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The heat conductivity of rubber at low temperatures Dauphinee, Thomas McCaul 1945

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/  • THE  HEAT  L  CONDUCTIVITY  OP  £  5 &?  RUBBER  - -AT LOW TEMPERATURES  by  THOMAS  MoC.  DAUPHINEE  A thesis submitted i n p a r t i a l  fulfilment  of t h e r e q u i r e m e n t s f o r t h e degree o f Master o f A r t s i n t h e Department o f P h y s i c s .  The U n i v e r s i t y o f B r i t i s h April  194.5  Columbia  A GKNQWLEDGEDiMT The Author wishes to thank Dr. H. D. Smith whose s u p e r v i s i o n of t h i s work has been o f great and  assistance  encouragement.  And,  i n a d d i t i o n , the Author wishes to express  h i s a p p r e c i a t i o n t o the f o l l o w i n g f o r t h e i r c o n t r i b u t i o n s :  The Department o f Physics, U n i v e r s i t y o f Notre Dame, i n p r o v i d i n g samples of elastomers o f known composition, as w e l l as valuable information  gained through correspondence  with Drs. E. Guth and R. S. Anthony o f that department.  Mr. L. V. Holroyd f o r c o n s t r u c t i n g the thermocouples and a s s i s t i n g instrument  i n t h e i r i n s t a l l a t i o n , , and f o r w i r i n g the  panel.  Mr. N. Barton f o r a l l photography.  INDEX I.  II.  III.  IT.  INTRODUCTION Elastomers The theory.of e l a s t i c i t y Thermal c o n d u c t i v i t y Methods o f measuring c o n d u c t i v i t y  1 2 6 6  EXPERIMENTAL The cryostat and evacuation c i r c u i t The c o n d u c t i v i t y measuring u n i t The s t r e t c h e r s The heat leads and c o o l i n g c i r c u i t The h e a t i n g c i r c u i t . : The thermocouple c i r c u i t The potentiometer c i r c u i t The c a l i b r a t i o n and i n s t a l l a t i o n o f thermocouples i. Fixed p o i n t s ii. Calibration lii. Installation The method o f t a k i n g readings The readings taken  17 18 19 20 21  RESULTS The equation and method o f c a l c u l a t i o n i* The power f a c t o r ii; The dimension f a c t o r ill. The temperature ^factor Probable e r r o r The rubber sample Experimental r e s u l t s Interpretation  23 23 24 25 25 27 28 35  CONCLUSION  36  9 10 11 11 15 14 16  I.  INTRODUCTION An elastomer i s d e f i n e d as a substance  long-range, r e v e r s i b l e e l a s t i c i t y .  exhibiting  The best known of these  i s , of course, rubber, the q u a l i t y being so t y p i c a l i n i t s case that the r a p i d l y expanding group of other elastomers i s f r e q u e n t l y c a l l e d ^ s y n t h e t i c rubber*" As a result, of recent rubber shortages much t h e o r e t i c a l and experimental work has been done on elastomers, but the study of t h e i r thermal c o n d u c t i v i t y i s one which, to date, has r e c e i v e d l i t t l e a t t e n t i o n .  T h i s has been due not  so much to the greater u s e f u l n e s s of other f i e l d s of r e s e a r c h i n the understanding of the problem of e l a s t i c i t y as to the n e c e s s i t y of concentrating on production i n quantity and velopment of the immediately-useful primary  de-  characteristics  such as s t r e t c h , wear r e s i s t a n c e and s t r e n g t h .  I t seems safe  to assume, however, that w i t h decreased s t r e s s on immediate production the study of f u r t h e r c h a r a c t e r i s t i c s - w i l l p l a y a much more prominent r o l e . A knowledge of thermal c o n d u c t i v i t y and the e f f e c t on i t of change of temperature,  amount of s t r e t c h and  composition has an important b e a r i n g on many f i e l d s of both commercial and t h e o r e t i c a l elastomer r e s e a r c h .  Examples of  t h i s are: (a)  Removal of the heat produced by constant f l e x i n g .  T h i s i s a major problem i n the t i r e industry and i n many other cases where elastomers a c t as shock ab, sorbers. (b) Obtaining homogeneous v u l c a n i z a t i o n o f large masses. T h i s r e q u i r e s a knowledge of temperature g r a d i e n t s w i t h i n the mass i n order to determine the d i s t r i b u t i o n o f sulphur required. (c) Determination o f equations o f state o f elastomers. (d) Determination o f the temperatures at which changes o f state occur,  (e.g. c r y s t a l l i z a t i o n etc* J  Changes o f  c o n d u c t i v i t y , c o e f f i c i e n t o f volume expansion, e t c , o f t e n accompany these  changes,  (e) A s s i s t a n c e i n a n a l y z i n g other long-chain hydrocarbons. The rubber molecule, because o f i t s r e l a t i v e l y simple s t r u c t u r e , i s e a s i e r t o study than more complex molecules but behaves i n a manner s i m i l a r to many o f them* The theory o f e l a s t i c i t y Elastomers have c e r t a i n p r o p e r t i e s i n common^ both i n behaviour and molecular composition, which must be explained by any theory o f e l a s t i c i t y .  The most evident a r e :  (a) They e x h i b i t long-range, r e v e r s i b l e  elasticity.  (b) They heat when s t r e t c h e d and c o o l i f allowed to r e l a x . (c) S t r e s s f o r any given degree o f s t r e t c h i s a l i n e a r f u n c t i o n o f temperature. the s t r e s s increases with  For a l l but s m a l l s t r e t c h temperature.  (d) They e x h i b i t both temporary and permanent (e) They harden when cold and tend to be  plasticity.  thermoplastic  at high temperature. ( f ) They show c r y s t a l l i n e c h a r a c t e r i s t i c s at extreme stretches. ( g | They have c h a r a c t e r i s t i c molecular s t r u c t u r e : 1.  Very long chain molecules with many s i n g l e bonds.  ii.  More or l e s s f r e e r o t a t i o n around the s i n g l e bonds.  iii.  ,  lew cross bonds between molecules.'  The  sec-  t i o n s between cross bonds long and r e l a t i v e l y f r e e to move. It i s only r e c e n t l y that the f i r s t  successful  theory to e x p l a i n these phenomena was put forward by Guth and Mark ( l ) and extended l a t e r by Guth ( 2 ) , James and Guth (3) and Anthony, Caston and Guth (4)*  I t was shown that the above  c h a r a c t e r i s t i c s could be q u a l i t a t i v e l y and q u a n t i t a t i v e l y exp l a i n e d on the b a s i s of a s t a t i s t i c a l model having the s t r u c ture p r e v i o u s l y described.  T h e i r p i c t u r e i s as f o l l o w s .  The elastomer molecules are long and have r e l a t i v e l y few cross bonds.  Consequently l a r g e numbers o f the  b a s i c u n i t w i l l be f r e e of intermo1ecular t i e s .  Since  there  are s i n g l e bonds between the u n i t s r o t a t i o n about these bonds w i l l be p o s s i b l e , subject to the p r o v i s i o n that the valence angle remain r e l a t i v e l y constant.  T h i s quasi-freedom of  r o t a t i o n means that the molecule can c o i l up i n almost any c o n f i g u r a t i o n and that we might expect thermal a g i t a t i o n to keep the p a r t s i n constant motion. Thus i n the unstretched  s t a t e the molecule would  "be c u r l e d up i n a d i s o r d e r e d . c o n f i g u r a t i o n corresponding to i t s most probable  position.  I f we are c o n s i d e r i n g l a r g e  numbers o f molecules s t a t i s t i c a l l y i t can be shown, f o r the case o f a chain made up o f successive molecules,  that the  p r o b a b i l i t y o f the ends of the chain being i n a region dL at a distance L from one another i s : P r o b a b i l i t y - P(nN:b) L dL = Ae  L^dL  where n i s the number of s i n g l e bonds per molecule; N> the number of molecules i n the chain; b, the l e n g t h o f the u n i t molecule (isoprene, f o r example, i n the case of pure rubber); and B *  ^  .  ft—•  •  A i s a n o r m a l i z i n g constant. ^ 2 A L ( e " ) ( l - BL ). to  SnW b*By d i f f e r e n t i a t i o n .  — dL T h i s gives minima at L 0 and 8  ... —  B L  , and a maximum at 1 =  , t h i s being the most probable  length.  Correcting  3 f o r constant to be  valenoe angle, a, we get the most probable  3nNbL  where b^s b Tan  length  We note here that the  s t r a i g h t l i n e c o n f i g u r a t i o n and the case where the two ends are together are almost e q u a l l y improbable. From the above d i s c u s s i o n we can assume that i n the unstretched  state the average separation o f the ends i s  the most probable  one.  On s t r e t c h i n g , the ends o f the chains  would "be moved from the most probable p o s i t i o n to one probable with the n e c e s s i t y of doing work. turn, i s converted i n t o increased  T h i s work, i n  energy o f thermal a g i t a t i o n , H  with consequent increase  less  i n temperature ( b ) .  When the mole-  cules are i n any but the most probable state the Brownian movement tends to b r i n g them to that s t a t e causing p u l l on the ends and (a), accompanied by  a constant  r e t u r n to the o r i g i n a l form i f r e l e a s e d c o o l i n g (b).  I f the substance i s held i n  a stretched p o s i t i o n and heated the increased Brownian move,  ment should cause a greater p u l l on the •ends.( o)» The  p l a s t i c e f f e c t s (d) are l i n k e d up with  bonding of the molecules. s l i p past one  cross  I f there are few bonds the molecules  another e a s i l y and  the substance can  change form.  I f there are many bonds the u n i t s should hold t h e i r r e l a t i v e positions.  C r y s t a l i z a t i o n i s explained  up of the molecules when almost s t r a i g h t  on the b a s i s o f l i n i n g (e)»  In the s t a t i s t i c a l a n a l y s i s of s t r e s s - s t r a i n c h a r a c t e r i s t i c s the substance i s compared with a gas at constant volume and ponents; P , u  the e f f e c t s d i v i d e d i n t o the sum  the i n t e r n a l energy c o n t r i b u t i o n due  molecular f o r c e s , and P  s  of two  com-  to i n t e r -  the k i n e t i c energy c o n t r i b u t i o n .  s P r o p e r t i e s explained l i s t e d on page 2*  are r e f e r r e d to by l e t t e r  as  1  By comparison  with Yan Der Waal s gas equation (4)  (P + or  p  s  V  Compare  p »  f>)(V - b) = RT " -  ^  43  Y" ^ P  u  + P  ,  Y - b s  .  By a n a l y s i s of t h i s and other thermodynamic r e l a t i o n s (3) explanations have been given f o r i n v e r s i o n p o i n t s i n the s t r e s s temperature  curves (c) and the t y p i c a l , S-shaped,  s t r e s s - s t r a i n curve shown by a l l elastomers. Thermal Conductivity The theory of thermal c o n d u c t i v i t y of elastomers i s p r a c t i c a l l y an untouched  field.  Since they e x h i b i t pro-  p e r t i e s of s o l i d s , l i q u i d s , and even gases they could be expected to e x h i b i t c o n d u c t i v i t y p r o p e r t i e s of a l l three. There would- almost c e r t a i n l y be a h i g h p r o p o r t i o n of conduct i o n by interbombardment of the Brownian type.  In a d d i t i o n  i •  some conduction could be expected due to t r a n s f e r of  energy  along the l e n g t h of the molecule through the bonds.  Gross  conduction by means of i n t e r m o l e c u l a r bonds would be  expected  to  increase with v u l c a n i z a t i o n while thermal bombardment  would decrease because of reduced freedom of motion.  No  s t a t i s t i c a l treatment o f t h i s problem has been made to date. Methods of Measuring C o n d u c t i v i t y The p r i n c i p l e o f measurement o f c o n d u c t i v i t y i s the same f o r a l l methods, i»e. to measure the q u a n t i t y of heat passing through given cross s e c t i o n of m a t e r i a l with a given  temperature conductivity  gradient  across i t . The d e f i n i t i o n of thermal  (10) i s - "The time r a t e o f t r a n s f e r of heat, by  conduction, through u n i t thickness, d i f f e r e n c e i n temperature,"  across u n i t area f o r u n i t  In the c a l c u l a t i o n o f the amount  o f heat t r a n s f e r r e d i n any system o f u n i t s the c o e f f i c i e n t o f thermal c o n d u c t i v i t y occurs as a p r o p o r t i o n a l i t y f a c t o r , and can be defined by the equation  or  5*  Kt.  K s  2t  A  • .A  t  A  (V  ~  *  )  f  T  ' ?•:  T  3  ',„..  - T  A  where K i s the c o e f f i c i e n t of thermal c o n d u c t i v i t y ; quantity T  and T  Q,, the  of heat t r a n s f e r r e d ; A, the c r o s s - s e c t i o n a l area; , the temperatures on e i t h e r side; d, the thickness;  and t , the time. .( Oal; S e o r  1  1  Gm"  In c . g . s . u n i t s K has the dimensions Deg*" }, 1  Methods o f measuring  conductivity f a l l  into  three main c l a s s e s . (a) Measurement o f r a t e s o f c o o l i n g .  One such method (5)  consisted o f measuring the r a t e s o f c o o l i n g at the centre o f l a r g e rubber spheres kept i n a constant temperature  chamber.  I t has the disadvantage that i t a c t u a l l y measures the quotient K , where K i s the thermal c o n d u c t i v i t y ; 'Cd~ heat; and d* the d e n s i t y .  C, the s p e c i f i c  8  e  (b) Measurement of heat c a r r i e d through to the low temperature side* . i . Measurement of the r i s e i n temperature o f a l i q u i d or s o l i d absorbing the heat t r a n s f e r r e d . . T h i s may be done by measuring the r i s e per u n i t time, or by measuring the r i s e i n temperature when a constant flow of l i q u i d passes through the  apparatus;  11. Measurement o f the rate o f evaporation or melting  caused by the heat t r a n s f e r r e d *  One ex-  periment o f t h i s type (6) consisted of measuring the  quantity of n i t r o g e n evaporating from a bag  of the substance t o be measured when the bag was immersed i n l i q u i d oxygen; T h i s method i s most s u i t a b l e f o r high conduct i v i t i e s or l a r g e surfaces, otherwise the amourits become unmeasurable. (e) Measurement o f the quantity of heat r e q u i r e d to maint a i n a constant temperature g r a d i e n t . ( 7 ) , ( 8 ) . T h i s method i s the one used i n the experimental work herein described.  FLATS I (a)  Front view of apparatus showing r e l a t i v e p o s i t i o n s , (b)  Back view of apparatus showing m u l t i p l e  /  switch.  PLATE I I I  II.  EXPERIMENTAL  The oryostat and evacuation o i r o u i t ( P l a t e IV) In order to p r o p e r l y i n s u l a t e the apparatus at the low temperatures at whioh the experiments were conducted i t was necessary t o construct a oryostat that could he evacuated, to provide i n l e t s and o u t l e t s f o r c o o l i n g tubes, thermocouples  and evacuation apparatus, and at the same time  provide reasonable f a c i l i t i e s f o r adjustment stretch. The  o f the degree o f  T h i s was accomplished by the u n i t shown on P l a t e IV.  sides o f the cryostat were made of 1/8 i n . brass p l a t e , as  was the c y l i n d r i c a l tower, A, c o n t a i n i n g the c o o l i n g u n i t . The top o f the tower and the sides o f the oryostat were faced with 1/2 i n . wide brass f l a n g e s , B, with tapped holes, C, part way through f o r studs, D, which held the side p l a t e s , E, (also constructed of 1/8 i n . brass) i n p l a c e .  Between these  p i e c e s and the f l a n g e s where rubber gaskets, F, held i n p l a c e on one side by g l y p t o l and sealed on the other with stopcock lubricant.  The thermocouples were l e d i n t o the cryostat  through a double gasket (see small diagram) on one side which i n s u l a t e d them from the metal.  The cover p l a t e , G, of the  tower had two holes f o r c o o l i n g tube o u t l e t s , H; the s e a l around them being accomplished by means o f rubber stoppers, I, and stopcock l u b r i c a n t .  At each end of the c r y o s t a t was a  PLATE V  THE • CONDUCTIVITY  MEASURING  UNIT  Bottom view. Thermocouples leading away from the bottom are shown by s o l i d l i n e s , those on top are shown by dotted l i n e s .  I n s t a l l a t i o n of Method of wiring thermocouples c e n t r a l heating blocks.  a. Copper block. b. G l y p t o l . o. Thermocouple.  -  10.  hook, J , to which the s t r e t c h e r s were attached, and at the f r o n t ( i n s i d e ) were thumbscrew clamps, K, to hold the s t r e t cher cords.  Suspension of the main apparatus was  accomplished  by b a k e l i t e supports (not shown i n the diagram) which under the l i p , M, o f the c o o l i n g u n i t .  The cryostat  fitted was  evacuated by means of a Cenco Hyvac pump through the o u t l e t , N, and pressure was measured by a small manometer attached to tube, 0.  The small screw, P, was used to l e t a i r i n t o the  cryostat' when •necessary; The c o n d u c t i v i t y measuring apparatus ( P l a t e s IV, V, VI - 5) T h i s apparatus was modelled a f t e r (8) apparatus f o r measuring  Schallamach*s  c o n d u c t i v i t y at low temperatures,  with very considerable r e v i s i o n to allow f o r s t r e t c h i n g experiments and the consequent to be absorbed.  increase i n the amount of heat  The heat was generated i n r e s i s t a n c e wire,  A, (Plate Y) which was threaded through holes i n the copper h e a t i n g blocks, B and long, 3.2  C.  The o e n t r a l block, G, was 4  cm.  cm. wide and .6 cm. t h i c k while the blocks, B, were  each 2 cm. l o n g and the same width and t h i c k n e s s .  The o u t s i d e  copper blocks, D, were tapped f o r studs, E, (to hold the heat leads, I ,  securely i n place).  Clamp, F, pressed the whole  u n i t t i g h t l y against the two rubber p i e c e s , G, to ensure good contact.  A t o t a l o f twelve thermocouples were attached to  the b l o c k s as shown i n the diagram at. H.  The method o f i n -  s t a l l i n g i s also shown on P l a t e Y (bottom). The method by which the thermal c o n d u c t i v i t y  was  11. measured.can r e a d i l y be seen.  E l e c t r i c a l energy was converted  into heat i n the heating b l o c k s and the only path f o r the heat to f o l l o w was through the rubber s t r i p s .  Heat would flow  only when there was a temperature drop across the rubber. The temperature drop was measured by means of the thermocouples and t h i s , along with the amount of heat produced and the  dimensions of the rubber, was  conductivity.  sufficient  to determine the  The inner heating block, C, was  the one used  f o r a c t u a l measurements^ the outside heating blocks, B, served the purpose o f a guard r i n g to prevent conduction l a t e r a l l y along the rubber. The s t r e t c h e r s  ( P l a t e IV) The rubber s t r i p s ; Q,,- were clamped securely at  each end by means of clamps, R (Plate IV), to which were a t tached small p u l l e y s , S. the  Other p u l l e y s , T, were attached to  hooks, J , at each end o f the c r y o s t a t .  The p u l l e y arrange-  ment was threaded with strong cord, U, g i v i n g a mechanical advantage of three. the  When s t r e t c h i n g was  cords were held by thumbscrews, K.  completed the ends o f Two  l i n e s , V, marked  on the rubber, served as markers and s t r e t c h was  c a l c u l a t e d by  measuring between them. Heat Leads and c o o l i n g c i r c u i t  ( P l a t e s IV, V, VII)  The heat that passed through the rubber s t r i p s , as w e l l as any heat that was  c a r r i e d to the apparatus by the  s t r i p s and by r a d i a t i o n from the side w a l l s , was through t h i n f l e x i b l e double s t r i p s o f 1/52 wide, a ( P l a t e IV).  c a r r i e d away  i n . copper,. 1 i n .  P i e c e s o f aluminum f o i l ,  b, between these  and the main blocks ensured good heat contact. were soldered and b o l t e d to r i g i d 1/4  The t h i n  strip  i n . copper leads, c,  which c a r r i e d the heat to the top piece, d, also o f 1/4 i n . copper.  At the centre of the top p i e c e was a r a i s e d part, e,  with a l i p , M, to support the u n i t , and an i n t e r n a l thread i n t o which the threaded end, f , of the s o l i d copper core o f the  c o o l i n g c o i l , g, was  screwed.  The outer part of the core  had a s p i r a l groove turned i n i t , and a f t e r the c o o l i n g c o i l was wound i n t o the.groove i t was soldered i n p l a c e .  An end  view o f the heat lead system i s shown i n P l a t e VII-5. Cooling was P l a t e VI.  accomplished by the c i r c u i t shown i n  The vacuum f l a s k , A, was f i l l e d with l i q u i d oxygen  which was drawn through the c i r c u i t by a small compressor, operated as a s u c t i o n pump.  B,  From the vacuum f l a s k , a mixture  of gaseous and l i q u i d oxygen was  drawn through a t h i n ,  insul-  ated, g l a s s tube, C, to one end of the c o o l i n g c o i l , D, i n the cryostat. the  Here the remaining l i q u i d oxygen was evaporated by  heat c a r r i e d up from the main u n i t .  From the c o i l the  gaseous oxygen was drawn through a warming c o i l , E, and thence to a needle valve, F, which r e g u l a t e d the amount o f oxygen drawn through.  The manometer, G, was  equipped with a two-way  stopcook, H, and could be used to i n d i c a t e the amount o f vacuum on e i t h e r side o f the valve, F.  In close p r o x i m i t y to  v a l v e F . , was a second needle valve, I, used to permit a i r to enter the c i r c u i t .  T h i s valve served the double purpose o f  decreasing the vacuum against which the compressor worked and  13. of reducing the concentration of oxygen, and consequently the danger of explosion.  (The compressor was  oil-lubricated).  From t h i s valve, I, the mixture was drawn into a carboy, J , which served to cut down f l u c t u a t i o n s caused by the  compressor,  thence to a second warming c o i l , K, on to the compressor,  B,  and out into the a i r . The method described above i s by no means the f i r s t one that was  employed.  c o n t r o l used by Sohallamach  The o r i g i n a l method of heat (8) was  t r i e d but found inadequate  to carry the g r e a t e r amounts of energy r e q u i r e d f o r t h i s apparatus.  Diagrams o f t h i s and three other methods t r i e d ,  as w e l l as the o r i g i n a l type o f heat lead, are shown i n Plate VII.  A l l o f these methods had the disadvantage of r e -  q u i r i n g a l i q u i d a i r container w i t h i n the apparatus.  The  method shown i n f i g . 4 was the most s u c c e s s f u l of a l l as f a r as c o n t r o l was  concerned, but f a i l e d to reach s u f f i c i e n t l y  low temperatures* The h e a t i n g c i r c u i t  ( P l a t e VII)  Power f o r the three c e n t r a l h e a t i n g c o i l s of the main u n i t , H - l , H-2,  H-3.  ( P l a t e VII) was  supplied by four  6-volt storage b a t t e r i e s , B, arranged to give 12 v o l t s across the u n i t as shown i n the diagram.  Control of the whole was  provided by a master switch, S, and a 40 ohm v a r i a b l e rheostat, C, w i t h a 380 ohm rheostat i n p a r a l l e l f o r f i n e  adjustment.  The c i r c u i t was  Part 1 l e d  then d i v i d e d i n t o three p a r t s .  d i r e c t l y to a double-pole, double-throw switch, S - l , connected  to make i t p o s s i b l e to shut o f f the c i r c u i t , n e c t i o n through, series.  get a d i r e c t  or put a 0 - 600 m.a. milliammeter  con-  A- 1 i n  From the switch the c i r c u i t went d i r e c t l y to the  cryostat and the c e n t r a l heating c o i l , H - l , and then back to the b a t t e r i e s .  The p o t e n t i a l d i f f e r e n c e across the heating  c o i l was measured by means o f a 0 - 5 v o l t voltmeter, V, graduated to 1/30 v o l t . were i d e n t i c a l .  Branches 2 and 3 o f the heating  circuit  Each had a 40 ohm rheostat, R - 2, R - 3, to  give i n d i v i d u a l c o n t r o l , followed by a double-pole,  double-  throw switch, S -2, S - 3, which made i t p o s s i b l e to put i n s e r i e s a small milliammeter, readings, ammeter A - 1.  A - 2, A - 3, or, f o r accurate  From the switch each c i r c u i t  ran to  one o f the other heating blocks, H - 2, H - 3, and back to the b a t t e r i e s . The  thermocouple c i r c u i t  ( P l a t e IX)  Considerable d i f f i c u l t y was encountered i n s e t t i n g up a s a t i s f a c t o r y thermocouple c i r c u i t . pyrometer i s by f a r the best instrument because o f i t s n e g l i g i b l e heat  The thermocouple  f o r t h i s type o f work  capacity, small s i z e ,  small  time l a g and f l e x i b i l i t y , but i t s o p e r a t i o n r e q u i r e s great care i f accurate r e s u l t s are to be a t t a i n e d . Contact p o t e n t i a l s made i t necessary a circuit of  completely o f copper except  the copper-copel  to design  f o r the copel element  thermocouple and the potentiometer  minals which could not be changed.  ter-  Copper s t r i p s were placed  over a l l contacts, thumbscrews, e t c . , to make a complete c i r -  PLATE  IX  15. c u l t and an a l l - c o p p e r m u l t i p l e switch,A,was made to replace the radio switch f i r s t  used.  To check f o r stray e.m.f's. i n the switches and potentiometer the c i r c u i t was made completely r e v e r s i b l e , to the current i n the potentiometer.  even  This was accomplished by  p l a c i n g ordinary r e v e r s i n g switches with copper s t r i p s over the brass p a r t s i n the cold j u n c t i o n and the potentiometer power c i r c u i t , and connecting the two by means of a rod to make them move as one.  In a d d i t i o n the m u l t i p l e  switch,A»  (Plate IX) had a double set of contacts to reverse the hot junctions* The c i r c u i t ends of the thermocouples and cold j u n c t i o n were kept at the same temperature by running them into a f e l t - l i n e d zone box,B,with f r e e space i n s i d e about 6 i n . each way.  There, the ends were wound around copper leads  and clamped t i g h t with thumbscrews on two v e r t i c a l panel boards , C. The hot j u n c t i o n s of the twelve thermocouples were fastened i n grooves i n the heating blocks,H, the leads, D, taken out between the gaskets o f the cryostat, E, and into the zone box,B.  The ends of the thermocouples were wound around  the copper leads, F, and clamped t i g h t on the panels, Q by means o f thumbscrews, G-.  The copper leads were taken d i r e c t l y to the  large m u l t i p l e r e v e r s i n g switch, A.  By w i r i n g the two r i n g s of  contacts i n p a i r s , as shown i n the diagram at I, the r e v e r s i n g of the thermocouples was  seoured.  Spring contacts, L, covered  with copper, were connected  by means of copper s t r i p s , K, and  other s p r i n g contacts, J , to copper r i n g s , M, from which one lead went, d i r e c t l y to the r e v e r s i n g switch, N, and the other went to the potentiometer, of  the r e v e r s i n g switch*  0, and thence  to the other contact  From the r e v e r s i n g switch leads  were taken hack to the zone box where the ends of the cold j u n c t i o n were attached.  The cold j u n c t i o n , P, was immersed  i n an i c e bath. The potentiometer  circuit  ( P l a t e X)  Power was s u p p l i e d f o r the potentiometer by a 2 - v o l t storage battery, B ( P l a t e X ) .  One side of the c i r -  c u i t was taken d i r e c t from the double pole switch, 0, to a r e v e r s i n g switch, D. ammeter, •E, with a  A, then t o an oil-immersion, s l i d e - w i r e rheostat, f i n e adjustment and on to the other side of the  r e v e r s i n g switch. connected  The other side was taken f i r s t to an  The other terminals of the switch were  d i r e c t l y t o the potentiometer, P*  An Eppley stan-  dard c e l l , F, (P.D. m 1.01890 v o l t s ) was used to set the potentiometer.  The e.m.f• terminals were connected  as des-  cribed i n the thermocouple c i r c u i t to the m u l t i p l e switch, G, and the cold j u n c t i o n r e v e r s i n g switch, H.  A Leeds and North-  rup m i r r o r galvanometer, I, s e n s i t i v e to l e s s than 10  volts  was used with a 600 ohm damping r e s i s t a n c e , J , i n p a r a l l e l . L i g h t f o r the m i r r o r was supplied by a small s p o t l i g h t and r e f l e c t e d to a t r a n s l u c e n t s c a l e near the instrument The potentiometer  panel.  i t s e l f was a Weston model -5  having three ranges with s e n s i t i v i t i e s of 10  —6 , 10  and  17. -7 10  -6 volts, respectively.  Since the 10  v o l t range was suf-  f i c i e n t f o r t h i s work i t was used throughout. C a l i b r a t i o n and i n s t a l l a t i o n of thermocouples i.  Fixed P o i n t s . Three f i x e d p o i n t s were used i n c a l i b r a t i o n , the  f r e e z i n g point o f water, the f r e e z i n g point o f mercury and the sublimation point o f COg. The i c e point was obtained was obtained  by immersing the thermocouples i n a bath of crushed  i c e and water i n a vacuum f l a s k .  At no time was any measur-  able change i n the i c e point n o t i c e d .  T h i s i s t o be expected,  as the i c e point i s e a s i l y reproducible t o 1/1000 ° C, (9a) The mercury used f o r the mercury f r e e z i n g point had been r e d i s t i l l e d by the Chemical Engineering  department o f  the U n i v e r s i t y o f B r i t i s h Columbia and seemed t o be of good purity.  When a c o o l i n g t e s t was made the f r e e z i n g point proved  to be very sharply defined, and could be maintained constant to the nearest m i c r o v o l t  (1/30 °C.) f o r over an hour.  ( P l a t e XI)  When c a l i b r a t i n g i n mercury the blocks and the thermocouples were ooated with Duco Cement to prevent amalgamation, and held w e l l below the surface o f the mercury.  The  mercury container was placed i n d r y i c e . Readings were taken as the mercury cooled and the f r e e z i n g point was considered reached when there had been no d i f f e r e n c e i n thermocouple readings  f o r f i f t e e n minutes.  When the f r e e z i n g point was  reached the remaining thermocouples were checked  repeatedly.  The sublimation point of carbon dioxide r e q u i r e d a completely d i f f e r e n t arrangement  because  crushed dry i c e  has a d i f f e r e n t temperature when mixed with a i r from when i t i s i n an atmosphere  o f carbon d i o x i d e .  used as checks on one another.  Two methods were  In the f i r s t the thermo-  couples were placed i n a large Dewar f l a s k and crushed dry ice packed around them.  The f l a s k was then covered to pre-  vent a i r from r e - e n t e r i n g and the whole l e f t f o r t h i r t y - n i n e hours when readings were taken without d i s t u r b i n g the f l a s k in any way*  In the second method the procedure was  changed  by p u t t i n g a small h e a t i n g c o i l at the bottom of the Dewar. The carbon dioxide evaporated by the c o i l f l u s h e d out any a i r that was l e f t  i n the f l a s k a f t e r f i l l i n g ,  and an e q u i l i b r i u m  temperature was reached very q u i c k l y (9b)(Plate X I I ) .  This  e q u i l i b r i u m temperature gave the same thermocouple r e a d i n g as the previous method.  Temperature  was  corrected for. baro-  m e t r i c pressure by u s i n g the formula:2  T = ( -78 +• 0.1595 (P - 760) - 0.000011 (P - 760) ) C ii.  (10a)  Calibration* U s i n g the d i f f e r e n c e s i n thermocouple reading  from the Bureau of Standards values f o r copper-constantan at these three p o i n t s (9b) a p a r a b o l i c d e v i a t i o n curve of the form  dE = a - b b t + c t  was drawn.  The constants a, b and c  were determined by s u b s t i t u t i n g f o r t and dE at the f i x e d points.  "A" i s the d e v i a t i o n at 0°0.  N O .  S  3 6  GRAPH  PAPEE,  SMITH  DAVIDSON  a  WEIGHT,  LTD.  19. b .=  (dE, ~a)tt-(dE„-a)t'~  c «  (dE.^a)t, -(dE,-a)t,.  With t h i s graph and the standard copper-constantan t a b l e s (9b) any temperature could be c a l c u l a t e d . -  When-, tiro • thermocouples had been c a l i b r a t e d i n  t h i s manner the remaining ones were compared with them at various temperatures u s i n g a mixture of a l c o h o l and dry i c e i n a vacuum f l a s k *  Dry i c e was packed around the outside of  the f l a s k to prevent any r i s e i n temperature, and rock wool around the whole to i n s u l a t e i t .  By t h i s means graphs of  d e v i a t i o n from the p r e v i o u s l y c a l i b r a t e d thermocouples were drawn f o r each of the remaining ones.  I t was found that  because of the f a c t that a l l thermocouples were made from the same piece o f Copel wire most d e v i a t i o n s were very small and almost independent o f temperature, apparently being c h i e f l y due to i n d i v i d u a l contact p o t e n t i a l s i n the zone box or leads, iii.  Installation* The thermocouples were set i n t o the blocks by  making a groove from the edge of the block with a f i n e cold chisel*  ( P l a t e V)  This groove was f i l l e d with g l y p t o l and  the thermocouple i n s e r t e d i n i t .  The r a i s e d edges of the  groove were then pounded down over the wires and the surface f i l e d and sandpapered smooth again.  In t h i s manner i t was  p o s s i b l e to get the thermocouples very close to the surface  and yet keep the surface p e r f e c t l y smooth and so ensure good contact. The method of t a k i n g readings The procedure i n t a k i n g readings was as follows, (using the case where the desired temperature i s lower as an example). 1.  The oxygen valve was turned on f u l l to make the apparatus cool q u i c k l y .  2.  When the r e q u i r e d temperature was almost reached the to  3.  oxygen was turned o f f and heat turned on f u l l stop the c o o l i n g .  As soon as the temperature d r i f t was slowed down the  oxygen valves were manipulated u n t i l an almost  s t a t i o n a r y state was reached. 4.  By a d j u s t i n g the current i n the heater c o i l s the temperature d r i f t  i n the outside blocks was com-  p l e t e l y stopped* 5«  As soon as the outer b l o c k s were s t a t i o n a r y the current i n the heater b l o c k s was adjusted to give constant temperature i n them as w e l l .  6.  The temperatures of the two small heater blocks (guard b l o c k s ) were compared with the temperature of the centre one and adjusted u n t i l very n e a r l y the  7.  same.  Both outer and inner b l o c k s were checked f o r d r i f t of temperature, and i f there was any i t was stopped  21. 8*  When the temperature  was s t a t i o n a r y everywhere read-  ings were taken o f the current and voltage of the . centre block. 9.  Two complete sets of readings were taken of the thermocouples.  I f , during the course of a set of  readings, there was a d r i f t of more than one microv o l t the system'was readjusted and a l l readings repeated. 10.  Current and voltage were again read.  In any appre-  c i a b l e change occurred a l l readings were repeated. This process r e q u i r e d on the average f o r t y minutes to complete, running w e l l . minutes.  around  provided that the apparatus ?;as  The f a s t e s t time f o r any reading was twenty  Because the heating c o i l s could only carry a l i m i t e d  current the readings taken f o r r i s i n g temperature  r e q u i r e d an  hour or more. Readings taken i  Many p r e l i m i n a r y readings and t e s t runs were  made before the a c t u a l f i n a l readings were taken.  Almost at  once i t became obvious that the apparatus was not reaching s u f f i c i e n t l y low temperatures.  The o r i g i n a l design was i n -  tended f o r use down to about -100 °C, but because of the much l a r g e r s i z e and heat c a p a c i t y of the main u n i t considerable changes had to be made before the heat removing system ivould  •  22. reach that  temperature* A f t e r more readings were taken i t became  ent t h a t much lower temperatures  appar-  would be needed to overcome  supercooling e f f e c t s and the cooling u n i t was redesigned to -the form f i n a l l y used.  ( P l a t e IV, V, VI)  I t i s with t h i s  form that a l l the f i n a l readings were taken. Readings were taken f o r i n c r e a s i n g and decreasing temperatures  i n the range from -170° C. to 4-40° C. and f o r  0%, 50% and 100% s t r e t c h . ings were completed  A f t e r the 0% and 50% s t r e t c h read-  i t became apparent  from 100% s t r e t c h r e -  s u l t s that more readings would have t o be taken to check p a r t s of the r e s u l t s .  T h i s was done f o r both 0% and 50% s t r e t c h  with the r e s u l t t h a t readings formerly thought  to represent  experimental e r r o r s were shown to f i t i n t o . t h e general p a t t e r n . F o r each degree of s t r e t c h measurements o f the rubber were taken u s i n g a p a i r of t h i n c a l i p e r s f o r width. Thickness was determined  by measuring with a micrometer the  t o t a l t h i c k n e s s of the b l o c k s w i t h no rubber between and again when the s t r i p s were s t r e t c h e d i n p l a c e . In a l l cases the a c t u a l measurement o f conduct i v i t y was based on the centre heating block.  The outer  blocks were used only to prevent l a t e r a l conduction. way edge e f f e c t s were e l i m i n a t e d .  In t h i s  Since the only surface of  the inner b l o c k that was exposed to r a d i a t i o n from a warmer surface was the bottom edge extraneous heat sources were neglected.  III. The  RESULTS equation and method of c a l c u l a t i o n The  previously,  equation of thermal conductivity,  as shown  can be put i n t o the form:'E  £ . d . t  A  1 T^-T,  where Q, i s the amount of heat t r a n s f e r r e d ;  ty the time; A, the  area o f the conducting surface (assuming here that faces are p a r a l l e l ) ; ture difference  opposite  d, the thiokness; and T^-T , the tempera(  between the two  faces.  We may t h i n k o f K as c o n s i s t i n g o f three f a c t o r s , namely:  a power f a c t o r , £ ; a . t temperature f a c t o r , 1 or T^-T,  f a c t o r required i.  dimension f a c t o r , A ; and a ' d 1 • The determination of each dT  a separate set of readings.  Power f a c t o r . To  determine the power f a c t o r i t was necessary  to f i n d what p r o p o r t i o n o f the e l e c t r i c a l energy was used up i n the heating c o i l i t s e l f .  Using subscripts  G, v, a, 1 to  represent c o i l , voltmeter, ammeter and leads r e s p e c t i v e l y have; *c  =  J  a - .  =  *a ~ ^7  we  24. = Y  Y  Q  - IcR!  v  Ik Power = P =  » (I - R  IqV  a  Q  8  -  v  ) ( Y - I R!) V  C  - I I o H i YylcRi a  watts.  +  Ignoring the s l i g h t d i f f e r e n c e between I  c  and I  watts.  a  f o r small  c o r r e c t i o n s , and u s i n g the r e l a t i o n s  Y  y  a  - Y I (R +Ri) v  a  n  d  I  0  a » I  Y a  v  Rn+Rn P = I Y a  where R j * 0.14 ohms;  Thus  ii»  v  (; R R  B  - R#f-Ri)  t  » 300 ohmsj R  v  £ « 0.954 I Y t = 0*328 l Y  Dimension  -  v  Rj  a  a  a  a  c  watts.  R i « 5 ohms.  watts, Calories/second.  factor  The dimension f a c t o r i s e a s i l y obtained from the measurements taken.  C a l l i n g the width of the s t r i p of rubber,  w; the t o t a l t h i c k n e s s of rubber as measured, 2d; and p u t t i n g i n the length o f the c e n t r a l h e a t i n g block, 4.01 cm., the dimension f a c t o r becomes jd A  d  •  2 x 4.01 x w  T h i s f a c t o r v a r i e d s l i g h t l y each time the rubber was put i n , but was always between 0.0075 and 0.0079.  25. iii.  Temperature  factor;  The readings o f a l l the thermocouples on the i n s i d e b l o c k were corrected to correspond to the one used as the o r i g i n a l standard, and then averaged.  The d e v i a t i o n graph  was then used to convert i t to the Bureau o f Standards copperconstantan t a b l e s (9b) and the temperature c a l c u l a t e d by i n t e r polation.  •' S u b s t i t u t i n g F f o r the dimension f a c t o r and cor-  r e c t i n g f o r lead r e s i s t a n c e the f o l l o w i n g expression f o r cond u c t i v i t y i s obtained* E = 0.228 IY * F T^~ T,  Gal* Sec* Gm.Beg, C.  Probable e r r o r The absolute determination o f temperature does not need to be as accurate as the d i f f e r e n c e i n temperature between the two sides of the m a t e r i a l .  Since the readings are  taken over a temperature i n t e r v a l of'"around 8 °G the reading i s only an average determination over that range.  For graphing  purposes the nearest degree to the middle of the range was chosen.  As the r a t e o f change o f c o n d u c t i v i t y i n most p a r t s 4  of the curve i s l e s s than 0.01 x 10 ~ /°G.this introduces an e r r o r o f l e s s than 0»5$» In the determination of the dimension f a c t o r i t i s d i f f i c u l t to t e l l t o what extent the volume o f the rubber changed i n s t r e t c h i n g .  However, since i n the two cases where  two dimension f a c t o r s were obtained f o r the same degree o f  s t r e t c h the change was approximately 1/80,or 1.2$,  This  could he due p a r t l y to an increase i n length a f t e r being stretched o f 0,6% and also to s l i g h t d i f f e r e n c e s i n the degree o f s t r e t e h . Measurement o f the degree o f s t r e t c h was coml i o a t e d by the f a c t that the s t r i p s were compressed sides.  on the  There was a very s l i g h t widening o f the s t r i p  than 1%) caused by the clamping o f the blocks.  (less  However, t h i s  was accounted f o r i n the dimension f a c t o r , and because o f the small changes caused by the amount of s t r e t c h would have little  effect.  As f a r as any one set of readings was concerned  t h i s would have no b e a r i n g on r e l a t i v e values. The accuracy o f determination o f the temperat u r e s d i f f e r e n c e i s hard to estimate.. The o r i g i n a l r a t i o n o f thermocouples  calib-  should be accurate at l e a s t to + 2  m i c r o v o l t s , and since the readings were the r e s u l t of averaging four thermocouples, and at no time was any s i g n i f i c a n t d i f f e r e n c e o f temperature throughout the copper blocks noted, the maximum e.m.f. e r r o r i n each case should be l e s s than 3 microvolts.  T h i s g i v e s a maximum e r r o r i n temperature  rence o f l e s s than 2fo o f an 8°G.  diffe-  interval.  The ammeter and voltmeter were t e s t e d and o a l i * brated beforehand and during the t e s t s proved to have a maximum e r r o r o f l e s s than 0.5%*  Consequently, with c o r r e c t i o n  f o r lead r e s i s t a n c e (around 5%) the power f a c t o r should be r e l i a b l e to w i t h i n 1$.  Using the g e n e r a l l y accepted approximations f o r s p e c i f i c heat of rubber and copper, i t can be shown that a temperature  d r i f t o f l/30°C. per minute*-  ( Corresponding to  1 microvolt/min.) corresponds to an absorption or emission o f power amounting to l e s s than 0.5% o f the power input. a l l readings were taken f o r a d r i f t t h i s f a c t o r i s not important.  Since  l e s s than 1 microvolt/min.  Experimentally i t was found  that very small changes i n the power supplied would cause noticeable  drift. The t o t a l o f these f a c t o r s gives a maximum e r r o r  of  4  5%, or a change i n K o f approximately 0.15 x 10"" .  The rubber sample The"sample o f rubber used was one o f a group o f samples obtained from the U n i v e r s i t y of Notre Dame.  I t was  prepared under c a r e f u l l y c o n t r o l l e d c o n d i t i o n s to make i t p o s s i b l e f o r r e s e a r c h to be done on rubber s i m i l a r to commerc i a l brands, and of e x a c t l y known composition. The sample was prepared to the f o l l o w i n g s p e c i fications. pure l a t e x carbon b l a c k z i n c oxide stearic acid pine t a r sulphur antioxidant captax  100 p a r t s 3 4 2 2.7 1.5 0.9  Length o f cure  120 min.  Temperature o f 'cure  274°F.  T h i s rubber was intended to be roughly comparable of  t o standard t r e a d stock with the exception that 50 p a r t s carbon b l a c k were omitted.  I t s measured p r o p e r t i e s  o H  o  PH  H  >  0  CM N O O I A r l  1 I  1  K \ L F \ C O C O O N R H N Q R H O O CMN£> £>• K V S J - O N N Q CM R H CM C ~ - I A N O LfN'VFL ! > I > H r l r l W ON O H W W W W ^ K \ W H O 0 \ C O rlrAr-\rl r-\ r-\ r^ r-i rl rA H rl rl rl  Hr O N I A C O N O C M ^ - O ^ H N \ N \ . H ^" C K O N O ^ Q N O C O C O "SI" CO. O N O R - l T - R \ V O C M C O C O R H C — O C O C - C M N O C " - - 5 H - C M C M 0 ^ > T A - = * O O N}" ' A ' A C — C . • » • • • • • • • * # • • • • • • • • « • • • * • • • * I A K \ K \ N \ I A K \ C M C M C M K \ C M C M H C M C M C M H C M C M C M C M C M C M H C M C M C M CM C M  TAON^J.CM  c—  t£>CO o  .  \ 0 0 " - 0 O C O M 3 H CM C - r A < A O H K \ C O C ~ « H - ^ j - K \ Q H W O r H r l W C V l v O ^ H - s h c O H O N CM t A v Q r H N O O N O N N D t A C O N Q CO r A CM 1ACM N O O N C O N O O C ~ H / \ f l t f \ ItrfCM O J A C M W l A H H H K \ H W H N ^ H W H H l A H W r l H K \ W C V I O J W r_) • • • d • • b • • • • • « e « « * • « • « « « • o e a c • . • ra  • • • •  .  « .  .  .  .  e  »  .  »  «  6  «  •  •  «  •  .  «  W W H H H C ^ W W H W W W C J H H W H W H H W M . W C V I W  «  CM  « • • « • . . . « * « . « « # • « * • . • • • « •  l  ppO ^ N O K \ N O " A ^ Y r A r A C — ^ K N O N W r - I A H K X H C O v D O N r - ^ O C V l H ^ <-iii\M3 CM O ' t - ^ - l > r 1 C O C O H o r ~ o \ r - o 1 A K \ ^ I A ! > 0 C M > H O N N O CO <=t CM LT\ i r \ ^ J - LT\ K \ K \ K \ L f \ ^ j - I A K \ < ^ "N-vJ- ^ r A K \ A r A L f \ t A K \ l A ' H ; ^ -^J- •^J-  Ira .  CM r H CM CM  .  p H O ( A r A I A I A O O s C - H l A I T - t r - I A C K C M K \ l > ' * O ' t T - KN CO C O C— I A O O I A I A N Q I A CM C - C O l A O N O N O CM CO <=t C O O CM N O IT-vO CO L C \ ONCO I A •** • I A  {>  H  •  H  •  C-~KyA  CM  •NI- O  •  •  •  •  .  •  •  I  1  «  «  I  I  .  .  .  I  I  .  I  I  V  .  I  .  c  I  •  »  I  r-i  %t o I  r-\  .  I  H  .  I  L f  .  » l  .  .  . |  .  CM  I  W  .  •  •  *  *  .  .  *  ^  I  .  I  •  H  .  H  a  .  •  .  •  *  •  .  I  •  . . .  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O K \  ^ 'LfN tr- v O IC\ o -sh rH O lAhT\vX) L f \ C O N O H N O C — N O C — C O N O O N C O H O N t>CO O N O r H r H NO O N O r H LT\,NO ^J-vOvX) H CM r H K \ CM NO CM L T \ C O LT\ LT\ Q K \ H O N~vO u r \ O N ^ ONi~c\i-^\NO L T \ N O L r \ c r ^ o N C M c - c o c o O N O N ^ O c - - L r \ ^ i - H o o  H  • A N D CM H C O C O K \ H L T N t r - L X X O K \ C O v O O N t A CM K V - O \ J D l ^ O H ^ K \ C O O C - H I T - N O RH-=H/-=H--=tvONOcM^L- O M 3 K \ K \ H s(- -H- C—NO CM CO K \ C O LT\ CM H <&X> K\ CM R H C — C M N O O N i - C O C O C - ~ O N C ~ O H v O c O O S O O OJ 1 A K \ 0 CT-vO K \ ^  I  C ' - O O ' A CM r H K .  • r ^ H H ' t A ^ O ONCO ON t r \ CM VO ONCO O K \ C - N t C O H O N O  I  p c M c o c—  H  L f \ r H C—-£> l A I > ' ^ ^ - ^ 0 H  •  CM tr~tT~ CM M3 CO N O M ) ' C — N O ( A H C - - 0 O M A ' A ^ i M O J ^ - H H ( X ) r l O N C - t T - O J OJ I . 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H o l>  o  o  o  t> £J  CO  NO  O J O J H H  H  H  OJ OJ H  H  r-4 H  OJ OJ  oj OJ OJ K \ O J K \ K \  C - N O N O H -=t L T \ ^ J - O O ^ K\*3-NO o o O N O N - ^ - O O C ~ - C O C K H N O tr-c© ON<VJ- O N K V O J  1  C O K \ o C O -sh O J N Q O N O J N O H C-~LT\OJ O N H co N O C K O C - ~ O N X O , O C — C - - N O O J O J K M T - K \ K \ *tf K \ K \ K \ . ^ - H KN.KN » • © I^T\ • • « • to « * e « e «  •  Lr\0NOJ!^\NQ t > t > 0 WOO 1A1A1AOJ O C K OJ K \ L f \ v O ^ C ~ - O C O C ~ - L T \ f ^ O J H H H H H OJ H i i i i H I i l i i n i t i i i i  CO  •  •  »  tr-LTyojco  N Y K \ * t f  CO O N K N . ^ O N O C—C-C--CO t r - C — C — K \ * ^ - O J ^ tr-CO H Q O KN. C O O NIT-CO N O O NON 0 - N O " A L T \ N O Lr\Lr\Lr\ir\ir\ur\Lr\LOv t r \ i r \ LT\ L T \ UT\  O N HC " - 0  •  «  •  1  • . '• • &  «  «  ONOO  •  O JCr-K\.OJ K \ P > 0 O N N O O N O N C-~ C— L£\ O N  »'« ^ C O C O  •  C— C - N O  K\ON-=H/  C - C — K N O K \ K M r - O J KNOO OO K \ K \ C ~ C — C — O J C©N£> O LTy LT\vO CO CO ON ON O O ONOO G N O N O O C O ft 9 « • fc O • « 4 • e • • • « e « OJOJKNOJOJOJOJOJOJOJOJOJOJOJHOJOJ ^  •  K \ l > K \ H CO LT\  . •• •- •  H O  I  A ^ K \ O K \ ^ i r \ ^ r o H O O H H H H H H H H H H H H  A  S  *  i  l  IT-CO  e  «  «  <  B  i ~ i  s  s' i  •  I  •  I  e  •  I  •  •  i  O  *  • «  i  H O J  i  CO  K\  OJ O  « « © LfN-^  I  H  e  •  • o  OJ K \ H O OJNO H L:\CO  I  I  LT\CO K \  I  K N OJ H  I  »  •  I  OJ O  i  ON c—Lr\-^-K\H  i  OJhTs O N Lf\O0 O  C ~ - C ~ - K N K \ 0  i l l  "^h  I  L T \ K \ OJ O N C O N O  H I  i  OJ-vfirs^NOCOh^OONON-H/KXNN.  4  L A O N C O LT\^}- ON^J-NO LT\ K \ O N K \ - v j NO rH OJ ON O H O tr-LTNKNLOjC© ^ L f s c ~ - c O O C — C O o •  OJNOONO  O  O C O OJ "sh ^ - "sj- O  i  K \ - = d - i A ir~ L T \ K \ H  • i  H  CO  rc\  H H H H I I I I  I  * • • <* « © « e m « « a C — O J L T \ O N O N O O N O OJ N O OJ O O  I  H  H  •  O N t r \ a o C ~ O J c o o j - ^ - c~- K N . N O C O - I A ^ H O N H N O N O ONNO C OC O K \ C I X \ C T - O N O O JI T ~ H N O O ^ H C - I A O OJ  K\<^<sj-'vi--^K\K\.OJOJHH  i—I  U  ON NO N O O K S C O O ^i" O N N O H O J O N K \ H OJ<vh O J C O H O N O O N KN.NO O J O O Lr\oo O O O N - ^ i CO H L'ACO K \ O O K M T - O J N O O J C ~ - K > O O H >  «  ^  C - ~ H N D ^ J - O N «sf- O J c o O  O J^ -=j- c  C O - = d - O K \ O N " ^ - v X ) r H C N . O N O N C O i-] •st •  ,  H  , !  W  \  , , 1 I  K  ^  t  I  ^ • 9 Sl^t H  - +  *  «  »  •  ,  O C — O N H C— N O O J O N O N I—I O J  •  , I I I  I  o o \ 0 i' T  *  •  «  1  l  l  |  N O OJvO ONONOO O J  O J O J tr-co N O r - N O o j l A . - ^ ^j- c o  O JIT-KNNONQ O  |  |  i |  J i  j  i  |  | H  I I  I  K N K N K N N O -^-NO t r - i A C M A H ^ > O i A H H L T \ O " N . H . O J r < W LTYLCNNO U N , - ^ K N H O J K N ^ - ^ N C O N O i^r^ ^ H ~ H H H H H H H H H H H H  "7* T ! t i  1  •  •  *  •  ^J-OJO H CO OJ H K N C O (T-sh O N C O C O  •  O J O J O J O J O J O J O J O J O J O J O J O J O J O J O J O J O J O J O J O J O J O J O J O J O J O J O J O J O J  * • • • • • • • • • • • • • • • • • • • • • • • • • . « •  O C O O C — K N O J N O Q O N O N C ~ - O N O K N C - I T - H H N O O N C—K \ K N C O L A K N A C - I T N O O N L T \ L O V N O C - H O N C O N O O C O ^ •KN L A ^ COCO CO NOCO ONCO C - ^ H D - O N  O C \ J ( T - O N O N C ~ - O J i r \ o O O J O N ONNO O O N IT- C—ONCO NO IT-CO K N I T - O N C O LT\CO K \ N O ON •sh LT\ 'sh ^ Lr\ur\Lf\lX\L£N,LT\Lr\Lr\-^- .^j- U\IC\ « * ft fe * » e » * » e « e » « a •  C O ^ -sf- O N N O O N - = d , - " ^ - N O O J - ^ - - ^ - ^ O 'sh O O ^ - N O K \ N O c o - ^ W H H ^ ' d - ^ O O N C O O N I—| K N . i—1 C O I T - K N O C O N O Lf\ K % C O I T - N O C C O O J N O O N C O l-Oi ,—j U N . o K N KN. O J O J K \ K N O J K N K N K N K \ O J O J K \ O J O J KN, K \ K \ K N K \ K N K \ KN. O J OJ K\-vJm v • 6 a « 0 a £ * • « • • • * « « • « ' « < « « -# *  I A V O  • • *• •'*' • • * • • • » • • ' . . • • • • • • • ON * • • • « • « KN K N K N K N O J K N O J K N O J O JO JOJ O J H OJ H O J O J OJ OJ O J • OJ OJ OJ H H OJ OJ H  o  .  H  +  OJ  ON  *  O OJ K"\  CO OJ  •  •  OJ  NO NO  i  i 0  i  i  H  r s  H  I  H  i  H  i  H  i  H  H  i  H  i  H CO C — N O O 0  I  H  H  J  I  H  I  H  i  H  i  H  i  H  H  j  H  ^NOJ  i i  H  0 C — N O I T - L A I T - L T \ C— O C— KN O N H C O N O N O L A KNCO « • « « » « • O O K Y O N O N O -JJ- O 1 A O rc\ O J ^ LT\NO I T ~ I X \ ^ T  H  H  H  OJ ^ j - N O N O L T \ L T \ ONCO H  i . i  O C— C — L A K N H H L A O 0 \ 0 ^ i ^ 0 H C O O N - S [ - -=3* ^ j - N O L f \ 0 O NONNO * * • • . • • • • « • • « • O K\lA.C"~CO.CO O O H O N O N N IT-CO O N O H O J Lf\NO N ON ON O  i  ON OJ CO h C \ N O OO  i  ONOJ CO H ^ KNOJ H K V * t H • • • NO • • H LT\ «I T - O H H OJC NO  - •r  .1  i  L  s  i  i  K \ K \ 1ANO C - C O  as i  .IT-:-: H  <H  L  A C O CO O N ^NJ-  i  ON O  i  KNNO  i  i  H  i  H  i  H  i  H  i,  H  i  H  i  H  r  H  K \ K \ L O \ ^ - N O ir\K\CM  H  H  H H W  H  H  i i i  K \  H  i  H  :  i:  H  I.  H  i  H  trxLTN'sh OJ  H  i i  L O \ c O IT— OJ OJ I—1 K N O C — *vh C — OJ i—1 N O CO O N O N L T \ L T \  L I M T - L A O N O O N t T - O K N K N LT\co O J ^ N 0 1 T - - ^ - N O ^ - H C O h r \ O O J - ^ - 0 IT--shNO ^ K N K N C O H K \ 0 \ C O 1<N ONCO H K \ O r l r i ON ON ON KN CO K N OJ H OJ H ON LT\ O N K N IT- H •^j-CO OJ l A C O O H N O CO O N O C M A O J t O C M K N l A c - O N O l T - t A • $ • • < > • * * » • • • * • • e « « « « • « • « ' « « »• m a m r l H W N Cvl I f \ « \ T f \ ^ - ! j ' ^ ^ ^ • ^ M N ^ - s f ' ' ^ . ^ - ^ ^ ^ ^  H  O NO O O N KN.NO O -vh KNCO H H H tT-CO l A C O L r \ O O O N O ' s h h ( M T - C O N O I T - K N O N "^j" • • • • • • « • « « • • « • « • • • • • • • • • • • • • .••ICVOO'O 0 \ W ^ ^ - M 3 o O C D C b H I T - 0 O N O K N C ~ - I A H ON ON Lf\ H ON ^ ON  C * 0 \ 0  K\  C— H O N K N H N O C O O N ^ t 0 N K N , N O C — O J OJ ^ - C—OJ ^ H O OJ O C O C — N O L f \ L T \ C— O l - f N O N C - H - ^ - O K N . N O L T N O J O J ' s J - C O H O N O K\N£> t A c O LO\CO H C - ONCO CO O N 9 • *O • • • • • • • • • • • • • • • • • • • • • • • • • • L f \ N O CO »NOcO C ~ - N O ON ONCO O O O N O J O O N H OJ O t O ^ O H H OJ O o o ^ H H H H H H H H r-\ H r~\ r-{ H H H H  ON KN, • NO OJ  NO  H • OJ  K\  A  NO ^ O H  OJ  I  N O OJ N O H  CO OJ L T N O N K N I A O O  K N K \ N O  IACONO  w o ^ c o H c y ^ - v o o ^ H  C O C O H C — ^ } - K N O N N O O N L £ N , H L f N K N C — H OJ ON KNCO K N KNNO N O OJ I T - C O KNCO C — KN  I  H OO CM O K \ < H ; \ 0 ON O N O r H CM ON CM CMCO C - C M N O r A r A A C M N O O CM NO K \ H NO NO L f \ CM OO CM CM l A O N N O ^ NO r A rH I A I A  I  H  I  CM t A *sh  (M I  I  I  I  I A MD C — C O O  1  I  C-NO  I  IA-^-  I  CM  I  H  I  I  H f A H ( f M A C - ' v i - OJ O M ) I A  I A K \ K \ CM I A I A r A r A CM CM CM CM I A K \ r-C\ K \  H  I  O  NO CO N O NO  r A 1ACO ^ o  Lf\ I A I A L T \ N O N O  I T - C O ON N O  I A LT\ L T \ LT\ L T \ LC\ l A ^ N O  CO NO  NO  " M A H O N l A H l A N i - N O H ONCO ONCO CO H H ONCO O K \ i A i A r > t > o O - S } - N O l A O O  CM O ^ C — C - C — U " \ M D c O O C— H NO H H l A O C O O N C M l A r A C — I A H ON-shvOlACM H -^t f A CM I A t A r A I A CM ^ CM l A r A t A ^ "sh  I  CM I A I A I A CM K \  vh  • »  H  I t  t A ^  I  A O N I A C M C O N O H O N C - C ^ I A - ^  I ON  ,• •• I A  , c-  A  #  i  CM NO.  • ON  I  CO  O N  O C O CM 9 -e e IT- CM O  I  I  I  H  «  •  •  •  •  c-  •  •  c-coNO  • •  •  «  H  O NO  rH  H  • • C O C O ONO N  • •  I A O O C - C -H ON C -H O C O O C O I A C M c— c - O N N O c—co I A O K > c- tr~  o  O N O O c-  CM  tA-vh  I  C ON O C O A  I. I O  i  NO  I  c  I  I  I  c-co  I  I  I  |  IA-4-  I  CO N O ^  I  O C O N O H  C - I A N O CO H  I  I A N O  A  I  I  ON O  I  I  ON I A  I  !  rA I A ^ O N H  "vf"  H  I  ON  i  I A H  O  I  I  O !A CM CM CM ^  H  IA  H  I  O N C - O C - C - O N C - O N C - C M COCO I A H o H t A I A N t A N O c - O N t — - A - v } - r A CM H  H  ft  H  •  H  •  H  •  ft  •  •  •  •  •  C M CM CM I A CM CM CM H  •  4  H  •  «  ON I A N O C - r A N O O N A C O -sf O N O H C —  NO C O C — N O r A C - N O  ONO  •  NO N O CM O I A C— CM A H  NT- CM O N C O C— t A C-• I A  O O r A l A O N ' v h «^ l A ^ - N O O CM O I A H C— H O ( A C— H  HHrHCMCMCMlACMCMHH  CO C— C— H CM I A N O H  A  •  ' H IA  +  I A H I A C O O C - N O H v O O N I A C O ON I A I A l A C - C O O -=t A O H O CM O N H C O H O  S  ' H  CO K \ l A c o C~- "vh O rA O I AI AON K \ N O l A l A C O O J H OJ O C — C M O N C O C — 1 A A O * • • • • • • • • • » « • « • « «  *  o O N O N I A N O C — C - C O r A O N i A c — c o c--o o r A CM CM CM CM CM CM CM CM CM CM CM CM CM I A I A  O N O N O N O N  ON NO  O CM  1  H H I " I  ON  e-  O N C O CM C OC O C O 1AO ON ON ON ON LT\NO I A A > A> A  ON ^ O >A I A I A >A ON l A C M ON O O O r A I A - ^ tA*=d- vrj- ^ J -  LT\ ON LT\  r>o  *=tf- c o I A K \ c— c— c ON  *  CM CM ( A CM CM CM CM  *  H H  •  I  H  i  o  co  H "3-NO ON CM CM L A CO O I A N O A -sj- -=d#  I  I A I A N O CM  «  co  CM O IT-NO  *  H  A  H  H  H O C O C—NO IA  O N ^  •  " A O N O ON ON O ON H rH H  ON  • CM  I  CO H  C D  NO H V Q O N I A Nt C O '« - « -4 •'• • , ft • CM  a s  H  O  «  a  O ^-CO O I A r—- A C O N O CM C —  i-  .i  o r A O N tr- C M o H i G \ C — N O A-<vh H rH -  «  -^CM  «  NOND CO  i  •i  H  O  O H  •  1 A C - H C - A C M  Nf- r A I A l A CM CM H  Nf  H  ON C M N O N O C— CO ON N O N O H C— r A CO ^  I A t A I A C M CM H  H H Ml  CP  <!  EH  w o  KN  4 O  H  CM  EH  EH pq W EH 02 1  v—  H EH  rH  o o  CM  EH  H EH  CM  O EH  O EH  © ra S H  o '02  I ra  e  £>  -p H O  o  0  O 0"  P  H NO  •  LA^h OJ KNCO OO H LT\ C — L A , — j K N H C M O  • » » « « * »  I  I  i  I  I  I  I  I  I  I  I  I  I  I  O J K N N O C — K \ rr-LT\ L T \ L C \ o  I  I  ONLANO  I  I  LT\  I  N O N O O N K N "'d* H OJ UN,  OJKN K \ K \ K N KNK N  • • • « • • «  C K H CM H O N N O ^ O N O O C O O N W O C O W ^ - C N H OJ O JO JK \ C O ( M H N D C O I A O K N W C O H"=t K N OJ O  e » » » » a » * e * * « .  i  C O ^d- O J N O O J c — O N - v h c o  I" I  ON K N O K N C M H O N N O I—| K N O J O J O J i—1 O O O N O O N L A ^ O J KN^d- K N LTNLTN CO NO IT-CO ON O O OJ K N ^ - NO H I • H H H H H H  K N K \ K \ K N K \ K N K N K N K N K N K N O J K N CM K N O J O J CM O J O J H  I  OO U N K N H OJ H H  KN:  LA C—NO ^  CM H ^CO O C—UNIT-NO C M M H C O ^ H O ^ O N O O N O H ^ f A H W O O N KN O J KN O J O J O J K N CM K N O J K N KN KN O J CM KN H O J KN KN "=3* KN ^ j - K N OJ  U N L A ^  K N UN NO NO u \ U N U N  O J O J O J O J CM K N K N O J O J O J  (—1 K N O O N c — K N O N N O H H K N O O J O O C — - s j O N IT— O L C \ K N L A U N O H N O C — H O N O ONON  L f \ . U N - U \ sj- U \ U N N O L A ^ J -  OO K N H O O O O N O N H " A ONCO K N O N K N O N U N L — O LANO O NO H K V A N O ON K N O L T N O N O J O O N D O N N O O K N K N C O - s h O H C— O O J H O J K N ^ " O JO K N 0 N C O  K N L A O O L A L A IT— H N O O O C O C — • A N O ^ J - K N ^ - O O LT\NO' H  •sh N O L T Y ^ - U V s f  KNOJ  L  O OJ O J O J CM O J O J O J O J O J O J O J O J K N O J O J O J  OJ  •  •  •  «  •  « «  •  «  • LT\  •  H  •  H  OJ K N  i  H  •  •  »  I  •  a  I  * CD  •«  1 1 1  1 1  I  I  •  I  •  I  « •  1  « •  •  H  © ©  •  •  H  •  H  e »  I r i t ' H H r S H I I I I I  H  i  I  •  •  «  I  OJ K N  1  • LA  i  I  LAOO O N  C—KVsf O O  i  CM K N  i  H H I  i  ON-sj- O H O O CM C — CO  •  OJ W O O H ONNO O L A KNCO C— I T — O N K N O C - O O O O N O •  i  r-\  OJ K N " A C — H  •  i  H  « N O C—  r-\  K N L A N O C—CO N O N O CO O N O  i l l  I  ITi i i  r-{  i i  i  i  r-H  t  r-i  i t  •  r~{  - 5 J - N O OJND U N U N O J K N ^ t C — t i  •  C O O N O C - H O O N O O O N O O O O C - O N O N  C — O J O N L T - C — O J O C — H CM H C O O C O N O O N K N C - O N N O U N U N N O H O C O O ^ t L A N D C — C O O J O O O H C O N O L A O N O N D CM CM L T \ O N C O C O ^ j - L T \ H O N H O N O  •  ^vh C O N O L T \ c — N O L A N O C O N O C — C — C O  •  i  •  OO K N H KNNO *sf" CO C — O KN O K N C—• O ^ ON ^ OJ O C O C — H K N C — L A H L A K T f L A L A ^ C O •  LAO OJ H  •  i  *  CO L A L A O O N D O N O J K N O O N H O N U \ C— C - H L A H LAKN"NS- ^f-NO L A L A O L A O L A H L A C— • O J C O O N L A - v j - C—OO K N O N V O H C — L A O . C O N O N O  •  «  O ONNO CO ONNO ^ O N N O U N L A C - O O tT— C—NX) c — K N L A O J "^S* O N C — KN H H OJ •O J L A N D C - I A N O c—OO O N O H K N ^ L A H  «  H  H  H  * *  H  « • «  » • • •  CM O J O J O J O J O J K N K N K N  fa « «  «  e • » ' "<h L f \  0  H  * • H OJ  O N L — C O H O N O N ! A O J K N N O r i O H C O ' O L A OJ CO NO OJ CO OJ K N H H K N H O J Q O K N O N O C — O O N H L A C - C — LANO I—CO O ND O OJKN C—'-A H O O N O N ! O L A O N O J N O KNONOJLTNCO K \ N O ONOJ C — OK N C — O K \ C — . O J C—• O  • H .. 1  I  1  H  H HOJOJOJOJ  OJOJOJKNKNhA-^-"sf'  N  C — O CM 1—1 NO -sd* N-O K N ON O O N *sj" I—i i—] i—I O N L T \ UN ON ON OJ "^d* ^ A i—I NO ^ i—| HLALAHKYCKC-COONOHCOCTsCOCOIT-tT-KNITONNO H ON OJ OJ LT\ ON C — OJ C — CM K N C — O N - ^ O NO O KNNO O h A - 0 ONOJ-^C-H^CONOO-^ONKNIT-  H 1  *—s  o  o  -—•  H H H P3 d| EH  o 1—i  id  O H  H  > CM EH •I 1—1 EH  OJ •EH •  H EH  o EH  o EH  O  o  m H CtJ  o ra  &  to  -p H  o  •  o  0  a  o  •  ^ • O D O t M A H W ^ ^ N A H O ON ON ONCO NO A  H I A I A C O CM CM H CO N}- i r \ c o ^ ^ j - c O LT\ LT\ ON C - C O CO C - O N O N  CM CM C O K \ O I A IT—NO K \ H O N C O C— A I A CM — 1 H I I I i i I I i  t A N A CM H r — I C M C M C M C M C M C M H H C M H C M C M C M C M C M CM  ••NA.tT-ON CM IT— CM *sf- O N I A N O N O N O t r — C O O CM O N C O O H O J ^ J - A N O r j H O H t — I H H H H H i ' I I H I 1 I I I I I I I  xf tA  ^JlAO^CMOtAONONOCMHCMNOCOCOCMCMCO^j-A CM H t A t A N O CM H A t A tr- ONCO O J v O C - p O \ NA C— ONCO ^ N t K A C M I A ^ | - r A ^ t A t A CM CM NA t A I A I A I A t A I A I A * • • * « • » « • « * • • > • • • » « » *  rAtr-OO ON^d• • • CM CM CM  O • ON H ON  I A ' A tr-co O > A I A C M -^j- H C O ^ H -  CMtr-OtAOON-<H-0 c o c o N O O N c—co O N O N • • • • » • » • • CM CM CM CM CU W  H N - ' H - K A O N C — K A N O H C— E — O N O N O C — O C — H O N C O CM H O H ^ - t r - H O A C M tr—co O N O N C — C — C M C O -*H- tr-co c o N O N ON O A ^ I A N O I A N O LT\> A L T \ A A tA A tA < A A  O E - O O O N O N O CO N O O ootr-^-iAoc—oco • * * • * • • • • t A IA IA CM CM CM IA C M I A CM  t A *sh I A N O c-<sf ^ J - N O N O c o c o N O N O I A A C - - = H - O N o t r - c — i A - = t tr— C M I A x h ^ O N O N i A C M O N C O O ONCM H H H K A O ^ C O O C O H H H H H H H H H H H  • • • •  • • • • • • • • • •«  O H C M C M O O ^ i - C M - ^ - r A A l A C M c O N O H C O (ACM N A A CO C M ^ C M t r - O O C M A C - H t A O K A ^ N O l A H H C O H  •• • *l • • • •  C— CM MD CO NO H C O ON A O CM H I A tr- ON CM CO <sh CO H H C - O N H O ON ON O H I A A N O C I A I A I—1 O CO C— t A ^ I A H H . H H H H ' r H H H i — l r - 1 H I I I I I I I I I I I I I I I I I I I I I  tANA'^h " H - O O N N O CM ON C - A O N N O N O H C- A CM O A C Q • • • • N A IA t A IA t A t A IA  H C O O H C O C M C M O O N N A N A N O IA C— H N O X H - N O H t r - C M H C O C-CM"^CM N O CO O N O rACO ^ - O i A O ^ r l • • .• • • • • • • « • • • *sh A - v h -sh IA IA t A CM CM H H  c— c o o N ' ^ - t A O c o c o t r - c — I A N O CM CM O N I A N O I A tr•sj- C—NO C — t r - O N t A - s h O N C M NA O N O O N O C M I A N O O N O N O » NO • « • • • • « • • • * • • • « • * • * CO • O A N O CM C - O N CM O N O O O N N O lA-vh CO A C — C M H NO CM O ON GO CO O N O CM r A A ^ O t A CM O O x C - N O -xj- t A C M CO H H H H r - i H H r - l H I I I I I I I i t I I I I I I I I I I I I  NO ON NO * CM  Lf  -  ^  K\K\OJ W H  H  NO *H.- C-CO A C M H CO C M O N O NO NO H H I A N O N O <sf O O ^NO-CMNO L r \ l r - O M 3 u r \ H i - l C O N O C O C O H H NACO H co N ACM a x c o CMN O O N K \ V O c o r r \ 0 - ^ H C - - N A t r - H o o CM ( M f C M A O J CJ l A M M A ^  •  include: Specific gravity T e n s i l e strength l l b s . / s q . in.) % elongation p o s s i b l e % set Durometer hardness 300% s t r e t c h modulus ( l b s . / s q . in.)  .98 3365 760 14 40 198  For use i n the apparatus two s t r i p s were used each approximately 15 cm. by 3 cm. by 0.2  cm.  The same s t r i p s  were used throughout* Experimental r e s u l t s The,readings and r e s u l t s obtained are tabulated i n t a b l e s I, I I and I I I . For convenient comparison the r e s u l t s obtained are shown g r a p h i c a l l y i n P l a t e s XIII, XIY and XY,  as f o l l o w s : Normal Length  Table I  and P l a t e X I I I  50% s t r e t c h  Table I I  and P l a t e XIY  100% s t r e t c h  Table I I I  and P l a t e XY  Certain o f the more evident l i n e s have been drawn i n .  Those dotted are t e n t a t i v e l i n e s .  Some drops from  -the top curve to the bottom one have been shown to i n d i c a t e the temperatures at which they occurred. The average value of the thermal c o n d u c t i v i t y f o r t h i s sample f o r a l l degrees o f s t r e t c h appears to be between 5,5 x 10~ around 0°C.  4  and 3.8 x 10~  4  Cal./cm.sec.deg. C. i n the range  T h i s i s i n quite good agreement with the r e s u l t s  obtained f o r a d i f f e r e n t type o f rubber by Schallamaoh (8) who gets 3.1 x 10"  4  and Frumkin and Dubinker (7) with 4.9 x  4  10~ .  A c t u a l l y I t Is d i f f i c u l t  to compare these values as conduc-  t i v i t y depends on composition and d i f f e r e n t rubbers vary g r e a t l y i n t h i s respect.  An important point to note, a l s o , i s  that h i g h p o r o s i t y tends to decrease c o n d u c t i v i t y by causing a smaller conducting area. There i s d e f i n i t e l y a decrease i n c o n d u c t i v i t y with decrease o f temperature.  For a l l degrees of s t r e t c h  there are no l a r g e changes i n the slope of the top l i n e of the graph.  The decrease  i s not n e c e s s a r i l y a l i n e a r change, as  shown by P l a t e s XIV and  XV.  For normal l e n g t h and 50% s t r e t c h there i s no i n d i c a t i o n of two o r more p o s s i b l e c o n d u c t i v i t i e s above 15°C» T h i s i s i n agreement with temperature  volume r e l a t i o n s h i p s  111) and s p e c i f i c heat curves (12) obtained by Bekkedahl and associates.  s t r e t c h there i s d e f i n i t e l y  an  i n d i c a t i o n that two values o f K can e x i s t f o r temperatures  as  high as  However, f o r 100%  30 °C.  Guth (14) r e p o r t s that i n some cases where  two p o s s i b l e s t a t e s occur at lower temperatures comes up to room temperatures  on  the e f f e c t  stretching.  Below 10°C., i n a l l cases, there are apparently two thermal c o n d u c t i v i t i e s p o s s i b l e .  There seems t o be no  consistent p a t t e r n to decide which state the rubber w i l l be i n since consecutive readings o f t e n gave p o i n t s on d i f f e r e n t curves.  In f a c t , on s e v e r a l occasions the change a c t u a l l y  occurred while readings were being taken.  T h i s would i n d i c a t e  that there i s not a very great energy d i f f e r e n c e between the two  states.  The d i f f e r e n c e of c o n d u c t i v i t y between the  two  4  s t a t e s from 10°C. to -40° C. i s around 0.5 x 10" . teresting  to note that Schallamach  It i s in-  (8) found no e f f e c t o f t h i s  sort with North B r i t i s h Cycle Tubing which the company c a l l s "pure e l e c t r o d e p o s i t e d l a t e x . "  A p o s s i b l e explanation f o r  t h i s could be that e l e c t r o d e p o s i t e d rubber i s purer and has more consistent p a r t i c l e s i z e .  However, Bekkedahl (11} found  that h i s temperature volume r e l a t i o n s two p o s s i b l e s t a t e s below  definitely  indicated  11°C. f o r unstretched rubber, and  Bekkedahl and Matheson (12) corroborated t h i s when they  found  a d e f i n i t e peak i n the s p e c i f i c heat curve at that p o i n t . (11*0.1 In the r e g i o n below -70 °C. there are a l s o two p o s s i b l e curves; but the lower of the two i s not i d e n t i c a l with the corresponding one i n the upper r e g i o n .  F o r zero 4  s t r e t c h the s e p a r a t i o n appears to be around 1.5 x 1 0 ~ and fairly  constant.  With i n c r e a s i n g s t r e t c h  the separation de-  creases at the upper end o f the curves which are no longer parallel.  Here again there i s apparently no set p a t t e r n f o r  change from one curve to the other as the p o i n t s on the lower curve represent i s o l a t e d  readings i n many cases.  However,  there does seem to be an increased tendency to drop o f f i n the r e g i o n between -120°C. and -160 °G.  The temperature at which  the drop o f f occurrs being lower i f the c o o l i n g i s dane quickly.  The range i n which t h i s tendency seems greatest i s i n d i -  cated by dotted l i n e s on the graphs. two  The f a c t that there are  s t a t e s p o s s i b l e i s amply corroborated by Schallamaoh (8)  and Bekkedahl (11) hut the r e v e r s i b i l i t y of the change from low to high c o n d u c t i v i t y observed by us i s i n marked contrast to Schallamach's work, as i s the f a c t that p o i n t s on the top curve occur as low as -165° C.  Schallamach reported that i n  the neighbourhood o f -120 °C. the c o n d u c t i v i t y changed abruptly to the lower value,  and t h e r e a f t e r a l l p o i n t s were on the  lower curve which r e j o i n e d the upper one i n the region -80° C« to -60° C. with no d i s c o n t i n u i t y . the unstretched  I t w i l l be noticed that f o r  state t h i s form occurred,  p o i n t s both f o r i n c r e a s i n g or decreasing the region -70"C. to -35 °C.  but i n i s o l a t e d temperatures, and i n  Both Bekkedahl (11) and Guth (14)  report that t h i s change can be brought to higher by v a r y i n g the composition. readings  temperatures  The same e f f e c t i s i n d i c a t e d i n  f o r 50% s t r e t c h , but no p o i n t s were obtained  f o r that  part of the curve f o r 100% s t r e t c h . I t w i l l be seen that f o r a l l degrees of s t r e t c h p o i n t s occurred curves.  about h a l f way between the upper and lower  T h i s i s a t t r i b u t e d to the f a c t that there were two  pieces of rubber used simultaneously one  i n each measurement, and  piece could be at the lower c o n d u c t i v i t y while the other  was at the higher one,  and v i c e - v e r s a .  In view of the above r e s u l t s and from a t i o n o f the graphs the f o l l o w i n g observations  consider-  on the e f f e c t  of i n c r e a s i n g s t r e t c h may be made,, (a)  The slope o f the room temperature p o r t i o n o f the curve increases and c o n d u c t i v i t y tends t o increase  slightly. (b)  At very low temperatures the slope The  decreases.  lower l i n e appears to extend up to room tempera-  , , tures, remaining  about the same distance from the  upper l i n e . (c)  The  slope of the lower curve at low temperatures  increases, and the separation of the two becomes l e s s . (d)  The  curves  ,  top c\irve has a changing slope throughout i t s  length* As yet no mention has been made of the anomalous c o n d i t i o n found i n the -80 *C. to -40 °C. region and p o s s i b l y below, as shown by p o i n t s o c c u r r i n g above the top l i n e of the graph i n that region.  To avoid confusion no l i n e s have been  drawn through these p o i n t s , but i t w i l l be observed i n the zero stretchgraph that a s t r a i g h t l i n e could be drawn from -160"C. to -30°C. c u t t i n g at l e a s t f i v e points w e l l above the main curve.  T h i s , i n i t s e l f , would hardly be conclusive, but  at 50% s t r e t c h there i s a d e f i n i t e high spot i n the graph i n the -80 °C» to -40 °C. region, and f o r 100%  s t r e t c h there i s a  very d e f i n i t e s e r i e s o f p o i n t s c l o s e l y grouped and some d i s tance from the main l i n e .  I t should be pointed out that  p o i n t s were not a l l obtained or l e s s random readings  these  i n one run, but occurred as more  i n the same manner as the low  conduc-  t i v i t y points. The  o b t a i n i n g of complete curves was  complicated  by s e v e r a l f a c t o r s which cannot be shown g r a p h i c a l l y , but  which caused considerable inconvenience. (a) Time l a g .  There was d e f i n i t e evidence that  the value obtained f o r K i n c e r t a i n cases depended p a r t l y on the previous h i s t o r y of the run*  I t was n o t i c e d on s e v e r a l  occasions that the drop from higher t o lower ourve that usual l y occurs around -140°'C. d i d not occur u n t i l as low as -165° G, i f the change from room temperature to that temperature had been r a p i d .  Conclusive proof that time i s a f a c t o r was ob-  t a i n e d on one occasion when a steady state was obtained and i n the space of approximately 10 minutes i t was necessary to increase the current supplied gradually from „57 to .62 amperes i n order to maintain the same temperature d i f f e r e n c e . This represents  a power change of almost 20% or a change o f  conductivity of  almost 0.5 x 10~ .  cause d i f f i c u l t y  c h i e f l y i n the region from -170° C. to -110°C.  4  The time l a g appeared to  and at temperatures above t h i s region was l e s s n o t i c e a b l e . T h i s l a g d i d not always occur; u s u a l l y the apparatus could be h e l d steady f o r some time.  Guth (14) has reported that work  on other phases of rubber research has been hampered considerably by t h i s time l a g e f f e c t , and has made i t d i f f i c u l t to evaluate r e s u l t s .  Bekkedahl (11) also r e p o r t s a s i m i l a r con-  d i t i o n i n the r e g i o n -55°C. to -15°C. where a tendency to pass from one curve to another extended over a considerable p e r i o d of time. (b) The random i nature of the occurrence of low c o n d u c t i v i t y readings.  At no time was i t p o s s i b l e to f o r e t e l l  when low c o n d u c t i v i t y readings would occur*  Consequently,  many more readings than necessary were obtained f o r the upper curve i n order to get enough p o i n t s on the lower one. of t h i s f a c t i t was not p o s s i b l e to f i l l completely i n  Because  i n the bottom curve  some regions. (c) Both pieces of rubber not i n the same s t a t e .  As stated before there was one piece of rubber was  some d i f f i c u l t y encountered when  i n a d i f f e r e n t state from the other.  In many cases the values obtained gave a good idea of the s e p a r a t i o n of the two  curves, but as f a r as exact  t i o n of one of them were of l i t t l e  or no use.  determina-  As the number  of times the rubber had been s t r e t c h e d and cooled increased t h i s tendency  to change at- d i f f e r e n t times became greater, i n -  d i c a t i n g that the u s e f u l l i f e o f p a i r e d samples t i v i t y work-is  f o r conduc-  limited.  (d) Varying c o n d u c t i v i t y w i t h i n one p i e c e .  The  commercial methods of making rubber do not, as a r u l e , produce a m a t e r i a l that i s completely homogeneous.  Moreover, the  measurements must be taken over a considerable area of any piece. red  Consequently*  one  i t i s p o s s i b l e that when'a change occur-  i t d i d not always extend over the e n t i r e area covered by  the c e n t r a l h e a t i n g block.  T h i s would cause a poor reading.  I t w i l l be n o t i c e d that c e r t a i n readings do not f i t i n with the general p a t t e r n but might be explained i n t h i s manner.  It  would r e q u i r e an apparatus that employed only one piece of rubber but measured s e v e r a l adjacent  p a r t s simultaneously to  determine whether t h i s a c t u a l l y  occurred.  Interpretation From these r e s u l t s i t i s p o s s i b l e to make some deductions, subject, l i n e s of research,  of course, to v e r i f i c a t i o n by other  as to changes of state that may occur i n  rubber at the temperatures (a)  considered.  The s t a t e e x i s t i n g o r d i n a r i l y at room temperatures (amorphous) can e x i s t as f a r down as -170° 0.  •(b)  Below+10°C, and above -60° 0. a second state can exist.  The upper l i m i t of temperature f o r t h i s  state appears to r i s e with increased  s t r e t c h , but  t h i s state does not appear to e x i s t below -60 C* ( o)  Below -60°^ C. there are s t i l l two states p o s s i b l e , but one i s o f much lower  (d)  conductivity,  In the region -80°0. to -40"c. a continuous,  rever-  s i b l e t r a n s i t i o n i s p o s s i b l e from the state o f lower c o n d u c t i v i t y to that of higher (e)  conductivity.  I t i s p o s s i b l e that a t h i r d state may e x i s t i n the -80° C, t o -40° C. region with a higher  conductivity.  However, the higher p o i n t s might be caused by a heat of f u s i o n or c r y s t a l l i z a t i o n i n that  region,  although t h i s seems u n l i k e l y , as no ordinary  heat  of f u s i o n would be s u f f i e i e n t to maintain the r e duced temperature i n t e r v a l f o r the period  required  f o r two complete sets o f readings. (f)  Because of t h e frequency of t r a n s i t i o n , and i t s r e -  versibility,  i t appears that the amount of energy involved i n  t r a n s i t i o n s between any  IV".  two  states must be f a i r l y small.  CONCLUSION It  i s apparent from the above that a great  deal  remains to be done i n the f i e l d of heat c o n d u c t i v i t y of e l a s tomers.  The  work described  herein i s but the beginning of an  extensive  program which w i l l be  c a r r i e d out with samples of  different  compositions which have been k i n d l y provided by  Department of P h y s i c s of the U n i v e r s i t y of Notre Dame»  the  REFERENCES (1) (2) (3) (4) ,.. . (5) (6) (7) > (8) (9) . .  (10) (11) (12) (15) (14) (15) (16)  Guth,E. and Mark, H, Monatsch f . Chem. 65, 93, 1934 Guth,E., Kautchuk 13, 201. 1937 James,H. M. and Guth,E» Phys. Rev. 59, 111. 1941 Anthony,R. L., Gaston, R.H. and Guth, E. J . Phys. Ghem. 46, No. 7. 1942 Frumkin, L. and Dubinker, Yu. Rubber Chem. Tech. 13, 361, 1940 Schallamaoh, A. Nature 145, 67, 1940 Frumkin, L. and Dubinker, Yu. Rubber Chem. Tech. 11 559, 1938 Schallamach, ,A. . . Proc. Phys. Soc. 53, 214, 1941 Temperature, I t s Measurement and Control i n Science Industry* Symposium published by the American Ins of Physics. (a) R e p r o d u c i b i l i t y of the Ice P o i n t . Thomas, J . L. (b) C a l i b r a t i o n o f Thermocouples at Low Temperatures. R. B. S c o t t . Handbook o f Chemistry and P h y s i c s . Chemical Rubber P u b l i s h i n g Co. Bekkedahl, N. J o u r n a l of Research 15, 411. 1934 Bekkedahl, N. and Matheson* J„ J o u r n a l of Research 15, 503. 1935 Woodj E. A., Bekkedahl, N. and Roth, F. L. J o u r n a l of Research 29, 591; 1942 Guth, E . L e t t e r to Dr; H. D. Smith Lindsay, R. B. An I n t r o d u c t i o n to P h y s i c a l Statistics. (Wiley), 1941). Barron, II. Modern Synthetic Rubbers. ( Chapman and H a l l , 1945) 8  

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