DOCSLIB.ORG

Simple Models for Complex Nonequilibrium Uids

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

Available online at www.sciencedirect.com Physics Reports 390 (2004) 453–551 www.elsevier.com/locate/physrep Simple models for complex nonequilibrium &uids Martin Kr)ogera;b;∗ aPolymer Physics, Materials Science, ETH Zentrum, 8092 Zurich, Switzerland bInstitut f. Theoretische Physik, Techn. Univ. Berlin, 10623 Berlin, Germany Accepted 15 October 2003 editor: E. Sackmann Abstract This review is concerned with the nonequilibrium dynamics and structure ofcomplex &uids based on simple micro- and mesoscopic physical models which are not rigorously solvable by analytic methods. Special emphasis is placed on the ÿnitely extendable nonlinear elastic (FENE) chain models which account for molecular stretch, bending, and topology. More coarse-grained descriptions such as primitive path models, and elongated particle models are reviewed as well. We focus on their inherently anisotropic material—in particular rheological—properties via deterministic and stochastic approaches. A number ofrepresentative examples are given on how simple (often high-dimensional) models can, and have been implemented in order to enable the analysis ofthe microscopic origins ofthe nonlinear viscoelastic behavior ofpolymeric materials. These examples are shown to provide us with a number ofroutes fordeveloping and establishing coarse-grained (low-dimensional) models devoted to the prediction ofa reduced number ofsigniÿcant material properties. At this stage approximations which allow for an analytical treatment are discussed as well. Concerning the types ofcomplex &uids, we cover the range from&exible to semi&exible polymers in melts and solutions, wormlike micelles, structural suspensions including ferro&uids in ÿeld-induced anisotropic or liquid crystalline phases. c 2003 Elsevier B.V. All rights reserved. PACS: 05.10.−a; 83.10.Mj; 05.20.Dd Keywords: Polymer; Non-Newtonian rheology; Flow; Structure; Dynamics; Viscosities; Orientation; Microscopic models; Mesoscopic models; Computer simulation; Molecular dynamics; Brownian dynamics; Stochastic di?erential equation; Constitutive equation; Kinetic theory; Liquid crystal; Ferro&uid; Semi&exible chain; Network; Tube model; Primitive path; Elongated particle; Order parameter ∗ Corresponding author. Polymer physics, Materials Science, ETH Zentrum, 8092, Zurich, Switzerland. E-mail address: [email protected] (M. Kr)oger). 0370-1573/$ - see front matter c 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.physrep.2003.10.014 454 M. Kroger / Physics Reports 390 (2004) 453–551 Contents 1. Introduction ........................................................................................ 456 2. FENE dumbbell models in inÿnitely diluted solution ..................................................... 463 2.1. FENE-PMF dumbbell in ÿnitely diluted solution .................................................... 464 2.2. Introducing a mean ÿeld potential ................................................................ 465 2.3. Relaxation equation for the tensor of gyration ...................................................... 465 2.4. Symmetry adapted basis ......................................................................... 466 2.5. Stress tensor and material functions ............................................................... 469 2.6. Reduced description ofkinetic models ............................................................ 471 3. FENE chain in dilute solution including hydrodynamic interactions ........................................ 471 3.1. Long chain limit, Cholesky decomposition ......................................................... 473 3.2. NEBD simulation details ........................................................................ 473 3.3. Universal ratios ................................................................................ 474 4. FENE chains in melts ............................................................................... 476 4.1. NEMD simulation method ....................................................................... 478 4.2. Stress tensor ................................................................................... 478 4.3. Lennard-Jones (LJ) units ........................................................................ 479 4.4. Flow curve and dynamical crossover .............................................................. 479 4.5. Characteristic lengths and times .................................................................. 479 4.6. Origin ofthe stress-optic rule (SOR) and its failures ................................................ 482 4.7. Interpretation ofdimensionless simulation numbers .................................................. 485 5. FENE-CB chains .................................................................................... 486 5.1. Conformational statistics of wormlike chains (WLC) ................................................ 486 5.1.1. Functional integrals for WLCs ............................................................. 487 5.1.2. Properties ofWLCs, persistence length, radius ofgyration .................................... 488 5.1.3. Scattering functions ...................................................................... 488 5.2. FENE-C wormlike micelles ...................................................................... 489 5.2.1. Flow-induced orientation and degradation ................................................... 490 5.2.2. Length distribution ....................................................................... 491 5.2.3. FENE-C theory vs simulation, rheology, &ow alignment ...................................... 492 5.3. FENE-B semi&exible chains, actin ÿlaments ....................................................... 493 5.4. FENE-B liquid crystalline polymers ............................................................... 499 5.4.1. Static structure factor ..................................................................... 503 5.5. FENE-CB transient semi&exible networks, ring formation ............................................ 505 6. Primitive paths ...................................................................................... 508 6.1. Doi–Edwards tube model and its improvements .................................................... 509 6.2. Reÿned tube model with anisotropic &ow-induced tube renewal ...................................... 511 6.2.1. Linear viscoelasticity ofmelts and concentrated solutions ..................................... 512 6.3. Nonlinear viscoelasticity, particular closure ........................................................ 513 6.3.1. Example: reÿned tube model, stationary shear &ow ........................................... 514 6.3.2. Example: transient viscosities for rigid polymers ............................................. 514 6.3.3. Example: Doi–Edwards model as a special case ............................................. 515 6.4. Nonlinear viscoelasticity without closure, Galerkin’s principle ........................................ 516 7. Elongated particles .................................................................................. 519 7.1. Director theory ................................................................................. 520 7.2. Structural theories ofsuspensions ................................................................. 520 7.2.1. Semi-dilute suspensions ofelongated particles ............................................... 522 7.2.2. Concentrated suspensions ofrod-like polymers ............................................... 522 7.3. Uniaxial &uids, micro-macro correspondence ....................................................... 522 7.3.1. Application: concentrated suspensions ofdisks, spheres, rods .................................. 523 M. Kroger / Physics Reports 390 (2004) 453–551 455 7.3.2. Example: tumbling ....................................................................... 524 7.3.3. Example: Miesowicz viscosities ............................................................ 524 7.4. Uniaxial &uids: decoupling approximations ......................................................... 526 7.4.1. Decoupling with correct tensorial symmetry ................................................. 527 7.5. Ferro&uids: dynamics and rheology ............................................................... 528 7.6. Liquid crystals: periodic and irregular dynamics .................................................... 531 7.6.1. Landau–de Gennes potential ............................................................... 531 7.6.2. In-plane and out-of-plane states ............................................................ 531 8. Connection between di?erent levels ofdescription ....................................................... 533 8.1. Boltzmann equation ............................................................................. 533 8.2. Generalized Poisson structures ................................................................... 534 8.3. GENERIC equations ............................................................................ 534 8.4. Dissipative particles ............................................................................. 535 8.5. Langevin and Fokker–Planck equation, Brownian dynamics .......................................... 536 8.6. Projection operator methods ...................................................................... 536 8.7. Stress tensors: Giesekus–Kramers–GENERIC ....................................................... 538 8.8. Coarse-graining: from atomistic chains
Recommended publications
  • Contribution to the Historical Development of Macromolecular Chemistry – Exemplified on Cellulose

    Contribution to the Historical Development of Macromolecular Chemistry – Exemplified on Cellulose

    CELLULOSE CHEMISTRY AND TECHNOLOGY CONTRIBUTION TO THE HISTORICAL DEVELOPMENT OF MACROMOLECULAR CHEMISTRY – EXEMPLIFIED ON CELLULOSE PETER ZUGENMAIER Institute of Physical Chemistry, Clausthal University of Technology, D-38678 Clausthal-Zellerfeld, Germany Dedicated to Professor Elfriede Husemann, on the occasion of her 100th birthday in December 2008. She was an admirable and internationally highly recognized scientist and the first director of the Institute of Macromolecular Chemistry (Hermann-Staudinger-Haus) of the Albert-Ludwigs-Universität Freiburg; the foundation of the institute owing to the eminent scientific success and recognition of the work of Hermann Staudinger, leading to the Nobel Prize in the field of macromolecular chemistry. Received October 20, 2009 The development of the structure determination for cellulose and its derivatives as macromolecules is described from the beginning of the 20th century to the 1940s. The first correct presentation of the constitution of cellulose as a linear chain macromolecule of 1-4 linked β-D-anhydroglucopyranose, with the help of organic chemistry, dates from 1928. The size and shape of cellulose molecules still remained a controversial topic for some time. On the one hand, there were proposals of micelles i.e. aggregates of cyclic mono- or oligoanhydroglucose or micelles of small macromolecules of 30-50 glucose units. On the other hand, cellulose was seen as large macromolecules with more than 3000 glucose units for structures considered in solution as well as in fibres. The final clarification of the cellulose structure as a semi-flexible macromolecule of high molecular weight was extremely hindered by the inadequate interpretation of experimental results. Later, additional experimental and theoretical methods led to a consistent picture of the cellulose structure with high precision.
  • Polyelectrolytes

    Polyelectrolytes

    POLYELECTROLYTES A. KATCHALSKY Weizmann Institute of Science, Rehovot, Israel ABSTRACT A general review of the behaviour of polyelectrolyte systems is presented. It deals primarily with the colligative properties of aqueous solutions of polyelectrolytes in salt-free and salt-containing mixtures, as well as with several transport phenomena (such as conductance, transference and diffusion). The theoretical model underlying this account is that of charged macromolecules surrounded by a dense cylindrical counterion atmosphere. This model proves a quantitative description of osmotic pressure, of activity coefficients, of the heat of dilution and of Donnan distribution between polyelectrolyte solutions (or gels) and an external salt solution. For the analysis of transport phenomena a non-equilibrium thermodynamic treatment was introduced which allows the identification of straight and coupling phenomena in polyelectrolyte systems. This anslysis led to an explicit consideration of relaxation and electrophoretic effects in polyelectrolytes. Some attention was paid to the biophysical significance of polyelectrolyte interactions, and in particular to the combination of polyelectrolytes with divalent ions and to the complex formation of polyelectrolytes with other charged polyions. These interactions play an important role in the organization of nucleic acids and in their combination with basic proteins. Since the double- or triple-stranded complexes of some polynucleotides exhibit hysteresis— related to the conformation of the complex—the last part of the paper is devoted to the discussion of molecular hysteresis and its significance as a biomolecular memory imprint. 1. INTRODUCTION 1.1 Polyelectrolyte research is concerned with the study of the electro- chemical properties of charged polymers; it may be regarded as a direct descendant of the classical colloid chemistry of hydrophilic biocolloids.
  • Research Journal of Pharmaceutical, Biological and Chemical Sciences

    Research Journal of Pharmaceutical, Biological and Chemical Sciences

    ISSN: 0975-8585 Research Journal of Pharmaceutical, Biological and Chemical Sciences A Review: Conducting Polymers and Their Applications. Nirmala Kumari Jangida*, Narendra Pal Singh Chauhanb ,Kiran Meghwala, Rakshit Ametac , and Pinki B Punjabia. aDepartment of Chemistry, Mohanlal Sukhadia University, Udaipur – 313001 (Raj.), India bDepartment of Chemistry, B. N. P. G. College, Mohanlal Sukhadia University, Udaipur – 313001 (Raj.), India cDepartment of Chemistry, Pacific College of Basic and Applied Sciences, PAHER University, Udaipur – 313001 (Raj.), India ABSTRACT During the past two decades, both fundamental and applied research in conducting polymers like polyaniline, polyacetylene polythiophene and polypyrrole has grown enormously. Conducting polymers are unique due to its ease of synthesis, environmental stability and simple doping/dedoping chemistry. polyaniline is one of the most studied conducting polymers of the past 50 years. The most common chemical synthesis of polyaniline is by oxidative polymerization with ammonium per sulfate as an oxidant. Conducting polymers owing to its ease of synthesis, remarkable environmental stability and high conductivity in the doped form has remained thoroughly studied due to their varied applications in fields like biological activity, drug release systems, rechargeable batteries and sensors. Keywords: Doping, Effect on conductivity, conducting polymers, applications *Corresponding author May-June 2014 RJPBCS 5(3) Page No. 383 ISSN: 0975-8585 INTRODUCTION Perhaps the first modern example of polymer science is Henri Braconnot's work in the 1830s. He and his coworkers developed derivatives of the natural polymer cellulose, producing new, semi-synthetic materials, such as celluloid and cellulose acetate. The term “polymer” was firstly coined by Berzelius. Friedrich Ludersdorf and Nathaniel Hayward discovered that the addition of sulfur to raw natural rubber (polyisoprene) helped in the prevention of material from becoming sticky.
  • Rubber Science a Modern Approach Rubber Science Yuko Ikeda • Atsushi Kato Shinzo Kohjiya • Yukio Nakajima

    Rubber Science a Modern Approach Rubber Science Yuko Ikeda • Atsushi Kato Shinzo Kohjiya • Yukio Nakajima

    Yuko Ikeda · Atsushi Kato Shinzo Kohjiya · Yukio Nakajima Rubber Science A Modern Approach Rubber Science Yuko Ikeda • Atsushi Kato Shinzo Kohjiya • Yukio Nakajima Rubber Science A Modern Approach 123 Yuko Ikeda Shinzo Kohjiya Center for Rubber Science and Technology, Kyoto University Faculty of Molecular Chemistry and Kyoto Engineering Japan Kyoto Institute of Technology Kyoto Yukio Nakajima Japan Department of Mechanical Science and Engineering, School of Advanced Atsushi Kato Engineering Department of Automotive Analysis Kogakuin University NISSAN ARC, LTD. Hachioji, Tokyo Yokosuka, Kanagawa Japan Japan ISBN 978-981-10-2937-0 ISBN 978-981-10-2938-7 (eBook) https://doi.org/10.1007/978-981-10-2938-7 Library of Congress Control Number: 2017948624 © Springer Nature Singapore Pte Ltd. 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made.
  • 2008 APS March Meeting New Orleans, Louisiana

    2008 APS March Meeting New Orleans, Louisiana

    2008 APS March Meeting New Orleans, Louisiana http://www.aps.org/meetings/march/index.cfm i Monday, March 10, 2008 8:00AM - 11:00AM — Session A8 DFD: Colloidal Self-Assembly I Morial Convention Center RO6 8:00AM A8.00001 Directed Self-Assembly of Spherical Particles NATALIE ARKUS, GUANGNAN MENG, VINOTHAN MANOHARAN, MICHAEL BRENNER, Harvard University — We examine the kinetics and energetics of self-assembly in systems containing a small number of spherical colloidal nanoparticles using a combination of theory, simulation, and experiment. We then explore how the addition of spherically symmetric binding specificity can be used to direct the self-assembly of a given structure. Using graph theoretic, numerical, and algebraic geometric techniques, we denumerate all possible packings for a system of n particles. We map out the energy landscape of these packings, which is determined not only by the value of the potential energy at these minima, but also by the vibrational normal modes of the structures. Experiments for a 6 particle system show that the likelihood of a given packing follows this expected equilibrium distribution. To explore the kinetics of packing formation, we simulate the self-assembly of these systems in the irreversible binding limit. For the 6 particle system, this reveals that the kinetics required to form one of the packings is highly unlikely, resulting in the other packing forming with 100% probability. With the addition of binding specificity however, we can cause the unlikely packing to form with 100% probability. We show how the addition of binding specificity effects the energetic landscape of these systems, and that it alone is sufficient to direct self-assembly.