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A dielectric properties of natural and synthetic rubber-sulphur compounds Codrington, Robert Smith 1948

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£ £ 3  THE D I E L E C T R I C PROPERTIES OF NATURAL AND  SYNTHETIC  RUBBER-SULPHUR COMPOUNDS  by  Robert  Smith  Codrington  A Thesis submitted i n p a r t i a l the  fulfilment of  requirements f o r the degree o f MASTER OF ARTS in  t h e department of PHYSICS  THE UNIVERSITY OF B R I T I S H COLUMBIA April,  1948  ^7  J  ABSTRACT  The  dielectric; properties  rubber-sulphur tures  compounds have b e e n i n v e s t i g a t e d  range extending from  100 c y c l e s  i n v e s t i g a t i o n h a s shown t h a t  b u t y l rubber  i s l e s s than  that  a t tempera-  constants o f both types  increasing  temperature The  Gevers'  and i n c r e a s i n g  o f these rubbers  i n the rubbers,  plained  by a c o m b i n a t i o n  geneity  theory. The  been a p p l i e d  may be e x p l a i n e d theory.  the behaviour  of the dipole  rubber  and t h a t t h e  decrease  shown t h a t  with  the d i e l e c by t h e I f free  sul-  must be e x -  t h e o r y and t h e inhomo-  Kirkwood-Fuoss t h e o r y f o r p o l a r to natural  constant o f  extension.  e x t e n s i o n o f t h e Debye d i p o l e  phur i s p r e s e n t  rubber  o f rubber  i n v e s t i g a t i o n has a l s o  behaviour  t o 20 m e g a c y c l e s .  the d i e l e c t r i c  of natural  dielectric  tric  and b u t y l  o f 2G°C a n d 60°C a n d e x t e n s i o n s o f 0% a n d 2 0 0 % , i n a  frequency This  of natural  polymers,  w i t h 2% s u l p h u r .  has  The d i p o l e  moment p e r monomer u n i t o b t a i n e d f r o m t h e K i r k w o o d - F u o s s p l o t for  this  sample was 0.41 Debye u n i t s .  ACKNOWLEDGEMENT  This work was carried out with the aid of a r e search grant* to Dr.O.  Bliih from the Associate Committee on  Synthetic Rubber of the National Research Council of Canada. The author wishes to thank Dr. 0. Bluh f o r his many helpful suggestions, and f o r his constant interest i n the progress of the work. This investigation i s a continuation of the work of Mr. L. 7. Holroyd to whom the author i s indebted f o r several valuable suggestions.  The author i s also indebted  to the Research D i v i s i o n of the Polymer Corporation f o r the samples they have prepared f o r t h i s research. The author wishes to express his appreciation to the National Research Council of Canada f o r the Studentship f o r 1947/48 which has enabled him to complete t h i s work.  TABLE OF CONTENTS Page I.  II.  III.  IV.  V.  71. "VII.  INTRODUCTION 1. General Introduction 2. P r o p e r t i e s o f N a t u r a l Rubber 3. P r o p e r t i e s o f B u t y l Rubber 4. P r o p e r t i e s o f S t r e t c h e d Rubber THEORY OF DIELECTRICS 1. D e f i n i t i o n o f t h e Terms 2. The Maxwell-Wagner T h e o r y 3. The Debye T h e o r y 4. Summary  .  .  APPARATUS 1. The M e a s u r i n g I n s t r u m e n t s 2. D e s c r i p t i o n o f the Apparatus EXPERIMENTAL PROCEDURE 1. General Procedure . 2. Measurement o f t h e Sample T h i c k n e s s 3. Edge C o r r e c t i o n . . . . . . . 4. C o r r e c t i o n f o r L e a d Impedence RESULTS 1. C o m p o s i t i o n o f t h e Samples 2.. T a b l e s a n d G r a p h s 3. Discussion o f the Results  1 2 5 7 8 9 10 14 15 15  . .  . . . .  21 23 24 25  28 29 37  CONCLUSION  44  BIBLIOGRAPHY  .45  MATES  Page I.  The Standard C e l l  17  II.  Front View of the Apparatus  18  III.  The Measuring Instruments . . . . . . . . . . . .  19  IV.  Cross-seotion of the Apparatus  20  V.  Correction f o r the Twin-T Bridge  -VI.  Results f o r Natural Rubber  2% S  . .  27 ........  31  VII.  Results f o r Natural Rubber 10% S  32  VIII.  Results f o r Natural Rubber 15% S  IX.  Results f o r Butyl Rubber  2% S  X.  Results f o r Butyl Rubber  4% S  35  XI.  Results f o r Butyl Rubber 10% S  36  XII.  Debye and Maxwell-Wagner Curves  XIII.  Kirkwood-Fuoss Plots f o r Sample 1-A . . . . . .  . . . . . . . . .  .  33 34  40 41  THE DIELECTRIC PROPERTIES OF NATURAL AND SYNTHETIC RUBBER-SULPHUR COMPOUNDS  I.  1.  GENERAL  INTRODUCTION  The factor  INTRODUCTION  dielectric  constant  ( 6*) and t h e d i s s i p a t i o n  ( t a n S ) have been shown t o be i n t i m a t e l y r e l a t e d t o  the molecular constants o f d i e l e c t r i c s . of the d i e l e c t r i c  An  investigation  p r o p e r t i e s o f r u b b e r may t h e r e f o r e p r o v i d e  information which w i l l  indicate  the structure o f the rubber  molecule. The ly  applied  t e r m s " r u b b e r " and " e l a s t o m e r " a r e now g e n e r a l -  t o any s u b s t a n c e  showing t h e c h a r a c t e r i s t i c  p h y s i c a l p r o p e r t i e s o f long-range anomolous t h e r m o e l a s t i c b e h a v i o u r . a p p l i e d t o any s u b s t a n c e tion.  reversible  e l a s t i c i t y and  T h i s d e f i n i t i o n may be  regardless o f i t s chemical  composi-  However, t h e m a j o r i t y o f n a t u r a l and s y n t h e t i c  r u b b e r s h a v e now b e e n shown t o be l o n g c h a i n p o l y m e r s o f hydrocarbon  groups.  The  term polymer  b i n a t i o n o f small molecules  refers called  t o a c h e m i c a l v a l e n c e com"monomers" i n t o a  large  molecule c a l l e d a "macromolecule".  A copolymer i s a sub-  stance whioh has macromolecules composed of two or more d i f ferent monomers.  When the macromolecules are composed of  100 or more monomers the substance i s referred to as a high polymer.  2.  PROPERTIES OF NATURAL RUBBER X-ray and chemical analysis have shown that natural  rubber i s a high polymer composed of isoprene monomers i n a c i s configuration (see Eig.,1). CH*  H \  c=c  / CH  CHY  /  V  \ CH  2  / 2  CH  2  H c=c  CH*  /  H  \  \  c=c  / CH  2  CH  2  /  \ CH  2  Figure 1. The number of monomer units composing the macromolecule i s believed to be between 2000 and 4000. James and Guth ) have shown that a quasi-free 1  r o t a t i o n about a single carbon-carbon bond i n long chain molecules, i s s u f f i c i e n t for the development of rubberlike elasticity.  This free r o t a t i o n i s responsible f o r the d i -  e l e c t r i c losses i n vulcanized rubber since i t w i l l allow the rubber-sulphur dipoles to follow the o s c i l l a t i o n s of the electric  field. Vulcanization may  be defined to be any treatment  which maintains the e l a s t i c i t y of the rubber but reduces i t s 1  ^H.  James and E. Guth  J. of Chem Phys. 11, 455,  1943.  plasticity.  There  t h e most common one  a r e a number o f v u l c a n i z a t i o n  processes,  b e i n g the combination o f the rubber  sulphur which introduces rubber-sulphur d i p o l e s i n t o rubber  effect  o f v u l c a n i z a t i o n upon t h e  p r o p e r t i e s o f r u b b e r has Blake ), 1  Kitchin ^, 2  investigations  and  Scott  show t h a t  v a l u e f o r 12%  the d i e l e c t r i c  constant of  s u l p h u r c o n t e n t and  combined s u l p h u r .  this  initially  added t o t h e end d o u b l e  bonds o f t h e r u b b e r  addition activates  I n t h i s way,  the combination  R = = R  -  -  -  Bonds  The m o l e c u l e s hence a r e n o n - p o l a r . ^ C . R . B o g g s and ^D.W.Kitchin  2JA.Scott  o f raw  Ind.and  A  R =  R  R  2.  rubber are symmetrical  However, a s  J.T.Blake  the  >  -  Figure  with  2).  towards the c e n t r e (see P i g .  ' \ R  double  activate  p r o g r e s s i v e l y f r o m t h e ends o f  ;—Activated  macro-  the adjacent  the next double  molecule  have  the sulphur i s  t a k e on a s u l p h u r atom and  the sulphur proceeds  rubber  Blake  bonds w h i c h i n t u r n may bond.  These  reaches a maxi-  Boggs and  b e h a v i o u r by a s s u m i n g t h a t  This f i r s t  and  C u r t i s and M c P h e r s o n ^ .  explained  molecule.  dielectric  b e e n i n v e s t i g a t e d by Boggs  increases with increasing  2  the  configuration. The  mum  with  s u l p h u r i s added  Ind.and  Eng.Chem 24,  H . C u r t i s and A . M c P h e r s o n  Eng.Chem 22, H9,  748,  and  the 1930.  1932.  Bur.Stan.,  173, 1933.  J . o f Res.  11,  d i s s y m m e t r y o f t h e m o l e c u l e and molecule increases u n t i l with  sulphur  tent  i n c r e a s e s the  of the  atoms.  A  henee t h e  of  h a l f t h e d o u b l e bonds a r e further increase  symmetry and  i n the  the  saturated  sulphur  hence d e c r e a s e s t h e  con-  polarity  molecule. This  simple  explanation  of the  o f vulcanized rubber i s complicated  by  addition of sulphur  the  the  polarity  not  only alters  i n d i v i d u a l molecules,  characteristics of t h e i r Tuckett ) 1  has  the  fact  behaviour  that  the  d i p o l e moments o f  a l s o changes the  environment.  In  physical  particular,  suggested that v u l c a n i z a t i o n introduces  l i n k a g e s between t h e molecular  but  dielectric  rubber macromolecules c r e a t i n g  f o r c e s w h i c h oppose t h e f r e e r o t a t i o n o f  cross-  interthe  dipoles. The  theory  e x p l a i n the nature d i t i o n of the  of the  sulphur  such a dissymmetry The  o f Boggs and  to the  vulcanization.  The (it ) 3  large.  A small  -^R.F.Tuckett ^ H . J a m e s and  d i s s y m m e t r y p r o d u c e d by  atoms, and  a u t h o r has  such that f o r C <  attempt the  i t i s questionable  to  ad-  whether  actually exists.  maxima a r e due  cross-linkages  B l a k e does not  formation  of the  tan S  cross-linkages  during  f u n c t i o n ^ ) w h i c h r e l a t e s t h e number to the  12,  V  increase  concentration i s small in C  s  and  for C  T r a n s . F a r a d a y Soc. E.Guth  t ' and  suggested that the  s  38,  J . o f Chem.Phys.  of sulphur  for C <  s  >  12,  1 2 would 310, 15,  Cs  is  V  is  therefore  1942. 669,  of  1947.  result  i n the formation  latively  few c r o s s - l i n k a g e s , w h i l e  Cs > 12 w o u l d r e s u l t cross-linkages This  at a value  of 0  an i n c r e a s e  i n the formation  and r e l a t i v e l y explanation  would t h e r e f o r e  sult  o f a l a r g e number o f d i p o l e s a n d r e -  o f a l a r g e number o f  few d i p o l e s .  o f the vulcanization  r e q u i r e t h e £ » a n d t a n 6" S  such that a small  i n the formation  in O 3 for  o f equal  process  maxima  to occur  in C  would r e -  increase  a  0  numbers o f c r o s s - l i n k a g e s a n d  dipoles.  3.  PROPERTIES OF BUTYL RUBBER B u t y l rubber  i s a copolymer o f i s o b u t y l e n e  s m a l l amounts o f a d i o l e f i n  such as i s o p r e n e .  with  The number  o f monomer u n i t s c o m p o s i n g t h e b u t y l m a c r o m o l e c u l e i s b e t w e e n 1200 and 2400.  Rehner ^ 1  monomers a r e d i s t r i b u t e d  h a s shown t h a t  the isoprene  a t r e g u l a r i n t e r v a l s o f 50 t o 200  monomer u n i t s i n t h e p o l y i s o b u t y l e n e  chain.  A p o s s i b l e s t r u c t u r e f o r b u t y l rubber i s given i n Fig. 3. GH3 - C I  CH2 ~r~ CH2  CH,  CH-  CH3 3  Polyisobutylene  |  CH —C 2  CH  H  C HL  Isoprene Figure  J.Rehner  c  I n d . a n d Eng.Chem.  Polyisobutylene 3.  36,  47,  1944.  •3  The  isobutylene  bonds a n d a s a r e s u l t , p r e n e monomers  monomer u n i t s c o n t a i n no d o u b l e  are very  are introduced  stable.  However when i s o -  into the chain,  the molecule  becomes l e s s s t a b l e o r " t h e d e g r e e o f s a t u r a t i o n " ,The  decreases.  v u l c a n i z a t i o n o f b u t y l r u b b e r has n o t been  11 extensively treated i n the l i t e r a t u r e . t h a t t h e number o f c r o s s - l i n k a g e s is  Plory  between t h e b u t y l m o l e c u l e s  p r o p o r t i o n a l t o t h e number o f i s o p r e n e  the macromolecule. during  Since  This process  the isoprene  the majority  that  the s u l -  of the vulcanization are r e l a t i v e l y  vulcanization.  o f the dipoles exist  few  It in. the .  b e t w e e n t h e m o l e c u l e s where t h e y a r e h e l d  more o r l e s s r i g i d l y  by t h e i n t e r - m o l e c u l a r  t h e r e f o r e t o be e x p e c t e d t h a t canized  a r e formed  units.  there  d i p o l e s formed d u r i n g  shows, a l s o , t h a t cross-linkages  implies  q u a l i t a t i v e explanation  i n b u t y l r u b b e r shows t h a t  rubber-sulphur  monomer u n i t s i n  the cross-linkages  vulcanization, Elory's result  phur o n l y combines w i t h  ' h a s shown  b u t y l rubber w i l l  vulcanized natural  forces.  t h e £ ' and t a n S  Iti s  f o r vul-  be l e s s t h a n t h e £ ' a n d t a n S f o r  rubber.  This result  has been v e r i f i e d  by t h e p r e l i m i n a r y  measurements o f S p a r k s a n d h i s c o - w o r k e r s  '.  However, a  more t h o r o u g h i n v e s t i g a t i o n o f t h e d i e l e c t r i c p r o p e r t i e s o f b u t y l rubber i s necessary before  any d e f i n i t e  conclusions  may be d r a w n . 1  2  )p.J.Jlory  R u b b e r Chem.Tech.  1 9 , 552, 1946.  5w.Sparks, I . L i g h t b o w n , . L . T u r n e r , P . E r o l i e h , a n d C . K l e b a t t e l I n d . a n d Eng.Chem 32, 731., 1944.  7. 4.  PROPERTIES OF STRETCHED RUBBER  1) X-ray a n a l y s i s of stretched n a t u r a l  and  r u b b e r s have shown t h a t f o r a g i v e n t e m p e r a t u r e a critical the  e x t e n s i o n above w h i c h  rubber.  there  degree  and  '  exists  begin to form i n  i f the e x t e n s i o n exceeds  80%.  e x t e n s i o n i n c r e a s e s w i t h temperature.  temperature, the  butyl  F o r example, i n r u b b e r a t room t e m p e r a t u r e  c r y s t a l s a r e formed critical  crystals  21  the  This For a given  f o r e x t e n s i o n s above t h e c r i t i c a l  value,  o f c r y s t a l l i z a t i o n i s p r o p o r t i o n a l to the  exten-  sion. If the will  degree  the d i p o l e s form p a r t of the c r y s t a l  o f f r e e - r o t a t i o n w h i c h may  be s m a l l .  ber w i l l  be a s s i g n e d t o t h e m  Hence t h e f o r m a t i o n o f c r y s t a l s i n t h e  result  been o b s e r v e d  lattices  i n a decrease i n  .  This decrease  i n t h e c a s e o f n a t u r a l r u b b e r by  rub-  has  Schiller^  and H o l r o y d ^ ) .  1  2  ) j.R.Katz ) R.Brill  Report  and F . H a l l e  3) L . S c h i l l e r 4  t o Symposium on R u b b e r ;  ) LiV*Holroyd  Ann  R u b b e r Chem.Tech.  der Phys.  Master's  35,  931,  Delft, 11,  687,  1911.  T h e s i s , U.B.C., May  1947.  Oct. 1938.  1936.  8.  II,  1.  DEFINITION OF TERMS In  is  THEORY OF D I E L E C T R I C S  related  dielectric  media t h e d i e l e c t r i c  to the e l e c t r i c  field  the case o f i s o t r o p i c  D  s t r e n g t h E by t h e e q u a t i o n  ef  D = In  displacement  m a t e r i a l s where t h e s e v e c t o r s a r e  parallel D = &E If the  (1)  E represents an a l t e r n a t i n g  electric  field of  form, E  where E  0  denotes  denotes  =  E  e J  0  a c o n s t a n t , <*>  the time,  W  t  denotes  the frequency  then D = £ EoeJ*^  Experimental  results  (2)  show t h a t  f o r most  m a t e r i a l s t h e r e i s a s m a l l phase d i f f e r e n c e Hence  and t  dielectric  between D a n d E .  ( 2 ) becomes  D -  e BoeJ<  w t  o  - > 6  or D = ( t ooaj 0  Henoe  &  - j £ s i n $ )E e^ 0  0  t  (3)  has the form  The r e a l the d i e l e c t r i c  part o f the expression ( £') i s c a l l e d  constant.  The t a n g e n t  o f t h e phase a n g l e ,  9  tan 6 = t o as the d i s s i p a t i o n  is  referred  of  t h e energy d i s s i p a t e d  2.  THE MAXWELL-WAGNER  4r  factor  (5) a s i t i s a measure  i nthe d i e l e c t r i c .  THEORY  1864 Von Siemons o b s e r v e d an i n c r e a s e  In  t e m p e r a t u r e o f d i e l e c t r i c s when t h e y were p l a c e d nating f i e l d . rise  Hopkinson ^ 1  c o u l d be a t t r i b u t e d  assumed t h a t t h i s  t o an a f t e r - e f f e c t  ment, a n d u s i n g a p r i n c i p l e  i n an a l t e r -  temperature  of the displace-  o f s u p e r p o s i t i o n he w o r k e d o u t  and t a n 6  expressions f o r  i n the  i n terms o f an a f t e r - e f f e c t  f u n c t i o n 0*(t)  V  = £00(1-  jT  costut  aglil  I" = - f U ^ s i n u i t Pellat ^ 2  (6)  dt)  (7)  dt  gave t h e a f t e r - e f f e c t  f u n c t i o n t h e form  <?(t) = k e " * ^ where k r e p r e s e n t e d  the t o t a l f r a c t i o n a l dispersion o f £  1  l  and  X  was a t i m e c o n s t a n t c a l l e d  after-effect.  the relaxation  f o r 0 ( t ) i n (6)  Substituting  u* %  1 +k +  c  time o f t h e  a n d (7)  gives;  c a  T h e s e e x p r e s s i o n s were f o u n d t o b e t o o d e p e n d e n t Dj.Hopkinson 2  )  Pellat  Phil.Trans. J.of Physics  166, 9,  489, I876.  313, 1 9 0 0 .  10.  upon t h e f r e q u e n c y and that  t h e r e s h o u l d be  i t was  suggested  a distribution  by Yon  Schweidler" "^ 1  of relaxation  times  2)  G-("C)'.  Wagner  form;  hence, r e p l a c i n g  tegrating  are  T  t  between z e r o and  Jo  Coa+x where  denotes  0 ( f ) i n (8)  by  infinity  £ =  £  and  (11)  0  o> = o  when  (10)  can a l s o  and i n -  £  and  0  and  £  M  £ =  torily  predict  mixtures:  the d i e l e c t r i c  theory o f Maxwell^to  the  o f one  derived  dielectric  These e q u a t i o n s  behaviour  of such  satisfac-  inhomogeneous  the d i e l e c t r i c  be-  DEBYE THEORY  by D e b y e ^ who 4  theory of d i e l e c t r i c s  i n t r o d u c e d the concepts  orientation polarizations.  ^E.Von  be  dielectrics.  A more f u n d a m e n t a l veloped  ex-  t h e y do n o t , however, p r e d i c t  haviour of pure  THE  by  i n f i n i t e number o f s p h e r e s  embedded i n a n o t h e r d i e l e c t r i c .  Schweidler  )K.W.Wagner  2)C.Maxwell 4  (9)  and  co = oo  c a s e o f an  2  Gaussian  gives,  t e n d i n g the two-layer inhomogeneity  and  of  t h e mean r e l a x a t i o n t i m e , and  Equations  3.  s h o u l d be  l + t»£ t r ^  constants such t h a t  when  G-( T )  ' assumed t h a t  )p.Debye  The  Ann.der Phys.  Ann.der Phys. Electricity  40,  de-  deformation  deformation p o l a r i z a t i o n 24,  817,  and M a g n e t i s m  Polar Molecules, 1929,  of  was  711,  1907.  1913. Vol.I,  328,  Chem.Catalogue  Co.  Oxford.  11. (PaJ  i s a t t r i b u t e d t o d i p o l e s w h i c h a r e f o r m e d when t h e d i -  electric  i s placed  i n an e l e c t r i c  field.  The f o r m a t i o n  of  these d i p o l e s  r e s u l t s from the d i s t o r t i o n of the e l e c t r o n i c  orbits within  t h e atoms.  The  o r i e n t a t i o n p o l a r i z a t i o n ( P ) i s a t t r i b u t e d to 0  permanent m o l e c u l a r d i p o l e s w h i c h o r i e n t a t e t h e m s e l v e s i n t h e direction of the applied  electric  field.  The r o t a t i o n o f  t h e s e d i p o l e s . under t h e i n f l u e n c e o f t h e e l e c t r i c opposed  field i s  by t h e t h e r m a l a g i t a t i o n o f t h e m o l e c u l e s , a n d i t i s  t h i s o p p o s i t i o n which gives Debye has shown  P  rise  loss.  that  - j ft N «  0  to the d i e l e c t r i c  (  0  where N = A v o g a d r o ' s number, rt, 0  = the p o l a r i z a b i l i t y  m o l e c u l e , 44, = t h e d i p o l e moment, k = B o l t z m a n ' s temperature.  which from the Clausius-Mosotti  p =  )  (12b)  Po -  and T = t h e a b s o l u t e  1 2 a  The t o t a l  of the  constant,  polarization P  J  equation i s ,  e-jV 1+2  where V = t h e m o l a r v o l u m e , i s g i v e n  by t h e sum o f P  Q  a n d Pa*  Hence P = f Equation  (13)  « N ( t  (13)  0  has t h e f o r m P• - a + %  '  •  w h i c h f o r t h e v a r i a b l e s P and i , i s t h e e q u a t i o n o f a s t r a i g h t  12. l i n e with slope  (14)  b = i^jLfd The  d i p o l e moment M  lated  from  The 6  and  (9)).  time  a s u b s t a n c e may  t h e r e f o r e be  from experimental  Debye t h e o r y l e a d s t o e q u a t i o n s f o r  to the time r e q u i r e d  their  equilibrium The  the d i p o l e s .  as i t does not  c o n s i d e r the  1  interaction  energy  behaviour o f polymers  dielectric  by t h e t h e o r i e s o f C o l e and latter  - cosh"  R  2  ) w.A.Yager  Physics  3) R.CO1S and K . C o l e 4  36,  Phys.Zeits  ) R.FUOSS and  7,  100, 434,  1  (i/)  £"m(  £"  and +  2  (2  been p r e -  o f Fuoss  and of  +  be-  the q u a n t i t y  l/fc' m) 2  1/V  )  2  1935. 1936.  J . o f Chem.Phys.  J.Kirkwood  these  there i s a l i n e a r relationship  tween t h e l o g a r i t h m o f t h e f r e q u e n c y (  a  solids. has  C o l e ^ ) , and  of  ( q ) , and  theory requires a d i s t r i b u t i o n  r e l a x a t i o n times such that  or  extend  Both o f  The  D p . Debye  to  2  i n t h e i r a p p l i c a t i o n to  V  turn  interaction  theories are r e s t r i c t e d  The  to  to s o l i d s  Gaussian d i s t r i b u t i o n of r e l a x a t i o n times.  Kirkwood^").  relaxation  position  D e b y e ) and Y a g e r ) have a t t e m p t e d  t h e t h e o r y b y p o s t u l a t i n g an  dicted  (8)  position.  Debye t h e o r y i s n o t a p p l i c a b l e  viscous liquids  £ ' and  f o r the d i p o l e s  t h r o u g h l / e ^ h o f t h e a n g l e between t h e i r d i r e c t e d and  may  (equations  However, i n t h e Debye e x p r e s s i o n s t h e refers  b  results.  which are i d e n t i c a l t o those of P e l l a t  X  calem-  (14) s i n c e k and N a r e known c o n s t a n t s and  be d e t e r m i n e d  tan  of  9,  341,  J . o f Amer.Chem.Soc.  1941. 63,  385,  1941.  13. where fc"m = maximum d i e l e c t r i c loss and &'m *= the d i e l e c t r i c constant at.the frequency of maximum l o s s . In the case of polymers, A  2  i s replaced i n (12b)  by the product of the dipole moment of the i s o l a t e d monomer a n d ^ which i s the vector sum of >c and the moment i n duced by the molecule i n i t s environment.  Substituting f o r  At?- i n (12b) gives;  P  =  4  n N M »xL  °  9kT  = 9kT P  or  (16)  Q  4JTN  The p o l a r i z a t i o n at zero frequency i s given by,  *b<o) =  y%r-v  where oc i s the slope of the straight l i n e given by p l o t t i n g V(  £") against log 1/ .  Substituting f o r P  c  i n (16)  gives  oc 7t  N  V  The dipole moment per monomer unit can: be shown to be M  =  (18)  where n = the number of monomer units per molecule. s t i t u t i n g f o r xc  %  Sub-  i n (18) gives >i -71 oc N n  and since V = nM^o  where M = the molecular weight of the  monomer unit and f> - the density, (19) becomes, 1 £"m k T M  /  2 0  *  14,. The Covers ^ 1  G(q).  who i The  Fuoss-Kirkwood  t h e o r y has  been extended  considers a d i s t r i b u t i o n of activation activation  energy  q i s the  energy  d i p o l e t o remove i t f r o m t h e p o t e n t i a l w e l l normally e x i s t s . bility  I f X(q)  energy  <*>  suscepti-  q,  M  1+  then;  (2i)  4  t-  t a n <f - - i - 2 £ N G | q o ) X ( q o ) k T  (22)  2  where q  4.  Q  « the c r i t i c a l  mena;  a r e two  distinct  types of d i e l e c t r i c  t h e t y p e a s s o c i a t e d w i t h inhomogeneous  o f inhomogeneous d i e l e c t r i c s and  (11)  a r e g i v e n by The  while the equations tan €  £ » and (21)  and  pheno-  dielectrics  the type a s s o c i a t e d w i t h p o l a r d i e l e c t r i c s .  tan 4 (10)  energy.  SUMMARY There  and  activation  the  i n which i t  t< = e • 4 « r^-§t4 a Jo  energies  supplied to  r e p r e s e n t s the s t a t i c  o f a d i p o l e h a v i n g an a c t i v a t i o n  by  a r e g i v e n by  The  £ *  and  equations  tan 6 of polar d i e l e c t r i c s (22).  maxima a s s o c i a t e d w i t h  (11)  are  referred  t o a s Maxwell-Wagner maxima w h i l e t a n 6 maxima a s s o c i a t e d with  (22)  are r e f e r r e d  C a r t e r , Magat and exhibit  t o as Debye maxima.  S m y t h ) have shown t h a t 2  Schneider, a dielectric  may  b o t h t y p e s o f t a n 6 maxima.  ^N.V.Gevers  P h i l i p s Res.Rep.  1,  298,  1946.  ^W.Schneider, W . C a r t e r , M.Magat, and C P . S m y t h Soc. 67, 959,  J.Amer.Chem.  1945.  15.  III.  1.  APPARATUS  THE MEASURING INSTRUMENTS The  quency r a n g e s (a)  (b)  100  measuring  i n s t r u m e n t s used  were; cycles  t o 15 M.c.  Schering Bridge  - General Radio  type  716-B  Oscillator  -  type  608-A  Null  - General Radio  Detector  50 K . c .  500 K . c . Twin-T  Signal Radio  2.  DESCRIPTION The  - Boonton type to  an i n c h .  rigidly shield  t y p e 12J1-A  160-A  20 M.c.  Impedence Bridge - General Radio  type  821-A  Generator -  type  805-C  Detector  General Radio  - Hammarlund  t y p e HQ.-129X  0 E THE APPARATUS  standard c e l l  consisted  p l a t e s whose f a c e s were g r o u n d of  General Radio  t o 1 M.c.  Q-meter (c>  i n the various f r e -  The l o w e r p l a t e  flat  o f two s t a i n l e s s  to better  ( d i a m e t e r = 5")  than  steel  l/lOOO**  1  was mounted  on a maple b l o c k a n d was g r o u n d e d t o t h e c o p p e r surrounding the standard c e l l .  The s m a l l e r t o p p l a t e  ( d i a m e t e r = 3") was h e l d c o a x i a l l y w i t h t h e l o w e r p l a t e  by a  pyrex tube through which p r e s s u r e from a 2 k i l o g r a m weight  16. was a p p l i e d  to the  The  sample.  t o p p l a t e was c o n n e c t e d t o t h e m e a s u r i n g  ments w i t h 1-1/2  o f 1/2"  feet  silvered  coaxial line.  instru The  c o n n e c t i o n a t t h e t o p p l a t e c o u l d be b r o k e n w h i l e t h e i n i t i a l b r i d g e b a l a n c e s were b e i n g made. The Starrett the  d i a l micrometers  t o p p l a t e by p y r e x The  (see  t y p e 25-T6 w h i c h were c o n n e c t e d t o  rods.  r u b b e r was h e l d by two e c c e n t r i c  brass  clamps  P l a t e I V ) w h i c h w e r e moved i n and o u t by m o t o r - d r i v e n  screws. shield  The c l a m p s were c o n n e c t e d t o t h e g r o u n d e d surrounding the standard The  standard c e l l ting  t h i c k n e s s o f t h e sample was m e a s u r e d w i t h t h r e e  system.  insulated  chamber c o n t a i n i n g t h e c l a m p s a n d t h e  The t e m p e r a t u r e  o f the a i r could  of the desired  (T) which  heaters (H).  cell.  ( s e e P l a t e I V ) was h e a t e d by a h o t a i r c i r c u l a -  w i t h i n one d e g r e e thermostat  copper  controlled  temperature  be h e l d t o  by t h e m e r c u r y  t h e power d e l i v e r e d  to the  17.  PLATE I  The S t a n d a r d C e l l  18.  PLATS  II  F r o n t View o f t h e  Apparatus  PLATE I I I The M e a s u r i n g  Instruments  CROSS  ThermoRegulator  110 Volts A.C  PLATE J3T 3ECTIQN OF THE  APPARATUS  21.  IV.  1.  GENERAL PROCEDURE The  denser any  EXPERIMENTAL PROCEDURE  rubber  s a m p l e s were p l a c e d between t h e c o n -  p l a t e s and l e f t  u n d e r p r e s s u r e f o r 24 h o u r s  r e a d i n g s were t a k e n .  I t was f o u n d  t h e c o n t a c t between t h e r u b b e r  that after  before 24 h o u r s  a n d t h e e l e c t r o d e s was  almost  a s good a s was o b t a i n e d by t h e f o i l - e l e c t r o d e method o f ( r e f . p . 7).  Holroyd carded  The f o i l - e l e c t r o d e method was  a s i t was f o u n d  mixture  used  the rubber  that the petroleum  t o secure  to swell  jelly-carbon  t h e e l e c t r o d e t o t h e sample  blaok  caused  slightly.  Measurement o f t h e c e l l sipation factor  dis-  c a p a c i t y ( C ) and t h e d i s x  (D ) i n the various frequency 2  ranges,  were  made i n t h e f o l l o w i n g ways: (a)  0.1 t o 15 K . c . The  standard  c e l l was c o n n e c t e d  s t a n d a r d c o n d e n s e r w h i c h f o r m e d one r a t i o Sobering bridge.  i n p a r a l l e l with a arm o f a b a l a n c e d  The b r i d g e was r e b a l a n c e d w i t h  condenser and a conductance c o n d e n s e r c a l i b r a t e d the d i s s i p a t i o n f a c t o r . final the  settings  initial  If C  o f the standard  and f i n a l  settings  the standard i n terms o f  and C a r e t h e i n i t i a l and c o n d e n s e r and i f D' and D a r e o f the conductance  condenser,  22.  50  (b)  The standard tuned  700  to  K.c.  standard  c e l l was  condenser forming  circuit.  condenser,  and  The  final Q's into  I f C»  o f the c i r c u i t  b e f o r e and  the c i r c u i t ,  ' .  standard  to  The  standard  The  c o n d e n s e r and  and  and  G  Before s i l i c a g e l was  initial  and  i f  a and  and  Q are  connected  = x  in parallel  s e c t i o n of a balanced  If C  standard  final  D  with  a  parallel-T  then rebalanced w i t h the  and  f  G  of  connected  s e t t i n g s o f the  then since  a  - C  a conductance condenser.  G are the i n i t i a l  condenser,  the  c e l l was  a  standard  measured w i t h  G are  a f t e r the  c e l l was  n e t w o r k was  final  with  M.c.  c o n d e n s e r i n one  network.  initial  20  0.5  and  was  condenser,  = C»  X  re-tuned with the  circuit  s e t t i n g s of the standard  (c)  G'  was  the % o f the  0  in parallel  the c a p a c i t a t i v e element o f  circuit  thermocouple voltmeter.  connected  and  standard C^" a r e  condenser,  s e t t i n g s of the  the  and i f  conductance  0 = b c  ~  c  b  e a c h s e t o f r e a d i n g s were t a k e n ,  a  quantity  placed i n the c i r c u l a t i n g system i n order  23. to  keep t h e h u m i d i t y a s low as p o s s i b l e .  relative  h u m i d i t y o f t h e o e l l was k e p t  I n t h i s way t h e  b e l o w 4 0 % a t 20°C a n d  b e l o w 35% a t 6 0 ° C .  2.  MEASUREMENT OF THE SAMPLE THICKNESS The  three Starrett  z e r o w i t h t h e condenser  d i a l micrometers  p l a t e s clamped  was t h e n p l a c e d between t h e p l a t e s  were s e t t o  together.  and a s l i g h t  The s a m p l e p r e s s u r e was  applied.  The t h i c k n e s s was t h e n t a k e n t o be t h e mean o f t h e  three d i a l  micrometer  r e a d i n g s when b o t h p l a t e s were m a k i n g  good c o n t a c t w i t h t h e s a m p l e .  The t h i c k n e s s o f t h e s a m p l e  was a l s o m e a s u r e d w i t h a n Ames s o f t m a t e r i a l d i a l and  a Gaertner  cathetometer.  Changes i n t h e sample t h i c k n e s s due t o and  stress  meters.  micrometer  changes,  temperature  were m e a s u r e d w i t h t h e t h r e e " d i a l  micro-  A c o r r e c t i o n t e r m h a d t o be s u b t r a c t e d f r o m t h e  m e a s u r e d t h i c k n e s s change s i n c e the d i a l micrometer  the bottom p l a t e  mounting had d i f f e r e n t  support and  coefficients of  expansion. The bottom p l a t e s against  t o g e t h e r and p l o t t i n g  the temperature The  found  c o r r e c t i o n was f o u n d  by c l a m p i n g  t h e t o p and  t h e mean d i a l  r e a d i n g (R)  (T) ( s e e F i g . 4 ) .  c o r r e c t i o n f o r a g i v e n temperature  change i s  by s u b t r a c t i n g t h e v a l u e s o f R c o r r e s p o n d i n g t o t h e  initial  and f i n a l  temperatures.  24. 12  10 3  8  6 4  2 °  10  ©  SO  ZO  40  Figure  3.  4.  EDGE CORRECTION The  standard  cell  thickness, the  716-B  edge c o r r e c t i o n was f o u n d plates with  small quartz  bridge.  blocks  o f t h e same (C ) with x  The edge c o r r e c t i o n ( C ) i s g i v e n by, e  = C  x  - C  where Ca i s t h e c a p a c i t y o f t h e c e l l Kirchoff's  by s e p a r a t i n g t h e  and m e a s u r i n g t h e c a p a c i t y o f t h e c e l l  Ce  A  *0  50  a  c a l c u l a t e d from  formula,  = t h e a r e a o f t h e t o p p l a t e , and d = t h e p l a t e s e p a r a t i o n .  The  mean v a l u e  of C  e  found  by t h i s method was 4.3  A number o f p u r e p a r a f f i n t h i c k n e s s e s were p r e p a r e d t i o n of the c e l l with plate  separations  samples o f d i f f e r e n t  and t h e v a l u e s  o f t h e edge c o r r e c -  containing the d i f f e r e n t  t h e 7l6-Bi b r i d g e .  I t was f o u n d  i n v e s t i g a t e d , (0.8  /4>*4f.  that t o 2.5  s a m p l e s was m e a s u r e d i n the range o f mm.),  t h e change  2<J. i n the edge c o r r e c t i o n was l e s s t h a n 0.2 ^ f .  The edge c o r -  r e c t i o n was t h e r e f o r e assumed t o be c o n s t a n t w i t h r e s p e c t the p l a t e  to  separation. The edge c o r r e c t i o n c a l c u l a t e d f r o m the e m p i r i c a l  f o r m u l a o f S c o t t and C u r t i s ^ 1  Ce = 1.11,  - 3 •  Z.}  where D = d i a m e t e r o f the t o p p l a t e o f t h i c k n e s s t ,  d = plate  s e p a r a t i o n , and Z» = a f u n c t i o n o f t / 2 d , was found t o be 3.4  A n a d d i t i o n a l c o r r e c t i o n due t o t h e c a p a c i t y  MyM£.  of  the t o p p l a t e t o the copper s h i e l d was c a l c u l a t e d t o be 0.7 MM£>  The t o t a l c o r r e c t i o n i s t h e r e f o r e 4 , l x ^ w h i c h  i s i n agreement w i t h t h e measured v a l u e o f 4 . 3 >t>fcf.  4.  CORRECTION FOR LEAD IMPEDENCE At high frequencies  impedence.  I t was t h e r e f o r e  a c o a x i a l l i n e has a n a p p r e c i a b l e found n e c e s s a r y  to r e - s o l v e  the  t w i n - T network i n o r d e r t o o b t a i n t h e n u l l c o n d i t i o n s when a n impedence o f the t y p e shown i n F i g . 5 was connected  across  t h e "unknown" t e r m i n a l s  C  r  = Lead C a p a c i t a n c e  R  L  r  = Lead Impedence  Gx = Unknown Conductance Figure  • ^ A . H . S c o t t and H . L . C u r t i s  r  = Lead  Resistance  5.  Nat.Bur.Stan. J.of  Res. 22, 747, 1939.  26. Actually not  the c a p a c i t a n c e o f a c o a x i a l l i n e  be lumped a t t h e i n p u t end.  silvered  coax, t h i s  below 25 M.o.  At  25 M.c.  the  i s made w i t h  bridge equations  Since G »  e r r o r i n v o l v e d i s about  in  (24) may  Gh  = A Cb and  Gx  = -R C a/  b  x  r  C  x  =  10" , 10  = (Cb - C b ) ,  The  +  + (1  2  be n e g l e c t e d .  (24)  and  L (c;  i f the  a. }  -  2  initial b,  the  (23)  1  R  =  If  6 = (1  r  T = (1  (24)  2  0.08  and  i f  eg) 2  , the f i r s t  term  + L r C b o ; ) where 2  + L C r  a* ), 2  x  equations  become Cx  -  (Cb - C^) S"  Ox  =  (2 - ir  inductance  used  at each frequency  (see P l a t e V).  same c u r v e s  i f A Cb  (25)  1  (26)  ) G  of the l i n e  lated  from the  parallel  - LpCxcc ) ®  Q-meter and  A Cb  -  r  m e a s u r e d w i t h t h e 160-A  against  4%.  become - (Ci - C ' } { l  -7  and  in  t h e c i r c u i t o p e n a t p o i n t s a and  Cx  10 ,  1/2"  i s j u s t i f i e d at frequencies  the standard condenser o f the twin-T,  balance  (23)  approximation  t h e impedence i n F i g . 5 i s c o n n e c t e d  If with  However, f o r t h e  should  2  ( L y = 0.27  ><-h)  the values of  6  i n t h e measurements, w e r e The  values of  i s r e p l a c e d by  Y  may  C . x  be  was calcuplotted found  28.  7. RESULTS  1.  COMPOSITION OF THE SAMPLES (a)  Cure:  Natural Rubber ) 1  20 min at 296°F Parts by Weight Sample 1-B Sample 1-C Sample 1--A  COMPOSITION Smoked Sheet Combined Sulphur Free Sulphur Zinc Oxide Zinc Dibutyldithocarbamate  100 1.8 0.2 1.0  Total Parts by Weight  103.1  (b)  Cure:  100 •  0.1  3.9  6.11.0  0.1 lii.i  100 4.4 10.6 1.0 0.1 116.i  Butyl Rubber ) 2  60 min at 307°F  COMPOSITION  Parts by Weight Sample 2--A  Butyl Combined Sulphur Free Sulphur Zinc Oxide Tetramethylhiuram Disulfide  100 1.6 0.4 1.0  Total Parts by Weight  104.0  1.0  Sample 2-B  Sample 2-C  1.0 1.0  100 4.4 5.6 1.0  1.0 106.0  1.0 112.0  100  A l l the rubber samples were s p e c i a l l y prepared f o r ^L.A.Wood and F.L.Roth 2  )p.J.Flory  J.of App.Phys.  Rubber Chem.Tech.<  15, 781, 1944.  19, 552, 1946.  29. t h i s research by the Research D i v i s i o n of the Polymer Corporation at Sarnia.  The samples were 6 inches square and  had been c a r e f u l l y molded to ensure plane p a r a l l e l faces. The amounts of free sulphur i n the samples were determined  by the acetone extraction method.  (A.S.T.M. Pro-  cedure D-297-42T).  2.  TABLES AND GRAPHS A sample set of calculations for sample 2-A at 20°C  and Of. extension, i s given i n Table I. sample at higher temperatures for  The results f o r t h i s  and extensions, and the results  the other samples are given i n the form of graphs (see  Plates 71 to H ) . In Table I, C  represents the i n i t i a l setting of  the standard condenser, and C  x  represents the measured  capacity of the standard c e l l containing the sample. capacitance bridge range,  In the  & D represents the difference i n  the d i s s i p a t i o n factor readings f o r the i n i t i a l and f i n a l balances;  i n the Q-meter range A D represents the difference  of the Q/s of the i n i t i a l and f i n a l tuned c i r c u i t s ;  and i n  the twin-T range A D represents the conductance of the samples i n M mhos. The probable errors given for £' and tan S ,. are the mean errors from ten measurements of the of a wax sample.  and tan 6  The large errors involved i n the Q-meter  measurements should be noted.  TABLE I  Sample 2-A; 20.2°C, 0% Extension. Average Thickness = Frequency 0.1 0.2 0.4 0.75 1 1.5 2 4 7.5 10 15 50 80 100 150 400 0.7 1 1.5" 2 3 6 10 15 20  K.c. tt tt  11  tt tt n tt n tt tt  K.c. tt tt tt tt  M.c. tt tt tt tt tt tt it it  O.I867  cms.;  C  a  = 23.29 u^£.  Ox  AD  Ox — Ce  ct c  340.9 341.1 341.2 341.2 341.2 341.3 341.3 341.4 341.6 341.9 342.7  64.3 64.3 64.3 64.2 64.1 64.1 64.1 64.0 64.0 63.9 63.8  .033 .033 .038 .042 .053 .060 .062 .072 .097 .110 .135  60.0 60.0 60.0 59.9 59.8 59.8 59.8 59.7 59.7 59.6 59.5  2.58 2.58 2.58 2.57 2.57 2.57 2.57 2.56 2.56 2.55 2.55  354.4 347.4 454.6 . 175.1 271.8  64.1 63.8 62.3 62.9 63.O  7 10 9 21 14  59.8 59-5 58.0 58.6 58.7  2.57 2.55 2.49 2.52 2.52  58.6 58.6 58.6 58.6 58.5 58.5 58.4 57.5 57.3  2.52 2.52 2.52 2.52 2.51 2.51 2.51 2.47 2.46  C» MM-t  250 250 600 250 250 250 250 350 250  • 62.9 62.9 62.9 62.9 62.8 62.8 62.7 61.8 61.6  O.69 1.0 1.8 1.9 2.8 6.4 15.0 32.2 59.3  =  Cx- Ce ca  ±  iz  ±  ±  dt i  =t iz =fc  =fc  db d= 4  tan S percent  .01 .01 .01 .01 .01 .01 .01 .01 .01 .01 .02  .175 .175 .201 .223 .282 .319 .330 .384 .517 .589 .725  .05 .05 .05 .05 .04  .54 .32 .35 .24 .20  .01 .01 .01 .01 .01 .01 .02 .02 .02  .249 .253 ..303 .239 .237 .270 .381 .553 .764  ± ± is  ± :fc iz iz  ± sfc  *: iz iz iz  ±  iz  ±  .015 .015 .015 .015 .015 .015 .015 .015 .015 .020 .030 .10 .10 .10 .10 .10 .022 .024 .028 .030 .030 ,. 0 3 0 .035 .040 .070  37. 3.  DISCUSSION OF RESULTS (a)  Natural Rubber The r e s u l t s f o r the natural rubber samples are given  i n Plates VI, VII, and VIII.  The results f o r the samples at  room temperature were calculated from two separate sets of measurements.  At higher temperatures, however, only one set  of measurements was taken f o r each sample. Values of  £* and tan 6  measured after a high tem^-  perature run were found to be s l i g h t l y lower than the corresponding values measured before the run. values of  £* and tan 3  These lower  probably resulted from a reduction  i n the moisture content of the rubber at the high temperature since the  £' and tan 6  returned to t h e i r i n i t i a l values  a f t e r 24 hours. The graphs of  11  vs. l o g i ' " show that i n the f r e -  quency range extending from 500 cycles to 200 K . c ,  the d i -  e l e c t r i c constant of the rubber i s approximately independent of the frequency.  For sample 1-A,  i n t h i s range i s 2.89.  the average value of  £»  This value i s i n agreement with the  values found by previous experimenters. A comparison of the r e s u l t s f o r natural rubber with the results of Scott Curtis and McPherson (Ref. 3),  p. 3)  shows that increases i n the d i e l e c t r i c constant of vulcanized rubber which correspond to the differences i n the d i e l e c t r i c constants of samples 1-A,  1-B,  and 1-C, require an increase  i n the sulphur concentration which corresponds to the i n -  38. c r e a s e i n combined s u l p h u r c o n c e n t r a t i o n s o f t h e samples. The  dielectric  constant of v u l c a n i z e d rubber  f u n c t i o n o f t h e combined  s u l p h u r c o n c e n t r a t i o n and i s i n -  d e p e n d e n t o f t h e amount o f f r e e It  i s shown t h a t  of n a t u r a l rubber with increasing  300%  decreases with i n c r e a s i n g This result  o f Holroyd  A logj/"  temperature and  who f o u n d  constant o f rubber  curves a t  20°0  causes  of the " £ and  60°C  T  shows t h a t a n i n c r e a s e i n t h e  t h e anomolous p o r t i o n s o f t h e c u r v e s c o r -  a higher frequency.  it  This large  also £'  i n v u l c a n i z e d rubber.  shows t h a t  (21) An  dependence o f  o f p o l a r substances and  rubber-sulphur dipoles a r e The t e m p e r a t u r e  dependence  t h e t a n 6 maximum i s o f t h e Debye t y p e .  and  The  (22).  interesting  result  s e c o n d a r y maximum s u p e r i m p o s e d  that  t o be moved t o  and t a n <f o f t h e r u b b e r may t h e r e f o r e be r e p r e s e n t e d by  equations  The  temperature  maximum i s c h a r a c t e r i s t i c  c a n t h e r e f o r e be assumed t h a t  present  increased -  V s . l o g */" a n d " t a n S v s .  r e s p o n d i n g t o t h e maximum d i s s i p a t i o n f a c t o r ,  the t a n £  that a t  temperature.  comparison  temperature  constant  i s n o t i n agreement  ( R e f . 4 ) , p . 7)  extension, the d i e l e c t r i c  with increasing  sulphur i n the rubber.  i n general the d i e l e c t r i c  extension.  with the r e s u l t s  i s therefore a  s m a l l temperature  i s the appearance  of a  upon t h e Debye c u r v e a t 0.9  d e p e n d e n c e o f t h i s maximum  M.c.  indicates  i t i s o f t h e Maxwell-Wagner t y p e a n d i s p r o b a b l y due t o  the presence rubber.  o f f r e e sulphur which a c t s as a f i l l e r  The o b s e r v e d  i n the  t a n 6 c u r v e s must t h e r e f o r e be t h e  39. resultants of the Debye curves and the Maxwell-Wagner curves (see Plate XII). As the amount of free sulphur i n the rubber i s i n creased, the Maxwell-Wagner maximum becomes less pronounced, and the Debye curve i s f l a t t e n e d .  The tan S maximum i s  also observed to decrease. Sample  % Free Sulphur  tan 6  max.  1-A  0.2  0.031  1-B  6.1  0.030  1-0  10.6  0.028  These r e s u l t s are i n agreement with the theory of Gevers (Ref. 1), p. 14) who  has shown that as a mixture  be-  comes more inhdmogeneous, the d i s t r i b u t i o n of the a c t i v a t i o n energies i s broadened and as a r e s u l t the tan 6 curve i s flattened. Plate XIII shows plots of the Kirkwood-Fuoss funct i o n if  (  S) n  vs. the logarithm of the frequency {i/ )  f o r sample 1-A at 20°C and 0% extension, and at 20°C and 200% extension.  The resultant curves are very nearly  straight l i n e s with slopes of 0.769 f o r the unstretched sample and 0.812  f o r the stretched sample.  This r e s u l t i s  rather unexpected as the Kirkwood-Fuoss theory applies to polymers having a dipole i n each monomer unit and hence having a large dipole i n t e r a c t i o n . Since natural rubber can contain 32% combined sulphur, sample 1-A with 1.8% sulphur would only have one  42. dipole f o r every 18 monomer units and hence should have a N  r e l a t i v e l y small dipole i n t e r a c t i o n .  I t has of course been  assumed that f o r 32% combined sulphur, every monomer unit contains one dipole.  This i s not s t r i c t l y correct as i t has  been shown that more than one sulphur atom may be associated with a single monomer u n i t ) . 1  The dipole moments per monomer unit calculated from equation (20), and the mean relaxation times calculated from  X  Q  = l/«J , M  where <*» = the frequency corresponding to the m  maximum l o s s , are given i n the following table f o r sample 1-A. Temp. °C  Extension Percent  t  Dipole Moment per Monomer  Q  x 10^ sec.  20°G  0  0.41 D  2*04  20°C  200  0.40 D  3.96  1 D = 1 Debye unit = 10""** e.s.u. 1  The larger relaxation time of the stretched sample shows that the a c t i v a t i o n energy i s greater for stretched rubber than f o r unstretched rubber. I f again i t i s assumed that there i s only 1 dipole f o r every 18 monomer units i n sample 1-A, the average moment of the carbon-sulphur dipole must be  V18,  X* = 0.41 D f o r the unstretched sample, /Utu/. =  and since  1.7 D.  This  value corresponds to the moment of 1.6 D observed f o r the d i e t h y l sulphide d i p o l e ) . 2  J ^ M . l . S e l k e r and A.R.Kemp 'R.LeFevre  Ind.Eng.Chem.  39, 895, 1947.  Dipole Moments, Menthuen Co., 1938.  43. (b)  Butyl Tne  I X , X, a n d X I .  Rubber.  results  for butyl  rubber are given i n P l a t e s  The c u r v e s f o r s a m p l e s 2-B a n d 2-C a t 125%  e x t e n s i o n a n d t h e c u r v e f o r sample 2-A a t  60°C  and  e x t e n s i o n c o u l d n o t be o b t a i n e d a s t h e sample b r o k e these  i s less  than that  of natural  decrease w i t h i n c r e a s i n g temperature extension. constant  The t e m p e r a t u r e  shows t h a t  r u b b e r a n d i s shown t o and w i t h  increasing  b u t y l rubber  i s a polar  substance.  The  by c a r b o n - s u l p h u r l i n k a g e s  t h e i s o p r e n e monomer u n i t s . The  very f l a t is  constant o f butyl  dependence o f t h e d i e l e c t r i c  b u t y l d i p o l e s a r e p r o b a b l y formed in  under  conditions. In general, the d i e l e c t r i c  rubber  125%  "£» v s . l o g y " c u r v e s f o r b u t y l r u b b e r a r e  i n t h e range  investigated,  a l t h o u g h a l o s s maximum  i n d i c a t e d a t a frequency g r e a t e r than  temperature  dependence o f t  1  Debye maximum. t i o n time  shows t h a t  2 0 M.e. this  I f t h i s maximum d o e s e x i s t ,  of the butyl dipoles w i l l  be l e s s  s h o u l d be a t h e mean r e l a x a t h a n t h e mean  r e l a x a t i o n time o f the n a t u r a l rubber d i p o l e s . t h e r e f o r e be assumed t h a t i n t e r a c t i o n than n a t u r a l  butyl  The  I t may  rubber has a s m a l l e r d i p o l e  rubber.  The maximum w h i c h o c c u r s i n t h e t a n S c u r v e o f b u t y l r u b b e r a t 3 0 K . c . i s assumed t o be o f t h e M a x w e l l Wagner t y p e s i n c e  i t has a v e r y s m a l l temperature  T h i s maximum may be a t t r b u t e d sulphur i n the rubber.  to the presence  dependence.  of the free  44.  VI.  The  dielectric  CONCLUSION  properties  of natural  b e r s have been i n v e s t i g a t e d a t t e m p e r a t u r e s and  a t e x t e n s i o n s o f 0 % and  tending from as  100 cycles  and  butyl  o f 2 0 ° C and  2 0 0 % , i n a f r e q u e n c y range  t o 2 0 M.c.  The  rub60°C,  ex-  r e s u l t s obtained  are  follows: (1)  The  dielectric  c o n s t a n t s o f b u t y l and  bers decrease w i t h i n c r e a s i n g temperature  and  natural  with  rub-  increasing  extension. (2) is  In general,  l e s s than (3)  of  that  The  of natural  The  distribution  distribution {5)  greater  The  than that (7) hibit  The  may  rubber  interaction  be  and  dipoles. of  r e p r e s e n t e d by t h e  d i p o l e moment p e r monomer u n i t  r e l a x a t i o n time  natural Kirkwood-  of stretched  rubber.  Both  natural  b u t y l and  Maxwell-Wagner maxima. may  rubbers.  is  rubber  rubber. is  greater  r u b b e r - s u l p h u r compounds  T h e s e maxima a r e be  slightly  than f o r stretched  of unstretched  sulphur i n the  rubber  function.  on t h e Debye c u r v e s and free  hence t h e d i p o l e  o f r e l a x a t i o n times  f o r unstretched rubber  (6)  of butyl  are l e s s than the r e l a x a t i o n time  rubber-sulphur dipoles Fuoss  and  i n t e r a c t i o n o f the n a t u r a l  (4)  constant  rubber.  r e l a x a t i o n time  the b u t y l d i p o l e s  dipole  the d i e l e c t r i c  ex-  superimposed  a t t r i b u t e d to the presence  of  45.  VII.  BIBLI0 GRAPHY  BOOKS  1.  Alexander, J . T.  C o l l o i d Chemistry, V o l . V, Reinhold Publishing Co., 1944.  2.  Barron, H.  Modern Synthetic Rubbers, and H a l l , 1 9 4 3 .  3.  Davis, C. and Blake, J .  4.  Debye, P.  Polar Molecules, Chemical Catalogue Co., 1 9 2 9 .  5.  Le Fevre, R.  Dipole Moments,  6 . . Mark, H. and Whitby, G. S, 7.  Smyth, C  8.  Weissberger, A.  P.  Chapman  Chemistry and Technology of Rubber, Reinhold Publishing Co., 1 9 3 7 .  Menthuen Co., 1 9 3 8 .  Advances i n C o l l o i d Science, Vol. I I , Interscience Publishers, 1 9 4 6 . D i e l e c t r i c Constant and Molecular Structure, Chemical Catalogue Co., 1 9 3 1 . Physical Methods of Organic Chemistry Vol. I I , Interscience Publishers, 1 9 4 6 .  PAPERS 1.  Boggs C. R. and Blake «T. T.  Ind.Eng.Chem.  Zi  Cole K. S. and Cole R. H.  J.of  3.  Debye P.  Phys.Zeits.  4.  Flory P. J .  Rubber Chem.Tech.  5.  Fuoss R. and Kirkwood J".  J.Amer.Chem.Soc.  2 2 , 748, 1 9 3 0 .  Chem.Phys.  9 , 341, 1941.  36, 100, 1935. 19, 552, 1946. 6 3 , 3 8 5 , 1941.  46. 6.  Gevers  7.  Holroyd  8. 9.  N.  V.  1,  P h i l i p s Res.Rep.  298,  1946. 1947.  Master's Thesis,  U . B . C , May  James H. a n d Girth E .  J.of  Chem.Phys.  11,  455,  1943.  James H. a n d Guth E .  J.of  Chem.Phys.  15,  669,  1947.  10.  Katz  R e p o r t t o t h e Rubber Delft, 1936.  11.  Kit chin  12.  Pellat  13.  Rehner  14.  Schneider C a r t e r W., and Smyth  L . V.  J . R.  ;  D.  W.  Ind.Eng.Chem.  E.  J.of  J.  Ind.Eng.Chem. W., Magat M., C. P.  9,  1932.  313,  36,  J.Amer.Chem.Soc.  47,  67,  1944.  959,  711,  1945. 1907.  16.  S e o t t A. H., M c P h e r s o n A . T.. and Curtis H. L .  U.S.Bur.Std.,  J . o f Res.  11,  173,  S o o t t A. H. a n d Curtis H. L.'  U.S.Bur.Std., J . o f Res.  22,  747,  S e l k e r M. L . and Kemp A. R.  Ind.Eng.Chem.  39,  895,  1947.  Wagner  Ann.der  40,  8.17,  1943.  -19.  K.  W.  1933.  24,  1900.  Schweidler  18.  Ann.der Phys.  549,  15.  17.  E. von  Physics  24,  Symposium,  1939.  Phys.  

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