Modulus and Relaxation of Elastomers in Torsion at Low Temperatures UELVIN MOONEY AND W. E. WOLSTENHOLME General Laboratories. U. S. R1166erCo., Possoic, N. J . by Gehman, Woodford, and Wilkinmn ( 7 ) . In the present work thermo-stress measurements were made on a few elastomers at temperatures extending down as close te T. as w&s experimentally feasible. APPARATUS
For this work it was essential to have B large number of controlled cold births that could he maintained in continuous operation over long periods oi time. To economize on space and cost, a single unit, called a cold bar, was built, providing 18 baths about cquslly spaced in the temperature range from -70' to +!Lo C.
IMails of the cold bar are shown by the photegrsph in Figure 1 and the skotch in Figure 2. The storage box a t t h e left end holds four 25-uourrd cakes of dry ioe and is filled usu~llvon altrrnate Figure 1.
(
old Bar v i l l i Temperature Range from -70" tu 0" C.
11.)-rco cheat at l d r , therrnostet bath at right
s
WOND-ORDER transition temporatures, Ts,indicated by volume or specific heat data, hnve been reported ( I f ) far many high polymer elastomers. Studies (3, 7 , X) of the modulustemperature relationshipin bhe vicinity oi T,have revealcd that the modulus helow T. is always enormously higher than above T,. In the transition region, roughly from T, 10" C. to T,,the niodulus values, as usually measured, show a progressive rise with decreasing temperature. However, these modulus values, usually measured less than 1 minute after loading, are strictly transient modulus v d u c ~BY , at 1 minut.8 the deformation under oonstant load is far from being constant. The present investigation was undertaken to determine haw the equilibrium modulus, if any exists. varies with temverature in the transition reeion - above the 1'. temperature. The method cmilloyed was,. in .principle. to impose a fincd d e b .~ mation and to meamre the stress aiter a lapse of time sufficient for the s t r e a to booome constant. Cylindrical samples, of 0.25inch diameter, were twisted one turn per inch in a cold bath and tho torque at constant twist WBS mcasnred as a function of time. l l r e measurements werc continued in many eases for months, hut in no case did the torque show any indication of approaching a limiting value other than zero. These tests therefore iniled in their initial purpose, which was to establish and measure the equilibrium modulus. However, the torque-relaxation teats did yield some interesting dnta, which indioated that all the tevted elastomers develop crystallinity or a similar-ordered state when subjected to prolonged strain at reduced temperature. Moreover, the equipment used was wkll suited to low temperature thermo-stress measurements-that is, measurements of stress in a cycle oi temperature variat,ion a t constant deformation. Two thermo-stress Curves on Hevea gum stocks extending to low temperatures have previously
+
hnnn *nnnrinrl
nn,r
h . . C""...."^"_I
T
LL"
....
~~L, c > /
~
~
2
..
W Sketch of Cold Bar Shoving Aluminum Channel Containing Individual Cold B a t h and Insulation of Bar Figure 2.
cimnnel, 7 inches deep and 7 inches widc. The dry-ice chamber and the water bath are bolted and welded to the opposite ends of the channel. A t Ginch intervals dona the channel, aluminum
h&ched along one side to the 0.25.inch thick dartitiouing crosspieces. The bottom and other three sidcs of each cold bath are th~~mallyjnsul&dfrom the cold bar. Commercial methyl alto-
INDUSTRIAL AND ENGINEERING CHEMISTRY
There bas no swelling sufficient to he detectedhy micrometer gage measurements. Also, all recovered samples---Le., Sam lee returned to room temperature after several months in the ?ow temperature alcohol baths--oxhihited torque restoration to values expected iar mn les in air a t room temperature. It was concluded that neitier swelling nor leeching by the alcohol wm sufficient to Rffect appreciably the rorquc of twisted samples. v
Figure 3. Temperature of Individual Cells along Cold Bar
The design of the cold bar, including the insulation, was based on three requirements: the temperature gradient along the bar should he reasonably constant; the total daily heat absorption should he less than that required to evaporate two 26pound cakes of dry ice; and approximately 80% of the heat should he absorbed from the thermostat bath. The insulation used w w U. S. Royal Soft Cellular Sponge, which has 5 thermal conduction coefficient of 0.24 B.t.u. per hour pcr square foot per e F. per 1 inch thickness a t 70" F. The thickness of the insulation ww uniformly graded in I-inch Bteps from 8 inches a t the cold end to 2 inches a t the w ~ r mend. The approximate uniformity of the temperature gradient dong the bar is shown in Figure 3, where temperatures of the cold baths are plotted against position along the cold bar. Dry-ice consumption averages a b o u t 20 pounds a dny except d u r i n g h o t summer weather, when consumption increases to roughly 30 pounds a day. Each test sample is mounted in an individual holder. In order to keep the Bsmples imm apiraling when twisted, they are held s t r e t c h e d 10%. During torque messurement the stratoh is increased Figure 4. Torqueometer w i t h hy a slight amount, Sample Mounted in Position for hut the twist ia Measurement .--
.
.
.. ..
.
. .
Val. 44, No. 2
stant within experimental error. Before settling on this p r o m dure it was established that the required stretch varintions did not alter appreciably the measured torque. The torqueometer and holders designed to meet these requirements are shown in the photograph of Figure 4 and the sketch of Figure 5. The torqueometer frame fits into the channel of the cold bar, sud samples are not removed from the cold baths for measurement. Individual sample holders, A, of 0.05O-inch gage sheet aluminum are clamped during measllrement to the lower part of the frame by m a n s of a small cam (not shown). The fork, B, a t the lower end of the vertical shaft, C, fits into the saddle-shaped piece, D, attached to one end oi the sample, E. To free the upper end of the sample for torque measurement, this saddle piece is lifted free of the sample holder body by the adjusting screw, F , in the ring, 0,a t the upper end oi the vortical shaft. ,The twisting moment of the sample then pulls tho side of the ring against one side of the gap in the retaining bar, H. To measure the torque the sam le is balanced by.the chsinomatie, I, which is adjusted just to [ r a k the metallic c.nntact hot.wcan ,the ring and r c t a i n i n g bar. A milliarnetex, J , connected through the contact to a dr cell, K , and suitahre resistor. serve8 w an indic8tor The torque range for the chsinomatic alone is 10 msm-cm. Additional-weiahts a r e a d d e d a < required. The torque ometer ia canable of detecting a 0.3% change in i twisting couple of the order of 100 gram-ems. EXPERIMENTAL PROCEDURE
In tiie experimental
0.169 inch in dism-
rod is secured in s Figure 5.
Schematic Diagram of Torqueornetec
u o b e r e n d of t h e holder hy two removable ins Each sample is then stretched until 1C-cm. benchmarks on $e &utral portion of the rod are elongated 10%. In the stretched state of the s a m ~ l ethe distance between the 8uDnOpt8 is approximately 6 inches.' Two starting rocedures were employed. In one procedure the sample is helgchilled for 20 minutes and then twisted; in the other i t is held twisted for 20 minutes st room temwerature and then chilled. The 88m le is twisted 6 revolutions, the saddle ieco is pinned to the holger and the whole assembly is then c k m ed in the torqueometer. After fittine the fork, B, into the ssddfe, %e fork and saddle are raised simultaneously by mems of the adjusting
moved. The torque is &en measured in.&
msnnk; previoualy
a m p l e holder & rcmoved from the frame. Subsequentreading are taken more or leas a t convenience hut approximately xt equal intervala on B log time scale.
- ~----~ -
In the thermo-stress investigation the twiated samples were ",,".."> sa--,"- ^* t ""t'.~" L.:-l.". in"" -"*L.,i -I
C_^,
n-
INDUSTRIAL AND ENGINEERING CHEMISTRY
February 1952
337
AND CUREOF STOCKS TESTED TABLE I. COMPOSITION
Elastomer Heves Hevea 5-948 0
Sulfur 0 25 0.5 1.0 2 5 0 25
Compounding, Parts/100 Parts Elastomer Accelerator Lauric acid Stearic acid Antioxidant 5.0 1 . 0 BLEa 3 . 0 MBTb
ZnO 5.0
...
...
5 0 5.0
2.0
...
5.0
01 .50
...
1.OBLE 1 . 0 BLE
Additional
...
Cure Temp;, O F. Minutea 287 180
1 . 0 MBT 3 . 0 MBT
... 0 5 5 0 5.0 1 . 0 BLE 3 . 0 MBT 1.5 1 . 5 MBT 1.5 5.0 0 5 5.0 .. 3.0 ... 1 . 0 Monexf Butyl No. 15 4 . O'Mag. i 0 5 552)h 1.0 0.5 2.09 Neoprene G N 1 oLTsr i i 5.0 .. 1.6 Paracril B ? 0.8 MBT 0 . 3 'bPGm 3.0 41° F. P B D l 2.0 5.0 1 . 0 MBTS ... 1.0 5.0 1.0 i'.o Hycar OR 16 Reaction roduct of diphenylamide and acetone. b Mercapto%enzothiazole. 0 Butadiene/styrene 90/10, polymerized a t 4 1 O F. d Butadiene/styrene)isoprene, 80/10/10. polymerized a t 41' F. Butadiene/styrene, 72/28, pol merized a t 122' F. f Tetramethylthiuram monosulflhe. a Phenylbetanaphthylamine. h Piperidinium pentamethylene dithiocarbamate. i Light calcined ma nesia. 9 Copolymer, butadjene with 26% acrylonitrile, Naugatuck Chemical Co. k Benzothiazyl dtsplfide. I Sodium-polym?r?zed polybutadiene, 60' C., supplied by Government Laboratoriea, Akron, Ohio. Cured stocks contained 40 parts m Diphenylguanidine. J-294:d
... ...
GR-S
...
...
... ...
...
274 287
35 180
287 298 298 298 298 298 298
180 30 30 15 15 45 30
(1
1 hour or longer. For torque measuremenfa the samples were then immersed in an adjustable low temperature bath, and the temperature was reduced in steps of a few degrees. A check measurement at room temperature or higher w a made a t each step. At sufficiently low temperatures the samples became too sluggish for satisfactory torque measurement in the equipment used. The low temperature limit thus imposed was only 2 O or 3" C. above T,. The compounding and curing data for the nine gum stocks used in this program are listed in Table I. EXPERIMENTAL R E S U L T S
Before presenting the data and curves obINTERPRETATION. tained, certain questions of interpretation should be discussed. The normal curve for stress relaxation of a cured elastomer a t or near room temperature follows closely the law s = A Blogt (1)
-
within the time range from 10-8 to 10 +s days. Here 8 is stress, t is time, and A and B are constants. This empirical law is indicated not only by the data of the present report, but also by 2401
I
8
I
I
I
I
.I 1 TIME. DAYS
IO
1
J
too
Figure 6. Torque Relaxation Curves of Hevea Gum Stocks I. Extrapolated standard relaxation curve at room temperature. La and t e are respectively, the twisting cou le and time in days at iast observation or end I f Torque drop LI to L for sample started at Mom temperature, and then immersed in -20' C. bathi t i is induction time or time at which expenmental curve begins to drop below standard relaxation curve III. Relaxation curve for 6le etatted at -20" C.; t o is time at which torque%ecomesmro .'FI In oomparison with curve III, shows effeet of inoreased sulfur on torque relaxation at -20° C. La is torque on standard relaxatinn curve extrapolated tot.
V. For linear relaxation law, L = Lo (1
- t/l.S)
Wyex ( M P C black).
many other data, published and not published, and i t is assumed here that a linear torque-relaxation curve on a semilog plot is normal and standard. It is to be suspected therefore that, whenever a departure from a linear plot i e found in the present measurements, some factor is affecting the results other than simple relaxation by release of secondary bonds and intermolecular slippage. If there is any true equilibrium torque, as originally assumed, the relaxation curve must eventually develop positive curvature and level off. Such curves, if obtained, would be interpreted as indicating the true thermodynamic equilibrium torque under the imposed twist at the given temperature. RELAXATION AND CRYSTALLINITY. In Figure 6, curves Z, ZZ, and ZIZ show results which are typical of an elastomer known to crystallize under favorable conditions. Curve Z is the normal or standard relaxation curve a t room temperature. When a sample, started at room temperature, is chilled to -20' C., the torque drops, as would be predicted by the kinetic theory of elasticity. This is shown in curve ZZ. The complete drop LI to Lt, due directly t o temperature change, requires about 2 minutes, this time interval being required for approximate temperature equilibrium. The curve is then horizontal, or nearly so, for a time which varies with stock and temperature. Then the curve starts down, often abruptly, and reaches zero rather soon on the log-time scale. The zero torque reading is not due to any failure of the sample, for such samples develop torque again when restored to room temperature, It can only be concluded that the loss of torque is due to crystallization of the sample, for there is no other known phase change which could be similarly induced in a high polymer elastomer. (Instead of true crystallization there may also be subcrystallization, or the formation of crystal-like molecular groups too small or too irregular to develop all crystal properties. Since in the present work it is impossible t o distinguish between crystals and subcrystals, the two terms will be used interchange ably.) According to the principle of le Chetalier, if an elastomer develops crystallinity under strain the required stress ie necessarily thereby reduced; but reduction of stress t o zero in well-cured stocks has not been previously observed. Unfortunately, there is no quantitative theory ef the effect of crystallization on stress. The growth of crystallinity in a sample under constant twist is a transition from a nonequilibrium state toward an equilibrium state, and is therefore not covered by the crystallization theory developed by Flory ( 6 ) . Consequently, while proportionality between crystallization and stress effect may be assumed, the factor of proportionality remains unknown
INDUSTRIAL AND ENGINEERING CHEMISTRY
338
Vol. 44, No. 2
TABLE 11. TORQUE I N TWISTED SAMPLES STOREDAT VARIOUSTEMPERATURES Hevea, 0.25 S
Test No. 1 2 3
4 5 6 7
8
9 Hevea, 0.518 Hevea. 1 S
10 11
Temp., C. Btarting Testing RT i RT RT 0 0
RT -20 RT -36 RT - 47 RT -20 RT RT 0 RT - 20 RT -36 RT 46 RT RT RT 0 RT - 20 RT 37 RT 46 RT RT 0 RT 20 RT 36 RT - 47 RT 37 RT RT
0
- 20 - 20 - 36 - 36 - 47 - 47
- 20
- 20
I
L~", G.-CJn. 114 133 123 122 134 128 132 126 103 165 135 190 173 180 222 190 204 158 175 146 190 158 165 140 168 138 158 224 163 138
0 034 0 031 0 035 0 050 0 031 0 140 0 020 0 138 0 041 0.030 0.012
0 873
0 917
0.853
0 849
0 703
0 795
0 710
0 758
0.830
0.853
12 RT 13 0 0.953 14 0 15 - 20 0.857 16 - 20 17 - 36 0.800 18 36 19 46 0.760 20 - 46 21 - 70 0.690 22 nevea, 2.5 S 0.012 RT 23 0 0.031 0.952 24 0 0.025 25 -20 0.018 0.816 26 -20 0.024 27 -37 0.015 0.822 28 - 37 0.006 29 - 46 0.015 0.752 30 -46 0.012 5-948, 90/10,41' F., 0.25 9 31 RT 81 0.129 32 0 70 0.060 0.883 33 69 0 0.037 34 52 -20 0.097 0.760 35 -20 90 0.063 36 - 36 72 0.020 0.686 37 82 - $6 0.063 38 - 47 61 0.040 0.633 39 - 47 96 0.033 40 70 65 0.523 5-948, 90/10, 41' F., 0 . 5 ' s 41 - 37 80 0.020 42 231 RT 0.018 5-948, 90/10, 41' F., 1 . 5 S 43 0 170 0.021 0 900 44 0 0 166 0.016 45 188 RT -20 0.014 0.793 46 -20 -20 0.038 190 47 RT - 36 226 0.029 0.723 48 169 36 - 36 0.016 49 160 RT -46 0.010 0.676 50 173 46 46 0.008 51 RT RT 166 J-2943, 80/10/10, 41" F., 0.5 S 0.048 0 112 52 RT 0.014 0.818 53 0 0 0.058 106 54 RT - 20 0.047 105 0 750 122 20 55 20 0.019 148 - 36 RT 56 0.025 0 744 57 132 - 36 36 0,020 58 162 RT 46 0.008 0,679 - 46 128 59 46 0.020 60 112 - 70 RT 0,575 n LI = twisting couple a t t = 0.01 day, just before reducing temperature of those started a t room b n = coefficient of relative relaxation rate in equation L = Lo (1 n log c L2 = twisting couple immediately after reducing temperature of those started a t RT.
-
-
-
-
-
-
0.917 0.849 0.795 0.758 0.682 0.917 0.849 0.795 0.758 0.917 0.795 0.758 0.682
0.917 0.849 0.795
-
-
0.849
--
-
and the amount of crystallinity cannot be calculated from the torque changes. The sample, shown by curve 111,which was started and maintained a t the test temperature, -20" C., is initially a bit higher in torque than the room temperature sample, but it soon relaxes and also crystallizes, going down t o zero torque in about the same time. The significance of the higher initial value is questionable, because of variability in the dimensions of the cured cylinders. Curve ZV shows, by comparison with ZI and ZZI,how more sulfur, 2.5 parts as compared with 0.25 part, inhibits crystallization. The curves of Figure 7 show the difference in behavior of 5-948 (41" F., 90/10 butadiene-styrene) with amount of sulfur. With only 0.5 part of sulfur the compound shows marked crystallinity starting at 0.1 day, while the compound with 1.5 parts of sulfur only begins to crystallize at about 30 days, and crystallizes much more slowly on a linear time scale. Rates of crystallization, as indicated by the torque-time curves, vary not only in magnitude but also in the manner of variation with time. Some torque-time curves follow closely the linear taw
I.,).
6a 6a Oa Oa If Oa 6f If 0.03s
0.8s 0.2s 0.02s 0.1s 0.01s 0. l u 0.04s Broke Broke Broke Broke Broke
0
0 0 1 0.95 0.95 0
4
50
50 1
55 120 120
3
9
0.35 1
0.2 10
0.95 0.95 1 0.86 0.9 0 0 0
0.5 0.7 1 0.5
0
0 0 0
0
0
0.8 0.4 0.35 0.9 0.8 0.8 1 0.7 0.9 0.7 0.9 0 8
0 . 4 ~
0.04s 0.795 20s 0.4s 0.758 0 . Is 27s 0.682 Froze temperature
160 33 33
0 0 0 0 0 0
0.8
35s 0.1s 0.1s
0.917
0 0
3 3 7
20 20 9 9
160
0 0
1
l4um 24u 24f 4f 2f 6Of 30f
0.9 0 0 0
35 35 2 2 1
0.lu 0,3511
0.849
0.758
14f1 14f 0 3f Oak Oa 0 09a 0 0581 0 02s 0.3a 0.3a
200 92
200 200 150 95 95 35 150 150 170 95 95
(Colatinued on page 999)
L = Lo (1 - c t )
(2)
L being torque, t time, c a constant, and LOthe initial torque. r
s
I
/
0
f
STARTED AT R.T.
J-948, . _ _ 1.5
S
160
40 TIME, DAYS
Figure 7 .
Torque Relaxation Curve of 5-948
Gum Stocks All samples s t a r t e d a n d teated at -32' indicated
C. except as
INDUSTRIAL AND ENGINEERING CHEMISTRY
February 1952
TABLE 11.
TORQUE I N
Test
No.
61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85
GR-8, 1 . 5 S
Butyl, 0 . 5 S
I
Neoprene
GN
86
Paracril B, 1 . 2 S
Polybutadiene. 41." F., 2 6, Sodium-polymerized
Hycar OR-15, 1. O 8
87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113
TWISTED SAMPLES STORED AT VARIOUS TEMPERATURES (Continued)
Temp., O C . Starting Testing RT RT 0 RT 0 0 -20 RT 20 - 20 36 RT 36 36 46 RT 46 46 70 RT RT RT 0 RT
----
-
-
0
0
--20 20
RT -20 RT -36 RT 46 RT RT RT 0 RT 20 RT 37 RT
-38 -36 -46 -46
-
-70 RT
0 0
-20 20 -37 -37 -47 70 RT
-
-
-
RT
RT RT
0
0 20 -20 -37 - 70 RT 0 0 -20 -20 -37 37 46 46 70 RT
0
-
-RR20TT
RT RT RT 0 RT -20 RT 37 RT
-
-46
-
RT RT RT
- 8
- 8 12 12 20 20
- 8
-
RT
- 12 RT RT
L1" G.-Ch. 69 70 89 86 78 78 80 74 68 78 84 75 78 74 74 79 81 86 70 78 190 189 207 219 178 214 211 172 185 127 148 152 148 250n 156 129 200 184 187 233 207 183 133 184 105 172 194 222 257 244 220 200 210
?ab
0.027 0.012 0.028 0,019 0.033 0.039 0.020 0.046 0.035 0.052 0.025 0.084 0.032 0.023 0.040 0.022 0.021 0.019 0.0768
0.013
0.028 0.049 0.0264 0.030 0.0256 0.134 0.Q65 0.084 0.008 0.024 0.091 0.073 0.037 0.044 0.036 0.050 0.169 1.28 0.176 0.072 0.038 0.045 0.012 0.034 0.006
tic,
LlC/LI
9/K1*
Days 0.1s 0.18 0.3s 0.1s 0.3s 28 0.3s 1s Froze 30
1.0
0.917
0.775
0.849
0.737
0.795
0.768
0.758
0.26
0.682
0.96
0.917
0 833
0.849
0.728
0.795
t(O)f.
Le/Lag 0.1 0.6 0.6 0.8 0.46 0.8 0.45
Days
0.62
0.8
0.683 0.663
1ou 135 1Of 100 268 100 0.04s 1s 0.758 0.3s Froze 0.682 Sample failed, due to defect 0.917 0.01s 7 7 0.Ola 6 0.849 la la 6 0.795 0.8f 28 0.8f 28 0.758 Froze in 1 hour 0.682 Froze
0.895
0.917
0.739 0.525 0.892 0.805 0.744
0.778 0.849 Slipped in holder 0.702 0.795 0.433 0.682 0.866
4811 48u Froze
0.783
0.849
0.889
0.795
OS
0 653
0.758
0.541
0.682
Of 0.005s Froze
0,848
0.889
0.870
0.875
0.798 0.786
0.862 0.848
os
50
170 300 85
150 60 50
0.74 0.78
86 42
0
86
0
0
0
0 0 0
1 0.9 0.9 1
150 100 100 70
0.94
14
1
1 0
0 1 0.2
tCh
Days 150 66 65 42 86
0.9 0.95 0.95 0.65 0 0
1 1 1 1 1
0.917
2 100 100 70 70 14 86
0
1
0.2s 2 . os 0.05
0.8 0.9 0.556 0.85
5s
150 90 90 90 00 400
'
d K, Kz = corresponding absolute temperatures, K.,for h and La. a ti induction time, or time a t which experimental curve begins t o deviate from standard relaxation curve. / t ( 0 ) = time a t which becomes zero.
L
339
fi
u Le and La are, respectively, twisting couple a t end or a t last observation, and couple on standard relaxation curve extrapolated to h t s = time a t end or a t last observation. i R T = room temperature. 'Y f = faster than linear. k a = approximately linear. I a = slower than linear. m u = curve incomplete, form uncertain. n Different mix and cure, not to be compared with other
1..
LI values in the same group.
This law is valid for curve IZI in Figure 6. The degree of approximation is shown by curve V,representing the above equation with c = 1/1.3 and t expressed in days. In Figure 7,on the other hand, the torque of 5-948with 0.5 part of sulfur d r o p s off m o r e slowly t h a n t h e linear curve, drawn with c = 1. Still ' 0 OTIME I N DAYS m 0 other curves, not shown in the report, Figure 8. Hycar OR-15 Torque drop more abruptly Relaxation Curve than the linear law. To ue drop La to L: for this gum stwk This matter of rate with? part aulfur indicates rapid initial relaxation by cryscrystallization up to 0.03 day
tallization will be discussed further in connection with the summarizing data in Table 11. Hycar, when started at room temperature and tested at -16O C., gave the curve shown in Figure 8. This curve indicates considerable crystallization taking place up to 0.03 day, after which there was no further crystallization up t o 1day, when the sample broke. Polybutadiene, started at room temperature and tested at -37' C., showed a somewhat similar effect, except t h a t in the last stage the rate of crystallization was reduced, but not to zero. Each stock tested has been tried at -70" C. The stocks could not be twisted at thii temperature; hence in these tests the samples were all twisted at room temperature, then lowered into the dry-ice box at the colder end of the cold bar. I n all cases when the imposed torque was reduced to zero, the samples remained twisted, without any reduction in twist. However, this observation ia not very significant, as the definition of "remaining twisted" rests upon a method of angle measurement which is inadequate for the purpose. There might be an undetectable return twist of a small fraction of a degree which, considering the stiffness in the vitreous state, would correspond to sizable torque. Curves have been obtained on over 100 torsion relaxation
340
INDUSTRIAL A N D ENGINEERING CHEMISTRY
samples. Rather than show so many curves, it is preferable to give the results in tabular form, Table 11. The notation, defined a t the end of the table, will be clarified by referring to Figures 6 and 7. Data in some of the columns of Table I1 will not be discussed. Such data are recorded merely for possible future reference or for their possible ,value in other researches. The values of n, for example, may be of interest in connection with studies of relaxation rate as a function of temperature. The columns of greatest present interest are columns 7 to 12. The value of Lg/Ll, the ratio of the torque after and before chilling from room temperature, has a predicted value, based on the kinetic theory of elasticity, equal to the corresponding ratio of the absolute temperatures, K 2 / K I . Comparison shows that many of the observed values agree essentially with prediction; some are appreciably lower, and none are appreciably higher. The only apparent interpretation is that in those cases where the observed value of &/LI is lower than predicted, some crystallinity develops immediately on chilling of the sample. On the basis of the expected form of the relaxation curve, the expected value of L,/L, is unity, Lebeing the final observed torque and L, the torque on the extrapolated standard relaxation curve. A value greater than unity would be found if the torque curve levels off at an equilibrium value. If L,/L, = 0, crystallinity is definitely indicated. Study of the table will show that whenever L J L , = 0 the elastomer concerned is one which by other tests is known to be capable of crystallization. When L,/L, = 1, the simple interpretation would be that there has been relaxation entirely by intermolecular slippage, without any crystallization. However, this interpretation would not be correct for polybutadiene, samples No. 97 to 106. There is conclusive evidence that at -37' C. as well as -47' C. this stock crystallizes; the value L,/L1 = 1 simply results from the fact that with this compound there is no appreciable induction period before crystallization begins, and the subsequent rate of crystallization or relaxation is such as to give a linear torque-log time curve.
I
w
-37.C.
a
0
a 0
t-
Figure 9. Effect of Recovery and Rechilling on Sodium-Polymerized Polybutadiene Carbon Black Stock A. B. C.
D.
Sample started at -37' C. Same sample recovered at morn temperature for 1 hour Relaxation of this sample on rechilling to -37' C. Relaxation of a sample started at room temperature and then chilled to -37' C.
The evidence for this interpretation is shown in Figure 9, curve I , sections A , B, and C, obtained in the indicated special treatment of sample No. 103, started and tested a t -37" C. If the large relaxation over the period of 85 days was due exclusively to molecular slippage, then the increase in torque on warming to room temperature would be in the ratio of the absolute temperatures concerned, or 1.26. The observed increase, from 34 to 166 gram-cms., is in the ratio 4.9; and it therefore definitely establishes cryshllinity a t -37" C. When the temperature was again reduced to -37' C., the immediate drop in torque was in the ratio 0.700, whereas the expected drop would be 0.795. This
Vol. 44, No. 2
shows that some of the crystallization is immediately re-established on chilling. Furthermore, the crystallization thus re-established is greater than the crystallization established immediately by chilling a fresh sample first twisted for 20 minutes at room temperature. This is seen by comparing the drop from the end of curve B to the beginning of curve C with the drop in curve D at 0.013 day, when the temperature of this sample was reduced to -37" c. The procedure indicated by curves A and B of Figure 9 was used to test for crystallinity in a number of other samples for which the torque had dropped, but had not dropped to zero. The results of these tests are given in Table 111. Values of L,/L, are as given in Table 11. L,/L, is the ratio of the torque after return to room temperature to the last measured torque at test temperature. K,/K, is the ratio of the corresponding absolute temperatures, as given in column 8 of Table 11.
TABLE 111. TESTFOR CRYSTALLINITY Ratio of final room temperature torque, LT, to final test temperature torque. L B Test Final Torque Abs. Temp. Sample Temp., Rate, Rate, Stock No. c. L e / L s Lr/Le Kr/Ke - 46 5-948, 1.5 S 49 0.4 2.47 1.32 67 0.45 1.44 1.26 GR-S - 36 68 0.52 2.86 1.31 GR-S -4 6 Paracril B 0 91 1.25 1.09 0.9 2.03 Paracril B 37 0.94 95 1.26 Polybutadiene, 1.0 sodium-type 103 - 37 4.88 1.26 0.566 1.24 111 - 12 Hyoar OR 1,14 0.85 1.27 112 16 1.16 Hycar OR 1.45 1.18 Hycar ORa - 20 a Sample of Figure 10 returned to room temperature after 3 days at -200 c.
-
The data in columns 5 and 6 of Table I11 show that in all cases > K,/K, and crystallinity is indicated. The observed ratio differences in some cases are small, notably for the elastomer Hycar; but the smallest difference is several times the estimated probable error, and all observed differences are in the same direction. Consequently the conclusion seems justified that all the above polymers are capable of some crystallization or subcrystallization under the highly favorable conditions of this testnamely, prolonged constant deformation a t a low temperature. If the crystallization effect on torque is strong enough to reduce it to zero in many cases, it would be expected that in some cases a t least, it could even reverse the sign of the torque. The apparatus in these experiments was not designed to measure negative torque, but when negative torque is suspected it is possible to release the sample and observe the twist angle assumed under zero torque. In a few samples the twist under zero torque was greater by a few degrees than the initially imposed six revolutions, The observed excess twist was as shown in Table IV.
LJL,
TABLE1v.
EXCESS
Stock Hevea, 0.25 S
5-948
Neoprene
TWISTON RELE.4SE OF SAMPLE TEMPERATURE
Sample
Test Temp.,
NO.
0
2 3 8 9 38 39 82 83
0
0
0 0
TEsr
Excess Twist, Circular Degrees
c.
- 47 - 47 - 47 - 47
AT
7 12
3 3 maximum 36 maximum h-oted but not Noted but not S o t e d but not Noted but not
measured measured measured measured
Samples 8 and 9 were left released for an extended time. The maxima, given in the table, occurred a t 8 to 16 days. The last readings, a t 43 days, were 4" and 3 " , respectively. The excess twist in these experiments is similar to the buckling phenomenon observed by Smith and' Saylor (IO)in samples of stretched raw rubber stored a t -25' C.
February 1952
INDUSTRIAL AND ENGINEERING CHEMISTRY
All experimental curves were compared with linear torquetime curves t o see whether the linear law was obeyed and, if not, whether the departure was toward a slower rate or a faster rate of relaxation a t the higher relaxation time. The conclusions from such comparisons are indicated by the letters a, 8, f, or u following the ti figures in Table 11. The significance of these letters is given at the end of the table.
341
DISCUSSION
The present experimental results require of any theory of the second-order transition in elastomers t h a t it predict at T,a discontinuity in equilibrium or quasi-equilibrium modulus, or at least a very abrupt rise to the high value at temperatures below T.. A theoryrecently developed by Boggs ( 4 ) deals with equilibrium modulus near T,, but in its present form the theory is only semiquantitative and cannot be tested by the experimental thermo-stress data. Also, the present results could be taken as support for the point of view, favored b y some, t h a t there is no real second-order transition, the apparent appearance of a new phase being due entirely to the very great increaae in the relaxation timeand the relatively short testing timeso far used in observing apparent T,phenomena. The torque relaxation data of this report preclude any possibility that the low temperature thermo-stress data could represent any truly equilibrium state. The actual state is, a t best, only one of quasi-equilibrium, dependent on the fact that the series of terque measurements can be completed before there is time for appreciable crystallisation or for appreciable further relaxation by molecular slippage. Since the present experiments have established a profound effect of crystallization on relaxation at low temperatures, they suggest that similar effects, though reduced in magnitude, may Figure 10. Effect of Temperature on Shear Modulus at Constant exist also a t higher temperatures, at least up to the melting point Twist of the polymer. I n current theories (1) of relaxation, creep, hysteresis, and their interrelationships, the only mechanism conEach elastomer, except Hycar, measured at room temperature for 10 te 15 minutes sidered is a release of stress by intermolecular slippage and movebefore immersing for 30 minutea or longer in the next lower temperature bath ment to a configuration of lower free energy but equal internal Dashed line passes through absolute zero energy. With a release mechanism involving crystallization, a Short vertical bar at left is T s of elastostate of lower internal energy, the interrelationships of various mer hysteretic phenomena will certainly be different. Static moduSTRESS-TEMPERATURE MEASUREMENTS; QUASI-EQUILIBRIUM lus tests of long duration, particularly a t low temperature, may give different results depending on whether they are carried out MODULI. The thermo-stress, or temperature-torque, curves were a t constant load or at constant strain. obtained on a number of samples by the method described in the experimental section. On the assumption that neoprene has a melting point above room temperature and somewhat above that NEOPRENE 2 of Hevea, the neoprene sample was raised to 50" C. between the I low temperature tests. The results obtained on all samples are shown in Figures 10 and 11. Torque values have been converted to shear modulus. In spite of some scattering due to continued relaxation and to some torque hysteresis in the cycle, the general modulus-temperature relationship is clearly established. At and near room temperature the modulus follows, at least approximately, the law of proportionality t o absolute temperature. At lower temperatures, as T,is approached, there is departure from the proportionality law in the direction of lower modulus. Such a departure is presumably due to crystallization that occurs within the time of the measurements. There is no evidence of a rise in modulus even at temperatures only 2" or 3" C . above T.. These results differ somewhat from the two published thermostress curves on Hevea gum stocks referred to above (7, 8). Figure 11. Effect of Temperature on Shear Modulus at Constant Twist While tabulated data were not published, it appears from the curves themselves that in both cases the increase in stress with Dashed line passes through absolute zero Short vertical bar at left is T8 of elastomer temperature above -50" C., while approximately linear, is somewhat less than proportional t o absolute temperature. FurThe extreme complexities of low temperature modulus lead to thermore, the curve of Greene and Loughborough, which, was gross irregularities in the low temperature stress, strain, relaxacarried toJower temperatures, paases through a minimum a t about tion, and set relationships. From a practical viewpoint, this -60° C., the stress at the lowest temperature, -65" C., being signifies that laboratory methods intended t o predict low tempera. higher than at -60" C . With reference to this result it is importure performance should duplicate as closely as possible the contant to note that the sample was tested under tension, not shear, a t templated service conditions. For example, the proper type of a fixed length, with no adjustment to allow for the thermal test for a low temperature gasket material would be a relaxation expansion of the sample or its support. This means t h a t when test, which measures the stress while the sample is under an the temperature was lowered, the sample elongation was slightly imposed strain, not a compression set test @), which measares the increased, because the coefficient of expansion of the rubber is set after release from strain. The occasional induction times of higher than that of any rigid support. The slight increase in 10 days or more in Table I11 mean t h a t a 4 d a y compression set stress at -65' C . , therefore, cannot be taken as applying t o a test ( 9 ) is too short for some elastomers. sample tested at constant elongation.
342
INDUSTRIAL AND ENGINEERING CHEMISTRY
Likewise, the low-temperature modulus tests described b y Clash and Berg (6),and Gehman, Woodford, and Wilkinson ( 7 ) , are much too short to be used as measures of static modulus. The transient character of the modulus measured in these tests has, of course, been recognized; but there has not been previously any suggestion or demonstration that the long-time static moduli may fall so extremely low as to become zero or negative. ACKNOWLEDGMENT
The authors of this paper are indebted to G. F. Schrappel for obtaining the experimental data contained herein. LITERATURE CITED
(1) Alfrey, T.,“Mechanical Behavior of High Polymers,” New York,
Interscience Publishers, Inc., 1948. (2) “A.S.T.M. Standards,” Designation D 39546T, Method B, p. 1001, Philadelphia, Pa., American Society for Testing Materials, 1946. (3) Beatty, J. R.,and Dnvies, J. M., J . Applied Phys., 20, 633 1949.
Vol. 44, No. 2
(4) Boggs, F. W.,“Statistical Mechanics of Rubber,” paper presented a t the 58th Meeting of the Division of Rubber Chemistry, AMERICAN CHEMICAL SOCIETY, Washington, D. C. (5) Clash, R. F., Jr., and Berg, R. M., IND.ENG.CHEM.,36, 279 (1944). (6) Flory, P. J., J . Chem. Phvs., 15, 397 (1947). (7) Gehman, S. D.,Woodford, D. E., and Wilkinson, C. S., IND. ENG.CHEM.,39, 1108 (1947); Rubber Chem. and Technol., 21, 94 (1948). (8) Greene, H.E., and Loughborough, D. L., J . Applied Phys., 16, 3 (1945); Rubber Chem. and Technol., 18, 587 (July 1945). (9) “Rubber, Synthetic, Medium-Soft; Molded, Sheet, and Strip (For Airport, Hatch, and Watertighband-Airtight-Door Gaskets),” U. S. Govt. Printing Office, MIL-R-SOOA, 1950. (IO) Smith, W. H., and Saylor, C. P., J . Research Natl. Bur. Standards, 21, 257 (1938). (11) Wood, L.A., “Advances in Colloid Sciences,” Vol. 11, Rubber, New York, Interscience Publishers, Inc., 1946. RECEIVED March 23, 1951, This work was supported by funds under contract W44-109QM-2030, Office of the Quartermaster General. Contribution 112 from the General Laboratories of the U. S. Rubber Co., Passaic. N. J. Presented a t the 58th Meeting of the Division of Rubber Chemistry, AMERICAN CHEMICAL SOCIETY, Washington, D. C., 1951.
Crystal Size Distri ution of Electrolytic Metal wders J
POWDERS FROM FUSED ELECTROLYTE BATHS CHUIC-CHING MA School of C h e m i c a l Engineering, T u l a n e University, N e w Orleans, La.
ru’ DETERMINING the usefulness of metal powders for powder metallurgy applications, it is important to study their chemical and physical properties. The influences of physical properties are considered to be equally important as those of chemical properties. It is not infrequent that a powder with a high degree of purity may not be suitable for a powder metallurgy process because of the inferiority of one of its physical properties. The workability of a green compact made from loose metal powders and the mechanical strength of the resulting article are affected to a marked degree b y such physical characteristics as particle size, particle shape, crystal structure, and surface conditions. The apparent density as well as the compactability depend entirely on these fundamental physical properties. Based on a statistical analysis, there is a definite and close relationship between the physical characteristics of the metal powders and the ultimate properties of the finished products. It cannot be overemphasized, therefore, that the success or failure of a powder metallurgy process relies upon the physical character of the metal powders employed. Metal powders may be produced by a great variety of mechanical, physical, and chemical methods. At present, most of the powders employed for molding processes are made either by reduction of metallic oxides or halides, or by electrolysis. The powders of the same metal, but prepared by different processes, may differ in crystal size and shape. For instance, iron powders are of irregular dentritic structure when produced electrolytically, but of regdar spherical shape when they are obtained from thermal decomposition of iron carbonyls. It is a known fact that electrolytic metal powders are of nonuniform size. As explained later there is a n advantage in having a wide range of crystal size distribution for pressing. From the results of the present investigation, it appears that metal powders obtained from fused electrolyte baths are suitable materials for powder metallurgy processes. The desired sizes of metal pow-
ders may be obtained by controlling such variables as temperature, current density, and composition of the bath. The problem of correlating the crystal size distribution of electrolytic tungsten to the temperature, current density, and other variables was first attacked by Fink and Ma (5, 6),who studied
THERMOCOU PCE
-SILICA
SCALE
1
&”= 1”
Figure 1. Graphite Crucible
INSULAT \N6 TUBE
