EQUATION OF STATE OF SOME SYNTHETIC RUBBERS L. E. Peterson, R. L. Anthony, and Eugene Guth University OF N o t r e Dame, N o t r e Dame, Ind. HE synthetic rubbers thus far developed bid fair t o T replace rubber permanently in hundreds of its varied uses. Though no one synthetic can, as yet, replace rubber in
flow and permanent set are much more pronounced in synthetics than in rubber. Until these undesirable properties can be suppressed in synthetics, rubber will remain irreplaceable in many of its present uses. To guide future development toward a better understanding of these problems, it is necessary t o study the properties of the materials a t hand and, from an analysis of the data, attempt to prescribe the course of further improvements. Such a program requires not only intensive experimental research, but also a theory of the phenomena being studied. I n the case of rubber, the equation of state was developed from statistical theory (3) and was verified experimentally ( 2 ) . Since this theory was derived from the consideration of the general characteristics of long-chain or highly polymerized
all of its applications, there are several synthetics available, each one of which excels rubber in one particular property. For example, some synthetics are oil and gasoline resistant, others resist the aging effects of heat, light, and oxygen, while still others surpass rubber in their resistance to flexing and abrasion. On the other hand, there are no synthetics that can match the tensile strength, extensibility, and retractability of rubber at extreme temperatures. At low temperatures a stiffening and leathery behavior with large loss of elasticity is characteristic of most synthetics. At higher temperatures plastic
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Figure
1. Sample of Stress-Temperature D a t a
Figure 2. 1349
Stress-Relative Length Curve a t Two Temperatu res
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
1350
molecules, it is not confined to natural rubbers but may be expected to apply also t o synthetic polymers. The purpose of this work was thus twofold. First it was desired to obtain experimentally the equations of state for several representative synthetic rubbers. Secondly, by comparing the results so obtained with the statistical theory of James and Guth, the applicability of the theory to synthetic rubber could be checked and its usefulness thereby extended.
HYCAR
COMPOUND
12
Vol. 34, No. 11
H
Experimental Procedure
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T =300°K.
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In general, the thermodynamic equation of state of a stretched material can be expressed in terms of the force of extension as a function of relative length and temperature, where the relative length is taken as the ratio of the stretched and unstretched lengths. The relaxation method of obtaining this relation was employed as follows. The samples were held a t constant extension in a constanttemperature water bath. The force necessary t o maintain constant extension was measured by a platform balance, one arm of which was connected to the upper end of the sample. By raising or lowering the balances with respect t o the fixed lower clamp, all desired extensions could be attained, and these extensions were measured with a cathetometer. The samples were allowed t o relax a t the highest temperature to be used in the experiment, and the decay of force in time was noted. Gradually the rate of relaxation approached a nearly constant value which vas small enough so that a state of virtual equilibrium existed. After this nearly constant rate of decrease of stress (less than 50 grams per sq. cm. per hour) was reached, the stresstemperature data were recorded by lowering the temperature of the bath in steps of 10-15" C. and noting the value of force necessary to maintain constant extension. After the lowest temperature was reached, about 10" C., the procedure was reversed by increasing the temperature to check for reversibility. The value of 50 grams per sq. em. per hour mentioned above for the final time rate of decrease of stress was found to be sufficiently small so that during the time required for a complete stress-temperature run (about 45 minutes), the decrease in stress due to relaxation was not detectable, as evidenced by complete reversibility of the stress-temperature curve to within experimental accuracy. This experiment was performed on three samples: Hycar OR H, Neoprene 1333N191A,and Neoprene 1333N192A. A sample of the stress-temperature data is shown in Figure 1. The circles represent the original data taken with decreasing temperatures, and the crosses represent the data observed with increasing temperatures. The consistency of these points, taken over an interval of about 45 minutes, demonstrates the existence of the state of virtual equilibrium. The general characteristics of these curves, the straight lines, the negative slopes a t low relative lengths, and the increasing slopes a t higher elongations, are all in agreement with the data obtained for rubber. The highest temperature indicated for Hycar is 50" C. Both neoprene samples, however, were tested up to 65" C. The relatively low maximum temperature for Hycar was adopted because preliminary tests showed that this sample broke a t higher temperatures even though the extensions were very low. At the lower temperature the range of relative lengths was greatly increased.
I 1-0
1.6 2.2 RELATIVE LENGTH
2.E
Figure 3. Resolution of Total Stress with Two Components
INDUSTRIAL AND ENGINEERING CHEMISTRY
November, 1942
From these families of stress-temperature curves, a cross plot of stress-relative length curves a t a constant temperature can be obtained. Figure 2 shows a stress-relative length curve for two different temperatures, The crossing of these curves a t a low relative length is consistent with the inversion of the slopes of the stress-temperature curves. The inversion of slopes of the stress-temperature curves has been attributed t o thermal expansion in the past, and in the case of rubber definite proof has been given (8).
COMPOUND
H
T= 300'K.
compared with the general equation of state derived from thermodynamics for a stretched material:
F where U
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Figure 4.
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1.6 2.2 RELATIVE LENGTH
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Modified Comparison between Experiment and Theory
I n an attempt to explain this behavior, the following considerations are presented: When an unloaded strip is subjected to an increase in temperature, the length of the sample is increased according to the ordinary expression for thermal expansion,
- (as/dL)T.T
(2)
(au/&?J)T
internal energy X = entropy =
Comparison of these two equations indicates that A ( L ) , which is the intercept of the stress-temperature curves on the T = 0 axis, is a measure of that part of the total force due t o the change in internal energy accompanying the extension of the materials studied; the term, B(L).T,which is the product of the slope of the curves and the temperature, is a measure of that part of the total force which is due to entropy changes involved in the same extension. The identification becomes clearer if Equation 2 is written in the form: F =
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1351
(g)T +
($),ST
(3)
Here the entropy term is clearly the product of the slope of the stress-temperature curves and the temperature. The resolution of the total stress into its two components can be done analytically, and Figure 3 shows graphically the results of such an analysis. The greater part of the total stress is accounted for by the entropy contribution, and the characteristic S-shape of the stress-relative length curve results from the entropy term. The theory of Guth and James (3), which is derived from statistical considerations, should agree with the entropy contribution here. Although the extended theory is valid over a large range of relative lengths, i t reduces to a simple form for small L. This approximate form of the extended theory a t small elongations is
""2
F = K T k + whereF = total stress K = a constant L = relative length a = coefficient of expansion TO = room temperature T = temperature at which F is measured
(4)
The two components may be derived from Equation 4. The entropy contribution is:
L = L~ (1 + ; A T ) where a = volume coefficient of thermal expansion The physical model (3) of a network of stretched long-chain molecules predicts that an increase of temperature causes the molecules to tend t o a more disordered or curled-up state. Therefore, if a sample is extended to a certain critical relative length and the temperature is raised, the thermal expansion increases the original unstretched length, thereby decreasing the relative length, This decrease in relative length requires less force to maintain the constant extension. But the increased retractive force due to the tendency of the molecules t o curl up results in a n increase in force necessary t o maintain constant extension. At the critical elongation referred to above, these two opposite changes in force exactly counterbalance each other, and the net result is no change in force required to maintain constant extension. This critical elongation is referred to as the inversion point. Discussion ol Results
The stress-temperature curves obtained for the synthetics can be expressed in the form, F = A ( L ) B(L).T (1) where A and B are functions of relative length only. This is the equation of state of the materials studied and is t o be
+
I n order to compare theory to experiment, constant K must be evaluated. Since, however, no values for a, the thermal coefficient of volume expansion, were available, i t was determined also from theory. If T ( ~ F / ~ Tis) plotted L as a function of relative length, the relative length a t which this quantity is equal to zero can be determined. From Equation 5, if T ( b F / b T ) L = 0, then L* = 1 a(2T - To) (7)
+
At the chosen temperature, T = To = 300' K., Equation 7 reduces to : a = (La - 1)/300 (8) From Equation 8, a was determined for the three samples. With the values determined for a,constant K can be evaluated by comparing Equation 5 to the entropy portion on Figure 3. The values thus obtained are: Sample
Hyoar OR H
Neoprene l333NlQlA Neoprene 1333N192A
11
14 22
19.76 17.0
28.0
1352
INDUSTRIAL AND ENGINEERING CHEMISTRY
Using these values for a: and K in the equations, the theoretical and experimental components can be compared. As the graphs indicate, agreement for the entropy contributions is good. Since the theory is developed only from entropy considerations, the internal energy contribution, ( ~ U / ~ L ) KaT2/L2, T cannot be expected t o account for all the observed internal energy contribution. However, the data on Figure 3 show surprisingly good agreement between experiment and theory for HYcar and both neoprene samples. To obtain a more valid comparison, the volume coefficient of thermal expansion was recently measured by means of a mercury dilatometer ( 1 ) . The values for a: differ from those predicted by theory by as much as a half a magnitude. With these values and the correspondlng ralues for K , Figure 4 shows the modified comparison between experiment and theory.
Vol. 34, No. 11
Conclusions
Although the three synthetic samples exhibit plastic flow and permanent set to a greater degree than rubber, they are truly rubberlike in physical properties. All three types display the same general features of stress-temperature behavior. The stress-relative length curves have the same shape. The Same equation of state that characterizes the behavior of rubber also describes, in terms of relative length and temperature, the retractive force exerted by these samples when stretched. As far as we know, this equation of state for Hycar and tTTo neoprene compounds is the first t o appear in the literature for any synthetic rubber. Literature Cited (1) Belckedahl, N., and Wood, L. A,, IND.ENO.CHEX.,3 3 , 3 8 1 (1941).
ti! ~ 34, 1365 ~ ~ (1942).
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EFFECT O F TEMPERATURE AND PRESSURE
ON OXYGEN PRESSURE AGING A
n increase i n the temperature of the oxygen pressure test from 70' t o 80' C. greatly increases the rate of aging of rubber vulcanizates. The temperature coefficients of aging rate for the six stocks tested vary between 1.63 and 3.48. The state of cure markedly affects the temperature coefficient of some stocks. I t i s obvious that no change i n the specification from 70" t o 80" C. should b e made witho u t first determining the temperature coefficient o f the stock involved. A decrease i n the pressure of the oxygen pressure test decreases the rate of aging, b u t the rate i s n o t proportional t o pressure. The relative rates of aging between 0.5 and 300 pounds oxygen pressure for the stocks tested vary between 1.09 and 4.87 for the normal cures, and between 1.50 and 6.74 for the longer cures. The state of cure markedly affects the change i n rate of aging w i t h change i n pressure. The data s h o w that changes i n the pressure of the oxygen pressure test must b e accompanied b y a revision o f a l l aging specifications, w h i c h will involve an individual study of each stock and every cure o f each stock, since n o correlation between stocks seems t o exist for the changes i n rate o f aging that occur w i t h changes i n pressure.
HE oxygen pressure test a t 70" C. and 300 pounds per T square inch oxygen pressure has proved a valuable tool in the hands of the rubber technologist for evaluating the age resistance of rubber vulcanizates. With the development of modern accelerators and antioxidants, however, the test has been considered too slow for many purposes; as a result there has been considerable agitation for more rapid methods of testing, directed principally toward changing the conditions of the oxygen pressure test. The simplest of these proposed changes consists in raising the temperature a t which the test is carried out; changes in pressure have also been suggested. A certain amount of work on the effects of changing the
A. M. Neal, H. G. Bimmerman, and
J. R. Vincent
E.
I. du Pont de Nernours & Company, Inc., Wilrnington, Del. temperature and pressure in the oxygen pressure test has already been reported. Morgan and Kaunton (1%)found that the temperature coefficient of the oxidation of rubber varies with the nature of the stock and with the antioxidant used, and concluded that measurements a t one temperature will not give a true indication of the relative rates of oxidation of different stocks a t another temperature. These workers also report that the oxidation is different above SO" C. than it is a t lower temperatures. Williams and Kea1 (18) found that in the neighborhood of 70" C. a second type of oxidation reaction seems to become evident. They also report that the decrease in tensile strength is not proportional to the oxygen pressure a t 50" C., and warn against the use of higher temperatures and pressures in aging tests if a close relation to natural aging is to be maintained. Yamazaki and Okuyama (19) followed the oxidation of rubber stocks by the acetone extraction method and found a marked difference between oxidation a t 70" and 90" C. Davey (4) points out the differences in oxidation a t 70" and 100" C. Ingmanson and Kemp (8) report that changes in oxygen pressure a t 70" C. affect different stocks differently, and that the same is true to a smaller extent of differences in temperature; but these authors recommend 50 pounds oxygen pressure and SO" or 85" C. as conditions for the oxygen pressure test. Kemp (9) shows a change in oxidation above 90" C. and warns against changing the temperature specifications of aging tests without obtaining the proper correlation with service conditions. The work of Booth and Beaver (2) shows a variation in the aging of a single stock in a number of the standard tests. Kumerous workers have pointed out a lack of correlation between natu-
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