(Desorption of Unreacted Isoprene from Synthetic Rubber Latex)
EFFECT OF TEMPERATURE AND AGITATION ORRINGTON E. DWYER AND LOWELL T. BURKE’ Uniaersity of Rochester, Rochester 3, N. Y. latex being vented and the other to collect the vapors. By following the rate of pressure rise in this second chamber, the venting rate at any instant could be determined. The venting chamber was basically a glass cylinder, 75 mm. in inside diameter and 150 mm. in length, and had a wall thickness of approximately 3 mm. It fitted into two grooved brass end plates, gasketed with neoprene rubber packing. The plates were drawn tight with four tie rods, each rod having wing nuts on both ends. The upper plate contained a packing gland to admit the stirrer shaft, a neoprene stopper to hold a thermometer, and a 0.25-inch brass take-off line. The lower plate was slightly dished and contained a 0.25inch brass needle valve for draining the latex after a run. The propeller-type stirrer was driven by a variable-speed motor through a pulley system; the propeller itself was 0.75 inch in diameter, had a blade pitch of 45 ’, and was located in the center of the chamber and 7 mm. from the bottom. The direction of rotation was such as to lift the latex. The volume of the venting chamber, including the manometer line, was 0.590 liter. A satisfactory gastight seal was obtained in the packing gland with the use of Palmetto packing.
T h i s investigation has been concerned primarily with the effects of temperature and degree of mechanical agitation on the rate of removal of unreactcd isoprene from synthetic rubber latex. The experimental results have been satisfactorily correlated by the empirical equation:
In the above equation the exponent, 8, is taken to be independent of temperature, the exponent, a, is found to be independent of temperature, and the rate constant, K’,is found to be greatly dependent on temperature. As the degree of mechanical agitation is increased, IC’ increases a t a very rapid rate while a decreases. The net result, however, is t h a t the promoting effect of agitatibn is tremendously great. The beneficial effect of mechanical agitation over ho agitation lessens as t h e driving force is increased. As for the effect of latex depth, a limited a m o u n t of data showed that a fourfold increase in latex depth caused a 40% decrease i n the venting rate per unit volume of latex. It was not possible t o study the effect of pressure because of limitations imposed by the experimental apparatus. The exponent, 9, on r , in the equation was taken as -2.0 from the paper by Dwyer and Raumann (1).
T
HIS paper is a companion paper to another on the same subject appearing on page 1230. The paper by Dwyer and Baumann ( 1 ) is based on data obtained on 6~ batch venting process where the vapor was condensed and measured as a liquid, whereas this paper is based on data from a batch process where the rate of monomer release from the latex was determined by measuring the accumulated vapor directly. Both investigations were carried out simultaneously, the one complementing the other. The other study specialized in determining the effects of pressure, degree of agitation, and latex depth on the venting rate; this one, the effects of temperature and degree of agitation. In fact, it was not possible to study pressure as an independent variable with the vapor-measurement method because the pressure varied during a run. The venting chambers used for both studies were of similar design, except that the chamber used in the vapor-measurement method was considerably smaller. Each method involved the flash-distillation, or venting, of isoprene from a bulk volume of latex under unsteady-state conditions. A quantitative knowledge of the process and the effects of the several operating variables thereon are necessary for the proper design and operation of commercial size equipment in the manufacture of synthetic rubber. All the introductory remarks made in the other paper are applicable here. It is suggested that the reader refer to them. The same is true of the equilibrium data.
d
:I
APPARATUS
The experimental venting apparatus is shown in Figure 1. Essentially, it consisted of two chambers: one to contain the 1 Present address. Distillation Products Division, Eastman Kodak Company, Rochester, N. Y.
--=.
Figure 1. Venting Apparatus
Variable speed a.c. motor B Lightnin mixer C Manometer, 1200-mm. length, wrapped with Nichrome wire D = Constant temperature bath E Heater F Isoprene vapor receiver R
1240
G = Stopcook H = Latcx venting chaml,er J = Thermometer and thermoregulator K Agitator L = Tranatat M = Relay N Standard ta r Joint P = Neoprene tu%g joint
-
-
INDUSTRIAL AND ENGINEERING CHEMISTRY
lune 1950
1241
2. A small quantity of water was introduced to the isoprene vapor receiver to balance the effect of water vapor pressure over the latex. 3. The system was evacuated and the pressure read (usually, water vapor pressure plus a very slight partial pressure of air). 4. After isolating the ventin chamber from the vapor receiver, a measured amount of fatex, introduced through the three-way stopcock, was allowed to reach equilibrium in the venting chamber. During this period, the latex was agitated at a moderate rate. From this equilibrium prewure, the initial amount of is0 rene in the latex is determined. 5. When t i e e uilibrium pressure had been read and the agitator adjusted to %e desired rate, the venting chamber and isoprene vapor receiver were connected so that venting could take place. 6. Pressure readings were then taken ag often a necessary to adequately follow the process, usually every 2.5 minutes for the first 15 minutes, then every 5 for the next 15, and then every 10 to the end of the run. After the first couple of minutes, the ressures of the two chambers were the same, indicating no signigant pressure drop across the stopcock during a run. A run was terminated when the rate of pressure rise was so low as to make it difficult to calculate the ventin rate therefrom. 7. A run lagted from 1 to 2%0urs, during which time barometer readings, manometer leg temperatures, and room temperature were checked periodically. This information was necessary to convert the manometer readings to corrected pressures. RESULTS
The experimental data have been quite slttiifactorily correlated by the equation 60
W
Cb>b,),
L
- -dN'
W
d0
mm. b
Figure 2. Effect of Temperature on Venting Rate
The venting chamber was connected to thejsqprene vapor receiver, F,through a three-way glass stopcock, #, having a Zmm. bore. A short length of neoprene tubing connected the brass tubing on the venting chamber with the glass vapor line. The volume of the receiver, including the manometer line, was 2.040 liters. The vertical arm of the three-way stopcock was used both for charging the venting chamber with latex and &g a vacuum connection, Two manometers were attached to the system, one on either side of the stopcock. The lines leading to these manometers were wound with Nichrome wire to prevent condensation of vapor. The constant temperature bath held approximately 15 gallons of water, which was electrically heated with two 5Wwatt and one 300-watt heaters. The small heater was operated by an electrical relay activated by a thermostat. Open steam was often used to shorten the heat-up period. A Lightnin mixer reduced temperature gradients to a minimum. Vacuum was provided by a Cenco-Hyvac pump. All glass parts were made of heat-resistant glass.
= K ' V ~ d ( p r- pi).
as were the data obtained in the other study (1). The scope of the present investigation, together with the recommended values of K', u , and p in Equation 1, is presented in Table I. Whereas in the previous paper, variation of V Lwith time during a run was taken into consideration, in this study the volume of the latex. V L ]was assumed to remain constant during a run. This assumption is valid because the decrease in latex volume was extremely small and well within the accuracy of the experimental data. In thia study, because of limitations of apparatus] only a minor fraotion of the isoprene in the original latex was removed during a run.
OPERATING PROCEDURE
The procedure for making a run was as follows: 1. The constant temperature bath waa adjusted to the desired operating temperature.
TABLEI I. SCOPBOF INVESTIGATION T:nx,, 40
Latex Depth,
Cm.
2.26
60
2.26
60
9.04
80
2'26
Stirrer Rate
R.PA
[ {
0 0 260 1025 ol' 0 51:
NO. RUM
K'
2 2 2 2
0.000a02 0.000858 0.626 1.69 4-20
a
2 2
1
o.ooa7i
o.ooiia 4.66
a
2.45' 2.46 1.26 1.20. 1.10 2-46 2.45 1.20.
(1)
0
-2.0
W-kl ,mm. th
Figure 3. Effect of Temperature on Venting Rate
1242
INDUSTRIAL AND ENGINEERING CHEMISTRY Since it wm not possible to determine the effect of pressure on the venting rate with the type of apparatus employed, the exponent p on r in Equation 1 was taken as -2.0 from t h e o t h e r study. The fact that, for a given run, a s t r a i g h t line is o b t a i n e d dNi when - ( T )X
(E) is
plotted
on the value of B. However, the test is not a good one because the pressure change during a single run was not sufficiently great, generally about 150 mm. of mercury. Actual venting pressures ranged from about 200 mm. of mercury up to atmospheric pressure. Figure 4. Effect of Temperature on Rate Constant, K
DISCUSSION OF RESULTS
Temperature. The effect of temperature is indicated in Figures 2 and 3. It is apparent from the parallel nature of the lines in these figures that the effect of temperature is essentially the same at all driving forces; this means that as far as Equation 1 is concerned, the only term that is affected is K’. The lines in each figure were drawn parallel to each other, giving a value for a of 2.45 for no agitation and 1.20 for a stirrer speed of 510 r.p.m. The value of 2.45 at no agitation was also obtained for some additional runs where the latex depth was increased 300% (Figure 8). Thus, for zero mechanical agitation, the value of 2.45 for CY seems well established for the system. Owing to the limited data, the value of a a t 510 r.p.m. is not so firmly established. Since the rate coefficient, K’, is directly affected by the isoprene-water diffusivity, one would expect K’ to increase materially with temperature, particularly since the diffusing material is hydrophobic. Figure 4 is the conventional type of semilogarithmic plot where K’ is plotted against the reciprocal of the absolute temperature. The slope of the straight line drawn on this plot, for the three points available, indicates an “energy of activation” of about 7 kg.-cal. per gram mole. For materials diffusing through water very limited data show the corresponding value is about half this (8, t?), indicating that diffusion is only part of the release mechanism for the case under study. If bubble formation were the only other factor, it would appear that diffusion and bubble formation were about equally affected by temperature rise. The data a t 510 r.p.m. indicate an even higher energy of activation, but these are too few to be taken seriously. Agitation. The venting rate is increaaed by two types of agitation: mechanical agitation, that produced by the stirrer; and self-agitation, that produced by ebullition. The effectiveness of these two types is reflected in the values of K’ and CY, respectively, in Equation 1. The effect of mechanical agitation is constant throughout a run, whereas that of self-agitation decreases as the venting rate decreaaes. The tremendous effect of mechanical agitation is evident from
Vol. 42, No, 6
the curves shown in Figure 5, where the difference between agitation rates of 0,260, 510, and 1025 r.p.m. are clearly shown, For the sake of clarity, the data points for the 0- and 510-r.p.m. lines have been omitted from this plot, the lines having been transplanted from Figures 2 and 3, respectively. The curves tend to converge at high values of the driving force. In other words, at high driving forces the rate of evolution is so great that the latex is self-agitated to a considerable degree. For example, at 60’ C., above a driving force of 350 mm., an agitator speed of 260 r.p.m. does not increase the venting rate because self-agitation is more effective than the mechanical agitation. Not until the driving force falls below 350 mm. is agitation at 260 r.p.m. beneficial. However, as the driving force continuesto fall, the beneficial effect of agitation greatly increases, as is evident from the diverging curves. Still referring to Figure 5, the experimental data for an agitator speed of 260 r.p.m. follow along the 0-r.p.m. line a t driving forces above 350 mm. The data points in question are admittedly few, but the trend is nevertheless apparent. It would be expected that data for agitator speeds below 260, say 100 r.p.m., would show two straight lines, the break appearing probably around a driving force of 200 mm. In other words, Iow agitation speeds are only beneficial a t low driving forces. The exponent, a,as shown by the curve in Figure 6, is found to be a function of the degree of agitation, having a maximum value of around 2.5 at no mechanical agitation and approaching unity as the agitation is increased. Values of CY greater than unity are taken to indicate the effective presence of self-agitation. At very high mechanical agitation rates this effect becomes negligible because self-agitation is relatively insignificant. When a is actually unity, it might be said that self-agitation is for practical purposes “drowned out” by the mechanical agitation. The tremendous effect of mechanical agitation on the rate coefficient K’ is shown in Figure 7. One thing is evident-the venting of isoprene from synthetic rubber latex is a separation operation in which agitation is a very important operating variable. The great beneficial effect of agitation is probably more the result of increased rate of bubble formation than decreased diffusional resistance to material transfer in the aqueous film separating the rubber particle from the vapor in the vapor bubbles. Latex Depth, I n this investigation, only a very limited amount
Ibi-b.)
Figure 5.
, mm Ha.
Effect of Agitation on Venting Rate
June 19%
INDUSTRIAL A N D ENGINEERING CHEMISTRY
1243
TABLE 11. LATEXANALYSIS Per Cent 26.5 7 (approx.) 3.07 22 (approx.) 24.6 0.035 0.950 g./ml.
Total soli& Free isoprene oontent Free styrene oontent Combined styrene in polymer Polymer content Hydroquinone (inhibitor) Density at 2So C.
the end of a run, and consequently the last few points were usually ignored when drawing the straight l i e s through the data. SUMMARY AND CONCLUSIONS
Figure 6. Effect of Agitation Rate on Exponent, a
*
of work was done to study this variable; consequently, definite conclusions cannot be drawn. The available results are presented in Figure 8. From the way the straight lines are drawn, a fourfold increase in depth caused a 40% decrease in the venting rate from a given volume of latex. The two lines are drawn parallel, aa the data points suggest, indicating that the effect of depth is the same a t all driving forces. This is not in agreement with the results of the other study (1 ). It is felt that the data presented here are too few and not sufficiently accurate to be significant. It is clear, however, that increase in latex depth, for the relatively small depths (by industrial standards) studied, does cause an appreciable decrease in the venting rate. Foaming and Coagulation. From visual observation, with the venting conditions employed, no undue amount of foaming or latex coagulation was noticed in the course of the experimental work. At the very beginning of a run, where driving forces in excess of 400 mm. were encountered, the foam height may have occasionally reached 2 inches, but it soon subsided to a height of less than 0.5 inch. Comparison with Other Study. It is possible to make a few comparisons of the results presented here with those presented in the preceding paper (1). These comparisons are shown graphically in Figure 9. When there was no mechanical agitation, agreement is very good between the results of the two studies, but where there was mechanical agitation, the l i e s for the two sets of data cross with consequent poor agreement a t the very low and very high driving forces. With the larger apparatus used in the other study, for a given agitation rate, the value of (Y was appreciably greater than that found in the present study. This accounts for the steeper slope of line c as compared with line C in the graph. Even though both venting chambers, including the impellers, were geometrically similar, there is no ironclad reason why the same agitator speed in each vessel would produce the same degree of agitation. Thus, a proper comparison can only be made between the two investigations when there is no mechanical agitation; even then there is the uncertainty of latex depth entering the picture, but this is a minor variable compared to agitation. All in all, agreement between the two separate investigationsthat is, where valid aomparisons are possible-is reasonably good. Precision of Results. The acauracy of the experimental data can be determined from Figures 2, 3, 6 , 6 , and 8. Venting rates calculated by means of Equation 1, using the values of the constants in Table I, would have an estimated average deviation from the observed rates of about * 5 to 7%. The design and operation of the apparatus and the complex nature of the system were such that many runs, because of operational difficulties, were not carried to completion. This was particularly true at the beginning while the operator was acquiring his skill. The number of satisfactory runs increased as the operator and his techniques improved. For several reasons, the data were not sufficientlyaccurate neai
I t is felt that sufficient evidence has been presented to show that Equation 1 reliably expresses the relationship between the venting rate of isoprene, from an isoprene-styrene-latex system, and the pertinent operating variables. These variables are: temperature, pressure, degree of mechanical agitation, and latex depth, Variations are taken care of by changes in K’, a,and T@, aside from the fact that pressure will of course affect the value of pc. In general, the results indicate that K’ is primarily a function of temperature and agitation, a a function of degree of mechanical agitation and latex depth, and fl a constant. Mechanical agitation, temperature, and pressure are all very important variables. Moderate changes in any one of these can change the venting rate severalfold: the first two have a beneficial effect, but increase in pressure causes a decrease in the venting rate. At the latex depths investigated, increase in depth caused an appreciable decrease in venting rate per unit volume of latex. To show the quantitative effect of agitation, a t 60’ C., a latex depth of 2.26 am., and a driving force of 100 mm., the venting rate wm found to increase with agitation rate as fpllows:
0 a00 610 1025
48 200 400 070
I
I
I
1
I
I
E
I
I
I
I
! !
llxD I
I
Q ‘
I
Figure 7. Effect of Agitation on Rate Constant, K’
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
1244
Vol. 42, No. 6 ~
TABLE 111. EXPERIMENTAL DATA Run No. 26 34 37 38 39 40 Agitation rate, r.p.m. 0 250 510 1025 1025 1025 60 60 80 60 60 60 Venting temp., O C. Latex oharged. ml. 100 100 100 100 100 100 Initial pressure" in venting chamber (before charging latex), mm. Hg abs. 150 149 153 152 150 155 Initial equilibrium pressure" (before start of venting). mm. 893 910 901 893 880 884 HIJabs. Time, minutes __- Isc,prene Vapor
417 387
5 7.5 10 12.5 15 20 25 30 40 50 60
429 404 437 416 427 440 436 456 452 464 Lia 474 478 490 503 488 514 497 528 503 539 508 548 513 552
80 100
120 140 160 180
413 432 447 458 469 484 497 507 520 530 537 540 551 554
439 461 478 487 496 510 520 526 535 540 545
424 447 482 474 483 497 507 514 523 530 533 539
41 45 46 48 49 53 510 260 0 0 0 0 60 60 60 40 40 80 100 100 100 100 100 100 151 154 153
57
59 351
56 80 100
57 610 80 100
60 61 0 0 60 60 400 400
359
378
165 146
0
864 958 925 513 512 964 1158 1186 1020 976 Absolute
418 439 459 467 475 489 498 508 518 525 529
535 5bi 660 565
629 639
851 670 680 689 700
574 578
659
6il
71'5
5'85
589
..
..
839 508
595 808 624 618
723
667 873 877
..
641 564 584 609 823 642 658 678 694 708 728 743 754 783 771
..
Pressure8 are mm. Kg abaolute based on density of mercury at On C.
+
IV. CALCULATED RESULTSFOR RUNNo. 48 TABLE pi
5 7.5 10 15 20 30 40 65 80 100 120 140 160 180
195 206 215 228 239 252 262 277 284 291 297 301 305 308
+ pa
138 149 158 171 182 195 205 220 227 234 240 244 248 251
pi
~i
137 148 157 170 181 194 204 218 225 232 238 242 246 249
0.0658 0.0644 0.0632 0.0615 0.0601 0.0584 0.0571 0.0552 0.0544 0.0534 0.0526 0.0521 0.0516 0.0512
I/P
0.191 0.187 0.183 0.178 0.175 0.169 0.168 0.160 0,158 0.155 0.153 0.151 0.150 0.149
pt 420 413 406 396 389 377 371 359 355 348 344 340 338 336
pi
139 150 159 172 183 196 206 220 227 234 240 244 248 251
p?
- pi 281 263 247 224 206 181 165 139 128 114 104 96 90 85
- (%) X 104
'
8.00 6.10 4.65 2.65 1.95 1.35 1.05 0.62 0.51 0.35 0.27 0.22 0.19 0.18
As for the effect of temperature, with no mechanical agitation and e latex depth of 2.26 cm., the venting rate increased 100% as the
temperature was increased from 40" to 60" C. and another 100% from 60' to 80" C. Limited data showed a 40% reduction in venting rate for a 300% increave in latex depth. Some unpublished results obtained at Princeton University ( 4 ) , during the war, on the removal of butadiene from butadiene-styrenelatex mixtures showed that agitation and temperature were very important, severalfold increases in removal rate being possible with moderate changes in these variables, Beyond this, it is not advantageous to make a more quantitative comparison with the r e sults presented here, because the systems, types of agitation, and methods of treating the data in the two cases were different. It is hoped that, as a result of the laboratory scale studies diacussed here, sufficient interest will be aroused in the industry to check the applicability of the results to pilot plant and full scale plant equipment. It is further hoped that a forward step has been made for more rational design of monomer recovery equipment in the manufacture of synthetic rubber. SAMPLE CALCULATIONS-RUN
NO. 48
The experimental data are presented in Table 111. The partial pressure of air equals the initial total preasure in the venting chamber before charging latex minus the vapor pressure of water. Vapor prevsure of water at 40" C. = 55.3 mm. Hg. pa
a
- .P
= 57
- 55
= 2
+ p:
= r*
- p , - p.
= 513
h),
gram mole. The total vapor volume during venting equals the volume of venting chamber, vapor receiver, and average manometer line volume less the space occupied by the latex and the small amount of water added to the vapor receiver. Or, Vt = 0.590 2.040 0.100 = 2.530 liters. The volume correction for the latex due to loss of isoprene aa a run progressed waa negligible. The amount of isoprene remaining in the latex at any time, e,
+
h
bl9
W
I
mm. Hg
Is0 rene content of the latex before venting begins is determineBfrom the initial equilibrium pressure, r*, and a plot of the equilibrium data for the system. These data are summarized in the preceding paper (1 ). p,'
304 258 209 135 111 85 72 51 41 30 24 20 18 17
At this value of (p: p:) the equil i b r i u m curve shows t h a t Z p: =I 455 mm. Hg and - 0.210 gram P of isoprene per gram of 01 mer. From the latex analysis (Tab{ the polymer concentration is 234 grams per liter of latex. Therefore, at time zero,
- 55 -
2 = 456 mm. Hg
(tf-b,), mm.HO.
Figure 8. Effect of Latex Depth on Venting Rate
-
INDUSTRIAL AND ENGINEERING CHEMISTRY
June 1950
1245
Moreover, another assumption is made-that the actual value of 1 is the same as the equilibrium value of y. Since the diffusivity of is0 rene in water is greater than that of styrene, the actual value will be greater than the equilibrium value; but since a, is very cyose to unity anywa ,there can be no appreciable merence between actual and equigbrium values, at least as far M the results of these calculations are concerned. During venting, it is assumed that no air remains in the venting chamber but is swept to the vapor receiver. Hence the isoprene partial pressure over the latex during venting is slightly greater than the avera e artial pressure in the system. Or, p, in the driving force p i ) will be (a - pl)y and not ( X p, p&. At e = 10,
OF
?
(4
-
- p,
p:
= 406
-
- 159 = 247 mm.
From the values of Nd at each time interval a plot of Nd against dN. At de dNi = -4.55 X IO-‘gram mole per minute and = 10, de
0 is made; from this: a plot of 2 against 0 can be1derived.
e
-
-
r$)(E)
= (4.55
x
10-4)
(m) 215O
= 209
A complete summary of the above calculations for run 48 is eiven in Table IV. Values of K’ and u are obtained from the log-log plot of
-
- (%)
(6)us.
- p i ) shown in Figure 2.
(pt
ACKNOWLEDGMENT
Figure 9. Comparison of Results with Those of Dwyer and Baumann (I)
equals the total amount in the s tem less that in the vapor. At time aero, number of gram mors of isoprene in vapor space of venting chamber will be
ptVe
RT
-
455 X 0.490 62.35 X 313
N4 = 0.0836
- RT
= 0.0836
NOMENCLATURE
I = isoprene, gram K’ = rate constant, defined by Equation 1 NC = isoprene in volume, VL,at time, e, gram moles = partial pressure, mm. Hg
o.0114
Therefore, total isoprene in system 0.0722 gram mole. At any time, e,
The authors wish to express their appreciation to the Office of Rubber Reserve, Reconstruction Finance Corporation, Washington, D. C., under whose flnancial sponsorship the research described in this paper was carried out, for their kind permission to publish the experimental results. Thanks are also due the Government Synthetic Rubber Laboratories of the Vniversity of Akron and the United States Rubber Company for providing latex and analyses thereon. Joseph D. Helwig’s valuable assistance with the calculation work is also gratefully acknowledged.
+ 0.0114 = 0.0836 S R
- (1.300 X tO-‘)pi
*
pc
=I
VJ(P
- p , - pa)
0.994 (215
- 55 - 2)
157 ~IYI.
The value of is estimated from the previous calculation when e = 7.5. The partial remure of water above latex is the same aa the vapor pressure o!water a t the same temperature. Therefore,
N I = 0.0836 - (1.800 X lo-‘) X 157
-
a,
0.0632 ,X 6S.li o.184 234 X 0.1
The equilibrium curve shows that p: = 406 mm. Hg,and 0.994. If the estimated value of y had differed materially rom the value finally obtained from the equilibrium curve a recalculation using the new value would have to be made. kctually, however, a,. changes so slowly that it is e a i l estimated for each succemive time increment. Also, since a, dbes change so slowly, no significant error is introduced by assuming that the average for an increment of vapor produced in each short time interval IS the same as the value of a, at the end of the interval.
I
= hydracarbon vapor composition, mole fraction a
total preMure, mm. Hg
= time, minutes
Subscripts and superscripts = air = empirical constant = empirical constant c = renting chamber i = isoprene L latex s styrene t = total vapor to = water * equilibrium a a
5
0,0632 gram mole
and,
‘Ip
K.)
V = volume, liters
e
= 10
poly er, gram
= gas anstant, 62.35 (liters)(mm. Hg)/(g. mole)(
T = K.
a
For example, a t
=
LJTERATURE CITED
(1) Dwyer, 0. E.,
and Baumann, J. A., IND.ENQ.CEEM.,42, 1230
(1960). (2)Glasstone, Laidler, and Eyring, “Theory of Rate Processes,” pp. 622-30,McGraw-Hill Book Co.,New York, 1941. (3)’Taylor, H.S.,J. Chem. Phgs., 6, 331-4 (1938). (4) Whitwell, J. C., et al., private report to Rubber Reserve Company. R E C E ~ ~January ED 7, 1960,
