Rate of Ethylene Polymerization F. R. RUSSELL' AND H. C. HOTTEL Massachusetts Institute of Technology, Cambridge, Mass.
The rate of polymerization of ethylene in the gas phase differs little from the rate of polymerization when dissolved in liquid naphthalene to the same concentration, in spite of the presence in the latter case of fourteen molecules of naphthalene for every one of ethylene. The polymerization in its early stages is a second-order reaction in the gas phase. I n the liquid phase (dissolved in naphthalene) the polymerization reaction in its early stages is of an order between second and third. As polymerization proceeds, the reaction rate does not fall off. I t is con-
cluded that secondary reactions occur between ethylene and its polymers. No detectable reaction occurred between the naphthalene and the dissolved ethylene. The addition of extra surface in the reaction bomb was without appreciable effecg on the reaction, indicating the polymerization reaction to be homogeneous. The effect of temperature on the primary reaction was to double the rate every 26" F. over the range 640-180" F. The corrected energy of activation was 40,000 calories per gram mole for the liquid-phase reaction, 42,100 for the gasphase reaction.
T
HE voluminous literature on polymerization of hydrocarbons indicates a primary interest in the character of the products rather than the mechanism or rate of reaction under clearly defined conditions of phase and of absence of catalytic action. Studies of rate and mechanism of uncatalyzed olefin polymerization reactions published to date have been confined solely to ethylene in the gas phase. The present investigation was prompted by the desire to determine how cracking and uncatalyzed polymerization differ as to reaction order and effect of temperature on reaction rate, when the reaction is carried out in a single phase, either gaseous or liquid. Previous published studies of the rate and mechanism of the uncatalyzed gas-phase polymerization of ethylene (9, 13, 17) show the polymerization to be a second-order reaction with an activation energy between 35,000 and 42,000 calories per gram mole, corresponding to a doubling of reaction rate approximately every 14" C. (25" F.) a t about 370" C. (700" F.). I n contrast, the studies made of the cracking of several different saturated hydrocarbons (2, 5, 6 ) indicate that cracking is a first-order reaction with an activation energy above that of polymerization and corresponding to a doubling of rate approximately every 11" C. (20' F.) in the neighborhood of 370' C. The knowledge of polymerization available plainly indicates that the interpretation of any study of it must of necessity be complicated by the tendency of the polymerizing substance to react, not only with itself but with any products of polymerization already formed. Francis and Kleinschmidt (4) showed by free-energy data that below 4 2 5 O C. unsaturated hydrocarbons tend to polymerize, and that above that temperature they tend to crack. Ethylene was chosen for the present investigation. Since its critical temperature is 9" C., the only possible method of getting it completely into a liquid phase is to dissolve it under pressure in a solvent capable of remaining liquid a t the polymerizing temperature. Naphthalene was chosen for the solvent because of its high critical temperature, resistance to 1
cracking a t high temperature, ease of separation from ethylene, and chemical stability towards ethylene. Approximate fugacity calculations according to the method suggested by Lewis (IO)indicated that for a 10 per cent solution by weight a pressure of about 1000 atmospheres (15,000 pounds per square inch) would be required to keep the ethylene in solution in the naphthalene; for a 1 per cent solution, about 200 atmospheres (3000 pounds). Inasmuch as these calculations were only approximate, positive evidence of the complete absence of any gas phase was necessary, for a t such high pressures a few cubic centimeters of gas phase would contain the greater portion of the ethylene put into the reactor. For purposes of comparison, several gas-phase runs were made with no solvent present and with approximately the same concentrations of ethylene as in the liquid-phase runs.
Apparatus and Procedure The apparatus was designed to permit the filling of a pressure chamber with a known quantity of ethylene, the introduction of naphthalene under pressure to dissolve the ethylene completely, the accurate metering of the naphthalene to guarantee the presence of but one phase in the chamber, the rapid heating and cooling of the chamber before and after its maintainence a t the high temperature of polymerization for a measured time, and the determination of the quantity of ethylene unpolymerized. This was accomplished in equipment assembled as shown in Figure 1: At the extreme left is an injector used to meter naphthalene and to produce the high pressures necessary. It consists of a threaded rod which can be turned by hand through a packing gland into a cylinder of heavy oil, displacing 0.836 cc. per revolution. The displacement of oil was communicated to molten naphthalene through two chambers containing mercury and connected at their lower ends. The upper chamber was maintained at about 115" C. (239" F.) which is 35" C. (63" F.) above the melting point of naphthalene. A measured quantity of liquid naphthalene was thus forced into the reactor which had previously been filled with a quantity of gaseous ethylene measured by its pressure to an accuracy of about 0.25 per cent. During the introduction of the naphthalene, the solution of the
Present address, Standard Oil Development Company, Elizabeth, N. J.
183
INDUSTRIAL AND ENGINEERING CHEMISTRY
184
ethylene was aided by rocking the reactor, which had a steel ball inside. The reactor was made by drilling a ?/*-inch hole in a 2-inch bar of S. A. E. 6145 (chrome-vanadium) steel and plugging the open end. Its volume was about 100 cc. The gas and liquid inlet lines entered at one end, and a thermocouple extending to the center of the reactor entered at the other. Since an accurate measure of the temperature inside the reactor was most essential (1' F. is equivalent to a 2.8 per cent change in reaction rate) the thermocouple had to maintain a constant calibration a t
VOL. 30, NO. 2
was temporarily shut off and the furnace rolled off and on the reactor a few times to dissipate its excess heat. Then every effort was made to keep the temperature constant for the time desired, after which the furnace was pulled off and the reactor rapidly cooled with a fan. In this way the heating-polymerizingcooling curve of temperature us. time could be made to approach so closely t o the ideal rectangle that accurately corrected runs of only 5-minute duration were possible. A typical temperaturetime curve is shown in Figure 2. As soon as the reactor had cooled to about 300" F., valve F (Figure 1) was opened, and the mixture of ethylene, naphthalene, and reaction products was passed through a hot-water condenser into a glass separator. Here the molten naphthalene was separated from the gaseous ethylene and products. The gas passed through a trap and into a gas holder filled with saturated sodium chloride solution. The brine displaced was the measure of the quantity of gas. Two samples of the gas were analyzed in a Williams gas analysis apparatus by absorption successively in ( a ) 87 per cent sulfuric acid (3,19),( b ) 20 per cent mercuric cyanide in 2 N sodium hydroxide (18, 20), (c) saturated bromine in 5 per cent potassium bromide solution in a dark pipet (12) (followed by caustic solution) to determine unsaturated hydrocarbons above ethylene, acetylene, and ethylene itself; the remainder is designated as residue in the tabulated results. Samples taken from the two tanks of ethylene analyzed 99.4 and 99.6 per cent ethylene, 0.2 per cent acetylene, and 0.4 to 0.2 per cent residue.
I I
OIL
M SEPARATOR PHTHALENE MERCURY
DEAD-WLIGHT RELIASE
FIGURE 1. DIAGRAM OF APPARATUS
temperatures up to 500' G. (900' F.) and, in so far as possible, be of a form capable of insertion directly into the reactor without the use of a well in order to follow rapidly any changes in temperature. In addition, it had to have high mechanical strength up to 500" C. (900" F.), a good resistance to both oxidizing and reducing atmospheres, and absolute freedom from leakage. The only base-metal couple meeting these requirements is chromel-alumel with only the chromel exposed to the reducing atmosphere. S'uch a couple was made by drilling an eighth-inch hole through an 8-inch piece of "Chromel-P" No. 2 B and S gage wire (0.26 inch 0. d.), fusing (in an arc) one end into a ball and then welding a No. 16 B and S gage alumel wire to the inside of this ball. The alumel wire was insulated from the chromel tube by a piece of quartz tubing fitting inside the eighthinch hole. The couple was sealed into the reactor by a steel cone tightened by a hollow cap screw threaded into the reactor. Electrical connection was made to the chromel by means of a chromel wire welded to its outer end. The couple was calibrated to an absolute accuracy of 1" F., and read to l/Q" F. A small chromel-alumel couple was peened into the reactor to read surface temperature also. As soon as sufficient naphthalene had been introduced into the reactor to raise the pressure to that desired for the run (and sufficient to ensure the absence of a gas phase), the reactor was heated rapidly by surrounding it with an electric furnace of low heat capacity mounted on wheels and running in a track on a tilting table. The tilting table alternately raised and lowered one end of the reactor, thereby causing the steel ball inside the reactor to roll back and forth and stir the contents. The furnace was 6 inches longer than the reactor, which was admitted through a hole cut in one end of the furnace and rested in the center of the furnace on two steel rods. Heating was chiefly by radiation from a helical heating grid of chromel ribbon supported on six insulated rods surrounding the reactor. The furnace contained no refractory material because of the necessity for keeping down its heat capacity. Instead, the heating coil was surrounded with chromium-plated reflectors covered on the outside by several layers of aluminum foil. The heat in ut was controlled by a hand-operated rheostat. Tests showecf the temperature to be so uniform throughout the furnace that use of the stirrer affected the inside reactor temperature only about l oF. During the rapid heating period, the pressure was maintained constant by venting the expanding liquid through valve C into the separator; the weight of the naphthalene thus expanded out of the reactor was determined for reasons discussed later. As soon as the reactor reached polymerizing temperature, the power
Polymerization Studies The results of the studies o c the amount of polymerization for five temperatures and for initial concentrations of about 0.37, 0.57,and, in a few cases, 0.79 or more mole per liter are presented in Table I. The corrected reaction time was obtained by graphical integration of a plot of reaction rate (based upon unity reaction rate a t the desired polymerizing temperature) against time for the entire heating-polymerizingcool ng cycle. The plot was based upon an assumed doubling of rate every 25" F. (14" C.), a value which was proved adequate by the results obtained in this investigation. A considerable error in this figure produces but a small error in 700
760
140 w
g 720 700
680
660 10
I5
20
25
30 35 T I M E , MINUTES
40
45
$0
FIGURE 2. TOPPORTION OF TEMPERATURE-TIME CURVEFOR RUN5
the total "effective time" of reaction because of the steep slope of the heating and cooling curves. I n calculating the naphthalene injected into the reactor system, corrections were made for leakage (about 0.1 cc. per hour a t 5800 pounds pressure), for line holdups, and for changes in mercury or naphthalene temperatures throughout the system. The symbols a and /3 are used t o represent the grams of pure naphthalene that the reactor would hold at the temperature just preceding the rapid heating period and at the temperature of polymerization, respectively. The data for the determination of a: and /3 were obtained in a separate investigation of the temperature-density relations of naphthalene ( 1 4 ) .
FEBRUARY, 1938
INDUSTRIAL AND ENGINEERING CHEMISTRY
Because of the small mass of ethylene dissolved in the naphthalene, the mass of the latter forced out of the reactor by expansion during heating, which was measured, should differ negligibly from the value ( a - p), a calculated quantity based on independently determined expansion properties of pure naphthalene. This comparison served as an indication of the absence of a gas phase during polymerization, through run 13. Since by that time the conditions necessary for establishing a single phase were fairly well known and the presence of a mixed phase could be detected by the necessity for continually feeding in more naphthalene during the polymerization period in order to maintain pressure, the experimental technic was modified slightly for the sake of convenience but a t the expense of accuracy in determining the amount of naphthalene expanded out during heating. Those runs which were definitely mixed phase, as determined by the criteria described (labeled M in Table I), were not used in subsequent interpretation of the data. Additional evidence of the presence of but one phase and of the accuracy of measurements comes from a comparison of a , the amount of pure naphthalene which the reactor could hold a t the temperature and pressure just prior to rapid heating, with the grams of naphthalene actually put in with the ethylene (columns 9 and 12). The difference of these quantities should measure the volume occupied by the ethylene in solution. Figure 3 shows this difference plotted against the dissolved ethylene, and permits the conclusion that ethylene when dissolved has an effective specific volume about 50 per cent greater than naphthalene. Figure 3, the ordinate of which corresponds to the difference of numbers of approximately the same magnitude, indicates the substantial absence of any gas phase in those runs not marked M (mixed phase) in Table I. An exception is run 17M which was thought to have a small amount of gas phase present because of the action of the injector during polymerization but which, according to Figure 3, was substantially one phase. The calculation of the ethylene concentration a t the start of the polymerization period involves not only the small corrections for holdup of the connecting tubing and expansion of the reactor, but also a large correction for the ex-
TABLE I. RESULTSO F Run N0.a
Inside Reactor Temp. O
6 5 7 25 11G 8G 90 IOG
35c 13M 17M1 27
777
733
18
12 28 36Cat.b 22 21 16M 24 23 32 31 330 300 29G 26 3 2
710 675
675 640 518 249
pansion of the solution in the reactor during the rapid heating period. This correction was calculated in two ways, first, by using the weight of naphthalene actually expanded out and, secondly, by using the value of (a - p). About a fifth of the ethylene was expanded out each time. The two methods usually checked so closely that the concentration could be considered reliable to one part in two hundred. The volume and analysis.of the product gas were both corrected for the air in the separator. T o test the accuracy of measure5 z ments involved in making a material balance and the right to assume no holdup of ethylene by the 2 solidified naphthalene, run 2 was 55 made a t 249" F. (121" C.) where no polymerization c o u l d o c c u r . The calculated loss of ethylene was $$ &cc one part in two hundred-i. e., zero within experimental error. 3 In order to test for the catalytic 4 0 0 1 2 3 effect of the walls, the reactor for GRAMS ETHYLENE PRESENT one run was filled with S.A. E. 6145 steel shavings having a surface a t A~~~~~ least four times that of the reactor, PIED BY ETHYLENE DISSOLV~D IN NAPHand some chrome1 filings. Only 3 THALENE per cent more of the ethylene disappeared in a total disappearance of 30 per cent. Since experimental errors might account for part of this difference (3" F. would account for all of it, and the stirrer could not be used in this run), it was concluded that the reaction is essentially homogeneous. The naphthalene used did not crack, as shown by the absence of gas formation when pure naphthalene was heated to over 800" F. (425" C.) in one of the runs. To determine whether there was any possibility that naphthalene was reacting with ethylene, a run was made in which 32.2 grams (0.25 mole) of naphthalene were heated with ethylene three times under conditions of temperature, time, and concentration many times more severe than those used in other runs14 minutes a t 777" F. (414" C.) 15 minutes a t 777" F.
POLYMERIZATION
z-
,
Ep$O:;TME
+
Phase Liquid Liquid Liquid Liquid Gas Gas Gas Gas Gas Mixed Liquid? Liquid Liquid Liquid Liquid Liquid Liquid Liquid Mixed Liquid Liquid Liquid Liquid Gas Gas Gas Liquid Liquid Liquid
Pressure Reaction Vol. of Analysis of Product Gasduring Time Product Gas High Run (Cor.) (70' F.,1 Atm.) CZHI polymers Residue CzHz L b . / s q . in. Min. cc. % % % % 68.9 375 87.0 6.745.84(0.45) 31.8 (0.45) 636 95.5 2.6 1.4 19.2 1.4 732 97,25 0.9+ (0.46) 0.5 9.4f 1133.5 1.7+ 96,75 1.0+ 47 ... 50.95 (0.45) 13.5 79.4 -. -1 6.6 32.8 9.5 86.9 (0.45) ... 660 3.0 779 17.45 91.3 (0.45) 6.4 1.8 ... 810 4.75 11.92 1.75 93.05 (0.45) 117540.30 5.15 10.37 1.36 93.2 5800 34.7 1246 88.1 6.85 4.6 (0.45) 5800 28.0 1291 95.6 0.60 2.3 1.6 5800 34.66 1055 96.05 0.55 2.2+ 1.25800 2S.4+ 1113 97.45 0.5 1.65 0.5 90.7 629 (94.9) 1 1 1 3030 64.0 725.5 95.7 3030 2.0 1.5 0.8 64.17 3030 689.5 93.841.95 3.75 0.51.1+ 0.55800 70.85 975 96.1 2.3 5800 47.83 1183 97.15 0.5 1.15 1.2 2.11.20.25 5800 48.9 2783 96.5 2.0+ 1.0+ 0.5 5800 169.8 1019 96.45 1.2 1.0+ 0.5 5800 126.0 1150 97.3 87,56 1260 97.4 5800 0.9 1.25 0.45 254.1 750 95.3 3030 1.4 2.65 0.65 ... 44.3 3204 96.9 1.65 1.0 0.45 115.4 1299 ... 95.2 0.35 ... 203.8 820 93.5+ 2 . 78 + 3 0.45 5soo 1.4 0.7 0.5 336,6 1190 97.4+ 3030 51 =I= 1075 98.9 0.0 1.31 . . .? 3030 480 * ............. Not analyzed . . . . . . . . . . . . . . . . . .
...
i:;
.....
+
EXPERIMENT8
--
F.
185
7 CZH4 Concn. a t Concn. a t start of poly- end of polymerization merization Moles per liter 0.362 0.111+ 0.358 0.2266 0.359 0.270 0,540 0.415 0.134 0.3596 0.2158 0.3595 0.3624 0.272 0.364 0.290 0.4145 0.569 1.651 0.429 0,793 0.469 0.56440.3819 0.571 0.41040.3754 0.2225 0.372+ 0.26340.2503 0.3706 0.5676 0.3485 0.5662 0.4385 1.754 1.048 0.580 0.36840.4258 0.579 0.469 0.576 0.2715 0.38642.012 1.180 0.47940.578 0.2968 0.3680.5855 0.4425 0.420 0.416 0.4935 0.491
-
7
Polymeriaed
% 69.2 36.5 24.6 23.2 62.7 40.0 24.9 20.2 27.0 74.1 42. I ? 32.4 28.1 40.6 29.3 32.4 38.6 22.6 40.37 36.4 26.4418.5 29.5 41.3417.1 19.26 24.4 Nil Nil
Runs 1, 4, 14, 15, 19, 20,. and 24 are not included because they were either of a preliminary nature or were unsuccessful because of leakage or breakdown. b R u n 36Cat. was made with extra reactor surface added i n the form of metal turnings.
186
INDUSTRIAL AND ENGINEERING CHEMISTRY
35 minutes a t 733' F. (389" C.). I n all, 0.58 mole (or 16.2 grams) of ethylene was put into the reactor in three separate chargings. No noticeable coke was formed. The liquid recovered from the reactor weighed over 12 grams in excess of the naphthalene put in, Cpon fractionation in a Podbielniaktype column, it yielded 3.5 cc. of liquid boiling below 200" C . , 33.1 grams between 200" and 220" C. (almost pure naphthalene), with the remainder in the still as a brown residue, about a gram of which solidified upon cooling. This solid residue
TIME. MINUTES
CONCENTRATION us. TIME FIGURE 4. ETHYLENE
c
was filtered and recrystallized. It was organic, with a melting point above 170" C. and therefore could not have been an ethylene-naphthalene compound (monoethyl naphthalene, for example, melts below -12" C.). It was probably a condensation product of naphthalene, since such products are known to form a t higher temperatures (16). Although slightly more naphthalene was recovered than was charged into the reactor, this is to be expected from the findings of other investigators ( 1 , 11) mho report naphthalene as one of the products of polymerization of ethylene. The only method revealed in the literature by which ethylene can be made to react with naphthalene involves the use of acid catalysts. I n Figure 4 the Concentration of ethylene is plotted against reaction time, and smooth curves have been drawn through data points corresponding to the same initial concentration. Every effort was made to obtain an over-all accuracy of 1 or, a t the most, 2 per cent, based on the total ethylene present. Although no check runs as such were made, runs 27 and 18 (Figure 4,curve for 733" F., 0.570 initial concentration) are near enough together to give proof of the probability of such accuracy. The nature of the gaseous products of the polymerization could not be determined readily because of the small quantities formed each time. The quantity of acetylene was always so small as to be largely accounted for by the trace of it found in the original ethylene. A rather complete analysis of the gaseous products from run 33G indicated that the "residue" had a molecular weight of about 26 and contained 44 per cent air and 11 per cent hydrogen; the remainder of the residue had a molecular weight of about 29 and probably consisted of saturated hydrocarbons. Smith and Woodruff ( I @ , in an investigation carried out as part of the present program, studied the gases produced by polymerizing ethylene in the presence of a partial liquid phase of naphthalene in contrast to the present investigation involving only single phases.
VOL. 30,NO. 2
They found the unsaturated hydrocarbons above ethylene (the gas fraction soluble in 87 per cent sulfuric acid) to have a molecular weight of about 70.
Discussion of Results If ethylene disappearance followed a reaction mechanism of first, second, or higher order, the negative slopes of the lines of Figure 4 would decrease continuously with time. Although their failure to do this might a t first suggest a reaction order less than one, such a conclusion is not consistent with the large effect of a change in initial rate found when the initial concentration is changed. This inconsistency suggests immediately that secondary reactions between ethylene and the polymers produced by the primary polymerization reaction are superimposed on the latter and that there is no possibility of assigning any simple order to the reaction going on after much product has been formed. Consequently, a determination of the reaction order of the primary polymerization reaction should preferably be based on the effect of concentration on the slope of the lines of Figure 4 a t the zero time axis. Since the amount of ethylene disappearing during a run was obtained from the difference in the measurements of ethylene charged and ethylene recovered a t the end of an experiment, i t is obvious that experiments involving a small percentage conversion of ethylene would have low accuracy. It was not considered feasible to make runs in which less than 15 per cent of the ethylene disappeared. The question naturally arises as to whether a t that stage the primary products of polymerization react with ethylene sufficiently to vitiate any treatment of the data based on the assumption of a single reaction occurring. It will be seen that there is a fair degree of consistency of results so long as they are based on runs in which no more than 20 to 30 per cent of the ethylene has disappeared. For a determination of the order of the reaction in its early stages there are two possible methods of analyzing data: (a) a study of the variation with time in residual ethylene concentration for a fixed initial concentration, and ( b ) a comparison of times required in two experiments to produce disappearance of equal fractions of the initial ethylene present when the initial concentration differs in the two runs. The objections to the first method as applied to the present problem are that the data used may properly extend only over a small range of disappearance of ethylene because of complications attending reaction of ethylene with products, and that the curvature of the line representing ethylene concentration us. time is so low near the origin as to constitute a n unsatisfactory basis for differentiating among different possible reaction orders. Figure 5 , center section, center group of curves, shows, for example, the variation in ethylene concentration with time to ,be expected for a simple secondor third-order reaction, the constant of which is chosen to make the line go through the double-circled datum point a t 28 minutes. Between that point and the origin, the two lines differ too little to make additional data of much use if they could be obtained. The second method of determining reaction order, involving the effect of a change in initial concentration on the rate of reaction in its early stages, is more satisfactory. Referring again to Figure 5 , center section, the constants for the simple second- and third-order reactions necessary to put the lines through the double-circled datum point were used to calculate the expected variation of ethylene concentration with time, for an initial concentration of 0.794 mole per liter.
FEBRUARY, 1938
INDUSTRIAL AND ENGINEERING CHEMISTRY
The resultant lines, solid for second-order and dashed for third-order, indicate that the single datum point obtained for this high initial concentration calls for a reaction order of approximately 3. Similar comparisons a t other temperatures are presented in Figure 5 ; a t each temperature a secondand third-order reaction rate constant is determined from one datum point (solid black symbol) and curves are drawn representative of other initial concentrations. If attention is confined to points corresponding to the minimum polymerization studied, the plot indicates that the order of the reaction is between second and third. I n all cases datum points a t high percentages of polymerization indicate higher reaction rates than are called for by an extension of a second- or thirdorder curve which passes through data a t lower percentages of polymerization; this is consistent with the expected effect of superimposed secondary reactions between ethylene and its polymers. The possibi'ity that the order of the ethylene polymerization reaction may be higher than second is not inconceivable, even though we accept the common belief that a true thirdorder collision is too improbable to account for many known reactions. Taylor ( I S ) showed how a polymerization reaction of ethylene could appear to be of second or third or intermediate order if unstabilized product molecules are considered an intermediate product. Another possible mecha-
187
nism which permits interpretation mathematically as a second-, third-, or intermediate-order reaction is based upon the assumption that in the early stages of polymerization the two following reactions predominate:
+ C2H4 ka
C4H8' or C4H8
TZ
CaHlt
(2)
k4
Priming indicates an unstabilized molecule. Assume kr to be negligible compared to ka [free energy data indicate this to be the case below about 425" C. (800"F.)] :
-d E = 2k1E2 dt
$
=
klEz
- 2kzB
+ kaBE
- &B - ksBE
(3) (4)
where E = concentration of ethylene B = concentration of butylene or activated butylene H = concentration of hexylene 1 =
time
Two limiting cases will be considered. I n the first, assume that reaction 1 is substantially in equilibrium or
Thus, the reaction is an apparent third-order reaction. I n the second limiting case, assume that B is destroyed by reaction 2 so readily that the concentration of it which accumulates is negligible; and assume that k2is small compared to ka: -dE = 3kiE2 dt
The reaction is now one of second order. The above discussion indicates that the experimentally determined order of the reaction may be nonintegral without being unreasonable, though the equation expressing rate will be valid only in a restricted range of the variables involved. A convenient relation for determining the order of a reaction from two experiments a t different initial concentrations but identical fractional disappearance of reactant is: Ratio of reaction timesof 2 runs
=
1
(ratio of initial concn. for 2 runs where n
L---- ijO ----- -.- - -0 OR
A
5 ORIER OR ER REACTION 0 OR ER REACTION POINT USED TO CALCULATE THE CONSTANT USED FOR EQUATION OF LINES
~ ~ _ _ _
CONCENTRATION WITH FIQUREy5. CALCULATED CHANQE I N REACTANT TIMEFOR DIFFERENT REACTION ORDERS
=
)*-l
reaction order
The results of an analysis of the liquid-phase data using this relation are given in Table I1 which indicate that the reaction is approximately 2.6 order. Since the data show plainly that other reactions enter when the percentage of polymerization is appreciable and throw some doubt on the validity of assuming no complications even a t as low a p o l y m e r i z a t i o n as 20 per cent, it is doubtful whether there is justification for assuming the reaction to be 2.6 rather than third or second order. Analysis of the figures on the gas-phase reaction (Table 11) indicates that, within the accuracy of the data, the r e a c t i o n is second order. (Al-
L
TABLE 11. CALCULATED REACTION ORDERS Reaotion Pply Temp. merisation O
VOL. 30, NO. 2
INDUSTRIAL AND ENGINEERING CHEMISTRY
188 c
F.
Nearest Run No.
%
Initial Conon.
Time
Mole&.
Min.
Order
Liquid-Phase Data 777
23.2
733
30 30 42.1 36
675
29.5 20.0
25 7 18-27 28 17 18-27 17M 12
17M
27 23-24 31 32-23 31
0 540 0.360 0.568 0.374 0 .. 5 76 98 4 0 0.794 0 375 0 794 0 567 0.579 0 384 0 573 0.384
9.43 18.0 31 66 31 18 28.0 94.7 23 39 137 254 95 173
2.6 2.8 2.6 2.62 2.57 2 52 2.50
Gas-Phase Data 777
27.0 24.9*
675
19.3
35G 9G-8G 35G QG 30G 29G
0.572 0.362 0.572 0.362 0.578 0.368
10.4 20.6 9.5 17.5 115 204
possibly insignificant difference in reaction order in the two cases, indicates that the approximately 14 molecules of naphthalene per molecule of ethylene in the liquid-phase experiments are substantially without effect on the ability of ethylene molecules to react with one another. The next consideration is the effect of temperature on rate of polymerization. The reaction rate constant for the liquidphase reaction a t each temperature and a t 24.4 per cent polymerization has been calculated on each of the two assumptions that the reaction is 2, 2.6, or 3 order. Figure 6 (upper part) is a plot of the logarithm of the reaction rate constant us. the reciprocal of absolute temperature. The data for different initial concentrations spread somewhat less when based on the assumption of 2.6 order. The equations of the lines, of substantially identical slope, are:
2.5 2.33
2 order:
40 600 I n k = 26.839 - A 1.987 T
2.00
2.6 order:
In k = 27.400 -
40,600 1.987 T
3 order:
I n k = 27.826 -
40,600 1.987 T
though the calculated order a t 777" F. is 2.3, time measurements on these very short runs were of low accuracy.) It is interesting to n i t e that the absolute magnitude-of the rate of ethylene polymerization in the gas phase is about the same as in the liquid phase a t identical temperatures and concentrations. This, together with the small and
where
k
=
= (mole/liter)l -n/minute
A similar treatment of the small amount of gas-phase data, assuming a second-order reaction, is shown in the lower part of Figure 6. The equation of the line is: In k = 28.387 -
+ X io4 (T =
FIGURE6.
Of.,
ABSOLUTE)
EFFECTOF TEMPERATURE ON REACTION-RATE CONSTANT : (Above) Liquid phase (Below) Gas phase
42,700 1.987 T
For comparison of the absolute magnitude of the reactionrate constants for the gas-phase experiments with those of the liquid-phase experiments, the lower part of Figure 6 includes a dotted line from the upper part for the liquid-phase data, assuming the reaction to be second order. The absolute magnitude of the rate is not very different in the two cases. I n comparison with the results of the gas-phase polymerization, Pease (IS) found an activation energy of about 35,000 calories per gram mole os. the 42,700 found here, and rates similar to those found in this investigation. Storch (17) found a value of 42,000 for the gas-phase polymerization, and noticed that with a higher degree of polymerization the rate had a tendency to increase just as in this investigation. Krauze, Nemtzov, and Soskina (9) found a value of 37,700 for the gas-phase polymerization. I n all three cases the reaction was found to be bimolecular. The application,, to the present data on gas-phase polymerization, of kinetic calculations (8) indicates that, of the collisions occurring between sufficiently activated molecules, only about one in sixty results in the production of a polymer. Mhether the gas- and liquid-phase reactions are actually of different order is open to conjecture. It has already been pointed out that the determination of order of the reaction would preferably have been made from runs involving a smaller percentage polymerization. If such experiments had been feasible, the results might have been modified somewhat in the direction of greater similarity of the liquid- and gasphase results. On the other hand, the two reactions may actually have different mechanisms. There is the possibility that the naphthalene may have a mild catalytic effect (either negative or positive) upon the reaction, possibly aiding in the formation of free radicals, just as solvents play a large part in "ion" reactions ( 7 ) . Similar investigations, using substances other than naphthalene for the solvent, would check this point.
Literature Cited (1) Berl and Forst, 2.angew. Chem., 44,193 (1931). (2) Bragg, D.Sc. thesis, Mass. Inst. Tech., 1933.
FEBRUARY, 1938
INDUSTRIAL AND ENGINEERING CHEMISTRY
Davis and Quiggle, IND. ENG.CHEM.,Anal. Ed., 2, 39 (1930). Francis and Kleinsohmidt, Oil Gas J.,28, No. 29, 118 (Dec. 5, 1929). Frey, IND.ENG.CHEM.,26, 198 (1934). Geniesse and Reuter, Ibid., 24, 219 (1932). Hinshelwood, J . Chem. SOC.,1933, 1357. Hinshelwood, “Kinetics of Chemical Change in Gaseous Systems,” 2nd ed., pp. 53 and 55, Oxford Univ. Press, 1929. Krauze, Nemtzov, and Soskina, Compt. rend. acad. sci. U .R. S. S., 2 , 301, 305 (1934). Lewis, Trans. Am. Inst. Mining M e t . Engrs., 107, 11 (1934). Norton and Noyes, Am. Chem. S.,8 , 362 (1886). Obersheider and Boyd, IND.ENG. CHEM.,Anal. Ed., 3, 123 (1931).
189
(13) Pease, S. Am. Chem. SOC.,53, 613 (1931). (14) Russell and Hottel, IND.ENG. CHEM., to be published i n 1938. (15) Sachanen and Tilioheyev, Ber., 62B,658 (1929). (16) Smith and Woodruff, M.Sc. thesis, Mass. Inst. Tech., 1935. (17) Storch, J. Am. Chem. Soc., 56, 374 (1934). (18) Treadwell and Tauber, Helv. Chim. Acta, 2, 601 (1919). (19) Tropsch and Philippovich, Brennst0.f.-Chem., 4, 147 (1923). (20) Wood, Fuel, 9, 289 (1930). RECDIVED December 4, 1937. Abstracted from a thesis by F. R. Russell submitted i n partial fulfillment of the requirements for the degree of D.Sc. from the Massachusetts Institute of Technology.
STRENGTH OF NITROCELLULOSE SOLVENTS Comparative Toluene Dilution Ratios of Pure Solvents and Solvent-Coupler Mixtures Several criteria have been proposed t o evaluate solvent strength as related t o the use of solvents in lacquers. This paper makes available some new data that provide a more comprehensive view of the subject. The criteria studied here are (1) toluene dilution ratios, (2) viscosities of solutions of nitrocellulose in the solvents and mixtures, and (3) phase diagrams which provide a complete evaluation of solvent strength by combining both dilution ratio and viscosity data. Dilution ratios and viscosities of nitrocellulose solutions are given for the pure solvents belonging t o homologous series of acetic esters, ketones and ether-alcohols and for some thirty binary mixtures of pure solvents with various alcohols. Tables indicate the composition of maximum solvent strength in each of the binary mixtures studied. Phase diagrams are given for nitrocellulose solutions in four lacquer solvents of commercial purity, and the preparation and interpretation of the diagrams are discussed.
ARTHUR K. DOOLITTLE Carbide and Carbon Chemicals Corporation, South Charleston, W. Va.
HE value of a solvent for nitrocellulose depends upon a
T
number of factors which vary in their importance according to the type of lacquer in which the solvent is to be used. Among the factors which must be considered in evaluating a solvent for a particular purpose are cost, odor, color, stability, evaporation rate, solvent strength, compatibility with gums and resins, blush characteristics, and flow characteristics. It is not the intention of this paper to place undue emphasis on the importance of the solvent strength of lacquer solvents, since this is but one of the factors contributing to the value of a solvent. The purpose is, rather, to make available to the industry new data that provide a more comprehensive view of the subject and to draw certain obvious conclusions from the data. A number of methods of evaluating the solvent strength of solvents have been proposed by investigators in this field (2, 4, 8, 20, 22, 27, 88)l but only two methods are commonly employed which are related to the actual performance of the solvents in lacquers. These two methods are known as the dilution ratio method and the viscosity method. Baker (2) in 1913 first proposed that the viscosity of solutions of nitrocellulose in mixtures of solvents might serve as an index to the solvent strength of the mixtures, and much subsequent matter appears in the literature in regard to the viscosities of solutions of nitrocellulose in mixtures (1, 3, 1416, 19-23). To Sproxton (l7), however, belongs the credit 1 The list of literature citations is given a t the end of the third paper i n this series (page 203).
