This book provides an introduction to lattice models of polymers. This is an important topic both in the theory of critical phenomena and the modelling of polymers. The first two chapters introduce the basic theory of random, directed and self-avoiding walks. The next two chapters develop and expand this theory to explore the self-avoiding walk in both two and three dimensions. Following chapters describe polymers near a surface, dense polymers, self-interacting polymers and branched polymers. The book closes with discussions of some geometrical and topological properties of polymers, and of self-avoiding surfaces on a lattice. The volume combines results from rigorous analytical and numerical work to give a coherent picture of the properties of lattice models of polymers. This book will be valuable for graduate students and researchers working in statistical mechanics, theoretical physics and polymer physics. It will also be of interest to those working in applied mathematics and theoretical chemistry.

This book surveys and explains the mathematical methods and techniques used in the study of lattice models of polymers in solvents. The techniques include the self-avoiding walk and its related models including animal and tree graphs, surfaces and vesicles. The important feature in all thesemodels in the contribution of conformational degrees of freedom to the free energy, and this leads on to the idea of a tricritical point. The book explores the theory of tricriticality showing how it can be used to interpret the limiting free energy and generating functions. Density function andpattern theorems are also discusssed and finally these ideas are applied to models of collapsing and adsorbing walks, to composite polygons and crumpling surfaces.

The self-avoiding walk is a classical model in statistical mechanics, probability theory and mathematical physics. It is also a simple model of polymer entropy which is useful in modelling phase behaviour in polymers. This monograph provides an authoritative examination of interacting self-avoiding walks, presenting aspects of the thermodynamic limit, phase behaviour, scaling and critical exponents for lattice polygons, lattice animals and surfaces. It also includes a comprehensive account of constructive methods in models of adsorbing, collapsing, and pulled walks, animals and networks, and for models of walks in confined geometries. Additional topics include scaling, knotting in lattice polygons, generating function methods for directed models of walks and polygons, and an introduction to the Edwards model. This essential second edition includes recent breakthroughs in the field, as well as maintaining the older but still relevant topics. New chapters include an expanded presentation of directed models, an exploration of methods and results for the hexagonal lattice, and a chapter devoted to the Monte Carlo methods.

Vols. for 1963- include as pt. 2 of the Jan. issue: Medical subject headings.

The proceedings of this workshop contains 5 important papers by S A Edwards on the Edwards Model and includes discussions on recent theoretical developments in polymer physics.A few decades ago, polymers were not considered part of conventional physics. However, the scenario changed drastically in the sixties and seventies with the introduction of path integral methods, fields theory in the n → limits, and renormalization group approach. A vital step in this progress is the path integral Hamiltonian that S F Edwards proposed in 1965-66 to study a single chain. This model now called the Edwards model, is considered to be the minimal model for polymers, and it has been phenomenal in unraveling the universal properties of polymers, be it a single chain or many, equilibrium or dynamics. It has now crossed the boundary of polymers and is finding applications through appropriate generalizations in many other problems.