Helical Wormlike Chains in Polymer Solutions

Erscheinungsjahr 1997
ISBN: 978-3-540-62960-3
Verlag: Springer

Buch, Englisch, 420 Seiten, Book, Format (B × H): 155 mm x 235 mm, Gewicht: 785 g

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.- 2.1.1 Average Chain Dimensions.- 2.1.2 Random-Flight Chains — The Gaussian Chain.- 2.1.3 Freely Rotating Chains.- 2.1.4 Chains with Coupled Rotations— The Rotational Isomeric State Model.- 2.2 Continuous Models.- References.- 3 Chain Statistics — Wormlike Chains.- 3.1 Definition of the Model.- 3.2 Diffusion Equations.- 3.2.1 Green Functions.- 3.2.2 Fokker—Planck Equations.- 3.2.3 Path Integrals and Formal Solutions.- 3.3 Moments.- 3.3.1 ?(R?uo)n?.- 3.3.2 ?R2m?.- 3.4 Distribution Functions.- 3.4.1 Asymptotic Behavior — Daniels-Type Distributions.- 3.4.2 Near the Rod Limit.- 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.- 4.2.1 Path Integrals and Fokker—Planck Equations.- 4.2.2 The Free-Particle Green Function.- 4.2.3 Formal Solutions.- 4.3 Moments.- 4.3.1 ?(R?uo)n?.- 4.3.2 ?R2m? and ?S2?.- 4.3.3 Persistence Vector.- 4.4 Angular Correlation Functions.- 4.4.1 Explicit Expressions for ? = 0.- 4.4.2 The Rotational Isomeric State Model.- 4.4.3 Symmetry Relations.- 4.4.4 Numerical Results.- 4.5 Helical Nature of the Chain.- 4.6 Distribution Functions.- 4.6.1 General Developments.- 4.6.2 Daniels-Type Distributions.- 4.6.3 Moment-Based Distributions.- 4.6.4 Convergence.- 4.7 Approximations.- 4.7.1 Weighting Function Method.- 4.7.2 Epsilon Method.- 4.7.3 Convergence.- 4.8 Some Other Topics.- 4.8.1 Multivariate Distribution Functions, Etc.- 4.8.2 Temperature Coefficients of (R2).- 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.- 5.1.1 Basic Equations and Model Parameters.- 5.1.2 Chain Stiffness and Local Chain Conformations.- 5.1.3 HW Monte Carlo Chains.- 5.2 Scattering Function.- 5.2.1 Scattering Function for the Chain Contour.- 5.2.2 Comparison with the RIS Model.- 5.2.3 Effects of Chain Thickness.- 5.2.4 Comparison with Experiment.- 5.3 Anisotropic Light Scattering—Mean-Square Optical Anisotropy.- 5.3.1 Basic Equation.- 5.3.2 Components of the Scattered Intensity.- 5.3.3 Mean-Square Optical Anisotropy.- 5.3.4 Isotropic Scattering Function.- 5.3.5 Near the Rod Limit.- 5.4 Electrical Properties.- 5.4.1 Mean-Square Electric Dipole Moment.- 5.4.2 Electric Birefringence.- 5.4.3 Electric Dichroism.- 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.- 6.2.1 Cylinder Model.- 6.2.2 Touched-Bead Model.- 6.3 Translational Friction Coefficient.- 6.3.1 Cylinder Model.- 6.3.2 Touched-Bead Model.- 6.4 Intrinsic Viscosity.- 6.4.1 Cylinder Model.- 6.4.2 Touched-Bead Model.- 6.5 Analysis of Experimental Data.- 6.5.1 Basic Equations and Model Parameters.- 6.5.2 Reduced Hydrodynamic Volume and Radius.- 6.5.3 Negative Intrinsic Viscosity.- 6.5.4 Draining Effect.- 6.6 Ring Polymers.- 6.6.1 Translational Friction Coefficient.- 6.6.2 Intrinsic Viscosity.- 6.6.3 Application to DNA.- 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.- 7.1.1 Definitions.- 7.1.2 Linking-Number-Dependent Ring-Closure Probability.- 7.1.3 Ring-Closure Probability with the End Orientations Specified.- 7.1.4 Other Ring-Closure Probabilities.- 7.1.5 Comparison with Experiment.- 7.2 Topoisomer Statistics.- 7.2.1 Basic Concepts and Equations.- 7.2.2 Distribution of the Writhe.- 7.2.3 Moments of the Writhe.- 7.2.4 Distribution of the Linking Number.- 7.2.5 Mean-Square Radii of Gyration.- 7.3 Iranslational Friction Coefficient of Topoisomers.- References.- 8 Excluded-Volume Effects.- 8.1 End-Distance and Gyration-Radius Expansion Factors.- 8.1.1 Perturbation Theory.- 8.1.2 Ring-Closure Probabilities and the First-Order Coefficient.- 8.1.3 Effects of Chain Stiffness — Quasi-Two-Parameter Scheme.- 8.1.4 Comparison with Experiment.- 8.2 Viscosity- and Hydrodynamic-Radius Expansion Factors.- 8.2.1 Effects of Chain Stiffness and Fluctuating Hydrodynamic Interaction.- 8.2.2 Comparison with Experiment.- 8.3 Second Virial Coefficient.- 8.3.1 Perturbation Theory.- 8.3.2 Effects of Chain Stiffness and Local Chain Conformations.- 8.3.3 Effects of Chain Ends.- 8.3.4 Comparison with Experiment.- 8.4 Third Virial Coefficient.- 8.4.1 Perturbation Theory for the Random-Flight Chain.- 8.4.2 Effects of Chain Stiffness and Three-Segment Interactions.- 8.4.3 Effects of Chain Ends.- 8.5 Some Remarks.- 8.5.1 Near the ? Temperature.- 8.5.2 More on Three-Segment Interactions.- 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.- 9.2.1 General Formulation — The Fixman—Kovac Chain.- 9.2.2 Some Further Remarks.- 9.3 Dynamic Helical Wormlike Chains.- 9.4 Diffusion Equations.- 9.4.1 Space of Bond and Infinitesimal Rotation Vectors.- 9.4.2 Space of Euler Angles — Local Motions.- 9.4.3 Space of Euler Angles — Global Motions.- 9.4.4 Approximation to the Constraining Matrix.- 9.4.5 Formal Solutions.- 9.5 Eigenvalue Problems and Time-Correlation Functions.- 9.5.1 Standard Basis Set.- 9.5.2 Crude Subspace Approximation.- 9.5.3 Block-Diagonal Approximation.- 9.5.4 Higher-Order Subspace Approximation.- Appendix 9.A Fluctuating Hydrodynamic Interaction.- References.- 10 Dynamical Properties.- 10.1 Dielectric Relaxation.- 10.1.1 Formulation.- 10.1.2 Eigenvalue Spectra and Mode Analysis.- 10.1.3 Comparison with Experiment.- 10.2 Nuclear Magnetic Relaxation.- 10.2.1 Formulation.- 10.2.2 Eigenvalue Spectra and Amplitudes.- 10.2.3 Spectral Densities.- 10.2.4 Comparison with Experiment.- 10.3 Fluorescence Depolarization.- 10.3.1 Formulation.- 10.3.2 Comparison with Experiment.- 10.4 Dynamic Depolarized Light Scattering.- 10.4.1 Formulation.- 10.4.2 Comparison with Experiment.- 10.4.3 Correlation with Nuclear Magnetic Relaxation.- 10.5 First Cumulant of the Dynamic Structure Factor.- 10.5.1 Formulation.- 10.5.2 Comparison with Experiment.- 10.6 Some Remarks.- 10.6.1 Elementary Processes of Chain Motions.- 10.6.2 Dynamic vs Static Chain Stiffness.- 10.6.3 Dynamic Intrinsic Viscosity.- References.- Glossary of Abbreviations.- Author Index.