lingua: Inglese
• ISBN 10: 0387985808
• ISBN 13: 9780387985800
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 241 L x 160 A x 17 P (millimetri) 241 millimetri di larghezza per 160 millimetri di altezza per 17 millimetri di profondità
• Peso: 500 grammi

Descrizione articolo

Riassunto

This book contains contributions from a workshop on topology and geometry of polymers, held at the IMA in June 1996, which brought together topologists, combinatorialists, theoretical physicists and polymer scientists, with a common interest in polymer topology. Polymers can be highly self-entangled even in dilute solution. In the melt the inter- and intra-chain entanglements can dominate the rheological properties of these phenomena. Although the possibility of knotting in ring polymers has been recognized for more than thirty years it is only recently that the powerful methods of algebraic topology have been used in treating models of polymers. This book contains a series of chapters which review the current state of the field and give an up to date account of what is known and perhaps more importantly, what is still unknown. The field abounds with open problems. The book is of interest to workers in polymer statistical mechanics but will also be useful as an introduction to topological methods for polymer scientists, and will introduce mathematicians to an area of science where topological approaches are making a substantial contribution.

Contenuti

1. Entanglement Complexity of Polymers.- Entanglements of polymers.- Entropic exponents of knotted lattice polygons.- The torsion of three-dimensional random walk.- 2. Knot Energies.- Self-repelling knots and local energy minima.- Properties of knot energies.- Energy and thickness of knots.- On distortion and thickness of knots.- 3. Random Linking.- Percolation of linked circles.- Minimal links in the cubic lattice.- 4. Effect of Geometrical Constraints.- Knots in graphs in subsets of Z3.- Topological entanglement complexity of polymer chains in confined geometries.- 5. Surfaces and Vesicles.- Survey of self-avoiding random surfaces on cubic lattices: Issues, controversies, and results.- Computational methods in random surface simulation.- A model of lattice vesicles.