高分子综述报道：Some geometrical and topological problems in polymer physics
Contents1. Introduction 2545.4. Probability of knotting and the role of2. Relevance of entanglements (somefinite size e?ects 299experimental facts and related theoretical6. Single chain problems which involveworks) 258geometrical and topological constraints 3002.1. Some properties of ring polymers in dilute6.1. Semi-flexiblepolymerchaininthenematicsolutions and in melts 258environment 3002.2. Polymer dynamics and topology 2606.2. Semi-flexible polymers confined between2.3. Polymer networks 264the parallel plates and in the half space 3053. Single chain problems which involve6.3. Polymers confined into semi-flexibleentanglements (general considerations) 267tubes 3073.1. Topological persistence length and the6.4. Configurational statistics of the planarprobability of knot formation 267random walks restricted by the area3.2. Knot complexity and the average writhe 268constraint 3103.3. The unknotting number and the number7. Knot complexity — detailed treatment 312of distinct knots for polymer of given7.1. Calculation of the topological persistencelength N 270length 3124. Methods of describing knots (links) 2717.2. Calculation of the averaged writhe 3154.1. Di?erential geometric approach 2717.3. Calculation of the knot complexity 3174.2. Path integral approach via Abelian7.4. Calculationofthe unknottingnumberandand non-Abelian Chern—Simons fieldthe number of distinct knots as a functiontheory 273of polymers length N 3224.3. Algebraic (group-theoretic) description of7.5. Some physical applications 323knots (links) via knot polynomials 2767.6. Link energy and the probability of4.4. Unifyinglinkbetweendi?erentapproaches 283entanglement between two ring polymers 3255. Probability of knotting: the detailed treatment 2858. Polymer dynamics: an interplay between5.1. Planar Brownian motion in the presencetopology and geometry 331of a single hole. The role of finite size8.1. Statistical mechanics of a melt of polymere?ects 285rings 3315.2. Quantum groups and planar Brownian8.2. Statistical mechanics of planar rings in anmotion 289array of obstacles (the replica approach) 3335.3. Jones polynomial, Temperley—Lieb8.3. Statistical mechanics of planar rings in analgebra and statistical mechanics of knotsarray of obstacles (the Riemann surface(links) 293approach) 3370370-1573/98/$19.00 Copyright 1998 Elsevier Science B.V. All rights reservedPII S0370-1573(97)00081-1
A.L. Kholodenko, T.A. Vilgis /Physics Reports 298 (1998) 251—370 2538.4. Statistical mechanics of planar rings in an Appendix A 359array of obstacles (QHE approach) 348 A.1. PlanarBrownianmotioninthepresenceof8.5. Connections with theories of quantum two holes 359chaos 355 A.2. SpatialBrownianmotioninthepresenceof8.6. Connections with theories of mesoscopic knots (links) 361systems 357 References 364
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