Rigid Polymer Networks By .S M. Aharoni, .S .F Edwards With 15 Figures galreV-regnirpS Berlin Heidelberg NewYork London Paris Tokyo HongKong Barcelona Budapest Dr. S. M. Aharoni Polymer Science Laboratory Corporate Research & Technology AlliedSignal Inc. Morristown, NJ 07962 / USA Sir Sam Edwards Cavendish Professor of Physics University of Cambridge Cambridge CB3 OHE / UK ISBN 3-540-58340-8 galreV-regnirpS Berlin Heidelberg NewYork ISBN 0-387-58340-8 galreV-regnirpS NewYork Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in databanks. Duplication of this publication or parts thereof is onlypermitted under the provisions of the German Copyright Law of September 9,1965, in its current version, and a copyright fee must always be paid. © Springer-Verlag Berlin Heidelberg 1994 Library of Congress Catalog Card Number 61-642 Printed in Germany The use of registered names, trademarks, 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. Typesetting: Macmillan India Ltd., Bangalore-25 Printing: Saladruck, Berlin; Bookbinding: Liideritz & Bauer, Berlin SPIN: 10470558 02/3020 5 4 3 2 1 0 Printed on acid-free paper Editors Department Akihiro Abe, Prof. of Institute Tokyo Chemistry, Industrial of Polytechnics, 3851 Iiyama, Atsugi-shi Japan 243-02, Macromol6cules, Ies sur Recherches de Centre Benoit, CNRS, Prof. Henri ,6 rue Boussingault, 67083 Strasbourg Cedex, France Materialforschungszentrum, Freiburger Cantow, Prof. Hans-Joachim Stefan Meier-Str. 3 la, Br., FRG . D-79104 Freiburg i 4, Mezzocannone Chimica, Via di Dipartimento Napoli, di Corradini, Paolo Prof. Universitb. 80134 Napoli, Italy Institute Du~ek, Prof. Karel of Academy Czech Chemistry, Macromolecular of Sciences, 60261 Prague 616, Czech Republic Edwards, University ofProf. Sam Department Cambridge, of Cavendish Physics, Laboratory, Cambridge Madingley Road, 3BC OHE, UK Prof. Fujita, Hiroshi 53 Kyoto Shimotakedono-cho, Shichiku, Kita-ku, Japan 306 Chemie, Sektion Dresden, Universitht Technische Gl0ckner, Gottfried Prof. Mommsenstr. ,31 D-01069 Dresden, FRG Prof. .rD Lehrstuhl H~cker, Hartwig fur Textilchemie und Chemie, Makromulekulare Veltmanplatz Aachen, RWTlq FRG Aachen, D-52062 ,8 Organische fur Institut Jena, Friedrich-Schiller-Universit~it H6rhold, Hans-Heinrich Prof. und Polymerchemie, Organische Humboldtstr. Makromolekulare Chemie, Lehrstuhl ,01 D-07743 Jena, FRG Prof. Hans-Henning de F6d6rale Polytechnique Ecole Polym~res, de Laboratoire Kausch, Lausanne, Switzerland 1015 Lausanne, MX-D, CH- Joseph Prof. Institute of Kennedy, .P University The Science, Polymer of Akron, Akron, Ohio 44 325, USA Jack Prof. .L Department Koenig, of Western Reserve Case Science, Macromolecular University, School of Cleveland, Engineering, HO USA 44106, Ormskirk, Laboratories, Lathom D & Prof. plc. R Brothers Anthony Ledwith, Pilkington Lancashire SUF, L40 UK Prof. .J Polytechnic Laboratory, Virginia Interfaces Materials and McGrath, Polymer .E and State University Blacksburg, Virginia 24061, USA Physique de Superieure Monnerie, Ecole Prof. Lucien et Industrielles, Chimie de Laboratoire de Physico-Chimie, et Macromol6culaire Structurale ,01 rue Vauquelin, 75231 Paris Cedex 05, France Okamura, Prof. Seizo .,o4N2 Japan 606, Minamigoshi-Machi Okazaki, Sakyo-Ku, Kyoto Overberger, Department G. Charles Prof. of University The Chemistry, of Michigan, Ann Arbor, Michigan 48109, USA Ringsdorf, Prof. Helmut Institut Johannes-Gutenberg-Universittit, Chemie, Organische fiir J.-J.-Becher Weg 18-20, D-55t28 Mainz, FRG Park International, Research Prof. Takeo Inc. Saegusa, Kyoto KRI ,71 Minamima- Chudoji chi, Japan Shimogyo-ku 600 Kyoto Prof. University of C. Salamone, .J Department Lowell, of College Chemistry, of Pure Science, Applied and One USA 01854, MA Lowell, Avenue, University University Schrag, .John LProf. of Wisconsin, Department of Chemistry, 1011 University Avenue. USA Madison, Wisconsin 53706, Ackermannweg Polymerforschung, Max-Planck-lnstitut fiir Wegner, G. Prof. ,01 Postfach 3148, D-55128 Mainz, FRG Preface Synthetic rigid polymer networks comprise part for the thermosetting class of polymers. Some members have now been in use for about a hundred years. These first pioneers, such as the phenolf ormaldehydes and furfurals, owed theipro pularity to a combination of several important features: monomer availability, ease and speed of processing, low cost of monomers, process and end-products, ability to be filled by various fillers, and a very desirable combination of good mechanical properties, high gloss surface, and excellent electrical insulation. As time progressed, the potential users elevated the performarnecqeu irements of the rigid polymer networks demanding ever-increasing thermal stability and mechanical properties. In response to these increasing expectations, novel rigid polymer networks were created with increasing fractions of thermally stable and mechanically robust moieties, initially as single rings and later as condensed aromatic groups. Laterly, rigid polymer networks whose stiff segments are liquid crystalline in nature were also introduced. In this case, very high modulus and strength may be obtained by first orienting the segments in the desired direction and then setting them in their final form by the addition or in-situ creation of rigid junctions. As we delved into the subject matter, we were struck by the huge amount of literature dealing with various synthetic aspects of rigid polymer networks, the smaller number of publications dealing with correlations between the molecular structure of the networks and commercially desirable properties, and thef ars maller number of publications, devoted to fundamental theoretical description of these networks, their properties, evolution and final structure, and the unique synthetic limitations imposed by the inherent rigidity of the structural units of the growing networks. The remarkably broad range of rigid polymer networks and the great ingenuity invested in their creation stood in stark contrast to the dearth of theoretical interest. It may be that the factor which made them theoretically less than popular is that so much of the literature in the field is patent literature, andt he non-Gaussian, non-elastomeric nature of the rigid polymer networks, both alien to most theoreticians. In this work we aim, therefore, to presentt he reader with an up-to-date overview of the field of rigid polymer networks with many of its synthetic complexities and challenges, and to whet the appetite of theoreticians and encourage them to solve the many fascinating theoretical problems presently existing in the field. S.M. Aharoni S.F. Edwards Table of Contents List of Symbols .................................. xiii 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Definitions ................................... 1 1.2 General Classification of Liquid-Crystal Polymers and Networks ................................. 7 1.2.1 Definition of Liquid-Crystal Polymers .............. 8 1.2.2 Flexible Chain Polymers with Mesogenic Groups ....... 10 1.2.3 Networks with Flexible Chains and Stiff Mesogenic Groups ................................ 31 1.2.3.1 Networks with Stiff Main-Chain Mesogens, Flexible Spacers and Flexible Junctions ......... 13 1.2.3.2 Networks with Stiff Main-Chain Mesogens, Flexible spacers and Rigid Branchpoints ........ 16 1.2.3.3 Networks with Stiff Pendant Mesogens, Flexible Main-Chains and Flexible Junctions .......... 18 1.2.3.4 Networks with Stiff Pendant Mesogens Connected at Both Ends to Flexible Main Chains ......... 21 1.2.4 Networks Containing No Flexible Spacers ........... 25 1.2.4.1 Uniform Main-Chain Mesogenicity: Flexible, Wormlike, Rodlike ..................... 26 1.2.4.2 LCPs from Biological Origin and Their Networks ....................... 33 1.2.4.3 Networks with Uniform Main-Chain Mesogeni-city and Flexible Crosslinking Residues . . 34 3.1 The Fractal Character of Pre-Gel and Post-Gel Highly Branched Polymers ........................ 38 Exclusions .................................... 43 Synthetic Highlights ............................... 46 1.3 One-Step and End-Capped Rigid Networks .............. 46 t 3.1. Networks with Stiff Hydrocarbon Segments .......... 46 3.1.1.1 Polyphenylenes and Poly (Substituted Phenylenes).. 46 3.1.1.2 Hydrocarbon Networks with Very Short Aromatic Segments ........................... 48 X Table of Contents 3.1.1.3 Stiff Aliphatic Segments .................. 52 3.1.1.4 Overview ........................... 52 3.1.2 Aromatic Polyamide Networks with Stiff Segments and Rigid Branchpoints ...................... 54 3.1.2.1 Rigid Polyamide Networks, Gels and Fractal Polymers Prepared in Solution in the Presence of Triarylphosphite 54 . . . . . . . . . . . . . . . . . . . . . 3.1.2.2 Rigid Polyamide Networks and Fractal Polymers Prepared in Solution by Other Procedures ....... 66 3.1.3 Rigid Aromatic Polyester Networks ............... 68 3,1.4 Rigid Aromatic Networks Containing Single-Atom Bridges . 70 3.1.4.1 Aromatic Hydrocarbons with Methylene Bridges... 72 3.1.4.2 Phenol-Formaldehyde Type Networks ......... 73 3.1.4.3 Furan-Containing Networks ............... 76 3.1.4.4 Aromatic Polyether and Ether-Containing Networks .......................... 78 3.1.4.5 Bridged Aromatic Networks with Uncommon Electronic Structure .................... 80 3.1.4.6 Morphology and Possible Fractality .......... 84 3.1.5 Rigid Networks with Triazine Branchpoints .......... 85 3.1.6 Rigid Networks from Stiff End-Capped Segments ....... 92 3.t.6.1 Networks with Unsaturated Imide Junction Precursors .......................... 93 3.1.6.2 Networks Crosslinked by Strained-Ring Precursors . 96 3.1.6.3 Networks Crosslinked by Ethynyl End-Caps and Pendant Groups ................... 102 3.2 Two-Step Aromatic Networks ..................... 107 3.2.1 Two-Step Aromatic Polyamide Networks ........... 108 3.2.2. Two-Step Networks from Poly (Ether Ketone Ketone) (PEKK) ............................... 112 3.2.3 Networks from Aromatic Linear Chains Created by Reacting Backbone Diacetylene or Pendant Acetylene Groups ......................... 113 32.4 Potential Two-Step Polyarylene Networks .......... 116 3.2.5 Supernetworks ........................... 117 4 Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 4.1 Pre-Gel State ............................... 121 4.1.1 Fractal Nature of Growing One-Step Species and Comparison with Two-Step Species ............ 121 4.1.2 Co*, the Critical Concentration for Gelation ......... 135 4.2 Post-Gel State .............................. 142 4.2.1 Fractal Nature of Gelled Rigid Networks ........... 142 4.2.2 Manifestations of Rigid Network Defects ........... 149 4.2.3 Mechanical Properties of Rigid Networks and Their Gels . 152 Table of contents XI 4.2.4 Observations on Effects of Gravity and Flow-Stress During the Formation of Rigid Network Gels ............. 155 4.2.5 High Temperature Stability of Rigid Aromatic Networks.. 157 4.3 Some Properties of Liquid-Crystal Polymer Networks ....... 159 4.4 Modes of Segmental Deformation ................... 161 4.4.1 Description of Segments ..................... 161 4.4.1.1 Mathematical Description of the Molecules ..... 161 4.4.1.2 General Empirical Description of Network Segments .......................... 164 4.4.2 Deformation of Aromatic Segments with Bridges Consisting Exclusively of Coaxial Single Bonds ....... 166 4.4.3 Deformation of Stiff Aromatic Segments with Bridges Consisting of a Single Non-Coaxial Bond Connecting Two Coaxial Bonds Between Aromatic Groups ....... 168 4.4.4 Deformation of Aromatic Segments with Swivels Consisting of Two Single Bonds Connected by a Single Atom .................. 175 4.4.5 Deformation of Networks with Stiff Aromatic Segments and Relatively Flexible Aliphatic Junctions Created from Reactive End-Caps ..................... 177 4.5 Questions of Elastic Constants .................... 179 5. Theory ..................................... 192 5.1. The Problem ............................... 193 5.1.1 Responses of Flexible and Rigid Networks to Stress Fields ............................... 193 5.1.2 Complexities Uniquely Linked to Network Rigidity .... 193 5.2 Theoretical Description of Rigid Networks ............. 194 5.2.1 One-Step Networks ....................... 194 5.2.1.1 General Mathematical Description .......... 200 5.2.1.2 Field Formalism for Deformation .......... 203 5.3 Simpler Theoretical Approaches ................... 206 5.3.1 Simple Calculations of the Concentrated Rigid Network . 206 5.3.2 Simple Calculations in a Dilute Rigid Network ....... 208 6 References .................................... 214 Author Index Volumes 101-118 ......................... 233 Subject Index .................................... 239 List of Symbols, Abbreviations dna Acronyms a Persistence length a Average tube diameter, network mesh size a Coefficient in replica procedure in Sect. 5 A Kuhn segment length A Free energy of a particular member of an ensemble Free energy of the deformed state Average free energy of the deformed state Ael Elastic free energy Ar Aromatic unit in chain or pendant group c Concentration C Equilibrium concentration of gel Co Polymer concentration in "as prepared" gel Co* Critical concentration for "infinite" network formation Cf Number density of fractal polymers C. Characteristic ratio of chain with n bonds ooC Characteristic ratio of a chain in the limit of infinity Cos 0 Angular energy d Average diameter of chain or segment 2 d Effective segment cross-sectional area D Bond dissociation energy D Fractal dimension Ds Fractal surface dimensionality Df Fractal mass dimensionality DP Degree of polymerization DP Average degree of polymerization of chain or segment DABA 4,4'-Diaminobenzanilide DLA Diffusion limited aggregation DMAc N,N-Dimethylacetamide DMF N,N-Dimethylformamide % Strain E Strain modulus E Young's modulus of reinforced ensemble Ef Young's modulus of reinforcing fiber or segment El Longitudinal tensile modulus E. Young's modulus of the bulk or matrix Er Rod material modulus f Branchpoint or junction functionality f Tensile force applied to segment Average retractive force F Force FP, FPs Fractal polymer, fractal polymers g(rl )2r Mathematical description of monomer in Sect. 5 XIV tsiL of slobmyS G Equilibrium shear modulus H-bond Hydrogen bond AH~ Activation energy for glass transition (h2)o Average square unperturbed end-to-end distance I(q) Intensity of scattered radiation at q IR Infrared k Boltzman constant Ki Force constants 1 Length of actual or virtual bond; average bond length o1 Length of average stiff or flexible segment in network or FP L Chain contour length L Total length of segments in a FP Lc Segment length between entanglements LALS Low angle light scattering M Molecular weight ~M Molecular weight between entanglements M. Number average molecular weight M~ Weight average molecular weight N Number of repeat units N Number density of rods, rodlike segments NF Number of FPs NF Network fragment NMP N-Methyl-2-pyrrolidinone NMR Nuclear magnetic resonance NTPA Nitroterephthalic acid P Fraction of monomer consumed, probability that monomer was consumed P Probability Py Pyridine PPh 3 Triphenylphosphine q Scattering vector r Displacement length of a chain or segment r Chain or segment end-to-end vector (r2)o Mean square magnitude of r R Aliphatic or general organic unit in chain, segment or pendant group R Gas constant R Radius of polymeric species, radius of FP aR Average distance between centers of FPs Ro Radius of gyration HR Hydrodynamic radius WGR Radius of gyration of worm-like chain 1R Length of non-coaxial, actual bond in polyamide segment 2R Length of coaxial, virtual bond in polyamide segment List of Symbols XV Area S S Entropy S Spring constant SANS Small angle neutron scattering SAXS Small angle X-ray scattering T Absolute temperature gT Glass transition temperature o~gT Glass transition temperature of uncrosslinked polymer TPA Terephthalic acid TPP Triphenylphosphite Uo Thermal activation energy for bond scission Volume V V Potential energy of rod )1(V Potential energy of bond Vf Volume fraction WAXD Wide-angle X-ray diffraction X Numerical value of DP Axial ratio X Axial ratio of stiff segment of average length Critical axial ratio for the onset of liquid crystallinity Zf Number of reactive groups belonging to all species larger than monomers Z Number of reactive groups belonging to monomers m Valence angle of carbonyl in amide group Coefficients of expansion in the glass, liquid states ~G~O CO L Valence angle at nitrogen in amide group 7 Stress concentration factor for brittle failure Strain 0 Scattering angle, angle between segment axis of symmetry and network draw direction Wavelength of scattered beam Measure of tube deformation, extension Measure of material deformation A Deformation matrix t~ Shear modulus Number concentration of elastically effective network segments V P Polymer density (~ Stress Breaking strength Torsional angle around bond between aromatic ring and nitrogen in amide group Volume concentration 4,4" Parameters used in integrations in Sect. 5 1% Extensibility