UBC Theses and Dissertations

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UBC Theses and Dissertations

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

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/ L £ 5 &? • THE HEAT CONDUCTIVITY OP RUBBER - -AT LOW TEMPERATURES by THOMAS MoC. DAUPHINEE A t h e s i s s u b m i t t e d i n p a r t i a l f u l f i l m e n t o f the re q u i r e m e n t s f o r the degree o f Master o f A r t s i n the Department o f P h y s i c s . The U n i v e r s i t y of B r i t i s h Columbia A p r i l 194.5 A GKNQWLEDGEDiMT The Author wishes to thank Dr. H. D. Smith whose supervision of thi s work has been of great assistance and encouragement. And, in addition, the Author wishes to express his appreciation to the following for the i r contributions: The Department of Physics, University of Notre Dame, in providing samples of elastomers of known composition, as well as valuable information gained through correspondence with Drs. E. Guth and R. S. Anthony of that department. Mr. L. V. Holroyd for constructing the thermocouples and assisting in their installation,, and for wiring the instrument panel. Mr. N. Barton for a l l photography. INDEX I. INTRODUCTION Elastomers 1 The theory.of e l a s t i c i t y 2 Thermal conductivity 6 Methods of measuring conductivity 6 II . EXPERIMENTAL The cryostat and evacuation c i r c u i t 9 The conductivity measuring unit 10 The stretchers 11 The heat leads and cooling c i r c u i t 11 The heating circuit.: 15 The thermocouple c i r c u i t 14 The potentiometer c i r c u i t 16 The calibration and i n s t a l l a t i o n of thermocouples i . Fixed points 17 i i . Calibration 18 l i i . I n s t a l l a t i o n 19 The method of taking readings 20 The readings taken 21 II I . RESULTS The equation and method of calculation 23 i * The power factor 23 i i ; The dimension factor 24 i l l . The temperature ^factor 25 Probable error 25 The rubber sample 27 Experimental results 28 Interpretation 35 IT. CONCLUSION 36 I. INTRODUCTION An elastomer is defined as a substance exhibiting long-range, reversible e l a s t i c i t y . The best known of these i s , of course, rubber, the quality being so t y p i c a l in i t s case that the rapidly expanding group of other elastomers i s frequently called ^synthetic rubber*" As a result, of recent rubber shortages much theoretic a l and experimental work has been done on elastomers, but the study of their thermal conductivity i s one which, to date, has received l i t t l e attention. This has been due not so much to the greater usefulness of other f i e l d s of research in the understanding of the problem of e l a s t i c i t y as to the necessity of concentrating on production in quantity and de-velopment of the immediately-useful primary characteristics such as stretch, wear resistance and strength. It seems safe to assume, however, that with decreased stress on immediate production the study of further c h a r a c t e r i s t i c s - w i l l play a much more prominent role. A knowledge of thermal conductivity and the ef-fect on i t of change of temperature, amount of stretch and composition has an important bearing on many f i e l d s of both commercial and theoretical elastomer research. Examples of th i s are: (a) Removal of the heat produced by constant fl e x i n g . This i s a major problem in the t i r e industry and in many other cases where elastomers act as shock ab-, sorbers. (b) Obtaining homogeneous vulcanization of large masses. This requires a knowledge of temperature gradients within the mass in order to determine the d i s t r i b u -tion of sulphur required. (c) Determination of equations of state of elastomers. (d) Determination of the temperatures at which changes of state occur, (e.g. crystallization etc* J Changes of conductivity, coefficient of volume expansion, e t c , often accompany these changes, (e) Assistance in analyzing other long-chain hydrocarbons. The rubber molecule, because of i t s r e l a t i v e l y simple structure, i s easier to study than more com-plex molecules but behaves in a manner similar to many of them* The theory of e l a s t i c i t y Elastomers have certain properties in common^  both in behaviour and molecular composition, which must be explained by any theory of e l a s t i c i t y . The most evident are: (a) They exhibit long-range, reversible e l a s t i c i t y . (b) They heat when stretched and cool i f allowed to relax. (c) Stress for any given degree of stretch i s a linear function of temperature. For a l l but small stretch the stress increases with temperature. (d) They exhibit both temporary and permanent p l a s t i c i t y . (e) They harden when cold and tend to be thermoplastic at high temperature. (f) They show cry s t a l l i n e characteristics at extreme stretches. (g| They have characteristic molecular structure: 1. Very long chain molecules with many single bonds. i i . More or less free rotation around the single bonds. , i i i . lew cross bonds between molecules.' The sec-tions between cross bonds long and r e l a t i v e l y free to move. It i s only recently that the f i r s t successful theory to explain 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)* It was shown that the above characteristics could be qualitatively and quantitatively ex-plained on the basis of a s t a t i s t i c a l model having the struc-ture previously described. Their picture i s as follows. The elastomer molecules are long and have r e l a t i v e l y few cross bonds. Consequently large numbers of the basic unit w i l l be free of intermo1ecular t i e s . Since there are single bonds between the units rotation about these bonds w i l l be possible, subject to the provision that the valence angle remain r e l a t i v e l y constant. This quasi-freedom of rotation means that the molecule can c o i l up in almost any configuration and that we might expect thermal agitation to keep the parts in constant motion. Thus i n the unstretched state the molecule would "be curled up in a disordered.configuration corresponding to i t s most probable position. I f we are considering large numbers of molecules s t a t i s t i c a l l y i t can be shown, for the case of a chain made up of successive molecules, that the probability of the ends of the chain being in a region dL at a distance L from one another i s : Probability - P(nN:b) L dL = Ae L^dL where n i s the number of single bonds per molecule; N> the number of molecules in the chain; b, the length of the unit molecule (isoprene, for example, in the case of pure rubber); and B * ^ • ft—• . A i s a normalizing constant. SnW b*- ^ to By d i f f e r e n t i a t i o n . — - 2 A L ( e " B L ) ( l - BL ). dL This gives minima at L 8 0 and , and a maximum at 1 = .. — , t h i s being the most probable length. Correcting 3 for constant valenoe angle, a, we get the most probable length to be 3nNbL where b^s b Tan We note here that the straight l i n e configuration and the case where the two ends are together are almost equally improbable. From the above discussion we can assume that i n the unstretched state the average separation of the ends i s the most probable one. On stretching, the ends of the chains would "be moved from the most probable position to one less probable with the necessity of doing work. This work, in turn, i s converted into increased energy of thermal agitation, with consequent increase in temperature ( b ) H . When the mole-cules are in any but the most probable state the Brownian movement tends to bring them to that state causing a constant p u l l on the ends and return to the o r i g i n a l form i f released (a), accompanied by cooling (b). If the substance i s held in a stretched position 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 effects (d) are linked up with cross bonding of the molecules. If there are few bonds the molecules s l i p past one another easily and the substance can change form. If there are many bonds the units should hold their r e l a t i v e positions. Crystalization i s explained on the basis of l i n i n g up of the molecules when almost straight (e)» In the s t a t i s t i c a l analysis of stress-strain characteristics the substance i s compared with a gas at con-stant volume and the effects divided into the sum of two com-ponents; P u, the internal energy contribution due to i n t e r -molecular forces, and P s the k i n e t i c energy contribution. s Properties explained are referred to by l e t t e r as l i s t e d on page 2* By comparison with Yan Der Waal 1s gas equation (4) (P + f>)(V - b) = RT " or p s - 4 - ^ , V Y3" ^ Y - b Compare p » P u + P s . By analysis of this and other thermodynamic relations (3) explanations have been given for inversion points in the stress temperature curves (c) and the t y p i c a l , S-shaped, stress-strain curve shown by a l l elastomers. Thermal Conductivity The theory of thermal conductivity of elastomers i s p r a c t i c a l l y an untouched f i e l d . Since they exhibit pro-perties of solids, liquids, and even gases they could be expected to exhibit conductivity properties of a l l three. There would- almost certainly be a high proportion of conduc-tion by interbombardment of the Brownian type. In addition i • some conduction could be expected due to transfer of energy along the length of the molecule through the bonds. Gross conduction by means of intermolecular bonds would be expected to increase with vulcanization while thermal bombardment would decrease because of reduced freedom of motion. No s t a t i s t i c a l treatment of t h i s problem has been made to date. Methods of Measuring Conductivity The princi p l e of measurement of conductivity i s the same for a l l methods, i»e. to measure the quantity of heat passing through given cross section of material with a given temperature gradient across i t . The d e f i n i t i o n of thermal conductivity (10) i s - "The time rate of transfer of heat, by conduction, through unit thickness, across unit area for unit difference in temperature," In the calculation of the amount of heat transferred i n any system of units the coefficient of thermal conductivity occurs as a proportionality factor, and can be defined by the equation 5* Kt. A ( V ~ Tf ) or K s 2t • .A * ' ?•: ',„.. t A T 3 - T A where K i s the coefficient of thermal conductivity; Q,, the quantity of heat transferred; A, the cross-sectional area; T and T , the temperatures on either side; d, the thickness; and t, the time. In c .g.s. units K has the dimensions .( Oal; S e o r 1 Gm"1 D e g * " 1 } , Methods of measuring conductivity f a l l into three main classes. (a) Measurement of rates of cooling. One such method (5) consisted of measuring the rates of cooling at the centre of large rubber spheres kept in a constant temperature chamber. It has the disadvantage that i t actually measures the quotient K , where K i s the thermal conductivity; C, the s p e c i f i c 'Cd~ heat; and d* the density. 8 e (b) Measurement of heat carried through to the low temp-erature side* . i . Measurement of the r i s e in temperature of a l i q u i d or s o l i d absorbing the heat transferred.. This may be done by measuring the r i s e per unit time, or by measuring the r i s e in temperature when a constant flow of l i q u i d passes through the apparatus; 11. Measurement of the rate of evaporation or melt-ing caused by the heat transferred* One ex-periment of th i s type (6) consisted of measuring the quantity of nitrogen evaporating from a bag of the substance to be measured when the bag was immersed in l i q u i d oxygen; This method i s most suitable for high conduc-t i v i t i e s or large surfaces, otherwise the amourits become un-measurable. (e) Measurement of the quantity of heat required to main-ta i n a constant temperature gradient. (7), (8). This method i s the one used in the experimental work here-in 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 oirouit (Plate IV) In order to properly insulate the apparatus at the low temperatures at whioh the experiments were conducted i t was necessary to construct a oryostat that could he evacuated, to provide i n l e t s and outlets for cooling tubes, thermocouples and evacuation apparatus, and at the same time provide reasonable f a c i l i t i e s for adjustment of the degree of stretch. This was accomplished by the unit shown on Plate IV. The sides of the cryostat were made of 1/8 i n . brass plate, as was the c y l i n d r i c a l tower, A, containing the cooling unit. The top of the tower and the sides of the oryostat were faced with 1/2 i n . wide brass flanges, B, with tapped holes, C, part way through for studs, D, which held the side plates, E, (also constructed of 1/8 i n . brass) in place. Between these pieces and the flanges where rubber gaskets, F, held in place on one side by glyptol and sealed on the other with stopcock lubricant. The thermocouples were led into the cryostat through a double gasket (see small diagram) on one side which insulated them from the metal. The cover plate, G, of the tower had two holes for cooling tube outlets, H; the seal around them being accomplished by means of rubber stoppers, I, and stopcock lubricant. At each end of the cryostat was a PLATE V THE • CONDUCTIVITY MEASURING UNIT Bottom view. Thermocouples leading away from the bottom are shown by solid lines, those on top are shown by dotted li n e s . Method of wiring central heating blocks. Installation of thermocouples a. Copper block. b. Glyptol. o. Thermocouple. - 10. hook, J, to which the stretchers were attached, and at the front (inside) were thumbscrew clamps, K, to hold the s t r e t -cher cords. Suspension of the main apparatus was accomplished by bakelite supports (not shown in the diagram) which f i t t e d under the l i p , M, of the cooling unit. The cryostat was evacuated by means of a Cenco Hyvac pump through the outlet, 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 into the cryostat' when •necessary; The conductivity measuring apparatus (Plates IV, V, VI - 5) This apparatus was modelled after Schallamach*s (8) apparatus for measuring conductivity at low temperatures, with very considerable revision to allow for stretching ex-periments and the consequent increase in the amount of heat to be absorbed. The heat was generated in resistance wire, A, (Plate Y) which was threaded through holes in the copper heating blocks, B and C. The oentral block, G, was 4 cm. long, 3.2 cm. wide and .6 cm. thick while the blocks, B, were each 2 cm. long and the same width and thickness. The outside copper blocks, D, were tapped for studs, E, (to hold the heat leads, I , securely in place). Clamp, F, pressed the whole unit t i g h t l y against the two rubber pieces, G, to ensure good contact. A t o t a l of twelve thermocouples were attached to the blocks as shown in the diagram at. H. The method of i n -s t a l l i n g i s also shown on Plate Y (bottom). The method by which the thermal conductivity was 11. measured.can readily be seen. E l e c t r i c a l energy was converted into heat in the heating blocks and the only path for the heat to follow 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 thermo-couples and t h i s , along with the amount of heat produced and the dimensions of the rubber, was s u f f i c i e n t to determine the conductivity. The inner heating block, C, was the one used for actual measurements^ the outside heating blocks, B, served the purpose of a guard ring to prevent conduction l a t e r a l l y along the rubber. The stretchers (Plate IV) The rubber st r i p s ; Q,,- were clamped securely at each end by means of clamps, R (Plate IV), to which were at-tached small pulleys, S. Other pulleys, T, were attached to the hooks, J, at each end of the cryostat. The pulley arrange-ment was threaded with strong cord, U, giving a mechanical advantage of three. When stretching was completed the ends of the cords were held by thumbscrews, K. Two li n e s , V, marked on the rubber, served as markers and stretch was calculated by measuring between them. Heat Leads and cooling c i r c u i t (Plates IV, V, VII) The heat that passed through the rubber strips, as well as any heat that was carried to the apparatus by the str i p s and by radiation from the side walls, was carried away through thin f l e x i b l e double s t r i p s of 1/52 i n . copper,. 1 i n . wide, a (Plate IV). Pieces of aluminum f o i l , b, between these and the main blocks ensured good heat contact. The thin s t r i p were soldered and bolted to r i g i d 1/4 i n . copper leads, c, which carried the heat to the top piece, d, also of 1/4 i n . copper. At the centre of the top piece was a raised part, e, with a l i p , M, to support the unit, and an internal thread into which the threaded end, f, of the s o l i d copper core of the cooling c o i l , g, was screwed. The outer part of the core had a s p i r a l groove turned in i t , and after the cooling c o i l was wound into the.groove i t was soldered in place. An end view of the heat lead system i s shown in Plate VII-5. Cooling was accomplished by the c i r c u i t shown in Plate VI. The vacuum flask, 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, B, operated as a suction pump. From the vacuum flask, a mixture of gaseous and l i q u i d oxygen was drawn through a thin, i n s u l -ated, glass tube, C, to one end of the cooling c o i l , D, in the cryostat. Here the remaining l i q u i d oxygen was evaporated by the heat carried up from the main unit. 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 regulated the amount of oxygen drawn through. The manometer, G, was equipped with a two-way stopcook, H, and could be used to indicate the amount of vacuum on either side of the valve, F. In close proximity 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 . This valve served the double purpose of 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 o i l - l u b r i c a t e d ) . From th i s valve, I, the mixture was drawn into a carboy, J, which served to cut down fluctuations 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. The o r i g i n a l method of heat control used by Sohallamach (8) was t r i e d but found inadequate to carry the greater amounts of energy required for t h i s apparatus. Diagrams of th i s and three other methods t r i e d , as well as the o r i g i n a l type of heat lead, are shown in Plate VII. A l l of these methods had the disadvantage of re-quiring a l i q u i d a i r container within the apparatus. The method shown in f i g . 4 was the most successful of a l l as far as control 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 heating c i r c u i t (Plate VII) Power for the three central heating c o i l s of the main unit, H-l, H-2, H-3. (Plate VII) was supplied by four 6-volt storage batteries, B, arranged to give 12 volts across the unit as shown in the diagram. Control of the whole was provided by a master switch, S, and a 40 ohm variable rheostat, C, with a 380 ohm rheostat in p a r a l l e l for fine adjustment. The c i r c u i t was then divided into three parts. Part 1 led d i r e c t l y to a double-pole, double-throw switch, S-l, connected to make i t possible to shut off the c i r c u i t , get a direct con-nection through, or put a 0 - 600 m.a. milliammeter A- 1 in series. 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 central heating c o i l , H-l, and then back to the batteries. The potential difference across the heating c o i l was measured by means of a 0 - 5 volt voltmeter, V, gra-duated to 1/30 volt. Branches 2 and 3 of the heating c i r c u i t were i d e n t i c a l . Each had a 40 ohm rheostat, R - 2, R - 3, to give individual control, followed by a double-pole, double-throw switch, S -2, S - 3, which made i t possible to put in series a small milliammeter, A - 2, A - 3, or, for accurate readings, ammeter A - 1. From the switch each c i r c u i t ran to one of the other heating blocks, H - 2, H - 3, and back to the batteries. The thermocouple c i r c u i t (Plate IX) Considerable d i f f i c u l t y was encountered in set-ti n g up a satisfactory thermocouple c i r c u i t . The thermocouple pyrometer i s by far the best instrument for this type of work because of i t s negligible heat capacity, small size, small time lag and f l e x i b i l i t y , but i t s operation requires great care i f accurate results are to be attained. Contact potentials made i t necessary to design a c i r c u i t completely of copper except for the copel element of the copper-copel thermocouple and the potentiometer t e r -minals which could not be changed. Copper strips were placed over a l l contacts, thumbscrews, etc., to make a complete c i r -P L A T E IX 15. cult and an all-copper multiple switch,A,was made to replace the radio switch f i r s t used. To check for stray e.m.f's. in the switches and potentiometer the c i r c u i t was made completely reversible, even to the current in the potentiometer. This was accomplished by placing ordinary reversing switches with copper st r i p s over the brass parts in the cold junction 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 addition the multiple 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 junction were kept at the same temperature by running them into a f e l t - l i n e d zone box,B,with free space inside about 6 i n . each way. There, the ends were wound around copper leads and clamped tight with thumbscrews on two v e r t i c a l panel boards , C. The hot junctions of the twelve thermocouples were fastened in grooves in the heating blocks,H, the leads, D, taken out between the gaskets of the cryostat, E, and into the zone box,B. The ends of the thermocouples were wound around the copper leads, F, and clamped tight on the panels, Q by means of thumbscrews, G-. The copper leads were taken d i r e c t l y to the large multiple reversing switch, A. By wiring the two rings of contacts in pairs, as shown in the diagram at I, the reversing of the thermocouples was seoured. Spring contacts, L, covered with copper, were connected by means of copper strips, K, and other spring contacts, J, to copper rings, M, from which one lead went, d i r e c t l y to the reversing switch, N, and the other went to the potentiometer, 0, and thence to the other contact of the reversing switch* From the reversing switch leads were taken hack to the zone box where the ends of the cold junction were attached. The cold junction, P, was immersed in an ice bath. The potentiometer c i r c u i t (Plate X) Power was supplied for the potentiometer by a 2 - volt storage battery, B (Plate X). One side of the c i r -cuit was taken direct from the double pole switch, 0, to a reversing switch, D. The other side was taken f i r s t to an ammeter, A, then to an oil-immersion, slide-wire rheostat, •E, with a fine adjustment and on to the other side of the reversing switch. The other terminals of the switch were connected d i r e c t l y to the potentiometer, P* An Eppley stan-dard c e l l , F, (P.D. m 1.01890 volts) was used to set the potentiometer. The e.m.f• terminals were connected as des-cribed in the thermocouple c i r c u i t to the multiple switch, G, and the cold junction reversing switch, H. A Leeds and North-rup mirror galvanometer, I, sensitive to less than 10 volts was used with a 600 ohm damping resistance, J, in p a r a l l e l . Light for the mirror was supplied by a small spotlight and reflected to a translucent scale near the instrument panel. The potentiometer i t s e l f was a Weston model -5 —6 having three ranges with s e n s i t i v i t i e s of 10 , 10 and 17. -7 -6 10 volts, respectively. Since the 10 volt range was suf-f i c i e n t for this work i t was used throughout. Calibration and i n s t a l l a t i o n of thermocouples i . Fixed Points. Three fixed points were used in calibration, the freezing point of water, the freezing point of mercury and the sublimation point of COg. The ice point was obtained was obtained by immersing the thermocouples in a bath of crushed ice and water in a vacuum flask. At no time was any measur-able change in the ice point noticed. This i s to be expected, as the ice point i s easily reproducible to 1/1000 ° C, (9a) The mercury used for the mercury freezing point had been r e d i s t i l l e d by the Chemical Engineering department of the University of B r i t i s h Columbia and seemed to be of good purity. When a cooling test was made the freezing point proved to be very sharply defined, and could be maintained constant to the nearest microvolt (1/30 °C.) for over an hour. (Plate XI) When calibrating in mercury the blocks and the thermocouples were ooated with Duco Cement to prevent amal-gamation, and held well below the surface of the mercury. The mercury container was placed in dry ice. Readings were taken as the mercury cooled and the freezing point was considered reached when there had been no difference in thermocouple readings for f i f t e e n minutes. When the freezing point was reached the remaining thermocouples were checked repeatedly. The sublimation point of carbon dioxide required a completely different arrangement because crushed dry ice has a different temperature when mixed with a i r from when i t i s in an atmosphere of carbon dioxide. Two methods were used as checks on one another. In the f i r s t the thermo-couples were placed in a large Dewar flask and crushed dry ice packed around them. The flask was then covered to pre-vent a i r from re-entering and the whole l e f t for thirty-nine hours when readings were taken without disturbing the flask in any way* In the second method the procedure was changed by putting a small heating c o i l at the bottom of the Dewar. The carbon dioxide evaporated by the c o i l flushed out any a i r that was l e f t in the flask after f i l l i n g , and an equilibrium temperature was reached very quickly (9b)(Plate XII). This equilibrium temperature gave the same thermocouple reading as the previous method. Temperature was corrected for. baro-metric pressure by using the formula:-T = ( -78 +• 0.1595 (P - 760) - 0.000011 (P - 760) 2) C (10a) i i . Calibration* Using the differences in thermocouple reading from the Bureau of Standards values for copper-constantan at these three points (9b) a parabolic deviation curve of the form dE = a-bbt+ct was drawn. The constants a, b and c were determined by substituting for t and dE at the fixed points. "A" i s the deviation at 0°0. NO. S 36 GRAPH PAPEE, SMITH DAVIDSON a WEIGHT, LTD. 19. b .= (dE, ~a)tt-(dE„-a)t'~ c « (dE.^a)t, -(dE,-a)t,. With this graph and the standard copper-constantan tables (9b) any temperature could be calculated. - When-, tiro • thermocouples had been calibrated in this manner the remaining ones were compared with them at various temperatures using a mixture of alcohol and dry ice in a vacuum flask* Dry ice was packed around the outside of the flask to prevent any rise in temperature, and rock wool around the whole to insulate i t . By this means graphs of deviation from the previously calibrated thermocouples were drawn for each of the remaining ones. It was found that because of the fact that a l l thermocouples were made from the same piece of Copel wire most deviations were very small and almost independent of temperature, apparently being chiefly due to individual contact potentials i n the zone box or leads, i i i . I n stallation* The thermocouples were set into the blocks by making a groove from the edge of the block with a fine cold chisel* (Plate V) This groove was f i l l e d with glyptol and the thermocouple inserted in i t . The raised edges of the groove were then pounded down over the wires and the surface f i l e d and sandpapered smooth again. In th i s manner i t was possible to get the thermocouples very close to the surface and yet keep the surface perfectly smooth and so ensure good contact. The method of taking readings The procedure in taking 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 quickly. 2. When the required temperature was almost reached the oxygen was turned off and heat turned on f u l l to stop the cooling. 3. 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 stationary state was reached. 4. By adjusting the current in the heater coi l s the temperature d r i f t in the outside blocks was com-plete l y stopped* 5« As soon as the outer blocks were stationary the current in the heater blocks was adjusted to give constant temperature in them as well. 6. The temperatures of the two small heater blocks (guard blocks) were compared with the temperature of the centre one and adjusted u n t i l very nearly the same. 7. Both outer and inner blocks were checked for d r i f t of temperature, and i f there was any i t was stopped 21. 8* When the temperature was stationary everywhere read-ings were taken of the current and voltage of the . centre block. 9. Two complete sets of readings were taken of the thermocouples. If, during the course of a set of readings, there was a d r i f t of more than one micro-volt the system'was readjusted and a l l readings repeated. 10. Current and voltage were again read. In any appre- • ciable change occurred a l l readings were repeated. This process required on the average around forty minutes to complete, provided that the apparatus ?;as running well. The fastest time for any reading was twenty minutes. Because the heating c o i l s could only carry a limited current the readings taken for r i s i n g temperature required an hour or more. Readings taken i Many preliminary readings and test runs were made before the actual 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 for use down to about -100 °C, but because of the much larger size and heat capacity of the main unit considerable changes had to be made before the heat removing system ivould 22. reach that temperature* After more readings were taken i t became appar-ent that much lower temperatures would be needed to overcome supercooling effects and the cooling unit was redesigned to -the form f i n a l l y used. (Plate IV, V, VI) It i s with t h i s form that a l l the f i n a l readings were taken. Readings were taken for increasing and decreas-ing temperatures in the range from -170° C. to 4-40° C. and for 0%, 50% and 100% stretch. After the 0% and 50% stretch read-ings were completed i t became apparent from 100% stretch re-sults that more readings would have to be taken to check parts of the results. This was done for both 0% and 50% stretch with the result that readings formerly thought to represent experimental errors were shown to f i t into.the general pattern. For each degree of stretch measurements of the rubber were taken using a pa i r of thin calipers for width. Thickness was determined by measuring with a micrometer the t o t a l thickness of the blocks with no rubber between and again when the strips were stretched i n place. In a l l cases the actual measurement of conduc-t 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. In this way edge effects were eliminated. Since the only surface of the inner block that was exposed to radiation from a warmer surface was the bottom edge extraneous heat sources were neg-lected. III. RESULTS The equation and method of calculation The equation of thermal conductivity, as shown previously, can be put into the form:-' E £ . d . 1 t A T^-T, where Q, i s the amount of heat transferred; ty the time; A, the area of the conducting surface (assuming here that opposite faces are p a r a l l e l ) ; d, the thiokness; and T^-T( , the tempera-ture difference between the two faces. We may think of K as consisting of three factors, namely: a power factor, £ ; a dimension factor, A ; and a . t ' d temperature factor, 1 or 1 • The determination of each T^-T, dT factor required a separate set of readings. i . Power factor. To determine the power factor i t was necessary to find what proportion of the e l e c t r i c a l energy was used up in 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 respectively we have; -*c = J a - . = *a ~ ^7 24. YQ = Y v - IcR! I k Power = P = IqVQ » ( I a - R v )(Y V - I CR!) watts. 8 - - I a I o H i + YylcRi watts. Ignoring the slight difference between I c and I a for small corrections, and using the relations Y y - Y vI a(R 0+Ri) a n d I a » I a Y v Rn+Rn Rj P = I a Y v (; R v - B t - R#f-Ri) watts. where Rj * 0.14 ohms; R v » 300 ohmsj R c R i « 5 ohms. Thus £ « 0.954 I a Y a watts, t = 0*328 l a Y a Calories/second. ii» Dimension factor The dimension factor i s easily obtained from the measurements taken. Calling the width of the s t r i p of rubber, w; the t o t a l thickness of rubber as measured, 2d; and putting i n the length of the central heating block, 4.01 cm., the dimension factor becomes jd - d • A 2 x 4.01 x w This factor varied s l i g h t l y each time the rubber was put in, but was always between 0.0075 and 0.0079. 25. i i i . Temperature factor; The readings of a l l the thermocouples on the inside block were corrected to correspond to the one used as the o r i g i n a l standard, and then averaged. The deviation graph was then used to convert i t to the Bureau of Standards copper-constantan tables (9b) and the temperature calculated by inter-polation. • ' Substituting F for the dimension factor and cor-recting for lead resistance the following expression for con-ductivity i s obtained* E = 0.228 IY * F Gal* T^~ T, Sec* Gm.Beg, C. Probable error The absolute determination of temperature does not need to be as accurate as the difference in temperature between the two sides of the material. Since the readings are taken over a temperature in 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 rate of change of conductivity in most parts of the curve i s less than 0.01 x 10 ~ 4/°G.this introduces an error of less than 0»5$» In the determination of the dimension factor i t is d i f f i c u l t to t e l l to what extent the volume of the rubber changed in stretching. However, since in the two cases where two dimension factors were obtained for the same degree of stretch the change was approximately 1/80,or 1.2$, This could he due partly to an increase i n length after being stretched of 0,6% and also to slight differences in the deg-ree of streteh. Measurement of the degree of stretch was com-lioated by the fact that the strips were compressed on the sides. There was a very slight widening of the stri p (less than 1%) caused by the clamping of the blocks. However, th i s was accounted for in the dimension factor, and because of the small changes caused by the amount of stretch would have l i t t l e effect. As fa r as any one set of readings was concerned t h i s would have no bearing on re l a t i v e values. The accuracy of determination of the tempera-tures difference i s hard to estimate.. The o r i g i n a l c a l i b -ration of thermocouples should be accurate at least to + 2 microvolts, and since the readings were the result of averag-ing four thermocouples, and at no time was any significant difference of temperature throughout the copper blocks noted, the maximum e.m.f. error in each case should be less than 3 microvolts. This gives a maximum error in temperature d i f f e -rence of less than 2fo of an 8°G. i n t e r v a l . The ammeter and voltmeter were tested and o a l i * brated beforehand and during the tests proved to have a maxi-mum error of less than 0.5%* Consequently, with correction for lead resistance (around 5%) the power factor should be re l i a b l e to within 1$. Using the generally accepted approximations for 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 of l/30°C. per minute*- ( Corresponding to 1 microvolt/min.) corresponds to an absorption or emission of power amounting to less than 0.5% of the power input. Since a l l readings were taken for a d r i f t less than 1 microvolt/min. t h i s factor i s not important. Experimentally i t was found that very small changes in the power supplied would cause noticeable d r i f t . The t o t a l of these factors gives a maximum error of 5%, or a change in K of approximately 0.15 x 10""4. The rubber sample The"sample of rubber used was one of a group of samples obtained from the University of Notre Dame. It was prepared under carefully controlled conditions to make i t possible for research to be done on rubber similar to commer-c i a l brands, and of exactly known composition. The sample was prepared to the following speci-f i c a t i o n s . pure latex 100 parts carbon black zinc oxide 3 stearic acid 4 Length of cure 120 min. pine tar 2 sulphur 2.7 Temperature of antioxidant 1.5 'cure 274°F. captax 0.9 This rubber was intended to be roughly compara-ble to standard tread stock with the exception that 50 parts of carbon black were omitted. Its measured properties o H Hr ONIACO NO CM ^- O ^ H N\N\.H ^" CKONO^ Q NO CO CO "SI" CO. 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I I I O -^CM O ^-CO O O NOND IA r—- ACO H CO O NO CM C— • « « « a « o Nf- rAIAlA CM CM H ' H IA H NO c ON O "vf" ON IA rA H H O !A H NO CO C—NO rA C-NO IA^ONH CM CM CM ^ IA ONO ON IANO C-rANO ONACO -sf ONO H C— • • ft • • • • ft • • • • • 4 • « H H H CM CM CM IA CM CM CM H H Nf 1AC-HC-ACM AO O rAlAON'vh «^ lA^-NO O CM O IAH ON CMNONO C— CO ON CO C— C— H C— H O NO NO CM O NT- CM ONCO NO NO H C— rA CO ^ CM IANO H (A C— H IA C— CM A H C— tA C-• IA IA tAIACM CM H H HHrHCMCMCMlACMCMHH H H Ml CP <! EH 4 KN O H © ra S H o '02 I ra w -p o H EH O pq £> W EH CM 02 EH 1 e v— H o o EH 0 o rH CM EH O 0" H EH CM O EH O EH P H LA^h OJ KNCO OO H CKH CM H ONNO ^ O NO OCO ON W OCO W ^- CN H NO LT\ C— LA,—j KNH CM O OJ OJ OJ K\CO (MHNDCOIAOKNWCO H"=t KN OJ O • •»»««*» e»»»»a»*e**«. •••«••« KNK\K\KNK\KNKNKN KNKNKNOJ KN CM KN OJ OJ CM OJ OJ H OJ KN K\K\KN KN KN ON OO UN KN H KN O KN CM H ONNO I—| KN OJ OJ OJ i—1 OO ONO ON LA ^ NO NO ON KN "'d* OJ H H OJ KN^d- KN LTNLTN CO NO IT-CO ON O O OJ KN^- NO H H OJ UN, I • H H H H H H I I " I I I i i I I I I I I I I I I I I I I I I KN: LA C—NO ^ CO d^- OJ NO OJ c—ON-vh co OJ KNNO C— K\ rr-LT\ LT\ LC\ o ONLANO LT\ CM H ^CO O C—UNIT-NO CMMHCO^HO^ONOONOH^fAHW O ON OJ KN OJ KN OJ OJ OJ KN CM KN OJ KN KN KN OJ CM KN H OJ KN KN "=3* KN ^j- KN OO KN H OO O ON ON H "A ONCO KN ONKNONUNL—O LANO O NO H KVANO ON KN O LTNONOJOOND ONNO O KNKNCO-sh OH C— O OJ H OJ KN^" OJ O KN0NCO •sh NO LTY^- UVsf Lf\.UN-U\ sj- U\UNNO LA^J- UNLA^ KN UN NO NO u\ UN UN O KN LA O O LA LA IT— H NO OO C (—1 KNO ON c— KN ONNO HHKNOOJOOC—-sj-OJ O C—•LANO ^J- KN^- OO LT\NO' H ON IT— O LC\ KN LA UN O HNO C—HONO ONON OJ KNOJ OJ OJ CM OJ OJ OJ OJ OJ OJOJOJKNOJOJOJ OJ OJ OJ OJ CM KN KN OJ OJ OJ C—OJ ONLT-C—OJO C— H CM H CO OCONOONKNC- ONNO UN UNNO HOCOO^t LAND C—CO OJOOO HCONOLAONOND CM CM LT\ ONCO CO ^j- LT\ H ONH O NO v^h CO NO LT\ c—NO LANO CO NO C—C—CO COONOC-HOONOOONOOOOC-ONON H H HHH OO KN H KNNO *sf" CO C— O KN O KN C—• O^ OJ W O O H ONNO O LA KNCO ON ^ OJ OCOC—H KNC—LAHLAKTfLALA^CO C— IT—ON KN O C-OOO ONO • • • • • • « • «« • « • LT\ ••••••••• • • • « • LAO -5J-NO OJND UNUNOJ KN^t C— «NO C— ON-sj- O H O O CM C— CO OJ H H OJ KN KN LANO C—CO NO NO CO ON O H OJ KN "A C— H H CM KN LA IT- r~{ r-i r-H r-{ r-\ r-\ i ti i it t i ii iii ill i I i i i i i i i CO LA LAOO ND ONOJ KNO ONH ON U\ C— C-H LAH LAKN"NS- ^f-NO LA LAO C—KVsf LA O LA H LA C— • OJCO ONLA-vj- C—OO KNONVO H C— LAO.CONONO O O • • • • • * CD • •« • • «• «• • © © e » O ONNO CO ONNO ^ ONNO UN LA C-OO tT— C—NX) c—KN LA OJ "^S* ONC— KN H H OJ • OJ LAND C-IANO c—OO ONO H KN^ LAH i I I 111 11 I I I I 1 Irit'HHrSH I I I I I H LAOO ON H OJ KN I I 1 I I ONL—CO H ONON!AOJ KNNO riOHCO'O LA OJ CO NO OJ CO OJ KN H H KN H OJQOKNONOC— OONHLAC-C— LANO I—CO O ND O OJ KN C—'-A H O ON ON! O LAONOJNO KNONOJLTNCO K\NO ONOJ C—O KNC—O K\C—.OJ C—• O • « « » *a* * fa «« «•« »••• « e • » 0 * • H H H H CM OJ OJ OJ OJ OJ KN KN KN ' "<h Lf\ H ... 1 H H OJ C— O CM 1—1 NO -sd* N-O KN ON O ON *sj" I—i i—] i—I ON LT\ UN ON ON OJ "^d* ^A i—I NO ^ i—| HLALAHKYCKC-COONOHCOCTsCOCOIT-tT-KNIT- ONNO H ON OJ OJ LT\ ON C— OJ C— CM KNC—ON-^ O NO O KNNO O hAN-0 ONOJ-^C-H^CONOO-^ONKNIT-H 1 I 1 H H HOJOJOJOJ OJOJOJKNKNhA-^-"sf' o 1—i id O H H EH o EH o EH O o m H CtJ o ra *—s & H o to o -p -—• > H > o H H H P3 d| CM EH • •I o EH 1—1 0 EH a OJ o •EH • • ^•ODOtMAHW^^ H IAIACO CM CM H CO N}- ir\co NA HO ON ON ONCO NO A^ ^j-cO LT\ LT\ ON C-CO CO C-ONON tA NA CM Hr—ICMCMCMCMCMCMHHCMHCMCMCMCMCM CM ••NA.tT-ON CM IT— CM *sf- ON IANO NO NO CM CM CO K\ O IA IT—NO tr—CO O CM ONCO OHOJ^J- ANO rj- K\ H ONCO C— A IA CM HO- Ht—IHHHHHi—1H ' I I H I 1 I I I I I I I I I I i i I I i xf tA ^J- lAO^CMOtAONONOCMHCMNOCOCOCMCMCO^j-A CM H tA tANO CM H A tA tr- ONCO OJvO C-pO\ NA C— ONCO ^NtKACM IA^|-rA^ tA tA CM CM NA tA IA IA IA tA IA IA * *••*«•»«•«*••>•••»«» H N-'H- KAONC— KANO H C— E—ON ONO C—O C—H ONCO CM HOH^-tr-HOACM tr—co ON ON C— C— CM CO -*H- tr-co co NO NO NO A ^ IANO IANO LT\ >A LT\ A A tA A tA <A A OE-OO ONO NO CO NO rAtr-OO CMtr-OtAOON-<H-0 O ootr-^-iAoc—oco ON^d- co co NO ON c—co ON ON • **•*•••••••••••»•»•• tA IA IA CM CM CM IA CM IA CM CM CM CM CM CM CM CM CU W tA *sh IANO c-<sf ^J-NONO co co NO NO IA'A tr-co O >A IA AC--=H- ON o tr-c— iA-=t tr— CM IA xh ^ IACM -^j- HCO^H-ON ONiACM ONCO O ONCM H H H KAO ^ CO OCO O • ON H H H H H H H H H H H H ON O HCMCMOO^i-CM-^-rAAlACMcONO HCO (ACM NAA CO CM^CMtr-OOCMAC-HtAOKA^NOlAHHCOH •• • *l •••• •••• • • • • • • • • • •« • C— CM MD CO NO HCO ON AO CM H IA tr- ON CM CO <sh CO H H C- ONH O ON ON O H IA ANO C IA IA I—1 O CO C— tA ^ IA HH. HHHH'rHHHi—lr-1H I I I I I I I I I I I I I I I I I I I I I c— cooN'^-tAOcocotr-c— IANO CM CM ON IANO IA tr-•sj- C—NO C—tr-ONtA-sh ONCM NA O NO ON O CM IANO ON O NO » NO • «••••«•••*•••«•*•* CO • O ANO CM C-ON CM ONO O ONNO lA-vh CO AC—CM H NO CM O ON GO CO ONO CM rA A^O tA CM O Ox C-NO -xj- tACM CO H HHHr-iHHr-lH I I I I I I I I i t I I I I I I I I I I I NO tANA'^h "H- O ONNO HCOOHCOCMCMO ONNANANO IA ON CM ON C-A ONNO NO C— HNO XH-NO H tr-CMHCO C-CM"^-NO H C- A CM O ACQ CM NO CO O NO rACO ^-OiAO^rl * • • • • • • . • • • • • • • « • • • CM NA IA tA IA tA tA IA *sh A-vh -sh IA IA tA CM CM H H NO *H.- C-CO LfA CM H CO CM ON O NO NO H H IANO NO <sf O O ^NO-CMNO Lr\lr-OM3 ur\Hi-lCONOCOCOHH NACO H co NA CM axco CM NO ON K\VO corr\0-^HC--NAtr-Hoo CM (MfCMAOJ CJ lAMMA^- ^ K\K\OJ W H H include: Specific gravity .98 Tensile strength llbs./sq. in.) 3365 % elongation possible 760 % set 14 Durometer hardness 40 300% stretch modulus (lbs./sq. in.) 198 For use in the apparatus two strips were used each approximately 15 cm. by 3 cm. by 0.2 cm. The same strips were used throughout* Experimental results The,readings and results obtained are tabulated in tables I, II and I I I . For convenient comparison the re-sults obtained are shown graphically in Plates XIII, XIY and XY, as follows: Normal Length Table I and Plate XIII 50% stretch Table II and Plate XIY 100% stretch Table III and Plate XY Certain of the more evident lines have been drawn i n . Those dotted are tentative l i n e s . Some drops from -the top curve to the bottom one have been shown to indicate the temperatures at which they occurred. The average value of the thermal conductivity for this sample for a l l degrees of stretch appears to be bet-ween 5,5 x 10~ 4 and 3.8 x 10~ 4 Cal./cm.sec.deg. C. in the range around 0°C. This i s i n quite good agreement with the results obtained for a different type of rubber by Schallamaoh (8) who gets 3.1 x 10" 4 and Frumkin and Dubinker (7) with 4.9 x 10~ 4. Actually It 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 different rubbers vary greatly in t h i s respect. An important point to note, also, i s that high porosity tends to decrease conductivity by causing a smaller conducting area. There i s d e f i n i t e l y a decrease in conductivity with decrease of temperature. For a l l degrees of stretch there are no large changes i n the slope of the top l i n e of the graph. The decrease i s not necessarily a linear change, as shown by Plates XIV and XV. For normal length and 50% stretch there i s no indication of two or more possible conductivities above 15°C» This i s in agreement with temperature volume relationships 111) and s p e c i f i c heat curves (12) obtained by Bekkedahl and associates. However, for 100% stretch there i s d e f i n i t e l y an indication that two values of K can exist for temperatures as high as 30 °C. Guth (14) reports that in some cases where two possible states occur at lower temperatures the effect comes up to room temperatures on stretching. Below 10°C., in a l l cases, there are apparently two thermal conductivities possible. There seems to be no consistent pattern to decide which state the rubber w i l l be in since consecutive readings often gave points on different curves. In fact, on several occasions the change actually occurred while readings were being taken. This would indicate that there is not a very great energy difference between the two states. The difference of conductivity between the two states from 10°C. to -40° C. i s around 0.5 x 10" 4. It i s i n -teresting to note that Schallamach (8) found no effect of thi s sort with North B r i t i s h Cycle Tubing which the company c a l l s "pure electrodeposited latex." A possible explanation for this could be that electrodeposited rubber i s purer and has more consistent p a r t i c l e size. However, Bekkedahl (11} found that his temperature volume relations d e f i n i t e l y indicated two possible states below 11°C. for unstretched rubber, and Bekkedahl and Matheson (12) corroborated t h i s when they found a definite peak in the spec i f i c heat curve at that point. (11*0.1 In the region below -70 °C. there are also two possible curves; but the lower of the two i s not ident i c a l with the corresponding one in the upper region. For zero stretch the separation appears to be around 1.5 x 10~ 4 and f a i r l y constant. With increasing stretch the separation de-creases at the upper end of the curves which are no longer p a r a l l e l . Here again there is apparently no set pattern for change from one curve to the other as the points on the lower curve represent isolated readings in many cases. However, there does seem to be an increased tendency to drop off in the region between -120°C. and -160 °G. The temperature at which the drop off occurrs being lower i f the cooling i s dane quick-l y . The range i n which th i s tendency seems greatest i s i n d i -cated by dotted lines on the graphs. The fact that there are two states possible 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 conductivity observed by us i s in marked contrast to Schallamach's work, as i s the fact that points on the top curve occur as low as -165° C. Schallamach reported that in the neighbourhood of -120 °C. the conductivity changed abruptly to the lower value, and thereafter a l l points were on the lower curve which rejoined the upper one in the region -80° C« to -60° C. with no discontinuity. It w i l l be noticed that for the unstretched state this form occurred, but in isolated points both for increasing or decreasing temperatures, and in the region -70"C. to -35 °C. Both Bekkedahl (11) and Guth (14) report that this change can be brought to higher temperatures by varying the composition. The same effect is indicated in readings for 50% stretch, but no points were obtained for that part of the curve for 100% stretch. It w i l l be seen that for a l l degrees of stretch points occurred about half way between the upper and lower curves. This is attributed to the fact that there were two pieces of rubber used simultaneously in each measurement, and one piece could be at the lower conductivity while the other was at the higher one, and vice-versa. In view of the above results and from consider-ation of the graphs the following observations on the effect of increasing stretch may be made,, (a) The slope of the room temperature portion of the curve increases and conductivity tends to increase s l i g h t l y . At very low temperatures the slope decreases. (b) The lower lin 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 curves becomes less. , (d) The top c\irve has a changing slope throughout i t s length* As yet no mention has been made of the anomalous condition found in the -80 *C. to -40 °C. region and possibly below, as shown by points occurring above the top li n e of the graph in that region. To avoid confusion no lines have been drawn through these points, but i t w i l l be observed in the zero stretchgraph that a straight l i n e could be drawn from -160"C. to -30°C. cutting at least f i v e points well above the main curve. This, in i t s e l f , would hardly be conclusive, but at 50% stretch there is a definite high spot in the graph in the -80 °C» to -40 °C. region, and for 100% stretch there i s a very definite series of points closely grouped and some dis -tance from the main l i n e . It should be pointed out that these points were not a l l obtained in one run, but occurred as more or less random readings in the same manner as the low conduc-t i v i t y points. The obtaining of complete curves was complicated by several factors which cannot be shown graphically, but which caused considerable inconvenience. (a) Time lag. There was definite evidence that the value obtained for K i n certain cases depended partly on the previous history of the run* It was noticed on several occasions that the drop from higher to lower ourve that usua-l l y occurs around -140°'C. did not occur u n t i l as low as -165° G, i f the change from room temperature to that temperature had been rapid. Conclusive proof that time i s a factor was ob-tained on one occasion when a steady state was obtained and in the space of approximately 10 minutes i t was necessary to increase the current supplied gradually from „57 to .62 amp-eres i n order to maintain the same temperature difference. This represents a power change of almost 20% or a change of conductivity of almost 0.5 x 10~ 4. The time lag appeared to cause d i f f i c u l t y chiefly in the region from -170° C. to -110°C. and at temperatures above this region was less noticeable. This l ag did not always occur; usually the apparatus could be held steady for some time. Guth (14) has reported that work on other phases of rubber research has been hampered consider-ably by thi s time lag effect, and has made i t d i f f i c u l t to evaluate results. Bekkedahl (11) also reports a similar con-d i t i o n in the region -55°C. to -15°C. where a tendency to pass from one curve to another extended over a considerable period of time. (b) The random i nature of the occurrence of low conductivity readings. At no time was i t possible to f o r e t e l l when low conductivity readings would occur* Consequently, many more readings than necessary were obtained for the upper curve in order to get enough points on the lower one. Because of this fact i t was not possible to f i l l in the bottom curve completely in some regions. (c) Both pieces of rubber not in the same state. As stated before there was some d i f f i c u l t y encountered when one piece of rubber was in a different state from the other. In many cases the values obtained gave a good idea of the separation of the two curves, but as far as exact determina-tion of one of them were of l i t t l e or no use. As the number of times the rubber had been stretched and cooled increased t h i s tendency to change at- different times became greater, i n -dicating that the useful l i f e of paired samples for conduc-t i v i t y work-is limited. (d) Varying conductivity within one piece. The commercial methods of making rubber do not, as a rule, produce a material that i s completely homogeneous. Moreover, the measurements must be taken over a considerable area of any one piece. Consequently* i t i s possible that when'a change occur-red i t did not always extend over the entire area covered by the central heating block. This would cause a poor reading. It w i l l be noticed that certain readings do not f i t in with the general pattern but might be explained in this manner. It would require an apparatus that employed only one piece of rubber but measured several adjacent parts simultaneously to determine whether th i s actually occurred. Interpretation From these results i t i s possible to make some deductions, subject, of course, to v e r i f i c a t i o n by other li n e s of research, as to changes of state that may occur in rubber at the temperatures considered. (a) The state existing ordinarily at room temperatures (amorphous) can exist as far 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 for this state appears to r i s e with increased stretch, but this state does not appear to exist below -60 C* ( o) Below -60°^ C. there are s t i l l two states possible, but one i s of much lower conductivity, (d) 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 possible from the state of lower conductivity to that of higher conductivity. (e) It i s possible that a th i r d state may exist in the -80° C, to -40° C. region with a higher conductivity. However, the higher points might be caused by a heat of fusion or c r y s t a l l i z a t i o n in that region, although this seems unlikely, as no ordinary heat of fusion would be suffieient to maintain the re-duced temperature i n t e r v a l for the period required for two complete sets of readings. (f) Because of the frequency of transition, and i t s re-v e r s i b i l i t y , i t appears that the amount of energy involved in transitions between any two states must be f a i r l y small. IV". CONCLUSION It is apparent from the above that a great deal remains to be done in the f i e l d of heat conductivity of elas-tomers. The work described herein i s but the beginning of an extensive program which w i l l be carried out with samples of different compositions which have been kindly provided by the Department of Physics of the University of Notre Dame» REFERENCES (1) Guth,E. and Mark, H, Monatsch f. Chem. 65, 93, 1934 (2) Guth,E., Kautchuk 13, 201. 1937 (3) James,H. M. and Guth,E» Phys. Rev. 59, 111. 1941 (4) Anthony,R. L., Gaston, R.H. ,. . and Guth, E. J. Phys. Ghem. 46, No. 7. 1942 (5) Frumkin, L. and Dubinker, Yu. Rubber Chem. Tech. 13, 361, 1940 (6) Schallamaoh, A. Nature 145, 67, 1940 (7) Frumkin, L. and Dubinker, Yu. > Rubber Chem. Tech. 11 8 559, 1938 (8) Schallamach, ,A. . . Proc. Phys. Soc. 53, 214, 1941 (9) Temperature, Its Measurement and Control i n Science . . Industry* Symposium published by the American Ins of Physics. (a) Reproducibility of the Ice Point. Thomas, J . L. (b) Calibration of Thermocouples at Low Temperatures. R. B. Scott. (10) Handbook of Chemistry and Physics. Chemical Rubber Publishing Co. (11) Bekkedahl, N. Journal of Research 15, 411. 1934 (12) Bekkedahl, N. and Matheson* J„ Journal of Research 15, 503. 1935 (15) Woodj E. A., Bekkedahl, N. and Roth, F. L. Journal of Research 29, 591; 1942 (14) Guth, E. Letter to Dr; H. D. Smith (15) Lindsay, R. B. An Introduction to Physical S t a t i s t i c s . (Wiley), 1941). (16) Barron, II. Modern Synthetic Rubbers. ( Chapman and Ha l l , 1945) 


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