Manufactured Fibre Technology

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Manufactured Fibre Technology

Edited by

V.B. Gupta and V.K. Kothari Indian Institute of Technology, Delhi, India

luni SPRINGER-SCIENCE+BUSINESS MEDIA, BV

First edition 1997

© 1997 Springer Science+Business Media Dordrecht Originally published by Chapman & Hali in 1997 Softcover reprint of the hardcover I st edition 1997

Typeset in 1O/12pt Palatino by Academic & Technical Typesetting, Bristol

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Contents

List of contributors Preface Acknowledgements 51 units and symbols Note on equivalence and equivalent weight

1 Introduction V.B. Gupta and V.K. Kothari 1.1 Definition and classification 1.2 Evolution of manufactured fibres 1.3 Fibre-forming processes 1.4 Fibre products and properties 1.5 Production trends 1.6 Application areas 1.7 Scope of this book

References

2 Structural principles of polymeric fibres V.B. Gupta 2.1 Introduction 2.2 Molecular size and interaction 2.3 Molecular orientation and crystallinity in fibres 2.4 Polymers as fibres, plastics and rubbers 2.5 Fibre morphology 2.6 Thermal transitions

References

3 Basic principles of fluid flow during fibre spinning V.B. Gupta and y.c. Bhuvanesh 3.1 Introduction

xi xiii xvi xxi

xxv

1

1 2 3 4 5 8

11 13

14

14 15 17 18 23 25 30

31

31

vi Contents

3.2 Shear flow 3.3 Elongational flow 3.4 Molecular theories of fluid flow 3.5 Spinnability and flow instabilities

References

34 50 55 60 65

4 Melt-spinning processes 67 V.B. Gupta 4.1 Introduction 67 4.2 The melt-spinning line 69 4.3 Melt-spinning variables and conditions for

continuous spinning 78 4.4 Special features of high speed spinning 80 4.5 The role of some critical parameters and their variation

along the spinline 83 4.6 Structure formation during spinning 90 4.7 Integrated spin-draw process 94 4.8 Other techniques to produce fibrous structures 96

References 96

5 Computer simulation of melt-spinning 98 V.M. Nadkarni

Notations 5.1 Introduction 5.2 Theoretical background 5.3 Spinline orientation 5.4 Sensitivity analysis 5.5 Process implications 5.6 Stress-orientation relationship for PET 5.7 Case study for process optimization 5.8 Case studies for product development 5.9 Conclusions

References

6 Solution-spinning processes V.B. Gupta 6.1 Introduction 6.2 The process variables for solution-spinning 6.3 Dry-spinning 6.4 Wet-spinning 6.5 Development of structure and morphology

during solution-spinning 6.6 Some salient comparative features of the spinning

processes References

98 99

102 104 106 108 112 112 117 122 123

124

124 126 126 133

136

137 137

Contents vii

7 Spin finishes for manufactured fibres 139 P. Bajaj 7.1 Introduction 139 7.2 Properties of spin finishes 140 7.3 Role of spin finishes 140 704 Spin finish components 145 7.5 Spin finish application techniques 147 7.6 Spin finishes for staple fibre production and processing 151 7.7 Spin finishes for filament yarns 154 7.8 Influence of spin finish on dyeing of yarn/fabric 160 7.9 Analysis of spin finish formulations 160 7.10 Problems encountered in finish application 167

References 168

8 Drawing of melt-spun fibres 170 AK Sengupta 8.1 Introduction 170 8.2 The drawing unit 171 8.3 The drawing behaviour of thermoplastic polymers 172 8.4 Influence of drawing on structure and properties of fibres 178 8.5 Orientation stretching for high strength 184 8.6 High speed spinning and the spin-draw process 185 8.7 Drawing of preoriented yarns and draw-warping 186

References 186

9 Heat-setting of thermoplastic fibres 188 A.K. Sengupta 9.1 Introduction 188 9.2 Nature of set 190 9.3 Heat-setting behaviour of polyamide and polyester fibres 193 904 Heat-setting of cellulose triacetate fibres 199 9.5 Settability and the measurement of the degree of set 200

References 202

10 Characterization of polymers and fibres 203 A.K. Gupta 10.1 Introduction 203 10.2 Characterization at the molecular level 204 10.3 Characterization of physical structure 219 lOA Thermal characterization 238 10.5 Microscopic characterization 243

References 246

viii Contents

11 Testing of manufactured fibres 248 V.K. Kothari 11.1 Introduction 248 11.2 Fineness 248 11.3 Fibre crimp 250 11.4 Tensile properties 251 11.5 Evenness testing 256 11.6 Frictional properties 263 11.7 Shrinkage behaviour 264 11.8 Entanglement testing 267

References 270

12 Poly(ethylene terephthalate) fibres 271 V.B. Gupta, A.K. Mukherjee and 5.5. Cameotra 271 12.1 Introduction 12.2 Polymer production 272 12.3 Fibre production 296 12.4 Structure and mechanical properties of fibres 311 12.5 Application areas 313

References 315

13 Nylon 6 and nylon 66 fibres 318 B.L. Deopura and A.K. Mukherjee 13.1 Introduction 318 13.2 Nylon 6 polymer production 319 13.3 Nylon 66 polymer production 332 13.4 Degradation reactions 338 13.5 Additives 339 13.6 Fibre production 340 13.7 Post-spinning operations 349 13.8 Glass transition temperature and fibre structure 351 13.9 Mechanical behaviour 353 13.10 Applications 356

References 356

14 Speciality polyamide and polyester yams: an industrial approach to their production and rheology 360 T.Manabe 14.1 Introduction 360 14.2 Production of modified polymers for making yarns with

different dyeability characteristics 361 14.3 Antistatic nylon and polyester yarns 374 14.4 Flame retardant yarns 380

Contents ix

14.5 Polyester yams with microgrooves, microvoids and microcraters 382

14.6 Super micro filament yams by conjugated bicomponent yam spinning 384

14.7 Fibres with non-circular cross-section and hollow fibres 386 14.8 Melt rheology during spinning of speciality yam 394

References 404

15 Acrylic fibres 406 P. Bajaj 15.1 Introduction 406 15.2 Polymer manufacture 407 15.3 Influence of polymerization conditions on properties of

acrylic polymer 415 15.4 Characterization of acrylonitrile polymers 420 15.5 Spinning processes 425 15.6 Tow processing 442 15.7 Mechanical properties of acrylic fibres 448 15.8 Speciality fibres 448

References 453

16 Polypropylene fibres 457 Kushal Sen 16.1 Introduction 457 16.2 Polymerization 458 16.3 Stabilization against degradation 464 16.4 Fibre production 468 16.5 Structure development during solidification 473 16.6 Fibre properties 476 16.7 Application areas 478

References 478

17 Rayon fibres 480 A.K. Sengupta 17.1 Introduction 480 17.2 The viscose process 481 17.3 Advances in viscose rayon technology 493 17.4 Viscose fibre variants 497 17.5 Alternatives to the viscose process 503

References 513

18 Manufactured fibres for high performance, industrial and non-conventional applications 514 Satish Kumar and V.B. Gupta 18.1 Introduction 514

x Contents

18.2 Fibres for industrial applications 18.3 Fibres for high performance applications 18.4 Fibres for non-conventional applications

References

19 Spunbonding and melt-blowing processes B.C. Goswami 19.1 Introduction 19.2 Spunbonded fabrics 19.3 Melt-blown fabrics

References

20 Reuse of polymer and fibre waste P. Bajaj and N.D. Sharma 20.1 Introduction 20.2 Utilization of PET waste 20.3 Recovery from nylon 6 waste 20.4 Nylon 66 yarn waste 20.5 Polypropylene yarn waste 20.6 Acrylic waste

References

Index

516 518 553 557

560

560 561 577 592

595

595 598 615 623 625 627 629

633

Contributors

P. Bajaj Professor, Department of Textile Technology, Indian Institute of Technology, Hauz Khas, New Delhi -110016, India

y.c. Bhuvanesh Research Associate/Assistant Professor, School of Textiles, Fiber and Polymer Science, 161 Sirrine Hall, Clemson University, Clemson, SC 29634-1307, USA

5.5. Cameotra Vice President (Plant Operations), Swadeshi Polytex Limited, New Kavi Nagar, Ghaziabad - 201002, India

B.L. Deopura Professor, Department of Textile Technology, Indian Institute of Technology, Hauz Khas, New Delhi - 110016, India

B.c. Goswami Professor, School of Textiles, Fiber and Polymer Science, 161 Sirrine Hall, Clemson University, Clemson, SC 29634-1307, USA

A.K. Gupta Professor, Centre for Polymer Science and Engineering, Indian Institute of Technology, Hauz Khas, New Delhi -110016, India

V.B. Gupta Professor, Department of Textile Technology, Indian Institute of Technology, Hauz Khas, New Delhi - 110016, India

V.K. Kothari Professor, Department of Textile Technology, Indian Institute of Technology, Hauz Khas, New Delhi - 110016, India

xii Contributors

Kushal Sen Professor, Department of Textile Technology, Indian Institute of Technology, Hauz Khas, New Delhi - 110016, India

T. Manabe Consultant, Modipon Limited, Modinagar - 201204, India

A.K. Mukherjee Professor, Department of Textile Technology, Indian Institute of Technology, Hauz Khas, New Delhi - 110016, India

V.M. Nadkarni Techcel1ence Consultancy Services Pvt. Ltd, 10 Narendra Society, Senapati Bapat Road, Pune - 411016, India

Satish Kumar Associate Professor, School of Textile and Fiber Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0295, USA

A.K. Sengupta Advisor, Ahmedabad Textile Industry's Research Association, Ahmedabad - 380015, India

N.D. Sharma Senior General Manager (R & D), J.K. Synthetics Ltd (PSG Group), Jakaynagar, Kota - 324003, India

Preface

The need for a book on manufactured fibre technology has been felt by us for several years while teaching undergraduate and postgraduate students taking courses on or related to the subject. While there are excellent books dealing with the chemistry of fibre production or with the fundamentals of the spinning processes or with newer fibres, there is a dearth of books dealing with the subject in an integrated manner at an appropriate level and suitable for a course lasting one or two semesters. The present book has been designed to fulfil this need. It covers in considerable detail the two principal stages in the manufacture of fibre, namely the production of the fibre-forming polymers and their conversion to fibre. Adequate emphasis is laid on fundamental principles and newer developments without recourse to advanced mathematics.

That such a book will have a much wider base became clear to us while conducting a two-week continuing education programme organ­ized in our department for teachers from textile colleges and tech­nologists from industry. The faculty for this programme was drawn from academic institutions, industry and research laboratories. From our experience of running several such programmes, we feel that this book will also be useful to such teachers and to technologists in industry. In addition, it will provide the basic material to those interested in organizing and running intensive training courses on this topic.

The book has been designed with the following features:

• the treatment is at an undergraduate level for a course on fibre produc­tion; however, the needs of students taking a Master's level course have also been kept in mind;

• the treatment is intensive rather than extensive; • the emphasis is on fundamental principles, wherever basic concepts

are involved;

xiv Preface

• the industrial practices obtaining on a global scale have been included, as far as possible;

• the information is up-to-date and state-of-the-art.

Emphasis on in-depth treatment of the subject required careful selec­tion of the topics to be covered. In the present book, the various aspects of fibre production centre around 20 chapters as outlined below .

• Processes: the fibre production processes of melt-, wet- and dry­spinning, drawing and heat-setting are covered in detail in five chapters with adequate emphasis being placed on fundamentals.

• Fibre types: all important commodity fibres, namely polyester, poly­amide, acrylic, polypropylene and viscose rayon, are treated in detail in five chapters. The vinyl fibres, namely polyvinyl alcohol, polyvinyl acetate and polyvinyl chloride, and the modified cellulosic fibres, namely cellulose diacetate and cellulose triacetate, have not been included.

• Recent developments: newer developments including high performance fibres and the techniques of dry-jet wet-spinning and gel-spinning, spunbonding and melt-blowing, computer simulation of melt-spinning and modification of fibres for value addition are covered in four chapters.

• Characterization and testing: the methods used for characterization of polymers and fibres and for testing fibres for both quality control and R&D are described in two chapters.

• Others: important industrial aspects relating to spin finishes and their application and of reuse of waste generated in the plant and elsewhere are covered in two chapters. One chapter is devoted to the develop­ment of basic structural concepts and the other is introductory in nature and traces the history of manufactured fibres and gives some statistics and typical applications.

The diverse topics listed above were handled by fifteen authors with basic background in one or more of the following subjects: physics, chemistry, materials science, textile technology and chemical engineer­ing. They were drawn from academic institutes, research laboratories and industry and all have considerable expertise in various aspects of fibres and textile materials and processes. We have tried to retain the flavour of the author's experience and approach while ensuring an in­depth coverage of the different topics with a minimum overlap between the chapters. We hope that we have succeeded in meeting the objectives for which the book was designed and that the users will find it useful in teaching, research, production and applications.

A book of this magnitude is the joint effort of a number of persons and as editors we would like to express our gratitude to them. We

Preface xv

thank the authors for their contributions. The understanding shown and cooperation extended by them during the prolonged editorial exercise is gratefully acknowledged. We would also like to acknowledge with thanks the reviewers for their generous advice and comments. The editorial staff of the publishers, Chapman & Hall, deserve special thanks for the assistance rendered during different stages of publication. The generosity of several publishers and authors in permitting the reproduction of figures and tables (listed in a separate section) from their published work is gratefully acknowledged. We are indebted to Mr RK. Arora for doing the entire word-processing work single­handed. We are thankful to Mr K.G. Pad am for line sketches, Ms Sujata Caprihan and Mr T. Vineet for some artwork, and Mr K.P. Vetrival and Mr J.K. Sensarma for computer graphics. We would be failing in our duty if we did not thank the many generations of students whom we had the privilege to teach and whose association has been stimulating and educative for us.

Finally, we would like to thank our wives, Lata and Purnima, for support, patience and encouragement without which it would have been difficult to undertake this project.

New Delhi May, 1997

V.B. Gupta V.K. Kothari

Acknowledgements

The editors wish to gratefully acknowledge the following for reproduc­tion of material from their publications:

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Acknowledgements xvii

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xviii Acknowledgements

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Acknowledgements xix

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xx Acknowledgements

The Textile Institute, Manchester. J.W.S. Hearle and R.H. Peters, Eds., Fibre Structure, (1963), 486 (Fig. 4.9(a)); C.C East, J.E. McIntyre and C.C Patel, J. Textile Institute, (1984), 197 (Fig. 15.16); J.E. Ford, Textiles (3) (1991), 5 (Fig. 17.1(a)); S.K. Mukhopadhyay, Ed., Advances in Fibre Science (1992), 11 (Fig. 18.4).

The Textile Machinery Society of Japan, Osaka. F. Fujimoto, K. Yama­guchi, H. Ikide, H. Kishida and T. Arai, Journal of the Textile Machinery Soc. of Japan, 19(1) (1973), 1-6 (Figs. 8.6,8.7,8.8,8.11 & 8.13); Journal of Textile Machinery Soc. of Japan, 41 (1988), 109 (Figs. 14.1 & 14.2).

Textile Research Institute, Princeton. A. Dutta and V.M. Nadkarni, Textile Res. J. (Jan. 1984), 35 (Figs. 5.1 to 5.6, Table 5.1); A.V. Shenoy and V.M. Nadkarni, Textile Res. J. (Nov. 1984), 778 (Figs. 5.7 to 5.10, Tables 5.2 to 5.4); A.K. Sengupta, R.K. Singh and A. Majumdar, Textile Res. J., 44 (1974), 155 (Fig. 8.15); D. K. Smith, Textile Res. J. 29 (Jan. 1959), 34 (Figs. 17.2 & 17.3); Wayne A. Sisson, Textile Res. J., 30 (Mar. 1960), 154 (Table 17.1); T.E. Muller, F.P. Barch and C.C Daul, Textile Res. J., 46 (Mar. 1976), 186 (Tables 17.8, 17.9 & 17.10); A.S. Chegolya, D.O. Cuishpan and E.Z. Burd, Textile Res. J., 59 (Sept. 1989), 503 (Table 17.12); J.P. Knudsen, Textile Res. J., 33 (1963), 13 (Table 15.4); J.P. Bell and J.H. Dumbleton, Textile Res. J., 41 (1971), 200 (Fig. 15.19); CH. Chen, J.L. White, J.E. Spruiell and B.C Goswami, Textile Res. J., 53 (1983), 47 (Fig. 19.9), 48 (Figs. 19.10 & 19.11), 49 (Fig. 19.12 and Table 19.2), 50 (Fig. 19.13); CW. Ericson and J.F. Baxter, Textile Res. J., 43 (1973), 371 (Table 19.1).

U.S. Patent and Trademark Office, Washington DC. T.I. Blair and P.W. Morgan, U.S. Patent 3,673,143 (1972) and 3,817,914 (1974), (Fig. 18.3).

Walter C. McMickle, Atlanta. A.V. Shenoy and V.M. Nadkarni, Fiber World, (Sep. 1985),52 (Tables 5.5 & 5.6); E. Maslowski and A. Urbanska, Fiber World, (May 1989), 6 (Table 15.5).

Woodhead Publishing Co., Cambridge. K. Kajiwara and J.E. McIntyre, Eds., Advanced Fibre Spinning Technology, (1994), 42 (Fig. 4.13).

World Textile Publications Ltd., Bradford. Andrew Thornton, Textile Month, (Feb. 1993),43 (Table 17.14 and Fig. 17.10).

Zellweger Uster AG, CH-8610 Uster. Uster News Bulletin, 35 (Oct. 1988), 19-21 (Figs. 11.3 & 11.7); Uster Publication, "Fault Lexicon for man-made continuous filament yams - Examples of tests carried out with Evenness Testers IC & IIC", 31-50 (Figs. 11.4, 11.5 & 11.6).

Zimmer A.G., Germany. International Fiber Journal, 7(5) (1982), 34 (Fig. 20.11).

81 units and symbols

The International 5ystem of Units (51) divides units into three classes: base units, supplementary units and derived units. 51 is based on seven well-defined base units (Table A) which by convention are regarded as dimensionally independent. There are two supplementary units - the radian and the steradian (Table A).

Derived units are formed by combining base units, supplementary units, and other derived units according to the algebraic relations linking the corresponding quantities. The symbols for derived units are obtained by means of the mathematical signs for multiplication, division, and use of exponents. For example, the 51 unit for velocity is the metre per second (m/s or ms- I ), and that for angular velocity is the radian per second (rad/s or rads-I ). Derived units are given in Table B. Table C gives the preferred 51 units and conversion factors for some of the non-51 units used in this book.

Table A Base and supplementary SI units

Quantity Unit Symbol

Length metre m Mass kilogram kg Time second s Electric current ampere A Thermodynamic temperature kelvin K Amount of substance mole mol Luminous intensity candela cd Plane anglea radian rad Solid anglea steradian sr

a Supplementary units.

xxii 81 units and symbols

Table B Derived SI units with special names

Quantity Unit Symbol Formula

Frequency (of a periodic phenomenon) hertz Hz S-l

Force newton N kg m S-2

Pressure, stress pascal Pa Nm-2

Energy, work, quantity of heat joule J Nm Power, radiant flux watt W Js-1

Electric charge coulomb C As Electric potential,

potential difference, electromotive force volt V WA-1

Electric capacitance farad F CV-1

Electric resistance ohm n VA-1

Electric conductance siemens S AV-1

Magnetic flux weber Wb Vs Magnetic flux density tesla T Wbm-2

Inductance henry H WbA-1

Celsius temperature degree Celsiusa °c a

Luminous flux lumen 1m cd sr Illuminance lux Ix Imm-2

Activity (of a radionuclide) becquerel Bq S-l

Absorbed dose gray Gy J kg-1

Dose equivalent sievert Sv J kg-1

a The Sl unit of thermodynamic temperature is the kelvin (K), and this unit is properly used for expressing thermodynamic temperature and temperature intervals. Wide use is also made of the degree Celsius (0C), which is the SI unit used for expressing Celsius temperature and temperature intervals. The Celsius scale (formerly called centigrade) is related directly to thermodynamic temperature (kelvin) as follows:

The temperature interval one degree Celsius equals one kelvin exactly. Celsius temperature (I) is related to thermodynamic temperature (D by the equation:

1 = T - To

where To = 273.15 K by definition.

81 units and symbols xxiii

Table C Units used in this book and conversion factor to obtain preferred SI unit1

Quantity Unit used at some Preferred Conversion places in this book SI unit factor

Length inch (in) m 2.54 x 10-2

mm 25.4 p,m 2.54 x 104

Area inch2 (in2) m2 6.4516 x 10-2

Volume cm3 m3 10-6

dl m3 10-4

I m3 10-3

Density gcm-3 kgm-3 103

Linear density denier (den) tex 0.1111 dtex 1.1111

Tenacity gfden-1 Ntex-1 8.829 x 10-2

(mass stress) gftex-1 Ntex-1 9.81 x 10-3

Surface tension dyncm-1 Nm-1 10-3

Viscosity pOise (P) Nsm-2 10-1

centipoise (cP) Nsm-2 10-3

Specific heat cal (g0C)-1 J kg-1 K-1 4.19 X 103

Force gf N 9.81 x 10-3

kgf N 9.81 dyne N 10-5

Ibf N 4.44822 Stress/pressu re kgfmm-2 N m-2 (Pa) 9.81 x 106

kgfcm-2 Nm-2 (Pa) 9.81 x 104

Ibf in-2 (p.s.i./psi) Nm-2 (Pa) 6.89 x 103

Pressure mmHg N m-2 (Pa) 133.322 atmosphere (atm) N m-2 (Pa) 1.013 x 105

Energy cal Nm-1 (J) 4.1868

1 Conversion factors between various units of stress and mass stress are given in Table D.

Tab

le D

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un

it

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in

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top

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the

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ty o

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, W

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PA

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02)

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-1

gft

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kg

f m

m-2

dy

n cm

-2

Pa

Ibf

in-2

Co

lum

n I

1

gfd

-1

9 p

x9

P

x 8

.83

X 10

8 P

x 8

.83

X 10

7 P

x 1

.28

X 10

4

gft

e[1

0.

111

p P

x 9

.81

X 10

7 p

x9

.81

x1

06

P x

1.4

2 X

10

3

kgf m

m-2

0.

111

9.81

x

107

9.81

X

10

6 1.

42 x

103

P

P

dyn

cm

-2

1.13

x 1

0-9

1.

02 X

10

-8

1.02

X 1

0-8

0.

1 1.

45 x

10

-5

p p

Pa

1.13

x 1

0-8

1.

02 X

1

0-7

1.

02 X

1

0-7

10

1.

45 X

1

0-4

p P

Ibf

in-2

7.

81

5 --

X 1

0-

7.03

4

--

x 1

0-

7.03

x 1

0-4

6.

90 x

104

6.

90 X

10

3

p p

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mpl

es:

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co

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s st

ress

in g

l d-1

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to a

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Pa,

the

gl d

-1 v

alue

will

hav

e to

be

mul

tiplie

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p x

8.8

3 x

10J

A s

tres

s va

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in

kg

lmm

-2 ca

n b

e co

nver

ted

into

a m

ass

stre

ss i

n g

lte

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by

mul

tiply

ing

it by

1!p

.

Note on equivalence and equivalent weight

The concept of equivalence and its quantification in terms of equivalent weight has been used in Chapters 10, 12, 14 and 15 of this book to estimate the end group content in polymers or the amount of reactants in specific chemical reactions, e.g. the amount of water to be charged into caprolactam at the beginning of polymerization in a VK tube. Since different units have been used by different authors to denote equivalent weight, a brief description of the concept and the units that have been used is given below, mainly to facilitate conversion from one unit to another.

In chemical compounds, equivalent weight can be expressed as weight associated with unit functionality, where functionality is the number of reactive functional group(s) per molecule. 'Equivalent weight' for chemical compounds (or polymers) is thus defined as that weight which contains one gram equivalent weight of the component taking part in the reaction. It often happens that the same compound will possess different equivalent weights in different reactions. An example relevant to the use of this term in the present book is given below:

Consider a simple chemical compound, viz. pure hexamethylene diamine, H2N-(CH2)6-NH2, which has two amino groups and an approximate molecular weight of 116.2. The equivalence in terms of its reaction with acids may be expressed as

• equivalent weight = 116.2/2 = 58.1, expressed as a number, • gram equivalent = 58.1 g, expressed in grams.

Alternatively, the equivalence may also be expressed in terms of

• eq g -1 and related units: since 58.1 g is the gram equivalent of one amino group in the compound, 1 gram will be the equivalent of 1/58.1 amino gr?~p, w~ch may be exrre~s~d as 1!58.1 i.e. 17.2 x 10-3 eq g-1 or 17.2 mllh eq g 1 or 17.2 x 10 milh eq kg 1 or 17.2 x 103 eq ton-1.

xxvi Note on equivalence

• eq mole-I: this can be obtained by multiplying equivalence in eq g-I by molecular weight in g mole-I, i.e., 17.2 x 10-3 eq g-I x 116.2 g mole-I = 2 eq mole-I.