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

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£ £ 3 ^7 THE DIELECTRIC PROPERTIES OF NATURAL AND SYNTHETIC RUBBER-SULPHUR COMPOUNDS by Robert Smith Codrington A T h e s i s submitted i n p a r t i a l f u l f i l m e n t o f the requirements f o r the degree o f MASTER OF ARTS i n the department o f PHYSICS THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1948 J ABSTRACT The d i e l e c t r i c ; p r o p e r t i e s o f n a t u r a l and b u t y l r ubber-sulphur compounds have been i n v e s t i g a t e d a t tempera- t u r e s o f 2G°C and 60°C and extensions o f 0% and 200%, i n a frequency range extending from 100 c y c l e s to 20 megacycles. T h i s i n v e s t i g a t i o n has shown t h a t the d i e l e c t r i c constant o f b u t y l rubber i s l e s s than t h a t o f n a t u r a l rubber and t h a t the d i e l e c t r i c constants o f both types o f rubber decrease w i t h i n c r e a s i n g temperature and i n c r e a s i n g e x t e n s i o n . The i n v e s t i g a t i o n has a l s o shown t h a t the d i e l e c - t r i c behaviour o f these rubbers may be e x p l a i n e d by the Gevers' e x t e n s i o n o f the Debye d i p o l e theory. I f f r e e s u l - phur i s present i n the rubbers, the behaviour must be ex- p l a i n e d by a combination o f the d i p o l e theory and the inhomo- g e n e i t y t h e o r y . The Kirkwood-Fuoss t h e o r y f o r p o l a r polymers, has been a p p l i e d to n a t u r a l rubber w i t h 2% s u l p h u r . The d i p o l e moment per monomer u n i t o b t a i n e d from the Kirkwood-Fuoss p l o t f o r t h i s sample was 0.41 Debye u n i t s . ACKNOWLEDGEMENT This work was carried out with the aid of a re- 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 for his many helpful suggestions, and for 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 for several valuable suggestions. The author is also indebted to the Research Division of the Polymer Corporation for the samples they have prepared for this research. The author wishes to express his appreciation to the National Research Council of Canada for the Studentship for 1947/48 which has enabled him to complete this work. TABLE OF CONTENTS Page I . INTRODUCTION 1. General I n t r o d u c t i o n 1 2. P r o p e r t i e s o f N a t u r a l Rubber 2 3. P r o p e r t i e s o f B u t y l Rubber . 5 4. P r o p e r t i e s of S t r e t c h e d Rubber 7 I I . THEORY OF DIELECTRICS 1. D e f i n i t i o n o f the Terms 8 2. The Maxwell-Wagner Theory . 9 3. The Debye Theory 10 4. Summary 14 I I I . APPARATUS 1. The Measuring Instruments 15 2. D e s c r i p t i o n o f the Apparatus 15 IV. EXPERIMENTAL PROCEDURE 1. General Procedure . 21 2. Measurement of the Sample Thickness . . 23 3. Edge C o r r e c t i o n . . . . . . . 24 4. C o r r e c t i o n f o r Lead Impedence 25 V. RESULTS 1. Composition o f the Samples . . 28 2.. Tables and Graphs 29 3. D i s c u s s i o n o f the R e s u l t s . . 37 71. CONCLUSION 44 "VII. BIBLIOGRAPHY .45 MATES Page I. The Standard Cell 17 II. Front View of the Apparatus 18 III. The Measuring Instruments . . . . . . . . . . . . 19 IV. Cross-seotion of the Apparatus . . 20 V. Correction for the Twin-T Bridge 27 -VI. Results for Natural Rubber 2% S . . . . . . . . 31 VII. Results for Natural Rubber 10% S 32 VIII. Results for Natural Rubber 15% S . 33 IX. Results for Butyl Rubber 2% S . . . . . . . . 34 X. Results for Butyl Rubber 4% S 35 XI. Results for Butyl Rubber 10% S 36 XII. Debye and Maxwell-Wagner Curves . 40 XIII. Kirkwood-Fuoss Plots for Sample 1-A . . . . . . 41 THE DIELECTRIC PROPERTIES OF NATURAL AND SYNTHETIC RUBBER-SULPHUR COMPOUNDS I. INTRODUCTION 1 . GENERAL INTRODUCTION The d i e l e c t r i c constant ( 6*) and the d i s s i p a t i o n f a c t o r ( t a n S ) have been shown to 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 . An i n v e s t i g a t i o n o f the d i e l e c t r i c p r o p e r t i e s o f rubber may t h e r e f o r e p r o v i d e i n f o r m a t i o n which w i l l i n d i c a t e the s t r u c t u r e o f the rubber molecule. The terms "rubber" and "elastomer" are now g e n e r a l - l y a p p l i e d to any substance showing the 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 r e v e r s i b l e e l a s t i c i t y and anomolous t h e r m o e l a s t i c behaviour. T h i s d e f i n i t i o n may be a p p l i e d t o any substance r e g a r d l e s s o f i t s chemical composi- t i o n . However, the 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 rubbers have now been shown to be l o n g c h a i n polymers o f hydrocarbon groups. The term polymer r e f e r s t o a chemical v a l e n c e com- b i n a t i o n o f s m a l l molecules c a l l e d "monomers" i n t o a l a r g e molecule called 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 in a cis configuration (see Eig.,1). CH* H CHY H CH* H \ / V / \ / c = c c = c c = c / \ / \ / \ CH2 CH2 CH2 CH2 CH2 CH2 Figure 1. The number of monomer units composing the macro- molecule i s believed to be between 2000 and 4000. James and Guth1) have shown that a quasi-free rotation about a single carbon-carbon bond in long chain molecules, i s sufficient for the development of rubberlike ela s t i c i t y . This free rotation is responsible for the d i - electric losses in vulcanized rubber since i t w i l l allow the rubber-sulphur dipoles to follow the oscillations of the electric f i e l d . 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. p l a s t i c i t y . There are a number o f v u l c a n i z a t i o n p r o c e s s e s , the most common one b e i n g the combination o f the rubber w i t h sulphur which i n t r o d u c e s rubber-sulphur d i p o l e s i n t o the rubber c o n f i g u r a t i o n . The e f f e c t of v u l c a n i z a t i o n upon the d i e l e c t r i c p r o p e r t i e s o f rubber has been i n v e s t i g a t e d by Boggs and B l a k e 1 ) , K i t c h i n 2 ^ , and S c o t t C u r t i s and M c P h e r s o n ^ . These i n v e s t i g a t i o n s show t h a t the d i e l e c t r i c c o n s t a n t o f rubber i n c r e a s e s w i t h i n c r e a s i n g sulphur content and reaches a maxi- mum v a l u e f o r 12% combined s u l p h u r . Boggs and Blake have e x p l a i n e d t h i s behaviour by assuming t h a t the sulphur i s i n i t i a l l y added to the end double bonds o f the rubber macro- molecule. T h i s f i r s t a d d i t i o n a c t i v a t e s the a d j a c e n t double bonds which i n t u r n may take on a sulphur atom and a c t i v a t e the next double bond. In t h i s way, the combination w i t h the sulphur proceeds p r o g r e s s i v e l y from the ends o f the molecule towards the c e n t r e (see P i g . 2). ; — A c t i v a t e d Bonds > ' \ A R R = = R - - - - R = R R F i g u r e 2. The molecules of raw rubber are symmetrical and hence are non-polar. However, as sulphur i s added the ^C.R.Boggs and J.T.Blake Ind.and Eng.Chem 22, 748, 1930. 2^D.W.Kitchin Ind.and Eng.Chem 24, H9, 1932. 2 J A . S c o t t H . C u r t i s and A.McPherson Bur.Stan., J . o f Res. 11, 173, 1933. dissymmetry o f the molecule and henee the p o l a r i t y o f the molecule i n c r e a s e s u n t i l h a l f the double bonds are s a t u r a t e d w i t h sulphur atoms. A f u r t h e r i n c r e a s e i n the s u l p h u r con- t e n t i n c r e a s e s the symmetry and hence decreases the p o l a r i t y o f the molecule. T h i s simple e x p l a n a t i o n of the d i e l e c t r i c behaviour o f v u l c a n i z e d rubber i s complicated by the f a c t t h a t the a d d i t i o n o f s u l p h u r not o n l y a l t e r s the d i p o l e moments o f the i n d i v i d u a l molecules, but a l s o changes the p h y s i c a l c h a r a c t e r i s t i c s o f t h e i r environment. I n p a r t i c u l a r , T u c k e t t 1 ) has suggested t h a t v u l c a n i z a t i o n i n t r o d u c e s c r o s s - l i n k a g e s between the rubber macromolecules c r e a t i n g i n t e r - m o l e c u l a r f o r c e s which oppose the f r e e r o t a t i o n o f the d i p o l e s . The theory of Boggs and Blake does not attempt t o e x p l a i n the nature o f the dissymmetry produced by the ad- d i t i o n o f the sulphur atoms, and i t i s q u e s t i o n a b l e whether such a dissymmetry a c t u a l l y e x i s t s . The author has suggested t h a t the t ' and tan S maxima are due to the f o r m a t i o n of the c r o s s - l i n k a g e s d u r i n g v u l c a n i z a t i o n . The f u n c t i o n ^ ) which r e l a t e s the number o f c r o s s - l i n k a g e s (it ) to the c o n c e n t r a t i o n o f sulphur Cs i s such t h a t f o r C 3 < 1 2 , V i s s m a l l and f o r C s > 1 2 , V i s l a r g e . A s m a l l i n c r e a s e i n C s f o r C s < 1 2 would t h e r e f o r e -^R.F.Tuckett Trans.Faraday Soc. 3 8 , 3 1 0 , 1 9 4 2 . ^H.James and E.Guth J . o f Chem.Phys. 1 5 , 6 6 9 , 1 9 4 7 . r e s u l t i n the f o r m a t i o n o f a l a r g e number o f d i p o l e s and r e - l a t i v e l y few c r o s s - l i n k a g e s , w h i l e an i n c r e a s e i n O 3 f o r Cs > 12 would r e s u l t i n the f o r m a t i o n o f a l a r g e number o f c r o s s - l i n k a g e s and r e l a t i v e l y few d i p o l e s . T h i s e x p l a n a t i o n o f the v u l c a n i z a t i o n p r o c e s s would t h e r e f o r e r e q u i r e the £ » and t a n 6" maxima t o 0 o c c u r a t a va l u e of 0 S such t h a t a s m a l l i n c r e a s e i n C a would r e - s u l t i n the f o r m a t i o n o f equal numbers of c r o s s - l i n k a g e s and d i p o l e s . 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 w i t h 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 . The number of monomer u n i t s composing the b u t y l macromolecule i s be- tween 1200 and 2400. Rehner 1^ has shown t h a t the i s o p r e n e monomers are d i s t r i b u t e d 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 the p o l y i s o b u t y l e n e c h a i n . 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 g i v e n i n F i g . 3 . - C CH, I CH3 CH2 ~r~ CH2 c CH- C H 2 — C CH GH3 •3 CH L3 Isoprene H P o l y i s o b u t y l e n e | P o l y i s o b u t y l e n e F i g u r e 3 . J.Rehner Ind.and Eng.Chem. 36 , 47, 1944. The i s o b u t y l e n e monomer u n i t s c o n t a i n no double bonds and as a r e s u l t , are v e r y s t a b l e . However when i s o - prene monomers are i n t r o d u c e d i n t o the c h a i n , the molecule becomes l e s s s t a b l e o r "the degree o f s a t u r a t i o n " decreases. ,The v u l c a n i z a t i o n o f b u t y l rubber has not been 11 e x t e n s i v e l y t r e a t e d i n the l i t e r a t u r e . P l o r y ' has shown t h a t the number o f c r o s s - l i n k a g e s between the b u t y l molecules i s p r o p o r t i o n a l to the number o f is o p r e n e monomer u n i t s i n the macromolecule. S i n c e the c r o s s - l i n k a g e s are formed d u r i n g v u l c a n i z a t i o n , E l o r y ' s r e s u l t i m p l i e s t h a t the s u l - phur o n l y combines w i t h the i s o p r e n e u n i t s . T h i s q u a l i t a t i v e e x p l a n a t i o n o f the v u l c a n i z a t i o n process i n b u t y l rubber shows t h a t t h e r e are r e l a t i v e l y few rubbe r - s u l p h u r d i p o l e s formed d u r i n g v u l c a n i z a t i o n . I t shows, a l s o , t h a t the m a j o r i t y o f the d i p o l e s e x i s t i n . the . c r o s s - l i n k a g e s between the molecules where they are h e l d more or l e s s r i g i d l y by the i n t e r - m o l e c u l a r f o r c e s . I t i s t h e r e f o r e to be expected t h a t the £ ' and t a n S f o r v u l - c a n i z e d b u t y l rubber w i l l be l e s s than the £ ' and t a n S f o r v u l c a n i z e d n a t u r a l rubber. T h i s r e s u l t has been v e r i f i e d by the p r e l i m i n a r y measurements of Sparks and h i s co-workers '. However, a more thorough i n v e s t i g a t i o n o f the 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 b e f o r e any d e f i n i t e c o n c l u s i o n s may be drawn. 1 ) p . J . J l o r y Rubber Chem.Tech. 19, 552, 1946. 25w.Sparks, I.Lightbown,.L.Turner, P . E r o l i e h , and C . K l e b a t t e l Ind.and Eng.Chem 32, 731., 1944. 7. 4. PROPERTIES OF STRETCHED RUBBER 1) 21 X-ray a n a l y s i s of s t r e t c h e d n a t u r a l and b u t y l ' rubbers have shown t h a t f o r a g i v e n temperature t h e r e e x i s t s a c r i t i c a l e x t e n s i o n above which c r y s t a l s b e g i n to form i n the rubber. For example, i n rubber a t room temperature the c r y s t a l s are formed i f the e x t e n s i o n exceeds 80%. T h i s c r i t i c a l e x t e n s i o n i n c r e a s e s w i t h temperature. For a g i v e n temperature, and f o r extensions above the c r i t i c a l v a l u e , the degree 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- s i o n . I f the d i p o l e s form p a r t of the c r y s t a l l a t t i c e s the degree o f f r e e - r o t a t i o n which may be assigned to them w i l l be s m a l l . Hence the f o r m a t i o n of c r y s t a l s i n the rub- ber w i l l r e s u l t i n a decrease i n . T h i s decrease has been observed i n the case of n a t u r a l rubber by S c h i l l e r ^ and H o l r o y d ^ ) . 1 ) j.R.Katz Report to Symposium on Rubber; D e l f t , Oct. 1936. 2 ) R . B r i l l and F . H a l l e Rubber Chem.Tech. 11, 687, 1938. 3) L . S c h i l l e r Ann der Phys. 35, 931, 1911. 4 ) L i V * H o l r o y d Master's T h e s i s , U.B.C., May 1947. 8. I I , THEORY OF DIELECTRICS 1. DEFINITION OF TERMS In d i e l e c t r i c media the d i e l e c t r i c displacement D i s r e l a t e d to the e l e c t r i c f i e l d s t r e n g t h E by the equ a t i o n D = e f I n the case o f i s o t r o p i c m a t e r i a l s where these v e c t o r s a re p a r a l l e l D = & E (1) I f E r e p r e s e n t s an a l t e r n a t i n g e l e c t r i c f i e l d o f the form, E = E 0 e J W t where E 0 denotes a constant, <*> denotes the frequency and t denotes the time, then D = £ E o e J * ^ (2) Experimental r e s u l t s show t h a t f o r most d i e l e c t r i c 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 between D and E. Hence (2) becomes D - e o B o e J < w t - 6 > or D = ( t0ooaj - j £ 0 s i n $ )E0e^t (3) Henoe & has the form The r e a l p a r t o f the e x p r e s s i o n ( £') i s c a l l e d the d i e l e c t r i c c o nstant. The tangent o f the phase angle, 9 t a n 6 = 4r (5) i s r e f e r r e d t o as the d i s s i p a t i o n f a c t o r as i t i s a measure of the energy d i s s i p a t e d i n the d i e l e c t r i c . 2. THE MAXWELL-WAGNER THEORY In 1864 Von Siemons observed an i n c r e a s e i n the temperature o f d i e l e c t r i c s when they were p l a c e d i n an a l t e r - n a t i n g f i e l d . Hopkinson 1^ assumed t h a t t h i s temperature r i s e c o u l d be a t t r i b u t e d to an a f t e r - e f f e c t o f the d i s p l a c e - ment, and u s i n g a p r i n c i p l e o f s u p e r p o s i t i o n he worked out expressions f o r and tan 6 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 = £ 0 0 ( 1 - jT c o s t u t a g l i l d t ) (6) I" = - f U ^ s i n u i t d t (7) P e l l a t 2 ^ gave the a f t e r - e f f e c t f u n c t i o n the form <?(t) = k e " * ^ where k re 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 d i s p e r s i o n o f £ 1 l and X was a time constant c a l l e d the r e l a x a t i o n time o f the a f t e r - e f f e c t . S u b s t i t u t i n g f o r 0 ( t ) i n (6) and (7) g i v e s ; 1 + k + u*c %c a These e x p r e s s i o n s were found t o be too dependent D j . H o p k i n s o n P h i l . T r a n s . 166, 4 8 9 , I 8 7 6 . 2 ) P e l l a t J . o f P h y s i c s 9, 313, 1 9 0 0 . 1 0 . upon the frequency and i t was suggested by Yon Schweidler" 1"^ t h a t t h e r e should be a d i s t r i b u t i o n o f r e l a x a t i o n times 2 ) G-("C)'. Wagner ' assumed t h a t G-( T ) should be o f Gaussian form; hence, r e p l a c i n g t by 0 ( f ) i n ( 8 ) and ( 9 ) and i n - t e g r a t i n g between zero and i n f i n i t y g i v e s , Coa+x Jo l + t»£ t r ^ where T denotes the mean r e l a x a t i o n time, and £ 0 and £ M are constants such t h a t £ = £ 0 when o> = o and £ = when co = oo Equations ( 1 0 ) and ( 1 1 ) can a l s o be d e r i v e d by ex- t e n d i n g the two-layer inhomogeneity theory o f Maxwell^to the case of an i n f i n i t e number o f spheres of one d i e l e c t r i c embedded i n another d i e l e c t r i c . These equations s a t i s f a c - t o r i l y p r e d i c t the d i e l e c t r i c behaviour o f such inhomogeneous mixtures: they do not, however, p r e d i c t the d i e l e c t r i c be- h a v i o u r of pure d i e l e c t r i c s . 3 . THE DEBYE THEORY A more fundamental theory o f d i e l e c t r i c s was de- veloped by Debye 4^ who i n t r o d u c e d the concepts o f d e f o r m a t i o n and o r i e n t a t i o n p o l a r i z a t i o n s . The deformation p o l a r i z a t i o n ^ E . V o n Schweidler Ann.der Phys. 2 4 , 711, 1 9 0 7 . 2)K.W.Wagner Ann.der Phys. 4 0 , 8 1 7 , 1 9 1 3 . 2)C.Maxwell E l e c t r i c i t y and Magnetism V o l . I , 3 2 8 , Oxford. 4)p.Debye P o l a r M o l e c u l e s , 1 9 2 9 , Chem.Catalogue Co. 11. (PaJ i s a t t r i b u t e d to d i p o l e s which are formed when the d i - e l e c t r i c i s p l a c e d i n an e l e c t r i c f i e l d . The f o r m a t i o n o f 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 o f the e l e c t r o n i c o r b i t s w i t h i n the 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 0 ) i s a t t r i b u t e d to permanent mo l e c u l a r d i p o l e s which o r i e n t a t e themselves i n the d i r e c t i o n o f the a p p l i e d e l e c t r i c f i e l d . The r o t a t i o n o f these dipoles. under the i n f l u e n c e o f the e l e c t r i c f i e l d i s opposed by the thermal a g i t a t i o n o f the molecules, and i t i s t h i s o p p o s i t i o n which g i v e s r i s e to the d i e l e c t r i c l o s s . Debye has shown t h a t P 0 - j ft N « 0 ( 1 2 a ) Po - (12b) where N = Avogadro's number, rt, 0 = the p o l a r i z a b i l i t y o f the molecule, 44, = the d i p o l e moment, k = Boltzman's const a n t , and T = the a b s o l u t e temperature. The t o t a l p o l a r i z a t i o n PJ which from the C l a u s i u s - M o s o t t i equation i s , p = e - j V 1+2 where V = the molar volume, i s g i v e n by the sum of P Q and Pa* Hence P = f « N ( t 0 (13) E q u a t i o n (13) has the form P • - a + % ' • which f o r the v a r i a b l e s P and i , i s the equation o f a s t r a i g h t 12. l i n e w i t h s l o p e b = i^jLfd (14) The d i p o l e moment M of a substance may t h e r e f o r e be calem- l a t e d from (14) s i n c e k and N are known constants and b may be determined from experimental r e s u l t s . The Debye theory l e a d s to equations f o r £ ' and t a n 6 which are i d e n t i c a l t o those of P e l l a t ( equations (8) and (9)). However, i n the Debye expr e s s i o n s the r e l a x a t i o n time X r e f e r s to the time r e q u i r e d f o r the d i p o l e s t o t u r n through l / e ^ h o f the angle between t h e i r d i r e c t e d p o s i t i o n and t h e i r e q u i l i b r i u m p o s i t i o n . The Debye theory i s not a p p l i c a b l e to s o l i d s o r v i s c o u s l i q u i d s as i t does not c o n s i d e r the i n t e r a c t i o n o f the d i p o l e s . Debye 1) and Y a g e r 2 ) have attempted to extend the theory by p o s t u l a t i n g an i n t e r a c t i o n energy ( q ) , and a 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. Both o f these t h e o r i e s are r e s t r i c t e d i n t h e i r a p p l i c a t i o n to s o l i d s . The d i e l e c t r i c behaviour o f polymers has been p r e - d i c t e d by the t h e o r i e s o f Cole and C o l e ^ ) , and o f Fuoss and Kirkwood^"). The l a t t e r theory r e q u i r e s a d i s t r i b u t i o n o f r e l a x a t i o n times such t h a t t h e r e i s a l i n e a r r e l a t i o n s h i p be- tween the l o g a r i t h m o f the frequency ( i /) and the q u a n t i t y V ( - c o s h " 1 £ " m ( 2 + l / f c ' 2 m ) R £ " ( 2 + 1 / V 2 ) D p . Debye P h y s . Z e i t s 36, 100, 1935. 2) w.A.Yager P h y s i c s 7, 434, 1936. 3) R.CO1S and K.Cole J . o f Chem.Phys. 9, 3 4 1 , 1 9 4 1 . 4 ) R.FUOSS and J.Kirkwood J . o f Amer.Chem.Soc. 63, 385, 1 9 4 1 . 13. where fc"m = maximum dielectric loss and &'m *= the dielectric constant at.the frequency of maximum loss. In the case of polymers, A 2 i s replaced in (12b) by the product of the dipole moment of the isolated monomer a n d ^ which i s the vector sum of >c and the moment i n - duced by the molecule in i t s environment. Substituting for At?- in (12b) gives; P = 4 n N M »xL ° 9kT or = 9 k T P Q (16) 4JTN The polarization at zero frequency i s given by, *b<o) = y%r-v where oc i s the slope of the straight line given by plotting V( £") against log 1/ . Substituting for 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. Sub- stituting for xc% in (18) gives >i -71 oc N n and since V = nM̂ o where M = the molecular weight of the monomer unit and f> - the density, (19) becomes, 1 £"m kTM / 2 0* 14,. The Fuoss-Kirkwood t h e o r y has been extended by Covers 1^ who c o n s i d e r s a d i s t r i b u t i o n o f a c t i v a t i o n e n e r g i e s i G(q). The a c t i v a t i o n energy q i s the energy s u p p l i e d to the d i p o l e t o remove i t from the p o t e n t i a l w e l l i n which i t normally e x i s t s . I f X(q) r e p r e s e n t s the s t a t i c s u s c e p t i - b i l i t y o f a d i p o l e having an a c t i v a t i o n energy q, then; t< = eM • 4 « r^-§t4 a 4 (2i) Jo 1 + <*> t- t a n <f - - i - 2 £ 2 N G | q o ) X ( q o ) k T (22) where q Q « the c r i t i c a l a c t i v a t i o n energy. 4. SUMMARY There are two d i s t i n c t types of d i e l e c t r i c pheno- mena; the type a s s o c i a t e d w i t h inhomogeneous d i e l e c t r i c s and 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 . The £ * and t a n 4 o f inhomogeneous d i e l e c t r i c s are g i v e n by equations (10) and (11) w h i l e the £ » and t a n 6 of p o l a r d i e l e c t r i c s a re g i v e n by equations (21) and (22). The t a n € maxima a s s o c i a t e d w i t h (11) are r e f e r r e d t o as Maxwell-Wagner maxima w h i l e t a n 6 maxima a s s o c i a t e d w i t h (22) are r e f e r r e d t o as Debye maxima. Sch n e i d e r , C a r t e r , Magat and Smyth 2) have shown t h a t a d i e l e c t r i c may e x h i b i t both types of t a n 6 maxima. ^N.V.Gevers P h i l i p s Res.Rep. 1, 298, 1946. ^W.Schneider, W.Carter, M.Magat, and CP.Smyth J.Amer.Chem. Soc. 67, 959, 1945. 15. I I I . APPARATUS 1. THE MEASURING INSTRUMENTS The measuring instruments used i n the v a r i o u s f r e - quency ranges were; (a) 100 c y c l e s to 15 M.c. Sc h e r i n g B r i d g e - General Radio type 716-B O s c i l l a t o r N u l l D e t e c t o r (b) 50 K.c. t o 1 M.c. Q-meter (c> 500 K.c. to 20 M.c. Twin-T Impedence Bridge S i g n a l Generator Radio D e t e c t o r - General Radio type 608-A - General Radio type 12J1-A - Boonton type 160-A - General Radio type 821-A - General Radio type 805-C - Hammarlund type HQ.-129X 2. DESCRIPTION 0E THE APPARATUS The standard c e l l c o n s i s t e d o f two s t a i n l e s s s t e e l p l a t e s whose f a c e s were ground f l a t t o b e t t e r than l/lOOO** 1 o f an i n c h . The lower p l a t e (diameter = 5") was mounted r i g i d l y on a maple b l o c k and was grounded to the copper s h i e l d s urrounding the standard c e l l . The s m a l l e r t o p p l a t e (diameter = 3") was h e l d c o a x i a l l y w i t h the lower 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 sample. The top p l a t e was connected t o the measuring i n s t r u ments w i t h 1-1/2 f e e t o f 1/2" s i l v e r e d c o a x i a l l i n e . The connect i o n a t the top p l a t e c o u l d be broken while the i n i t i a l b r i d g e balances were being made. The t h i c k n e s s o f the sample was measured w i t h t h r e e S t a r r e t t d i a l micrometers type 25-T6 which were connected t o the top p l a t e by pyrex rods. The rubber was h e l d by two e c c e n t r i c brass clamps (see P l a t e IV) which were moved i n and out by motor-driven screws. The clamps were connected to the grounded copper s h i e l d s urrounding the standard c e l l . The i n s u l a t e d chamber c o n t a i n i n g the clamps and the standard c e l l (see P l a t e IV) was heated by a hot a i r c i r c u l a - t i n g system. The temperature o f the a i r c o u l d be h e l d t o w i t h i n one degree of t h e d e s i r e d temperature by the mercury thermostat (T) which c o n t r o l l e d the power d e l i v e r e d to the heaters (H). 17. PLATE I The Standard Cell 18. PLATS I I Front View o f the Apparatus PLATE I I I The Measuring Instruments PLATE J3T CROSS 3ECTIQN OF THE APPARATUS Thermo- Regulator 110 Volts A.C 21. IV. EXPERIMENTAL PROCEDURE 1. GENERAL PROCEDURE The rubber samples were p l a c e d between the con- denser p l a t e s and l e f t under p r e s s u r e f o r 24 hours b e f o r e any readings were taken. I t was found t h a t a f t e r 24 hours the c o n t a c t between the rubber and the e l e c t r o d e s was almost as good as was obtained by the f o i l - e l e c t r o d e method of Holro y d ( r e f . p. 7). The f o i l - e l e c t r o d e method was d i s - carded as i t was found t h a t the petroleum j e l l y - c a r b o n b l a ok mixture used to secure the e l e c t r o d e t o the sample caused the rubber t o s w e l l s l i g h t l y . Measurement o f the c e l l c a p a c i t y ( C x ) and the d i s - s i p a t i o n f a c t o r (D 2) i n the v a r i o u s frequency ranges, were made i n the f o l l o w i n g ways: (a) 0.1 to 15 K.c. The standard c e l l was connected i n p a r a l l e l w i t h a standard condenser which formed one r a t i o arm of a balanced Sobering b r i d g e . The b r i d g e was rebalan c e d w i t h the standard condenser and a conductance condenser c a l i b r a t e d i n terms o f the d i s s i p a t i o n f a c t o r . I f C and C are the i n i t i a l and f i n a l s e t t i n g s o f the standard condenser and i f D' and D are the i n i t i a l and f i n a l s e t t i n g s o f the conductance condenser, 22. (b) 50 to 700 K.c. The standard c e l l was connected i n p a r a l l e l w i t h a standard condenser forming the c a p a c i t a t i v e element o f a tuned c i r c u i t . The c i r c u i t was re-tuned w i t h the s t a n d a r d condenser, and the % of the c i r c u i t was measured w i t h a thermocouple v o l t m e t e r . I f C» and G are the i n i t i a l and f i n a l s e t t i n g s o f the standard condenser, and i f and Q are Q's o f the c i r c u i t b efore and a f t e r the c e l l was connected i n t o the c i r c u i t , ' . 0 X = C» - C (c) 0.5 to 20 M.c. The standard c e l l was connected i n p a r a l l e l w i t h a standard condenser i n one s e c t i o n o f a balanced p a r a l l e l - T network. The network was then r e b a l a n c e d w i t h the standard condenser and a conductance condenser. I f C D and C^" are the i n i t i a l and f i n a l s e t t i n g s o f the standard condenser, and i f G' and G are the i n i t i a l and f i n a l s e t t i n g s o f the conductance condenser, then s i n c e Gf = 0 G x = c b ~ c b Before each s e t o f r e a d i n g s were taken, a q u a n t i t y of s i l i c a g e l was p l a c e d i n the c i r c u l a t i n g system i n o r d e r 23. to keep the humidity as low as p o s s i b l e . I n t h i s way the r e l a t i v e humidity of the o e l l was kept below 40% a t 20°C and below 35% a t 60°C. 2. MEASUREMENT OF THE SAMPLE THICKNESS The t h r e e S t a r r e t t d i a l micrometers were s e t to zero w i t h the condenser p l a t e s clamped t o g e t h e r . The sample was then p l a c e d between the p l a t e s and a s l i g h t p r e s s u r e was a p p l i e d . The t h i c k n e s s was then taken t o be the mean of the th r e e d i a l micrometer readings when both p l a t e s were making good c o n t a c t w i t h the sample. The t h i c k n e s s o f the sample was a l s o measured w i t h an Ames s o f t m a t e r i a l d i a l micrometer and a Gaertner cathetometer. Changes i n the sample t h i c k n e s s due to temperature and s t r e s s changes, were measured w i t h the three " d i a l m i c r o - meters. A c o r r e c t i o n term had to be s u b t r a c t e d from the measured t h i c k n e s s change s i n c e the bottom p l a t e support and the d i a l micrometer mounting had d i f f e r e n t c o e f f i c i e n t s o f expansion. The c o r r e c t i o n was found by clamping the top and bottom p l a t e s together and p l o t t i n g the mean d i a l r e a d i n g (R) a g a i n s t the temperature (T) (see F i g . 4 ) . The c o r r e c t i o n f o r a g i v e n temperature change i s found by s u b t r a c t i n g the v a l u e s of R co r r e s p o n d i n g t o the i n i t i a l and f i n a l temperatures. 24. 1 2 10 3 8 6 4 2 ° © 1 0 ZO SO 40 5 0 *0 F i g u r e 4. 3. EDGE CORRECTION The edge c o r r e c t i o n was found by s e p a r a t i n g the standard c e l l p l a t e s w i t h s m a l l quartz b l o c k s of the same t h i c k n e s s , and measuring the c a p a c i t y o f the c e l l ( C x ) w i t h the 716-B b r i d g e . The edge c o r r e c t i o n ( C e) i s giv e n by, Ce = C x - C a where Ca i s the c a p a c i t y of the c e l l c a l c u l a t e d from K i r c h o f f ' s formula, A = the ar e a o f the top p l a t e , and d = the p l a t e s e p a r a t i o n . The mean va l u e o f C e found by t h i s method was 4.3 /4>*4f. A number of pure p a r a f f i n samples o f d i f f e r e n t t h i c k n e s s e s were prepared and the valu e s o f the edge c o r r e c - t i o n of the c e l l c o n t a i n i n g the d i f f e r e n t samples was measured w i t h the 7l6-Bi b r i d g e . I t was found t h a t i n the range o f p l a t e s e p a r a t i o n s i n v e s t i g a t e d , ( 0 . 8 to 2.5 mm.), the 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 cor- r e c t i o n was t h e r e f o r e assumed to be constant w i t h r e s p e c t t o the p l a t e s e p a r a t i o n . The edge c o r r e c t i o n c a l c u l a t e d from the e m p i r i c a l f o r m u l a o f Sco t t and C u r t i s 1 ^ Ce = 1.11, - 3 • Z .} where D = diameter of the top p l a t e of t h i c k n e s s t , d = p l a t e s e p a r a t i o n , and Z» = a f u n c t i o n of t / 2 d , was found to be 3 .4 MyM£. An a d d i t i o n a l c o r r e c t i o n due to the c a p a c i t y o f the top p l a t e to the copper s h i e l d was c a l c u l a t e d to 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 the measured v a l u e o f 4 . 3 >t>fcf. 4. CORRECTION FOR LEAD IMPEDENCE A t h i g h f r e q u e n c i e s a c o a x i a l l i n e has an a p p r e c i a b l e impedence. I t was t h e r e f o r e found necessary to r e - s o l v e t h e t w i n - T network i n o r d e r to o b t a i n the n u l l c o n d i t i o n s when an impedence o f the type shown i n F i g . 5 was connected across the "unknown" t e r m i n a l s C r = Lead Capaci tance R r = Lead R e s i s t a n c e L r = Lead Impedence Gx = Unknown Conductance F i g u r e 5. • ^ A . H . S c o t t and H . L . C u r t i s N a t . B u r . S t a n . J . o f Res . 22, 747, 1939. 26. A c t u a l l y 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 should not be lumped at the i n p u t end. However, f o r the 1/2" s i l v e r e d coax, t h i s approximation i s j u s t i f i e d a t f r e q u e n c i e s below 25 M.o. A t 25 M.c. the e r r o r i n v o l v e d i s about 4%. I f the impedence i n F i g . 5 i s connected i n p a r a l l e l w i t h the standard condenser o f the twin-T, and i f the i n i t i a l balance i s made w i t h the c i r c u i t open at p o i n t s a and b, the b r i d g e equations become Cx - (Ci - C b ' } { l + L r ( c ; - eg) a. 2 } - 1 (23) Gx = - R r C x a / 2 + (1 - L p C x c c 2 ) 2 ® (24) S i n c e G » 10 - 7, C x = 10" 1 0, and R r = 0.08 , the f i r s t t e r m i n (24) may be n e g l e c t e d . I f 6 = (1 + LrCbo; 2) where Gh = A Cb = (Cb - Cb), and i f T = (1 + L r C x a* 2), equations (23) and (24) become Cx - (Cb - C^) S"1 (25) Ox = (2 - ir ) 2 G (26) The inductance of the l i n e (Ly = 0.27 ><-h) was measured w i t h the 160-A Q-meter and the v a l u e s o f 6 c a l c u - l a t e d at each frequency used i n the measurements, were p l o t t e d a g a i n s t A Cb (see P l a t e V ) . The v a l u e s o f Y may be found from the same curves i f A Cb i s r e p l a c e d by C x.  28. 7. RESULTS 1. COMPOSITION OF THE SAMPLES (a) Natural Rubber1) Cure: 20 min at 296°F COMPOSITION Sample 1- Parts by Weight -A Sample 1-B Sample 1-C Smoked Sheet 100 100 100 Combined Sulphur 1.8 3.9 4.4 Free Sulphur 0.2 • 6.1- 10.6 Zinc Oxide 1.0 1.0 1.0 Zinc Dibutylditho- carbamate 0.1 0.1 0.1 Total Parts by Weight 103.1 l i i . i 116.i (b) Butyl Rubber2) Cure: 60 min at 307°F COMPOSITION Parts by Weight Sample 2--A Sample 2-B Sample 2-C Butyl 100 100 100 Combined Sulphur 1.6 4.4 Free Sulphur 0.4 1.0 5.6 Zinc Oxide 1.0 1.0 1.0 Tetramethylhiuram Disulfide 1.0 1.0 1.0 Total Parts by Weight 104.0 106.0 112.0 A l l the rubber samples were specially prepared for ^L.A.Wood and F.L.Roth J.of App.Phys. 15, 781, 1944. 2)p.J.Flory Rubber Chem.Tech.< 19, 552, 1946. 29. this research by the Research Division of the Polymer Cor- poration at Sarnia. The samples were 6 inches square and had been carefully molded to ensure plane parallel 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 in Table I. The results for this sample at higher temperatures and extensions, and the results for the other samples are given in 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. In the capacitance bridge range, & D represents the difference in the dissipation factor readings for the i n i t i a l and f i n a l balances; in 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 circuits; and in 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 and tan 6 of a wax sample. The large errors involved in the Q-meter measurements should be noted. TABLE I Sample 2-A; 20.2°C, 0% Extension. Average Thickness = O . I 8 6 7 cms.; C a = 23.29 u^£. Frequency C» Ox AD Ox — Ce ct = Cx- Ce tan S MM-t c c a percent 0 . 1 K.c. 3 4 0 . 9 6 4 . 3 . 0 3 3 6 0 . 0 2 . 5 8 . 0 1 . 1 7 5 ± . 0 1 5 0 . 2 tt 3 4 1 . 1 6 4 . 3 . 0 3 3 6 0 . 0 2 . 5 8 . 0 1 . 1 7 5 . 0 1 5 0 . 4 tt 3 4 1 . 2 6 4 . 3 . 0 3 8 6 0 . 0 2 . 5 8 ± . 0 1 . 2 0 1 ± . 0 1 5 0 . 7 5 11 3 4 1 . 2 6 4 . 2 .042 5 9 . 9 2 . 5 7 . 0 1 . 2 2 3 . 0 1 5 1 tt 3 4 1 . 2 6 4 . 1 . 0 5 3 5 9 . 8 2 . 5 7 . 0 1 . 2 8 2 is . 0 1 5 1 . 5 tt 3 4 1 . 3 6 4 . 1 . 0 6 0 5 9 . 8 2 . 5 7 . 0 1 . 3 1 9 ± . 0 1 5 2 n 3 4 1 . 3 6 4 . 1 . 0 6 2 5 9 . 8 2 . 5 7 . 0 1 . 3 3 0 :fc . 0 1 5 4 tt 3 4 1 . 4 6 4 . 0 . 0 7 2 5 9 . 7 2 . 5 6 . 0 1 . 3 8 4 iz . 0 1 5 7 . 5 n 3 4 1 . 6 6 4 . 0 . 0 9 7 5 9 . 7 2 . 5 6 . 0 1 . 5 1 7 iz . 0 1 5 1 0 tt 3 4 1 . 9 6 3 . 9 . 1 1 0 5 9 . 6 2 . 5 5 . 0 1 . 5 8 9 ± . 0 2 0 1 5 tt 3 4 2 . 7 6 3 . 8 . 1 3 5 5 9 . 5 2 . 5 5 iz . 0 2 . 7 2 5 sfc . 0 3 0 5 0 K.c. 3 5 4 . 4 6 4 . 1 7 5 9 . 8 2 . 5 7 ± . 0 5 . 5 4 *: . 1 0 8 0 tt 3 4 7 . 4 6 3 . 8 1 0 5 9 - 5 2 . 5 5 . 0 5 . 3 2 iz . 1 0 1 0 0 tt 4 5 4 . 6 . 6 2 . 3 9 5 8 . 0 2 . 4 9 . 0 5 . 3 5 iz . 1 0 1 5 0 tt 1 7 5 . 1 6 2 . 9 2 1 5 8 . 6 2 . 5 2 ± . 0 5 . 24 iz . 1 0 400 tt 2 7 1 . 8 6 3 . O 14 5 8 . 7 2 . 5 2 .04 . 2 0 ± . 1 0 0 . 7 M.c. 2 5 0 • 6 2 . 9 O . 6 9 5 8 . 6 2 . 5 2 dt . 0 1 .249 . 0 2 2 1 tt 2 5 0 6 2 . 9 1 . 0 5 8 . 6 2 . 5 2 i . 0 1 . 2 5 3 .024 1 . 5 " tt 6 0 0 6 2 . 9 1 . 8 5 8 . 6 2 . 5 2 =t . 0 1 . . 3 0 3 . 0 2 8 2 tt 2 5 0 6 2 . 9 1 . 9 5 8 . 6 2 . 5 2 iz . 0 1 . 2 3 9 . 0 3 0 3 tt 2 5 0 6 2 . 8 2 . 8 5 8 . 5 2 . 5 1 =fc . 0 1 . 2 3 7 . 0 3 0 6 tt 2 5 0 6 2 . 8 6 . 4 5 8 . 5 2 . 5 1 =fc . 0 1 . 2 7 0 iz , . 0 3 0 1 0 tt 2 5 0 6 2 . 7 1 5 . 0 5 8 . 4 2 . 5 1 db . 0 2 .381 ± . 0 3 5 1 5 it 3 5 0 6 1 . 8 3 2 . 2 5 7 . 5 2 . 4 7 d= . 0 2 . 5 5 3 .040 2 0 it 2 5 0 6 1 . 6 5 9 . 3 5 7 . 3 2 . 4 6 4 . 0 2 . 7 6 4 . 0 7 0       37. 3. DISCUSSION OF RESULTS (a) Natural Rubber The results for the natural rubber samples are given in Plates VI, VII, and VIII. The results for the samples at room temperature were calculated from two separate sets of measurements. At higher temperatures, however, only one set of measurements was taken for each sample. Values of £* and tan 6 measured after a high tem̂ - perature run were found to be slightly lower than the cor- responding values measured before the run. These lower values of £* and tan 3 probably resulted from a reduction in the moisture content of the rubber at the high temperature since the £' and tan 6 returned to their i n i t i a l values after 24 hours. The graphs of 11 vs. l o g i ' " show that in the fre- quency range extending from 500 cycles to 200 K.c, the d i - electric constant of the rubber i s approximately independent of the frequency. For sample 1-A, the average value of £» in this range i s 2.89. This value i s in agreement with the values found by previous experimenters. A comparison of the results for natural rubber with the results of Scott Curtis and McPherson (Ref. 3) , p. 3) shows that increases in the dielectric constant of vulcanized rubber which correspond to the differences in the dielectric constants of samples 1-A, 1-B, and 1-C, require an increase in the sulphur concentration which corresponds to the i n - 38. crease i n combined sulphur c o n c e n t r a t i o n s o f the samples. The d i e l e c t r i c constant of v u l c a n i z e d rubber i s t h e r e f o r e a f u n c t i o n o f the combined sulphur c o n c e n t r a t i o n and i s i n - dependent o f the amount of f r e e sulphur i n the rubber. I t i s shown t h a t i n g e n e r a l the d i e l e c t r i c constant o f n a t u r a l rubber decreases w i t h i n c r e a s i n g temperature and w i t h i n c r e a s i n g e x t e n s i o n . T h i s r e s u l t i s not i n agreement w i t h the r e s u l t s o f Holroyd (Ref. 4 ) , p. 7) who found that a t 300% e x t e n s i o n , the d i e l e c t r i c constant o f rubber i n c r e a s e d - w i t h i n c r e a s i n g temperature. A comparison o f the " £ T Vs. l o g */" and "tan S v s . l o g j / " curves a t 20°0 and 60°C shows t h a t an i n c r e a s e i n the temperature causes the anomolous p o r t i o n s o f the curves c o r - responding t o the maximum d i s s i p a t i o n f a c t o r , t o be moved to a hig h e r frequency. T h i s l a r g e temperature dependence o f the t a n £ maximum i s c h a r a c t e r i s t i c of p o l a r substances and i t can t h e r e f o r e be assumed t h a t rubber-sulphur d i p o l e s a r e present i n v u l c a n i z e d rubber. The temperature dependence a l s o shows t h a t the t a n 6 maximum i s of the Debye type. The £' and tan <f o f the rubber may t h e r e f o r e be r e p r e s e n t e d by equations (21) and (22). An i n t e r e s t i n g r e s u l t i s the appearance of a secondary maximum superimposed upon the Debye curve a t 0.9 M.c. The s m a l l temperature dependence o f t h i s maximum i n d i c a t e s t h a t i t i s o f the Maxwell-Wagner type and i s probably due to the presence o f f r e e s u lphur which a c t s as a f i l l e r i n the rubber. The observed tan 6 curves must t h e r e f o r e be the 39. resultants of the Debye curves and the Maxwell-Wagner curves (see Plate XII). As the amount of free sulphur in the rubber i s i n - creased, the Maxwell-Wagner maximum becomes less pronounced, and the Debye curve i s flattened. The tan S maximum is 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 results are in agreement with the theory of Gevers (Ref. 1), p. 14) who has shown that as a mixture be- comes more inhdmogeneous, the distribution of the activation energies i s broadened and as a result the tan 6 curve i s flattened. Plate XIII shows plots of the Kirkwood-Fuoss func- tion if ( Sn) vs. the logarithm of the frequency {i/ ) for sample 1-A at 20°C and 0% extension, and at 20°C and 200% extension. The resultant curves are very nearly straight lines with slopes of 0.769 for the unstretched sample and 0.812 for the stretched sample. This result i s rather unexpected as the Kirkwood-Fuoss theory applies to polymers having a dipole in each monomer unit and hence having a large dipole interaction. Since natural rubber can contain 32% combined sulphur, sample 1-A with 1.8% sulphur would only have one   42. dipole for every 18 monomer units and henceNshould have a relatively small dipole interaction. It has of course been assumed that for 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 XQ = l / « J M , where <*»m = the frequency corresponding to the maximum loss, are given in the following table for sample 1-A. Temp. Extension Dipole Moment tQ x 10^ °C Percent per Monomer sec. 20°G 0 0.41 D 2*04 20°C 200 0.40 D 3.96 1 D = 1 Debye unit = 10""1** e.s.u. The larger relaxation time of the stretched sample shows that the activation energy i s greater for stretched rubber than for unstretched rubber. If again i t is assumed that there i s only 1 dipole for every 18 monomer units in sample 1-A, the average moment of the carbon-sulphur dipole must be V18, and since X* = 0.41 D for the unstretched sample, /Utu/. = 1.7 D. This value corresponds to the moment of 1.6 D observed for the diethyl sulphide dipole 2). J^M.l.Selker and A.R.Kemp Ind.Eng.Chem. 39, 895, 1947. 'R.LeFevre Dipole Moments, Menthuen Co., 1938. 4 3 . (b) B u t y l Rubber. Tne r e s u l t s f o r b u t y l rubber are g i v e n i n P l a t e s IX, X, and XI. The curves f o r samples 2-B and 2-C a t 125% e x t e n s i o n and the curve f o r sample 2-A a t 60°C and 125% e x t e n s i o n c o u l d not be obt a i n e d as the sample broke under these c o n d i t i o n s . In g e n e r a l , the d i e l e c t r i c constant o f b u t y l rubber i s l e s s than that o f n a t u r a l rubber and i s shown to decrease w i t h i n c r e a s i n g temperature and w i t h i n c r e a s i n g e x t e n s i o n . The temperature dependence o f the d i e l e c t r i c constant shows t h a t b u t y l rubber i s a p o l a r substance. The b u t y l d i p o l e s are probably formed by carbon-sulphur l i n k a g e s i n the isop r e n e monomer u n i t s . The "£» v s . l o g y " curves f o r b u t y l rubber are very f l a t i n the range i n v e s t i g a t e d , although a l o s s maximum i s i n d i c a t e d at a frequency g r e a t e r than 2 0 M.e. The temperature dependence o f t1 shows t h a t t h i s should be a Debye maximum. I f t h i s maximum does e x i s t , the mean r e l a x a - t i o n time o f the b u t y l d i p o l e s w i l l be l e s s than the 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 . I t may t h e r e f o r e be assumed t h a t b u t y l rubber has a s m a l l e r d i p o l e i n t e r a c t i o n than n a t u r a l rubber. The maximum which o c c u r s i n the tan S curve o f b u t y l rubber at 3 0 K.c. i s assumed to be of the Maxwell- Wagner type s i n c e i t has a ve r y s m a l l temperature dependence. T h i s maximum may be a t t r b u t e d to the presence o f the f r e e sulphur i n the rubber. 44. VI. CONCLUSION The d i e l e c t r i c p r o p e r t i e s o f n a t u r a l and b u t y l rub- bers have been i n v e s t i g a t e d a t temperatures o f 20°C and 60°C, and a t extensions o f 0 % and 2 0 0 % , i n a frequency range ex- t e n d i n g from 100 c y c l e s to 2 0 M.c. The r e s u l t s o b t a i n e d are as f o l l o w s : ( 1 ) The d i e l e c t r i c c o n s t a n t s o f b u t y l and n a t u r a l rub- bers decrease w i t h i n c r e a s i n g temperature and w i t h i n c r e a s i n g e x t e n s i o n . ( 2 ) I n g e n e r a l , the d i e l e c t r i c constant o f b u t y l rubber i s l e s s than t h a t of n a t u r a l rubber. (3) The r e l a x a t i o n time and hence the d i p o l e i n t e r a c t i o n o f the b u t y l d i p o l e s are l e s s than the r e l a x a t i o n time and d i p o l e i n t e r a c t i o n o f the n a t u r a l rubber d i p o l e s . (4) The d i s t r i b u t i o n o f r e l a x a t i o n times o f n a t u r a l r ubber-sulphur d i p o l e s may be r e p r e s e n t e d by the Kirkwood- Fuoss d i s t r i b u t i o n f u n c t i o n . {5) The d i p o l e moment per monomer u n i t i s s l i g h t l y g r e a t e r f o r unstretched rubber than f o r s t r e t c h e d rubber. ( 6 ) The r e l a x a t i o n time of s t r e t c h e d rubber i s g r e a t e r than t h a t o f u n s t r e t c h e d rubber. (7) Both b u t y l and n a t u r a l r u b b e r - s u l p h u r compounds ex- h i b i t Maxwell-Wagner maxima. These maxima are superimposed on the Debye curves and may be a t t r i b u t e d t o the presence o f f r e e sulphur i n the rubbers. 4 5 . VII. BIBLI0 GRAPHY BOOKS 1 . Alexander, J. T. 2 . Barron, H. 3 . Davis, C. and Blake, J. 4. Debye, P. 5 . Le Fevre, R. 6 . . Mark, H. and Whitby, G. S, 7 . Smyth, C P. 8. Weissberger, A. Colloid Chemistry, Vol. V, Reinhold Publishing Co., 1944. Modern Synthetic Rubbers, Chapman and Hall, 1 9 4 3 . Chemistry and Technology of Rubber, Reinhold Publishing Co., 1 9 3 7 . Polar Molecules, Chemical Cata- logue Co., 1 9 2 9 . Dipole Moments, Menthuen Co., 1 9 3 8 . Advances in Colloid Science, Vol. II, Interscience Publishers, 1 9 4 6 . Dielectric Constant and Molecular Structure, Chemical Catalogue Co., 1 9 3 1 . Physical Methods of Organic Chemistry Vol. II, Interscience Pub- lishers, 1 9 4 6 . PAPERS 1 . Boggs C. R. and Blake «T. T. Zi Cole K. S. and Cole R. H. 3 . Debye P. 4 . Flory P. J. 5 . Fuoss R. and Kirkwood J". Ind.Eng.Chem. 2 2 , 748, 1 9 3 0 . J.of Chem.Phys. 9 , 341, 1941. Phys.Zeits. 3 6 , 1 0 0 , 1 9 3 5 . Rubber Chem.Tech. 1 9 , 5 5 2 , 1 9 4 6 . J.Amer.Chem.Soc. 6 3 , 3 8 5 , 1941. 46. 6. Gevers N. V. 7. Holroyd L. V. 8. James H. and Girth E. 9. James H. and Guth E. 10. Katz J . R. 11. K i t c h i n D. W. 12. P e l l a t ; E. 13. Rehner J . 14. Schneider W., C a r t e r W., Magat M., and Smyth C. P. 15. Schweidler E. von 16. Seott A. H., McPherson A. T.. and C u r t i s H. L. 17. Soott A. H. and C u r t i s H. L.' 18. S e l k e r M. L. and Kemp A. R. -19. Wagner K. W. P h i l i p s Res.Rep. 1, 298, 1946. Master's T h e s i s , U.B.C, May 1947. J . o f Chem.Phys. 11, 455, 1943. J . o f Chem.Phys. 15, 669, 1947. Report to the Rubber Symposium, D e l f t , 1936. Ind.Eng.Chem. 24, 549, 1932. J . o f P h y s i c s 9, 313, 1900. Ind.Eng.Chem. 36, 47, 1944. J.Amer.Chem.Soc. 67, 959, 1945. Ann.der Phys. 24, 711, 1907. U.S.Bur.Std., J . o f Res. 11, 173, 1933. U.S.Bur.Std., J . o f Res. 22, 747, 1939. Ind.Eng.Chem. 39, 895, 1947. Ann.der Phys. 40, 8.17, 1943.

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