Douslin, D. R., Harrison, R. H., J. Chem. Thermodyn., 5, 491 (1973). Edwards, C., Lipa, J. A., Buckingham, M. J., Phys. Rev. Lett., 20, 496 (1968); value of (r = 0.08 f 0.08 has been revised to 0.14 f 0.007: see J. A. Lipa, Thesis, University of Western Australia, 1970. El Hadi, Z. E. H. A,, Durieux. M., Van Dijk, H., Physica. 41, 289, (1969). Eubank, P.T., Adv. Cryo. fng., 17, 270 (1972). Feke, T. T., Lastovka, J. B.. Benedek, G. B., Langley, K. H., Elterman, P. 6.. Opt. Commun., 7, 13 (1973). Garnbill, W. R., Chem. Eng., 64, 261 (1957). Gielen. H.. Jansoone, V., Verbeke, O., J. Chem. Phys., 59, 5763 (1973). Giglio. M.. Benedek, G. B., Phys. Rev. Lett., 23, 1145 (1969). Goodwin. R. D., J. Res. Natl. Bur. Stand., 74A, 655 (1970). Goodwin, R. D., NBS Tech. Note 653, April 1974. Green, M. S.. Cooper, M. J., Levelt Sengers, J. M. H., Phys. Rev. Lett., 26,492 (1971). Griffiths. R. B., Phys. Rev., 158, 176 (1967). Habgood. H. W., Schneider, W. G., Can. J. Chem., 32, 98 (1954). Hall, K. R., Canfield, F. B., Physica, 33, 481 (1967). Hall, K. R., Eubank, P. T., lnd. fng. Chem., Fundam., 15, 80 (1976). Jacobsen, R. T., Stewart, R. B., J. Phys. Chem. Ref. Data, 2, 757 (1973). Jansoone, V., Gielen, H.. De Boelpaep, J., Verbeke, 0.B., Physica, 46, 213 (1970). Kagoshima, S., Ohbayashi, K., Ikushima, A., J. Low Temp. Phys., 11, 765 (1973). Keenan, J. H., Keyes, F. G., Hill, P. G., Moore, J, G., "Steam Tables", Wiley, New York, N.Y., 1969. Kierstead, H. A., Phys. Rev., A7, 242 (1973). Kreglewski, A., Therrno. Res. Center, Texas A&M University, private communication, 1975. Levelt Sengers, J. M. H., Straub, J.. Vicentini-Missoni, M., J. Chem. Phys., 54, 5034 (1971). Levelt Sengers, J. M. H., Greer, S. C., int. J. Heat Mass Transfer, 15, 1865 (1972). Levelt Sengers, J. M. H., Greer, W. L. Sengers, J. V., J. Phys. Chem. Ref. Data, in pressr(1976). Lipa, J. A,, Edwards, C., Buckingham, M. J., Phys. Rev. Lett., 25, 1086 (1970).
Lunacek, J. H., Cannell, D. S., Phys. Rev. Len., 27, 841 (1971). Michels, A . , Blaisse, B., Michels, C., Proc. Roy. SOC.,A160, 358 (1937); temperature scale corrected as recommended by J. M. H. Levelt Sengers, W. T. Chen, J. Chem. Phys.. 56, 595 (1972). Michels, A., Levelt, J. M. H., de Graaff, W., Physica, 24, 659 (1958); with correction of temperature scale as in J. M. H. Levelt Sengers, lnd, fng. Chem., Fundam.. 9, 470 (1970). Moldover, M. R., Phys. Rev., 182, 342 (1969). Mulholland, G. W., Zollweg. J. A., Levelt Sengers, J. M. H., J. Chem. Phys., 62, 2535 (1975). Narsimhan. G. J. Phys. Chem., 67, 2238 (1963). Osborne, N. S., Stimson, H. F., Ginnings, D. C., J. Res. Mtl.Bur. Stand., 18,389 (1937). Roach, P.. Phys. Rev., 170, 213 (1968). Roder, H. M., Weber, L. A.. NASA, SP-3071, Vol. I(1972). Rowlinson, J. S., Ber. Bunsenges. Phys. Chem., 76 (3/4). 281 (1972). Stanley, H. E., "Introduction to Phase Transitions and Critical Phenomena," Chapter 2, Oxford University Press, Oxford, 1971. Thiesen, M.. Verhl. Deut. Phys. Ges., 16, 80 (1897). Thoen, J.. Vangeel, E., Van Dael, W., Physica, 52,205 (1971). Verbeke, 0. B., J. Res. Natl. Bur. Stand., 76A, 207 (1972). Vicentini-Missoni, M., Levelt Sengers, J. M. H., Green, M. S., J. Res. Mtl. Stad., 73A, 563 (1969). Voronel, A. V., Physica, 73, 195 (1974). Wallace, B., Meyer, H., Phys. Rev., A2, 1563 (1970); "Tabulation of the Original P-V-T Data for 3He-4He Mixtures and for 3He", Physics Dept., Duke University, 1971. Weber, L. A,, Phys. Rev., A2, 2379 (1970). Weiner, J., Langley, K. H., Ford, N. D.. Phys. Rev. Len., 32, 879 (1974). Widom. B., J. Chem. Phys., 43, 3898 (1965). Widom, B., Rowlinson, J. S., J. Chem. Phys., 52, 1670 (1970). Yang. C. N., Yang, C. P., Phys. Rev. Lett., 13,303 (1964). Zollweg, J. A,, Mulholland, G. W., J, Chem. Phys., 57, 1021 (1972).
Received for review M a r c h 11, 1976 Accepted June 8,1976
Solubilities of Gases and Volatile Liquids in Polyethylene and in Ethylene-Vinyl Acetate Copolymers in the Region 125-225 O C David D. Liu and John M. Prausnitz' Chemical Engineering Department, University of California, Berkeley, Berkeley, California 94 720
Gas-liquid chromatography was used to measure low pressure solubilities of nine volatile solutes in polyethylene and in copolymers of ethylene and vinyl acetate containing 3.95, 9.2, and 30.3 wt % vinyl acetate. Solubilities in ethylene-free poly(viny1 acetate) were reported earlier. The solutes studied are methyl ethyl ketone, acetone, isopropyl alcohol, vinyl acetate, sulfur dioxide, methyl chloride, ethane, ethylene, and carbon dioxide. While gas-liquid chromatography provides a rapid and simple method for measuring solubilities, experimental precautions must be observed to assure reliable results. Such precautions are particularly important for sparingly soluble solutes (e.g., ethane, ethylene, carbon dioxide) where the measured solubilities tend to be less accurate than those attained with higher-boiling solvents.
Introduction Ethylene-vinyl acetate copolymers are widely used in competition with plasticised vinyl resins or vulcanized rubbers. They are also used as modifiers of wax and similar materials and as strength-contributing polymers in hot-melt adhesives. Since ethylene is a gas as well as a sluggish monomer, high pressure must be used in the synthesis of ethylene-containing copolymers rich in ethylene and to achieve reasonably rapid reaction rates. Typical reaction conditions are in the range 100-300 "C and 1000-2500 atm. Since the reaction is rarely complete, low pressure separators are used to separate unreacted monomers from the copolymer for recycling. These separators also separate other volatile ad330
Ind. Eng. Chern., Fundarn., Vol. 15, No. 4, 1976
ditives in the reaction mixture. For engineering design, therefore, it is necessary to have available accurate solubilities of volatile compounds in the polymer.
Thermodynamic Analysis The equation for vapor-liquid equilibrium for volatile component i is
where y , is the vapor phase mole fraction, P is the total pressure, w ,stands for the weight fraction in polymer phase, R is the gas constant, and T is the absolute temperature. The
A
A
DETECTOR
n
BUBBLE FLOW-METER
CARRIER GAS iHelium1
MERCURY MANOMETER
Table I. Properties of Volatile Solutes Purity, %
Solute
Supplier
Methyl ethyl ketone Acetone
99+
Aldrich Chemical Co., Inc.
99+
Vinyl acetate Isopropyl alcohol Methyl chloride Sulfur dioxide Carbon dioxide Ethane Ethylene
99+ 99+ 99.5+ 99.98 99.8 99.0 99.5
MC & B Manufacturing Chemists Union Carbide Corp. Aldrich Chemical Co., Inc. The Matheson Co., Inc. The Matheson Co., Inc. The Matheson Co., Inc. The Matheson Co., Inc. The Matheson Co., Inc.
RECORDER
Figure 1. Gas chromatographic apparatus.
weight-fraction activity coefficient, O,*, is unity when the solubity w,is low. Correlations discussed by Prausnitz (1969) and by Maloney and Prausnitz (1976b) can be used to estimate the fugacity coefficient, +,, and the liquid-phase, infinitedilution, partial-molar volume, E, -. The only parameter which cannot be estimated accurately is the weight-fraction Henry's constant, H,, defined by L L H, p lim f(2) w,-0 tu, where f L L is the fugacity of component i in the liquid phase. The weight-fraction Henry's constant is the most important parameter in the calculation of w,.
Experimental Section Henry's constants were measured for several volatile solutes used in industrial copolymerization process. A few other solutes were also selected for basic interest. Experiments were carried out from 125 to 200 "C using gas-liquid chromatography (GLC). The use of GLC for thermodynamic measurements has been reviewed by Kobayashi et al. (1967) and by Young (1968). Applications of GLC to the study of polymer melts were discussed by Smidr6d and Guillet (1970), Guillet and Stein (1970), Patterson et al. (1971), Hammers and de Ligny (1971), Newman and Prausnitz (1972, 1973a,b), Brockmeier (1972), Brockmeier et al. (1972, 1973), Lichtenthaler et al. (1974), Liu and Prausnitz (1976), Maloney and Prausnitz (1976a,b), and others. These articles provide the general background for the work reported here. Apparatus. Figure 1 shows the essential features of the apparatus. The helium carrier gas flow rate was controlled with a Negretti and Zambra pressure regulator. Solute samples were injected into a Hamilton 86800 injection block with a 1-pl Hamilton syringe or with a 100-p1gas syringe. A Carle Model 1000 thermal conductivity detector and a Honeywell 1-mV recorder were used to detect and to record solute concentrations in the carrier gas. A stopwatch and a 10-ml bubble flowmeter were used to measure flow rates. The column was placed in a 3/4-ft3constant temperature bath. Dow Corning 200 silicone fluid was used as bath fluid from 125 to 175 "C. For higher temperature measurements, a fused-salt mixture with 40% NaN02, 7% NaN03, and (53%) K N 0 3 was used. The temperature was controlled by a Hallikainen Thermotrol temperature controller to f 0.1 "C. Silicone oil bath temperatures were measured with a mercury-in- glass thermometer while fused-salt bath temperatures were measured with a calibrated copper-constantan thermocouple. Temperature fluctuations within the bath were a t most fO.l "C. Materials. All solutes were used as obtained from standard suppliers without further purification; details are given in
Table I. Since all the GLC elution peaks are single and symmetric, there appear to be no significant impurities in the samples. One low-density, branched polyethylene and three ethylene-vinyl acetate copolymers were used. Their properties, as provided by the manufacturer, are shown in Table 11. Column Preparation. Columns were prepared by dissolving a weighed amount of polymer into 100 ml of rn-xylene a t 130 "C. After the polymer was completely dissolved, a weighed amount of preheated SO/lOO mesh Chromsorb W (acid washed, DMCS treated) was stirred into the solution. The mixture was then placed in a vacuum oven a t 100 "C to evaporate the m-xylene completely; this required 2 days. The coated support was then packed into Shs-in. i.d. stainless steel tubing which had been previously washed with hexane and acetone. Columns details are summarized in Table 111.The amount of polymer inside each column is known to better than f0.5%. Data Reduction. Assuming that the gas phase in the column behaves as an ideal gas, that the solute fugacity is proportional to its weight fraction in polymer, that true thermodynamic equilibrium is attained in column, and we can utilize a simple relation between solute-retention data and weight-fraction Henry's constants given by Newman and Prausnitz (197313) (3) The specific retention volume, V,, is given by
V, = Qtr
(2-
(4)
The factor j 2 corrects the finite pressure drop through the column. According to James and Martin (1952),j 2 is
The solute net retention time, t,, is measured by subtracting the dead time of the column from the solute injection-peak maximum retention time
t, = ti - td
(6)
The injection-peak maximum retention time for nitrogen provided a good estimate for the dead time in eq 6. However, to correct to the finite solubility of nitrogen in polymer, we used a previously given equation (Liu and Prausnitz, 1976)
Ind. Eng. Chem., Fundam., Vol. 15,No. 4, 1976
331
Table 11. Polymer Properties
(1
Polymer
Sample name
Bn
XL
Poly(ethy1ene) Ethylenevinyl acetate copolymersb
DYNH-9 DXM-228 DXM-231 DXM-196
36 600 36 600 42 300
147 900 415 500 325 800
Ici,
Melting index,' dg/min
Density g/cm3
392 700 2 793 000 2 238 100
0.5 0.91 2.9 14.0
0.9193 0.9302 0.9266 0.9530
Vinyl acetate content, w t % 0 3.95 9.2 30.3
From Union Carbide Corp., polymerized by the high-pressure process. From Union Carbide Corp. See ASTM D1238-65T.
,
Table 111. Column Characteristics
Column
Wt 96 vinyl acetate in copolymer
Mass of polymer, g
Coverage mass ratio X 100 (polymer/support)
I I1 I11 IV V VI VI1 VI11 IX X
0 0 0 3.95 3.95 3.95 9.2 9.2 30.3 30.3
16.541 14.307 9.308 16.352 10.683 6.468 15.820 7.209 15.906 12.500
40.0 27.1 21.0 35.4 24.0 21.2 36.9 23.0 40.0 32.0
I
I
16-
I
I
I
"12
E
L!
O
I
0
I4 -
P
I
-
0.6
0.028 cc/g
1 1 1 1 1 , 1 1 o
b
B
0
Q
2
4 6 8 1 0 1 2 1 4 Peak H e i g h t , mV
Figure 3. Sample-sizeeffect of carbon dioxide in column VI11 at 131.6 "C.
I
,-. - Methyl Ethyl Ketone
--a,?
?' I -
0
+ IsopropyI Alcohol o CorbonDioilde V l n y l Acetate V Methyl Chloride 0 Methyl Ethyl Ketone Sulfur D i o x i d e
-
Vinyl Acetate
"
"
.y--=--
' 41z7'G
0
lsapmpyl Alcohol
Acetone
-
r
Methyl Chloride
Sulfur Dioxide
2
-0.5 p g m a l e
-5 pg mole
Peak Height, mV
Figure 2. Sample-size effect in an EVAC ( W V X = 9.2%);column at 131.4 "C.
2 I
120
140
I
160
I
I
180
200
Temperature,
I
1
220
240
260
"C
Figure 4. Weight-fraction Henry's constants of volatile solutes in polyethylene. where H Nis~Henry's constant for nitrogen. Since H N>> ~ it is not necessary to know HN*accurately but even an approximate value is better than the commonly made assumption that *" = m. Henry's constants for nitrogen in copolymers were estimated by the approximate equation
Hiapparent,
In HN~,EVAC = (WE In HN~,PE) + (WAC In HN*,PVAC) (8) Maloney and Prausnitz (1976a) have shown that Henry's constant for nitrogen in liquid polyethylene is In HN,(atm) = 7.49
666 +T(K)
Henry's constant for nitrogen in poly(viny1 acetate) was estimated to be 18 000 atm by Liu and Prausnitz (1976); this estimate is used for all temperatures encountered here. Sample-Size Effect. To assure that the measurements were in the Henry's law region, sample sizes were kept small, generally between 0.5 and 2 Fg-mol of solute. Larger sample 332 Ind. Eng. Chem., Fundam., Vol. 15, No. 4, 1976
sizes were also used to check if retention volumes depend on sample size. Figure 3 shows the result of one study using Column VI11 a t 131.4 "C with flow rate 23.4 cm3/min. As indicated, no sample-size dependence was observed for any of the polar solutes. Figure 4 shows a similar plot for carbon dioxide at experimental conditions similar to those prevailing in Figure 3. The scatter of the data is due to random error in reading the extremely small retention time difference between carbon dioxide and nitrogen. No significant sample-size effect was observed for any of the nonpolar solutes. The polar solute peaks, as well as those for nonpolar solutes, were consistently symmetric. These observations justify the use of Chromosorb W as an appropriate support material for our GLC Studies. Effect of Flow Rate and Polymer Loading. Carrier gas flow rate was always in the region 10 to 24.0 cm3/min. No flow rate effect was observed for all columns.
Table IV. Weight Fraction Henry's Constants (atm) for Volatile Solutes TemDerature. "c 125 PE EVAC (3.95%VAC) EVAC (9.2% VAC) EVAC (30.3% VAC) PE EVAC (3.95% VAC) EVAC (9.2% VAC) EVAC (30.3%VAC) PE EVAC (3.95% VAC) EVAC (9.2% VAC) EVAC (30.3% VAC) PE EVAC (3.95% VAC) EVAC (9.2% VAC) EVAC (30.3%VAC) PE EVAC'(3.95%VAC) EVAC (9.2% VAC) EVAC (30.3% VAC) PE EVAC (3.95%VAC) EVAC (9.2% VAC) EVAC (30.3% VAC) PE EVAC (3.95%VAC) EVAC (9.2% VAC) EVAC (30.3%VAG) PE EVAC (3.95% VAC) EVAC (9.2% VAC) EVAC (30.3% VAC) PE EVAC (3.95%VAC) EVAC (9.2%VAC) EVAC (30.3% VAC)
150
A. Methyl Ethyl Ketone 34.5 53.5 31.5 48.0 27.5 43.5 21.2 34.0 B. Acetone 90 130 84 118 73 104 51 79 C. Isopropyl Alcohol 90 128 75 103 59 87 40 63.5 D. Vinyl Acetate 34 53.4 32 48.5 28 44 22.5 35.5 E. Sulfur Dioxide 269 330 222 276 182 241 112 165 F. Methyl Chloride 204 257 200 256 190 240 151 210 G. Ethane 1180 1220 1010 1200 1070 1210 1080 1280 H. Ethylene 1340 1500 1400 1520 1330 1520 1320 1500 J. Carbon Dioxide 1400 1270 1380 1250 1290 1130 1190 1000
Polymer loading is expressed as the weight ratio of polymer to support. Maloney and Prausnitz (1976a) have shown that for polyethylene on Chromosorb W, no coverage-ratio effect was observed when the coverage ratio is at least 0.08. In this work, all columns were prepared with a coverage ratio above 0.15. At least two columns with different coverage ratios were prepared for each kind of polymer. Experimental GLC results for three columns assured that the retention data are independent of coverage ratio.
Results Measured weight-fraction Henry's constants are presented in Table IV and in Figures 4 to 7. The ethylene-vinyl acetate copolymers started to decompose slowly a t 220 OC. However, reliable data a t 225 "C were obtainable because the 225 "C experiments were finished within 4 h for each column. The column was then tested at 150 "C to assure that the amount of polymer decomposed was not significant. Table V compares some results for polyethylene columns
175
200
225
250
78 69 65.5 51.5
100
120 124 112 101
141
97 86 73
160 153 140 113
204 200 182 158
258 255 236 194
300
168 135 124 96
200 175 170 136
231 223 220 184
272
102 94 86 73
128 123 120 103
157
386 330 303 225
448 404 356 330
509 478 421 388
563
324 312 300 270
385 366 360 346
450 440 424 433
510
1370 1360 1370 1480
1500 1540 1480 1750
1650 1700 1700 2000
1800
1640 1700 1720 1760
1850 1870 1930 2000
1980 2000 2070 2230
2070
1520 1480 1440 1370
1620 1580 1560 1550
1700 1670 1700 1740
1760
78 69.5 64 53
with those reported previously by Maloney and Prausnitz (1976a). Both sets of data were measured using low-density polyethylene. Except for vinyl acetate at 250 "C, all data agree to f1.7% or better. The discrepancy for vinyl acetate a t 250 "C is not surprising because Maloney and Prausnitz reported an error of f15% for vinyl acetate a t this temperature. Error Analysis. There are three major sources of error: (1) random error due to reading injection-peak maximum distance on recorder chart; (2) error caused by inaccuracy of estimated Henry's constant for Nz;(3) other systematic errors. The random error was estimated from the scatter in the data. This error is based on a 95% confidence interval, which was calculated using a Student's t -distribution with the measured standard deviation as outlined by Dixon and Massey (1969). This error is no more than 0.2% for acetone, methyl ethyl ketone, vinyl acetate, and isopropyl alcohol; it is about 0.5 to 1%for methyl chloride and sulfur dioxide; however, it is about 6 to 12% for sparingly soluble gases ethane, ethylene, and carbon dioxide. Ind. Eng. Chem., Fundarn., Vol. 15,No. 4, 1976
333
I1
I
1
I
1
4 Acetone
d Ethane
+Isopropyl Alcohol o Carbon Dioxide x Vinyl Acetate V Methyl Chloride OMethyl Ethyl Ketone
d Ethane
4 3 -
+Isopropyl Alcohol Carbon Dioxide Vinyl Acetate 0 Methyl Chloride 0 Methyl Ethyl Ketone 0 Sulfur Dioxide 0
2 -
=E
I 8 Ethylene
P P H H
% 102-8
e
g
7 -
c
-
0
4
-In
g
V
3 -
2
V
2 -8
c
.e
V
u
e
?
hd
d
@
0
102-
f c" 7 I$ -
t
4
.1
P
+ es
4 3 -t3
2 -
II
125
1
150
I
175 Temperature,
I
200
I
I
225
I
'125
'C
Figure 5. Weight-fraction Henry's constants of volatile solutes in ethylene-vinyl acetate copolymer (WAC = 3.95%).
I
4
-
--9 E
I
I
1
I
4 Acetone dEthane +Isopropyl Alcohol 0 Carbon Dioxide Vinyl Acetate v Methyl Chloride 0 Methyl Ethyl Ketone @ Sulfur Dioxide
.8 Ethylene
-
%
*B
%
$
-
x-
IO+
t
-
7 0
--
E I al c
4
B
3 -
0 2 ...
3
9
B
9
-
-
Q
-
6
-
0
0
;
4
102:
f
c " 7 14
t
+
0
8
-
8
4 -
-e 2 I
125
L
150
I
I
I
175
200
225
The inaccuracy of the estimated Henry's constants for nitrogen in polyethylene using eq 9 is f1096. Henry's constants for nitrogen in copolymers are probably accurate only to 20 to 70%, depending on the vinyl acetate content. Other systematic errors include the error in carrier-gas flow rate measurement, uncertain;ty for the mass of polymer in the column, and errors due to the assumptions in eq 3 and 4. These errors are about f l %except for copolymers a t 225 OC. Due to the somewhat larger uncertainty in the mass of polymer in the column, an error of about f 2 % is expected. Contributions of each type of error are summarized in Table VI for representative solutes a t extreme temperatures. The vertical bars in Figures 4,5,6, and 7 represent the worst possible error expected. 334
I
I
I
175
200
225
Temperature,
I
OC
Figure 7. Weight-fraction Henry's constants of volatile solutes in ethylene-vinylacetate copolymer (WAC = 30.3%).
Table V. Comparison of Weight-Fraction Henry's Constants (atm) for Vinyl Acetate and Ethylene in Polyethylene Temperature, "C Solutes Vinylacetate Ethylene
125 (a); (b) (a); (b)
150
200
34 53.5 102 34.3c 52.0 99.7 1340 1500 1850 139OC 1550 1830
250 157 168
2040 2050
a This work. * Maloney and Prausnitz (1975). Measured at 124 " C
-
m
I+
I
150
Ind. Eng. Chern., Fundarn., Vol. 15,No. 4, 1976
Discussion The GLC technique is a simple and rapid method for measuring solubilities of volatile solutes in nonvolatile solvents. By careful design of experiment and by varying experimental conditions, one can assure that the data obtained so quickly are not affected by flow rate, sample size, and coverage ratio. The usefulness of the rapid GLC technique is shown by the solubility data in copolymers a t 225 "C. The traditional slow static method is unpractical at this temperature since a significant amount of polymer decomposes during a long-time experiment. A molten salt bath is used in this work instead of the hot-air oven used by previous workers (Newman and Prausnitz, 1972, 1973a,b; Lichtenthaler et al., 194; Maloney and Prausnitz, 1976a) to eliminate significant temperature gradients. Error due to column temperature uncertainty is negligible in a molten salt bath. The physical properties of copolymers depend significantly on the ethylenehinyl acetate ratio. Figure 8 shows the effect of composition on the weight-fraction Henry's constants for several solutes. Henry's constants for polar solutes at first change little as vinyl acetate concentration in the polymer increases, but then change rapidly as we approach ethylenefree poly(viny1 acetate). This nonlinear behavior is probably due to nonrandom mixing in the liquid state. Attempts are
Table VI. Summary of Error Analysis for Three Volatile Solutes (5%) Methyl ethyl ketone Error
Ethane
Methyl chloride
125 "C
225 "C
125 "C
225 "C
0.1
0.2
0.5
1.5
6
0 0 0 0 1
1.0 1.0 1.2 1.5 2
0.2 0.2 1
1.4 2 2
4 4 4
1 1
0.8 0.8 1.5 2 2
8 1
9 1
1.1 1.1 1.1 1.1
3.2 3.2 3.4 3.7
1.7 1.7
4.3 4.3
2.5
5.0 5.5
8.4 9 9
15 15 15 20
Random Uncertainty in HN*for: PE EVAC (3.95 wt % VAC) EVAC (9.2 wt % VAC) EVAC (30.3 wt % VAC) Other systematic errors
125 "C
250 "C 10
Maximum total errorn
PE EVAC (3.95 wt % VAC) EVAC (9.2 wt % VAC) EVAC (30.3 wt % VAC) a
2.5
15
Assuming no cancellation of various error sources.
0
Carbon Dioaide
+ Isopropyl Alcohol X Vinyl Acetate
2 0
I
I
I
I
0.2
04
0.6
0.8
1
j , = pressure gradient correction factor (see eq 5) Mi = molecular weight of solute i MN* = molecular weight of nitrogen m2 = mass of polymer in GLC column PE = polyethylene P = pressure PI = GLC column inlet pressure PO = GLC column outlet pressure PVAC = poly(viny1 acetate) Q = volumetric carrier gas flow rate R = gasconstant T = absolute temperature t d = dead time of a GLC column t i = injection-elution-peak-maximum time t , = net retention time (= ti - t d ) V , = specific retention volume uj = liquid-state, infinite-dilution, partial molar volume of solute i wi = liquid-state, weight-fraction concentration of solute i & = gas-phase fugacity coefficient of i Di* = weight-fraction activity coefficient of i in the condensed phase WE = weight fraction of ethylene in copolymer WVAC = weight fraction of vinyl acetate in copolymer
1.0
Vinyl Acetote Weight Fractton in Copolymer
Figure 8. Effect of polymer composition on weight-fraction Henry's
constants at 150 "C. now in progress to interpret these and similar experimental observations with a suitable statistical-mechanical model. Henry's constants shown in Table IV are of direct application in process design. Equation 1 (with Qi* = 1) is applicable as long as the liquid-phase-solute weight fractions are in the order of a few percent.
Acknowledgment For financial support, the authors are grateful to the National Science Foundation, the Donors of the Petroleum Research Fund, administered by the American Chemical Society, Gulf Chemicals Company, and Union Carbide Corporation. Nomenclature EVAC = ethylene-vinyl acetate copolymer f i L = liquid-state fugacity of component i Hi = weight-fraction Henry's constant of solute i 2" - weight-fraction Henry's constant of nitrogen
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Received for review March 25, 1976 Accepted July 26, 1976 Ind. Eng. Chem., Fundam., Vol. 15, No. 4, 1976
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