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The solubility of hydrogen in glassy poly(vinyl acetate) at elevated pressures
of Membrane Science, 50 (1990) 19-29 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
19
THE SOLUBILITY OF HYDROGEN IN GLASSY POLY(VINYL ACETATE) AT ELEVATED PRESSURES
S. ZHOU and S.A. STERN* Department of Chemical Engineering NY 13244 (U.S.A.)
and Materials
Science,
Syracuse
University,
Syracuse,
(Received April 10,1989; accepted in revised form September 9, 1989)
Summary The solubility of H, in glassy poly (vinyl acetate) (PVAc) has been determined by a gravimetric technique at 5.0 and - 5.O”C in the pressure range from 1 to 20 atm. The solubility is a nonlinear function of the gas pressure and can be described by the “dual-mode” sorption model. The solubility decreases with increasing temperature. The values ofthe solubility coefficient (S) vary from a maximum of 6.5 X 10-x cm3 (STP) / ( cm3 polym.-atm) at 1.5 atm and -5.O”C to a minimum of about 1.9 X 10-x (in the same units) at 19 atm and 5.O”C. The fact that the H,/PVAc system exhibits dual-mode sorption behavior was anticipated from the observation of Meares that a plot of log S versus l/T, the reciprocal absolute temperature, exhibits changes in slope in the glasstransition region of the polymer. The possible effect of the size of penetrant gas molecules on dualmode sorption is discussed.
Introduction
It is well known that the solubility coefficients, S, and the effective diffusion coefficients, D, for light gases in glassy polymers can be strongly nonlinear functions of the penetrant pressure or concentration in the polymers [l-8]. This behavior has been observed with a number of gases in a variety of glassy polymers, and can be described quantitatively in terms of a “dual-mode” sorption model [l-8]. The model predicts that the onset of the nonlinear dependence of S or D on pressure (or concentration) for a given penetrant/polymer system, which commonly occurs when the temperature is lowered through Tg, should be accompanied by a change in the slopes of log S or log D versus l/T plots [ 2,101, and vice versa; T is here the absolute temperature and Tg is the glass transition temperature of the polymer. The above behavior, which reflects a change in the mechanism of gas solution and transport, may occur at temperatures much lower than T, if the “excess” free volume of the polymer is small [ 9,101. *To whom correspondence should be addressed.
0376-7388/90/$03.50
0 1990 Elsevier Science Publishers B.V.
20
In order to further test the relationship between the dependence of S on p and the slope of log S versus l/T plots, the solubility of H, in glassy poly (vinyl acetate) (PVAc, Tg = 23 ‘C ) was measured at 5.0 and - 5.0’ C in the pressure range l-20 atm. The H,/PVAc system was selected for the following reasons: (1) Meares [ 11,121 has determined apparent solubility coefficients for HZ, He, Ne, 02, and Ar in PVAc in the temperature range 4-44’ C. Meares reported that the log S and log D versus l/T plots for these gases exhibited two discontinuities, one at 15-18” C (depending on the penetrant ) and the other at 26 oC (near T,). The measurements were made at pressures which were too low to show dual-mode sorption behavior [lo]. However, the discontinuities in the log S and log D versus l/T plots suggest that the H,/PVAc system should exhibit dual-mode sorption behavior at higher pressures. (2) Some investigators have argued that a change in the slope of a log S or log D versus l/T plot at the T, of a penetrant/polymer system will occur only if the size of the penetrant molecules exceeds a certain critical value which depends on the mean free volume of the polymer [ 13-161. If this hypothesis is correct, the penetrant size should also be a factor in the appearance of dualmode sorption behavior at the Tg of a given polymer. Dual-mode sorption behavior has been observed with CO, in PVAc [ 171, and consequently it was interesting to determine whether it would be observed also with smaller molecules, such as H,. (3 ) No solubility data appear to have been reported for H, in any type of glassy polymer at elevated pressures. Experimental
Apparatus and procedure The solubility of H2 in poly(viny1 acetate) was measured by a gravimetric method. This method measures the weight gain of a polymer sample due to the absorption of penetrant gas. In the present study, the change in sample weight was determined by means of a recording electromicrobalance which was modified for high-pressure applications. A diagram of the microbalance and of the auxiliary components and instrumentation is shown in Fig. 1. The microbalance was manufactured by Cahn Instruments, Inc. (Paramount, CA), and was designated by the manufacturer as the Model Cl100 Pressure Balance. The balance consisted of two main units: a weighing unit and a control unit. The weighing unit was contained inside a stainless steel vessel rated for a maximum pressure of 300 atm at ambient temperature. The vessel could also be evacuated to a pressure of lo-” Torr. A sample of polymer membranes in flat-sheet form was suspended from one arm of the microbalance inside “hangdown” tube I, and was counterpoised by a tare weight on the other arm inside hangdown tube J, cf. Fig. 1. The weighing unit and the gas supply system were enclosed in a thermostated air bath. The
21
VACJJUM
PRESSURE
RALANCE
DATA COLLECTION
Fig. 1. Diagram of microbalance apparatus. A,B: thermocouple gauge; C: diffusion pump; D: mechanical pump; E: digital pressure gauge (O-60 psia); F: digital pressure gauge (O-1000 psia); G: gas reservior; H: high pressure gas purifier; 1,J: hangdown tube; S: polymer sample.
control unit of the microbalance was connected to a data acquisition unit which consisted of an ACRO-900 16 bit A/D converter manufactured by Acrosystems Co. (Beverly, MA) and an IBM PC-XT personal computer. The gas supply system consisted of a 3-l gas reservoir, two high-precision digital pressure gauges, and a series of stainless steel bellows valves. The two pressure gauges were manufactured by Dresser Industries Inc. (Newtown, CT) and designated Model 901B; these instruments were operative in the pressure ranges of O-60 and O-1000 psia, respectively, and had a span accuracy of 0.05%. The temperature of the polymer sample in hangdown tube I was controlled to within ? 0.05’ C of the desired value by means of circulating water from a Model RTE-8 constant-temperature circulator manufactured by Neslab Instruments, Inc. (Newington, NH). The temperature of the air bath was maintained within kO.l”C of the desired value by means of a heating tape whose power input was regulated by a proportional thermistor temperature controller manufactured by Cole-Parmer Instrument Co. (Chicago, IL) and designated Dyna-Sense Model 2156. Temperature uniformity inside the air bath was ensured by circulating compressed air. The following experimental procedure was employed. The apparatus containing the polymer sample was first evacuated until the weight of the sample became constant. The microbalance and the vacuum pumps were then isolated from the rest of the system. The penetrant gas, in this case HP, supplied from a high-pressure cylinder, was introduced into gas reservoir G, and allowed to reach the temperature of the air bath surrounding the reservoir. The valves
22
connecting the gas reservoir and the microbalance weighing unit were then opened, thus allowing the penetrant to contact the polymer sample. The weight gain of the sample caused by absorption of penetrant at the desired pressure and temperature was recorded by the data acquisition system. The measurement was continued until solution (absorption) equilibrium was attained, i.e., until the absorption rate became negligibly small (within the experimental error). Solution equilibrium was deemed to have been attained when the weight of the polymer sample remained constant for a period of at least one hour. Materials 1. Polymer The polymer used in this study was poly (vinyl acetate ) (PVAc) , which has the following structural formula: -[-CH,-CH-]I
n
0-C-CH, II 0 The polymer was used in the form of flat sheet membranes, which were cast from a solution of polymer beads in acetone. The polymer beads were obtained from Aldrich Chemical Co., Inc. (Milwaukee, WI) and were reported to have a Ford No. 4 viscosity of 24-30 set, at 25°C. Reagent-grade acetone was obtained from Fisher Scientific Co, (Rochester, NY). The procedure of casting the membranes was reported elsewhere [lo]. The membrane used in the solubility measurements had a nominal thickness of 633.0 /rn (24.92 mil) and a density of 1.191 g/cm3. The glass transition temperature, Tg, of the polymer was found to be about 23’ C, as determined by differential scanning calorimetry. The ?“, value was taken at the mid-point of the heat capacity change during the glass transition. Values of T, between 25 and 32 ‘C have been reported in the literature. 2. Gas The H, gas used was obtained from the Linde Division of Union Carbide Corp. The gas was stated by the supplier to have a minimum purity of 99.99 mol% and was used without further purification. Treatment of experimental data The solubility of H, in PVAc was calculated from the weight gain of the polymer sample at solution equilibrium by means of the following relation: c=22,414M,/(M.W:V,),
(1)
23
where c is the equilibrium concentration of H, absorbed by the membrane at pressure p and a given temperature, in cm3 (STP)/cm3 polym.; M, is the equilibrium weight gain of the membrane, i.e., the total amount of penetrant absorbed by the membrane at solution equilibrium, in g; M.W. is the molecular weight of the penetrant gas, in g/mol; and VP is the volume of the polymer, in cm3. The solubility coefficient, S, is given by the relation: (2)
S=CIP,
where S is in units of cm3 (STP ) / [ cm3 polym.-atm] . The maximum experimental error in the concentration c and in the solubility coefficient S was estimated to be ? 16.1% and t 16.5%, respectively. These relatively large errors were due to the very low solubility of H2 in PVAc at the experimental conditions. Experimental results The solubility of H, in glassy PVAc was determined at two temperatures, 5 and - 5 oC, in the pressure range from 1 to 20 atm. The results of the solubility
0
5
Applied
10
20
Pressure,
Fig. 2. Solubility isotherms for Hz in poly(viny1 acetate). eqn. (3) using the parameters listed in Table 1.
The solid curves are calculated
from
24
Fig. 3. Solubility coefficient S vs. applied pressurep are calculated from (4) using the parameters
for H, in poly (vinyl acetate) in Table 1.
The solid curves
measurements are presented in Fig. 2 in the form of solubility isotherms, i.e., as plots of the equilibrium penetrant concentration, c, versus the applied pressure, p. The solubility isotherms are seen to be nonlinear at both temperatures studied. The solubility of Hz in PVAc decreases with increasing temperature, as has been observed for many gases in both glassy and rubbery polymers. However, the temperature dependence of the solubility is very weak. Figure 3 presents a plot of the solubility coefficient, S, versus the applied pressure p. It is seen that S decreases with increasing pressure, the decrease being particularly marked at the lower pressures. S decreases with increasing temperature. The shapes of the solubility isotherms and of the S versusp plots for H, in glassy PVAc are similar to those observed with other gases in many glassy polymers [l-8]. Discussion The solubility isotherms in Fig. 2. can be represented in terms of the dualmode sorption model by the relation [l-8] : c=kDp+c;Ibp/(l+bp),
(3)
where kD is a solubility coefficient in the Henry’s law limit; c;I is a “Langmuir
25 TABLE 1 Dual-mode sorption parameters for H, in poly (vinyl acetate) Temperature, t (“C)
kD
5.0 -5.0
0.0173 0.0146
cm3(STP) cm3polym.-atm >
l/(1
b (atm-‘)
0.027 0.096
1.84 1.88
+ bp)
Fig. 4. Solubility coefficient S vs. 1/ (1 + bp) for Hz in poly (vinyl acetate ) . The solid lines are calculated from eqn. (4) using the parameters listed in Table 1.
saturation” constant; and b is a “Langmuir affinity” constant. Values of the parameters Izn,cn, and b are listed in Table 1; these values were obtained by fitting eqn. (3 ) to the experimental data by means of a nonlinear least-squares technique. The dependence of the solubility coefficients on penetrant pressure can be expressed by the relation: S=c/p=kD+c;Ib/(l+bp),
(4)
where all the symbols are as used in eqn. (3 ) . Equations (3 ) and (4 ) were used in conjunction with the parameters listed in Table 1 to draw the solid curves
26
in Figs. 2 and 3. These figures show that eqns. (3) and (4) describe satisfactorily the solubility of Hz in PVAc at the temperatures of this study. The applicability of the dual-mode sorption model to the present solubility data can be further tested as follows. Equation (4) indicates that a plot of the solubility coefficient S versus l/ (1 -I-bp) should be linear, and have kD as intercept and chb as slope. Such plots are presented in Fig. 4, where the solid curves were calculated from eqn. (4) using the parameters from Table 1, and where the symbols represent the experimental data. Figure 4 shows that the experimental data at - 5.0 oC are well represented by eqn. (4)) indicating dualmode sorption behavior. However, at 5.O”C, two data points at the lowest experimental pressures (at 1 and 2 atm) are not on the calculated line. This is a consequence of the fact that most data points were obtained at higher pressures, and that eqn. (4) is very sensitive to low pressure data. It is interesting to note from Table 1 that parameter kD increases with increasing temperature, which is contrary to the observations made with other gases in glassy polymers [ 18,211. Such a temperature dependence is expected for gases with very low critical temperatures, e.g., He, Hz, and Ne [ 13,14,18211 in rubbery polymers. Parameter kD characterizes the penetrant solubility in the quasi-liquid (Henry’s law) domains of glassy polymers, which are similar to the rubbery state. Parameter c;l, on the other hand, decreases with increasing temperature, in agreement with other observations [ 2,4,6]. Parameter b appears to be temperature independent, at least in the small temperature range investigated. However, it should be noted that parameter b is subject to a much larger error of estimation than parameters k,, and c~. The positive temperature dependence of kD suggests that the solubility of H, in PVAc will increase with increasing temperature at temperatures above T, (where c;I = 0). Meares [ 11,121 has shown that the solubility of H, in PVAc does indeed increase with increasing temperature when the polymer is in the rubbery state, but decreases with increasing temperature in the glassy state. TABLE 2 Comparison of solubility coefficients for H2 in poly (vinyl acetate) Temperature, t (“C)
5.0
-5.0 “At p = 120 Torr. bAt p rr 200 Torr. ‘At I, rr760 Torr.
S
cm3(STP) cm3polym.-atm >
Toi et al. [22]”
Meares [ 121b
Present study’
0.063 0.070
0.032
0.0487 0.0648
21
The same behavior has also been observed by Toi et al. [ 221 with H, in PVAc. The present study tends to confirm the findings of both Meares [ 11,121 and Toi et al. [ 221. The values of S obtained from this study are compared in Table 2 with similar data reported by Toi et al. [ 221 and Meares [ 11,121. The present data are seen to be 29% and 8% lower at 5.0 and - 5.0” C, respectively, than the apparent solubility coefficients reported by Toi et al., which were determined from permeability and diffusion coefficients obtained by the time-lag technique at pressures below 1 atm. Paul [ 231 has shown earlier that the solubility coefficients of gases in glassy polymers determined from equilibrium measurements should be smaller than those obtained from time-lag measurements. The solubility measurements of Meares were also made at pressures below 1 atm by a volumetric technique. The value of S at 5.0” C reported by Meares in Table 2 is 34% lower than found in the present study. This discrepancy may be due to the fact that the former value was obtained by extrapolating a plot of log S versus l/T prepared from the data of Meares at higher temperatures. Conclusions
The present study has shown that the solubility isotherms of H, in glassy PVAc are nonlinear and concave to the pressure axis, as was found with many gases in various glassy polymers. The H, isotherms are represented satisfactorily by the dual-mode sorption model. Such a behavior was anticipated from the work of Meares [ 11,121, who observed discontinuities in the slopes of log S and log D versus l/T plots for H, in PVAc near the Tgof the polymer. These results, together with the results of previous studies [ 11,12,22], provide further evidence that a change in the slope of a plot of log S versus l/T for a given penetrant/polymer system as the temperature is lowered through T,indicates the onset of dual-mode sorption behavior. It has been hypothesized by several investigators that changes in the slopes of log S and log D versus l/T plots at or near T,will be observed only if the size of the penetrant molecules exceeds a certain critical free volume in the polymer [ 13-161. This should also be a criterion for the development of dualmode sorption behavior, if the hypothesis is correct. The fact that dual-mode sorption behavior has been observed with very small molecules, such as H, in PVAc and He in polycarbonate (PC) [ 61, suggests that the sizes of Hz and He molecules are larger than the critical free volumes of PVAc and PC, respectively. PVAc and PC have a relatively large “excess” free volume. It is not known what relation exists between the excess free volume and the critical free volume mentioned above. In any case, dual-mode sorption behavior has been observed
with both small and large molecules in polymers with both small and large excess free volume [ 11,12,22,24]. The dependence of the solution and diffusion behavior of gases in glassy polymers on the size of penetrant molecules requires further study. Acknowledgements
The financial support of Department of Energy, through Energy Sciences, is gratefully acknowledged.
its Office of Basic
References 1
W. R. Vieth, J. M. Howell and J. H. Hsieh, Dual-sorption
2
171. W. J. Koros and H. B. Hopfenberg,
3
polymers, Ind. Eng. Chem., Prod. Res. Dev., 18 (1979) 353. D. R. Paul, Gas sorption and transport in glassy polymers, Ber. Bunsenges.
4
(1979 ) 294. S. A. Stern and H. L. Frisch, The selective permeation
5
Mater. Sci., 11 (1981) 523. H. L. Frisch and S. A. Stern, Diffusion
6
Mater. Sci., 11 (1983) 123. W. J. Koros, A. H. Chan and D. R. Paul, Sorption
7
8 9 10
11 12 13 14 15
theory, J. Membrane
Sci., 1 (1976)
Small molecule migration in products derived from glassyPhys. Chem., 83
of gases through polymers, Ann. Rev.
of small molecules in polymers, Crit. Rev. Solid State and transport of various gases in polycar-
bonate, J. Membrane Sci., 2 (1977) 165. W. J. Koros and R. T. Chern, Separation of gaseous mixtures using polymer membranes, in: R. W. Rousseau (Ed.), Handbook of Separation Process Technology, Wiley-Interscience, New York, NY, 1987, Chap. 20. S. Zhou and S. A. Stern, The effect of plasticization on the transport of gases in and through glassy polymers, J. Polym. Sci., Part B: Polym. Phys., 27 (1989) 205. S. Zhou and S. A. Stern, Submitted for publication. S. A. Stern, U. M. Vakil and G. R. Mauze, The solution and transport of gases in poly(nbutyl methacrylate) in the glass transition region. I. Absorption-desorption measurements, J. Polym. Sci., Part B: Polym. Phys., 27 (1989) 405. P. Meares, The diffusion of gases through polyvinyl acetate, J. Amer. Chem. Sot., 76 (1954) 3415. P. Meares, The solubilities of gases in polyvinyl acetate, Trans. Faraday Sot., 54 (1958) 40. C. A. Kumins and J. Roteman, Diffusion of gases and vapors through polyvinyl chloridepolyvinyl acetate copolymer films. I. Glass transition effect, J. Polym. Sci., 55 (1961) 683. V. Stannett and J. L. Williams, The permeability of poly(ethy1 methacrylate) to gases and water vapor, J. Polym. Sci., Part C, 10 (1965) 45. H. L. Frisch, Mechanisms for Fickian diffusion of penetrants in polymers, Polym. Lett., 3 (1965) 13.
16
B. P. Tikhomirov, H. B. Hopfenberg, V. Stannett and J. L. Williams, Permeation, diffusion, and solution of gases and water vapor in unplasticized poly (vinylchloride), Makromol. Chem., 118 (1968) 177.
17
K. Toi, Y. Maeda and T. Tokuda, Mechanisms of diffusion and sorption of carbon dioxide in poly(viny1 acetate) above and below the glass transition temperature, J. Membrane Sci., 13 (1983) 15.
29
18 19 20 21 22 23 24
W. J. Koros and D. R. Paul, CO2 sorption in poly (ethylene terephthalate) above and below the glass transition, J. Polym. Sci., Polym. Phys. Ed., 16 (1978) 1947. D. Machin and C. E. Rogers, Sorption, in: Encyclopedia of Polymer Science and Technology, Vol. 12, Interscience, New York, NY, 1964, pp. 679-700. A. S. Michaels and H. J. Bixler, Solubility of gases in polyethylene, J. Polym. Sci., 50 (1961) 393. R. Ash, R. M. Barrer and D. G. Palmer, Solubility and transport of gases in Nylon and polyethylene, Polymer, 11 (1970) 421. K. Toi, K. Takeuchi and T. Tokuda, Isotope effect in the diffusion of hydrogen and deuterium in polymers, J. Polym. Sci., Polym. Phys. Ed., 18 (1980) 189. D. R. Paul, The effect of immobilizing adsorption on the diffusion time lag, J. Polym. Sci., A-2,7 (1969) 1811. K. D. Ziegel and F. R. Eirich, Isotope effect in gas transport. II. Effect of the glass transition on the size of the free volume element, J. Polym. Sci., Polym. Phys. Ed., 12 (1974) 1127.
19
THE SOLUBILITY OF HYDROGEN IN GLASSY POLY(VINYL ACETATE) AT ELEVATED PRESSURES
S. ZHOU and S.A. STERN* Department of Chemical Engineering NY 13244 (U.S.A.)
and Materials
Science,
Syracuse
University,
Syracuse,
(Received April 10,1989; accepted in revised form September 9, 1989)
Summary The solubility of H, in glassy poly (vinyl acetate) (PVAc) has been determined by a gravimetric technique at 5.0 and - 5.O”C in the pressure range from 1 to 20 atm. The solubility is a nonlinear function of the gas pressure and can be described by the “dual-mode” sorption model. The solubility decreases with increasing temperature. The values ofthe solubility coefficient (S) vary from a maximum of 6.5 X 10-x cm3 (STP) / ( cm3 polym.-atm) at 1.5 atm and -5.O”C to a minimum of about 1.9 X 10-x (in the same units) at 19 atm and 5.O”C. The fact that the H,/PVAc system exhibits dual-mode sorption behavior was anticipated from the observation of Meares that a plot of log S versus l/T, the reciprocal absolute temperature, exhibits changes in slope in the glasstransition region of the polymer. The possible effect of the size of penetrant gas molecules on dualmode sorption is discussed.
Introduction
It is well known that the solubility coefficients, S, and the effective diffusion coefficients, D, for light gases in glassy polymers can be strongly nonlinear functions of the penetrant pressure or concentration in the polymers [l-8]. This behavior has been observed with a number of gases in a variety of glassy polymers, and can be described quantitatively in terms of a “dual-mode” sorption model [l-8]. The model predicts that the onset of the nonlinear dependence of S or D on pressure (or concentration) for a given penetrant/polymer system, which commonly occurs when the temperature is lowered through Tg, should be accompanied by a change in the slopes of log S or log D versus l/T plots [ 2,101, and vice versa; T is here the absolute temperature and Tg is the glass transition temperature of the polymer. The above behavior, which reflects a change in the mechanism of gas solution and transport, may occur at temperatures much lower than T, if the “excess” free volume of the polymer is small [ 9,101. *To whom correspondence should be addressed.
0376-7388/90/$03.50
0 1990 Elsevier Science Publishers B.V.
20
In order to further test the relationship between the dependence of S on p and the slope of log S versus l/T plots, the solubility of H, in glassy poly (vinyl acetate) (PVAc, Tg = 23 ‘C ) was measured at 5.0 and - 5.0’ C in the pressure range l-20 atm. The H,/PVAc system was selected for the following reasons: (1) Meares [ 11,121 has determined apparent solubility coefficients for HZ, He, Ne, 02, and Ar in PVAc in the temperature range 4-44’ C. Meares reported that the log S and log D versus l/T plots for these gases exhibited two discontinuities, one at 15-18” C (depending on the penetrant ) and the other at 26 oC (near T,). The measurements were made at pressures which were too low to show dual-mode sorption behavior [lo]. However, the discontinuities in the log S and log D versus l/T plots suggest that the H,/PVAc system should exhibit dual-mode sorption behavior at higher pressures. (2) Some investigators have argued that a change in the slope of a log S or log D versus l/T plot at the T, of a penetrant/polymer system will occur only if the size of the penetrant molecules exceeds a certain critical value which depends on the mean free volume of the polymer [ 13-161. If this hypothesis is correct, the penetrant size should also be a factor in the appearance of dualmode sorption behavior at the Tg of a given polymer. Dual-mode sorption behavior has been observed with CO, in PVAc [ 171, and consequently it was interesting to determine whether it would be observed also with smaller molecules, such as H,. (3 ) No solubility data appear to have been reported for H, in any type of glassy polymer at elevated pressures. Experimental
Apparatus and procedure The solubility of H2 in poly(viny1 acetate) was measured by a gravimetric method. This method measures the weight gain of a polymer sample due to the absorption of penetrant gas. In the present study, the change in sample weight was determined by means of a recording electromicrobalance which was modified for high-pressure applications. A diagram of the microbalance and of the auxiliary components and instrumentation is shown in Fig. 1. The microbalance was manufactured by Cahn Instruments, Inc. (Paramount, CA), and was designated by the manufacturer as the Model Cl100 Pressure Balance. The balance consisted of two main units: a weighing unit and a control unit. The weighing unit was contained inside a stainless steel vessel rated for a maximum pressure of 300 atm at ambient temperature. The vessel could also be evacuated to a pressure of lo-” Torr. A sample of polymer membranes in flat-sheet form was suspended from one arm of the microbalance inside “hangdown” tube I, and was counterpoised by a tare weight on the other arm inside hangdown tube J, cf. Fig. 1. The weighing unit and the gas supply system were enclosed in a thermostated air bath. The
21
VACJJUM
PRESSURE
RALANCE
DATA COLLECTION
Fig. 1. Diagram of microbalance apparatus. A,B: thermocouple gauge; C: diffusion pump; D: mechanical pump; E: digital pressure gauge (O-60 psia); F: digital pressure gauge (O-1000 psia); G: gas reservior; H: high pressure gas purifier; 1,J: hangdown tube; S: polymer sample.
control unit of the microbalance was connected to a data acquisition unit which consisted of an ACRO-900 16 bit A/D converter manufactured by Acrosystems Co. (Beverly, MA) and an IBM PC-XT personal computer. The gas supply system consisted of a 3-l gas reservoir, two high-precision digital pressure gauges, and a series of stainless steel bellows valves. The two pressure gauges were manufactured by Dresser Industries Inc. (Newtown, CT) and designated Model 901B; these instruments were operative in the pressure ranges of O-60 and O-1000 psia, respectively, and had a span accuracy of 0.05%. The temperature of the polymer sample in hangdown tube I was controlled to within ? 0.05’ C of the desired value by means of circulating water from a Model RTE-8 constant-temperature circulator manufactured by Neslab Instruments, Inc. (Newington, NH). The temperature of the air bath was maintained within kO.l”C of the desired value by means of a heating tape whose power input was regulated by a proportional thermistor temperature controller manufactured by Cole-Parmer Instrument Co. (Chicago, IL) and designated Dyna-Sense Model 2156. Temperature uniformity inside the air bath was ensured by circulating compressed air. The following experimental procedure was employed. The apparatus containing the polymer sample was first evacuated until the weight of the sample became constant. The microbalance and the vacuum pumps were then isolated from the rest of the system. The penetrant gas, in this case HP, supplied from a high-pressure cylinder, was introduced into gas reservoir G, and allowed to reach the temperature of the air bath surrounding the reservoir. The valves
22
connecting the gas reservoir and the microbalance weighing unit were then opened, thus allowing the penetrant to contact the polymer sample. The weight gain of the sample caused by absorption of penetrant at the desired pressure and temperature was recorded by the data acquisition system. The measurement was continued until solution (absorption) equilibrium was attained, i.e., until the absorption rate became negligibly small (within the experimental error). Solution equilibrium was deemed to have been attained when the weight of the polymer sample remained constant for a period of at least one hour. Materials 1. Polymer The polymer used in this study was poly (vinyl acetate ) (PVAc) , which has the following structural formula: -[-CH,-CH-]I
n
0-C-CH, II 0 The polymer was used in the form of flat sheet membranes, which were cast from a solution of polymer beads in acetone. The polymer beads were obtained from Aldrich Chemical Co., Inc. (Milwaukee, WI) and were reported to have a Ford No. 4 viscosity of 24-30 set, at 25°C. Reagent-grade acetone was obtained from Fisher Scientific Co, (Rochester, NY). The procedure of casting the membranes was reported elsewhere [lo]. The membrane used in the solubility measurements had a nominal thickness of 633.0 /rn (24.92 mil) and a density of 1.191 g/cm3. The glass transition temperature, Tg, of the polymer was found to be about 23’ C, as determined by differential scanning calorimetry. The ?“, value was taken at the mid-point of the heat capacity change during the glass transition. Values of T, between 25 and 32 ‘C have been reported in the literature. 2. Gas The H, gas used was obtained from the Linde Division of Union Carbide Corp. The gas was stated by the supplier to have a minimum purity of 99.99 mol% and was used without further purification. Treatment of experimental data The solubility of H, in PVAc was calculated from the weight gain of the polymer sample at solution equilibrium by means of the following relation: c=22,414M,/(M.W:V,),
(1)
23
where c is the equilibrium concentration of H, absorbed by the membrane at pressure p and a given temperature, in cm3 (STP)/cm3 polym.; M, is the equilibrium weight gain of the membrane, i.e., the total amount of penetrant absorbed by the membrane at solution equilibrium, in g; M.W. is the molecular weight of the penetrant gas, in g/mol; and VP is the volume of the polymer, in cm3. The solubility coefficient, S, is given by the relation: (2)
S=CIP,
where S is in units of cm3 (STP ) / [ cm3 polym.-atm] . The maximum experimental error in the concentration c and in the solubility coefficient S was estimated to be ? 16.1% and t 16.5%, respectively. These relatively large errors were due to the very low solubility of H2 in PVAc at the experimental conditions. Experimental results The solubility of H, in glassy PVAc was determined at two temperatures, 5 and - 5 oC, in the pressure range from 1 to 20 atm. The results of the solubility
0
5
Applied
10
20
Pressure,
Fig. 2. Solubility isotherms for Hz in poly(viny1 acetate). eqn. (3) using the parameters listed in Table 1.
The solid curves are calculated
from
24
Fig. 3. Solubility coefficient S vs. applied pressurep are calculated from (4) using the parameters
for H, in poly (vinyl acetate) in Table 1.
The solid curves
measurements are presented in Fig. 2 in the form of solubility isotherms, i.e., as plots of the equilibrium penetrant concentration, c, versus the applied pressure, p. The solubility isotherms are seen to be nonlinear at both temperatures studied. The solubility of Hz in PVAc decreases with increasing temperature, as has been observed for many gases in both glassy and rubbery polymers. However, the temperature dependence of the solubility is very weak. Figure 3 presents a plot of the solubility coefficient, S, versus the applied pressure p. It is seen that S decreases with increasing pressure, the decrease being particularly marked at the lower pressures. S decreases with increasing temperature. The shapes of the solubility isotherms and of the S versusp plots for H, in glassy PVAc are similar to those observed with other gases in many glassy polymers [l-8]. Discussion The solubility isotherms in Fig. 2. can be represented in terms of the dualmode sorption model by the relation [l-8] : c=kDp+c;Ibp/(l+bp),
(3)
where kD is a solubility coefficient in the Henry’s law limit; c;I is a “Langmuir
25 TABLE 1 Dual-mode sorption parameters for H, in poly (vinyl acetate) Temperature, t (“C)
kD
5.0 -5.0
0.0173 0.0146
cm3(STP) cm3polym.-atm >
l/(1
b (atm-‘)
0.027 0.096
1.84 1.88
+ bp)
Fig. 4. Solubility coefficient S vs. 1/ (1 + bp) for Hz in poly (vinyl acetate ) . The solid lines are calculated from eqn. (4) using the parameters listed in Table 1.
saturation” constant; and b is a “Langmuir affinity” constant. Values of the parameters Izn,cn, and b are listed in Table 1; these values were obtained by fitting eqn. (3 ) to the experimental data by means of a nonlinear least-squares technique. The dependence of the solubility coefficients on penetrant pressure can be expressed by the relation: S=c/p=kD+c;Ib/(l+bp),
(4)
where all the symbols are as used in eqn. (3 ) . Equations (3 ) and (4 ) were used in conjunction with the parameters listed in Table 1 to draw the solid curves
26
in Figs. 2 and 3. These figures show that eqns. (3) and (4) describe satisfactorily the solubility of Hz in PVAc at the temperatures of this study. The applicability of the dual-mode sorption model to the present solubility data can be further tested as follows. Equation (4) indicates that a plot of the solubility coefficient S versus l/ (1 -I-bp) should be linear, and have kD as intercept and chb as slope. Such plots are presented in Fig. 4, where the solid curves were calculated from eqn. (4) using the parameters from Table 1, and where the symbols represent the experimental data. Figure 4 shows that the experimental data at - 5.0 oC are well represented by eqn. (4)) indicating dualmode sorption behavior. However, at 5.O”C, two data points at the lowest experimental pressures (at 1 and 2 atm) are not on the calculated line. This is a consequence of the fact that most data points were obtained at higher pressures, and that eqn. (4) is very sensitive to low pressure data. It is interesting to note from Table 1 that parameter kD increases with increasing temperature, which is contrary to the observations made with other gases in glassy polymers [ 18,211. Such a temperature dependence is expected for gases with very low critical temperatures, e.g., He, Hz, and Ne [ 13,14,18211 in rubbery polymers. Parameter kD characterizes the penetrant solubility in the quasi-liquid (Henry’s law) domains of glassy polymers, which are similar to the rubbery state. Parameter c;l, on the other hand, decreases with increasing temperature, in agreement with other observations [ 2,4,6]. Parameter b appears to be temperature independent, at least in the small temperature range investigated. However, it should be noted that parameter b is subject to a much larger error of estimation than parameters k,, and c~. The positive temperature dependence of kD suggests that the solubility of H, in PVAc will increase with increasing temperature at temperatures above T, (where c;I = 0). Meares [ 11,121 has shown that the solubility of H, in PVAc does indeed increase with increasing temperature when the polymer is in the rubbery state, but decreases with increasing temperature in the glassy state. TABLE 2 Comparison of solubility coefficients for H2 in poly (vinyl acetate) Temperature, t (“C)
5.0
-5.0 “At p = 120 Torr. bAt p rr 200 Torr. ‘At I, rr760 Torr.
S
cm3(STP) cm3polym.-atm >
Toi et al. [22]”
Meares [ 121b
Present study’
0.063 0.070
0.032
0.0487 0.0648
21
The same behavior has also been observed by Toi et al. [ 221 with H, in PVAc. The present study tends to confirm the findings of both Meares [ 11,121 and Toi et al. [ 221. The values of S obtained from this study are compared in Table 2 with similar data reported by Toi et al. [ 221 and Meares [ 11,121. The present data are seen to be 29% and 8% lower at 5.0 and - 5.0” C, respectively, than the apparent solubility coefficients reported by Toi et al., which were determined from permeability and diffusion coefficients obtained by the time-lag technique at pressures below 1 atm. Paul [ 231 has shown earlier that the solubility coefficients of gases in glassy polymers determined from equilibrium measurements should be smaller than those obtained from time-lag measurements. The solubility measurements of Meares were also made at pressures below 1 atm by a volumetric technique. The value of S at 5.0” C reported by Meares in Table 2 is 34% lower than found in the present study. This discrepancy may be due to the fact that the former value was obtained by extrapolating a plot of log S versus l/T prepared from the data of Meares at higher temperatures. Conclusions
The present study has shown that the solubility isotherms of H, in glassy PVAc are nonlinear and concave to the pressure axis, as was found with many gases in various glassy polymers. The H, isotherms are represented satisfactorily by the dual-mode sorption model. Such a behavior was anticipated from the work of Meares [ 11,121, who observed discontinuities in the slopes of log S and log D versus l/T plots for H, in PVAc near the Tgof the polymer. These results, together with the results of previous studies [ 11,12,22], provide further evidence that a change in the slope of a plot of log S versus l/T for a given penetrant/polymer system as the temperature is lowered through T,indicates the onset of dual-mode sorption behavior. It has been hypothesized by several investigators that changes in the slopes of log S and log D versus l/T plots at or near T,will be observed only if the size of the penetrant molecules exceeds a certain critical free volume in the polymer [ 13-161. This should also be a criterion for the development of dualmode sorption behavior, if the hypothesis is correct. The fact that dual-mode sorption behavior has been observed with very small molecules, such as H, in PVAc and He in polycarbonate (PC) [ 61, suggests that the sizes of Hz and He molecules are larger than the critical free volumes of PVAc and PC, respectively. PVAc and PC have a relatively large “excess” free volume. It is not known what relation exists between the excess free volume and the critical free volume mentioned above. In any case, dual-mode sorption behavior has been observed
with both small and large molecules in polymers with both small and large excess free volume [ 11,12,22,24]. The dependence of the solution and diffusion behavior of gases in glassy polymers on the size of penetrant molecules requires further study. Acknowledgements
The financial support of Department of Energy, through Energy Sciences, is gratefully acknowledged.
its Office of Basic
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