Yamakawa Helical Wormlike Chains in Polymer Solutions

Erscheinungsjahr 2012
ISBN: 978-3-642-60817-9
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 420 Seiten, eBook

A new and general model, called the "helical wormlike chain", for both flexible and semi-flexible polymer chains is presented. Statistical-mechanical, hydrodynamic, and dynamic theories of their solution properties are developed on the basis of this model. There are also given analysis of recent experimental data by the use of these theories for flexible polymers over a wide range of molecular weight, including the oligomer region, and for semi-flexible polymers, including biological macromolecules such as DNA. The book includes a reasonable number of theoretical equations, tables, figures, and computer-aided forms, enough to provide understanding of the basic theory and to facilitate its application to experimental data for the polymer molecular characterization.

Zielgruppe

Research

Autoren/Hrsg.

Yamakawa, Hiromi

Inhaltsverzeichnis

1 Introduction.- 1.1 Historical Survey.- 1.2 Scope.- References.- 2 Models for Polymer Chains.- 2.1 Discrete Models.- 2.2 Continuous Models.- References.- 3 Chain Statistics — Wormlike Chains.- 3.1 Definition of the Model.- 3.2 Diffusion Equations.- 3.3 Moments.- 3.4 Distribution Functions.- Appendix 3.A Path Integrals.- Appendix 3.B Spherical Harmonics and the Free-Particle Green Function.- Appendix 3.C Modified Wormlike Chains.- Appendix 3.D Wormlike Rings.- References.- 4 Chain Statistics — Helical Wormlike Chains.- 4.1 Formulation of the Model.- 4.2 Diffusion Equations.- 4.3 Moments.- 4.4 Angular Correlation Functions.- 4.5 Helical Nature of the Chain.- 4.6 Distribution Functions.- 4.7 Approximations.- 4.8 Some Other Topics.- Appendix 4.A Generalization and Other Related Models.- Appendix 4.B Corresponding Discrete Chains.- Appendix 4.C Wigner D Functions and 3-j Symbols.- References.- 5 Equilibrium Properties.- 5.1 Mean-Square Radius of Gyration..- 5.2 Scattering Function.- 5.3 Anisotropic Light Scattering—Mean-Square Optical Anisotropy.- 5.4 Electrical Properties.- Appendix 5.A Chain-Thickness Correction.- Appendix 5.B Spherical Vectors and Tensors.- Appendix 5.C Proof of Nagai’s Theorem.- References.- 6 Transport Properties.- 6.1 General Consideration of Polymer Hydrodynamics.- 6.2 Hydrodynamic Models.- 6.3 Translational Friction Coefficient.- 6.4 Intrinsic Viscosity.- 6.5 Analysis of Experimental Data.- 6.6 Ring Polymers.- Appendix 6.A Transport Coefficients of Spheroid-Cylinders.- Appendix 6.B Excess Stress Tensor for the Touched-Bead Model.- References.- 7 Applications to Circular DNA.- 7.1 Ring-Closure Probabilities.- 7.2 Topoisomer Statistics.- 7.3 Iranslational Friction Coefficient of Topoisomers.- References.- 8 Excluded-Volume Effects.- 8.1End-Distance and Gyration-Radius Expansion Factors.- 8.2 Viscosity- and Hydrodynamic-Radius Expansion Factors.- 8.3 Second Virial Coefficient.- 8.4 Third Virial Coefficient.- 8.5 Some Remarks.- Appendix 8.A Mean-Square Electric Dipole Moment.- Appendix 8.B Determination of the Virial Coefficients for Oligomers.- References.- 9 Chain Dynamics.- 9.1 General Consideration of Polymer Dynamics.- 9.2 Conventional Bond Chains.- 9.3 Dynamic Helical Wormlike Chains.- 9.4 Diffusion Equations.- 9.5 Eigenvalue Problems and Time-Correlation Functions.- Appendix 9.A Fluctuating Hydrodynamic Interaction.- References.- 10 Dynamical Properties.- 10.1 Dielectric Relaxation.- 10.2 Nuclear Magnetic Relaxation.- 10.3 Fluorescence Depolarization.- 10.4 Dynamic Depolarized Light Scattering.- 10.5 First Cumulant of the Dynamic Structure Factor.- 10.6 Some Remarks.- References.- Glossary of Abbreviations..- Author Index..