Soft Matter, Volume 1 Polymer Melts and Mixtures

by Gompper, Gerhard; Schick, Michael

• ISBN13: 9783527305001
• ISBN10: 3527305009
• Edition: 1st
• Format: Hardcover
• Copyright: 2006-02-10
• Publisher: Wiley-VCH

Summary

Soft Matter encompasses a wide range of systems of varying components,including synthetic and biological polymers, colloids, and amphiphiles. The distinguishing features of these systems is their characteristic size, which is much larger than that of their atomic counterparts, and their characteristic energy, which is much smaller. Because of their ability to assemble themselves into complex structures, they form the major components of biological systems and technological applications. "Soft matter" is a unique series of books that strongly stresses the interdisciplinary character of this thriving field of research. The first volume offers a detailed description of the physical aspects of polymers, such as polymer dynamics in melts, and complex structure and phase behavior of mixtures of homopolymers with block copolymers. With contributions from highly acclaimed experts, it differs from the very specialized or proceedings-type books currently available. Aimed at both graduates and researchers, the book is an introduction to soft matter physics as well as a concise reference for those already working in this field.

Author Biography

<b>Gerhard Gompper</b> studied Physics at the Ludwig-Maximilians-Universitaet Muenchen, where he received his Physics Diploma and Ph.D. in Physics in the group of Herbert Wagner. After a postdoctoral stay with Michael Schick at the University of Washington in Seattle, he returned to Munich to earn his habilitation. An assignment as a staff scientist at the Max-Planck-Institute for Colloid- and Interface Science in Berlin-Teltow from 1994 to 1999 preceded his joint appointment as a director at the Institute for Solid-State Physics at the Research Center Juelich and as a full professor at the University of Cologne. He was recently honored with the Erwin-Schroedinger-Award for interdisciplinary research on the efficiency-boosting effect of amphiphilic polymers in microemulsions. <p> <b>Michael Schick</b> obtained his Ph.D. in Physics at Stanford University under Felix Bloch. After a post-doctoral position with Paul Zilsel at Case Western Reserve University, he joined the faculty of the University of Washington in 1969. His interests have included phase transitions in lower dimensional systems, wetting phenomena, microemulsions, the phase behavior of block copolymers and of lipids, and the fusion of biological membranes. He has been honored with Fellowship in the American Physical Society, and a Humboldt Foundation Research Award spent at the Ludwig-Maximilians-Universitaet Muenchen where he worked with Gerhard Gompper. He is married to the scholar of Norwegian Literature, Katherine Hanson, with whom he lives on their floating home in Seattle's Portage Bay. He is an avid, amateur cellist.

Table of Contents

An Introduction to Soft Matter	1	(16)
Gerhard Gompper
Michael Schick
Polymer Dynamics in Melts	17	(70)
Andreas Wischnewski
Dieter Richter
Introduction	18	(2)
What is a Polymer?	20	(5)
Synthesis of Polymers	21	(4)
Experimental Techniques	25	(13)
Neutron Scattering	25	(11)
Rheology	36	(2)
Static Properties	38	(7)
Brownian Motion, Viscous and Entropic Forces: the Rouse Model	45	(10)
Experimental Studies of the Rouse Model	49	(6)
Topological Constraints: the Tube Concept	55	(14)
Validating the Tube Concept on a Molecular Scale	59	(10)
Limiting Mechanisms for Reptation I: CLF	69	(8)
Limiting Mechanisms for Reptation II: CR	77	(4)
Summary and Outlook	81	(6)
Self-Consistent Field Theory and Its Applications	87	(92)
Mark W. Matsen
Introduction	87	(4)
Gaussian Chain	91	(5)
Gaussian Chain in an External Field	96	(6)
Strong-Stretching Theory (SST): the Classical Path	102	(1)
Analogy with Quantum/Classical Mechanics	103	(2)
Mathematical Techniques and Approximations	105	(9)
Spectral Method	106	(1)
Ground-State Dominance	107	(2)
Fourier Representation	109	(2)
Random-Phase Approximation	111	(3)
Polymer Brushes	114	(19)
SST for a Brush: the Parabolic Potential	115	(2)
Path-Integral Formalism for a Parabolic Potential	117	(3)
Diffusion Equation for a Parabolic Potential	120	(1)
Self-Consistent Field Theory (SCFT) for a Brush	121	(4)
Boundary Conditions	125	(2)
Spectral Solution to SCFT	127	(6)
Polymer Blends	133	(19)
SCFT for a Polymer Blend	135	(2)
Homogeneous Phases and Macrophase Separation	137	(3)
Scattering Function for a Homogeneous Blend	140	(3)
SCFT for a Homopolymer Interface	143	(2)
Interface in a Strongly Segregated Blend	145	(3)
Grand-Canonical Ensemble	148	(4)
Block Copolymer Melts	152	(15)
SCFT for a Diblock Copolymer Melt	152	(2)
Scattering Function for the Disordered Phase	154	(2)
Spectral Method for the Ordered Phases	156	(7)
SST for the Ordered Phases	163	(4)
Current Track Record and Future Outlook for SCFT	167	(2)
Beyond SCFT: Fluctuation Corrections	169	(3)
Appendix: The Calculus of Functionals	172	(7)
Comparison of Self-Consistent Field Theory and Monte Carlo Simulations	179	(104)
Marcus Muller
Introduction	180	(2)
Polymer Blends	182	(63)
Coarse-Grained Polymer Models	182	(5)
A Coarse-Grained Model for Binary Polymer Blends	187	(3)
Self-Consistent Field (SCF) Theory and Fluctuation Effects	190	(23)
Identifying the Effective Flory--Huggins Parameter, χ	213	(12)
Single-Chain Conformations in the Bulk	225	(4)
Interfaces	229	(16)
Liquid--Vapor Interfaces	245	(21)
Formalism	246	(2)
Approximating the Excess Interaction Free-Energy Functional ΔFex	248	(13)
Comparison to Computer Simulations	261	(5)
Outlook	266	(1)
Appendix	267	(16)
Fluctuations in the Spatially Homogeneous Phase	267	(4)
Alternative Derivation of the SCF Equations for Liquid--Vapor Systems	271	(12)
Index	283