Permeabilitv of Polvmer Films to Gases and Vapors J
J
RICHARD WAACK, N. H. ALEX, H. L. FRISCH, VIVIAN STANNETT, AND MICHAEL SZWARC C h e m i s t r y D e p a r t m e n t , College os Forestry, S t a t e University of N e w York, Syracuse 10, N . Y .
I
N RECENT years a number of investigators (1, 6, 7, 11), employing different experimental techniques, have reported data on the transmission of gases through polymer films. The present investigation was undertaken to supplement existing data, particularly with respect to the “permanent gases” nitrogen, oxygen, and carbon dioxide, and t o study the effect of variables such as temperature and film thickness on the rate of permeation. I n addition, the permeability of a number of polymer films to the two organid vapors methyl bromide and ethylene oxide has been studied at a number of temperatures and pressures. The experimental arrangement used to measure the rate of permeation was an adaptation of the high vacuum technique used by Barrer (3) and van Amerongen ( 2 ) . The permeation of gases and vapors through polymer films appears to be primarily diff usion-controlled. Thus, when the stationary state of flow is attained, the flux, q-i.e., the amount of gas passing through the polymer film per unit area and timesatisfies Fick’s first law in that
polymer films and the permeability was determined for each of them. I n general, good agreement was obtained between the various samples, as shown in Table 11. Measurements made a t different temperatures were always concluded by returning to the original temperature and repeating the determination. I n this way, the effects of any irreversible changes in the film, such as crystallization or degradation, could be detected, Literature values, when available, were either similar to or greater than the measured values. TheFe considerations led to the belief that the values reported in this paper are genuine characteristics of the polymer film concerned and that errors due to pinholes and other imperfections have been avoided.
Table I. Material Polyethylene Polyamide Polyester Poly(viny1idene chloride) Ethylcellulose (plasticized) Cellulose acetate (plasticized) Polvtrifluoromonochloroethylene Rubber hydrochloride Poly(viny1 alcohol)
where pl and p~ are the pressures of the gas on both sides of the barrier, 1 is the thickness of the film, D is the diffusion constant, S is the solubility coefficient, and P is the permeability constant, which is equal to DS. For the permanent gases, D and S are essentially constant for all pressures; this i s in contradistinction to the case of organic vapors, where D and S often increase with increasing pressure (6, 9). The temperature dependence of D and S is given by the usual exponential function; hence, the temperature dependence of the permeability constant is given also by the Arrhenius equation
Table 11.
Film Ceiluloseacetate Mvlar A
Polymer Films Used Trade Name Alathon Nylon6 Mylar Saran Ethocel
Grade
.. ..
A 517 610
Lumarith P-912 Trithene Pliofilm Reynolon
B
FM-1 GA134
Thickness, Mm. 0.026 0.113 0.031
Supplier Du Pont Du Pont Du Pont Dow Dow
0.025
0.075
Celanese
0.025
Visking Goodyear Reynolds Metal
0,025
0.063
0,025
Reproducibility of Measured Permeability Constants Thickneas, Mm. 0.025 0.031
Gas Nz
Nz
Tzmp., C. 0 0
P = Poexp ( - E , / R T )
Sample 2 3 4 Permeability Constant X 10’0 0.87 0.82 0.86 0.76 0.029 0.018 0.029 . .
.,0.;7
...
..
where E,, the permeation activation energy, is the sum of the activation energy for diffusion Ed and the heat of solution, A H , of the gas in the polymer. RESULTS EXPERIMENTAL PROCEDURE
The experimental method used to measure the rate of gas transmission is essentially similar to that used by Barrer (3,4). The apparatus consists of a stainless steel permeability cell connected by means of Kovar seals to a high vacuum system. The permeability cell and the equipment and method of operation have been described in detail (8). The permeability constants are given in units of cubic centimeters of gas a t standard temperature and pressure per second per square centimeter of area, 1 mm. in thickness, a t a pressure difference of 1 cm. of mercury across the film. The gases used in this study, obtained from the Matheson Co., were of the following purities: nitrogen, 99.9%; oxygen, 99.6%; carbon dioxide, 99.9%; methyl bromide, 99.4%; and ethylene oxide, 99.5%. The polymer films used were donated by a number of companies and are described in Table I. To ensure accurate permeability values, several samdes were c u t from various parts of the
The permeability constants of nitrogen, oxygen, and carbon dioxide for a number of polymer films were calculated from the measured gas transmission by means of Equation 3 and are listed in Table 111. A typical plot showing the rate of transmission is given in Figure 1; its shape indicates that the permeation is diffusion-controlled. The data of Table IV for the permeation of nitrogen through polyethylene show the permeability constant to be independent of pressure and film thickness. This was found to be true in all the cases investigated, confirming the results of other workers ( 2 , 3, 6). Graphs of the logarithms of the permeability constant vs. the reciprocal of absolute temperature gave good linear plots, as exemplified in Figure 2. The values for Ep and POwere calculated in every case and are given in Table V, together with pertinent values taken from the literature. The permeability constants of ethylene oxide and methyl bromide were found often to be dependent on the pressure of 2524
INDUSTRIAL AND ENGINEERING CHEMISTRY
December 1955
2525
Table 111. Permeability Constants Film Lumarith P-912
Thickness, Mm.
Gas
0.025
Na
(Units. Temp.,
c.
- 25 0 30
Cc. STP/second/mm./sq. om./cm. Hg X 10'0) Permeability Thickness, Constant Film Mm. 0.28 Pliofilm F M - 1 0.025 0.85
60
- 25
Nz
0.031
Nylon 6
Nz
0.113
0.0045 0.022 0.11 0.18 0.24 0.37 0.046 0.13 0.45 1.1 0.028 0.095 0.47 1.47 2.87
0 30 60 70 80 - 25 0 30 60 0 30 60 80 90
01
N2
2.30 5.40 7.80 27.6
30 60 Mylar A
C. - 25 0 30 60 - 25 0 30 60 0 30 60 80 90
2.8 8.6
- 250
01
?rnp.,
Gas
0 2
Nz
0.025
Saran 517
0
02
30 60 90
coz
0
30 60 80 90
Permeability Constant 0.049 0.44 1.5 7.4
0.34 2.1 5.4 25.0 0.0005 0.0094 0.15 0.54 0.79
0.0016 0.051 0.65 4.0 0.061
0.29 3.1 5.0 14.7
vapor used. The values for a number of pressures and temperatures are listed in Table VI. The pressure dependence of the permeability constant, if any, obeyed approximately the relationship: log P = a
+ bp
where a and b are constants dependent on temperature and on the film and gas under consideration. Examples of this relationship are shown in Figure 3.
OE
0.7
0.6
-
2
0.5
I
w
0 4
3
fn w
a 0.3 5 z (0.1'
02
01
,x
I
I 10-14
'
1
I
I
2 8
32
3 6
4 0
f 00 0
I
2
3
4
5
TIME (HOURS)
Figure 1. Typical plot of pressure us. time Carbon dioxide through Mylar IOOA, 30' C., and 714-mm. pressure
X
IO',
O K
Figure 2. Temperature dependence of permeability constant
INDUSTRIAL AND ENGINEERING CHEMISTRY
2526
Vol. 47, No. 12
I XtO'
Table IV. Effect of Pressure and Thickness on Permeability Constants for Polyethylene Temp.,
c.
Gas
Xitrogen
Pressure, Mm. Hg
P X 108
0.025
500 750
0.18 0 19
0.050
253 494 74 1
0 20 0.19 0.19
I Ilo"
0.075
260 500 748
0.20 0.19 0.21
S I a-'
0.025 0 050 0 075
237 237 237
3.2 4.0 3.4
30
0
Ethylene oxide
5.10'
Thickness, 1Mm.
P I
Table V. Material Lumarith Mylar Nylon
Grade
Values of Po and Ep Gas
PO
Nn
coz
1 . 3 X 10-5 0 . 5 X 10-5 2 . 9 x 10-6
6.5 5.0 4.3
This paper This paper
A
Nn Oz
25-V-200
Con
1 . 3 X 101 . 2 X 104 . 1 X 10-6
7.5 6.4 6.2
This paper Thispaper (9)
6
Nz 01
1 . 4 X 10-3 1 . 3 X 10-3 1 . 6 X 10-8
11.2 10.4 9.7
Thispaper This paper This paper
3 . 2 X 10-3 0 . 7 7 X 10-3 1 . 9 X lo-*
10.0 8.4 8.6
Thispaper This paper
1.2 1.1 3 . 3 X 10-2
16.8 15.9 12.3
This paper This paper This paper
coz
0.36 0.0091 1 . 8 x 10-5
13.0 10.0 7.4
(9)
N2 Oz COz
9 . 2 X 10-6 2.9 X 10-5 3 . 5 X 10-7
4.2 4.2 1.3
Thispaper This paper Thispaper
Nz
0.26 0,031 0.0018
11,5 9,6 6.8
This paper This paper This paper
FM-1
NO Saran
517
Nz 0 2
Con Nz
0 2
COz
Trithene
B
Nz 0 2
Ethocel Polyethylene
Reference
Oz
COz Pliofilm
S I 104
Ep
P-903
P-912
610
DE 2500
0 2
coz
to.'
I
(9) IL IO'
5r 10''
(IO)
This paper This paper
DISCUSSION
The permeability constants €or any gas vary enormously with the nature of the polymers, such differences being related to the physical and chemical characteristics of the membrane. It is known, for example, that amorphous polymers have higher permeabilities than crystalline polymers. Thus, highly crystalline cellulose has a very low permeability, whereas the less crystalline cellulose acetate has a much greater permeability. However, crystallinity alone does not necessarily determine the transmission rate, as is shown by considering the permeation through polyethylene, polytrifluoromonochloroethylene, and poly(viny1idene chloride), all crystalline polymers, but with greatly differing permeabilities. Poly(viny1idene chloride) is a symmetrical molecule with a high cohesive energy density and, therefore, has a very low permeability. Polyethylene is even more symmetrical, but the cohesive energy is much lower and thus it has a much larger permeability constant. Polytrifluoromonochloroethylene is unsymmetrical but has a high cohesive energy and shows intermediate behavior. The activation energies for the over-all permeation process show a similar trend, with poly(viny1idene chloride) highest, polytrifluoromonochloroethylene intermediate, and polyethylene lowest (see Table V). I n an unsymmetrical molecule such as rubber hydrochloride, the poor symmetry which interferes with molecular packing results in a more open structure and consequently higher permeability. A similar effect should result from branching of the polymer chains, producing a less regular structure whiah can be less readily incorporated into a space lattice. An increase in the degree of cross linking may decrease the
IO'
I
I
I
1
100
150
200
250
1
1
1
300
350
400
Pressure m m Hg
Figure 3.
Pressure dependence of permeability constant for ethylene oxide and methyl bromide 0 Lumarith-ethylene oxide 0' C. oxide d o C. (3 Polyethylene-methyl biomide, - 15O C. Pliofilm-methyl bromide, 0' C.
0 Pliofilm-ethylene
8 Kel-F-Methyl bromide.
60' C.
Table VI. Permeability Constants for Ethylene Oxide and Methyl Bromide Temp.,
c.
Film
A. Lumarith P-912
Mylar
Pliofilm
Saran Kel-F (Trithene B)
Polyethylene
Ethooel Poly(viny1 alcohol)
Pressure, Mm. Hg
Ethylene Oxide 0 75 149 163 235 30 163 60 163 30 340 60 340 295 195 80 340 0 75 123 180 236 343 30 260 260 0 333 30 333 417 60 333 0 81 166 191 237 374 30 237 60 237 30 230 325 347 0 338
P
x
108
1.7 6.1 7.4 28.0 4.0 3.5 0.013 0,026 0.023 0,030 0.044 2.9 4.2 12.0 30.0 73.0 0,064 0.10 0.12 0.13 0.15 0.44 2.2 2.1 2.7 3.2 5.9 10.0 35.0 41.0 43.0 41 . O 0.0002
(Continued)
Table VI.
Permeability Constants for Ethylene Oxide and Methyl Bromide (Continued) T,emp., Pressure, Mm. Hg.
C.
Film
B. Luinarith P-912
20 30
80
90
394 313 287 405 141 262 386 155 262
378
30 60 80 90
Pliofilm
20 60
Saran
30
314 264 403 152 294 391 140 250 134 252 399 141 275 392 138 262 3 8.5 -_.
60 80
Kel-F (Trithene B)
90 30 60 80 90
Nylon
60 70 80 90
Polyethylene
P
x
106
Methyl Bromide 60
Mylar
2527
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
December 1955
- 15
153 284 397
130
229 375 3 14 137 268 393 152 294 393 141 249 370
133 255 380 144 262 389 140 272 387 141 287 388 92 213 323 412 378 264 395 136 267 390 ~
0
20
60
~~
0.58 0.56 0.71 0.68 0.95 0.96 0.96 1.2 1.2 1.3 0.0022 0,008 0,008 0.015 0.016 0.015 0.030 0,029 0.94 2.3 5.1 2.0 2.5 3.4 0.0079 0.013 0.029 - 0,057 0.065 0.079 0.26 0.29 0.40 0.009 0.31 0.39 0.46 1.o 0.85 0.63 1.2 1.2 1.4 0.067 0.077 0,084 0.10
0.12 0.12 0.25 0.28 0.28 0.46 0.38 0.41 2.0 5.4 24.3 40.4 10.4 12.5 15.0 61.2 54.5 47.2
rate of permeation owing to the consequent stabilization of segmental motion. Thus, irradiated polyethylene has been found less permeable than untreated polyethylene (IO). On the other hand, increasing chain flexibility would increase the ease of permeation. As for the effect of the natllre of the gas on permeabilities, the permeability constants of nitrogen, oxygen, and carbon dioxide are found to increase regularly in that order for all the polymer films examined. This trend is largely due to the influence of the molecular diameter of the gas molecule on the diffusion constant and to the increasing solubility of the gas In the film, which is known to follow the ease of condensation of the gas ( 3 , 1 1 ) . Thus, oxygen has a smaller molecular diameter than nitrogen or carbon dioxide, but carbon dioxide is overwhelmingly more soluble than oxygen, which in turn is more soluble than nitrogen. The permeabilities of methyl bromide and ethylene oxide are more difficult to interpret, as they are often pressure-dependent. I n general, however, their permeabilities through various polymer films follow the same order as those of the permanent gases. The relationship between the pressure and the permeability constant for the case of organic vapors is complex and will be the subject of a later communication. However, even with these vapore, the permeability constant is independent of film thicknesE B E shown, for example, in Table IV. ACKNOK LEDGMENT
The authors are glad to acknowledge the financial support of this work by the Quartermaster Corps. LITERATURE CITED
(1) Amerongen, G. J. van, J. A p p l . Phys., 17, 972 (1946). (2) Amerongen, G. J. van, J . Polymer Sci., 5 , 307 (1950).
(3) Barrer, R. M., “Diffusion in and through Solids,” Cambridge
University Press, Cambridge, 1951. (4) Barrer, R. RI., and Skirrow, G. J., J . Polymer Sci., 3, 549 (1948). (5) Ibid., p. 564. (61 ENG CHEM.. ~, Brubaker. D. W.. and Kaminermever. ’ K.. IND. 44, 1465 (1952); 45, 1148 (1953)( 7 ) Doty, P. M., Aiken, W. H., and Mark, H., TND. ENG.CHEW., ANAL.ED., 16, 686 (1944). (8) Heilman, W., Tammela, V., RIeyer, J. A., Stannett, V., and Szwarc, M., J. Polymer S c i . (in press). (9) Kokes, R. J., and Long, F. -4.,J . Am. Chem. Soc., 75, 6142 (1953). (10) Platenius, H., Modern Packaging, 17, 2103 (1943). (11) Simril, V. L., and Hershberger, A., Modern Plastics, 27, 95 (1950). (12) Sobolev, I., Meyer, J. A., Stannett, V., and Szwarc, M., J . Polymer Sci., 17, 417 (1955). RECEIVED for review April 27, 1955.
ACCEPTEDAugust 20, 1955.
