Permeability of Polymer Films to Hydrogen Sulfide Gas WILLIAM HEILNIAN, VILJO TAMMELA, J. A. MEYER, VIVIAN STANNETT, AND MICHAEL SZWARC D e p a r t m e n t of C h e m i s t r y , S t a t e University of New Y o r k College of Forestry, Syracuse 10, N . Y .
006
-
005
-
the other. Under these conditions, the concentration, C1, of the gas in the first layer of the film at the high pressure side is held constant, while essentially zero concentration is maintained a t the low pressure side. With these boundary conditions, Fick's second law may be integrated ( 7 ) and for large values of time, t, it is found that
2 004 -
Q =
+
D X C t X t
CiXl 6
vi
-
where Q is the amount of gas passing through the film in time t and C1is the concentration of gas in the first layer of film a t the high pressure surface. The increase of Q with time is shown graphically in Figure 1 for the permeation of hydrogen sulfide through a film of poly(vinylidine chloride) (saran) a t 30" C. Q is equal to zero where t equals the time lag, T , and
0
003
-
002
-
001
/
2
4
I
I
I
I
I
6
8
10
12
14
Time, hours
1
ti
Figure 1. Transmission of hydrogen sulfide through saran film at 30" C.
Thus, determination of T leads to the evaluation of the diffusion coefficient, D , w h i l e determination of the slope of the straight line leads t o the permeability constant, P . Finally, using the relation P = DS, the coefficient S may also be determined. For films with l a r g e diffusion constants, such as polyethylene, the steady state is established too quickly to obtain an accurate value of the time lag.
T
HE permeability of polymer films to a large number of different gases has been studied in recent years ( 2 , 5, 6). However, only one paper ( 1 1 ) has reported satisfactory data for hydrogen sulfide. As this gas is an analog of water, and its permeability constants are required for evaluating certain specialized packaging materials, the authors have undertaken systematic studies of its permeation through a number of polymeric films. I n most cases the data enabled them to determine the diffusion constants, D, and solubility coefficients, 8, as well as the permeation constant, P. The permeation of gases through polymer films is primarily a diffusion-controlled process. When the stationary state is reached, the amount of gas, q, passing through the unit area of a polymer film per unit of time satisfies Fick's first law, in that 4 =
DSbl
- P2)
- P(P1
T
- Pz)
1
1
where p l 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 P is normally given in cubic centimeters of gas, a t standard temperature and pressure, per second, per square centimeter of area, for 1-mm. film thickness, and 1 cm. of mercury pressure gradient across the film. D is given in square centimeters per second and S as cubic centimeters of gas at standard temperature and pressure per cubic centimeter of polymer a t 1 atm. pressure. The experimental method used was an adaptation of the (3)and van A ~ high technique described by B~~~~~ gen In this method, the film is initially freed from the dissolved air, and then exposed to pressure, pi, of the desired gas at one surface, while essentially zero pressure is maintained a t
Figure
tially
EXPERIMENTAL PROCEDURE
2. Scale drawing permeability cell
to that used by
T h e experimental method used t o measure the rate of gas transmission is essen-
of
(st
4).
The apparatus consists of a stainless steel permeability cell connected by means of Kovar seals to a high vacuum system; a ~scale drawing of in Figure 2. The film under ~ ~ the cell ~ is shown test is supported on a stainless steel screen and clamped between the two halves of the cell. A vacuum-tight closure is ensured by means of a rubber gasket and a mercury seal, When soft polymer films were used, a piece of filter paper was inserted 82 1
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
822
between the film and the screen, in order to prevent damage to the film by the screen wires. Two cells, each in its individual thermostatically controlled bath, were used; the arrangemcnt is shown schematically in Figuie 3. Two measurements can be made simultaneously with such a system, which is beneficial, because several days are often taken up with one measurement. Before a measurement is started, each plastic film is completely degassed by piimping down to a pressure of about mm. of mercury until a satisfactory vacuum is maintained in the system for a t least 1 hour. The gas is then introduced to the cell a t a constant pressure, PI, as recorded by the U-manometer. The rate of gas transmission through the polymer film is followed by nieasuring the pressure, p ~ on , the McLeod gage connected to the low pressure half of the cell. Hydrogen sulfide, obtained from the Rlatheson Co., was 99.9% pure. The gas was condensed and evacuated before it was admitted to the storage flask. Details about the polymer films used in this study are shown in Table I.
Vol. 48, No. 4
Table 11. Permeability, Diffusivity, and Solubilities of Hydrogen Sulfide in Nylon Temp., Samplen 0 c. so. 0 1
Pressure,
Mm. Hg
..
30
110 153 226 270 404 621 707 591
45 60
74 1 670 720 603 651 688
75 80
9,
D,
Sq. C m . /
Cc./Cc./ Atmos. ..... ..... 7 . 0 i 1.0 (by sorption) 3 . 0 x 10-10 7 . 9 3 . 2 x lo-" 10--10 3 . 9 3 . 1 x 10-19 6 . 0 1o-lJ 0.4 3 . 3 x 10-19 3 . 9 3 . 0 x 10--10 5 . 4 x 10-19 6 . 0 3 , 4 x 10-10 4 . 6 x 10-10 5 . 8 5.3 3 . 4 x 10-10 4 9 x 1 0 - 1 0 3 . 4 x 10-10 5 . 0 X 10-lO 5 . 2 ..... 4.4 i 1.0 ..... (by sorption) 9 . 8 X 10-10 1 . 6 X 10-9 4.7 2 . 4 X 10-Q 6 . 0 X 10-0 3 0 6 . 3 x 10-Q 3 . 5 2 . 4 X 10-9 1 5 x 10-8 2.2 4 . 2 x 10-9 1.7 X 10-8 2.1 5 . 9 x 10-9 2 . 0 x 10-8 3.0 7 . 9 x 10-9 Pb
See.
x x
Samples 1, 2, a n d 3 c u t f r o m s a m e sample of film. b As P is given in units corresponding t o thickness of film of 1 mm. and gradient of pressure of 1 cm. Hg, while S is given in cc./ec./atinos., conversion of P i n t o DS requires a factor of 7.6. a
Table I.
Polymer Films Investigated
Material Polyamide Cellulose acetate (unplas ticized) Cellulose acetate (plasticized with 15% dibutyl plithalate) Rubber hvdrochloride
TradeSame Nylon 6
PliofiGr; NO , . . , .
llylar' A Saran 61 7 Etliocel 610
Source Du P o n t Polaroid
Thickness, hlm. 0 114 0 028
Polaroid Goodypar Polaroid Polaroid Polaroid D u Pont Du P o n t Doiv DOW
0 0 0 0 0 0 0 0 0
028 019 023 018 018 0162 031 025 076
I n addition, sorption isotherms n-ere determined by variour; materials using a quartz helix microbalance. Measurements were carried out as described by Prager, Bagley, and Long (9). RESULTS
The values obtained for the permeability and diffusion constants and the solubility coefficients €or all the polymer films ~tiidiedare given in Tables I1 and 111. The figures for nylon
show t h a t good agreement was obtained between the two samples st,udied. The solubility of hydrogen sulfide in nylon films, measured with the quartz helix microbalance, is included in Table I1 to show that the direct method and the intercept method give results t,hat agree well within the experimental errors. For ethylcellulose a good agreement was obtained between these two methods a t 0" C.; a t -35" C. the sorption (direct) method gave four times larger results than the intercept method. Figure 4 and 5 illustrate the Arrhenius relationship of P and D on the absolute temperature. The slopes of the straight lines give E , and Eo-i.e., the energies of activation associated with the over-all permeation process and the diffusion process, respectively. The difference between E , and E D gives a measure of A H , t,he heat of solution. Values are listed in Table 117. DISCUSSION
The permeability constants of hydrogen sulfide through the various polymer films investigated vary across a several-thousandfold range a t any given temperature. Hom-ever, the values lie in a n order similar to those found with other gases such as nitrogen or oxygen through a similar series of polymeric films (12). The reasons for such a wide variation in permeability constants have recently been discussed (13). The permeability constants seem to be essentially independent
high
90s purification trap
to vacuum pump
McLead safely valve
Figure 3.
G a s permeability apparatus
Gages
-
Y O C U U ~
manifold
INDUSTRIAL AND ENGINEERING CHEMISTRY
April 1956
823
I0-8-
M P
;IO"-
0
n
Iom-
Figure 4. Temperature dependence of permeability constant 0
8
Figure 5.
0 Nylon
Poly(viny1 butyral) Cellulose acetate (plasticized) Cellulose acetate (unplasticized)
Saran
0 Mylar
8
Temperature dependence of diffusion constant
Poly(viny1 butyral) Cellulose acetate (plasticized) Cellulose acetate (unplasticized)
C,
Q
Nylon
Saran
0 Mylar
-359 '6.5
0 100
0 09 '75
.
;0080
t
0070
0060 0050 0 040
0 030 0020 0 010 0
o
100
200
u
aoo
400
PRESSURE
500
600
100
lmml
Figure 6. Sorption isotherms for hydrogen sulfide
8 0
Ethylcellulose -35' C. Cellulose a c e t i t e (unplasticized), O o C. Ethylcellulose, 0' C.
of pressure, although in nearly every case there is a compensating tendency toward lower solubility coefficients and higher diffusion constants at higher pressures. This tendency has been confirmed by measuring the sorption isotherms for ethylcellulose and cellulose acetate (see Figure 6). The higher solubility coefficients at lower pressures are probably due t o the presence of
strong absorbing sites in the polymer matrix. After their saturation, the additional absorbed gas is held by comparatively weak forces. Similar phenomena were observed in absorption of water vapor b y nylon ( l a )and keratin (8). T o explore these phenomena further, the permeability constants of ethylcellulose were measured a t -35' C. for a range of
INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY
824
Table 111.
Permeability, Diffusivity, and Solubilities Pressure,
D Sq. Cm./Sec. Plasticized a n d Unplasticized Cellulos,e Acetatea Plasticized o 711 2 . 2 x 109 0 . 7 5 X 109 (15% dibutyl 30 68 6.1 2.2 151 5.6 phthalate) 2.4 2.8 355 5.3 3.4 728 5.7 7.2 45 742 7.7 14.4 60 728 12.0 Unplasticized 0.37 0 1.3 0.74 15 2.0 1.0 30 3.5 1.4 3.0 1.6 3.4 3.0 45 4.5 5.05 60 6.1 Film
T$mp.,
C.
Mm. Hg
S, Cc./Cc./ Stmos.
22 21 17.5 14.5 13.0 8.1 6.3 27 21 27 17 16 13 9.1
Permeability, Polymer Films
Poly(viny1 butyral)
Poly(viny1 trifluoroacetate)
758 716 30 156 332 641
30
244 463
2.8 X 2.9
7.52 .~
2 6
45 60 Polyethylene
643 653 668 418 434 396 426 46 103 407 726 407 715 394 694 734 747
0 15 30
Mylar A ( D u Pont polyester film)
10-10
3.9 5.9 7.0 7 . 5 X 10-9 7.5 19.8 19.2 43.3 42.2 43.9 44.1 98.5 1 . 9 X 10-1' 7.2 6.9 13.6 22.5
1.5 X 3.4 4.4 4.4 5 5 6.3
10 18 11 9 8
5 , 5 X 10-9 4.9 6.8 14.7 22 29
0.4 0.4 0.3 0.2 0.2 0.2
,.... .....
.. ..
..... , o . .
,....
.,... ..... .....
..
.. .. .. .. ..
..
Ethylcellulose 117 6.0 X 1W 628 10.0
fi.3 x 109 11.0
72 69
66 122 641 53 128 634
7.2 6.6 10 0 10.0 5.4 11.0
6.3 7.8 12.0 6.3 14.0 22.0
76 R5 65 58 49 39
0
126 704
12.0 13.0
28.0 39.0
33
14 0 15.0
51
l5
113 716
21 17.5
- 30
- 15
30 45 60
Conversion of P t o
DS
57 126 715 54 150 138 611 690 requires
16.0 17.0 16.0 19.0 20.0 23.0 21.3 21.6 a factor of 7.6.
Film
P O
Nvlon C&idose acetate Plasticized Unplasticired Pliofilm S O Cellophane Poly(viny1 butyral) Poly(viny1 trifluoroacetate) Polyethylene
Mvlar A Saran Ethylcellulose
DO
ET,
ED
AH
3.2
13.9
302
16.4
2 . 5 x 10-5 0 . 8 9 X 10-6 537 2800 8 . 7 x 10-0 5 . 1 X 10-6 0.58 1 . 4 X 10-5 210 3 . 2 X 10-6
5.1 4.5 17.6 21.4 4.3 5.9 10.0 7.4 17.8 1.8
0.011 0.001 1 . 3 X 10' 1 . 3 X 10" 8 . 9 x 10-3 5.9 X
9.2 4.1 3.2 8 2 23.0 5.4 32.9 11.5 8.5 4.2 10.0 4.1
0.032'' 1 . 6 X IO6 0.013
ii:s 22.9 6.9
2.5
4:4 5.1 5.1
Table V. Pressure Dependence of Permeability, Diffusion, and Solubility of Hydrogen Sulfide in Ethylcellulose at -35" c.
15
11.0 7 5 4 2.8
- 35
Table IV. Temperature Dependence of Permeability, Diffusivity, and Solubility of Hydrogen Sulfide
PwrQllPP
,.... 1 . 3 X 10-11 8.1 10.1 28.4 61.5
45 0 30 45 60
a
2.5 X 10-9 4.4 10.5 6.5 6.5 6.5
0 15 30
Vol. 48, No. 4
64 80 98 110 160 170 320 334 420
25
16 13 11 9.1 9.1 5.4 4.9 3.9
pressures. The pertinent data together with the solubility coefficients (obtained by the sorption technique), presented in Table V, made it possible t o compute the diffusion constants (collected in column 4 of Table V) and to show that they increase with increasing concentration of the gas in the film. The authors
believe that. this observation should be interpreted in the same way as observation of the decreasing solubility coefficient-the presence of strong absorption sites in the polymeric matrix immobilizes the initial quantity of absorbed gas, while the additionally absorbed molecules can move more freely (8, IO). The activat,ion energies of diffusion follow the usual pattern. Polymers with high cohesive energies exhibit higher activation energies than those characterized by low cohesive energies. On the other hand, the heats of solution are similar for all the polymers with the exception of nylon and cellophane. The magnitude of the heat of solution is close to the heat of condensation of hydrogen sulfide, and this indicates that the heat of mixing is probably small for most of the polymers investigated. The effect of plasticizer on the permeability of cellulose acetate film is shown by the results given in Table 111. The addition of 15% of dibutyl phthalate approximately doubles the rate of permeation and the rate of diffusion, apparently without lowering the activation energy. Furthermore, the solubilit,y of hydrogen sulfide appears to be a little higher in the relatively more polar unplasticized material. The permeability of slightly plasticized ethylcellulose films has been measured a t both high and low pressures to temperatures as low as -35' C. The Arrhenius plots for both the permeability constant and the diffusion constant are given in Figure 7 . The permeability constant starts to increaje a t very low temperatures and high pressures-Le., for higher relative pressures. This phenomenon is believed to be general for all gases as they approach their saturation pressure (to be discussed in a separate communication). LITERATURE CITED
(1) Amerongen, G. F. van, J . A p p l . P h y s . 17, 972 (1946). (2) Amerongen, G. F. van, J . Polvmer Sci. 5 , 307 (1950). (3) Barrer, R. A%,, "Diffusion in and through Solids," AIacmillan,
New York, 1941. (4) Barrer, R. AI., Skirroa. G. J., J . Polymer Sci. 3, 549 (1948). (5) Brubaker, D. W., Kammermeyer, K., IND. ESG.CHEM.44, 1465 (1952). (6) I b i d . , 45, 1148 (1953). (7) Daynes, H. A., Proc. Roy. SOC.(London) A97, 273 (1920). (8) King. G.. Trans. Faraday Soc. 41,479 (1945). (9) Prager, S., Bagley, B., Long, F. A,, J . Am. Chem. SOC.75, 2742 (1953). (10) Rouse, P. E., Ibid., 69, 1068 (1947). (11) Simril, V. L., Hershberger, h.,;Modern Plastics 27, 95 (July 1950). (12) Stannett, V.. Szwarc, A I . , J . Polymer Sci. 16, 89 (1955). (13) Waack, R., Alex, N., Frisch. H. L., Stannett, V.,Szwarc, M., IND. ENG.CHEM.47, 2524 (1955). RECEIVED for review October 10, 1955. ACCEPTED December 19. 1955. Investigation supported b y the Quartermaster Corps a n d t h e Polaroid Corp.
