Statistics of Linear Polymers in Disordered Media - 1st Edition - ISBN: 9780444517098, 9780080460475

Statistics of Linear Polymers in Disordered Media

1st Edition

Editors: Bikas Chakrabarti
Hardcover ISBN: 9780444517098
eBook ISBN: 9780080460475
Imprint: Elsevier Science
Published Date: 9th June 2005
Page Count: 368
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Description

With the mapping of the partition function graphs of the n-vector magnetic model in the n to 0 limit as the self-avoiding walks, the conformational statistics of linear polymers was clearly understood in early seventies. Various models of disordered solids, percolation model in particular, were also established by late seventies. Subsequently, investigations on the statistics of linear polymers or of self-avoiding walks in, say, porous medium or disordered lattices were started in early eighties. Inspite of the brilliant ideas forwarded and extensive studies made for the next two decades, the problem is not yet completely solved in its generality. This intriguing and important problem has remained since a topic of vigorous and active research.

This book intends to offer the readers a first hand and extensive review of the various aspects of the problem, written by the experts in the respective fields. We hope, the contents of the book will provide a valuable guide for researchers in statistical physics of polymers and will surely induce further research and advances towards a complete understanding of the problem.

Key Features

  • First book on statistics of polymers in random media.
  • Contents straight away from research labs.
  • Chapters written by foremost experts in the respective fields.
  • Theories, experiments and computer simulations extensively discussed.
  • Includes latest developments in understanding related important topics like DNA unzipping, Travelling salesman problem, etc.
  • Comprehensive index for quick search for keywords.

Readership

Research students and practitioners in (a) Statistical Physics, (b) Theoretical Physics, (c) Physical Chemistry, (d) Polymer Chemistry, (e) Chemical Engineering, etc. Libraries of Basic Research Institutes. Industrial Laboratories on Polymer Chemistry, Chemical Engineering, etc.

Table of Contents

  • Preface
  • Polymers in random media: An introduction
    • 1 POLYMER STATISTICS AND SAW MODEL
    • 2 SAW STATISTICS IN DISORDERED MEDIUM
    • 3 ESTIMATES OF SAW SIZE EXPONENT ON PERCOLATION CLUSTER
    • 4 OUTLOOK
  • Directed polymers and randomness
    • 1 DIRECTED POLYMERS
    • 2 OUTLINE
    • 3 HAMILTONIAN AND RANDOMNESS
    • 4 RELEVANCE OF DISORDER
    • 5 ANALYSIS OF FREE ENERGY: SPECIALTY OF DIRECTED POLYMER
    • 6 OVERLAP
    • 7 UNZIPPING: PURE CASE
    • 8 NATURE OF GROUND STATES AND EXCITATIONS
    • 9 RANDOM INTERACTION - RANI MODEL
    • 10 HIERARCHICAL LATTICE
    • 11 SUMMARY
    • Acknowledgments
    • APPENDIX
  • Self-avoiding walks in constrained and random geometries: Series studies
    • 1 INTRODUCTION
    • 2 SELF-AVOIDING WALKS IN RANDOM GEOMETRIES
    • 3 RANDOM COPOLYMERS
    • 4 SAW IN WEDGES
    • 5 SELF-AVOIDING WALKS IN STRIPS AND SLABS
    • 6 SELF-AVOIDING WALKS IN SQUARES AND CUBES
    • 7 SELF-AVOIDING WALKS ON QUASIPERIODIC TILINGS
    • 8 SELF-AVOIDING WALKS AND POLYGONS ON HYPERBOLIC LATTICES
    • 9 BIOLOGICAL MODELS: SAW AS MODELS OF DNA
    • CONCLUSION
  • Renormalization group approaches to polymers in disordered media
    • 1 INTRODUCTION AND PHENOMENA
    • 2 MODELING THE SYSTEM
    • 3 TREATING THE THEORY BY RENORMALIZATION GROUP METHODS
    • Acknowledgments
  • Linear and branched polymers on fractals
    • 1 INTRODUCTION
    • 2 DEFINITIONS
    • 3 RENORMALIZATION EQUATIONS FOR THE 3-SIMPLEX FRACTAL
    • 4 RECURSION EQUATIONS FOR OTHER FRACTALS
    • 5 SELF-AVOIDING WALKS ON FRACTALS WITH DIMENSION 2 –
    • 6 COLLAPSE TRANSITION IN POLYMERS WITH SELF-ATTRACTION
    • 7 BRANCHED POLYMERS
    • 8 SURFACE ADSORPTION
    • 9 INTERACTING WALKS
    • 10 CONCLUDING REMARKS
    • Acknowledgements
  • Self-avoiding walks on deterministic and random fractals: Numerical results
    • 1 INTRODUCTION
    • 2 DEFINITIONS AND GENERALITIES
    • 3 NUMERICAL SCHEMES
    • 4 SAWs ON DETERMINISTIC FRACTALS
    • 5 SAWs ON RANDOM FRACTALS: PERCOLATION
    • 6 DISCUSSION
    • APPENDIX
  • Localization of polymers in random media: Analogy with quantum particles in disorder
    • 1 INTRODUCTION
    • 2 THE STATISTICS OF A GAUSSIAN CHAIN IN A RANDOM POTENTIAL
    • 3 LOCALIZATION OF POLYMERS IN A MEDIUM WITH FIXED RANDOM OBSTACLES
    • 4 LOCALIZATION AND DELOCALIZATION OF POLYMERS WITH SELF-AVOIDING INTERACTION IN THE PRESENCE OF DISORDER
    • 5 CONCLUSIONS
    • Acknowledgements
  • Geometric properties of optimal and most probable paths on randomly disordered lattices
    • 1 INTRODUCTION
    • 2 DIRECTED OPTIMAL PATHS AT ZERO TEMPERATURE
    • 3 MOST PROBABLE DIRECTED PATHS AT FINITE TEMPERATURES
    • 4 NON-DIRECTED OPTIMAL PATHS AT ZERO TEMPERATURE
    • 5 MOST PROBABLE NON-DIRECTED PATHS AT FINITE TEMPERATURES
    • 6 UNIFIED PICTURE OF OPTIMAL PATHS
    • 7 THE TRAVELLING SALESMAN PROBLEM ON A LATTICE
    • APPENDIX
  • Phenomenology of polymer single-chain diffusion in solution
    • 1 INTRODUCTION
    • 2 THEORETICAL BACKGROUND
    • 3 SELF-DIFFUSION
    • 4 DIFFUSION OF PROBE CHAINS THROUGH MATRIX POLYMER SOLUTIONS
    • 5 OTHER EXPERIMENTAL STUDIES ON POLYMERS IN SOLUTION
    • 6 EXPERIMENTAL STUDIES ON POLYMERS IN POROUS MEDIA AND TRUE GELS
    • 7 ANALYSIS
    • 8 CONCLUSIONS AND DISCUSSION
  • Index

Details

No. of pages:
368
Language:
English
Copyright:
© Elsevier Science 2005
Published:
Imprint:
Elsevier Science
eBook ISBN:
9780080460475
Hardcover ISBN:
9780444517098

About the Editor

Bikas Chakrabarti

Affiliations and Expertise

Saha Institute of Nuclear Physics, Kolkata, India