Topology and Geometry in Polymer Science

by Whittington, Stuart G.; Sumners, De Witt L.; Lodge, Timothy

• ISBN13: 9780387985800
• ISBN10: 0387985808
• Format: Hardcover
• Copyright: 1998-10-01
• Publisher: Springer Verlag

Summary

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.

Table of Contents

Foreword	v	(2)
Preface	vii
1. Entanglement Complexity of Polymers	1	(28)
Entanglements of polymers	1	(8)
S.F. Edwards
Entropic exponents of knotted lattice polygons	9	(14)
Enzo Orlandini
E.J. Janse van Rensburg
Maria Carla Tesi
S.G. Whittington
The torsion of three-dimensional random walk	23	(6)
Mikelis G. Bickis
2. Knot Energies	29	(50)
Self-repelling knots and local energy minima	29	(8)
Louis H. Kauffman
Milana Huang
Robert P. Greszczuk
Properties of knot energies	37	(12)
Y. Diao
C. Ernst
E.J. Janse van Rensburg
Energy and thickness of knots	49	(18)
Jonathan Simon
On distortion and thickness of knots	67	(12)
Robert B. Kusner
John M. Sullivan
3. Random Linking	79	(22)
Percolation of linked circles	79	(10)
Y. Diao
E.J. Janse van Rensburg
Minimal links in the cubic lattice	89	(12)
R. Uberti
E.J. Janse van Rensburg
E. Orlandini
M.C. Tesi
S.G. Whittington
4. Effect of Geometrical Constraints	101	(58)
Knots in graphs in subsets of Z(3)	101	(34)
C.E. Soteros
Topological entanglement complexity of polymer chains in confined geometries	135	(24)
Maria Carla Tesi
E.J. Janse van Rensburg
Enzo Orlandini
Stuart G. Whittington
5. Surfaces and Vesicles	159
Survey of self-avoiding random surfaces on cubic lattices: Issues, controversies, and results	159	(16)
T.L. Einstein
A.L. Stella
Computational methods in random surface simulation	175	(18)
Isabel Beichl
Francis Sullivan
A model of lattice vesicles	193
E.J. Janse van Rensburg