Processes of Fiber Formation
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Processes of Fiber Formation                Zbigniew K. Walczak                            2002                         EL...
E L S E V I E R S C I E N C E LtdT h e Boulevard, L a n g f o r d LaneKidlington, O x f o r d OX5 IGB, U K0 2 0 0 2 Elsevi...
PREFACE        More than twenty years have passed since the publication of my first bookon the subject of fiber formation....
via better stage to present a complex, systemic approach and a mutual confirmationof the different techniques, results, an...
CONTENTSPREFACE                                                                                  VI INTRODUCTION          ...
...Vlll                                                                              CONTENTS       IV.2     The Spinneret...
CONTENTS                                                                                 ix   VII.2   Diffusion in Fiber F...
x                                                                     CONTENTS    XI.5   References   .......................
I      INTRODUCTIONI. 1        Historical Background    The first artzficial fibers were made toward the end of nineteenth...
2                                                CHAPTER I. INTRODUCTIONprocess is given in Figure 1-1. To begin with, the...
I.1.   HISTORICAL BACKGROUND                                                       3equipped with means for rigid control ...
4                                                 CHAPTER I. INTRODUCTIONplace in further steps. It is quite understandabl...
1.2.     NONCONVENTIONAL FORMATION METHODS                                                         5the manufacturing of t...
6                                                C H A P T E R I. INTRODUCTIONsolvent selection represents a crucial point...
1.3.        TRADITIONAL UNDERSTANDING OF T H E PROCESS                                 7product properties. Similar sensit...
8                                                     CHAPTER r. INTRODUCTIONcomplete quantitative solutions available. Th...
I. 5.   REFERENCES                                                                  9quantitative predictability on the ba...
10                                                CHAPTER I. INTRODUCTION 18. R. R. Bentin, D. T. Lohkamp, TAPPI, 56 (1973...
I1 POLYMER AS RAW MATERIAL11.1           Structure and Character       The majority of polymers used for the manufacture o...
12                             CHAPTER II. POLYMER AS RAW MATERIALmost commonly used average, since the viscosity measurem...
11.1.   STRUCTURE AND CHARACTER                                                      13                                   ...
14                              C H A P T E R 1 . POLYMER A S RAW MATERIAL                                               1...
11.1.   STRUCTURE AND CHARACTER                                                  15figuration, often containing small amou...
16                               CHAPTER II. POLYMER AS RAW MATERIAL   Isotactic polypropylene, which cannot assume a plan...
11.1.    STRUCTURE AND CHARACTER                                                        17side products are built into the...
18                                 CHAPTER II. POLYMER AS RAW MATERIALare important, particularly in fibers aimed at appli...
II.2.   POLYMER CRYSTALS                                                            19Figure 11.4: h4odeJ o f polymer crys...
20                              CHAPTER II. POLYMER AS RAW MATERIAL                                                       ...
11.2.    POLYMER CRYSTALS                                                             21lene crystallizes with extended ch...
22                               CHAPTER 11. POLYMER AS RAW MATERIAL                            PARACRYSTALLINE MOSAICBLOC...
rr.2.    POLYMER CRYSTALS                                                          23    It has been s ~ g g e s t e d tha...
24                                CHAPTER II. POLYMER AS RAW MATERIAL     The total entropy, S, of a polymeric system cons...
11.2.    POLYMER,CRYSTALS                                                            25                  0   300F         ...
26                               CHAPTER II. POLYMER AS RAW MATERIALlatter is accompanied by an increase of the thickness ...
11.2.     POLYMER CRYSTALS                                                           27        Small temperature gradients...
28                               C H A P T E R 11. POLYMER A S RAW MATERIALduring annealing of single crystal mats. These ...
n.2.     POLYMER CRYSTALS                                                                   29T is temperature. A4* is the...
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Processes of fiber formation (www.isotextile.blogspot.com)
Processes of fiber formation (www.isotextile.blogspot.com)
Processes of fiber formation (www.isotextile.blogspot.com)
Processes of fiber formation (www.isotextile.blogspot.com)
Processes of fiber formation (www.isotextile.blogspot.com)
Processes of fiber formation (www.isotextile.blogspot.com)
Processes of fiber formation (www.isotextile.blogspot.com)
Processes of fiber formation (www.isotextile.blogspot.com)
Processes of fiber formation (www.isotextile.blogspot.com)
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Processes of fiber formation (www.isotextile.blogspot.com)

  1. 1. Processes of Fiber Formation
  2. 2. This Page Intentionally Left Blank
  3. 3. Processes of Fiber Formation Zbigniew K. Walczak 2002 ELSEVIERAMSTERDAM - LONDON -NEW YORK - OXFORD -PARIS - SHANNON - TOKYO
  4. 4. E L S E V I E R S C I E N C E LtdT h e Boulevard, L a n g f o r d LaneKidlington, O x f o r d OX5 IGB, U K0 2 0 0 2 Elsevier Science Ltd. All rights reservedThis work is protected under copyright by Elsevier Science. and the following terms and conditions apply to its use:PhotocopyingSingle photocopies of single chapters may be made for personal use as allowed by national copyright laws. Permission of the Publisherand payment of a fee is required for all other photocopying, including multiple or systematic copying. copying for advertising orpromotional purposes. resale. and all forms of document delivery Special rates are available for educational institutions that wish to makephotocopies for non-profit educational classroom usePermissions may be sought directly from Elsevier Science Global Rights Department. PO Box 800. Oxford OX5 I DX. UK: phone (+44)1865 843830, fax: (+44) 1865 853333. e-mail: permissions@lsevier.co.uk. You may also contact Global Rights directly throughElse iers home page (http:i/www.elsevier.com). by selecting Obtaining Permissions.In the USA, users ma? clear permissions and make payments through the Copyright Clearance Center. Inc.. 222 Rosewood Drive,Danvers. MA 01923. USA: phone: (+I) 7508400. f a x (+I) 7504744. and in the UK through the Copyright Licensing Agency (978) (978)Rapid Clearance Service (CLARCS). 90 Tottenham Court Road. London W I P OLP. UK: phone: (+44) 207 63 I 5 5 5 5 : fax (+44) 20763 I 5500 Other countries may have a local reprographic rights agency for payments.Derivative WorksTables of contents may be reproduced for internal circulation. but permission of Elsevier Science is required for external resale ordistribution of such materialPermission of the Publisher is required for all other derivative Narks. including compilations and translations.Electronic Storage or UsagePermission of the Publisher is required to store or use electronically any material contained in this work. including any chapter or partof a chapter.Except as outlined aboe. no part of this nark ma) be reproduced, stored in a retrieval system or transmitted in any form or by anymeans. electronic. mechanical. photocop)ing. recording or otherwise, without prior written permission of the Publisher.Address permissions requests to: Elsevier Science Global Rights Department. at the mail. fax and e-mail addresses noted above.NoticeNo responsibility is assumed by the Publisher for an) injury and/or damage to persons or property as a matter of products liability.negligence or otherwise. or from any use or operation of any methods. products. instructions or ideas contained in the material herein.Because of rapid advances in the medical sciences, in particular, independent verification of diagnoses and drug dosages should be made.First edition 2 0 0 2Library o f C o n g r e s s C a t a l o g i n g in Publication DataA catalog record f r o m t h e Library o f C o n g r e s s h a s b e e n applied for.British Library Cataloguing in Publication DataA catalogue record from t h e British Library h a s been applied for.You can contact t h e a u t h o r at:Zbigniew K . W a l c z a kP a s e o d e S a n G e r v a s i o 56, 5. 4aE-08022 Barcelona -Spain EspaiiaE-mail: zwalczak@fiberformation.comISBN: 0 0 8 044040 I8 T h e p a p e r u s e d in this publication m e e t s t h e requirements of ANSlMlSO 239 4 8 - 1 9 9 2 (Permanence o f Paper)Printed in T h e Netherlands.
  5. 5. PREFACE More than twenty years have passed since the publication of my first bookon the subject of fiber formation. Nonetheless, time has its own right. Thoughthroughout the last twenty-five years the fundamental research activity in the fieldwas low worldwide, some progress was made, and thus a presentation of the currentstatus appears to be necessary. It is almost a paradox that on the one hand, the fiber formation process haspassed its centennial birthday, while on the other hand, in some circles, it contin-ues to be considered a craft. In this book I intend to show that fiber formationis a multidisciplinary, complex, often difficult to comprehend science. The fiberformation presented here is based on the systematics published in my first book,on numerous important publications concerning different unit processes involved,as well as on my own research conducted over some thirty years. By taking thebroadest possible view, a sort of a "frontal attack", it was possible to develop theways of full description of the fiber formation process. The outcome of the processhas been made also predictable in principle. The reservation in principle meansthat the outcome of a process may be predicted on the basis of laboratory analyt-ical data and process parameters within a relatively narrow range of conditions.Obtaining full predictability requires additional fundamental research on the be-havior of viscoelastic spectra, and on development of new, solid fundamentals ofpolymer crystallization kinetics, especially of the kinetics of crystal growth. It can not be neglected to underscore that fiber formation is treated here asone process with three different variants: formation from melt and formation fromsolution either by the wet or by the dry method. In essence, the difference betweenthe formation from melt and solution differs only by one additional aspect: thepresence of a solvent, and this is insufficient to treat it as a separate process.The plural form, processes, relates to the many "unit processes" involved in theformation of a fiber. For this reason, the subject of fiber formation is treatedgenerally as formation from the melt. The additional unit processes pertinent tothe formation from solution are treated in a separate chapter which describes theadditional complications. Fiber formation consists of a number of physical processes with nonlinear be-haviors occurring and influencing each other simultaneously. In some cases, stillanother chemical process may be involved. Several disciplines are involved, manydifferent experimental techniques. For these reasons, some of the introductorychapters on raw material properties, rheology, or certain parts of the engineeringaspects may appear to some readers as unnecessary, too elementary, or outrightboring. Nonetheless, people educated in various disciplines enter into this field,and to facilitate access to the subject, such a broad range of background subjectshad t o be covered. Many of my own findings and solutions concerning some of the most vitalaspects of fiber formation are presented here for the first time. A book form gives
  6. 6. via better stage to present a complex, systemic approach and a mutual confirmationof the different techniques, results, and conclusions. Since, in my view, a theorywithout corroboration is useless, every original solution presented here has beenconfirmed experimentally numerous times and under various conditions. And hereis the need and place to express my greatest appreciation and gratitude to thosewith whom I was lucky to work during different periods on the experimental partsof the endeavors: Ms. Janet B. Fryzel, Mr. Nolan Smith, and Mr. Alan C.Smith. Some of the experimental tasks were very demanding for accuracy, some,like program debugging, were trying to the patience - nonetheless, execution ofevery task was really admirable. All the parts involving aerodynamics could not have been written without thegenerous consultations, or rather teachings, of Professor Juliusz Lukasiewicz, Jr .chief of von Karmhn Gas Dynamics Facility, Arnold Engineering DevelopmentCenter, Tullahoma, Tennessee and later of Carlton University, Ottawa, Ontario. I owe special gratitude to Mr. Rainer Typke for his learned and generoushelp at the time when my computer broke down and needed the hardware to bereplaced, the new operating systems introduced. His help saved many of my olderprograms, and much time and frustration. An expression of deep appreciation and thanks I direct to my daughter AgathaC. Walczak-Typke for the editing and proof reading of this book, despite the heavyload of her own work; a Dixie style: Thank you. Thank you. Thank you. And last, though not least, I would like to express my long standing and greatappreciation to my wife Krystyna for her patience over the time of our togethernesslost to this book. Instead of a display of dissatisfaction, she was generous enoughto apply her artistry to design the cover for this book. I owe a special thank you to all of the publishers who granted me their permis-sion for copying material from other publications. Also, some of the illustrationshave been made available by the authors and my gratitude is extended to them,though, sorry to say, many of them are already deceased. Zbigniew K. WalczakBarcelona. 2001.
  7. 7. CONTENTSPREFACE VI INTRODUCTION 1 1.1 Historical Background . . . . . . . . . . . . . ........... 1 1.2 Nonconventional Formation Methods . . . ............ 5 1.3 Traditional Understanding of the Process . . . . . . . . . . . . . 6 1.4 Newer Theoretical Approaches . . . . . . . . . . . . . . . . . . . 8 1.5 References . . . . . . . . . . . . . . . . . . . ........... 9I1 POLYMER AS RAW MATERIAL 11 11.1 Structure and Character . . . . . . . . . . . . . . ......... 11 11.2 Polymer Crystals . . . . . . . . . . . . . . . . . . ......... 18 II.2.a Crystal Structure . . . . . . . . . . . . . ......... 18 II.2.b Melting of Crystals . . . . . . . . . . . . ......... 23 11.2.~ Crystallization Kinetics . . . . . . . . . . . . . . . . . . . 28 11.3 Polymer Solutions . . . . . . . . . . . . . . . . . ......... 33 11.4 References . . . . . . . . . . . . . . . . . . . . . ......... 38I11 RHEOLOGY 44 111.1 Introductory Definitions . . . . . . . . . . . . . . . . . . . . . . . 44 111.2 Excitations and Responses . . . . . . . . . . . . . . . . . . . . . 48 111.3 Mechanical Models . . . . . . . . . . . . . . . . . . . . . . . . . . 56 111.4 Energy Considerations . . . . . . . . . . . . . . . . . . . . . . . . 69 111.5 Uniaxial Extension . . . . . . . . . . . . . . . . . . . . . . . . . . 71 111.6 Extrudate Swelling . . . . . . . . . . . . . . . . . . . . . . . . . . 73 111.7 Flow Instability in Extrusion . . . . . . . . . . . . . . . . . . . . 81 111.8 Molecular Rheology . . . . . . . . . . . . . . . . . . . . . . . . . 86 111.9 Viscosity of Solutions . . . . . . . . . . . . . . . . . . . . . . . . 92 111.10 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97IV POLYMER IN FIBER FORMATION 100 IV.1 Melting of polymer . . . . . . . . . . . . . . . . . . . . . . . . . . 100 vii
  8. 8. ...Vlll CONTENTS IV.2 The Spinnerette . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 IV.3 Forces Acting in Quench Zone . . . . . . . . . . . . . . . . . . . 107 IV.4 Diameter Attenuation . . . . . . . . . . . . . . . . . . . . . . . . 110 IV.4.a Basic Mechanics of Drawing . . . . . . . . . . . . . . . . 113 IV.4.b Extensional Flow Problems . . . . . . . . . . . . . . . . . 117 IV.4.c Andigraphic Solution of Attenuation . . . . . . . . . . . . 129 IV.4.d Spinline Stability . . . . . . . . . . . . . . . . . . . . . . 141 IV.5 Crystallization in Extensional Flow . . . . . . . . . . . . . . . . 142 IV.6 Cold Drawing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 IV.6.a Mechanism of Drawing . . . . . . . . . . . . . . . . . . . 155 IV.6.b Results of Cold Drawing . . . . . . . . . . . . . . . . . . 161 IV.6.c Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . 164 IV.7 Annealing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 IV.8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169V STRUCTURE OF FIBERS 175 v.l S p u n F i b e r s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 V.2 Cold Drawing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 V.3 Drawing Performance . . . . . . . . . . . . . . . . . . . . . . . . 188 V.4 Structure - Properties Relations . . . . . . . . . . . . . . . . . . 191 V.5 High Strength Fibers . . . . . . . . . . . . . . . . . . . . . . . . 193 V.6 Fibers from Block Copolymers . . . . . . . . . . . . . . . . . . . 194 V.7 Hard Elastic Fibers . . . . . . . . . . . . . . . . . . . . . . . . . 196 V.8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198VI ENGINEERING PHYSICS 201 VI.l Flow of Cooling Media . . . . . . . . . . . . . . . . . . . . . . . 201 VI.1.a Quench Systems . . . . . . . . . . . . . . . . . . . . . . . 201 VI.1.b Fluid Dynamics . . . . . . . . . . . . . . . . . . . . . . . 204 V1.l.c Fiber Jets . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 VI.2 Heat Exchange . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 VI.2.a Calculations . . . . . . . . . . . . . . . . . . . . . . . . . 219 VI.2.b Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . 238 V1.3 Mass Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 VI.3.a Polymer Transport . . . . . . . . . . . . . . . . . . . . . . 242 VI.3.b Spinnerette Design . . . . . . . . . . . . . . . . . . . . . . 244 VI.3.c Filament Transport. . . . . . . . . . . . . . . . . . . . . . 246 VI.3.d Machine Geometry . . . . . . . . . . . . . . . . . . . . . . 251 VI.4 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253VII FORMATION FROM SOLUTION 256 V11.1 Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
  9. 9. CONTENTS ix VII.2 Diffusion in Fiber Formation . . . . . . . . . . . . . . . . . . . . 258 VII.3 Wet Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266 VII.4 Dry Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 VII.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293VIII PROCESS VARIABLES 296 VIII.1 Theoretical Variables . . . . . . . . . . . . . . . . . . . . . . . . 297 VIII.2 Technological Variables . . . . . . . . . . . . . . . . . . . . . . . 299 VIII.2.a Polymer Related Variables . . . . . . . . . . . . . . . . . 301 VIII.2.b Variables in Fiber Extrusion . . . . . . . . . . . . . . . . 302 VIII.2.c Variables in Quench or Solvent Removal . . . . . . . . . . 302 VIII.2.d Variables of Cold Drawing . . . . . . . . . . . . . . . . . 304 VIII.3 Process Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . 304 VIII.4 Description of Quench and Coagulation . . . . . . . . . . . . . . 306 V111.5 Prediction of Quench and Coagulation . . . . . . . . . . . . . . . 310 VI11.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311IX SCALE CHANGE OF A PROCESS 312 IX.l Changing the Number of Filaments . . . . . . . . . . . . . . . . 313 IX.2 “Scaling by Equivalence” . . . . . . . . . . . . . . . . . . . . . . 315 IX.3 Experimental Formation Machines . . . . . . . . . . . . . . . . . 317 IX.4 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320X FIBER PROPERTIES 321 X.l Properties Dependent on the Polymer . . . . . . . . . . . . . . . 321 X.1.a Polymer Chain Structure . . . . . . . . . . . . . . . . . . 321 X.1.b Effect of Molecular Mass . . . . . . . . . . . . . . . . . . 328 X.1.c Thermal Properties . . . . . . . . . . . . . . . . . . . . . 331 X.2 Influence of Processing on Properties . . . . . . . . . . . . . . . 331 X.2.a Tensile Properties . . . . . . . . . . . . . . . . . . . . . . 332 X.2.b Thermal Properties . . . . . . . . . . . . . . . . . . . . . 336 X.2.c Sorption Related Properties . . . . . . . . . . . . . . . . 337 X.2.d Fiber Uniformity . . . . . . . . . . . . . . . . . . . . . . . 339 X.2.e ASummary . . . . . . . . . . . . . . . . . . . . . . . . . 342 X.3 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343XI PROCESSES OF “SPUNBOND” 346 XI.1 Spunbond Formation from Melt . . . . . . . . . . . . . . . . . . 347 XI.1.a Meltblown . . . . . . . . . . . . . . . . . . . . . . . . . . 349 XT.2 Thermal Bonding . . . . . . . . . . . . . . . . . . . . . . . . . . 351 XI.3 Properties of Fabrics . . . . . . . . . . . . . . . . . . . . . . . . . 369 XI.4 Spunbonded from Solution . . . . . . . . . . . . . . . . . . . . . 371
  10. 10. x CONTENTS XI.5 References .............................. 373XI1 SPECIAL TECHNIQUES 375 XII.1 Fibers with Noncircular Cross Sections . . . . . . . . . . . . . . 375 X11.2 Crimping - Bulking .Interlacing . . . . . . . . . . . . . . . . . . 377 XII.3 Biconstituent Fibers . . . . . . . . . . . . . . . . . . . . . . . . . 379 XII.3.a Bicomponent Fibers . . . . . . . . . . . . . . . . . . . . . 383 XJI.3.b Fibers from Blended Polymers . . . . . . . . . . . . . . . 386 XII.4 Microfibers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388 XII.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389Appendix A: NUMERIC DATA 391 A.l Data on Air . . . . . . . . . . ..................... 391 A.2 Data on Mass Transfer . . . . ..................... 394 A . 3 Data on Heat of Evaporation ..................... 394 A.4 Data on Polymers . . . . . . ..................... 395SUBJECT INDEX 397
  11. 11. I INTRODUCTIONI. 1 Historical Background The first artzficial fibers were made toward the end of nineteenth century on thebasis of natural polymers: cellulose and casein. The knowledge of fully syntheticpolymers was at that time still highly These natural polymers do not melt - they decompose at elevated temperature.This simple fact dictated the first methods of fiber formation. The polymers, ortheir modifications, could. however, be dissolved. In solution form the shape ofthe materials could be changed, and by subsequent solvent removal the shapecould be fixed. On these principles were based the first patents protecting fiberformat i ~ n . ~ - ~ Cellulose does not dissolve easily in any of the commonly used solvents of thattime. Later, the choice of solvents for cellulose was extended by the addition ofcuprammonium - a substance not very pleasant to work with. The realities of diffi-cult solubility led to the development of another way to prepare solutions: namelythrough formation of cellulose derivatives: nitrocellulose and cellulose xanthate- a product of reaction between cellulose and carbon disulfide. In the case ofxanthates, immediately after shaping the solution into fibers xanthate was regen-erated back to cellulose. This became known as the rayon process, which, withmany refinements, is still in commercial use. There are two applicable ways to remove the solvent: evaporation or extraction.Thus the processes which today are referred to as dry spinning and wet spinning , ormore correctly as dry or wet fiber formation, were born. In the former, the solventis removed through evaporation, while in the latter the solvent is removed throughextraction, with or without a chemical reaction taking place simultaneously. Inboth of the methods diffusion plays the key role. The rayon process involved achemical reaction to regenerate the cellulose, thus it was limited to a wet treatmentfor the sake of the reaction, as well as for an extraction of the byproducts. With continuing progress in the area of synthetic polymers, thermoplastic poly-mers eventually came under consideration for fiber formation. The thermoplasticnature of the polymers allowed the omitance of solvents as a processing aide, butextrusion and further processing of the highly viscous melt brought new problems.These were reflected primarily in new demands on hardware. The higher viscosityof polymer melts and larger emphasis on the attenuation of the fiber diametersnecessitated the involvement of the science of rheology; problems connected withfiber formation became for rheology an important field of research. In the past the three methods of fiber formation - dry, wet, and melt spinning- were treated as entirely different processes having very little in common. Froman operational point of view. this opinion may be justified to some extent. Indeed,from theoretical and technological points of view, these processes are very similar. Schematic representation of fiber formation by all three main variants of the
  12. 12. 2 CHAPTER I. INTRODUCTIONprocess is given in Figure 1-1. To begin with, the dry polymer is either meltedor dissolved, possibly after a modifying reaction. While the polymer melting iscontinuous in screw melters or extruders, or fed directly from continuous poly-merization units, dissolution is performed in batches. In the old days melting wasaccomplished on grill heaters located closely to the spinning blocks. In any of thecases, the polymer solution or melt is transported to spinning blocks. The neces-sary pressure is delivered either by extruder, as in contemporary melt spinning, orby compressed gas (nitrogen), as in spinning from solution or grill heater meltedpolymer. Polymer Solvent lution Feed Rollers Drawing Heater v - Drawing Rollers Relaxing Zone Relaxing or Receiving Rollers Figure I. 1: Schematic representation of the fiber formation process. The spinning block is equipped with a cavity for a fluid metering pump, andchannels which lead the polymer melt or solution to another cavity, where thefilter and spinnerette are located. The spinnerette is a metal plate, sufficientlythick to withstand the pressure gradient and equipped with a multitude of capil-laries through which the polymer or its solution are extruded. The block must be
  13. 13. I.1. HISTORICAL BACKGROUND 3equipped with means for rigid control of temperature. In the case of wet formation processes, spinnerettes are not mounted in thespinning block but on transfer tubes which allow the spinnerettes to be submergedin the coagulation bath or located few millimeters above the fluid surface. So far, for all three formation methods, processing is quite similar. Some dif-ferences begin from this point on. The purpose of the treatment of the extrudedstream is the same in each method: to solidify the polymer. The means of ac-complishing this goal vary with each method and constitute the main point ofdifferentiation. When a molten polymer is extruded through a capillary it will solidify on cool-ing. The cooling medium may be gas or liquid. If a stream of polymer solution isextruded into a gas atmosphere the solvent may be removed only by evaporation,the heat of evaporation must be delivered by the gas. In the wet methods thepolymer stream is extruded from spinnerettes submerged, or almost submerged,directly into a fluid which extracts the solvent from the filaments. If a chemicalreaction accompanies the process, the course of events is more complicated. Inregenerative processes the polymer is regenerated, it becomes insoluble - it co-agulates - and phase separation occurs. Polymer may also be synthesized fromprecursors, or may be cross linked by the coagulating baths which render it in-soluble. The diffusion processes are temperature dependent, so the coagulatingbath must be well thermostated. In case of chemical reactions taking place in thecoagulation bath, temperature control may become more complex due to the heatof reaction. Extraction by itself does not involve significant thermal effects. In the case of formation from solution, the solvents and nonsolvents used mustbe recovered for economical, as well as safety and ecological reasons. The prevalentmethod of solvent recovery from the gas is by adsorption on activated carbon,with subsequent steam regeneration of the carbon bed, and separation of waterand solvent (distillation). This method of regeneration is quite expensive. Incases of wet method, usually only distillation suffices; this method may be moreeconomical, particularly if the solvent is more volatile than water. Many industrial operations are interrupted at this point. Fibers obtained inwet processes at this point may require washing, and certainly drying. If dryformation is done using relatively high boiling solvents, the formed fibers may alsoneed additional washing to remove residual traces of solvent. Another reason tointerrupt the operation here may be crimping and/or heat treatment processes,which may proceed at a different rate than the formation itself. Besides, crimpingis usually done on dry fibers, or with steam, under controlled moisture level.There are, however, many operations where the fibers are subjected to plasticdeformation (neck drawing) in one line with the formation process. The process of polymer solidification is quite complex. The majority of thepolymers used for fiber formation do form a crystalline structure. The crystalliza-tion process usually takes place simultaneously with the solvent removal or due todecrease of temperature of the melt. Slower crystallizing polymers have only largeviscosity increase due to the cooling of polymer melts, crystallization process takes
  14. 14. 4 CHAPTER I. INTRODUCTIONplace in further steps. It is quite understandable that the crystallization processproceeds differently, depending on the temperature change, presence or absence ofa solvent. Besides the phase and temperature changes, the filament diameter is at-tenuated by stretching . And all that at the same time! The stretching is necessaryas it is essentially impossible to extrude the filaments at their final thickness. Forthis reason one extrudes as small a diameter as practical for all possible reasons,and then the filaments are extended while still molten or still containing enoughsolvent. The large number of processes and events taking place simultaneously inthe relatively small space and very short time contribute to the immense complex-ity of the whole problem of fiber formation. This complexity of quench, drying,and coagulation zone creates the greatest obstacle in unraveling the different phe-nomena, in developing a complete and sufficiently accurate theoretical descriptionof the whole process, as well as difficulties with the understanding of the natureand the essence of the process. The formed, undrawn fibers (”spun fibers” in the industrial slang), which havebeen washed and dried if necessary, do not have good physical, and particularlytensile, properties. Very early in the history of fiber making it was discovered thatthe fibers as formed may be permanently deformed by a relatively low stretchingforce. Such stretching results in an increase of the tensile strength. Therefore,almost all fibers, irrespectively of the method of their formation, are subjected tosuch a deformation. The stretching operation is usually carried out by transportingthe fibers through rollers driven at different surface speeds. In Figure 1-1the rollersare identified as feed (or take up) rollers and drawing rollers. From the pointof view of crystalline morphology of fibers, the stretching corresponds to plasticdeformation; it is often called ”neck drawing” due to the characteristic abruptdiameter change, which resembles a bottle neck, or simply the drawing. Theplastic deformation is usually performed at elevated temperature, though belowthe onset of melting of the crystalline structure. After the stretching operation,the fibers may show a tendency for some recovery. It is advisable to let themrecover under controlled conditions: to add a pair of relaxing rollers rotating atappropriately lower velocity than the drawing rollers. Depending on the polymer and process used, and on the type and quality ofproduct intended, the drawn fibers may be subjected to various finishing opera-tions: washing, heat setting, winding on bobbins, or cutting for staple. There is another finishing operation, which is not necessarily performed at theend of the manufacturing line. These are finishes applied for different purposes: tofacilitate drawing and/or crimping, to prevent electrostatic charging, and almostalways to improve textile processing . Depending on the type and the purpose ofthe treatment, the finish may be applied at different stages of the manufacturingline. The above description of fiber making is brief and highly simplified. It is toserve as a starting point for detailed discussion of all the essential phases andthe phenomena taking place during the process, and as the initial vocabulary orbridge for communication with the reader. The scheme given above concerns only
  15. 15. 1.2. NONCONVENTIONAL FORMATION METHODS 5the manufacturing of the classical fibers and disregards some newer methods andproducts. Some of the newer processes, raw materials, and products, such aspolymer blends, bicomponent fibers, spunbonded materials, are treated in an ab-breviated fashion, because the majority of the technological problems they involverepresents only modifications of the basic principles of fiber formation. However,some of these problems will be given some attention since they represent eitherinteresting solutions to problems, or a good example for the principles working indifferent processes, or because they have experienced commercial success1.2 Nonconventional Formation Methods As mentioned above, the fiber formation process is complex. This simple factrepresents a strong driving force to attempt to simplify the technology. The alwayspresent need for the reduction of manufacturing costs reinforces the drive towardnew and simpler formation methods. The initial efforts have been concentratedon attempts to eliminate the roller type transport of fibers and spinnerettes asexpensive pieces of high precision hardware. The first known attempts to eliminate fiber transport rollers in fiber formationfrom polymer solution date back to 1934. In place of rollers between the capillaryand collecting device, an electrostatic field of 50 to 300 kV was Sucha process usually bears the name of electrostatic spinning. Spraying of a polymer solution, or melt, by means of high pressure and highvelocity air15-” represents another technique leading to similar results. Extrusionof polymer melt through a long slit type die was still another method leading to thesame general goal. The extruded filaments may then be extended in a Venturi typejet with high velocity gas. Such jets are able to provide the necessary extensionalforce. This group of methods is normally referred to as spray spinning. In another attempt to eliminate the spinnerette, a process has been developedwhere a polymer solution or melt is introduced axially to the center of a rotatingcone or bell. The centrifugal force distributes the fluid over the internal surface ofthe bell into a film of progressively decreasing thickness. When the film leaves theedge of the cone, the film splits into fibers. Solidification takes place by the way ofdrying or cooling. The centrifugal force is sufficient to extend the fibers to as finediameter as fractions of denier*.I9 Such a process bears the name of centrifugalspinning. There exists a process which combines centrifugal and electrostatic forces. Thecentrifugal - electrostatic processes find an application mainly to manufacturingof spunbond Another group of nonconventional processes concentrates on facilitating meltprocessing of high molecular mass polymers. All of these methods invariably ”di-lute” the polymer with solvent what lowers the viscosity to various degree. The ‘Denier, den or dpf, is a measure of mass, or weight, titer; it is the weight of a filament of thelength of 9000 meters. A “metric” mass titer is tex, Tx: the weight of a 1000 m long filament.The ”decitex”, dTx, is most often used.
  16. 16. 6 C H A P T E R I. INTRODUCTIONsolvent selection represents a crucial point in those processes. In some cases sol-vents are selected so that they become non - solvents at lower temperature and/orpressure. In some cases the solvent violently evaporates when the extrusion pres-sure ceases upon leaving the spinnerette. Yet another processes, aimed at obtainingvery high strength and high modulus fibers, extrude the polymer only swollen bythe solvent to a state of gel. All of the nonconventional processes are governed by the same laws and prin-ciples as the conventional fiber formation methods. On the other hand, all of thenonconventional processes seem to have some deficiency, none of them is ideal. Themost common fallacies are: nonuniform fiber diameter] both fiber-to-fiber, and/oralong the fiber. For the majority of the processes without spinnerettes it is virtu-ally impossible to subject the spun fibers to cold drawing (plastic deformation).Generally] only certain products or raw materials, which do not require plasticdeformation at all, or only to a modest extent, are suited for such processes, e. g.elastomers. Some spunbonded processes, mainly for disposable products, wheredimensional stability of the fibers and higher tensile strength are not required,utilize the nonconventional methods. The inherent deficiencies of the nonconven-tional methods are serious enough to prevent, or seriously limit, application of theproducts as traditional textile fibers for apparels. Some of the semimelt processesyield high class fibers, but the high price limits their application to very specialpurposes.1.3 Traditional Understanding of the Process Development of new technologies is often done by trial and error. The tech-nology of fiber formation went through a similar period. Moreover] that periodlasted longer, relatively speaking, due to the complexity of the physics of the unitprocesses involved and the extraordinary many simultaneous and interrelated unitprocesses involved. It is well known that trial and error approaches usually resultin an abundance of errors, but every new inductive science must go through sucha difficult childhood. By now, the technology is over hundred years old. Duringall that time, a great wealth of observations and experience has been accrued.Alas, the majority of this knowledge has not been published. The commercialsignificance of fiber manufacturing explains the hesitation in the publication ofanything that may prove important. This was particularly true of the initial trialand error period. Nevertheless, as fiber formation has gradually obtained the rankof science, more and more information has found its way into scientific journals;though sometimes with substantial delay. 22-30 As a result of the specific spirit ofsecrecy in which the fiber industry has placed itself, the fiber makers and the fibermaking procedures have became surrounded with a peculiar aura of an art, if nota black magic. During the long studies of the raw material - process - product relation] it wasestablished quite early that despite the most scrupulously held constant polymerproperties, small changes in processing may cause “unduly” severe changes in the
  17. 17. 1.3. TRADITIONAL UNDERSTANDING OF T H E PROCESS 7product properties. Similar sensitivity of process - product relations were knownin metallurgy, but never to such a significant extent. In metallurgy, the majorityof such changes could be ultimately related to some minute variations of chemicalcomposition or to the crystalline polymorphism, or both. Gradually, with timeit became evident that, by their nature, macromolecules usually do not attainthermodynamic eq~ilibrium.~’ large chain-like molecules assume a multitude Theof different conformations depending on their thermal history and history of theirmechanical perturbations. Because of the lack of more accurate knowledge, thethermal history was held responsible for everything, particularly for everythingbad, that could happen. The lack of a sufficient explanation and of a well groundedunderstanding did not allow to lay a firm theoretical basis for fiber production.Empirical formulations and “the rule or thumb” became the last resort. On thebasis of mainly qualitative observations of different processes, a number of ”ironrules” for fiber formation have been gathered.32 They are: Narrow molecular mass distribution in a polymer facilitates the processing and generally improves the product properties. Increase of shear rate in the spinnerette increases the fiber tenacity. 0 Increase of the spin stretch usually increases the crystallinity of the formed fibers. Tension in neck drawing, at a given draw ratio, is proportional to the crys- tallinity in the undrawn fiber. Maximum crystallinity that is obtainable in the drawn fibers depends in inverse proportion on the degree of crystallinity present immediately before the neck drawing operation. Aside from the simplistic form, these rules represent an immensely significantbasis for the past development work, and they may still be helpful to understandingof the many results published under the headings of “surprising”. But it must bealso realized that the experimental verification of some of the points. although per-formed many times over, represents a difficult task. Proper separation of differentvariables is of utmost importance. In every formation process not all of the vari-ables are individually and independently adjustable. Modern testing equipmentallows the measurement of the spinline condition^,^^)^^ thus it has simplified theverification of those qualitative rules. More importantly the equipment provideda firm basis for the modern quantitative description of the process. In view of thequantitative information, some of the ”zron rules” were found to need qualifyingfootnotes. Aside from their historic significance and practical importance. ”the iron rules”describe the process neither completely, nor even adequately. Fiber formation isone of the most complex processes the chemical industry has ever dealt with.Therefore, one cannot expect it to be described sufficiently by only a few ”rules”.Despite the unquestionable progress, at this moment there are still no full and
  18. 18. 8 CHAPTER r. INTRODUCTIONcomplete quantitative solutions available. The fully quantitative scientific pre-dictability is still limited since several of the fundamental problems in polymerphysics have not been solved yet.311.4 Newer Theoretical Approaches In the early 1950s, work began on a more scientific approach to fiber formation.Earlier, products and processes were invented, studied, and developed only bychemists and engineers. The newer approach in fiber research involved manyp h y s i ~ i s t s . ~ - ~ ~ may distinguish two different methods characteristic to those Oneefforts. In one of the approaches, the exploratory work was carried out on certain as-pects of product or process. Usually the studied problems were selected so tocover a very narrow area of specialization, often limited to using only one experi-mental technique. Some of the investigations of this kind produced much valuabledata. Some of these studies of the unit processes were deep indeed. However,the isolated conditions sometimes put limitations on the general validity of theinterpretations. The experiments were simply too much out of context in relationto the entire process. In studying literature of that period, it is often necessaryto reevaluate and reinterpret the published conclusions. Taking into account theprinciples of the methodology of sciences,38 such studies of isolated aspects maybe justified, provided that the potential dangers of premature generalizations areheeded, so that misleading conclusions are avoided. As the first approach was predominant in more "descriptive" areas, e.g. fiberstructure: the second one involved attempts of quantifying the process. With suffi-cient fairness one may credit E. H. Andrews3 as its originator. Many quantitativedescriptions of great value have been obtained, though unfortunately, not alwayswere they immediately applicable in practice. As an example one may quote theAndrews solution of heat transfer equation13 which gives good results in caseof non-crystallizing polymers. Since the process of polymer crystallization un-der strain had not been solved at that time, it was a scientific distortion to putthe large heat of crystallization at an arbitrarily chosen point of the spinline. Acertain dose of impatience and underestimation of the process complexity can bedetected in some of the interpretations and conclusions assigned to these otherwisesubstantial achievements. The quantitative descriptions of the unit processes involved in fiber formationpose calculational difficulties, only a small fraction of them may be solved an-alytically. In recent years the application of widely available, potent, and fastcomputers to cope with the difficulties of the purely computational nature haveplaced the fiber formation technology where it is today. Computers allow a wideuse of numerical methods and simultaneous solution of systems of equations. Inthis way, today the fiber formation process may be fully quantitatively definedonly with the necessity of experimental analytical support. The full development of fiber formation technology, that is, to the point of total
  19. 19. I. 5. REFERENCES 9quantitative predictability on the basis of laboratory analyses, is still incomplete.The full predictability of the process appears to depend mainly on the filling of thegaps in polymer physics. It is also imperative that the future research endeavorsbe undertaken so that the complexity of the whole process be considered andrespected both in its theoretical and experimental aspects. On the other hand, we must be grateful to past researchers for the developmentof the starting points. After the thorny beginning, compilation of the availablemethods, proper reinterpretation of them, provided a strong base for the currentstate of knowledge in the field. In the following chapters, all theoretical treatment of the unitary processesand phenomena involved in fiber formation and available today will be given sep-arate accounts. Simultaneously, the theories will be confronted with the wealth ofthe available experimental evidence. The analysis of the mutual relationships andinfluences between the unit processes involved in fiber formation plays a crucialpart. The available quantitative descriptions and their agreement with experi-ments - ergo their applicability will be ascertained. The different aspects of theprocess will be brought into one entity: into a logical system of fiber formationscience: as it stands today. Though some areas of polymer physics still requiresolutions, the amount of confirmed information already gathered, when logicallyassembled, permits the fiber formation technology to be rightfully called the fiberformation science.1.5 References 1. J. Blyth and W. A. Hofmann, Ann., 53 (1845),283, 311 2. M. Berthelot, Bull. SOC.Chim. fiance, 6 (1866),294. 3. G. Gustavson, Ber., 7 (1874),731. 4. H. Staudinger, Helv. Chim. Acta, 5 (1922),785. 5. W. Carothers: Collected Papers, Vol. 1 of the High Polymers series, Interscience H. Publ., New York, 1940. 6. German Pat. No. 38,368 (1885). 7. French Pat. No. 203,741 (1890). 8. German Pat. No. 108,511 (1898). 9. German Pat. No. 170,051 (1904). 10. Brit. Pat. No. 609,796to Imperial Chemical Ind., Ltd. 11. U.S. Pat. No. 1 975 504, (1934)to A. Formahls and R. Schreiber - Gastell. 12. U.S. Pat. No. 2 116 942, (1938)to A. Formahls and R. Schreiber - Gastell. 13. U.S. Pat. No. 2 048 651, (1936)to Massachusetts Institute of Technology. 14. Can. Pat. No. 937 827, (1973)to Farbenfabriken Bayer A. G . 15. U.S. Pat. No. 2 988 469, (1961)to American Viscose. 16. U.S. Put. No. 3 689 342, (1973)to Celanese. 17. D. E. Till, Mod Textile Mag., (1959),36.
  20. 20. 10 CHAPTER I. INTRODUCTION 18. R. R. Bentin, D. T. Lohkamp, TAPPI, 56 (1973),74. 19. Brit. Pat. No. 1 132 135 (1968)to Monsanto. 20. J. Fine and S. A. De Tora, U.S. Pat., No. 4,223,101(1980),to Inmont Corp. 21. U.S. Pat. Appl. No. 486 567, to Inmont Corp. 22. R. Hill (Ed.): Fibers from Synthetic Polymers, Elsevier Polymer Series, Vol. 6, Amsterdam - New York - London, 1953; Fasern aus synthetischen Polymeren, Berliner Union, Stuttgart, 1956. 23. H. Hopf, F. Wenger, and A, Miiller: Die Polyamide, Springer Verlag, Berlin - Gotingen - Heidelberg, 1954. 24. H. Klare, E. Fritsche, and V. GrGbe, Synthetische Fasern aus Polyamiden, Akademie Verlag, Berlin, 1963. 25. H. Ludewig (Ed.): Polyesterfasern, Akademie Verlag, Berlin, 1965. 26. S. A. Rogovin: Chemiefasern, Grundlagen der Chemie und Technologie, Fachbuch- handlung, Leipzig, 1960. 27. F. Fourne: Synthetische Fasern, Wissenschaftliche Verlagsgesel-lschaft, Stuttgart, 1965. 28. T. Rosner, H. Wbjcikiewicz: Wldkna syntetyczne, Wydawnictwo Naukowo - Tech- niczne, Warszawa, 1969. 29. T. Rosner: Wldkna sztuczne, Wydawnictwo Naukowo - Techniczne, Warszawa, 1966 30. H. Mark, A. Atlas, and S. Cernia: Man - Made Fibers, Vol. 1-3, Interscience Publ., New York, 1967-68. 31. H. A. Stuart (Ed.): Die Physik der Hochpolymeren, Springer Verlag, Berlin - Wien - Heidelberg, 1956, Vol. 3, pp. 414 ff, 550 ff., 557 ff. 32. A. Nowakowski: Technology of Plastics and Synthetic Fibers, lectures at Polytech- nic of Lbdz, 1953. 33. K. L. Reifsnider: A New Device for Tame-Resolved Study of X-Ray Difiaction Events, Ph.D. Dissertation, Dept. of Mechanics, The John Hopkins Univ., Univer- sity Press, 1968. 34. K. L. Reifsnider, private communication. 35. E. H. Andrews, Brit. J . Appl. Phys., 10 (1959),39. 36. H. Berg, Kolloid-Z., 210 (1966),64. 37. A. Ziabicki and K. Kedzierska, Kolloid-Z., 171 (1960),51; A. Ziabicki: Fizyka procesdw jormowania wtdkien, Wydawnictwo Nau-kowo - Techniczne, Warszawa, 1970; findamentals of Fibre Formation, J. Wiley Publ., New York, 1976. 38. K. Ajdukiewicz: Logika pragmatyczna (Pragmatic logics), Panstwowe Wydawnictwo Naukowe, Warszawa, 1965, Part 111.
  21. 21. I1 POLYMER AS RAW MATERIAL11.1 Structure and Character The majority of polymers used for the manufacture of fibers are of organicnature. The physical behavior of polymers differs from the behavior of the or&-n a r y , low molecular mass, substances. The differences are caused principally bythe large and nonuniform size of the polymer molecules. In organic chemistry, thisis known as the notion of homolog series. Polymers, however, may be consideredrather as mixtures of homologs. In the case of ordinary compounds, we speak of molecular mass, while in thecase of polymers, we may speak only about an average molecular mass, since themolecules are of uneven size. The molecular mass may have various distributions,and here one needs the help of statistics to describe them. The commonly usedaverages, presented in a mathematical form, are: (11.1) (11.2) (11.3) (11.4) In equations 11.1 through 11.4 ni denotes the number of molecules of mass M ,( M ) is average molecular mass (colloquially molecular weight). The subscriptsmean: n represents number average molecular mass, where species of each molecular mass are represented by their number or mole fraction. w represents m a s s average (or weight average) molecular mass. Here, molecular mass of each of the species is represented by its weight. z represents the so called z-average molecular mass. This average has pri- marily mat hematical meaning, while physically, it is related t o some volume dependence, e.g. like radius of gyration in light scattering experiments. z + 1 is called z + 1 - average; it has only mathematical significance. There is one more - perhaps the most commonly used average: the viscosityaverage moIecular mass. Particularly until the advent of newer instrumental meth-ods, like the gel permeation (or size exclusion) chromatography this has been the
  22. 22. 12 CHAPTER II. POLYMER AS RAW MATERIALmost commonly used average, since the viscosity measurements are easier thanother techniques for molecular mass determination.. The unquestionable prob-lem connected with viscosity average is that it is not really constant: its relationto other averages depends on the solvent used. In limiting cases it may equalthe weight average. Otherwise it is smaller, down to a minimum reaching abouthalf the difference between the weight and number averages. Mathematically theviscosity average molecular mass may be presented as (11.5) Here, wi is weight fraction of species of molecular mass Mi, a is the Mark-Houwink exponent in the intrinsic viscosity equation [q]= K M a , which may varyfrom 0.5 for theta solvent to 1.0 for a very good solvent. As the a coefficientapproaches unity, the viscosity average approaches the weight average molecularmass, though this occurs rarely. 3 $ 4 The Gauss distribution is, perhaps, the most fundamental and common instatistics. Its mathematical formulation in relation to molecular mass is: W ( M )= -exp ( M UJZ;; [ iu?)’] (11.6)where Mm is the median value of molecular mass, around which the curve issymmetric, and at the same time it represents the number average molecularmass; o describes the breadth of the distribution, it corresponds t o the standarddeviation in statistics. The value of standard deviation, un,may be expressed interms of the average of molecular masses of different type: The molar fraction of 0.6826 lies within the limits of ho. Figure 11.1 shows aGaussian distribution of molecular mass. Unfortunately, there are few polymerswhich have Gaussian distribution. The normal logarithmic distribution seems tobe more common. The mathematical form of the “log-normal” distribution, as itis called for short, is the Gaussian distribution, where the molecular mass fractionin the exponent is substituted by its natural logarithm. The standard deviation,u w * , for the distribution where the number of molecules is substituted with a (11.8) An example of the log-normal distribution curve is presented in Figure 11.2.In the normal distribution the maximum of the curve coincides with the numberaverage molecular mass. In log-normal distribution this is not the case: log-normaldistribution is characterized by a larger fraction of smaller molecules. The distri-bution curves encountered experimentally often resemble log-normal distribution,
  23. 23. 11.1. STRUCTURE AND CHARACTER 13 MOLECULAR MASS 1 o -~ Figure 11.1: Gaussian distribution of molecular masses.though they do not fit exactly into its mathematical form. Therefore, a numberof modifications to the log-normal distribution equation have been suggested toaccommodate the discrepancies. For details on these distributions the reader isreferred to the polymer textbooks. ) 2 1.07 W v) 9 0.9- z 0.2- MOLECULAR MASS 1 o -~ Figure 11.2: Example of a normal logarithmic type of molecular mass distribution. Experimentally, molecular mass distribution and all the averages are commonlydetermined by the size exclusion chromatography. Other methods are used lessfrequently as they are experimentally more difficult. These methods usually yieldmolecular mass averages of different type. Particularly troublesome are othermethods for determination of mass distributions. However, from the direct spe-cialized methods like osmometry for number average, light scattering for weightaverage, and ultra centrifuge for weight and z-average, more accurate data may beobtained. The size exclusion chromatography requires calibration, which is basedon the direct methods. Polydispersity of polymers, as expressed by the weight average over numberaverage ratio, rarely is less then 2 and in some cases may reach as high as ten ortwelve. This is true both for commercial and for experimental polymers. The lower
  24. 24. 14 C H A P T E R 1 . POLYMER A S RAW MATERIAL 1values are more typical for condensation type polymers, the higher values occurprimarily with some vinyl-type polymers. Polymers of higher average molecularmass have a tendency toward having a somewhat broader mass d i s t r i b ~ t i o n . ~ Polydispersity may be high also due to the blending of different polymerbatches, or as a result of not very stable continuous polymerization processes.In such cases one may encounter bimodal, or even multimodal distributions whichdo not have any general mathematical representations given a prion. Practically, all the fiber forming polymers known currently have linear chainstructure. The molecular formulas predict such linearity quite clearly. The group of polyamides polyamides, is based either on a - w difunctionalacids and Q - w iamines or on a - w aminoacids. Aromatic diacids or diaminesmake the melting point very high and may increase the strength substantially.Examples of structural formula of an Q - w diacid and Q - w diamine, as well asStuart-Briegleb models of single mer of nylon 6 and a segment of nylon 66 withamid bonds and with one CH2 group on each side, respectively, are: Poly(acrylonitri1e) (usually called acrplic fiber) has an irregular stereo con-
  25. 25. 11.1. STRUCTURE AND CHARACTER 15figuration, often containing small amounts of comonomers, does not melt and isprocessed from solution: Polyesters in their most common version are based on terephthalic acid andglycols of different length, most often ethylene glycol. Structural formula andStuart-Briegleb model of one mer of poly(ethy1ene terephthalate) are: Polyethylene (or poZymeth?jlene,if it has a most regular structure). is a poly-mer of high theoretical interest due to the structure simplicity, commercially it isless attractive due to low melting. Structural formula and Stuart - Briegleb modelof three mer segment are: r 1 -CH,-CH,-CH,- CH,?CH,-CH, CH,-CHz-CHz-CH2- i fN
  26. 26. 16 CHAPTER II. POLYMER AS RAW MATERIAL Isotactic polypropylene, which cannot assume a planar zag - zag but insteadhas a helical conformation as found in crystals. Structural formula and Stuart-Briegleb model of a two mer segment are: Syndzotactzc-polypropylene, planar conformation but usually melts lower hasthan its isotactic counterpart: Naturally, t,he list, of polymers used for manufact,uring of fibers is substantiallylonger, especially when one takes into consideration the so-called high performancefibers and modifications of naturally occurring polymers. If any of the useful poly-mers, from the fiber formation point of view, have chain branching synthesizedintentionally, then the side chains are rather short. Unfortunately, almost allpolymers contain some fraction of chains with long branches built in unintention-ally, as imperfections, as a result of side reactions. In the case of low molecularmass compounds, products of side reactions are removed during purification pro-cesses; in the case of polymers, such purification is impossible, particularly if the
  27. 27. 11.1. STRUCTURE AND CHARACTER 17side products are built into the chains. It must be stressed that long chain branch-ing, particularly when it is severe enough to form cross linked, gel molecules, ismost detrimental to the polymer quality, to the ease of processing, and potentiallyto the polymer Doubtlessly, in commercial operations such chainimperfections often represent a strong economic factor. In melts and in solutions, the polymer molecules are coiled into what looks likea little balls. How tightly a polymer coils depends on the flexibility of chain, and inthe case of solutions, the quality of the s o l ~ e n t . It ~ lindeed difficult to imagine ~ is ~a rod with length to diameter ratio of several thousands staying fully extended,or close to it, especially when one considers interaction with other molecules.Conditions like this may be met only in cases of very rigid molecule structure (e.g.liquid crystal polymers). In concentrated solutions and in the melts, the coiled polymer molecules arenot entirely independent. To some degree, the coils are interpenetrated and thechains entangled. A fully quantitative description of the chain morphology inconcentrated solutions and in the melts is currently impossible. The problem ofchain conformation in solid state is also not less important; it will be discussed inthe next sections. As the molecules lack full freedom of motion, they cannot always assume suchspatial positions as would correspond t o a minimum of free energy in the sys-tem. Thus, polymers belong to the systems which are not in thermodynamicequilibrium.’l This fact is of great theoretical and practical importance:12 it is thebasis for the phenomenon that the very same polymer can have different proper-ties in solid state. The same specimen may be crystallized to different degrees,and many of the crystalline forms will be in a meta-stable state for practically anindefinite time under normal service conditions. The same specimen may also becrystallized to the same degree, but if the crystalline morphology is different, theproperties will be different also. Mostly the physical properties will differ to a largerdegree, e.g. tensile strength, Young’s modulus, creep, etc. The non-equilibriumcharacter of polymers is responsible for the influence of processing on the productproperties. Full knowledge of the appropriate relationships is necessary t o fullyutilize all the possibilities that any type of processing offers. Molecular structure, regardless of whether it is more or less ideal, has an ob-viously quite dominant role in determining fiber properties. So, the presenceor absence of polar forces, as well as their strength, determine many properties.Poly(acrylonitrile), which has very strong polar groups, is able to form good andstrong fibers even at low levels of crystallinity; the polar forces hold the super-molecular structure together. Polyolefines, with no polar forces to speak of, needmuch higher levels of crystallinity and higher molecular mass to form sufficientlystable, low creeping fibers.13 If well crystallizing polymers have, in addition, strongpolar forces or hydrogen bonds, or b ~ t h , ’ ~ like~ poly(ethy1ene terephthalate), )’the resulting fibers have excellent mechanical properties. On the other hand, thedense crystalline morphology of the fibers may create problems with diffusion re-lated properties such as dyeability and water absorption. The last two properties
  28. 28. 18 CHAPTER II. POLYMER AS RAW MATERIALare important, particularly in fibers aimed at applications in garments, sanitarymaterials, or insulating materials. Nonpolar polymers. like polyethylene or poly-propylene, are used for such applications where dyeing is not important or may besubstituted with pigmenting the polymer in bulk. The chemical structure of polymers also accounts for such properties as stabilityagainst heat, oxidation, microorganisms, and different kinds of radiation, as wellas resistance to hydrolysis, to attacks of different solvents, etc.16-1s In essence. the polymer presents a certain potential range of obtainable fiberproperties. Exactly which properties are utilized depends on the processing. Thedegree of development and the level of sophistication of the process are reflectedin the utilized fraction of the potential a polymer offers.11.2 Polymer CrystalsII.2.a Crystal Structure Some polymers have been found to be able to crystallize. Those polymers whichare able t o crystallize give X-ray diffractograms typical of crystalline structuresuperposed on a halo obtained normally from amorphous materials. The ”crys-talline part” of polymer diffractograms is similar to powder diffractograms of lowmolecular mass crystalline compounds. Fibers give usually diffractograms similarto single crystal, indicating presence of orientation. The duality of x-ray diffraction patterns suggests the notion of semicrystallinityin polymers. Although the first x-ray observations were made in the late twentiesor early thirties, the crystallography of polymers is still open for a developmenteffort.Figure 11.3: First depiction of crystalline structnre in polymers after Herrnann, Gern-gross, and A b i t ~ . ’ ~ - ’ ’ The first attempts to describe the structure of polymer crystals were published
  29. 29. II.2. POLYMER CRYSTALS 19Figure 11.4: h4odeJ o f polymer crystallinity by Hess and K i e s ~ i g . Reproduced by ~~~~permission o f the copyrights owner, Dietrich Steinkopf Verlag.by Hermann and G e r n g r o ~ s ~in~1932. Their model is presented schematically - ~in Figure 11.3. With only minor modifications, Statton reactivated the model in1959.22This interpretation of polymer crystals is usually referred to as the fringedmacelle model. Based on the low angle X-ray scattering obtained from fibers.Hess and K i e ~ s i g ~ ~ t ~ ~ in 1942 another model. which was characterized developedby substantially more order and alternating arrangement of areas of crystalline -non-crystalline material (see Figure 11.4). Kone of the models. though, was ableto provide explanation of the material properties, particularly, the properties offibers. In 1957, three different laboratories reported the discovery of polymer single~ r y s t a l s . ~ ~ - ~ ~ microscopic investigations of single crystals revealed that Electronthe crystal dimensions were incompatible with dimensions of fully extended poly-mer chains - ergo - the chains in the crystal must be folded. The folds werefound to be around 100 A in size. The large surfaces of the single crystals, thoughthey physically belong to the crystal, contain the molecule folds. The folds donot have the packing regularity of a crystal, hence they may then be considerednoncrystalline. The thickness of single crystal was found to be variable and de-pendent on the growth conditions: temperature and medium, e.g. solvent or melt.Thickness of the crystal lamellae, as they have been named. has been found tocoincide with the long periodicity, as determined by low angle X-ray scattering.Table 11.1 presents, as an example, the relationship between the growth conditionsof polyethylene crystals and corresponding long periods.28 Later investigationsindicated that at large supercoolings. the long periods reach a constant value in-dependent of the crystallization Further, it has been found thatthe long period grows also during isothermal crystallization beginning from someminimum. This minimum value of long period corresponds also to the long periodobtained in crystallization from solution.38 The most recent investigation^^^ showthat during crystallization of monodisperse polyethylene, the long period grows insteps. doubling. tripling, and quadrupling the minimum long period, 1 " . Figure11.5 presents a proposed mechanism of the jump changes of chain folding,3g which
  30. 30. 20 CHAPTER II. POLYMER AS RAW MATERIAL 0 QuodruplingFigure 11.5: Sketch illustrating a scheme for refolding which leads to multiplication ofthe minimum fold size. Reproduced from P. J . Barham and A. Keller3g by permissionof the copyrights holder, John Wiley & Sons, Inc.is observable irrespectively of the crystallization medium, but in the melt it pro-ceeds a t substantially higher rates. Table 11.1. Long Period of Polyethylene Crystals in Relation to Growth Conditions. Medium Temperature, "C Long Period, A o-Xylene 50 92.5 o-Xylene 60 102.0 o-Xylene 70 111.5 o-Xylene 80 120.5 o-Xylene 90 150.0 Polyet,hylene melt 120 190.0 Polyethylene melt 125 223.0 Polyethylene melt 130 355.0 A number of investigator^^"-^^ have suggested that one molecule may be in-volved in more than one lamella, creating tie molecules. The tie molecules connectdifferent lamellae with stronger bonds than might be provided by the poorly or-dered fold planes. E. W. Fischer and c o - ~ o r k e r s ~ ~ shown that in general, haveone molecule, 1*,32-37 crystallizes in more than one lamella. In the same paperFischer describes an X-ray based method of detailed quantitative analysis of themolecule involvement in lamellae. Based on thermodynamic consideration^,^^-^^ it was predicted that stabilityof polymer crystal has t,wo maxima: one at a limited thickness - which dependson crystallization temperature and is realized in folded chain crystals, the othermaximum of st,abilit>y corresponds to fully extended chain conformation. Crystalswith fully extended chains have been obtained experimentally. Namely, polyethy-
  31. 31. 11.2. POLYMER CRYSTALS 21lene crystallizes with extended chains when the crystallization process is carriedout at pressures in excess of 2300 a t m . 4 g Also, polymers with very rigid chains areunable to coil. Therefore, their normal mode of crystallization is with extendedchains. Some of the so-called hzgh performance fibers are based on such. or similar,polymers. What makes polymers crystallize? This is an important question. The answermay be: the tendency to give up an excess of energy which may be achieved byentering into proper positions in relation to other chains. Why is it then thatsome polymers crystallize and other do not? Regularity of crystalline latticesrequires some minimum of regularity in polymer chain. At some point it wasbelieved that the regularity needed is very high.50 so high that the chains wouldneed to be nearly perfectly stereoregular. Such rigid requirements may be cor-rect if “perfect” crystals are to be obtained. Commonly. however, crystals arenot so ”perfect” and are able to accommodate chain imperfections. Polypropyl-ene with four to five chlorine atoms per hundred carbon chain atoms shows onlyrelatively minor deformation of crystalline lattice.51 The degree of crystallinityof pol yet hylene decreases gradually with the increasing number of “foreign” sub-stituents, like chlorine, methyl, i s ~ p r o p y l Copolymers with three or five per- .~~cent of a comonomer are quite well able to form crystalline materials. Differentstereoisomers, in comparison to copolymers. represent only a minor disturbance ofthe chain r e g ~ l a r i t y . The’ feature most detrimental to crystallization is chain ~~ ~~branching, particularly long chain and frequent branching. There is evidence that,despite the imperfections, polymers do crystallize, but the imperfections influencethe resulting crystal morphology. as well as the crystallization rate.’40 Great progress in evaluation of X-ray diffraction data made by Hosemannand collaborator^^^^^^ in the early 1950’s led to the formulation of the notion ofparacrystallznzty. Crystalline structure ceased to be treated in terms of “black andwhite”, it moved into the “grey” area. Crystal structure may range from perfec-tion down, through paracrystals distinguishing srnectac and nematzc morphologies,all the way to an amorphous state. The nematic form describes some degree oflateral order between the molecules, though distances are not fully regular. Thesmectic form is somewhat more ordered, the chain elements or groups become or-dered laterally, though still not in the constraints of a regular crystalline lattice.Methods to analyze the imperfections became known. though the reasons for theimperfections would not be determined equally precisely. Generally. the causes ofimperfections are believed to belong to two categories. przmo - those resulting from the irregularities in chain conformation, and secundo - imperfections of the geometry of the polymer chain itself. The first category includes improper alignment of the chain in the lattice, un-usual configuration of folds. incorporation of chain ends in the lattice, inversion ofhelix turns, etc. The second category includes steric imperfections. chain branches,comonomer units, chemical imperfections built into the chains, end groups of dif-ferent chemical nature. et c,53I It has been shown that even well developed polymer crystals, including single
  32. 32. 22 CHAPTER 11. POLYMER AS RAW MATERIAL PARACRYSTALLINE MOSAICBLOCK I N P. E. SINGLE CRYSTAL W I T H TWIST BOUNDARY A N D SCREW DISLOCATIONS.Figure 11.6: Schematic drawing of a mosaic block boundaries, according to R.. Hose-rnann et al? Reproduced by permission of the copyright owner, International Union ofCrystallography.crystals, do not have a completely homogeneous structure. If a single polymercrystal is analyzed by X-ray diffraction, one obtains values for the size of the crystalsubstantially smaller than the whole crystal mat, usually only around 100 A. Thesame is true with any other polymer crystals. Crystals, including single crystals,are built of small blocks which have been given the name paracrystalline m o s a i cb l o ~ k s . ~ ~ The size of the small blocks is strongly related to the paracrystalline >’~lattice distortions: (11.9)Here, a is distance between the lattice planes, D represents t,he average size of theparacrystalline particle in a direction perpendicular to the considered lattice plane,9 is the paracrystalline lattice distortion factor, and (Y characterizes the forcesbinding the network planes. For many polymers, including polyethylene, the valueof (Y is around 0.15. This relationship indicates that the distortions in crystallinelattice are addit,ive, they superimpose in some way. Therefore the distortions areeffectively growing with the growth of the crystal. Depending on the magnitude ofthe distortions, what is reflected by the g-factor, depends the number of crystallineunit cells grown to the point where the distortion becomes large enough to createa discontinuity of the total structure. The local distortion of the order becomes solarge that the area appears to X-ray diffraction as noncrystalline (Figure 11.6). Thequestion of lattice distortions has been further refined and related to particularlattices by Blijchl and B0na1-t.’~’ Under the influence of relatively small forces, asingle crystal mat or lamella breaks down along the distorted and weak boundariesbetween mosaic bIocks.60>61
  33. 33. rr.2. POLYMER CRYSTALS 23 It has been s ~ g g e s t e d that ~ ~ process~of crystallization is preceded by ~ ~ the ~ ~ ~ precipitation of the molecules in their coiled form. Subsequently, the moleculescrystallize to a large extent within the coils. It has been suggested even that atthe conditions close to crystallization, the chain segments within a coil are alreadylargely parallel to obtain the maximum packings8 The connections between thelamellae are suggested to originate in the chain entanglements. From a mechanisticpoint of view these suggestions appear quite plausible. At the current state of knowledge it is easy to realize that the notion of crys-tallinity is quite ill-defined. Should the fold planes be considered as crystalline ornot? They belong, though, to a single crystal. Even a single crystal is not viewedas hundred per cent crystalline by X-ray. Density and heat of fusion must varywith the degree of crystal perfection. The only solution to the problem appears tobe adherence to the concept of paracrystallinity and observation of the necessityto indicate the method of analysis by which the degree of crystallinity has beendeduced. Naturally, closer description of the structural features, like the g-factor,type of distortions16 long period, etc., additionally clarifies the meaning, but theanalyses may be time consuming and expensive. Thus, very often we must remainsatisfied with the more or less approximate description of the order in the polymersolid ~ t a t e . ~ ~ ) ~ ~II.2.b Melting of Crystals If a thermodynamic equilibrium would exist in a partially crystalline system,then the change in free energy during ,the melting of a small crystal layer wouldequal: AGO = AHO - TASO = 0 (11.10)Here AGO is change in free energy, and AH, AS are changes of melting enthalpyand melting entropy, respectively. All the values are calculated per mole. Fromequation 11.10 one may find the equilibrium temperature: TI = AH/AS (11.11) If the actual temperature of a specimen would become greater than TI, thenAGO would become negative and the crystal would melt. If, on the other hand, thespecimen temperature would decrease below TI, then AGO would become positiveand further crystallization would proceed. In case of low molecular mass compounds, when the crystals are sufficientlylarge, AGO and AS are material constants which do not change. In such cases,equation 11.11defines the melting point. For high molecular mass compounds, bothenthalpy and entropy change during melting. The enthalpy of melting dependsquite strongly on the crystallization temperature and on the molecular mass of thepolymer. The value of ent halpy increases with increasing crystallization tempera-ture and decreases with increasing molecular mass to reach an equilibrium pointfor infinitely long polymer chains at the melting temperature.lo4
  34. 34. 24 CHAPTER II. POLYMER AS RAW MATERIAL The total entropy, S, of a polymeric system consists of: 1. Transition entropy, St , which is connected with vibrations of the center of gravity of the entire molecule. 2. Entropy of internal vibrations, S,, which is related to the vibrations of different segments of a molecule, while the center of gravity does not shift. 3. Configurational entropy, S,, which arises from changes of form and spatial arrangement of the molecule. In effect one may write: s = s, + S" + s, During the melting of polymers, the configurational entropy, S,, undergoeschanges and because of this the equilibrium temperature, 2 changes also. This "complicates an adequate description of the melting phenomena in polymers. Inaddition, the degree of crystallinity may also be affected by the crystallizationtemperat~re.~~ Polymer melting may be described adequately only in the formof a relationship between the crystallization temperature and the correspondingmelting temperature, as it is shown in Figure 11.7. The slope of melting tem-perature, T, , against crystallization temperature, T,, is usually around 0.5.l Inpractice, however, the values range from 0.3 to 0.8. The large deviations fromthe expected value of 0.5 may be partially due to the fact that experimental de-termination of the relationship is rather difficult. Also, a t larger supercoolingsthe melting temperature becomes constant and independent of the crystallizationt e m p e r a t ~ r e . ~ - ~ the point is not well defined, the experimental points may Ifbecome confused, leading to an incorrect slope. The slope, on the other hand, is ofutmost importance, as it determines the point where the temperature of meltingequals the temperature of crystallization, T, = T,, that is the equilibrium meltingpoint, 7, Practically, this point is determined by the point of intersection of ".the line of T versus T, with the line of slope equal one. The thermodynamic ,equilibrium melting pint is defined as the temperature a t which the free energyof an infinite crystal, consisting of fully extended chains, is equal to that of aliquid polymer.28 Equilibrium melting point is a material constant , barring anyalterations resulting from polymer chain imperfections. However, such cases arerather common. Polyethylene crystallized under high pressure does melt at theequilibrium melting temperature, or close to it. Molecular mass has an influence on melting (11.12)Here is the melting enthalpy of a monomer unit, R is, as usual, the gasconstant, and X is degree of polymerization. f ( X ) represents a long expression,but its numerical value is normally negligibly small. This influence is primarilya reflection of different chain end groups acting as impurities. Consequently, the
  35. 35. 11.2. POLYMER,CRYSTALS 25 0 300F 9.2 z801 E- --- 3 - 21 0 6 . 200t - 1926 . CRYSTALLIZATION TEMPERATURE, * CFigure 11.7: Relationship between crystallization and melting temperatures:poly(ethy1ene terephthalate):g5 = 0.694T,+88.43; nylon-6? T, = 0.7445Tc+64.91; T,p ~ l y p r o p y l e n e : ~ ~= ,0.4644T + T , 103.13 and T, = 0.5501 T 97.74. ,+influence decreases strongly with increasing molecular mass, so for the majorityof common cases it may be neglected. Recently, it has been also reported67 thatmolecular mass has some effect on the lamella growth, and this would, naturally,influence melting temperature. However, the influence becomes negligible alreadyabove degree of polymerization of 500, and its influence decreases further withincreasing degree of polymerization. As has been mentioned above, the crystalline long period depends on crys-tallization temperature. Now we see that melting point depends on the size oflong period; thus, melting temperature depends on crystallization temperature.The logic of structure and behavior is complete. However, one needs to take intoaccount the medium in which crystallization proceeds, and whether refolding ispossible or not. This may modify the melting point. Polymers do not usually have sharp melting points. It is still not entirely clearwhat are the thermodynamic reasons underlying this fact. The ratio of the foldsurface area to the crystal size depends on long period:68 1- 2 0 Tm = Tg [ (L*Hf)] (11.13)where is surface free energy of the fold surfaces, A H f heat of fusion, and L islong period. It is claimed"~70 that heat of fusion decreases with molecular mass.On the other hand, melting temperature is sensitive to molecular mass only at lowmolecular masses ( e . 9 . for polyethylene below 2 . 104)7 The theory of partial melting42)72i94 treats the fold sites differently. It assumesthat a polymer below its melting point reaches its absolute minimum of free energywhen it is almost completely crystalline. The steric hindrances do not allow theminimum of free energy to be reached. Only a relative, metastable equilibriumbetween the crystalline and unordered layers may be achieved. The length of theunordered chains reflects a temperature dependent equilibrium, and this explainsthe broad melting of polymers, as well as some decrease in crystallinity. The
  36. 36. 26 CHAPTER II. POLYMER AS RAW MATERIALlatter is accompanied by an increase of the thickness of interlamellar layers astemperature increases. In addition, surface melting results in an increase of specificheat. Taking these into account, the great influence of long periodicity on thethermal behavior of polymers becomes obvious. The dependence of the degree ofcrystallinity on temperature is:42 (11.14)Here pa is density of the unordered layer, pa is density of the crystalline layer, L isthickness of the crystalline layer, and d stands for the thickness of the unorderedlayer. Partial melting may take place only when the unordered molecules have bothends tied to the crystal surface. Figure 11.8 shows such situations as cases A and B.Case D, with only one end tied in the crystal, does not aid the surface melting. Incases of typical tie molecules, like case C, partial melting should not be expected,since the distance between the tied points is affected by melting. Cases like Eare not very likely to occur, but should they happen, melting may be affected.Significant experimental support, based on X-ray analyses, for the partial meltingtheory has been reported by Kavesh and S c h ~ l t z . ~ ~Figure 11.8: Possible chain arrangements, other than adjacent reentry, between crys-talline lamellae. After Fi~cher.~’ Newer investigation^^^ show that partial melting is due also to the “wander-ing” of paracrystalline portions between crystalline G paracrystalline (intermedi-ate) +j amorphous. Partial melting involves not only the chain folds; a large roleis played by the distribution of long period sizes.’38 Besides surface melting, there are several other reasons why melting may bebroadened:
  37. 37. 11.2. POLYMER CRYSTALS 27 Small temperature gradients during crystallization may cause small differ- ences in the size of long period, and furthermore in melting temperature. Imperfections in the crystalline lattice.2i28 Impurities lower the melting points of crystals, as in the case of low molecular mass compounds. Chain branching has a very complex influence on melting point, much more complex than formulated by Flory.74>75 The great number of possible combinations of length, frequency, and distri-bution of branches along the chains give a basis for the ~omplexity.~ true Thereasons for melting point broadening are, most likely, of very complex nature andattributable to many factors,76 including the broadening effect of the instrumentsused. If a polymer crystal is subjected to elevated temperature, though still substan-tially below its actual melting temperature, the melting temperature may increase.This process is called anmealing. The annealing effect is observable above a certaintemperature, T,, which coincides with a transition in the viscoelastic spectrum,the so called ac transition. In terms of structure, long period grows exponentiallywith time to an asymptotic v a 1 ~ e . ~Macroscopic ~ ~ ~ > ~ ~ - density of the crystal alsoincreases. There is no linearity in the relationship between the long period growthand temperature. Density increases show a linear relationship with the reciprocalvalue of the long period for a given constant temperature. When the annealingtemperature exceeds a certain maximum that is close to the melting point of thespecimen, the long period does not reach an equilibrium.82 Newer investigation^^ show that not all crystals have equally strongac relaxation, which is related to the translational chain motions. The transla-tion may proceed through various mechanisms, like chain rotation, helical jumps,"crankshaft" jumps. The translation is obviously more difficult, if possible, forpolymers with large side groups, rigid chains, and extensive chain entanglements.Some polymers do not have the a, transition; they form nonductile crystals , oraccording to other terminology, are crystal jixed. The rate of growth of long pe-riod is considered dependent on molecular mass,83 which is usually connected withhigher degree of chain entanglement. The growth of long period during annealingis accomplished by a mechanism similar to refolding during crystallization: bylongitudinal translation of the chains within the crystalline lattice after the latticehas been softened sufficiently for such a process to take place. The softening ispossible within the temperature interval beginning with T, and upwards to sometemperature close, but not reaching, the actual melting point of the specimen.802sIt is also possible that partial melting is involved in the p r o c e s ~ . There~are ~~) ~conflicting views regarding the influence of annealing on the crystal perfection:some authors believe that the perfection increases,s2 others claim the oppositeeffect to be true.28 Annealing processes are accompanied by macroscopic changes of the sampleshape, e . ~ shrinking when a sample was previously oriented, or formation of holes .
  38. 38. 28 C H A P T E R 11. POLYMER A S RAW MATERIALduring annealing of single crystal mats. These changes of shape may occur onlywhen a sample is annealed without a restraint imposed on its dimensions. All ofthe description given above concerns only such cases. During isometric annealing,polymers behave differently. Such cases will be discussed in other sections. It is not without significance whether a sample is annealed in air or in a liquid.Annealing in liquids is much more effective, the new equilibrium is reached fastereven when using liquids which do not interact physicochemically with the polymer.A more intense heat transfer must be responsible for the accelerating effect.84 In experimental practice, the measured melting temperature often depends onthe heating rate during the experiment. This effect may be related to the partialannealing.85 Heat treatment, sometimes even at relatively low temperature, can have aninfluence on the entropy of some noncrystalline elements of the structure. Stresseson noncrystalline molecules imposed by crystallization of other molecule segmentsmay gain a chance of relaxation. Such a relaxation would result in a change ofconfigurational entropy. Even without noticeable change in long periodicity, melt-ing point may be affected," but certainly the macroscopic shape of the specimenwill be altered. There are known cases when annealing caused changes of the crystallographic Such change, if it takes place, is responsible for the most serious changesof melting behavior. Other properties may be affected also, and quite strongly atthat.11.2.c Crystallization Kinetics It is generally accepted that the kinetics of polymer crystallization follows theAvrami equation originally developed for low molecular mass compounds and formetals in p a r t i c ~ l a r : ~ ~ - ~ ~ 1 - a: = exp(-Kin) (11.15) In this equation o represents the degree of crystallinity, t is time, n is constant,depending on the process of nucleation and assuming values 1 5 n 5 4, whichaccording to the original development must be integers. K is here a rate constant.The majority of polymers seem to follow the equation fairly well, but n is almostalways fractional. The equation reflects neither the influence of molecular masson the kinet,ics, nor the temperature dependence of the process. Another approach to crystallization kinetics is also based on thermodynamic R.considerations. The earliest notions go as far back as G i b b ~ . ~ Beckerg7 formu-lated the nucleation rate in a condensed phase, n*, as: n* = no exp (-A F * ~ A Q * ) (11.16)Here n,o is an unspecified constant, A F * is the free energy of activation for thetransport of a molecule across the phase boundary, k is Boltzmanns constant, and
  39. 39. n.2. POLYMER CRYSTALS 29T is temperature. A4* is the greatest contributor in the equation and representsa "barrier" which is inversely proportional to temperature. Fisher and Turnbullg8reformulated the equation: A4* = 4 bo 0 1 0 2 (11.17) Afwhere bo is thickness of the crystallizing entity, and is assumed constant; 01 and 0 2are the interfacial free energies per unit area for the nucleus faces a bo and cbo; A frepresents the free energy of fusion per unit of volume of the macroscopic crystal: (11.18) In equation 11.18 A h f is the heat of fusion per unit volume of the crystal, T$is the equilibrium melting point, T is crystallization temperature. Thus, equation (h) (-F ) [11.16 in the Fisher and Turnbull version may assume the following form: n* = NkT AF exp exp - Ahf x AT x bT The additional notation in equation 11.19 has the usual meaning: N is Avo-gadros number, h is Planck constant, AT = ? - T . , " Hoffman and co-workers" have modified the Fisher-Turnbull equation and forthree dimensional homogeneous nucleation of polymer crystal they suggest: I* = (w) NkT (-=) AF exp{-[ 32 oe(%) 0 Ahf x AT x kT]2 } (11.20)Here V, represents i m o l a r vo1um.e of t h e order of m a g n i t u d e of t h a t associatedw i t h a c h a i n length of t h e fold period"; as the free energy of activation for transport.WLF equation for activation energy of flow (see chapter on rheology) is used to +describe the transport,12 A F " = AFG,, = 4120T/(51.6 T - T g ) where Tg is ,the glass transition temperature. To improve the agreement between the resultscalculated from equation 11.20 and those obtained from experiment, the authorsggadd to the denominator of the last segment of the equation a correcting factor y2,with the value of ?j close to unity. There were attempts made to improve the agreement between equation 11.20and experimental data by dividing the problem into three "regimes". Defini-tion of the "regimes" is based approximately on the degree of super~ooling."~-"~These attempts appear to be somewhat artificial however, and the entire Hoffman-Lauritzen theory has been subjected to very severe criticism."8-23 Improvement sof the equation, as well as new solutions of the problem have been suggested bymany author^,"^-^^^ many of the solutions are based on extension of the Avramiequation to nonisothermal conditions. These efforts offer some small improve-ments, but none of them is significant, so far. A detailed review of the efforts maybe found in a paper by Di Lorenzo and Silve~tre.~

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