Figure 1. Drawing of Flwometez
S . D. GFBhfAN, P. J. JONES, A N D D. E. WOODFORD The Gwdyear Tire &Rubber Company, Akron, Ohio HE problem of heat generntion in tires Bssumes new importance with the advent of synthetic rubber and the increased we of reclaimed rubber. Even though reduced speeds may prevent heat blowouts, higher temperntures mean thnt both fabric and rubber are operating under unfavorable conditions. Synthetic rubber, in particular, is then working at reduced tensile strength and $earresistance. It is more susceptible to beat embrittlement, cuts, and abrasion. A number-of flexometers for rubber testing have been described (1, 3, IO, 18, I?, 2U); some of these instruments have been widely used (11, I S , 18, ,?a). The flexometer here described is characterized by simplicity of construction, high speed, and oonvenience of operation.
T
FI5XOMETER DESIGN
Figure 1 is a drawing of the fkxometer. Sixty-cycle current fmm a 12-volt filament transformer. the W rim am of whioh is mntrolled by a variable tnuurfomer; is su&ied "to B mil in a d i a l magnetic 6dd so thnt the wil and the system to which it is attached vibrate with this frequency. The coil hss an inside diameter of 3 inchesand consists of two layers of No. 18 enameled mppw wire wound on a thin fiber tube, twenty-three turn in each layer. The current through the cod is ususUy nbout 5 am rea, but it may be BB high 89 15 amperes. The magnetic 6dgs omduoed bv a lield mil owrated frum the llDvolt direct c-the and isabout 8wo &&sa. Figuna 2 shows the &tic force calibration c w e for the system. Figure 3 is a photograph of the instrument. Sinm the eentral s)-atem of md, mil, cantilever spring, and rubber teat piece is dnven st a frequencyof 60 cycles per second,
it is advantagenus to have the natural iresuency of the systam somewhere near this value. For this djustment, weights can be added or removed fmm the end of the md. In praotice, it is neDeyI81y only to change this sdjustment for stooha of a0 extreme range of stiffness. The antilever spring is a L/,-inoh gsge atsinleas steel plate, 3 inches wide and ?I/. inohes lone. The emtilever s ~ r i n nhae
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
September, 1943
where F = force, dynes z = current,amperea D = constant of proportionality The total impedance of the coil is given by
where Re
=
resistance of coil
= DP x 10-7 Le = self-induction
a
of coil
The amplitude of the motion for an applied alternating voltage of maximum value E is: (4)
Some of the values for the system can be given. The d. e. resistance of the coil is 0.26 ohm. Its self-induction, Le, is 217 microhenrys; hence its static impedance a t 60 cycles is 0.27 ohm. From Figure 2, D can be determined as 931,000 and G as 8.67 X 10'. The conatants for the mechanical system will depend upon the rubber test piece. Under suitable operating conditions, the impedance measured when running with a gum stock was 0.35 ohm and for a G R S tread stock, 0.75 ohm. As the test piece heats up, the impedance changes somewhat and an adjustment must be made in the coil current to maintain a constant amplitude. But the s y e tem is stable and tends to settle down rapidly to a eonstant amplitude. loo0
800
COIL CURRENl IAYPERE 0.C
-
I 2 FIELD CURRENT (AMPERES)
0
Figure 2.
Force Calibration Curve
The impedance of the coil, when the flexometer is running, can readily be determined by measuring the voltage and current. It is possible that some technique might be worked out to use this measurement in the evaluation of the stiffness or damping of the rubber, but the relations appeared to be so involved that no attempt was made to do this. TESTING PROCEDURE
The rubber test piece is a rectsngulsF block 2 inches long with a 1-inch square base. It is the same test piece used for the Goodyear pendulum rebound test. It is mounted between metal plates containing recessed fiber inserta. The test piece is put under a static compression of 6 per cent. This is determined by a spacer block. Figure 4 shows that the observed temperature rise is rather insensitive to this cornpression. The temperature in the middle of the block is measured by a needle thermocouple and a Leeds & Northrup tempera-
963
ture indicator. The needle thermocouple was made by running a silk-insulated constantan wire through a hypodermic needle and soldering the wire to the needle a t the point. The temperature of the block is measured at the start of the teat and after running for 10minutes at a fixed amplitude. The difference in these readings and the calibration of the thermocouple determine the temperature rise due to flexing. Figure 5 shows that after 10 minutes the temperature of the test piece approximates the equilibrium temperature. The test piece is enclosed in a jacket during the test, the temperature of which is controlled at 35" C. A small fan is provided to circulate the air. The amplitude is determined by the visual observation of a suitable target through a magnifying lens. The target aonsists of a solid black arrowhead pointing a t a broad black line on a white background. In vibration the arrowhead and the line are spread out or blurred due to the persistence of Vieion. The current through the coil is set so that the point of the blurred arrow just touches the edge of the blurred line. The amplitude is then one half of the distance between the arrowhead and the edge of the line when at rest. For different amplitudes one target can be readily replaced by another. The compounds here reported were accelerated with Captax (mercaptobenmthiazole) in conventional formulas published previously (7). F'igure 6 shows the cooling curve for a test piece mounted in the flexometer; the temperatures had been determined for various elapsed times with the needle thermocouple. The rrrtt, of cooling a t the start is about 7" C. per minute, which corresponds to the cooling rate to be expected while a reading i s being taken after a test piece is run. As the reading ia obtained within about 10 seconds after stopping, the technique used seems accurate enough in this respect for the
Aflexometer is described which i s adapted for the accurate and rapid determination of the temperature rise in a rubber test piece due toflexing in compression. Curves illustrate the eflect of amplitude, cure, pigment loading, and other factors on the tempemture rise for Hevea and GR-S stocks. Results of resiliometer tests indicate that about half the temperature rise in a tire tread can be ascribed to deformation cycles, such as bending, for which the amplitude i s independent of the stigness of the stock, and hay to cycles, such as compression, for which the amplitude is inversely proportioncrl to the stiflness. The baaring which this situation has on the interpretation of jlexometer tests and the m e t h o b of running the tests are discussed. The principles involved in heat generation by flexed rubber and synthetics as revealed by Jlexometer data and other vibration tests are examined with a view to understanding something of the fundamental molecular or structural mechanisms involved.
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
966
Figure 3.
Photograph of Fleromster
comparison of rubber compounds. Insertion of the needle at the end of the test, without stopping the flexometer, also gives accurate results. Figure 7 illustratm the temperature gradient along the kat piece after running. The maximum temperature occurs in the mid-plane of the test piece where the altermting strain is great& and the heat 1are a minimum. The curve shows some advantage in the technique of measuring the temperattire of the teat piece in the middle rat.her than at the end even il this preciudcs the posaibility of B continnow temperature record. It ia noteworthy that the tempature at the moving end is somewhat lower than that at the stationary end, probably due to a fanning action of the air on the moving end. Figure 8 shows the &ect of amplitude of vibration on heat generation. TheoreticaUy the heat generation i n c r a w with the square of the amplitude; but aa the kmpeTature rises, the reailience incream, the modulus decreases, and the heat losses increase so t.hat actually the relation between hait generation and amplitude is approximately linear. Figure 9 gives mme curves relating the observed temperature rise to various pigment loadings in Captax-accelerated stocks. The higher heat generation in G R S as compared to aatural rubber is emphasized. Figure 10 illustrates the effect of the initial uniform temperature of the test piece upon the ensuing temperature rise. The jacket temperature waa adjusted to- be eqnu! to t+ initial temperature in each case. When a test piece IS run in the flexometer, the final temperature reached represents an equilibrium value between heat generation and heat loanes. These curves show that the rate of heat generation is not constant hut falls off at the higher ambient temperatures so that equilibrium is reached sooner and with a lower temperature rise than would otherwise be the w e .
Vol. 35, No. 9
Calculated relative values of heat generation at constant amplitude, H., show a slight rise with inoreaaing cure, such as wa8 actually ohserved with the flexometer. For comparison ut constant force, the increase in modulus nnd resilience with cure would both tend to reduce the heat generation. Consequently there is a large drop in H,, the calculated relative heat generation for cyoles of constant force, as the cure progreeses. Similarly, the course of modulus and resilience curves witli temperature (87) antisipate the results shown in Figure 10.
2 4oL
HEVEA TREAD STOCK 25 VOL. GAS SLACK
1
AMPLITUDE- LJS MM
*
o
10 20 COMPRESSION X
30
In any given coniptuson in this work, all of the rubber rumyounds were flexed at the same amplitude. It is well recognised that conditions of deformation in a pneumatic tire tread are complicated and cannot he simulated exactly by a cowtant amplitude ramparison. In 8 general way, bending of the tread due to the tire deflection is an amplitude cycle relatively independent of the stiffness of the stock. On the other hand, the pressure between the rubber and the mad hringe into play a force cycle for which the deformation will vary inversely aith the stiffness of the stock. For the correct interpretation of the flexometer results, it is important to know the relative proportion of the heat generation which
September, 1943
INDUSTRIAL AND ENGINEERING CHEMISTRY
967
tread center, for Loth stocks, this
intercept is about 40 per cent of the temperature rise a t 65 pounds per square inch inftation, the normal inflation pressure. For the shoulder the intercept is about 60 per cent of the total rise. Presumably the intercept represents the temperature rise that can be attributed to amplitude cycles which are independent of the inflation pressure. The deformations involved are controlled by the change in shape of the deflected o HEVEA TRSAD STOCK carcass and are independent of the HEVEA GUM STOCK stiffness of the stock. The above analysis is an "averaging type" with obvious limitations in precision. The effect on the tread temperature of the heat developed in 0 5 10 IS 20 25 30 35 the carcass is assumed to be negliTIME OF RUNNING,(MINJ gible. I n spite of these limitations, . _ the experiment gives it is felt that Figure 5. Dependence of Temperature Rise on Tiiiio a picture of the mechanism of heat generation in tire treads which is essentially correct. The average ratio of the temperature rise for stock C to occurs under these two conditions. A resiliometer test was that for stock A in the resiliometer test was 1.17. A flexomrun to secure some information on this point and to try to eter comparison of the stocks showed a ratio of 1.27. In separate the two effects. general, flexometer comparisons at cycles of the same :tmpliTwo tread stocks of WPB qualities A uncl C were coinpared in a tire test on the resiliometer. For brevity the stocks will be referred to as tread stocks A and C, respectively. The results here given were obt:iined for a 9.00 X 20 tire with a Goodyear All Weather tread design. The tire had :I two-way tread, half the circumference being of stock A, the other half of stock d. It was run at a speed of 30 miles per hour on a resiliometer, the wheel p f which was 7 feet in diTREAO STOCK W ameter. Temperature measurements after running were t I I I I niade at tread shoulder and tread center by a needle thermoMIDDLE STATIONEND ARY END couple. The needle was inserted to a depth of 0.54 inch at the shoulder and 0.43 inch at the tread center. Figure 7. Temperature Gradient along Test The tire was run at a series of inflation presaures but at a Piece after Running constant deflection of 1.12 inches. This procedure had the effect of maintaining essentially constant the deformations tude can be expected to rate stocks in the correct order for which could be considered as strictly amplitude cycles; the tire tread temperature rise but to exaggerate the differences deformations which should be regarded as force cycles varied between the stocks, because about half of the tread temperature rise occiirs under conditions corresponding to constant force cycles. This mnie tendency is shown in results of an experiment reported by Mackey, Anderson, and Gardner (18) in which two stocks conteining different amounts of carbon black were compared. FIexometer tests at the same ampliGR -S tude showed temperature rises of 110" and 92" F. for the high20VOL. GAS BLACK black and low-black stock, respectively. I n a resiliometer TREkD STOCK test, tread temperstures of 146' and 140" F., respectively were observed. As long as this characteristic of the flexometer results is kept in mind, it is not a serious disadvantage for laboratory testing since it tends to emphasize trends and differences. For a more precise evaluation of the heat generation of rubber 10 IS 20 25 30 compounds in tire treads, more attention should be given to MINUTES sonie means of also taking into account the heat generation of the etocks under cycles of the same force. For solid tires Figure 6. Cooling Curw the constant force comparison would have much more sign& cniice than the constant amplitude comparison. If it is desired to compare rubber stocks when subjected to with the inflation pressure. The results of the test are shown cycles of the same force, it is necessary to determine the in Figure 14 where the temperature rise b plotted against the dynamic moduli of the compounds by an independent test inflation pressure. Smooth ciirves were obtained which have (7) and then to run them in the flexometer at amplitudes definite intercepts on the temperature rise axis. For the
INDUSTRIAL AND ENGINEERING CHEMISTRY
968
Vol. 35, No. 9
which are inversely proportional to the moduli. Alternatively, use may be made of the linear relation between amplitude and temperature rise (Figure 8) to correct observed temperature rises to values which are inversely proportional to the moduli. One of the difficulties with such procedures is that the variation of modulus with temperature is not taken into account. 90
1
Figure 9.
Effect of Pigment Loading on Heat Generation at Amplitude of 1.55 Mm. 1. Wyex-GR-S 2. Ziuo oside-GR-5 3. G a s blaok-Hevea 4. Zino oxide-Hevea 5. Therrnatomio-Hevea
AMPLITUDE, MM.
Figure 8.
Effect of Amplitude on Heat Generation
1. GR-S-20 volumas
2. 3. 4. 5.
Hevea-25 Hevea-20 Hevea-20 Hevea-20
volumes volumen volumen volumes
gan blaok
gas blaok @an blaok d u o oxide thermatomioblaok
The inherent advantage of a flexometer type of test to measurements at room temperature or even a t the same elevated temperature, is that it compares the stocks when operating, not at the same temperature, but at different temperatures built up by flexing. It is possible that a flexometer comparison of rubber stocks can be devised which will simulate more closely conditions in a tire tread than anything yet reported. It seems worth while to suggest that, in a flexometer of the type described, the test piece could be loaded against a dynamometer, the relatively small vibrations of which would be proportional to the alternating force. By suitable magnification of the motion of the dynamometer, the force amplitude could be observed and set at a constant value for a series of stocks. The average rating from the constant force and constant amplitude comparison should then give a precise rating of the stocks in respect to their heat generation as tire treads.
and more pronounced as the concentration is increased ; correspondingly, $he viscous nature will be suppressed. Consequently, raw rubber may be thought of as being at the end of such an elasto-viscous system. Vulcanization further enhances the elastic character at the expense of the plastic or viscous nature. But it is not unexpected that both aspects of the structure should be evident in the heat generation phenomena. It is customary to think of elasto-viscous systems in terms of mechanical models (9,9, 14, 19). The mechanical model for an elasto-viscous material represents the elastic and viscous elements as a spring connected in series with a piston which moves in a viscous liquid. Equations for such a system were first provided by Maxwell's relaxation theory. Since that time considerable work has been published on such systems both from the experimental and theoretical side. Reasonable success has been achieved in explaining the
I
m-
W"
RELATION OF HEAT GENERATION TO RUBBER STRUCTURE
The transformation of mechanical energy into heat, which occurs in the flexing of rubber, is naturally thought of as due to (a) some process similar to the frictional development of
c"
40 3
heat during the flow of a viscous liquid, or (b) solid friction
such as is responsible for vibration damping for metals and other solids (16,96). A dilute solution of rubber in an organic solvent will approximate a pure liquid in viscous behavior. As the concentration is increased, the phenomena become more complicated and the flow properties depend on the rate of shear. This is due to the interaction of the dissolved molecules or a tendency to assume equilibrium positions with respect to one another. In other words, it represents the appearance of a rudimentary type of elasticity. Such systems are called elasto-viscous. In the case of rubber, the elastic nature of the solution will become more
I
20
Figure
40
60 STARTING TEMP, 'G.
80
10. Effect of Temperature on Heat Generation at Amplitude of 2.46 Mm. 1. GR-9-25 volume5 gas blaok 2. Hevea-25 volumes gan blaok
3. GR-S-20 volumee duo oxide 4. Hevea-20 volumes 5iuo oxide
5. Hevea-20 volumes t h e m a t o d o blaok
INDUSTRIAL AND ENGINEERING CHEMISTRY
September, 1943
general pattern of the phenomenon, but quantitative discrepancies are usually found. The firnitations of the thwriw are well recognized and the more powerful concepts of modern theories of flow (4,84, N)might well be applied to this problem. The results with rubber vibrations should furnish a good experimental background for extension of the theory.
loo IX
where ‘0
3 :
viscosity for small stresses
w
= 2 1 X frequency
TO
=E
r o gives the
969
time oonstant of relaxation = time required for 5x1 a p p d stress to drop t o the fraction 1/e of ita v ue
order of magnitude of the time required for flow
to develop. It is equal to the ratio qo/SO, where & is the modulus of rigidity. It can be shown that the internal friction, q, for rubber, follows essentially this same frequency dependence and thus simulates the functional dependence of the viscosity of e l a s b v i m u s systems on the frequency. Equation 5 shows a falling off of q‘ aa the frequency increases. A transition between elastic and viscous behavior occurs when wr0 a p proaches unity.
100 MIN CURE AT 260%
MODULUS
.
~
0
I 2 AMPLITUDE, MM.
.J
i2
Figure 11. Etreot of Amplitude and Cure on Heat Generation of GRS-u) Volumes Gas Black
The quantity q which has been used in previouS publications (6,7, f l ) to denote the internalfriction for rubber vibrations has usually been called the “equivalent viscosity” (8, 16). It is not the same, by definition, as the coefficient of viscoSity of a liquid. It is the frictional streas per Unit of strain velocity. But it has the same dimensions as the coefficient of viscosity and can be thought of as arising from gradients of shear velocity. Its similarity to an ordinary viscosity coefficient will be emphasied in the following discussion. Phiiippoff (E?),making use of the theories of Hencky and Weissenberg and the Maxwell model, introduced a quantity called the “dynamic viscosity”, q’, to show the effect of frequency. He deduced the relationship:
I
‘I 60
30
50 70 90 110 130 TIME OF CURE (MIN. A T 260*E)
Figure 13. E f h t of Cure on Vibration Properties of GR-S Trsad Stock
Figure 15 illustrates how equations of the type of Equation 5 can be fitted to experimental data of Stambaugh for rubber (W). The pinta represent the experimental data; the curves are plots of the following equations: For GR13 tread stock:
7 lo6 ‘ 1 +1.6(0.0030 X
w)*
For Hevea tread stock at 110’ C.:
’
1.4 X 10’
1
+ (0.0097w)*
(7)
For Hevea tread stock at mom temperature:
I
/ GR-S
HEVEA 25 VOL. GAS BLACK AMP.-2.46 MM.
25VOL. WYEX AMR= 2.46 MM.
I
HEVEA 25%. GAS BLACK
A M . L55
I
50
I
MM.
I
100 I50 TIME OF CURE, MIN.AT 280.
F i g u r e 12. Effect of Cure on Temperature Rise
I
200
’
7.4 x 104
1
+ (0.0034~)~
Aside from the formal difference between q and q’, i t is doubtful whether muoh Signiscsnce can be given to r0 as a relaxation time. It has been generally realized that a single relaxation time is inadequate to deacribe the e l a e t o - v b m ~ nature of rubber. Although the equation should be used with much caution in this respect to secure insight into the structure of rubber, it does serve to classify the frictionfrequency phenomena for rubber vibrations as being elastoviscous in nature; and the load is alternakly supported by elastic and viscous elements of the structure. The molec& equilibrium positions when under stress are evidently alwap somewhat displaced with reference to the unstressed equiJjb rium positions. There is not ody an accommodation to the stress by displacement about the unstressed equilibrium
u‘
L n
5
60.
a
*--
I-
# -
-
-
g w
E
-
a
-.- -***.--
a
3 I-
___----* -
*/-* 40;4-r-----
~
-
TREAD SHOULDER TYPE C TREAD STOCK
_/-LI_O
c4
*--
0
0
0
A A
A A
A A
20:’G:00-20 0
TIRE NORMAL INFLATION: 65 LB. PER SQ.IN. DEFLECTION : I . 12 IN.
“
A
TREAD CENTER TYPE C TREAD STOCK “ A ”
INFLATION PRESSURE (Le.. PER sa. IN. 1
Figure 14.
Resiliometer Results
120 CR-S
TREAD STOCK
W I-
20
30
40
is twice the logarithmic decrement. The scale of the curves for aluminnm and Lucite shows that the energy loss for the metal is of a smaller order of magnitude, but for Lucite it is the same order of magnitude as that encountered with rubber vibrations. The rise of the curve at higher temperatures for these materials is genera1ly ascribed to increased plasticity. The fact that the losses for rubber decrease with rise of temperature emphasizes the fact that they probmore similar to that of liquids than
to t’hat of most solids. The decrease of internal friction for rubber at higher temperatures is not only analogous t o the decrease in viscosity which occurs for liquids but actually shows the same functional rehtion (27). Figure 18 is a plot of log,? against the reciprocal of absolute temperature. For a liquid which does not undergo any structural change i? the temperature range, such a plot for viscosity gives A straight line (or at least a good approximation). Thus, the plot indicates a change in structure for GR-S rubber which occurs Lt about ordinary room temperatures. For natural rubber, on the other hand, this transition point is at a lower temperature (27). The temperature a t which this change of structure occurs appears to be insensitive to cure in the technical range and, as shown, is also relatiyely insensitive to pigment loading. It is therefore reasonable to suppose that this change of structure is associated with localized and intimate molecular groupings rather than with a larger network structure. dctivation energies can be calculated from the equation:
!50 60 70 8 0 90 100 FREOUENCY(C.RS.)
Figure 15. Dependence of Internal Friction on Frequency
7 5 ~
positions, but also a rearrangement of the equilibrium positions which requires time. Further5( more, the range of mechanical vibrations appears to be in the transition region where WTO ap(3 FREQUENCY x 2 2c proaches unity. 2 The dependence of the internal friction for 1 rubber upon temperature is more illuminating P in regard to structure. It can be shown that 2! this dependence is abnorinal in comparison to that of metals and most other solids. Figure 16 gives a curve for the damping for aluminum at various temperatures as determined by Forster and Koster (6). “Damping” here means the logarithmic decrement or the logarithm of the . 400 500 ratio of the amplitudes of two successive free 200 . 6 0 I 100i vibrations. The rise in the damping curve with TEMPERATURE.*C. increase in temperature is characteristic of metal, glass, most plastics, and similar materials. With Figure 16. Damping for Aluminum (5) rubber, on the other hand, the resilience improves at higher temperatures. They have the same magnitude as do activation energies Figure 17 shows the specific loss for Lucite as a function of of organic liquid viscosities. For octane the value is 2.18 temperature, as measured by Rinehart (96). The specific loss (16). The values follow: is the loss of energy per cycle expressed as a fraction of the total
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
September, 1943
-
&,Kg.-Cd,/Mole Low temp. High temp. 7.10 2.06
Heves tread stock
QR-8 tread atoak GR-8 gum stock
9.80
4.83
2.48 0.m
The picture obtained from this experimental evidence and line of thinking is that heat generation in flexed rubber arises from the disturbance of equilibrium molecular configurations. The stre- incream the molecular disorder, and when new equilibrium configurations are established, some of the work done appears as h a t .
FREQUENCY ?a 68 ! &
0 .3
a cn
.2 I -50 -25
0 25 T E MPER ATUR E, C.
Figure 17. Specific Loss ill Litcite (26)
97 1
I t Beenis doubtful that the shape of the nionomer molecule could be of compelling influence on the internal friction of a polymer. The chain shape and structure should be more important, particularly the size and shape of the chain segments which act aa kinetic units and serve to build up a structure with configurational energy. The chain length and extent of cross linkages are other features which enter into the picture although their influence may be rather indirect. Just what characteristic of the molecular structure of synthetic rubber is responsible for its higher heat generation is difficult to say. The low resilience of all synthetic rubbers to date as compared to natural rubber leads us to look for the explanation in unique characteristics of the natural rubber structure rather than to specific features of the molecular structure of any one synthetic rubber. I n the natural rubber structure we feel reasonably certain of such characteristics as long linear molecules of &3 form, regular in structure and with the property of aligning themselves readily in the direction of stress. It is well known that the viscosity of elastoviscous systems decreases with increasing strew, in correlation with the orientation of the structure in the direction of flow. Similarly, with natural rubber this “streamlining” of the long molecules in the direction of stress may be one of the most important reasons for low heat generation. But until more is known of the molecular configurations existing in materials with rubberlike elastioity, such conclusions are only reasonable speculations. ACKNOWLEDGMENT
li‘hat effect various moleculur structures in polymers might have on the internal friction is u complicated question. I n the first place, the constitution of the monomers should probably be considered. A great deal of work has been done on the effect of constitution on the viscosity of liquids (16). Some generalizations have been reached but they are not satisfactory, and certainly nothing appears from them which could be carried over directly to polynier structure. Nissan, Clark, and Nash (22) made a thorough study of the effect of constitution on the viscosity of liquids. By relating the viscosities to the ratio of the absolute temperature of measurement and the boiling point, they were led to the conclusion that the molecular shape ivas the chief variable affecting their curves. Dipole moments and the nature of the atoms of the molecule were found to be relatively immaterial as compared fo the shape of the equipotential surfaces surrounding the molecule. A spheroidal shape gave the highest viscosity for a given temperature ratio.
‘i
GR-S
GR-S
st I
v
c
I
I
Figure 18. Temperatu~IriterrtcrlFriction Relatioil
The resiliometer measurements were made by J. S. Ward of the Goodyear Tire Testing Laboratory. LITERATURE CITED (1) Abbott, F. D., IND.ENQ. CHEM.,20, 863 (1928). (2) Burgers, J. M., 1st Rept. on Viscosity and Plasticity, by Comm. for Study of Viscosity of Acad. of Sci. at Amsterdam, 2nd ed., New York, Nordemann Pub. Co., 1939. (3) Cooper, L. V., TND. ENQ.CHUM.,ANAL.ED., 5, 350 (1933). (4) Ewell, R. H., J . Applied Phya., 9, 262 (1938). (6) F6rster, F., and KWer, W., J . Inst. Elea.‘Engrs., 658 (1939). (6) Gehman, 8. D., J . Applied phy8., 13, 402 (1942). (7) Gehman, 5. D., Woodford, D. E., and Stambaugh, R. B., IND. ENQ. C E ~ M 33. . . 1032 (1941). (8) Gemant, A., J : Adplied Phya.,‘ll, 047 (1940). (9) Zbid., 13, 210 (1942). (10) Cough, V. E., and Parkinson, D.,Tram. Inst. Rubber 2nd.. 17, 188 11941). ,-. (11) Havenhill, R. S., Physics, 7, 179 (1936). (12) Havenhill, R. S,, and MacBride, W. B., IND. ENQ. CHEM., ANAL.ED., 7, 00 (1936). (13) Havenhill, R. S.,and Rankin, J. J., India. Rubber World,107. 306 (1943). (14) Houwink, R., “Elasticity, Plasticity, and Structure of Matter”, London, Cambridge Univ. Press, 1937. (16) Jaeger, F. M., in 2nd Rept. on Viscosity and Plasticity, New York, Nordemann Pub. Co., 1938. (16) Kimball, A. L., T r a m Am. SOC.Meuh. Enars., 51, 227 (1929). (17) Le&, E. T., IND.ENQ.CEEM.,ANAL.ED., 9, 582 (1937). (18) Maakey, J. G., Anderson, J. G., and Gardner, E . R . , Tratu. Inat. Rubber I d . , 16, 123 (1940). (19) Mark, H., IND.ENQ.CHUM.,34, 449 (1942). (20) Memmler, K., “Science of Rubber”, p. 689, New York, Reinhold Pub. Corp.. 1934. (21) Morse, P. M., “Vibration and Sound”, p, 29, New York, McGraw-Hill Book Co., 1930. Clark, L. V. W., and Nash. A. W., J . Inat. Pe(22) Nissan, A. H., troleum, 26, 166 (1940). (23) Philippoff, W., Phyaik. Z., 35, 883 (1934). (24) Powell, R.E., and Eyring, H., in “Advances in Colloid Science”, p. 183, New York, Interscience Publishers, 1942. (28) Randall, R. H.,and Zener, C., Phys. Res., 58, 472 (1940). (20) Rinehart, J. S.,J . A p p l W Phvs., 12,811 (1941). (27) Stambaugh, R. B., IND.ENQ.CHEM.,34, 1368 (1942). (28) Tobohky, A., and Eyring. H., J . Chem. Phvs., 11, 125 (1943). (29) Vaderbdt NSWS, 10, 6 (lQ40). --I.
PR~SBNT before ~ D the Diviaion of Rubber Chemistry at the 1O.itli .\rc*rtiiig Of the h I E R I C A N CIimMtCAt 8O@IBITY, Drtroit, >fich.
