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The thermal conductivity of butyl rubber at low temperatures Thompson, William Bell 1947

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(?*) fir i ^  TV  THE THERMAL CONDUCTIVITY OF BUTYL RUBBER AT LOW TEMPERATURES.  by  WILLIAM BELL THOMPSON  A thesis submitted i n p a r t i a l f u l f i l m e n t of the requirements f o r the degree of Master of Arts i n the Department of Physics.  The University of B r i t i s h Columbia September  - 194-7  A C K N O W L E D G M E N T  The author i s p l e a s e d t o express h i s g r a t i t u d e to Dr. Otto B l u h , under whose a b l e  supervision  t h i s work was completed. He a l s o wishes t o acknowledge  the contributions  o f the Research D i v i s i o n o f the Polymer Corpor-r a t i o n who p r o v i d e d the samples, o f Messrs. F. Lang and D. S. C a r t e r who a s s i s t e d i n b u i l d i n g the a p p a r a t u s , and o f Mr. R.S. C o d r i n g t o n who d i d the photography f o r t h i s  thesis.  The r e s e a r c h was c a r r i e d out w i t h the a i d o f a grant from the A s s o c i a t e Committee on S y n t h e t i c Rubber Research o f the N a t i o n a l Research C o u n c i l of Canada.  I N D E X  Page I.  Introduction: D e f i n i t i o n o f thermal c o n d u c t i v i t y and fundamental equations. Thermal c o n d u c t i v i t y o f a n i s o t r o p i c media. Thermal c o n d u c t i v i t y as a f u n c t i o n o f temperature. Methods o f measuring thermal c o n d u c t i v i t y . P r e v i o u s measurement o f the thermal c o n d u c t i v i t y o f rubber.  II.  14-  15 17 18 18 19  Experimental Procedure: Thermocouple c a l i b r a t i o n . Method o f t a k i n g r e a d i n g s . Method o f a n a l y s i n g data. Guard b l o c k e r e c t i o n . Measurement o f power. Measurement o f t h i c k n e s s . E v a l u a t i o n o f Apparatus. i) E f f e c t o f temperature v a r i a t i o n over the cold plate. il) E f f e c t o f v a r i a t i o n o f temperature w i t h time.  IV.  3 8  Apparatus: C o n d u c t i v i t y measuring u n i t . ' The h e a t i n g c i r c u i t s . The c r y o s t a t and c o o l i n g system. The temperature measuring c i r c u i t s . The c o n t r o l c i r c u i t s .  III.  1 3  22 23 25 26 27 29 30 31  Results: The sample. Readings taken. Probable e r r o r . Discussion of r e s u l t s .  »  35 36 36 38  P L A T E S Pictures  F a c i n g Page  A f r o n t view of the apparatus.  14.  III.  A r e a r view o f the apparatus.  14.  III.  A close-up o f the measuring u n i t .  15  I.  Diagrams I¥. V. VI. VII.  The measuring u n i t .  16  The h e a t e r c o n t r o l c i r c u i t .  17  The Thermocouple c i r c u i t .  18  The A. C. automatic  control.  19  automatic, c o n t r o l .  20  V I I I . The D . C . IX.  The  c o n t r o l c i r c u i t potentiometer.  21.  Graphs - X. XI.. Xli.  K versus T f o r GR  - I w i t h 2% Sulphur Unstretched.  K. versus T f o r GR - I w i t h 2% Sulphur a t 100$ S t r e t c h . K versus T f o r GR  - I w i t h 10% Sulphur Unstretched.  36 36 36  ABSTRACT  The thermal c o n d u c t i v i t y of GR-I  gum s t o c k was  measured w i t h an improved a p p a r a t u s . The thermal c o n d u c t i v i t y o f b u t y l decreases w i t h temperature showing a double v a l u e a t temperatures between 0°C and -80°C.  Stoek c o n t a i n i n g 10% s u l p h u r showed no  h y s t e r e s i s c h a r a c t e r , and the c o n d u c t i v i t y changed only s l i g h t l y over the temperature range. stock a h y s t e r e s i s l o o p was  found.  For the s t r e t c h e d  I*  INTRODUCTION T h i s work has been done as p a r t of a  program o f rubber r e s e a r c h now  being  carried  general  out i n the  P h y s i c s Department of the U n i v e r s i t y o f B r i t i s h Columbia, w i t h the a i d o f a grant from the A s s o c i a t e Committee  on  S y n t h e t i c Rubber Research of. the N a t i o n a l Research C o u n c i l o f Canada. Definition  o f Thermal C o n d u c t i v i t y and Fundamental A simple and  satisfactory  c o n d u c t i v i t y o f an i s o t r o p i c experiment:  One  d e f i n i t i o n o f the thermal  s o l i d i s based on the f o l l o w i n g  s i d e o f a t h i n s l a b o f m a t e r i a l of  d i s h e l d a t a temperature temperature  Equation;  and  the other  thickness  s i d e a t a lower  u n t i l the temperatures o f a l l p a r t s o f the  reach a constant  value.  When t h i s s t a t e has  been  slab  reached  the heat near the centre of the w a l l w i l l f l o w d i r e c t l y from one  s i d e to the other, so t h a t a l l the heat e n t e r i n g through a  s m a l l area on one other.  s i d e w i l l l e a v e through an equal area on  Then i t . w i l l be found t h a t the amount of heat Q  i n a time t through a s m a l l area A near the i s given  the  passing  centre of the  slab  by: « = K A f  r  T  2  . t  (1)  _ _ The  constant & i n t h i s e x p r e s s i o n  i s d e f i n e d as the  thermal  c o n d u c t i v i t y o f the m a t e r i a l . For the mathematical theory o f heat  conduction  t h i s d e f i n i t i o n i s g e n e r a l i z e d i n the f o l l o w i n g way.  It is  2 assumed that the e x i s t e n c e o f a temperature g r a d i e n t i n an i s o t r o p i c medium causes a f l o w o f heat i n the d i r e c t i o n o f t h a t temperature g r a d i e n t and p r o p o r t i o n a l t o i t .  The temperature,  then becomes a s c a l e r space f u n c t i o n , and the v e c t o r f l o w o f heat per u n i t a r e a a c r o s s an i s o t h e r m a l i s g i v e n by: dQ~° - K V T dt -  (2)  I f the temperature changes w i t h time i t i s p o s s i b l e by w e l l known means (1) t o s e t up the c o n t i n u i t y equation:  ^7 . KV~T = C 9T at  / q  (3)  Here C i s the volume s p e c i f i c heat, i . e . the product o f d e n s i t y and s p e c i f i c heat, and q r e p r e s e n t s the net source o f heat per u n i t volume.  I t i s standard p r a c t i c e t o c o n s i d e r q as every-  where zero, and K as independent o f the temperature.  . The  equation then reduces t o : ky  2  T -  2>t  , where k s K and i s c a l l e d the C  thermometric c o n d u c t i v i t y o r thermal d i f f u s i v i t y .  (4.)  T h i s i s the  fundamental d i f f e r e n t i a l e q u a t i o n o f the mathematical t h e o r y o f the c o n d u c t i o n o f heat i n s o l i d s .  I f t h e temperature i s  independent o f time t h i s becomes 2  \7 T - 0  (5)  which i s L a p l a c e ' s e q u a t i o n , and has known s o l u t i o n s f o r many boundary c o n d i t i o n s .  ,  3 Thermal C o n d u c t i v i t y o f a n i s o t r o p i c media. Most mathematical work on heat conduction has been done f o r i s o t r o p i c s o l i d s .  However there i s a wide c l a s s o f  substances whose p h y s i c a l p r o p e r t i e s depend upon d i r e c t i o n . I n these substances the flow o f heat need not be p a r a l l e l to the temperature  g r a d i e n t and e q u a t i o n (2) need not h o l d .  such media the s i m p l e s t assumption  In  i s t h a t the component o f the  heat c u r r e n t i n any d i r e c t i o n depends l i n e a r l y upon the t h r e e components o f the temperature g r a d i e n t , i . e .  (6) By a proper c h o i c e of c o o r d i n a t e axes these equations may  be  reduced to (7) and the number of constants needed to c h a r a c t e r i z e the f l o w o f heat reduced from nine t o t h r e e ( 2 ) .  T h i s set o f axes, the  p r i n c i p a l axes o f thermal c o n d u c t i v i t y , u s u a l l y c o i n c i d e s with the o p t i c a l axes, and the p r i n c i p a l axes o f e l a s t i c i t y . Thermal  c o n d u c t i v i t y as a f u n c t i o n of  temperature.  For many substances, and i n p a r t i c u l a r f o r rubber, the thermal c o n d u c t i v i t y depends on the temperature, the mathematical assumption  and  since  t h e o r y of conduction has been based on the  that the c o n d u c t i v i t y i s constant, i t i s of i n t e r e s t  to see what e f f e c t such temperature  v a r i a t i o n has on the  measurement o f thermal c o n d u c t i v i t y .  A first  approximation  to the temperature dependence o f the c o n d u c t i v i t y i s g i v e n by K, (I MT)  K(T) =  (8)  The exact e f f e c t o f t h i s on the s l a b experiment used to d e f i n e thermal c o n d u c t i v i t y i s e a s i l y seen. thickness  d  Suppose t h a t a s l a b o f  has one side kept a t zero and the o t h e r s i d e a t  a temperature T  0  .  When the steady s t a t e has been reached  equation (3) y i e l d s  d_  K(T) . /Q_T  o  =  (9)  Since T depends o n l y on x a f i r s t i n t e g r a l i s immediately obtained. K(T) and  dT dx  c  =  from the d e f i n i t i o n of K, the constant c must equal the  heat c u r r e n t  across a u n i t area i n the s l a b . Using K  (8) we  obtain  ( 1 / aT) dT  =  dx  d£ dt  Separate the v a r i a b l e s and i n t e g r a t e .  ^  or  (ID but  K  (1 / a T«)  =  5 where K r e p r e s e n t s the average thermal c o n d u c t i v i t y o f the sample.  Thus the d e f i n i n g experiment remains The e f f e c t o f temperature dependent  valid. c o n d u c t i v i t y on  the g e n e r a l e q u a t i o n f o r heat f l o w must now be i n v e s t i g a t e d . S u b s t i t u t i o n o f -(B) i n t o (3) g i v e s  V-K (1 /  aT)  VT  s  C 3T  (12)  ^t which becomes, f o r the one-dimensional case K.7) T  "37"  /  a/lTV  -  2  C3T'  /  (13)  at  "  {-dx)  . "  I n many e x p e r i m e n t a l d e t e r m i n a t i o n s o f K a q u a n t i t y measured i s the temperature g r a d i e n t ^ T , which must t h e r e f o r e be f a i r l y large.  To n e g l e c t t h i s second term seems h a r d l y  j u s t i f i e d u n l e s s a i s extremely s m a l l . overcome by the f o l l o w i n g argument.  T h i s d i f f i c u l t y may be  F o r many substances, and  a g a i n f o r rubber, the volume s p e c i f i c heat as w e l l as the thermal c o n d u c t i v i t y i s temperature dependent, it  too shows a l i n e a r dependence.  and we may assume t h a t  Then e q u a t i o n (3) becomes  l o r the one d i m e n s i o n a l case 9. . K . ( l / aT)  T)x  2  T  s  - 0 . ( 1 / bT) '3T,  Dx  (u)  at  = - C . ( l / aT)  Tt / C (a - b) T 9T Dt  The l a s t term i n t h i s e x p r e s s i o n may be kqfc s m a l l -^y keeping the time v a r i a t i o n o f temperatures and the temperature s m a l l , and t o g e t an approximate  range  s o l u t i o n , may be o m i t t e d .  6 T h i s i s e q u i v a l e n t t o assuming a constant thermometric conductivity.  k  We may then w r i t e :  H  (1 / aT) 3 T  3x  2x  - (1 / a T ) ^ T  It  (15)  Make the s u b s t i t u t i o n  ,2  U = (1 / aT)' Then  2JJ  2a. (1 / aT) 21 3x  =  -gx  ?U  Tt  -  2a  (1 / aT) -3T  7t  _  and (15) may be w r i t t e n as  k l_5u -3 x 2  /QU  Tt  (16)  Compare t h i s w i t h the o r i g i n a l one-dimensional heat f l o w equation:  k 2f£« 9 x  2  s  / 21 • ?t  (17)  The f o r m a l i d e n t i t y o f these two equations permits c e r t a i n F i r s t , s i n c e a change i n U i m p l i e s a change i n T,  deductions.  the equations show that the r a t e o f t r a n s m i s s i o n o f a slow change i n temperature i s independent o f the temperature v a r i a t i o n o f K.  Second, i t i s p o s s i b l e t o show t h a t t h e s o l u t i o n s  to problems i n v o l v i n g slow changes i n temperature remain unchanged  by v a r i a t i o n o f K w i t h temperatures.  g e n e r a l s o l u t i o n s o f (16) and (17). U = f (c xTt) where c x , t  C o n s i d e r the  We may w r i t e  (18)  i n d i c a t e s some combination o f the v a r i a b l e s x and  ~7 t and f some a r b i t r a r y f u n c t i o n .  The s o l u t i o n f o r (17) i s  similarly T =  f ( c x~t)  (19)  I f we wish a s o l u t i o n t o f i t a c e r t a i n set o f boundary c o n d i t i o n s a r e s t r i c t i o n on the form o f f i s i m p l i e d . Suppose t h a t we are g i v e n a boundary c o n d i t i o n i n terms of T, i . e . T (o,t)  *  Q(o,t)  (20)  To solve (16) t h i s must f i r s t be w r i t t e n i n terms o f U, i . e . U (T (o,t) ) = P (o,t)  (21)  T h i s boundary c o n d i t i o n on U w i l l s e l e c t a s o l u t i o n  U *  f (cxTt)  (22)  and as U i s a f u n c t i o n o f T, we may  T (U) - g  determine T as  (cxTt)  (23)  but t h i s i s a f u n c t i o n T (c x,t) determined from (16) and s a t i s f y i n g c o n d i t i o n (20).  A t t h e same time i t i s o f the fonn  g (c xTt) and s a t i s f i e s (17).  Thus the s o l u t i o n of (16) w r i t t e n i n  terms o f T, which s a t i s f i e s the boundary  condition  T (o,t) = Q i s . at the same time the s o l u t i o n of (17) s a t i s f y i n g the same boundary c o n d i t i o n .  T h i s shows t h a t , t o the approximation  considered i n (15) temperature v a r i a t i o n o f the thermal c o n d u c t i v i t y produces no change i n the s o l u t i o n t o heat f l o w problems. (1) (1) T h i s argument i s weakened by the f a c t that (16) and  (17) a r e second order  d i f f e r e n t i a l e q u a t i o n s , hence the most g e n e r a l but two  s o l u t i o n s i n v o l v e not  arbitrary functions.  one  This  r e s t r i c t s the d i s c u s s i o n to those boundary c o n d i t i o n s which i n v o l v e o n l y o f the f u n c t i o n s Methods of Measuring Thermal We  s h a l l now  i n the s o l u t i o n .  Conductivity.  c o n s i d e r a few  thermal c o n d u c t i v i t y which may These methods may  one  methods o f measuring  be a p p l i c a b l e t o rubber.  be d i v i d e d i n t o t h r e e  c l a s s e s , depending  upon the nature of the mathematical problem posed by  each.  Type 1 Temperature c o n s t a n t , no r a d i a t i o n a t  surface.  Mathematically t h i s c a l l s f o r a s o l u t i o n of L a p l a c e ' s e q u a t i o n s u b j e c t to constant boundary conditions. between two one  U s u a l l y the temperature d i f f e r e n c e s u r f a c e s and  the f l o w o f heat  o f them are measured.  T h i s , w i t h the  constants of the apparatus and  shape and  The  geometrical  sample permit c a l c u -  l a t i o n o f the temperature g r a d i e n t , conductiyity.  across  hence the  thermal  methods d i f f e r c h i e f l y i n the  d i s p o s i t i o n o f the  sample,  a. W a l l o r s l a b method. A measured power passes through a o f m a t e r i a l from a hot  slab  to a c o l d p l a t e , whose  temperatures a r e measured, d i r e c t f l o w being a s s u r e d by a guard r i n g .  The  thermal c o n d u c t i v i t y i s c a l c u l a t e d from K = P  d  A where P  -T  T l  2  power i n p u t to measuring  =  A ~ a r e a o f measuring  plate  plate  d » sample t h i c k n e s s T^-T  = temperature d i f f e r e n c e s tween f a c e s .  be-  C y l i n d r i c a l methods. The sample i s prepared i n the form o f a c y l i n d e r , power being s u p p l i e d from the c e n t r e .  I f the sample i s l o n g  enough i n comparison t o i t s r a d i u s the heat l o s s e s from the ends may  be n e g l i g -  i b l e and a guard r i n g unnecessary. T h i s i s the method used by Bridgman (3) w i t h t h i n f i l m s of l i q u i d s . ductivity i s calculated K =• P 4 where 1 r  if  r ( 2y  ^  r  con-  (4)  l )  1 (T-j- T )  l e n g t h of  s  , r 1  In  from  The  2  sample.  » o u t e r and i n n e r r a d i i respectively.  S p h e r i c a l s h e l l methods. The source o f heat i s l o c a t e d i n tiie c e n t r e o f a s p h e r i c a l s h e l l of the  10  sample, thus making guarding p r e c a u t i o n s unnecessary.  When the  temperature i s constant over t h e s u r f a c e s the c o n d u c t i v i t y may  he  c a l c u l a t e d from:  K =  Temperature  P  r-, r„  c o n s t a n t , r a d i a t i o n from t h e s u r f a c e .  These methods assume Newton's law o f c o o l i n g ; the l o s s o f heat by " r a d i a t i n " from a body t o i t s environment i s p r o p o r t i o n a l t o the d i f f e r e n c e between t h e i r temperatures. the boundary  I f the environment i s a t z e r o ,  c o n d i t i o n s t o the mathematical probem  become 9T(s) .  f  h T(s)  a o  s i n c e the heat f l o w a c r o s s the boundary s u r f a c e i s p r o p o r t i o n a l t o both T and lT_  dx a . The method o f Forbes (5) One  end o f a long bar o f the sample  i s h e a t e d , and a l l t h e heat l o s t  by  r a d i a t i o n so t h a t the f a r end o f the bar i s a t the temperature o f the surroundings, which we take to be zero.  The temperature i s measured  at a number of p o i n t s and i s p l o t t e d  il of x, the d i s t a n c e along the b a r . t h i s graph 7)T any  p o i n t x.  may  be determined  From at  S i n c e a l l the heat i s  l o s t by r a d i a t i o n the power p a s s i n g x i s g i v e n by oO  d&s dt  =  r  a  T(x)  dx  where a i s the c o o l i n g constant of the bar, and may  be determined  by measur-  ing the r a t e at which the bar c o o l s . The  i n t e g r a l may  be evaluated from the  graph and the thermal c o n d u c t i v i t y c a l c u l a t e d d i r e c t l y from the d e f i n i n g equation dtj[ dt  =  KA  2_T "2 x  /  The method of Lees  (5)  A s m a l l sheet o f the sample i s wiched between two  sand-  p l a t e s , one c o n t a i n i n g  a h e a t e r , and the apparatus  i s varnished  so t h a t a l l p a r t s w i l l have the same emissivity.  I t i s then suspended  i n an enclosure and allowed to c o o l , so .that the  emissivity  12 may  be determined.  A measured q u a n t i t y  o f power i s then s u p p l i e d to the h e a t e r u n t i l t h e r m a l e q u i l i b r i u m has been established.  Temperatures  o f the p l a t e s  are then measured and the l o s s o f heat from each c a l c u l a t e d from the known emissivity.  T h i s determines the f l o w  o f heat a c r o s s the sample and K i s c a l c u l a t e d as i n the s l a b method. Type 3  Temperature  v a r y i n g w i t h time. T h i s group may  be s u b - d i v i d e d i n t o those  experiments i n which the sample i s a l l o w e d t o c o o l s u b j e c t t o constant boundary  c o n d i t i o n s , and those  i n which the steady s t a t e temperature i s measured mrlth v a r y i n g boundary  conditions.  a. The c o o l i n g sphere method. A sphere o f r a d i u s at a u n i f o r m temperature T  a 0  initially i s allowed  t o c o o l i n a medium a t constant temperature. •  I t may  be shown (6) that the  temperature a t the c e n t r e a t a time  t  i s approximately T s A j a ^ exp(- ka-^t ) where A-^  s  2T a  0  l  s i n a^a - a i a cos a i a a^a - s i n a^a cos a^a  13 anda-j_ i s the f i r s t p o s i t i v e r o o t o f ax cos ax / (ah - 1) s i n ax s 0 h being the e m i s s i v i t y .  The v a l u e s  o f ka-^ and A-^ a r e determined from two o b s e r v a t i o n s of t h e temperature and t h e v a l u e o f t h e thermal d i f f u s i v i t y calculated. The method o f King ( 7 ) . One  end o f a long r o d o f m a t e r i a l  was heated by a p e r i o d i c c u r r e n t obeyi n g a s i n e law. The v e l o c i t y  v with  which the corresponding v a r i a t i o n i n temperature was t r a n s m i t t e d down t h e sample was measured by use o f two thermocouples.  Expedients were made  w i t h waves o f two d i f f e r e n t p e r i o d s t-^ and t ^ and the v e l o c i t i e s , which depended on the p e r i o d s , determined as V-L and v «  Then the thermal  2  diffusiv-  i t y k i s g i v e n by k  s  t  l 2 l 2 t  v  v  < i v  2  ya 2 >  2  ,  Dr B l u h has suggested that t h i s method might be a p p l i e d t o rubber by h e a t i n g one s i d e o f a t h i n sheet by r a d i a t i o n and measuring  the temperature  o f the  o t h e r s i d e by a s e n s i t i v e b o l o m e t r i c  method.  T h i s enables temperatures t o  be measured a t p o i n t s approximately h a l f a wave l e n g t h a p a r t .  The wave l e n g t h  i s g i v e n (5) by  X  3  hence, f o r reasonable f r e q u e n c i e s , i s low f o r rubber. P r e v i o u s measurements o f t h e Thermal C o n d u c t i v i t y o f Rubber. In in  s p i t e o f the p r a c t i c a l importance o f t h i s p r o p e r t y  such processes as t h e i n c r e a s e i n temperature i n f l e x e d  samples, and i n v u l c a n i z a t i o n o n l y r e l a t i v e l y few measurements of t h e thermal c o n d u c t i v i t y o f rubber have been made. i n 184-8 measured the c o n d u c t i v i t y o f e b o n i t e . Griffith  Lees  (4.)  L a t e r , i n 1923,  and Kaye a t the N a t i o n a l P h y s i c a l L a b o r a t o r i e s made  measurements o f the thermal c o n d u c t i v i t i e s o f a g r e a t many substances, i n c l u d i n g bothhard and gum rubber o f u n i d e n t i f i e d composition u s i n g a two p l a t e method w i t h a guard r i n g .  They  determined t h e e f f e c t o f f i l l e r on thermal c o n d u c t i v i t y , but s p e c i f y t h e f i l l e r as " m i n e r a l matter".(8) Frumkin and Dubinker have determined the d i f f i s i v i t y  by measuring  t h e change I n  temperature w i t h time i n the centre o f a sphere which i s allowed t o c o o l i n an e n c l o s u r e by r a d i a t i o n . (9)  Recently  a s i m i l a r measurement has been made by J.Rehner, J r . (10) who immersed spheres o f a u n i f o r m temperature i n b o i l i n g  water,  and measured the d i f f u s i v i t y o f a wide v a r i e t y o f n a t u r a l and  PLATE I  A f r o n t view of the apparatus switch p a n e l s , c o n t r o l p a n e l s , instruments and automatic  showing the measuring  controls.  PLATE I I  A r e a r view o f t h e apparatus  showing  the a u t o m a t i c c o n t r o l s , t h e c r y o s t a t zone box and s e l e c t o r  switch;  15 synthetic stocks, a l l c l e a r l y i d e n t i f i e d .  Schallamaeh  measured the c o n d u c t i v i t y o f n a t u r a l rubber a t low temperatures u s i n g t h e h o t p l a t e method. (11) The p r o j e c t a t t h e P h y s i c s Department o f U n i v e r s i t y o f B r i t i s h Columbia was begun i n 194-4 by Dauphinee, who measured the c o n d u c t i v i t y o f n a t u r a l rubber, s t r e t c h e d and uns t r e t c h e d , a t temperatures between 20° and -160°C.  (12)  The  work was continued by Ivey (13) who r e d e s i g n e d t h e apparatus and made measurements on GR-S. the  The measurements d e s c r i b e d i n  present t h e s i s were made on an improved  form o f t h e  apparatus used by Ivey. IIAPPARATUS. The apparatus used by Ivey and Dauphinee  had been  l o c a t e d i n a s t o r a g e basement i n the S c i e n c e B u i l d i n g , had become u n t e n a b l e .  which  F o r t h i s reason, and s i n c e the apparatus  would have t o be moved t o t h e new P h y s i c s B u i l d i n g , i t was decided t h a t i t should be r e b u i l t i n a more p o r t a b l e form i n one o f t h e ground f l o o r l a b o r a t o r i e s .  While being r e b u i l t  two important improvements were made; a heat shunt was made between the guard b l o c k s and the c o l d b l o c k t o overcome t h e g r e a t o v e r h e a t i n g o f t h e guards, mentioned by I v e y , (13) and semi-automatic c o n t r o l s were put on t h e c o l d s i d e and t h e guard b l o c k s . C o n d u c t i v i t y measuring  unit.  The a c t u a l measuring u n i t ( p l a t e IV) had t h r e e p a r t s , one c o l d b l o c k and two h e a t i n g a s s e m b l i e s .  The c o l d b l o c k was  4  PLATE I I I  A close-up o f the measuring u n i t .  16 was a p i e c e o f c o p p e r / 1 cm t h i c k shaped i n the form o f a r e c t a n g l e 10 cm by U cm on top o f a t r i a n g l e , which l e d down t o a l a r g e tapped copper p l u g .  Into t h i s plug f i t t e d a copper  c y l i n d e r , threaded a t t h e top, and having a copper s o l d e r e d about i t ,  through which was drawn the c o l d vapour  from a f l a s k o f l i q u i d n i t r o g e n , and a t extreme the l i q u i d i t s e l f .  spiral  temperatures,  Around the b l o c k , immediately  c o l d c y l i n d e r were wound two h e a t e r s , one o f  above t h e  20 ohms, s u p p l i e d  from a 12 v o l t source, t h e c u r r e n t being manually c o n t r o l l e d , and  the o t h e r o f 700 ohms, s u p p l i e d by c u r r e n t a t 110 v o l t s  from the automatic  control.  I n each h e a t i n g assembly was a measuring b l o c k and a guard b l o c k .  The measuring block was a p i e c e o f copper 1 cm  t h i c k and machined to e x a c t l y 4 cm by 6 cm.  A 20 ohm h e a t e r  s u p p l i e d by power a t 12 v o l t s was wound i n t h i s b l o c k , near the side n o t i n c o n t a c t w i t h t h e sample. b l o c k f i t t e d t h e guard b l o c k .  Around the measuring  A p l a t e o f h a l f i n c h brass 10 cm  by 6 cm was machined down t o one q u a r t e r i n c h , l e a v i n g two r i d g e s h a l f an i n c h a p a r t and one q u a r t e r i n c h wide.  T h i s was  to combine s t r e n g t h with a low heat c a p a c i t y and h i g h conductivity.  intended_  thermal  A t e i t h e r end o f t h i s were f i t t e d two copper  b l o c k s , each 2 cm by 6 cm, c o n t a i n i n g h e a t e r s , one o f 20 ohms, s u p p l i e d by manually c o n t r o l l e d c u r r e n t a t 12 v o l t s , and one o f 300  ohms s u p p l i e d by power a t 110 v o l t s from t h e automatic' guard  block c o n t r o l .  The c e n t r e s e c t i o n o f t h e brass p l a t e was r e c e s s -  ed s l i g h t l y , and f o u r tapped h o l e s were made i n i t .  F i b r e plugs  P l a t e IV Top  elevation  The C o n d u c t i v i t y  measuring  unit  ^ 1  a  thermocouple  b 20 ohm h e a t e r  "OS  •oc  c 500 ohm h e a t e r d difference e cooling  . - • ••  Side  elev  v , , ,*  f  Enc  e l e v a t i o n  bakelite  thermocouple  coil block  h e l d i n r e c e s s e s i n the back o f the measuring b l o c k f i t t e d these h o l e s .  The measuring b l o c k was  into  adjusted f l u s h with  the  f a c e o f the c o l d b l o c k by f o u r screws which pressed a g a i n s t the f i b r e plugs.  Two  thermocouples were l o c a t e d near the tops o f  the measuring b l o c k , two near the tops o f the guards, and two . near the top o f the c o l d b l o c k , and one a t a p o i n t j u s t below the bottom o f the sample.  A d i f f e r e n c e thermocouple was  between one o f t h e measuring b l o c k s and i t s guard Two  closely fitting  block.  copper bars were sweated between  the r i d g e s on the back of each guard  block and a p l a t e of  e i g h t h i n c h copper o f the same shape as the e o l d b l o c k screwed to these.  The  put  lower end of the p l a t e was  was  connected  to  the c o l d block by a p i e c e o f f l e x i b l e copper s h e e t i n g which passed heat  between the c y l i n d e r and the tapped p l u g .  shunt, which was  A h e a t e r was  the p l a t e s to c o n t r o l the heat l o s s through The h e a t i n g c i r c u i t s .  storage b a t t e r i e s . " h e a t e r s was  the  intended t o p r o v i d e a low r e s i s t a n c e path  to heat p i c k e d up by the guards.  Power was  T h i s was  wound around  them.  ( P l a t e V)  p r o v i d e d by a s e t of twelve heavy duty The  c u r r e n t to each of the low r e s i s t a n c e  c o n t r o l l e d by a s e t of s l i d e wire r h e o s t a t s .  Small milliammeters  were put i n s e r i e s w i t h the guard  h e a t e r s (G^G ) and the c o l d block a u x i l i a r y h e a t e r 2  switching arrangement enabled a Weston Model 1  block  (A^).  A  milliammeter  to be put i n s e r i e s w i t h the h e a t e r i n e i t h e r o f the measuring b l o c k s , o r a Weston Model 1 voltmeter a c r o s s i t .  Ihe c r y o s t a t and c o o l i n g  circuit.  The measuring u n i t was p l a c e d i n a l a r g e brass box, the  thermocouples and h e a t e r l e a d s passing between rubber  gaskets, so t h a t t h e box c o u l d be evacuated.  T h i s was done by  means o f a Cenco Megavac pump, arid readings were taken a t p r e s s u r e s o f l e s s than 1 cm o f mercury, as shown by a c l o s e d tube manometer on the c o n t r o l p a n e l . The c o o l i n g f l u i d was drawn by a pump from a l a r g e Dewar f l a s k through the c o o l i n g c o i l s .  The r a t e o f f l o w was  c o n t r o l l e d by two v a l v e s , one a needle v a l v e between t h e c o o l i n g c o i l and the pump, and the second opening t o the atmosphere between the f i r s t v a l v e and the pump.  The r a t e o f  f l o w was estimated by measuring t h e p r e s s u r e i n t h e c o o l i n g c o i l s w i t h an open tube manometer.  T h i s manometer was p r o v i d e d  w i t h a two p o s i t i o n stop cock so t h a t i t c o u l d be used t o measure the  d i f f e r e n c e i n pressure a c r o s s t h e needle v a l v e .  Between  'these v a l v e s and the c o o l i n g c o i l , and a g a i n between the v a l v e s and t h e pump, the c o o l a n t passed through a l a r g e copper c o i l which jwarmed i t .  Immediately i n f r o n t o f the pump was a f i v e  j g a l l o n tank which served t o steady the i n t e r m i t t e n t a c t i o n o f the  pump.  The temperature measuring c i r c u i t .  ( P l a t e VI)  Temperature was measured by means o f a s e t o f twelve copper-copel thermocouples.  The c o p e l used was e s p e c i a l l y  made f o r thermocouple u s e s and proved completely s a t i s f a c t o r y .  P l a t e VI  Thermocouple C i r c u i t  s e l e c t o r  b v . i t c h  Zone box  Measuring  Junction  Reference  junction  \ \  LI TCP  TCQ  Potentiometer  19 The thermal e. m.  f . was  measured by means of a White Double  Potentiometer designed f o r thermocouple  pyrometry used w i t h a  Leeds and Northrup H . S .  The thermojunctions i n  the measuring  galvonometer.  u n i t were connected through a twenty-four  position  s e l e c t o r switch i n s e r i e s w i t h the r e f e r e n c e j u n c t i o n and the potentiometer.  The potentiometer c o u l d be read t o a t e n t h o f a  m i c r o v o l t , and had an arrangement whereby i n t e r n a l c o n t a c t e. m. f s could be compensated.  To do t h i s the power was  taken o f f the c i r c u i t and a s m a l l r e s i s t a n c e put i n s e r i e s w i t h the galvonometer. c i r c u i t was  The p o s i t i o n o f the galvonometer  c l o s e d was  instrument.  when tils  used as the n u l l p o i n t f o r b a l a n c i n g the  The White Double Potentiometer has a f u r t h e r  advantage i n t h a t the b r i d g e c u r r e n t i s p r o v i d e d from two sources, one g i v i n g 100 ma. other g i v i n g 10 ma.  f o r the coarse adjustment  f o r the f i n e adjustment.  separate  and the  This r e l i e v e d the  d r a i n on the b a t t e r i e s and made the b r i d g e c u r r e n t more stable. The  control  circuits. The apparatus as used by Ivey was  experimenters, one  operated by  two  c o n t r o l l i n g the c o l d b l o c k by means o f the  a u x i l i a r y heater, w h i l e the other made the a c t u a l measurement. T h i s year a system of automatic  c o n t r o l s was  designed and  built  which permitted data to be taken by a s i n g l e experimenter.  A  photo c e l l c o n t r o l c i r c u i t was used i n conjunction w i t h a galvonometer  and a constant impedance potentiometer.  Experiments  were made w i t h a p h a s e - c o n t r o l t h y r a t r o n c i r c u i t which proved unsatisfactory.  Two  types o f b i a s c o n t r o l c i r c u i t s were used,  . • PLATE V I I  Photocell control c i r c u i t  A.C.  type  one w i t h a n i . C . source and a s i n g l e t h y r a t r o n , and t h e other w i t h D.C. current and a p a i r o f t h y r a t r o n s .  The A.C. c o n t r o l  was based on t h e a b i l i t y o f a t h y r a t r o n t o a c t as an a m p l i f i e r when s u p p l i e d w i t h A.C. p l a t e v o l t a g e . to  The tube was b i a s e d  c u t - o f f by a cathode r e s i s t o r , and the g r i d t i e d t o a  p h o t o c e l l t h a t was grounded  through a one megohm r e s i s t o r .  When l i g h t reflected from t h e galvonometer m i r r o r f e l l on t h e p h o t o c e l l i t conducted curasnt, and drove t h e g r i d a l l o w i n g t h e tube t o conduct on each p o s i t i v e h a l f (Plate V I I ) . of  positive, cycle.  T h i s c o n t r o l had the v e r y d e s i r a b l e p r o p e r t y  self-damping, and brought the system t o s t a t i c  equilibrium.  However i t was u n s a t i s f a c t o r y since a sudden v a r i a t i o n i n temperature would make i t l o s e c o n t r o l , by throwing t h e g a l v o nometer spot r i g h t a c r o s s the p h o t o c e l l b e f o r e enough heat had been added.  F o r t h i s reason a D.C. c o n t r o l was used.  In this  c o n t r o l a t h y r a t r o n was f i x e d when the g r i d went p o s i t i v e i n response t o a stimulus on the p h o t o c e l l .  S i n c e the t h y r a t r o n  p l a t e was h e l d a t a constant D.C. v o l t a g e i t c a r r i e d u n t i l t h e v o l t a g e was removed.  current  To shut i t o f f a second photo-  c e l l and t h y r a t r o n assembly was used.  I n the p l a t e o f t h i s  t h y r a t r o n was a 10,000 ohm r e s i s t o r , so t h a t a e o n s i d e r a b l e drop i n v o l t a g e o c c u r r e d when the tube f i r e d .  Between the  p l a t e s o f t h e t h y r a t r o n was a 4-00 u.u.fd. condenser, which was charged when the f i r s t  t h y r a t r o n was f i r e d .  When the  second one conducted t h i s condenser d i s c h a r g e d and drove the p l a t e o f the f i r s t one n e g a t i v e , thus s h u t t i n g o f f the  Plate VII  Photocell control circuit D . C type  Rio  no  6.;  r,.rw  A.-cr^  . 1 0 0 0 0 ohm  R2,  R3, R5. Ht> 1 megohm  RA  1000 o h c  10 »  87  225 ohrr.  75 w  R8  500 o n e io w  R9  1000 ohm .10 w  RIO 500 oha heater. TI,  T2 2050  thyrEtron  T3, TA 918 photocell C y.^OO u u f d . co»>d.. :  current..  (Plate VIII)  Under o p e r a t i n g  galvonometer spot moved between the two  c o n d i t i o n s the p h o t o c e l l s , so t h a t  the system made small o s c i l l a t i o n s about i t s e q u i l i b r i u m temperature.  When complete e q u i l i b r i u m was  desired  o s c i l l a t i o n s were removed manually by decreasing under c o n t r o l o f the automatic system, and power under manual c o n t r o l . b u i l t , one having  Two  as p l a t e l o a d a 300  ohm  c o l d b l o c k , o r , s i n c e the c i r c u i t i t s e l f  telephone  and more power was  the  i n c r e a s i n g the  h e a t e r i n the  ohm  heater  could  in,the  provide  f r e q u e n t l y needed, a  r e l a y , which when c l o s e d p e r m i t t e d 24-0 ma.  flow through the 700  ohm  to  heater.  To a c t as a d e t e c t o r some s o r t o f a arrangement was  current  such c o n t r o l c i r c u i t s were  guard b l o c k , and the other e i t h e r a 700  only 100 ma.  these  necessary,  potentiometer  which would present  to the  galvonometer an approximation t o i t s c r i t i c a l damping resistance.  TO  c a n c e l out the e.m.f. of the thermocouple  used as a d e t e c t o r and  s t i l l d e t e c t v a r i a t i o n s i n temper-  a t u r e , the thermocouple was  connected i n s e r i e s w i t h  the  galvonometer and a s m a l l r e s i s t o r through which flowed  a  small v e r y s e n s i t i v e l y c o n t r o l l e d c u r r e n t , g i v i n g ' r i s e  to  a v o l t a g e drop which opposed the thermal e.m.f. galvonometer f a c e d a constant  Thus the  r e s i s t a n c e which was  made  equal to i t s c r i t i c a l damping r e s i s t o r .  I n order to have  c o n t r o l over s e n s i t i v i t y a potentiometer  was  put i n s e r i e s  w i t h the galvonometer, so t h a t the c u r r e n t c o u l d reduced and galvonometer overdamped at w i l l .  be  ( P l a t e IX)  Plate IX  Control Circuit Potentiometer  Thermocouple  R6  ""WW  1  R2 R3 R5  ywv  Rl  1 megohm  R2  20000 ohm  R3  20000 ohr,. t i slide  w i r e po'  R4,R6 100 oh,-n R5  lOuOu oh!..  Ill  EXPERIMENTAL PROCEDURE. Thermocouple c a l i b r a t i o n . The  thermocouple had been c a l i b r a t e d by Ivey a t  f i v e fixed points:  I t was  1. The  f r e e z i n g p o i n t of water  ,2. The  b o i l i n g p o i n t o f water  3. The  f r e e z i n g p o i n t of mercury  4. The  s u b l i m a t i o n p o i n t o f carbon d i o x i d e  5 . The  b o i l i n g p o i n t of oxygen  considered  s u f f i c i e n t t h i s year to check the  calibra-  t i o n a t the f r e e z i n g p o i n t of water, the s u b l i m a t i o n p o i n t o f carbon d i o x i d e and ment was  the b o i l i n g p o i n t o f oxygen.  found between the data o b t a i n e d now  Close  and t h a t  agreeobtained  by Ivey, the d i f f e r e n c e i n the average o f the readings l e s s than two m i c r o v o l t s a t any  point.  Therefore  i t was  considered t h a t the o r i g i n a l c a l i b r a t i o n charts c o u l d be used. was  The  being  still  d i f f e r e n c e between i n d i v i d u a l thermocouples  determined a t three f i x e d p o i n t s , and a comparison with  the e x i s t i n g d e v i a t i o n c h a r t s showed a n e g l i g i b l e v a r i a t i o n , approximate c o n f i r m a t i o n o f t h i s was The  apparatus was  assembled w i t h no  obtained as  smapie i n p l a c e , good  thermal contact between the p o l i s h e d copper f a c e s provided by s t r i p s o f f o i l ,  being  and h e l d i n e q u i l i b r i u m at  v a r i o u s temperatures.  The  and  T h i s method was  d i f f e r e n c e s noted.  folows:  thermocouples were then read found  satisfactory  o n l y a t r e l a t i v e l y h i g h temperatures where r a d i a t i o n from the w a l l s was  negligible.  23 When the apparatus was re-assembled i n the new ^ l a b o r a t o r y , a new zone box was made and t h e c a l i b r a t i o n a g a i n checked a t the i c e p o i n t and the l i q u i d oxygen p o i n t .  A  v a r i a t i o n o f l e s s than two m i c r o v o l t s was found, and r e - c a l i b r a t i o n c o n s i d e r e d unnecessary.  S i n c e t h e t h e r m o - e l e c t r i c power  v a r i e d between 20 and 4-0 m i c r o v o l t s p e r degree over t h e range used, t h e temperature measurements were c o n s i d e r e d a c c u r a t e t o at  l e a s t one-tenth o f a degree.  Method o f t a k i n g r e a d i n g s . Readings were taken i n two d i f f e r e n t ways t o o b t a i n the change i n c o n d u c t i v i t y o c c u r r i n g as t h e sample c o o l e d , and as i t warmed up.  F o r t h e f i r s t type, t h e  h e a t e r s were turned o f f and the system cooled as r a p i d l y as p o s s i b l e u n t i l the c o l d b l o c k was two o r t h r e e degrees below the  temperature d e s i r e d .  The a u x i l i a r y h e a t e r i n the c o l d  b l o c k was then turned on and the c o l d s i d e heated as r a p i d l y as p o s s i b l e t o the d e s i r e d temperature.  The c o n t r o l  circuit  potentiometer was then balanced, and the automatic c o n t r o l c i r c u i t a d j u s t e d t o h o l d the c o l d s i d e a t constant temperature. In the meantime the measuring b l o c k s and guards had been cooling.  When they reached a temperature some t e n degrees  above t h a t o f the c o l d s i d e , the h e a t e r s were turned on and a d j u s t e d manually t o stop the temperature drop. meter was put i n s e r i e s w i t h the d i f f e r e n c e between one measuring  A galvono-  thermo-couple  b l o c k and i t s guard, and t h e guard  temperature put under c o n t r o l o f the auotmatic c i r c u i t ,  24 the o t h e r guard b l o c k being a d j u s t e d by hand.  The apparatus  was then l e f t f o r t e n minutes t o reach e q u i l i b r i u m , and r e a d i n g s were taken f o r t h e next t e n minutes.  When t h e tempera-  t u r e d r i f t remained l e s s than one m i c r o v o l t per minute f o r f i v e minutes, temperatures o f a l l b l o c k s were r e c o r d e d , and the c u r r e n t and v o l t a g e i n the measuring h e a t e r s r e a d . To f i n d the changes produced on warming the sample, the apparatus was f i r s t  c o o l e d as r a p i d l y as p o s s i b l e t o the  lowest o b t a i n a b l e temperature  (about - 1 6 0 ° C ) , an o p e r a t i o n  which took a t l e a s t an hour.  The above procedure was then  r e v e r s e d , the apparatus being f i r s t heated a s r a p i d l y as p o s s i b l e , then the c o l d s i d e stopped and the warm s i d e b a l a n c ed.  These readings were o b t a i n e d i n much l e s s time than the  o t h e r s , s i n c e the hot b l o c k s could be warmed much more r a p i d l y than they could be c o o l e d . F o r most o f t h e readings the c o l d s i d e was adjusted t o complete  s t a t i c equilibrium, but many were t a k e n  w h i l e i t s temperature was o s c i l l a t i n g about the e q u i l i b r i u m position.  None of these temperature o s c i l l a t i o n s seemed t o  be t r a n s f e r r e d to the h e a t i n g b l o c k s , and the mean temperature o f the c o l d s i d e was used i n c a l c u l a t i o n s . j u s t i f i e d i n a l a t e r paragrahh.  T h i s w i l l be  A l l temperature r e a d i n g s  were made w h i l e the automatic c o n t r o l h e a t e r was o f f , s i n c e some o f the thermocouples  showed a d i s t u r b i n g tendency t o  respond t o the c l o s i n g o f the 110 v o l t c i r c u i t s , i n s p i t e of the f a c t t h a t when t e s t e d f o r e l e c t r i c a l p i c k up no e f f e c t was found.  T h i s t e s t was made when use o f an a l t e r n a t i n g  25 c u r r e n t c o n t r o l c i r c u i t was contemplated.  One t h e r m o j u n c t i o n  was p l a c e d i n the c e n t e r o f a l a r g e i n d u c t i o n c o i l , at  constant temperature by a stream o f a i r .  and h e l d  No change was  observed i n the e.m.f. r e g i s t e r e d by the b a l a n c i n g p o t e n t i o meter when a 60 c y c l e , c u r r e n t o f two amperes was passed through the c o i l . Method o f a n a l y s i n g d a t a .  .  Consider a hot b l o c k o f heat c a p a c i t y C a t a temperature T  surrounded by a guard r i n g a t a temperature T^  0  r e s t i n g on a sheet o f rubber o f c o n d u c t i v i t y K.  I f the b l o c k  i s p r o v i d e d w i t h a supply o f power P, the r a t e a t which i t heats up w i l l be g i v e n by C dTo "dt  s  (24)  P / a(T, - T J - KA3T 9x 1  I f the rubber sheet i s o f t h i c k n e s s d, and r e s t s on a p l a t e kept a t a temperature T^, the e q u i l i b r i u m c o n d i t i o n w i l l be .  0 - P f a ^  » T ) - KA(T 0  n  - T ) d 2  (25)  I f a t t h e same time the guard has been a d j u s t e d t o the same temperature as the h e a t i n g b l o c k , we have P s KA ( T - T ) d T  from which  K  s  Pd Adj.  9  = T  2  26  Guard M o c k correction'. Not a l l r e a d i n g s c o u l d be taken under t h e i d e a l circumstances d e s c r i b e d above, s i n c e i t was found i m p o s s i b l e , p a r t i c u l a r l y f o r the s t r e t c h e d sample,  t o g e t the guards  down t o a low enough temperature, even w i t h the heat  shunt.  There a r e two probable reasons f o r t h i s : 1. A t lowest temperature i t was found t h a t the b l o c k s became covered w i t h f r o s t , thus i n c r e a s i n g  their  emissivity. 2. A l a r g e p a r t o f the s t r e t c h e d sample extended the measuring  beyond  u n i t and p i c k e d up a g r e a t d e a l o f  'radiation. When the guards and t h e measuring  b l o c k s were a t d i f f e r e n t  temperatures a c o r r e c t i o n had t o be made, t a k i n g i n t o account the power t r a n s m i t t e d t o the h e a t e r b l o c k from the guard block.  I t was assumed t h a t to a f i r s t approximation the  heat t r a n s f e r depended l i n e a r l y on the temperature (v. e q u a t i o n 25).  difference  On t h i s assumption the t r a n s f e r co-  e f f i c i e n t a could be determined a t any temperature by making two r e a d i n g s employing  the same v a l u e o f T  Q  d i f f e r e n t readings o f T^.  and T  and  Such r e a d i n g s were taken, and  the average v a l u e o f a a t v a r i o u s temperatures as shown i n Table 1.  2  determined  The product o f a and the temperature  d i f f e r e n c e between guards and h e a t e r (which was k e p t small) was added to the measured power t o g i v e the time r a t e o f t r a n s f e r o f heat.  27 Table 1 Temperature degrees c e n t i g r a d e  Guard b l o c k transfer coefficient a watts per degree (x/o' ,) 1  f  ,01 .01 .01 .015 .015 .02 .02 .025 .025 .03  20  0 - 20  - AO » =  60 80 100 120  - 140  - 160  Measurement of power. The power s u p p l i e d t o the h e a t e r s was  determined  by reading the v o l t a g e a c r o s s them and the c u r r e n t f l o w i n g . I t was necessary to c o r r e c t these readings f o r two e f f e c t s . F i r s t , the v o l t a g e read was developed  not a c r o s s the h e a t e r  alone, but a c r o s s the h e a t e r and the l e a d s i n s e r i e s . the v o l t m e t e r and ammeter were not i n the c i r c u i t  Second,  under  o p e r a t i n g c o n d i t i o n s , hence t h e i r e f f e c t on the c i r c u i t had to be taken i n t o account.  An a n a l y s i s o f the c i r c u i t  leads  to the f o l l o w i n g approximate, formula: (26) where P  t r u e power measured power s E.I,  R  heater resistance  r  lead resistance  28  Rv - r e s i s t a n c e o f v o l t m e t e r Ra ~ r e s i s t a n c e o f ammeter When numerical v a l u e s a r e s u b s t i t u t e d we  o b t a i n f o r the  two  heaters: (Pt)  x  - .995  E ^  (Pt)  2  = . 997  E I 2  2  T h i s enables the c o n d u c t i v i t y K to be c a l c u l a t e d from the general  formula. K  Where dT  (Pt / a.dT).d A . DT  s  d i f f e r e n c e i n temperature between measuring  s  and DT  block  guard  d i f f e r e n c e i n temperature between measuring  s  and c o l d  block  block.  A ~ a r e a of measuring b l o c k d = t h i c k n e s s of  sample 2  Since the a r e a o f both b l o c k s was values may  e x a c t l y 24 cms  numerical  be s u b s t i t u t e d , g i v i n g f o r K as determined  two b l o c k s K  x  -  «• 9.88  x 1CT . 3  d  1  f 9.92  x 10~ .  d  / 9.93  x 10~ .  d .adT  3  x  DT K  2  - 9.90  x 10"* . d 3  2  Egl^ DT  I f d^ and d  from the  2  3  adT "DT  2  DT  a r e measured i n centimeters these formulae  K i n c a l o r i e s per second per degree per  centimeter.  give  29 Measurement o f t h i c k n e s s . T h i c k n e s s was measured i n t h r e e ways. (1) A.micrometer f o r s o f t m a t e r i a l s was used t o measure the sample b e f o r e i t was clamped i n p l a c e . (2) A t r a v e l l i n g m i c r o s c o p e was removed from a comparator and mounted on a s t a n d t h a t f i t t e d o v e r t h e cryostat.  P a r a l l e l bench marks were c a r e f u l l y  made a l o n g t h e t o p o f t h e b l o c k s , and t h e s e p a r a t i o n o f t h e s e marks was measured, w i t h and w i t h o u t t h e sample i n p l a c e .  The d i f f e r e n c e i n t h e s e measure-  ments gave t h e t h i c k n e s s o f t h e sample. (3) A l a r g e micrometer was used t o measure t h e d i s t a n c e between the backs o f t h e g u a r d s , w i t h a n d w i t h o u t the sample i n p l a c e .  F a i r agreement was o b t a i n e d  between t h e s e measurements,  e.g. f o r one sample:  S o f t m a t e r i a l s micrometer  »154 cm.  T r a v e l l i n g microscope  .152 cm.  Large micrometer  .150 cm.  Any v a l u e used i n c a l c u l a t i o n was t h e mean o f about ten readings.  These r e a d i n g s  showed a spread o f about .04  m i l l i m e t e r s w i t h t h e m i c r o m e t e r , and r a t h e r more t h a i t h a t w i t h the m i c r o s c o p e .  F o r t h i s r e a s o n t h e t h i c k n e s s measurements  are considered accurate  t o w i t h i n . o n l y about 5$.  When t h e u n i t was i n p l a c e t h e m i c r o s c o p i c measurement c o u l d be made o n l y a t t h e t o p o f t h e b l o c k s , t h e r e f o r e t h e a p p a r a t u s was removed and two bench marks  put on t h e ends o f the guards and the c o l d b l o c k .  Using  these, m i c r o s c o p i c d e t e r m i n a t i o n s o f the s e p a r a t i o n o f -6he p l a t e s was made.  T h i s agreed t o w i t h i n 5% w i t h t h e measure-  ments a t t h e top.  Measurements made w i t h the l a r g e  a t a number o f p o i n t s confirmed t h i s  calipers  agreement.  To determine t h e e f f e c t of l i n e a r expansion a P l e x i g l a s s window was  put i n t o the top o f the c r y o s t a t , and  measurements o f s e p a r a t i o n between bench marks made a t v a r i o u s temperatures.  These measurements were ratherrauncertain,  but when c o r r e c t e d f o r the expansion o f the copper i n d i c a t e d t h a t the average v a l u e o f the l i n e a r expansion c o e f f i c i e n t f o r t h e sample, over the temperature range used, c o u l d be taken as about 1 x 10"^.  T h i s i s o f the o r d e r expected from the  v a l u e s f o r the s p e c i f i c volume o b t a i n e d by Bekkedahl f o r n a t u r a l rubber.  (14,)  The r e l a t i v e v a r i a t i o n i n p l a t e  s e p a r a t i o n over the temperature range used was thus about 2%, hence could be n e g l e c t e d . E v a l u a t i o n o f the apparatus. Temperature v a r i a t i o n over t h e c o l d S i n c e the c o l d s i d e was there was the p l a t e .  plate.  cooled from the lower end,  some v a r i a t i o n i n temperature over the s u r f a c e o f T h i s v a r i a t i o n i s c e r t a i n l y l e s s than the  temperature v a r i a t i o n t h a t would be produced between the top and the bottom o f t h e b l o c k i f a l l i t e n t e r e d a t the t o p .  the power p a s s i n g through  The p a r t of the c o l d , b l o c k warmed  by the measuring h e a t e r s was  4- cms. h i g h , 6 cms. long  and  31  1 cm. thick, and the maximum power passing through i t was about 1.5 watts.  Since the thermal conductivity of copper i s  about 1 cal./deg.-sec.-cm. over the whole temperature range used, we have f o r the difference i n temperature over the block  , 1.5 x k  1 x 6 x 4-18  - .25 degrees  The a c t u a l measured temperature difference between the thermocouples a t the top and at the bottom was never as great as one-tenth degree, and was therefore neglected. V a r i a t i o n of Temperature with time. The condition of equilibrium was considered as obtained when the rate o f change of the boundary temperature remained less than one-twentieth degree per minute for ten minutes.  An approximation to the true temperature gradient  i n the sample may be obtained from a consideration of the mathematical solutions to the temperature d i s t r i b u t i o n problem. The temperature at any point i n the sample i s given by the sum of a term depending on the i n i t i a l "condition and one depending on the boundary state.  P h y s i c a l l y t h i s means that to the  stationary temperature must be added a quantity depending on the  rate of cooling inside the sample.  for  the temperature i n rod of length  Carslaw (6) gives i n i t i a l l y a t zero,  with one end suddenly raised to a temperature T-^ a condition approximating that of the sample oo  T  a  T]_ X  A  / 2  2-.  77  * i cos nTT s i n n  njx , e ~  I  2  k n  A1  2.,  -  32  I f we w r i t e T  f o r the s t a t i o n a r y temperature and  Q  consider  the temperature a t the c e n t r e f o r l a r g e v a l u e s o f t we get T  o  ~  T  exp. - k.7f  •  "  2  . t  I*  i f  To  .  .  hence, the time r e q u i r e d f o r the c e n t r e o f the sample t o reach w i t h i n 1% o f i t s f i n a l v a l u e i s t =  -P 2L  n (.01 x f  )  2  S u b s t i t u t i o n of numerical values gives t ~ 15 seconds.  From t h i s i t i s c l e a r t h a t the  p r i n c i p a l f a c t o r i n v o l v e d i n reaching e q u i l i b r i u m i s the time needed f o r heat t o f l o w from the copper b l o c k s .  The  i n f l u e n c e o f the slow change i n boundary temperature can a l s o be approximate.  Carslaw (6) g i v e s i n the case o f one  boundary a t a v a r y i n g temperature T =  Cx  (kt  el  - I  2  - x  C t 2  Y  ~~sf~'  which i s a v e r y rough approximation to the c o n d i t i o n i n our experiment. D i f f e r e n t i a t i n g t h i s p a r t i a l l y with respect to x a t the boundary, and changing n o t a t i o n , we get 72 ( i , t ) - 1 / I I dT ^x " I 3 k dt S u b s t i t u t i n g numerical v a l u e s , we f i n d the c o r r e c t i o n to  a temperature d r i f t o f one m i c r o v o l t per minute  due  as  ,o3 degrees per c e n t i m e t e r . S i n c e the tempa*ature g r a d i e n t used was on the o r d e r o f 50 degrees per centimeter t h i s term Is c l e a r l y n e g l i g i b l e .  I  33 Many o f the readings were taken while t h e c o l d block temperature  executed s m a l l o s c i l l a t i o n s about i t s e q u i l i b r i u m  position.  When such was t h e case, the temperature  of the  hot block was found t o be u n a l t e r e d , and the average v a l u e o f the c o l d f a c e temperature was used i n c a l c u l a t i o n s .  An  approximation t o the c o n d i t i o n s under t h i s type o f e q u i l i b rium i s : one s i d e a t a constant temperature T, the other s i d e a t a temperature a cos w t . The e f f e c t o f t h i s s i n u s o i d a l v a r i a t i o n on the temperature g r a d i e n t can be o b t a i n e d from Cai&aw's s o l u t i o n (6) f o r the temperature  i n a rod o f  l e n g t h , one s i d e being h e l d a t zero w h i l e the o t h e r i s a t a temperature a cos w t .  The s t a t i o n a r y p a r t o f the s o l u t i o n  is T = a 2 where u  | s i n uu (1 (1 f / i i? ) x.e x.« sin u (l/ i)X  1 w  / s i n u (1 - i ) x e  t  S l A LL ( / - t )  *  1 w  X  s  | :2k P a r t i a l d i f f e r e n t i o n with respect to x a t x = o gives, a f t e r a l i t t l e manipulation _T.(0,t) = a i ~f"/(cos u ( l / i K l . e ( s i n u A c o sh ul - a  )  1  W  t  - cos u (1 - p i e "  1 W  t  / ( cos U / ( s i n h U / ( )  ( s i n u - I cosh u - / s i n w t - cos u -i s i n h u ^ c o s w t ) ( s i n u A cosh u I )  2  ? (cos u i s i n h  MI)  2  C a r r y i n g out the d i f f e r e n t i a t i o n i n d i c a t e d , and s u b s t i t u t i n g numerical v a l u e s g i v e s f o r the maximum value o f t h i s c o n t r i b u t i o n t o t h e temperature g r a d i e n t , something to 10. a. per cm.  close  Since t h e maximum rage o f the o s c i l l a t i o n s  was L4 m i c r o v o l t s , the value o f a was l e s s than .25 degrees,  )  34 per centimeter,, less: than 4». of course,  Ihe. average c o n t r i b u t i o n was,  zero. T h i s d i s c u s s i o n o f the accountable  apparatus  would l e a d to an expected  about 2%.  e r r o r s i n the  e r r o r i n the readings o f  A c t u a l l y , the readings taken showed a much g r e a t e r  range of e r r o r than t h i s .  Some improvements a r e s t i l l  lobe  made, c h i e f l y i n the c o o l i n g c i r c u i t and i n t h e measuring unit. 1. The use o f a f l o w i n g l i q u i d as a c o o l a n t has two  disadvantages.  F i r s t , i t i s wasteful o f the l i q u i d  n i t r o g e n , and second, i t i s not s u f f i c i e n t l y  dependable t o  be l e f t f o r long p e r i o d s o f time, even w i t h t h e temperature control c i r c u i t s .  A b e t t e r c o o l i n g system would employ a  heat b r i d g e t o a f l a s k o f the l i q u i d  coolant.  2. The geometry o f the measuring u n i t could be improved.  As i t i s , the guard b l o c k surrounds  the measuring  b l o c k s on o n l y three s i d e s , two f a c e s being l e f t • e x p o s e d . A b e t t e r arrangement would employ a guard surrounding  the measuring h e a t e r .  of much g r e a t e r a r e a . heated  block  completely  The b l o c k should a l s o be  A t present the g r e a t e s t p a r t o f the  s u r f a c e i s used f o r making measurements.  T h i s was  done t o e l i m i n a t e e r r o r s i n the measurement a r e a , and t o minimize t h e e f f e c t o f s u r f a c e d e f e c t s . thermal c o n d u c t i v i t y . o f rubber reduces  However the low the importance o f  cbntact r e s i s t a n c e , and samples have been s u p p l i e d t h a t a r e f a i r l y free of surface flaws. presents no d i f f i c u l t y .  The exact measurement o f a r e a  I f the guard b l o c k has a l a r g e a r e a  the  c o n d i t i o n s i n the r e g i o n of measurement w i l l  be  • 35  c l o s e r t o those c a l l e d f o r by the t h e o r y , and a t the same any e f f e c t o f l a r g e temperature g r a d i e n t s on the s t a t e o f . the  sample w i l l be reduced.  Another f l a w i n the apparatus  l i e s i n the poor arrangements  f o r measuring t h i c k n e s s .  An  instrument has been designed which embodies some o f these improvements,  and .its. c o n s t r u c t i o n was l a i d a s i d e i n  o r d e r t o i n v e s t i g a t e the e f f e c t o f the m o d i f i c a t i o n s made t h i s year t o the o l d equipment.  2$  RESULTS 1.  ,  The Samples The rubber samples used were prepared from  GR - I gum  s t o c k s by the Research D i v i s i o n o f Polymer  Corporation.at Sarnia.  They had been c a r e f u l l y molded  to ensure plane p a r a l l e l s u r f a c e s , as f r e e as p o s s i b l e from d e f e c t s .  The formulae used were:  Sample 1  GR - I / 2% S  °  B u t y l rubber  -  100 p t s .  Sulphur  -  2 ptd.  Z i n c Oxide  -  l.Opts.  Tetramethyl thuiran disulfide Sample 11  -  '  l.Opts.  GR - I / 10% S  B u t y l rubber  -  100  pts.  Sulphur  -  10  pts.  Z i n c Oxide  -  Tetramethyl thuiran disulfide Cure 60» a t 307° F.  1.0  pts.  1.0 p t s .  . •• ,  Readings taken. Measurements were made on sample 1 a t zero and  100%  s t r e t c h , and on sample 2 u n s t r e t c h e d , a t temperatures between 20°G and -170°.  I t was  found t h a t the apparatus, was  unsatis-  f a c t o r y f o r r e a d i n g s beyond t h i s range; a t h i g h e r temperatures it  seemed i m p o s s i b l e t o get c o n s i s t e n t r e a d i n g s , and a t low  temperatures the guard b l o c k c o r r e c t i o n became unduly g r e a t . The r e s u l t s a r e t a b u l a t e d i n t h e f o l l o w i n g t h r e e t a b l e s , and f o r comparison the d u p l i c a b l e r e a d i n g s a r e p l o t t e d .  I n the  t a b l e s , E l , Eg and E2 i n d i c a t e the thermal e.m.f. produced the thermocouples i n the measuring and the c o l d s i d e , r e s p e c t i v e l y .  by  b l o c k s , the guard b l o c k s V, I i n d i c a t e the power  r e a d i n g s , DT the temperature d i f f e r e n c e a c r o s s the  sample,  dT the d i f f e r e n c e i n temperature between the guards and t h e measuring b l o c k s , T the average temperature i n the sample, and K t h e v a l u e of the thermal c o n d u c t i v i t y . Probable e r r o r . The e r r o r i n the measurement o f a r e a and  thickness,  o f power and o f a b s o l u t e temperature c o u l d a f f e c t o n l y the a b s o l u t e v a l u e o f the c o n d u c t i v i t y . had been c a r e f u l l y machined w i t h i n .2%. f a c e was  The measuring b l o c k s  and t h e i r dimensions determined t o  B e f o r e t h e sample was  clamped  cleaned and i n s p e c t e d f o r f l a w s .  i n p l a c e the s u r The presence o f  s m a l l s c r a t c h e s i s i n s i g n i f i c a n t because of the s m a l l a r e a they occupy, and because of the p l a s t i c nature o f b u t y l rubber.  C o n t a c t r e s i s t a n c e i s an unimportant source o f  K vs T  PLATE g for GR - T with 2% S - Unstretched  o  - -  o  4  3  0  ¥.' ' '"'  V  •  0 _  a  *0 1  I  1  |  o  1  ! 1  ,»  -Ho  »»4o  -loo T aegives C  i -6o  "°  - a  TABLE 11 GR - I El  Eg  E2  y  uv  uV  460 611 1586 3005 4453 3697 3156 2201 1048 759 514 370 552 770 995 1276 860 1494 1696 388 1663 . 2933 4569 4061 3629 3164 2175 3270 1686  334 900 1903 3295 5030 4081 3590 2635 ,922 448 210 674 864 977 1208 1488 1056 1694 1948 334 1903 3295 5030 4498 4085 3590 2635 3683 1948  u  - 445 631 1593 3J0O6 4751 3700 3163 2230 / 1029 745 495 - 373 560 773 - 995 1275 860 1492 1726 / 379 '" 1644 3024 4746 0  ;  1260 2240 3375 1774  V -. .  volts 2.60 4.91 4.5 4-65 4.70 5.50 5.80 5.42 4.90 5.00 4.64 4.79 4.79 3.81 3.82 3.82 3.61 3.65 3.80 1.70 4.77 4.76 4.78 4.78 7.00 5.20 5.90 5.90 3.33  ( 2.5% Smlphur) - UNSTRETCHED I  DT  amps  deg.C  .142 .265 .245 .247 .251 .374 .311 .294 .262 .266 .246 .254 .254 .202 .202 .202 .191 .192 .200 .098 .256 .256 .259 .258  :M  .366 .336 .179  2.85 7.50 9.3 9.15 3.8 15.0 15.75 13.95 7.35 7.25 6.95 10.10 8.4O 5.7 4.85 6.25 5.45 5.95 7.1 1.20 7.75 9.55 14.05 12.55  .: E:h  13.75 ll.A 5.75  dt  J  deg.C f  deg.C  .38 f .55 .2 0 0 0 .25 .9 .45 f .35 / .50 0 . 2 - 1 0 0 0 0 0 .85 •• .2 / .6-; 3.05 8.35 6.20  10 21 49 95 166 120 102 71 22 15 8.8 14 9 24 30 38 28 45 52° 10 50 95 165 141 .  2.05 3.7 2.5  71 108 53  s  Uo  0  K x. M cal.deg. cm. sec. 2.51 . • 3.30 2.24 3.30 1.62 2.10 2.15 2.18 " 3.37 3.50 3.10 2.25  2.70 2.55 2.80 2.31 2.28 2.22 2,00 2.67 3.00 2.20 1.77 1.90  . m - iM -  2.97 3.28 2.10  TABLE 111 GR - X  El uV 1405  lSf>0  2211  V2740  324& 3733 4265 4575 4867 1011L 815  3940 3240  2525 2078 1158 67G 192 k 286 - 263  Eg uV  1392 1884 2152 2645 31690 3585  E2 uV  1674  2140  4633 969 800  2462 3035 3560 3985 4535 4828 5135 804 925 4098  679 193 320 213  2675 2210 1278 768 300 154 491  4085 4366  3740 3128 2411 1918 1145  3400  (10# Sulphur) - UNSTRETCHED V  volts  4.96 4.32 4.32 4.30 5.22 4.26  4.40 4.02  4.43 4.4S  2.71 2.67 2.68 2.69 2.70 2.72 2.80 2.80 2.80  4.12  I amps  .266 .233 .233 .258 .272 .228 .237 .217 .238 .238  .147 .145 .145 .145 .146 .146 .152 .151 .151 .223  DT deg.C  7.55 8.85 8.00 10.9 11.7 9.7  11.05  12.25  14.05  9-25 3.15 6.75 6.1 5.15  4.3O  3.65 2.75 1.90 3.40 . 6.35  K x 104  dT deg.C  --.37  /1.0  1.8 3.1  2.5 5.75 7.5 9.4  11.5  1.2  .42 7.8 3.9 3.7  2.4  .37 - .25 / .03 2.1  A.34  deg.C  41  58 70 86 101 121  143 157 171  22 26  126 99 76 61  33  19 10 l 6 > 11  cal.deg. cm. sec<  3.1 3.83  4.26  2.192.28 1.91 2-33* 1-95 2.45 2.13 2-32  2.04 2.18  1.42 2.05 2.01  2.74  4.05 2.31 2.58  — •so  —  WO  - igo T  degrees  €  TABLE  Sulphur) - 100$ Stretch  GR - I El  1374 974  290 , 1881 2246 2782 3322 3835 4367} 4645 4947 295 765 3923 3232 2500 .2043' 1521 1108 620 131 /33t) -903 ;  Eg.  E2  uV  uV  1350 990 300 1972 2247 2752 . 3291 3717 4230 4513 4796 905 758 3848 3212 2470 2036 1531 1105 640 125 333 908  1676 1138 498 2141 2461 3036 3562 3984 4536 4829 5136 804 928 4IO6  3408 2677 2212 1686 1278 770 300 154 802  IV  i  deg.C  volts  5.89 4.10 5.08 4.80 4.80 5.10 4.80 2.66 . 2.75 3.05. 3.05 3.05 . 3.87 3.80 3.81 4.00 4.01 4.01 4.01 4.02 4.01 4.01 3.25  DT  3.05 .214 .247 .245 .245 .272 .253 .144 .147 .162 .160 .157 .208 .207 .207 .215 .216 .217 .216 .217 .217 .217 .176  9.0 4.5 5.6 7.95 6.80 9.'65 8.0 15.8 7.55 9.50 0;35 2.2 4,55 714 6.55 5.95 5.35 4.95 5.05 4.2 4.45 4*4 2.5  deg. C  deg. C  /0.5 -0.4  -40 29 11 57 68 86 110 123 146 159 174 /22.5 -24 127 100 75 60 46 33 19 10 fl /21 9  Qi25  2v7 0 ' 1.0 1.1 3.1 5.6 6.0 7.5 0.2 0.2 2.8 0;7 0.95 0.2 0.3 0.1 0.55 0.15 0.1 0.1  K x 104 cal.deg. cm. sec.  J  dT  a  2.45 2.30 2.55 1.81 1.95 « 2.26' 1.79 2.56 1.18 1.18 1.24 2 51 2.04 1.39 1.43 1.75 1.87 2.05 1.95 2.34 2.23 2.23 2.61  37 e r r o r i n measurements of low thermal t h i c k n e s s was  more d i f f i c u l t  conductivity.  to measure, and  The  the accuracy  i t s measurement cannot he c o n s i d e r e d to be more exact w i t h i n 5%  t  a major source o f e r r o r .  i n t r o d u c e d by thermal change i n a r e a .  expansion  The  of  than  change i n t h i c k n e s s  4as n e g l i g i b l e , as i s the  The measurement of power depended upon the  accuracy o f the currart and v o l t a g e r e a d i n g s , which were made on meters whose s c a l e s were c a l i b r a t e d to m i l l i a m p s , and  to .05 v o l t s r e s p e c t i v e l y .  S i n c e the needles passed  m i r r o r s i n o r d e r to e l i m i n a t e e r r o r s due  to parallax,  meters could be read to the n e a r e s t m i l l i a m p , and .01 v o l t .  the  the n e a r e s t  T h e r e f o r e the e r r o r i n measurements o f c u r r e n t  and v o l t a g e i s everywhere l e s s than 1$. was  over  The  lead resistance  about 1% of the h e a t e r r e s i s t a n c e , and the change i n  r e s i s t a n c e with temperature, measurements, was  as determined by the  small, therefore n e g l i g i b l e error i s  i n t r o d u c e d by t h i s e f f e c t . t u r e was  electrical  Measurement o f a b s o l u t e tempera-  good to the n e a r e s t degree, and  s i n c e the  conductiv-  i t y measurements i n v o l v e d a range o f t e n degrees over sample, t h i s may  be c o n s i d e r e d s u f f i c i e n t l y  the  accurate.  A more s e r i o u s d i f f i c u l t y l a y i n the measurement o f temperature d i f f e r e n c e .  The  thermocouples had  been  c a l i b r a t e d to the n e a r e s t 2 ^ V, which i s e q u i v a l e n t to the n e a r e s t t e n t h degree a t lowest one  temperatures,  t w e n t i e t h a t room temperature.  and  to about  T h i s I n d i c a t e s an  accuracy of about 2% i n t h i s measurement.  The guard b l o c k  e r r o r had been c a l i b r a t e d u s i n g a set o f p r e l i m i n a r y r e a d i n g s  38 and was n e g l i g i b l e throughout most of the work, except a t temperatures below -150.  I n a l l , the expected e r r o r  was  on the order of 5%; however the grouping o f the readings taken i n d i c a t e d a g r e a t e r e r r o r than t h i s , and probably the readings cannot be t r u s t e d to be more a c c u r a t e than  8$.  Discussion of Results. The r e s u l t s p l o t t e d f o r the u n s t r e t c h e d sample w i t h low sulphur content show s i m i l a r i t y and Ivey.  The hysteresis l o o p was  temperature this  found t o extend over a wider  range, and t o s t a r t a t h i g h e r temperatures.  r e s p e c t i t shows a s i m i l a r i t y  samples o f GR-S 40°  to those o b t a i n e d by Dauphinee  by I v e y . (13)  In  to t h a t found f o r the o l d  Some p o i n t s i n the range above  show s i g n s o f a double value f o r the thermal c o n d u c t i v i t y  as found by Dauphinee (12) f o r n a t u r a l rubber.  The n u m e r i c a l  v a l u e o f the thermal c o n d u c t i v i t y , I t w i l l be n o t i c e d , i s v e r y c l o s e to t h a t found f o r n a t u r a l rubber. are  These  similarities  to be expected, s i n c e b u t y l shows s i m i l a r i t i e s  G.R.S. and Hevea i n i t s o t h e r p h y s i c a l p r o p e r t i e s .  to both Like  G.R.S. i t has many weak secondary l i n k a g e s , and hence shows a considerable non-reversible e l a s t i c i t y . it  Like natural  i s capable o f g r e a t e l o n g a t i o n s and c r y s t a l l i z e s  stretching.  rubber  r e a d i l y on  *  The v a l u e s of the thermal c o n d u c t i v i t y f o r ^theij s t r e t c h e d samples are about 20$ lower than those f o r the same sample u n s t r e t c h e d , and  show the same g e n e r a l dependence on  temperature, however the h y s t e r e s i s l o o p has e i t h e r disappeared completely, or been g r e a t l y reduced i n magnitude.  This  39 This again  shows agreement w i t h the r e s u l t s fof n a t u r a l  rubber and G.R.S. i n which the h y s t e r e s i s l o o p i s reduced by s t r e t c h i n g . These measurements were made o n l y i n the d i r e c t i o n perpendicular  t o the s t r e t c h , hence f o r the a n i s o t r o p i c  s t r e t c h e d sample o n l y one o f t h e components o f the c o n d u c t i v i t y tensor was measured.  On the b a s i s o f the k i n e t i c theory  o f rubber a s developed by Guth (15) expected. chains  t h i s decrease i s to be  T h i s theory uses as a model o f rubber, a set o f  connected i n t o a network by l i n k s o f v a r y i n g  strength.  Along the c h a i n a r e strong m o l e c u l a r bonds, on the order o f magnitude o f those i n s o l i d s , w h i l e between the chains  act  weak Vaii d e r Waal's f o r c e s , s i m i l a r t o those a c t i n g between the molecules of a l i q u i d .  The p e c u l i a r p r o p e r t i e s o f rubber  a r i s e from the freedom o f the m o l e c u l a r u n i t s i n t h e chains to r o t a t e about the bonds, hence the freedom o f the chains to adopt v a r i o u s the  c o n f i g u r a t i o n s i n the m a t e r i a l .  sample i s s t r e t c h e d these chains  When  a r e l i n e d up i n the  d i r e c t i o n o f s t r a i n , and t h e e l a s t i c f o r c e s a r e produced as a r e s u l t o f the tendency o f Brownian motion t o b r i n g them back t o a s t a t e o f h i g h e r  entropy.  I t seems reasonable t o  expect t h a t the r a t e o f t r a n s f e r o f energy down the c h a i n would be on the order o f t h a t i n c r y s t a l l i n e s o l i d s , w h i l e t h a t across  the chains would be lower l i k e t h a t o f o r g a n i c  liquids. When the sample i s s t r e t c h e d then, the c o n d u c t i v i t y i n the d i r e c t i o n o f s t r e t c h should  i n c r e a s e , and t h a t  40 p e r p e n d i c u l a r to s t r e s s should decrease.  An attempt  made to use Forbes' method to get an approximation conductivity i n d i r e c t i o n of stretch.  was  to the  R e s u l t s were u n c e r t a i n  but i n d i c a t e d an i n c r e a s e . The more d i f f i c u l t  r e s u l t s f o r the sample w i t h 10$ to e x p l a i n .  sulphur were  The h y s t e r e s i s l o o p d i d not  occur, and the c o n d u c t i v i t y charged much more s l o w l y w i t h temperature. average  value.  A few p o i n t s were o b t a i n e d , g i v i n g twice the There were too many o f these to c o n s i d e r as  accidental,-but. an explanation i s rather d i f f i c u l t .  The  thermal c o n d u c t i v i t y o f sulphur has been measured by Kaye and H i g g i n s (16) but u s i n g the a d d i t i v e assumption  for  the e f f e c t o f f i l l e r s on the c o n d u c t i v i t y does not e x p l a i n the r e d u c t i o n i n thermal c o n d u c t i v i t y a t room If  temperature.  the r e s u l t s a r e s i g n i f i c a n t , the change must be due  to  some m o d i f i c a t i o n i n the s t r u c t u r e o f the polymer, and i t would be i n t e r e s t i n g to f i n d the e f f e c t o f i n c r e a s e d sulphur content on the thermal c o n d u c t i v i t y o f other rubbers. Using the v a l u e o f the volume s p e c i f i c heat o f GR  - I , found by Hamil, Mrowca and Anthony (17), the v a l u e  of  the thermometric c o n d u c t i v i t y a t room temperature  is  -4 found as about 7.5  x 10  cm/see. which i s i n f a i r agreement  w i t h t h a t found by Rehner//c>) Using the Bridgman formula  (3)  w i t h v a l u e s f o r the  s i z e of the u n i t c e l l o f B u t y l g i v e n by Bunn (1) for  the sound v e l o c i t y determined  and  values  by the author, g i v e s a  value f o r the thermal c o n d u c t i v i t y of 4.3  x 1074  cal/deg-sec-cm.  which i s about  20% too h i g h , b u t . i s i n the proper  range.  I n summary we may say t h a t , 1. The thermal c o n d u c t i v i t y o f B u t y l decreases w i t h temperature  showing a double v a l u e a t temperatures between  0?C. and - 8 0 ° , that i s down to the second order t r a n s i t i o n r  point.  The p r i n c i p a l curve may be roughly r e p r e s e n t e d  by three s t r a i g h t l i n e s . ^ From -180° to ^120° the thermal c o n d u c t i v i t y i s roughly g i v e n by K =(.5 f .01T) x 10 f from - 120 to - 50 i t has the constant v a l u e o f 2.1, and from -50 t o room temperature .017 (T - 100) x 10~4 "J3ie  ;  i s approximately  i n h e r e T i s i n degrees a b s o l u t e  v a r i a t i o n of thermal c o n d u c t i v i t y w i t h  temperature'  does not e x a c t l y f o l l o w t h a t o f the s p e c i f i c heat as determined f o r p o l y i s o b u t y l e n e by F e r r y and P a r k s ; (19) T h i s i s shown by the accompanying t a b l e o f thermal diffusivity. TABLE V temperature  Deg.C  / 20 0  D i f f u s i v i t y cm. per sec.XlO^ 7.25 6.2  . 6.4  - AO  - 80 -120 -160  9.3 11.6 9.8  2.The stock c o n t a i n i n g 10$ sulphur showed a d i f f e r e n t v a r i a t i o n , the c o n d u c t i v i t y changing o n l y s l i g h t l y over the temperature  range.  This i s surprising  the known v a r i a t i o n i n the s p e c i f i c heat.  considering  3.  F o r t h e s t r e t c h e d stock, an i n d e f i n i t e h y s t e r e s i s  loop was found, and t h e f l a t p a r t o f the curve w i t h the h y s t e r e s i s e f f e c t i n the unstretched Before t o o many c o n c l u s i o n s  associated sample vanished.  a r e drawn, a more  thorough study o f thermal c o n d u c t i v i t y o f polymers must be undertaken.  T h i s work, i t i s hoped, i s only a small  part  of the experimental s t u d i e s o f thermal c o n d u c t i v i t y t o be made a t the U n i v e r s i t y o f B r i t i s h Columbia, which s t u d i e s should l e a d to a c l e a r e r understanding o f the somewhat obscure mechanism i n v o l v e d i n heat t r a n s f e r through  solids.  BIBLIOGRAPHY A l l a n & Maxwell, "A Textbook o f Heat"- P a r t 1 (Macmillan - 1944) F. Henning,, ( E d i t o r ) , "Handbuch d e r P h y s i k " Jakob - "Warmeleitung"  (vol.11)  Bridgman, "The P h y s i c s o f H i g h P r e s s u r e s " ( B e l l & Sons - 1931) Glazebrook ( E d i t o r ) , " D i c t i o n a r y o f A p p l i e d S c h o f i e l d , "The Conduction o f Heat"  Physics" (vol.1)  A l l a n & Maxweil, " Textbook o f Heat" - P a r t 2 (Macmillan - 1944) Carslaw, " I n t r o d u c t i o n t o the Mathematical Theory o f the C o n d u c t i o n o f Heat i n S o l i d s " , (Dover P u b l i c a t i o n s - 194.5) K i n g , Phy. Rev. G r i f f i t h & Kaye,  6, 437, P r o c . Roy. Soc. A . —  (1915)  104. 71,  (1923)  L*. S. Frumkin & Y. B. Dubinker, Rubber Chem. & Tech.  12, 361, (1940)  J . Rehner, " J o u r n a l o f Polymer S c i e n c e — 2,263, (1947) A. Schallamach, P r o c . Phys. Soc. London-53.214. T. McC. Dauphinee, "Heat C o n d u c t i v i t y o f Rubber a t Low Temperatures" M.A.Thesis, U. B. C.(I945)  (1941)  D. G. 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