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Sorption and partial molar volumes of inert gases in rubbery polymers
journal of MEMBRANE SCIENCE
ELSEVIER
Journal of Membrane Science 93 ( 1994) 45-52
Sorption and partial molar volumes of inert gases in rubbery polymers Yoshinori Kamiya*, Keishin Mizoguchi, Yasutoshi Naito National Institute of Materials and Chemical Research, 1-I Higashi Tsukuba, Ibaraki 305, Japan Received 12 April 1993; accepted in revised form I4 March 1994
Abstract Sorption of inert gases (He, Ne, Ar, Kr, and Xe) in two rubbery polymers, 1,2_polybutadiene (PB) and poly(ethylene-co-vinyl acetate) (EVAc), and dilation of the polymers due to the sorption were measured as a function of the gas pressure at 25°C. For all the gases, the sorption isotherms followed the Henry’s law over the pressure ranges examined, and the dilation isotherms were linear in these ranges. From the sorption and dilation data, the partial molar volumes vR of the dissolved gases were determined. A linear relation was found between rR and the van der Waals volume VW; i.e., rR= 1.6 rw+ 20 in cm3/mo1. This is much the same as the relation for hydrocarbon gases dissolved in the same polymers and that between molar volume and rw for liquid n-alkanes. There also existed a linear relation between & and the logarithm of Henry’s law coefftcient for a series of inert gases in the polymers. Sorption and dilation for He/Kr mixtures in PB were measured at various total and partial pressures, and thereby the hydrostatic-pressure dependence of rR for dissolved Kr component was examined. From the dependence, the compressibility of the dissolved Kr molecules was estimated to be - 5 x 1O-4 atm- ‘. Keywords: Sorption; Dilation; Partial molar volume; Rubbery polymers; Inert gases
1. Introduction
In our previous papers [ l-41, sorption of various gases in rubbery polymers and dilation of these polymers due to the sorption were studied, and the partial molar volumes of the dissolved gases were determined. It was found that there is a linear relation between the partial molar volume and the van der Waals volume for organic gases (six alkanes and two alkenes) [ 3 1. The purpose of the present study is to reveal whether such a relation exists among inorganic gases dissolved in rubbery polymers. *Corresponding
In this paper, we investigate sorption and dilation for five inert gases and N20 in two rubbery polymers and determined their partial molar volumes. On the basis of the results, the relation between the partial molar volume and the van der Waals volume is discussed and compared with the relation for organic gases dissolved in the polymers. Sorption and dilation for He/Kr mixtures in one of the polymers were also measured at various total and partial pressures, and the effect of hydrostatic pressure on the partial molar volume of Kr was examined.
author.
0376-i’388/94/%07.00 @ 1994 Elsevier Science B.V. All rights reserved SSDIO376-7388(94)00071-6
46
Y. Kamiya et al. /Journal ofMembrane Srlence 93 (1994) 45-52
2. Experimental 2.1. Materials The rubbery polymers examined in this study were syndiotactic 1,2-polybutadiene (PB; density, 0.906 g/cm3; content of 1,2-unit, 92%) and poly (ethylene-co-vinyl acetate ) ( EVAc; density, 0.935 g/cm3; content of vinyl acetate, 15 wt%), which are the same as those used previously [ 1,35 ]. Detailed characterization of the polymers, such as isobaric expansion and isothermal compression, is given in the previous papers. PB film, - 200 pm thick, and EVAc film, - 300 pm thick, were employed in both the sorption and dilation experiments. Five inert gases (He, Ne, Ar, Kr, and Xe ) were tested and N20 was also used for comparison. These gases, supplied by Takachiho Chemical Industry and Showadenko Co., were of at least 99.9% purity and were used without further purification. Mixtures of He and Kr were prepared by introducing various amounts of He gas in a cylinder at a higher pressure into another cylinder containing Kr gas at a lower pressure. 2.2. Sorption and dilation measurements Sorption of gases in a polymer specimen ( - 200 mg ) was measured gravimetrically with a microbalance (Cahn Model 2000 ) placed in a pressure chamber. Dilation isotherms were obtained by observing the changes in the length of rectangular film strips (length - 60 mm and width - 3 mm) during the sorption of the gases with a cathetometer. Detailed procedures of both the experiments and magnitudes of experimental errors are reported elsewhere [ 1,3,4]. The experiments were performed at 25.O”C in an air bath controlled to + 0.5 ‘C.
3. Results and discussion 3.1. Sorption Sorption isotherms for Ne, Kr, Xe, and N20 in PB and for the five inert gases in EVAc were
20
P.
40 atm
Fig. 1. Sorption isotherms for Ne, Ar, Kr, Xe, NzO, and CO2 in polybutadiene. The isotherm of Ne is expressed in ten-fold values of concentrations. Ar and CO2 isotherms are from ref. 1.
measured. Measurements of sorption and desorption for each gas were done stepwise up to the maximum pressure (4-50 atm) and then down to vacuum ( 1Oe3 mmHg). The sorption isotherms for the inert gases in both PB and EVAc are linear over the pressure range investigated. Representative isotherms are shown in Fig. 1. The isotherms for N20 and CO2 in PB are also shown for comparison. From the figure, however, the sorption isotherm for Xe is expected to become convex to the pressure axis, if measurements are performed greater than 10 atm. Under the experimental conditions of this study, the sorption of the inert gases can be described by the Henry’s law C=k,p where C is the concentration, p is the pressure, and kD is the Henry’s law coefficient. Values of kD estimated by a least-squares method are presented in Tables 1 and 2, together with ranges of pressure used in the experiments. The values for He and Ar in PB were reported earlier [ 11. The values of kD for He in the two polymers are much the same as those in some rubbery polymers reported by van Amerongen [ 6 1. The sorption isotherm for N20 in PB, as well as that for CO2 in the same polymer [ 11, is con-
Y. Kamiya et al. /Journal ofMembrane Science 93 (1994) 45-52 Table 1 Henry’s law and elongation coefficients, and partial molar volume for polybutadiene Gas
Range of pressure
k,x lo2
dl,/dpx
He Ne Ar Kr Xe
50 50 50 40 4.5
1.14f0.05 1.66f0.02 9.9OkO.06 33.4 fO.l 142.9 f0.2
- 1.2f0.2 -0.8kO.l 4.3 f0.3 20.5f0.3 110.2f 1.8
47
at 25 “C” ref.
10’
2
23 f14 32 f5 40 f2 44.0f0.8 53.0f 1.0
2
‘Units: pressure, atm; kD, cm3 ( STP ) /cm3 ( polym ) atm; dl,/dp, atm- ’ ; Vrr,cm3/mol. Table 2 Henry’s law and elongation coefficients, and partial molar volume for poly(ethylene-c&vinyl
acetate) at 25°C”
Gas
Range of pressure
k,x lo2
dl,/dpx
He Ne Ar Kr Xe
50 30 50 25 4
0.87 kO.08 1.01 kO.02 6.47 f 0.07 20.3 fO.l 90.9 f0.2
-1.lfO.l -0.9kO.l 2.4fO.l 12.1 kO.2 75.3f0.6
10’
17 fll 28 +9 38 k2 44.3 f 0.9 56.7f0.6
‘See footnote a in Table 1 for units.
vex with respect to the pressure axis and is well described by the Flory-Huggins dissolution. According to a simplification of this equation [ 71, the concentration of dissolved gas is given by C= Wp exp(oC) lp where u is a constant related to the polymer/ penetrant interaction. By a least-square analysis, we got k,= 1.32 cm3(STP)/cm3(polym) atm and o= 0.0044 cm3 ( polym ) /cm3 (STP ) for the gas in the polymer.
isotherms (1, versus p) obtained in the sorption run for each inert gas in both PB and EVAc are linear and coincide well with the corresponding isotherms in the desorption run. The representative isotherms are shown in Fig. 2. Such isotherm can be characterized by its slope, dl,/dp, which is hereafter called elongation coefficient.
3.2. Dilation In the dilation measurements, the length elongation of the film was measured at various pressures. The elongation is given as Z,= (L-L,, ) /L,, where L is the length at p (at C) and & the length when p = 0 (when C= 0). Measurements for two specimens cut in cross directions of the films were performed during sorption and desorption runs in each experiment. No difference in the elongation between the two specimens was observed within the accuracy of the experiments. Dilation
0
40
20
PV
atm
Fig. 2. Dilation isotherms for Ne, Ar, Kr, Xe, NzO, and CO2 in polybutadiene. Ar and CO2 isotherms are from ref. 1.
Y. Kamiya et al. /Journal of Membrane Science 93 (1994) 45-52
48
Obtained values of the elongation coefficient are listed in Tables 1 and 2. The dilation isotherm of NzO is convex and very similar in shape to its sorption isotherm. The dilation isotherm for Xe, as well as its sorption isotherm, is expected to become convex, when the pressure is greater than 10 atm.
small ( < 0.2%) compared to the first term under the experimental conditions of this study, the partial molar volume is calculated from the slope of the straight line of ( 1 + I,)‘( 1 + j&p) versus C. 3.4. Relation between partial molar volume and other gas properties
3.3. Partial molar volume From the definition of the partial molar volume and the well-known thermodynamic equation for isothermal changes of volume with concentration and hydrostatic pressure, one derives, as a first approximation, the following relation for the partial molar volume of a penetrant gas following Henry’s law in a polymer [ 11.
z22,410(3dl,/dp+P,)/k,
(1)
where V is the volume of the polymer/gas mixture containing N moles of polymer and n moles of dissolved gas. Here, the dilation is assumed to be isotropic, i.e., V= V, ( 1 + ls)3, where V, is the volume Vat p= 0 (at C= 0) and the compressibility of the gas-sorbed polymer is approximated by that of the pure polymer, j&. Values of pn, at 25°C employed here are 4.75( kO.05)~ lo-’ atm-’ for PB and 3.92 ( ? 0.05) x 10e5 atm-’ for EVAc [ 1,3,4]. The partial molar volumes of the inert gases in the two polymers are presented in Tables 1 and 2. As can be seen in the tables, the partial molar volume of each gas in both polymers is almost the same and increases with atomic number of the gas, though fairly large errors are present in the r, determinations for He and Ne. The partial molar volume of N20 in PB is also shown in Table 3. Since sorption and dilation isotherms for N20 are nonlinear (Figs. 1 and 2 ) , the partial molar volume is estimated by using, instead of Eq. ( 1)) the following relation [ 41; ~R=22,410{d[(l+1,)3(1+j3mp)]/dC -/L,pd(
1 +03/dc)
(2)
As the second term in the braces is negligibly
Fig. 3 shows the partial molar volumes of the five inert gases versus the van der Waals volumes rw. The plots for all the gases except for He are between the lines of rR for dissolved hydrocarbon gases and molar volumes for liquid nalkanes [ 3 1. The relation for the inert gases is graphically determined as v, = 1.6 vw + 20 cm3/mol
(3)
The van der Waals volumes were calculated according to rw = 6 x 1O23x ( 7r/6)d3, using the collision diameters d of the gas molecules [ 8 ] : He, 2.576 A; Ne, 2.858 A; Ar, 3.465 A; Kr, 3.61 A; and Xe, 4.055 A. This linear relation with a coefficient of 1.6 supports the assumption that the gas molecules dissolved in rubbery polymers are in the liquid state [ 91. The value of vR at vw=O (20 cm3/mol) is regarded as the molar s
1
I
I
I
1
,’ ,’ ,’ ,’ ,’ ,
’ >
.-i
0 looi i
;-/
,,.*i
-2
.,i
;‘/
u ,-‘/
.-‘/
I3
0
, , , , , , 0
30
60
Fig. 3. Correlations of partial molar volume with van der Waals volume for inert gases in ( 0 ) polybutadiene and ( A ) poly (ethylene-co-vinyl acetate). Broken and dotted lines are, respectively, partial molar volumes of dissolved hydrocarbon gases in these polymers at 25°C and molar volumes of liquid n-alkanes (C+&) at 20°C [3].
Y. Kamiya et al. /Journal ofMembrane Science 93 (1994) 45-52
volume of the mass points that move as liquid molecules and interact with the polymer chains in the same manner as molecules of the homologous gases do. In Fig. 4, the logarithm of Henry’s law coefficient is plotted versus partial molar volume. Although the figure shows some scatter, a linear trend seems reasonable for each polymer. To confirm whether such a trend exists in other systems, k,, and & data for a series of n-alkane gases in the same polymers are also plotted in the figure [ 1,3 1. As can be seen, the same trend is found which must enhance the reliability of the present data. Considering the integrated van’t Hoff equation of kD= kwexp ( - AHJRT), this linearity which is limited to homologous series of gases can be thought to indicate that both the heat of dissolution, AH,, and Ink, vary linearly with the partial molar volume. The linear relationship between AH, and vR is predictable from the two-step mechanism of dissolution; formation of holes which accommodate gas molecules and their occupation by the molecules [ lo]. That is, the formation energy of holes, which is one of the two components of the heat of dissolution, will be proportional to the volume of holes, i.e., the partial molar volume. The other component, the
Ei-
0
100
50 VR,
cm3/mol
Fig. 4. Relations between Henry’s law coefficient and partial molar volume for inert gases in ( 0 ) PB and ( A ) EVAc and those for n-alkane gases in ( 0 ) PB and ( A ) EVAc [ 3 1.
49
polymer/gas interaction energy due to the occupation of holes by gas molecules, will depend linearly upon the surface area or the coordination number of the dissolved molecules, either of which is roughly proportional to the partial molar volume. However, the linear relation between Ink,, and v, is not apparent and, to our knowledge, there has been no experimental study of the relation. 3.5. Comparison between the twopolymers and other polymers As shown in Tables 1 and 2, gas solubilities of PB are N 60% greater than those of EVAc. Since the degrees of crystallinity of the two polymers are similar (PB, 0.26; EVAc, 0.3) [ 1,5], it is apparent that PB has a better affinity to the inert gases than EVAc. Because the kD values of EVAc are nearly equivalent to those of low-density polyethylene at the same crystallinity [ 111, the difference between the solubilities of PB and EVAc probably results from the affinity of the -CH ( CH=CH2)- group to the gases being greater than those of the -CH*- and -CH ( OCOCHj)groups. The partial molar volume of each gas in the two polymers, however, is almost the same, as mentioned above. Such characteristics have also been found for organic gases in the same polymers [ 3 1. For inert gases in other polymers, sorption and dilation isotherms and hence partial molar volume have been investigated only for Ar. The data for liquid and rubbery poly (dimethylsiloxane) (PDMS) are, respectively, 0.256 and 0.228 cm3 (STP) /cm3 (polym) atm for k,, and 48 and 40 cm3/mol for rR at 25°C [2]. The kD and rR values of poly (ethyl methacrylate) (PEMA) are 0.088 cm3(STP)/cm3(polym) atm and -40 cm3/mol at 75-80°C respectively [ 121. Comparing these values with the present data, one may find that the partial molar volume of dissolved Ar hardly depends upon the nature of the polymers. 3.6. Comparison with other inorganic gases There are a few data of partial molar volume for other inorganic gases in rubbery polymers
Y. Kamiya et al. /Journal of Membrane Science 93 (I 994) 45-52
51
partial molar volume of the dissolved gas by the following relation: (aV,lap)..=-(avg,lan), = -BTVR-22,410(aa,/aC),
1
0
0
2,
’
’
’
’
50
Pf
’
’
’
’
’
100
atm
Fig. 6. Isothermal compressibilities of dissolved Kr, liquid C02, and organic liquids: dotted line shows the value for dissolved Kr molecules; 270-300 K labeled curves are for liquid CO2 [ 171; curves 1 and 2 are for pentane (20°C) and acetone (14-25”C), respectively [ 161.
ecules are less than that of liquid CO2 and greater than those of organic liquids and rubbery polymers [ 1,4]. From the similarity between the profiles of the isothermal compressibility and the isobaric expansivity for these dissolved gases, the compressibility coefficient estimated here is regarded as a plausible value. Moreover, it may be important and worth comparing this compressibility with that of liquid Kr. The comparison, however, could not be made, because we have not examined the experimental data of the isothermal compressibility of the liquid in the literature. Considering that the compressibilities of solidified Kr and Ar are, respectively, 5.7 x 10m5 and 9.0~ 10m5atm- ’ at 77 K and that of liquid Ar is 2.2x 10m4 atm-’ at 87 K [ 181, the estimated compressibility of dissolved Kr molecules in the polymer is thought to be the probable value. 3.8. Concentration dependence of compressibility of polymer
According to the total differential of volume of a polymer/gas system at constant temperature, i.e., dV= - V,&dp+ rRdn, the concentration dependence of compressibility of the polymer is related to the effect of pressure on the
(4)
where BT is the compressibility of polymer containing n moles of gas. From Eq. (4) and the slope of the line in Fig. 5, the value of (a&/ aC) r,p is roughly estimated to be 10e6 atm- ’ [cm3(STP)/cm3(polym)]-‘, and hence, we have&=4.75~ 10e5( 1+O.O2C) for PBat 25°C. Accordingly, the errors in rR caused by employing in Eq. ( 1) the compressibility of the pure polymer /In, instead of & are evaluated to be between 4% for He and 0.2% for Xe. These errors are about the same as or less than the order of magnitude of errors, given in Table 1, inherent in the rR determinations by sorption and elongation measurements employed in this study. Therefore it may be concluded that fairly accurate partial molar volumes can be obtained by usingEq. (1) or (2).
4. Conclusions Sorption isotherms for inert gases in two rubbery polymers, syndiotactic 1,2-polybutadiene and poly (ethylene-co-vinyl acetate), follow the Henry’s law, and dilation isotherms in the form of length elongation versus pressure are linear. The linearity, however, is considered true only over the pressure ranges examined in this study. The partial molar volumes of the dissolved gases were determined from sorption and dilation data, and the volume of each gas in both polymers was nearly equal. A linear relation was found between the partial molar volume and the van der Waals volume; i.e., & = 1.6 rw + 20 in cm3/mol, which is nearly the same as that for organic gases dissolved in the same polymers. Also, there exists a linear relationship between the partial molar volume and the logarithm of Henry’s law coefftcient for a homologous series of inert gases as well as for n-alkane gases. By measuring the sorption and dilation for He/ Kr mixtures in the polybutadiene at various total
52
Y. Kamiya et al. /Journal ofMembrane Science 93 (1994) 45-52
and partial pressures, the pressure dependence of partial molar volume of dissolved Kr was examined. From the dependence, the compressibility of dissolved Kr was estimated to be - 5 x 10e4 atm-‘, which is less than that of liquid CO2 and greater than those of organic liquids and rubbery polymers. The present results make it possible to conclude that dissolved gas molecules, even He, are in almost the same thermodynamic state as the liquid molecules. The results will also give us the volumetric approach, one of the most fundamental approaches, to the understanding of the phenomena relating to polymer/gas systems such as sorption, diffusion, permeation, and plasticization.
f61
[71
[81
[91 [lOI [Ill
[I21
References iI31 111 Y. Kamiya, Y. Naito and K. Mizoguchi, Sorption and partial molar volume of gases in polyhutadiene, J. Polym. Sci., Part B: Polym. Phys., 27 (1989) 2243. VI Y. Kamiya, Y. Naito. T. Hirose and K. Mizoguchi, Sorption and partial molar volume of gases in poly(dimethy1 siloxane), J. Polym. Sci., Part B: Polym. Phys., 28 (1990) 1297. [31 Y. Kamiya, K. Terada, K. Mizoguchi and Y. Naito, Sorption and partial molar volumes of organic gases in rubbery polymers, Macromolecules, 25 (1992) 4321. [41 Y. Kamiya, Y. Naito and D. Bourbon, Sorption and partial molar volumes of gases in poly (ethylene-co-vinyl acetate), J. Polym. Sci., Part B. Polym. Phys., in press. [51 Y. Naito, D. Bourbon, K. Terada and Y. Kamiya, Permeation of high-pressure gases in poly( ethylene-co-vinyl acetate), J. Polym. Sci., Part B: Polym. Phys., 31 (1993) 693.
I141
[I51
[I61
[ 17 ]
181
G.J. van Amerongen. Influence of structure of elastomers on their permeability to gases, J. Polym. Sci., 5 ( 1950) 307; Diffusion in elastomers, Rubber Chem. Technol., 37 (1964) 1067. M.S. Suwandi and S.A. Stem, Transport of heavy organic vapors through silicone rubber, J. Polym. Sci., Polym. Phys. Ed., 11 (1973) 663. J.O. Hirschfelder, C.F. Curtiss and R.B. Bird, Molecular Theory of Gases and Liquids, Wiley, New York, 1964,~~. 1110-1113. D.W. van Krevelen and P.J. Hoftyzer, Properties of Polymers, Elsevier, Amsterdam, 1976, pp. 51-78. P. Mears, The diffusion of gases through polyvinyl acetate, J. Am Chem. Sot. 76 ( 1954) 34 15. Y. Naito, K. Mizoguchi, K. Terada and Y. Kamiya, The effect of pressure on gas permeation through semicrystalline polymers above the glass transition temperature, J. Polym. Sci., Part B: Polym. Phys., 29 (1991) 457. Y. Kamiya, K. Mizoguchi, Y. Naito and D. Bourbon, Ar sorption and partial molar volume in poly(ethy1 methacrylate) above and below the glass transition temperature, J. Polym. Sci., Part B: Polym. Phys., 29 (1991) 225. Y. Kamiya, K. Mizoguchi, T. Hirose and Y. Naito, Sorption and dilation in poly(ethy1 methacrylate)carbon dioxide system, J. Polym. Sci., Part B: Polym. Phys., 27 (1989) 879. G.K. Fleming and W.J. Koros, Dilation of polymers by sorption of carbon dioxide at elevated pressures. 1. Silicone rubber and unconditioned polycarbonate, Macromolecules, 19 ( 1986) 2285. B.J. Briscoe and S. Zakaria, Interaction of CO2 gas with silicone elastomer at high ambient pressures, J. Polym. Sci., Part B: Polym. Phys., 29 ( 1991) 989. J.A. Dean (Ed), Lange’s Handbook of Chemistry, 12th ed., McGraw-Hill, New York, 1979. S. Angus, B. Armstrong and K.M. de Reuck (Eds. ), International Thermodynamic Tables of the Fluid State, Carbon Dioxide, Pergamon, Oxford, 1976. A.C. Hollis Hallett, Liquid- and solid-state properties, in G.A. Cook (Ed.), Argon, Helium and the Rare Gases, Vol. 1, Interscience, New York, 196 1, pp. 3 13390.
ELSEVIER
Journal of Membrane Science 93 ( 1994) 45-52
Sorption and partial molar volumes of inert gases in rubbery polymers Yoshinori Kamiya*, Keishin Mizoguchi, Yasutoshi Naito National Institute of Materials and Chemical Research, 1-I Higashi Tsukuba, Ibaraki 305, Japan Received 12 April 1993; accepted in revised form I4 March 1994
Abstract Sorption of inert gases (He, Ne, Ar, Kr, and Xe) in two rubbery polymers, 1,2_polybutadiene (PB) and poly(ethylene-co-vinyl acetate) (EVAc), and dilation of the polymers due to the sorption were measured as a function of the gas pressure at 25°C. For all the gases, the sorption isotherms followed the Henry’s law over the pressure ranges examined, and the dilation isotherms were linear in these ranges. From the sorption and dilation data, the partial molar volumes vR of the dissolved gases were determined. A linear relation was found between rR and the van der Waals volume VW; i.e., rR= 1.6 rw+ 20 in cm3/mo1. This is much the same as the relation for hydrocarbon gases dissolved in the same polymers and that between molar volume and rw for liquid n-alkanes. There also existed a linear relation between & and the logarithm of Henry’s law coefftcient for a series of inert gases in the polymers. Sorption and dilation for He/Kr mixtures in PB were measured at various total and partial pressures, and thereby the hydrostatic-pressure dependence of rR for dissolved Kr component was examined. From the dependence, the compressibility of the dissolved Kr molecules was estimated to be - 5 x 1O-4 atm- ‘. Keywords: Sorption; Dilation; Partial molar volume; Rubbery polymers; Inert gases
1. Introduction
In our previous papers [ l-41, sorption of various gases in rubbery polymers and dilation of these polymers due to the sorption were studied, and the partial molar volumes of the dissolved gases were determined. It was found that there is a linear relation between the partial molar volume and the van der Waals volume for organic gases (six alkanes and two alkenes) [ 3 1. The purpose of the present study is to reveal whether such a relation exists among inorganic gases dissolved in rubbery polymers. *Corresponding
In this paper, we investigate sorption and dilation for five inert gases and N20 in two rubbery polymers and determined their partial molar volumes. On the basis of the results, the relation between the partial molar volume and the van der Waals volume is discussed and compared with the relation for organic gases dissolved in the polymers. Sorption and dilation for He/Kr mixtures in one of the polymers were also measured at various total and partial pressures, and the effect of hydrostatic pressure on the partial molar volume of Kr was examined.
author.
0376-i’388/94/%07.00 @ 1994 Elsevier Science B.V. All rights reserved SSDIO376-7388(94)00071-6
46
Y. Kamiya et al. /Journal ofMembrane Srlence 93 (1994) 45-52
2. Experimental 2.1. Materials The rubbery polymers examined in this study were syndiotactic 1,2-polybutadiene (PB; density, 0.906 g/cm3; content of 1,2-unit, 92%) and poly (ethylene-co-vinyl acetate ) ( EVAc; density, 0.935 g/cm3; content of vinyl acetate, 15 wt%), which are the same as those used previously [ 1,35 ]. Detailed characterization of the polymers, such as isobaric expansion and isothermal compression, is given in the previous papers. PB film, - 200 pm thick, and EVAc film, - 300 pm thick, were employed in both the sorption and dilation experiments. Five inert gases (He, Ne, Ar, Kr, and Xe ) were tested and N20 was also used for comparison. These gases, supplied by Takachiho Chemical Industry and Showadenko Co., were of at least 99.9% purity and were used without further purification. Mixtures of He and Kr were prepared by introducing various amounts of He gas in a cylinder at a higher pressure into another cylinder containing Kr gas at a lower pressure. 2.2. Sorption and dilation measurements Sorption of gases in a polymer specimen ( - 200 mg ) was measured gravimetrically with a microbalance (Cahn Model 2000 ) placed in a pressure chamber. Dilation isotherms were obtained by observing the changes in the length of rectangular film strips (length - 60 mm and width - 3 mm) during the sorption of the gases with a cathetometer. Detailed procedures of both the experiments and magnitudes of experimental errors are reported elsewhere [ 1,3,4]. The experiments were performed at 25.O”C in an air bath controlled to + 0.5 ‘C.
3. Results and discussion 3.1. Sorption Sorption isotherms for Ne, Kr, Xe, and N20 in PB and for the five inert gases in EVAc were
20
P.
40 atm
Fig. 1. Sorption isotherms for Ne, Ar, Kr, Xe, NzO, and CO2 in polybutadiene. The isotherm of Ne is expressed in ten-fold values of concentrations. Ar and CO2 isotherms are from ref. 1.
measured. Measurements of sorption and desorption for each gas were done stepwise up to the maximum pressure (4-50 atm) and then down to vacuum ( 1Oe3 mmHg). The sorption isotherms for the inert gases in both PB and EVAc are linear over the pressure range investigated. Representative isotherms are shown in Fig. 1. The isotherms for N20 and CO2 in PB are also shown for comparison. From the figure, however, the sorption isotherm for Xe is expected to become convex to the pressure axis, if measurements are performed greater than 10 atm. Under the experimental conditions of this study, the sorption of the inert gases can be described by the Henry’s law C=k,p where C is the concentration, p is the pressure, and kD is the Henry’s law coefficient. Values of kD estimated by a least-squares method are presented in Tables 1 and 2, together with ranges of pressure used in the experiments. The values for He and Ar in PB were reported earlier [ 11. The values of kD for He in the two polymers are much the same as those in some rubbery polymers reported by van Amerongen [ 6 1. The sorption isotherm for N20 in PB, as well as that for CO2 in the same polymer [ 11, is con-
Y. Kamiya et al. /Journal ofMembrane Science 93 (1994) 45-52 Table 1 Henry’s law and elongation coefficients, and partial molar volume for polybutadiene Gas
Range of pressure
k,x lo2
dl,/dpx
He Ne Ar Kr Xe
50 50 50 40 4.5
1.14f0.05 1.66f0.02 9.9OkO.06 33.4 fO.l 142.9 f0.2
- 1.2f0.2 -0.8kO.l 4.3 f0.3 20.5f0.3 110.2f 1.8
47
at 25 “C” ref.
10’
2
23 f14 32 f5 40 f2 44.0f0.8 53.0f 1.0
2
‘Units: pressure, atm; kD, cm3 ( STP ) /cm3 ( polym ) atm; dl,/dp, atm- ’ ; Vrr,cm3/mol. Table 2 Henry’s law and elongation coefficients, and partial molar volume for poly(ethylene-c&vinyl
acetate) at 25°C”
Gas
Range of pressure
k,x lo2
dl,/dpx
He Ne Ar Kr Xe
50 30 50 25 4
0.87 kO.08 1.01 kO.02 6.47 f 0.07 20.3 fO.l 90.9 f0.2
-1.lfO.l -0.9kO.l 2.4fO.l 12.1 kO.2 75.3f0.6
10’
17 fll 28 +9 38 k2 44.3 f 0.9 56.7f0.6
‘See footnote a in Table 1 for units.
vex with respect to the pressure axis and is well described by the Flory-Huggins dissolution. According to a simplification of this equation [ 71, the concentration of dissolved gas is given by C= Wp exp(oC) lp where u is a constant related to the polymer/ penetrant interaction. By a least-square analysis, we got k,= 1.32 cm3(STP)/cm3(polym) atm and o= 0.0044 cm3 ( polym ) /cm3 (STP ) for the gas in the polymer.
isotherms (1, versus p) obtained in the sorption run for each inert gas in both PB and EVAc are linear and coincide well with the corresponding isotherms in the desorption run. The representative isotherms are shown in Fig. 2. Such isotherm can be characterized by its slope, dl,/dp, which is hereafter called elongation coefficient.
3.2. Dilation In the dilation measurements, the length elongation of the film was measured at various pressures. The elongation is given as Z,= (L-L,, ) /L,, where L is the length at p (at C) and & the length when p = 0 (when C= 0). Measurements for two specimens cut in cross directions of the films were performed during sorption and desorption runs in each experiment. No difference in the elongation between the two specimens was observed within the accuracy of the experiments. Dilation
0
40
20
PV
atm
Fig. 2. Dilation isotherms for Ne, Ar, Kr, Xe, NzO, and CO2 in polybutadiene. Ar and CO2 isotherms are from ref. 1.
Y. Kamiya et al. /Journal of Membrane Science 93 (1994) 45-52
48
Obtained values of the elongation coefficient are listed in Tables 1 and 2. The dilation isotherm of NzO is convex and very similar in shape to its sorption isotherm. The dilation isotherm for Xe, as well as its sorption isotherm, is expected to become convex, when the pressure is greater than 10 atm.
small ( < 0.2%) compared to the first term under the experimental conditions of this study, the partial molar volume is calculated from the slope of the straight line of ( 1 + I,)‘( 1 + j&p) versus C. 3.4. Relation between partial molar volume and other gas properties
3.3. Partial molar volume From the definition of the partial molar volume and the well-known thermodynamic equation for isothermal changes of volume with concentration and hydrostatic pressure, one derives, as a first approximation, the following relation for the partial molar volume of a penetrant gas following Henry’s law in a polymer [ 11.
z22,410(3dl,/dp+P,)/k,
(1)
where V is the volume of the polymer/gas mixture containing N moles of polymer and n moles of dissolved gas. Here, the dilation is assumed to be isotropic, i.e., V= V, ( 1 + ls)3, where V, is the volume Vat p= 0 (at C= 0) and the compressibility of the gas-sorbed polymer is approximated by that of the pure polymer, j&. Values of pn, at 25°C employed here are 4.75( kO.05)~ lo-’ atm-’ for PB and 3.92 ( ? 0.05) x 10e5 atm-’ for EVAc [ 1,3,4]. The partial molar volumes of the inert gases in the two polymers are presented in Tables 1 and 2. As can be seen in the tables, the partial molar volume of each gas in both polymers is almost the same and increases with atomic number of the gas, though fairly large errors are present in the r, determinations for He and Ne. The partial molar volume of N20 in PB is also shown in Table 3. Since sorption and dilation isotherms for N20 are nonlinear (Figs. 1 and 2 ) , the partial molar volume is estimated by using, instead of Eq. ( 1)) the following relation [ 41; ~R=22,410{d[(l+1,)3(1+j3mp)]/dC -/L,pd(
1 +03/dc)
(2)
As the second term in the braces is negligibly
Fig. 3 shows the partial molar volumes of the five inert gases versus the van der Waals volumes rw. The plots for all the gases except for He are between the lines of rR for dissolved hydrocarbon gases and molar volumes for liquid nalkanes [ 3 1. The relation for the inert gases is graphically determined as v, = 1.6 vw + 20 cm3/mol
(3)
The van der Waals volumes were calculated according to rw = 6 x 1O23x ( 7r/6)d3, using the collision diameters d of the gas molecules [ 8 ] : He, 2.576 A; Ne, 2.858 A; Ar, 3.465 A; Kr, 3.61 A; and Xe, 4.055 A. This linear relation with a coefficient of 1.6 supports the assumption that the gas molecules dissolved in rubbery polymers are in the liquid state [ 91. The value of vR at vw=O (20 cm3/mol) is regarded as the molar s
1
I
I
I
1
,’ ,’ ,’ ,’ ,’ ,
’ >
.-i
0 looi i
;-/
,,.*i
-2
.,i
;‘/
u ,-‘/
.-‘/
I3
0
, , , , , , 0
30
60
Fig. 3. Correlations of partial molar volume with van der Waals volume for inert gases in ( 0 ) polybutadiene and ( A ) poly (ethylene-co-vinyl acetate). Broken and dotted lines are, respectively, partial molar volumes of dissolved hydrocarbon gases in these polymers at 25°C and molar volumes of liquid n-alkanes (C+&) at 20°C [3].
Y. Kamiya et al. /Journal ofMembrane Science 93 (1994) 45-52
volume of the mass points that move as liquid molecules and interact with the polymer chains in the same manner as molecules of the homologous gases do. In Fig. 4, the logarithm of Henry’s law coefficient is plotted versus partial molar volume. Although the figure shows some scatter, a linear trend seems reasonable for each polymer. To confirm whether such a trend exists in other systems, k,, and & data for a series of n-alkane gases in the same polymers are also plotted in the figure [ 1,3 1. As can be seen, the same trend is found which must enhance the reliability of the present data. Considering the integrated van’t Hoff equation of kD= kwexp ( - AHJRT), this linearity which is limited to homologous series of gases can be thought to indicate that both the heat of dissolution, AH,, and Ink, vary linearly with the partial molar volume. The linear relationship between AH, and vR is predictable from the two-step mechanism of dissolution; formation of holes which accommodate gas molecules and their occupation by the molecules [ lo]. That is, the formation energy of holes, which is one of the two components of the heat of dissolution, will be proportional to the volume of holes, i.e., the partial molar volume. The other component, the
Ei-
0
100
50 VR,
cm3/mol
Fig. 4. Relations between Henry’s law coefficient and partial molar volume for inert gases in ( 0 ) PB and ( A ) EVAc and those for n-alkane gases in ( 0 ) PB and ( A ) EVAc [ 3 1.
49
polymer/gas interaction energy due to the occupation of holes by gas molecules, will depend linearly upon the surface area or the coordination number of the dissolved molecules, either of which is roughly proportional to the partial molar volume. However, the linear relation between Ink,, and v, is not apparent and, to our knowledge, there has been no experimental study of the relation. 3.5. Comparison between the twopolymers and other polymers As shown in Tables 1 and 2, gas solubilities of PB are N 60% greater than those of EVAc. Since the degrees of crystallinity of the two polymers are similar (PB, 0.26; EVAc, 0.3) [ 1,5], it is apparent that PB has a better affinity to the inert gases than EVAc. Because the kD values of EVAc are nearly equivalent to those of low-density polyethylene at the same crystallinity [ 111, the difference between the solubilities of PB and EVAc probably results from the affinity of the -CH ( CH=CH2)- group to the gases being greater than those of the -CH*- and -CH ( OCOCHj)groups. The partial molar volume of each gas in the two polymers, however, is almost the same, as mentioned above. Such characteristics have also been found for organic gases in the same polymers [ 3 1. For inert gases in other polymers, sorption and dilation isotherms and hence partial molar volume have been investigated only for Ar. The data for liquid and rubbery poly (dimethylsiloxane) (PDMS) are, respectively, 0.256 and 0.228 cm3 (STP) /cm3 (polym) atm for k,, and 48 and 40 cm3/mol for rR at 25°C [2]. The kD and rR values of poly (ethyl methacrylate) (PEMA) are 0.088 cm3(STP)/cm3(polym) atm and -40 cm3/mol at 75-80°C respectively [ 121. Comparing these values with the present data, one may find that the partial molar volume of dissolved Ar hardly depends upon the nature of the polymers. 3.6. Comparison with other inorganic gases There are a few data of partial molar volume for other inorganic gases in rubbery polymers
Y. Kamiya et al. /Journal of Membrane Science 93 (I 994) 45-52
51
partial molar volume of the dissolved gas by the following relation: (aV,lap)..=-(avg,lan), = -BTVR-22,410(aa,/aC),
1
0
0
2,
’
’
’
’
50
Pf
’
’
’
’
’
100
atm
Fig. 6. Isothermal compressibilities of dissolved Kr, liquid C02, and organic liquids: dotted line shows the value for dissolved Kr molecules; 270-300 K labeled curves are for liquid CO2 [ 171; curves 1 and 2 are for pentane (20°C) and acetone (14-25”C), respectively [ 161.
ecules are less than that of liquid CO2 and greater than those of organic liquids and rubbery polymers [ 1,4]. From the similarity between the profiles of the isothermal compressibility and the isobaric expansivity for these dissolved gases, the compressibility coefficient estimated here is regarded as a plausible value. Moreover, it may be important and worth comparing this compressibility with that of liquid Kr. The comparison, however, could not be made, because we have not examined the experimental data of the isothermal compressibility of the liquid in the literature. Considering that the compressibilities of solidified Kr and Ar are, respectively, 5.7 x 10m5 and 9.0~ 10m5atm- ’ at 77 K and that of liquid Ar is 2.2x 10m4 atm-’ at 87 K [ 181, the estimated compressibility of dissolved Kr molecules in the polymer is thought to be the probable value. 3.8. Concentration dependence of compressibility of polymer
According to the total differential of volume of a polymer/gas system at constant temperature, i.e., dV= - V,&dp+ rRdn, the concentration dependence of compressibility of the polymer is related to the effect of pressure on the
(4)
where BT is the compressibility of polymer containing n moles of gas. From Eq. (4) and the slope of the line in Fig. 5, the value of (a&/ aC) r,p is roughly estimated to be 10e6 atm- ’ [cm3(STP)/cm3(polym)]-‘, and hence, we have&=4.75~ 10e5( 1+O.O2C) for PBat 25°C. Accordingly, the errors in rR caused by employing in Eq. ( 1) the compressibility of the pure polymer /In, instead of & are evaluated to be between 4% for He and 0.2% for Xe. These errors are about the same as or less than the order of magnitude of errors, given in Table 1, inherent in the rR determinations by sorption and elongation measurements employed in this study. Therefore it may be concluded that fairly accurate partial molar volumes can be obtained by usingEq. (1) or (2).
4. Conclusions Sorption isotherms for inert gases in two rubbery polymers, syndiotactic 1,2-polybutadiene and poly (ethylene-co-vinyl acetate), follow the Henry’s law, and dilation isotherms in the form of length elongation versus pressure are linear. The linearity, however, is considered true only over the pressure ranges examined in this study. The partial molar volumes of the dissolved gases were determined from sorption and dilation data, and the volume of each gas in both polymers was nearly equal. A linear relation was found between the partial molar volume and the van der Waals volume; i.e., & = 1.6 rw + 20 in cm3/mol, which is nearly the same as that for organic gases dissolved in the same polymers. Also, there exists a linear relationship between the partial molar volume and the logarithm of Henry’s law coefftcient for a homologous series of inert gases as well as for n-alkane gases. By measuring the sorption and dilation for He/ Kr mixtures in the polybutadiene at various total
52
Y. Kamiya et al. /Journal ofMembrane Science 93 (1994) 45-52
and partial pressures, the pressure dependence of partial molar volume of dissolved Kr was examined. From the dependence, the compressibility of dissolved Kr was estimated to be - 5 x 10e4 atm-‘, which is less than that of liquid CO2 and greater than those of organic liquids and rubbery polymers. The present results make it possible to conclude that dissolved gas molecules, even He, are in almost the same thermodynamic state as the liquid molecules. The results will also give us the volumetric approach, one of the most fundamental approaches, to the understanding of the phenomena relating to polymer/gas systems such as sorption, diffusion, permeation, and plasticization.
f61
[71
[81
[91 [lOI [Ill
[I21
References iI31 111 Y. Kamiya, Y. Naito and K. Mizoguchi, Sorption and partial molar volume of gases in polyhutadiene, J. Polym. Sci., Part B: Polym. Phys., 27 (1989) 2243. VI Y. Kamiya, Y. Naito. T. Hirose and K. Mizoguchi, Sorption and partial molar volume of gases in poly(dimethy1 siloxane), J. Polym. Sci., Part B: Polym. Phys., 28 (1990) 1297. [31 Y. Kamiya, K. Terada, K. Mizoguchi and Y. Naito, Sorption and partial molar volumes of organic gases in rubbery polymers, Macromolecules, 25 (1992) 4321. [41 Y. Kamiya, Y. Naito and D. Bourbon, Sorption and partial molar volumes of gases in poly (ethylene-co-vinyl acetate), J. Polym. Sci., Part B. Polym. Phys., in press. [51 Y. Naito, D. Bourbon, K. Terada and Y. Kamiya, Permeation of high-pressure gases in poly( ethylene-co-vinyl acetate), J. Polym. Sci., Part B: Polym. Phys., 31 (1993) 693.
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