Journal of Membrane Science 450 (2014) 380–388
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Temperature dependence of gas sorption and permeation in PIM-1 P. Li a, T.S. Chung b, D.R. Paul a,b,n a b
Department of Chemical and Biomolecular Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 117602, Singapore Department of Chemical Engineering, The University of Texas at Austin, Austin, TX 78712-1062, USA
art ic l e i nf o
a b s t r a c t
Article history: Received 31 May 2013 Received in revised form 16 August 2013 Accepted 17 September 2013 Available online 25 September 2013
In a prior paper gas sorption, permeation and diffusion coefficients were determined for He, H2, N2, O2, CH4, CO2, C2H4, C2H6, C3H6 and C3H8 in PIM-1, a polymer of intrinsic microporosity, at 25 1C over a range of pressures. Here similar measurements and analyses were made at temperatures from 25 to 55 1C over a wide range of pressure. In all cases, the sorption isotherms were generally consistent with the form of the dual-sorption model. For He, H2, N2, O2, CH4 and CO2, the effects of plasticization were minimal and the results could be effectively analyzed by the dual sorption-dual mobility model, and the temperature dependence of the model parameters were analyzed to obtain the energetic parameters for the sorption and diffusion processes. However, for C2H4, C2H6, C3H6 and C3H8, plasticization was quite significant and temperature dependent; as a result, a similar analysis in terms of the dual sorption-dual mobility model could not be meaningfully carried out. For all gases, a more phenomenological analysis of P, D and S was made in terms of simple Arrhenius and van't Hoff relations to obtain energetic parameters that subsequently depend on pressure because of some combination of dual mode and/or plasticization effects. & 2013 Elsevier B.V. All rights reserved.
Keywords: Polymer of intrinsic microporosity (PIM-1) Gas permeability Dual-mode sorption-mobility model
1. Introduction In 2004, Budd et al. reported a new class of soluble polymers with very rigid but contorted backbones and coined the term “polymers of intrinsic microporosity (PIMs)” to describe them [1,2]. The high free volume and the ready solubility of these materials in common solvents have led to a great deal of interest in them for gas storage because of their high levels of gas sorption [3,4] and for membrane separations owing to their high permeability [5–10]. The most well-known polymer in this class, PIM-1, whose structure is given in Fig. 1, has been extensively studied for membrane applications in areas such as organic solvent nanofiltration [9,10], gas separation [11,12], and pervaporation [13,14]. Several reports have evaluated the separation performance of PIM-1via measurement of the permeability, solubility and diffusion coefficients of various gas and vapor penetrants [15,16]. Most of these studies were carried out at 25 or 35 1C; however, at least two studies have reported results at other temperatures [12,17]. Recently, we reported sorption isotherms, obtained via a dualvolume sorption method, plus gas permeability coefficients over a range of upstream pressures, all at 25 1C, with the results analyzed in terms of the dual-mode sorption-mobility model [18]. A better
n Corresponding author at: Department of Chemical Engineering, The University of Texas at Austin, Austin, TX 78712-1062, USA. Tel.: þ 1 5124715392; fax: þ1 5124710542. E-mail address: [email protected] (D.R. Paul).
0376-7388/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.memsci.2013.09.030
understanding these properties over a wider range of conditions would assist any consideration of industrial use of PIM-1 for membrane applications. The purpose here is to extend the type of measurements and analyses reported earlier for PIM-1 to a wider range of temperatures, 25–55 1C, for the series of penetrants: He, H2, N2, O2, CH4, CO2, C2H4, C2H6, C3H6 and C3H8. The measured sorption and permeation coefficients plus the model parameters are analyzed to extract corresponding sorption energies and activation energies; these energy parameters should add useful insights about the nature of this unusual polymer. Because of the large number of plots generated in this work, the body of the manuscript presents graphs for only three penetrants, N2, CO2, and propane, C3H8, since these represent the range of behaviors observed while similar graphs for the remaining penetrants, plus all Arrhenius and van't Hoff plots, are included in Supplementary Information. 2. Background In this work, the equilibrium concentration, C, of each penetrant in PIM-1 was determined over a range of gas pressures, p. A secant solubility coefficient, S, can be computed from C/p at each pressure. The permeability coefficient, P, of each penetrant was measured as a function of upstream driving pressure. With these measurements, an effective or average diffusion coefficient, D, can be calculated from P/S. The temperature dependence of each of these phenomenological coefficients can be represented in terms
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law mode, i.e., H D H H 40, because more energy is required to create space in the polymer for the molecules of gas to be dissolved, i.e., sorbed by Henry's law mode, versus gas sorbed into presumed pre-existing spaces, i.e., by the Langmuir mode. The solubility coefficient, S, can be written in terms of the dualsorption model as S¼
Combining Eqs. (9) and (3) yields C H0 b Hs kD þ ¼ S0 exp 1 þ bp RT
Fig. 1. Molecular structure of PIM-1.
of appropriate Arrhenius or van't Hoff type expressions [19–21]. Ep ð1Þ P ¼ P 0 exp RT E D ¼ D0 exp d RT
ð2Þ
Hs S ¼ S0 exp RT
ð3Þ
where P0, D0, and S0 are pre-exponential factors and Ep, Ed, and Hs represent the activation energies of permeation and diffusion and the heat of sorption, respectively; R is the gas constant and T is the absolute temperature. Since P ¼D S, combining Eqs. (1–3) gives Ep ¼ Ed þH s
ð4Þ
When the coefficients P, D and S are pressure (or concentration) dependent, as expected for gases in glassy polymers or when plasticization is significant, the parameters in Eqs. (1–3) must also be dependent on the pressures used in their measurement. An alternate approach is to use pressure dependent models and to interpret the energetics in terms of the parameters of the model. The non-linear gas sorption isotherms for glassy polymers are typically well described by the so-called dual-mode sorption model [22]. C ¼ kD p þ
C H0 bp 1 þbp
ð7Þ
where the difference in the enthalpy between gas sorbed in Henry's law mode and in the gas phase is referred to as ΔH D while the difference in the enthalpy between gas sorbed in the Langmuir sites and in the gas phase is referred to as ΔH b . The enthalpy difference between the gas sorbed in the Langmuir sites, HD, and Henry's law mode, HH, can then be estimated as follows: H D H H ¼ ΔH D ΔH H
ð9Þ
ð10Þ
The pressure dependence of the gas permeability coefficient of glassy polymers is well represented by a dual-mode sorptionmobility model [18] of the form C H0 b FK P ¼ kD D D þ ð11Þ DH ¼ kD DD 1 þ 1 þbph 1 þ bph where DD and DH are the diffusion coefficients of Henry and Langmuir modes, respectively, while K ¼ C H0 b/kD, F¼DH/DD and ph is the pressure of the feed gas; the pressure on the permeate side in these measurements is usually very low and can be taken as zero. The temperature dependence of the parameters in Eq. (11) can be written using the analogous Arrhenius relationships ED ð12Þ DD ¼ DD0 exp D RT ED DH ¼ DH0 exp H RT
ð13Þ
where DD0 and DH0 are the pre-exponential factors and EDD and EDH are the activation energies of diffusion associated with the two envisioned modes of sorption and diffusion, respectively. The temperature dependence of the ratio F can be expressed as follows: DH DH 0 ED EDD ð14Þ F¼ ¼ exp H DD DD0 RT
ð5Þ
This model envisions the sorption of gas in both Henry's law dissolution mode and in Langmuir ‘hole filling’ mode where p is the pressure in the gas phase and kD , C H0 , and b are Henry's law solubility, Langmuir sorption capacity, and hole affinity parameters, respectively. The temperature dependence of C H0 is related to the volume of the glass in excess of the equilibrium volume and is proportional to the distance from the glass transition temperature, i.e., Tg T, and is not related to any energetic parameters. On the other hand, the temperature dependence of kD and b can be expressed as follows [21]. ΔH D ð6Þ kD ¼ kD0 exp RT ΔH b b ¼ b0 exp RT
C C H0 b ¼ kD þ p 1 þ bp
ð8Þ
As indicated by Costello and Koros [20], the enthalpy of gas sorbed in the Langmuir sites should be less than that in Henry's
3. Experimental PIM-1 was synthesized via polycondensation reactions described in previous papers [5–7]. All gases, i.e., He, H2, N2, O2, CH4, CO2, C2H4, C2H6, C3H6 and C3H8, were purchased from Soxal (Singapore) with purities higher than 99.9%. The solvents methanol and N-methyl-2-pyrrolidione were AR grade and purchased from Merck; while HPLC grade chloroform (99.9%) and hydrochloric acid (37.5% in H2O) were purchased from Fisher Chemical. Films of PIM-1 were prepared via solvent casting from a 2 wt% polymer solution in chloroform; the detailed procedure was provided in the previous paper [18]. PIM-1 films with a thickness around 507 5 μm were used for permeation and sorption measurements. Similar to our previous paper, pure gas permeability coefficients were determined using a constant-volume permeation cell while sorption isotherms were measured using a dual-volume pressure decay system. Details of these systems and the measuring protocols were provided earlier [18,23]. Since PIM-type materials exhibit severe physical aging behavior, the gas transport properties for PIM-1 were highly affected by both the film preparation and the testing protocols. Thus, we tried to maintain and adopt an identical film preparation process for all fresh PIM-1 samples as introduced in the previous paper [18]. For gas permeation measurements, the permeability of N2 was first determined for each fresh film at 25 1C and 1 atm; if the observed value was in the
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expected range (variation o10%), then further measurements were made for this film. Each film was replaced after one day of measurement or when there was a change in the temperature. For highly condensable gases such as the hydrocarbons, the film was replaced when there was a change of gas, temperature or the testing duration was longer than one day. On the contrary, for sorption measurements, it usually took 3–5 days to obtain a sorption isotherm; thus, the PIM-1 film would only be replaced after a complete sorption isotherm was obtained.
4. Results and discussion 4.1. Gas sorption Fig. 2 shows sorption isotherms for N2, CO2 and C3H8 in PIM-1 at temperatures from 25 to 55 1C; the sorption isotherms of the other 7 gases are shown in Supporting Information. All sorption isotherms exhibit the non-linear behavior typical of glassy polymers [18]. The experimental sorption data were fitted to Eq. (5) by a non-linear routine to obtain the parameters shown in Table 1. In a few cases, a parameter range is shown when the outcome of the fitting is sensitive to the initial parameter estimated. The solid lines in all the plots of C versus p were calculated using Eq. (5) and the parameters in Table 1; these lines provide an excellent representation of the experimental data. As the temperature increases, the extent of gas sorption gradually decreases in all cases, as expected, since the sorption enthalpy is negative or exothermic. For hydrocarbons like C3H6 and C3H8, the sorption isotherms show some indications that there might be upward curvature at higher pressures as observed for methanol, heptanes and toluene in PIM-1 at 25 1C [15]. Chiou et al. [24] made a systematic study of CO2 sorption isotherms in miscible blends of poly(methyl methacrylate) and poly (vinylidene fluoride) at 35 1C and found that as the amount of the absorbed CO2 increased, the glass transition
temperature, Tg, of the polymer blend continuously decreased. At a certain CO2 pressure, when the Tg drops below 35 1C by plasticization, the CO2 sorption isotherm becomes linear, indicating the loss of the Langmuir ‘hole filling mode’ as the blend became rubbery at 35 1C. It is believed that the high levels of sorption by the highly condensable C3H6 and C3H8 gradually lowers the Tg of PIM-1; however, because of the very high Tg of PIM-1, very high pressures would be required to reduce the Tg to the range of the current measurement temperatures. Table 1 shows that the dual-mode sorption parameters kD, C H0 , and b for all gases generally decrease as the temperature increases; however, for the hydrocarbons C2H4, C2H6, C3H6 and C3H8 the trends between the temperature and sorption parameters are not always so clear owing to the more significant effects of plasticization. The degree of plasticization decreases as the temperature is raised because the extent of sorption decreases, and this will have some effect on the temperature dependence of the parameters shown in Table 1. Koros et al. [21] proposed that gas dissolved via Henry's law mode requires energy to open space to accept the gas molecules; therefore, larger gas molecules should require more energy for opening the larger space needed. Hence, the energy difference between the two sorption modes, HD HH, should be greater for larger penetrants. The values of HD HH shown in Table 2 increase in the order: C3H8 oC3H6 oC2H6 oC2H4 oCO2 oHeoH2 oCH4 oO2 oN2, which is not the order of the kinetic diameters of these penetrants. However, for the less condensable gases He, H2, O2 and N2, the values of HD HH do increase with kinetic diameter as might be expected. For the more highly condensable gases CH4, CO2, C2H4, C2H6, C3H6 and C3H8, the values of HD HH decrease in almost the same order as their critical temperatures: C3H8 4C3H6 4C2H6 4 CO2 4C2H4 4CH4. The complicating issues of plasticization coupled with the stronger interaction of these more condensable gases with the polymer make arguments about the size of the space needed to accommodate the sorbed molecule too simplistic.
180 160
35
CO2 concentration cm3 (stp)/cm3 polymer
N2 concentration cm3 (stp)/cm3 polymer
40
30 25 20 15 2
10
4 5
5 0
0
10
20
140 120 100 80 60 4 5
20 0
30
2
40
0
5
N2 pressure (atm)
10
15
20
25
30
CO2 pressure (atm)
160
C3H8 concentration cm3 (stp)/cm3 polymer
140 120 100 80 60
2
40
4 5
20 0
0
2
4
6
8
C3H8 pressure (atm) Fig. 2. Gas sorption isotherms for N2, CO2 and C3H8 in PIM-1 from 25 to 55 1C. The solid curves were generated from the dual-mode sorption model and the parameters in Table 1.
P. Li et al. / Journal of Membrane Science 450 (2014) 380–388
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Table 1 Dual-mode sorption parameters for gases in PIM-1 at 25–55 1C. Unit (1C)
kD
C H0
b
He 25 35 45 55
0.065 0.047 70.003 0.048 0.050 7 0.004
6.60 6.58 7 0.32 5.28 4.737 0.30
0.037 0.036 7 0.002 0.036 0.026 7 0.002
H2 25 35 45 55
0.0677 0.027 0.032 7 0.005 0.029 7 0.007 0.0357 0.014
44.6 7 4.6 35.17 0.1 31.5 7 1.5 35.7 72.5
0.0137 0.001 0.0157 0.002 0.0167 0.001 0.0117 0.001
N2 25 35 45 55
0.493 0.472 0.457 0.462
31.0 30.5 30.8 28.6
0.076 0.064 0.050 0.044
O2 25 35 45 55
1.33 1.107 0.77 0.896 7 0.26 0.863 7 0.05
18.6 19.2 7 18.5 17.5 7 4.6 17.6 7 1.4
0.132 0.1057 0.03 0.0977 0.22 0.050 7 0.004
CH4 25 35 45 55
0.592 0.578 0.519 0.567
65.0 61.7 59.0 50.5
0.150 0.124 0.104 0.090
K
Unit (1C)
kD
C H0
b
K
CO2 25 35 45 55
2.35 2.01 1.54 1.16
106 96.8 92.4 92.0
0.421 0.341 0.291 0.212
19.1 16.4 17.4 16.8
C2 H 4 25 35 45 55
1.81 1.86 1.81 1.65
93.5 81.3 70.3 64.4
0.556 0.589 0.627 0.554
28.8 26.1 24.4 21.6
4.79 4.12 3.38 2.71
C2 H 6 25 35 45 55
2.76 2.49 2.00 1.58
81.1 71.6 70.4 66.4
1.09 1.13 0.827 0.745
31.9 32.5 29.2 31.6
1.85 1.83 1.89 1.02
C3H6 25 35 45 55
10.1 7.26 5.16 5.09
88.8 81.1 78.0 63.2
2.57 2.36 1.64 2.09
22.6 26.5 24.8 25.9
16.5 13.3 11.9 8.83
C3 H 8 25 35 45 55
10.5 7.82 6.40 4.89
78.1 70.4 65.5 59.3
3.43 4.03 3.52 3.05
25.4 36.2 36.0 37.1
3.76 4.67 3.91 2.37 16.0 14.7 13.8 12.1
kD [cm3 (stp)/cm3polymer atm]; C H0 [cm3(stp)/cm3polymer]; b (atm 1); K¼ C H0 b=kD .
Table 2 Sorption enthalpies Gas
He H2 CO2 O2 N2 CH4 C2H4 C2H6 C3H6 C3H8
ΔHD, ΔHb, and HD HH for gases in PIM-1.
Critical temperature Tc (K) [25]
Kinetic diameter dk (Å) [25]
ΔHD
ΔHb
(kcal/mol)
(kcal/mol)
HD HH (kcal/mol)
5.2 33.2 304.2 154.6 126.2 190.6 282.5 305.3 365.2 369.9
2.6 2.89 3.30 3.46 3.64 3.80 3.9 4.0 4.5 4.3
1.42 1.23 4.60 2.92 0.42 0.28 0.57 3.67 4.72 4.86
2.07 2.25 4.29 5.70 3.67 2.78 0.12 2.78 1.95 0.90
0.65 1.02 0.31 2.78 3.25 2.50 0.69 0.89 2.77 3.96
4.2. Gas permeation Fig. 3 shows the permeability coefficients of N2, CO2 and C3H8 in PIM-1 versus the upstream driving pressure from 25 to 55 1C; similar plots for the other 7 gases are included in Supporting Information. The permeability coefficients for He, H2, O2, N2 and CH4 increase with increasing temperature at all pressures. This is a general trend for penetrants where diffusion rather than sorption dominates the response of permeation to temperature. In these type of cases, the permeability coefficient decreases with increasing upstream pressure as expected from Eq. (11). For CO2, the permeability coefficient weakly depends on temperature, and when plotted on the expanded scale of logarithm of P versus 1/T shown in Fig. S7 of the Supporting Information, the data show a slight maximum. Consequently, the permeability shows a small decrease with increasing temperature in the higher temperature range. This is a consequence of the strong decrease in sorption with increasing temperature coupled with the weak plasticization of PIM-1 by CO2.
For the highly condensable gases including C2H4, C2H6, C3H6 and C3H8, the gas permeation isotherms cross each other at some pressure range as shown in Fig. 3(c) for C3H8 and in the Supporting Information for the other hydrocarbons. Except for the lowest pressure in Fig. 3(c), the permeability coefficient for C3H8 actually decreases with increasing temperature. Stannett et al. [26,27] reported similar behavior some time ago for the permeation of organic vapors in polymer films. This is generally the consequence of a stronger decrease in sorption with temperature than an increase in diffusion with temperature. In the case of strong plasticization, the diffusion coefficient may have an inverted temperature dependence. 4.3. Gas diffusion coefficients Effective diffusion coefficients were calculated from the experimentally measured permeability and solubility coefficients using the relation D ¼P/S where S is the secant slope of the sorption isotherm evaluated at the same pressure of the upstream gas in the permeation experiment. Fig. 4 shows these diffusion coefficients for N2, CO2, and C3H8 plotted versus pressure for each of the temperatures within the range from 25 to 55 1C; similar plots for the other 7 gases are included in the Supporting Information. For He, H2, O2, N2, CH4 and CO2, the diffusion coefficients increase more or less linearly with upstream pressure over the range from 1 to 10 atm. As discussed more fully in our previous paper [18], these trends do not stem from plasticization behavior but rather reflect the responses expected from the dual-mode sorptionmobility model summarized by Eq. (11). On the other hand, for the hydrocarbons C2H4, C2H6, C3H6 and C3H8, the plots of diffusion coefficients versus pressure exhibit similar trends as do the plots of their permeability coefficients versus pressure. At low temperatures, the diffusion coefficients increase sharply with upstream pressure due to serious plasticization of the PIM-1 film by the penetrants. However, at higher temperatures where the amount of sorption of these penetrants is less, the plasticization is also less
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6000
CO2 Permeability (barrer)
N2 permeability (barrer)
450
400
350
300
250
200
0
2
4
6
8
10
5500
5000
4500
4000
12
0
2
Pressure (atm)
4
6
8
10
12
Pressure (atm)
C3H8 Permeability (barrer)
6000 5000 4000 3000
2000 1000 0
0
2
4
6
8
10
Pressure (atm) Fig. 3. Permeability coefficients for N2, CO2 and C3H8 for pressures up to 10 atm and temperatures from 25 to 55 1C. The solid curves are to guide the eye.
0.5 CO2 Diffusion coefficient (10-5cm2/s)
N2 diffusion coefficient (10-5cm2/s)
0.25
0.2
0.15
0.1
0.05
0
2
4
6
8
10
12
0.4
0.3
0.2
0.1
0
2
Pressure (atm)
4 6 8 Pressure (atm)
10
12
C3H8 Diffusion coefficient (10-5cm2/s)
0.25
0.2
0.15
0.1
0.05
0
0
2
4
6
8
10
Pressure (atm) Fig. 4. Gas diffusion coefficients for N2, CO2 and C3H8 for pressures up to 10 atm and temperatures from 25 to 55 1C. The solid curves are to guide the eye.
P. Li et al. / Journal of Membrane Science 450 (2014) 380–388
severe. In some cases, as a result of these issues, the diffusion coefficients at high temperatures are not as great as those at low temperatures; of course, this trend is not really due to negative activation energies for diffusion as a simple phenomenological analysis would suggest. 4.4. Temperature dependence of the dual-mode model parameters: DD and DH The dual mobility model parameters DD and DH can be obtained from the slope and intercepts of plots of P versus 1/(1 þbph) as discussed previously [18]. Such plots for He, H2, O2, N2, CH4 and CO2 are shown in Supporting Information and the model parameters deduced from them are summarized in Table 3. Similar plots are not shown for the hydrocarbons C2H4, C2H6, C3H6 and C3H8 since the plots would be highly non-linear owing to the strong plasticization they exert on PIM-1 and obtaining meaningful parameters would not be possible. For the gases that do not plasticize PIM-1 significantly, both DD and DH increase with temperature as seen in Table 3. This dependence can be analyzed in terms of Eqs. (12) and (13), and the resulting activation energies are shown in Table 4 as well as the difference EDH EDD that characterizes how the parameter F depends on temperature, see Eq. (14). As noted previously, the values of F are considerably smaller for PIM-1 than for other glassy polymers that have been subjected to a similar analysis [18]. In glassy polymers, segmental rotations are highly restricted and only short-range chain motion is allowed [25], and this is especially true for PIM-1. Broadly speaking, the results in Table 4 show that the two activation energies EDH and EDD increase as the size of the penetrant molecules increase as expected for diffusion in all types of polymers according to various models [25]. Table 3 Values of DD, DH and F for gases in PIM-1 at 25–55 1C. Unit (1C)
DD
DH
F¼ DH/DD
Unit (1C)
He 25 35 45 55
150 201 215 206
177 242 215 370
0.012 0.012 0.010 0.018
O2 25 35 45 55
5.04 7.47 8.26 9.29
H2 25 35C 45 55
537 550 634 654
170 110 203 397
0.003 0.002 0.003 0.006
CH4 25 35 45 55
3.71 4.77 6.84 6.92
0.026 0.030 0.043 0.062
CO2 25 35C 45 55
N2 25 35 45 55
3.48 4.37 4.98 5.54
9.10 13.1 21.4 34.4
DD
13.0 12.2 15.2 19.7
DH
F¼DH/DD
33.8 40.3 78.5 138
0.067 0.054 0.095 0.148
3.34 4.77 10.3 15.0 34.1 65.7 90.0 120
0.009 0.010 0.015 0.022 0.026 0.054 0.059 0.061
DD 106 (cm2/s); DH 108 (cm2/s).
385
Interestingly, EDH is about 2–3 times larger than EDD for all penetrants, and their differences, EDH EDD , generally increase as the penetrant molecules get larger. It is important to note that the dual-mode sorption parameters C H0 , kD and b are needed to estimate DD and DH. The pressure range used here for measuring the sorption isotherms of H2 and O2 was 0–200 psi due to safety concerns while the range used for He, CO2, N2 and CH4 was 0– 450 psi. Barbari et al. [28] reported that the estimated dual mode sorption parameters can be somewhat dependent on the pressure range used to determine the sorption isotherms. For this and other reasons, it is important to look at only the broad trends from such an analysis and not over interpret the details.
4.5. Phenomenological analyses of the energetics of sorption, diffusion and permeation It is rather uncommon to find detailed analyses of the energetics of sorption and diffusion in glassy polymers like that presented above where the pressure dependence has been dealt with via descriptive models. More often the temperature dependence of the phenomenological parameters P, D, and S at a given pressure is analyzed in terms of Eqs. (1)–(3) to obtain effective activation energies. It is useful to examine the data reported here in this fashion at each pressure so that the current results can be compared with some of the other results reported in the literature for gas permeation in PIM-1, see Table 5. The results in Table 5 show that the activation energies for permeation of gases in PIM-1 from different research groups vary greatly. This may be due, in part, to the different thermal histories and/or different testing protocols for the PIM-1 films. It is important to remember that PIM-1 is a glassy polymer with an extraordinary high free volume, and its gas permeation behavior is highly dependent on the film preparation history. In the report by Thomas et al. [12], the PIM-1 films were soaked with methanol before the gas permeation test; while in the report by Budd et al. [17], the PIM-1 films were cast from chloroform, similar to our sample preparation procedure. Therefore, the activation energies from Budd et al. are more similar to our data except for He, CH4 and CO2. In our study, we frequently replaced the PIM-1 films during the gas permeation test to maintain a similar thermal history. While in the report by Budd et al., they did not mention the replacement of PIM-1 films during the gas permeation measurements. The different testing procedures may be responsible for the different estimated activation energies observed for He, CH4 and CO2. Table 6 compares the activation energies of permeation and diffusion and the heat of sorption of various gases in PIM-1 with those for a range of other glassy polymers: polycarbonate (PC) [29], poly[1-(trimethylsilyl)- l-propyne] (PTMSP) [30], polyimide [31], and Teflon AF 1600 [32]. For these gas/polymer pairs, the values of Hs varies over the range of 5.3 to 1.0 kcal/mol; and Table 5 Reported values of activation energies for gas permeation in PIM-1. Gas
Table 4 Activation energies for gas diffusion via Henry and Langmuir modes. Gas
He H2 CO2 O2 N2 CH4
Kinetic diameter dk (Å) [25]
EDD (kcal/mol)
E DH (kcal/mol)
EDH EDD (kcal/mol)
2.6 2.89 3.3 3.46 3.64 3.80
2.00 1.42 2.84 3.80 2.88 4.36
4.03 5.98 8.00 9.42 8.67 10.2
2.03 4.56 5.16 5.62 5.79 5.87
He H2 O2 N2 CH4 CO2
Ep (kcal/mol) Thomas et al. [12]
Budd et al. [17]
This studya
0.10 0.10 1.33 3.40 4.62 0.24
1.29 0.76 0.79 2.50 2.60 1.07
0.64 0.41 0.61 2.85 4.20 0.11
a The activation energies are estimated based on the permeability at 1 atm and the temperature range of 25–55 1C.
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Table 6 Activation Energies for permeation and diffusion and heat of sorption for six penetrants in polycarbonate (PC) [29], poly[1-(trimethylsilyl)-l-propyne] (PTMSP) [30], a polyimide (PI)[31], Teflon AF 1600 [32], and PIM-1. Polymer Tg FFV
PC 150 1C 0.16
PI 335 1C 0.18 [33]
PIM-1 4350 1C 0.25
Teflon AF 1600 160 1C 0.32
PTMSP 4350 1C 0.33
0.1 0.6 1.6 1.2 1.5 2.3
Ep (kcal/mol) He 4.2 H2 – O2 5.0 N2 6.0 CH4 6.2 CO2 3.0
– – 0.8 2.5 3.7 0.7
0.6 0.4 0.6 2.8 4.2 0.4
1.0 1.1 0.8 1.1 2.5 0.4
Ed (kcal/mol) He 6.7 H2 – O2 7.6 N2 9.7 10 CH4 CO2 8.3
– – 4.2 6.7 6.4 4.0
3.0 3.2 5.3 6.0 7.8 4.2
– – 2.0 2.9 4.4 3.6
Hs (kcal/mol) He 2.5 H2 – O2 2.6 N2 3.7 CH4 3.8 CO2 5.3
– – 3.4 4.2 2.6 3.3
2.4 2.8 4.7 3.1 3.7 3.8
– – 1.2 1.8 1.9 4.0
1.0 0.6 1.2 1.2 1.2 0.1 1.0 1.2 2.8 2.4 2.7 2.4
the Hs for PIM-1 seem to fall more or less in the middle of this range for most gases indicating there is nothing unusual about its energetics of sorption. The activation energy for diffusion, Ed, for the various gas/polymer pairs varies over the range of 0.6–10 kcal/ mol. Within this limited range of polymers, it seems that the higher the free volume and Tg the less gas diffusion depends on temperature; again, PIM-1 seems to fall in the middle range in line with its free volume. The activation energy for permeation, Ep, is more complex since it reflects both kinetic and thermodynamic issues. The values for PIM-1 are quite similar to those of the polyimide [31] shown in Table 6. Thus, it appears that these energetic parameters for PIM-1 are within a range that might be expected. Table 7 lists the activation energies of gas permeation and diffusion as well as the heat of sorption of all gases in PIM-1 at pressures from 1 to 10 atm. For He, H2, O2, N2, CH4, and CO2, the activation energies of diffusion decrease with increasing pressure while the heat of sorption increases (i.e., becomes less negative) with increasing pressure. The solubility coefficient, S, can be expressed in terms of the dual-sorption model as shown in Eq. (9). As seen there, the relative contribution of the Langmuir term to the total sorption amount decreases as pressure increases. The Langmuir capacity term has a strong temperature dependence owing to its connection to the excess volume of the glass that decreases as the temperature is increased [22,24]; thus, reducing its contribution via higher pressures reduces the temperature dependence of the overall solubility coefficient, S. The diffusion coefficient calculated from D ¼P/S can be expressed in terms of the dual-mode sorption-mobility model as follows [18] DðpÞ ¼
DD ð1 þ bpÞ þ KDH K ¼ DD ðDD DH Þ ð1 þ bpÞ þK ð1 þ bpÞ þ K
ð15Þ
Eq. (15) predicts that the diffusivity coefficient D increases as the upstream pressure increases, and that the phenomenological activation energy of diffusion, Ed , decreases with pressure. This is understandable by the observation that the activation energy for diffusion for Henry's law mode is less than that for the Langmuir
mode as seen in Table 4. As the pressure increases, a greater fraction of the gas is associated with Henry's law mode and a higher fraction of the diffusion occurs via this mode at higher pressures. Thus, the overall or phenomenological activation energy for diffusion is expected to decrease with pressure. For the less condensable gases He, H2, O2, N2, and CH4, the increase in the sorption energy with pressure counter-balances the decrease in the diffusion activation energy; thus, the activation energy for permeation remains a relatively constant and positive value for each gas over the range from 1 to 10 atm. However, for CO2, the diffusion activation energy and the heat of sorption are nearly equal in magnitude (but opposite in sign); thus, the activation energy for permeation of CO2 is nearly zero but the global average value over the temperature range studied appears to decrease as the pressure increases. For the hydrocarbons C2H4, C2H6, C3H6 and C3H8, the effect of temperature on P and D is quite complex (see plots in Fig. S7) due to the strong effect temperature has on the extent of sorption and its effect on diffusion via plasticization. Since PIM-1 is strongly plasticized by these hydrocarbons, DD and DH in the Eq. (11) are not constant and there is no practical way to evaluate them. Therefore, it is not appropriate to utilize the dual-mode sorptionmobility model parameters to analyze the dependence of the activation energy or heat of sorption on the pressure. Because of the strong coupling between temperature and plasticization behavior, the usual interpretations of activation energies in these systems becomes meaningless; and as a consequence no values for Ep or Ed are given in Table 7 for these penetrants.
5. Conclusions Solubility, permeability and diffusion coefficients for 10 gases were determined for films of PIM-1 at temperatures from 25 to 55 1C over a range of pressures. The following conclusions can be drawn: (1) All 10 gases exhibit typical dual-mode sorption isotherms, and the extent of sorption decreases as temperature increases. (2) The dual-mode sorption parameters kD,C H0 , and b decrease with temperature for He, H2, N2, O2, CH4 and CO2 while for the hydrocarbons C2H4, C2H6, C3H6 and C3H8 the trends are less clear owing to the varying effects of plasticization. (3) For He, H2, O2 and N2, the sorption energy difference HD HH increases as the kinetic diameter increases. For the highly condensable gases CH4, CO2, C2H4, C2H6, C3H6 and C3H8, HD HH decreases as the critical temperature increases. (4) For He, H2, O2, N2 and CH4, the permeability coefficients increase with temperature and decrease with pressure. For CO2 the activation energy for diffusion is nearly canceled by the heat of sorption so that the permeability coefficient is only weakly dependent on temperature. For C2H4, C2H6, C3H6 and C3H8, the permeability coefficients are often higher at low temperatures than high temperatures due to the effects of plasticization. (5) The diffusion coefficients of He, H2, O2, N2, CH4 and CO2 increase more or less linearly as the upstream pressure increases from 1 to 10 atm. This is not a consequence of plasticization but can be well explained by the dual-mode sorption-mobility model. However, for C2H4, C2H6, C3H6 and C3H8, plasticization causes an increase in the diffusion coefficient with pressure that is much greater than expected from the dual-mode effects. In certain cases, the diffusion coefficients of the hydrocarbons have an inverted temperature dependence, i.e., the apparent activation energy is negative, due to plasticization effects.
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Table 7 Apparent Arrhenius and van't Hoff energy parameters at different pressures. Penetrant
Pressure (atm)
Ep (kcal/mol)
Hs (kcal/mol)
Ed (kcal/mol)
Penetrant
Pressure(atm)
Ep (kcal/mol)
Hs (kcal/mol)
Ed (kcal/mol)
He
1.0 2.5 5.0 7.5 10.0
0.63 0.64 0.64 0.64 0.64
2.38 2.36 2.22 2.13 2.09
3.01 2.99 2.86 2.77 2.73
CO2
1.0 2.5 5.0 7.5 10.0
0.37 0.19 0.11 0.09 0.28
3.82 3.59 2.79 2.74 2.62
4.19 3.79 2.89 2.64 2.34
H2
1.0 2.5 5.0 7.5 10.0
0.41 0.41 0.40 0.39 0.40
2.79 2.67 2.52 2.51 2.57
3.19 3.08 2.93 2.90 2.97
C2H4
1.0 2.5 5.0 7.5 10.0
– – – – –
1.96 2.17 2.64 2.09 2.05
– – – – –
O2
1.0 2.5 5.0 7.5 10.0
0.60 0.60 0.61 0.64 0.66
4.73 4.31 3.79 3.43 3.21
5.33 4.90 4.39 4.07 3.87
C2H6
1.0 2.5 5.0 7.5 10.0
– – – – –
2.03 2.30 2.17 1.86 2.24
– – – – –
N2
1.0 2.5 5.0 7.5 10.0
2.83 2.85 2.88 2.86 2.84
3.14 2.84 2.53 2.34 2.03
5.97 5.68 5.41 5.20 4.87
C3H6
1.0 2.5 5.0 7.5 10.0
– – – – –
3.67 2.51 3.67 3.27 3.44
– – – – –
CH4
1.0 2.5 5.0 7.5 10.0
4.15 4.20 4.27 4.24 4.19
3.68 3.35 2.87 2.62 2.49
7.83 7.56 7.14 6.86 6.68
C3H8
1.0 2.5 5.0 7.5
– – – –
2.98 2.91 3.22 3.11
– – – –
(6) The diffusion coefficients DD and DH and their ratio, F, increase with temperature, and their activation energies, as well as the difference,EDH EDD , generally increase as the kinetic diameters of He, H2, O2, N2, CH4 and CO2 increase. (7) For He, H2, O2, N2, and CH4, the activation energies of diffusion decrease with pressure while the heat of sorption increases; as a result, the activation energies of permeation remain nearly independent of pressure. For the hydrocarbons C2H4, C2H6, C3H6 and C3H8, activation energies for permeation and diffusion are not meaningful owing to the effects of plasticization that cause Arrhenius plots to be non-linear.
The molecular picture of the solid-state structure of high free volume polymers like PIM-1 is still emerging. Clarification of the many issues involved is well beyond the scope of this and our previous [18] paper; however, this work adds the following to this picture. While PIM-1 clearly has exceptional sorption and permeation properties stemming from its very low packing density, it does share a number of features in common with other glassy polymers. First, the sorption isotherms for all gases are well described by the dual sorption model. Second, for gases with relatively low levels of condensability like He, H2, N2, O2, CH4 and CO2, the effect of upstream pressure on permeability is well described by the dual mobility model. In a much earlier paper [34], the relationship between values of DH and DH for CO2 at 35 1C in a series of about 15 glassy polymers, including polysulfones, polycarbonates, etc., was analyzed and it was found that the mobilities for the two sorption populations are about equally influenced by changes in the polymer molecular structure and that the ratio DH/DH was on average about 0.078 with some variation about this average. The results found for PIM-1 are well within this range. It is worth noting that gas sorption and permeation in a polymer having an even higher level of free volume and permeability than PIM-1, viz., poly[1-(trimethylsilyl)-1-propyne] or TMPSP, are also well described by these models as shown by Auvil
et al. [35]. The facts available confirm that gas permeation in both PTMSP and PIM-1 occurs by a solution-diffusion mechanism, and the main reason for their high permeability is high diffusion coefficients. Furthermore, PIM-1 is significantly plasticized by more condensable species such as the C2 and C3 hydrocarbons considered in this work, which is true for other glassy polymers.
Acknowledgments The authors would like to thank Mr. Fuyun Li, and Ms. Wai Fen Yong for their help in the synthesis of PIM-1 and Ms. Xiuzhu Fu and Mr. Yihui Sim for their valuable suggestions. The authors also express appreciation for financial support from NUS grant C-279000-019-101 for appointment of Prof. D.R. Paul as the Tan Chin Tuan Centennial Professor. The authors would also like to thank the Singapore National Research Foundation (NRF) for funding the project with grant number R-279-000-311-281.
Appendix A. Supporting information Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.memsci.2013.09.030. References [1] P.M. Budd, B.S. Ghanem, S. Makhseed, N.B. Mckeown, K.J. Msayib, C. E. Tattershall, Polymers of intrinsic microporosity (PIMs): robust, solutionprocessable, organic nanoporous materials, Chem. Commun. (2004) 230–231. [2] P.M. Budd, E.S. Elabas, B.S. Ghanem, S. Makhseed, N.B. Mckeown, K.J. Msayib, C. E. Tattershall, D. Wang, Solution-processed, organophilic membrane derived from a polymer of intrinsic microporosity, Adv. Mater. 16 (2004) 456–459. [3] B.S. Ghanem, M. Hashem, K.D.M. Harris, K.J. Msayib, M. Xu, P.M. Budd, N. Chaukura, D. Book, S. Tedds, A. Walton, N.B. Mckeown, Triptycene-based polymers of intrinsic microporosity: organic materials that can be tailored for gas adsorption, Macromolecules 43 (2010) 5287–5294. [4] B.S. Ghanem, K.J. Msayib, N.B. Mckeown, K.D.M. Harris, Z. Pan, P.M. Budd, A. Butler, J. Selbie, D. Book, A. Walton, A triptycene-based polymer of intrinsic microporisity that displays enhanced surface area and hydrogen adsorption, Chem. Commun. (2007) 67–69.
388
P. Li et al. / Journal of Membrane Science 450 (2014) 380–388
[5] F.Y. Li, Y.C. Xiao, Y.K. Ong, T.-S. Chung, UV-rearranged PIM-1 polymeric membranes for advanced hydrogen purification and production, Adv. Energy Mater. 2 (2012) 1456–1466. [6] F.Y. Li, Y.C. Xiao, T.-S. Chung, S. Kawi, High-performance thermally self-crosslinked polymer of intrinsic microporosity (PIM-1) membranes for energy development, Macromolecules 45 (2012) 1427–1437. [7] W.F. Yong, F.Y. Li, Y.C. Xiao, P. Li, K.P. Pramoda, Y.W. Tong, T.-S. Chung, Molecular engineering of PIM-1/Matrimid blend membranes for gas separation, J. Membr. Sci. 407–408 (2012) 47–57. [8] N. Du, G.P. Robertson, J. Song, I. Pinnau, S. Thomas, M.D. Guiver, Polymers of intrinsic microporosity containing trifluoromethyl and phenylsulfone groups as materials for membrane gas separation, Macromolecules 41 (2008) 9656–9662. [9] D. Fritsch, P. Merten, k. Heinrich, M. Lazar, M. Prike, High performance organic solvent nanofiltration membranes: development and thorough testing of thin film composite membranes made of polymers of intrinsic microporosity (PIMs), J. Membr. Sci. 401–402 (2012) 222–231. [10] S. Tsarkov, V. Khotimskiy, P.M. Budd, V. Volkov, J. Kukushkina, A. Volkov, Solvent nanofiltration through high permeability glassy polymers: Effect of polymer and solute nature, J. Membr. Sci. 423–424 (2012) 65–72. [11] N. Du, G.P. Robertson, M.M. Dal-Cin, L. Scoles, M.D. Guiver, Polymers of intrinsic microporosity (PIMs) substituted with methyl tetrazole, Polymer 53 (2012) 4367–4372. [12] S. Thomas, I. Pinnau, N. Du, M.D. Guiver, Pure- and mixed-gas permeation properties of a microporous spirobisindane-based ladder polymer (PIM-1), J. Membr. Sci. 333 (2009) 125–131. [13] S.V. Adymkanov, Y.P. Yampol'skii, A.M. Polyakov, P.M. Budd, K.J. Reynolds, N. B. Mckeown, K.J. Msayib, Pervaporation of alcolhols through highly permeable PIM-1 polymer films, Polym. Sci. Ser. A 50 (2008) 444–450. [14] C.R. Mason, M.G. Buonomenna, G. Golemme, P.M. Budd, F. Galiano, A. Figoli, K. Friess, V. Hynek, New organophilic mixed matrix membranes derived from a polymer of intrinsic microporosity and silicalite-1, Polymer 54 (2013) 2222–2230. [15] O. Vopicka, K. Friess, V. Hynek, P. Sysel, M. Zgazar, M. Sipek, K. Pilnacek, M. Lanc, J.C. Jansen, C.R. Mason, P.M. Budd, Equilibrium and transient sorption of vapours and gases in the polymer of intrinsic microporosity PIM-1, J. Membr. Sci. 434 (2013) 148–160. [16] O. Holck, M. Bohning, M. Heuchel, M.R. Siegert, D. Hofmann, Gas sorption isotherms in swelling glassy polymers-detailed atomictic simulations, J. Membr. Sci. 428 (2013) 523–532. [17] P.M. Budd, N.B. McKeown, B.S. Ghanem, K.J. Msayib, D. Fritsch, L. Starannikova, N. Belov, O. Sanfirova, Y. Yampolskii, V. Shantarovich, Gas permeation parameters and other physicochemical properties of a polymer of intrinsic microporosity: polybenzodioxane PIM-1, J. Membr. Sci. 325 (2008) 851–860. [18] P. Li, T.S. Chung, D.R. Paul, Gas sorption and permeation in PIM-1, J. Membr. Sci. 432 (2013) 50–57. [19] K. Ghosal, B.D. Freeman, Gas separation using polymer membranes: an overview, Polym. Adv. Tech. 5 (1993) 673–697.
[20] L.M. Costello, W.J. Koros, Temperature dependence of gas sorption and transport properties in polymers: measurement and applications, Ind. Eng. Chem. Res. 31 (1992) 2708–2714. [21] W.J. Koros, D.R. Paul, G.S. Huvard, Energetics of gas sorption in glassy polymers, Polymer 20 (1979) 956–960. [22] W.J. Koros, D.R. Paul, CO2 sorption in poly(ethylene terephthalate) above and below glass transition temperature, J. Polym. Sci.: Polym. Phys. Ed. 16 (1978) 1947–1963. [23] P. Li, D.R. Paul, T.S. Chung, High performance membranes based on ionic liquid polymers for CO2 separation from the flue gas, Green Chem. 14 (4) (2012) 1052–1063. [24] J.S. Chiou, Y. Maeda, D.R. Paul, Gas and vapor sorption in polymers just below Tg, J. Appl. Polym. Sci. 30 (1985) 4019–4029. [25] S. Matteucii, Y. Yampolskii, B.D. Freeman, I. Pinnau, Transport of gases and vapors in glassy and rubber polymers, in: Y. Yampolskii, I. Pinnau, B. D. Freeman (Eds.), Materials Sciences of Membranes for Gas and Vapor Separation, John Wiley & Sons, Ltd., The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England, 2006, pp. 1–40. [26] I. Sobolev, J.A. Meyer, V. Stannett, M. Szwarc, Permeation, diffusion, and solubility of methyl bromide and isobutene in polyethylene, Ind. Eng. Chem. 49 (1957) 441–444. [27] R. Waack, N.H. Alex, H.L. Frisch, V. Stannett, M. Szwarc, Permeability of polymer films to gases and vapors, Ind. Eng. Chem. 47 (1955) 2524–2527. [28] T.A. Barbari, W.J. Koros, D.R. Paul, Gas transport in polymers based on bisphenol-A, J. Polym. Sci.: Part B: Polym. Phys. 26 (1988) 709–727. [29] L.M. Costello, W.J. Koros, Effect of structure on the temperature dependence of gas transport and sorption in a series of polycarbonates, J. Polym. Sci.: Part B: Polym. Phys. 32 (1994) 701–713. [30] T. Masuda, Y. Iguchi, B.-Z. Tang, T. Higashimura, Diffusion and solution of gases in substituted polyacetylene membranes, Polymer 29 (1988) 2041–2049. [31] T.S. Chung, C. Cao, R. Wang, Pressure and temperature dependence of the gas transport properties of dense poly[2,6-toluene-2,2-bis(3,4-dicarboxylphenyl) hexafluoropropane diimide] membranes, J. Polym. Sci.: Part B: Polym. Phys. 42 (2004) 354–364. [32] A.Y. Alentiev, V.P. Shantarovich, T.C. Merkel, V.I. Bondar, B.D. Freeman, Y. P. Yampolskii, Gas and vapor sorption, permeation, and diffusion in glassy amorphous Teflon AF 1600, Macromolecules 35 (2002) 9513–9522. [33] K. Tanaka, M. Okano, H. Toshino, H. Kita, K.-I. Okamoto, Effect of methyl substituents on permeability and permselectivity of gases in polyimides prepared from methyl-substituted phenylenediamines, J. Polym. Sci.: Part B: Polym. Phys. 30 (1992) 907–914. [34] C.L. Aitken, W.J. Koros, D.R. Paul, Transport properties of biphenol polysulfones, Macromolecules 25 (1992) 3651–3658. [35] R. Srinivasan, S.R. Auvil, P.M. Burban, Elucidating the mechanism(s) of gas transport in poly[1-(trimethylsilyl)-1-propyne] (PTMSP) membranes, J. Membr. Sci. 86 (1994) 67–86.
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Temperature dependence of gas sorption and permeation in PIM-1 P. Li a, T.S. Chung b, D.R. Paul a,b,n a b
Department of Chemical and Biomolecular Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 117602, Singapore Department of Chemical Engineering, The University of Texas at Austin, Austin, TX 78712-1062, USA
art ic l e i nf o
a b s t r a c t
Article history: Received 31 May 2013 Received in revised form 16 August 2013 Accepted 17 September 2013 Available online 25 September 2013
In a prior paper gas sorption, permeation and diffusion coefficients were determined for He, H2, N2, O2, CH4, CO2, C2H4, C2H6, C3H6 and C3H8 in PIM-1, a polymer of intrinsic microporosity, at 25 1C over a range of pressures. Here similar measurements and analyses were made at temperatures from 25 to 55 1C over a wide range of pressure. In all cases, the sorption isotherms were generally consistent with the form of the dual-sorption model. For He, H2, N2, O2, CH4 and CO2, the effects of plasticization were minimal and the results could be effectively analyzed by the dual sorption-dual mobility model, and the temperature dependence of the model parameters were analyzed to obtain the energetic parameters for the sorption and diffusion processes. However, for C2H4, C2H6, C3H6 and C3H8, plasticization was quite significant and temperature dependent; as a result, a similar analysis in terms of the dual sorption-dual mobility model could not be meaningfully carried out. For all gases, a more phenomenological analysis of P, D and S was made in terms of simple Arrhenius and van't Hoff relations to obtain energetic parameters that subsequently depend on pressure because of some combination of dual mode and/or plasticization effects. & 2013 Elsevier B.V. All rights reserved.
Keywords: Polymer of intrinsic microporosity (PIM-1) Gas permeability Dual-mode sorption-mobility model
1. Introduction In 2004, Budd et al. reported a new class of soluble polymers with very rigid but contorted backbones and coined the term “polymers of intrinsic microporosity (PIMs)” to describe them [1,2]. The high free volume and the ready solubility of these materials in common solvents have led to a great deal of interest in them for gas storage because of their high levels of gas sorption [3,4] and for membrane separations owing to their high permeability [5–10]. The most well-known polymer in this class, PIM-1, whose structure is given in Fig. 1, has been extensively studied for membrane applications in areas such as organic solvent nanofiltration [9,10], gas separation [11,12], and pervaporation [13,14]. Several reports have evaluated the separation performance of PIM-1via measurement of the permeability, solubility and diffusion coefficients of various gas and vapor penetrants [15,16]. Most of these studies were carried out at 25 or 35 1C; however, at least two studies have reported results at other temperatures [12,17]. Recently, we reported sorption isotherms, obtained via a dualvolume sorption method, plus gas permeability coefficients over a range of upstream pressures, all at 25 1C, with the results analyzed in terms of the dual-mode sorption-mobility model [18]. A better
n Corresponding author at: Department of Chemical Engineering, The University of Texas at Austin, Austin, TX 78712-1062, USA. Tel.: þ 1 5124715392; fax: þ1 5124710542. E-mail address: [email protected] (D.R. Paul).
0376-7388/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.memsci.2013.09.030
understanding these properties over a wider range of conditions would assist any consideration of industrial use of PIM-1 for membrane applications. The purpose here is to extend the type of measurements and analyses reported earlier for PIM-1 to a wider range of temperatures, 25–55 1C, for the series of penetrants: He, H2, N2, O2, CH4, CO2, C2H4, C2H6, C3H6 and C3H8. The measured sorption and permeation coefficients plus the model parameters are analyzed to extract corresponding sorption energies and activation energies; these energy parameters should add useful insights about the nature of this unusual polymer. Because of the large number of plots generated in this work, the body of the manuscript presents graphs for only three penetrants, N2, CO2, and propane, C3H8, since these represent the range of behaviors observed while similar graphs for the remaining penetrants, plus all Arrhenius and van't Hoff plots, are included in Supplementary Information. 2. Background In this work, the equilibrium concentration, C, of each penetrant in PIM-1 was determined over a range of gas pressures, p. A secant solubility coefficient, S, can be computed from C/p at each pressure. The permeability coefficient, P, of each penetrant was measured as a function of upstream driving pressure. With these measurements, an effective or average diffusion coefficient, D, can be calculated from P/S. The temperature dependence of each of these phenomenological coefficients can be represented in terms
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law mode, i.e., H D H H 40, because more energy is required to create space in the polymer for the molecules of gas to be dissolved, i.e., sorbed by Henry's law mode, versus gas sorbed into presumed pre-existing spaces, i.e., by the Langmuir mode. The solubility coefficient, S, can be written in terms of the dualsorption model as S¼
Combining Eqs. (9) and (3) yields C H0 b Hs kD þ ¼ S0 exp 1 þ bp RT
Fig. 1. Molecular structure of PIM-1.
of appropriate Arrhenius or van't Hoff type expressions [19–21]. Ep ð1Þ P ¼ P 0 exp RT E D ¼ D0 exp d RT
ð2Þ
Hs S ¼ S0 exp RT
ð3Þ
where P0, D0, and S0 are pre-exponential factors and Ep, Ed, and Hs represent the activation energies of permeation and diffusion and the heat of sorption, respectively; R is the gas constant and T is the absolute temperature. Since P ¼D S, combining Eqs. (1–3) gives Ep ¼ Ed þH s
ð4Þ
When the coefficients P, D and S are pressure (or concentration) dependent, as expected for gases in glassy polymers or when plasticization is significant, the parameters in Eqs. (1–3) must also be dependent on the pressures used in their measurement. An alternate approach is to use pressure dependent models and to interpret the energetics in terms of the parameters of the model. The non-linear gas sorption isotherms for glassy polymers are typically well described by the so-called dual-mode sorption model [22]. C ¼ kD p þ
C H0 bp 1 þbp
ð7Þ
where the difference in the enthalpy between gas sorbed in Henry's law mode and in the gas phase is referred to as ΔH D while the difference in the enthalpy between gas sorbed in the Langmuir sites and in the gas phase is referred to as ΔH b . The enthalpy difference between the gas sorbed in the Langmuir sites, HD, and Henry's law mode, HH, can then be estimated as follows: H D H H ¼ ΔH D ΔH H
ð9Þ
ð10Þ
The pressure dependence of the gas permeability coefficient of glassy polymers is well represented by a dual-mode sorptionmobility model [18] of the form C H0 b FK P ¼ kD D D þ ð11Þ DH ¼ kD DD 1 þ 1 þbph 1 þ bph where DD and DH are the diffusion coefficients of Henry and Langmuir modes, respectively, while K ¼ C H0 b/kD, F¼DH/DD and ph is the pressure of the feed gas; the pressure on the permeate side in these measurements is usually very low and can be taken as zero. The temperature dependence of the parameters in Eq. (11) can be written using the analogous Arrhenius relationships ED ð12Þ DD ¼ DD0 exp D RT ED DH ¼ DH0 exp H RT
ð13Þ
where DD0 and DH0 are the pre-exponential factors and EDD and EDH are the activation energies of diffusion associated with the two envisioned modes of sorption and diffusion, respectively. The temperature dependence of the ratio F can be expressed as follows: DH DH 0 ED EDD ð14Þ F¼ ¼ exp H DD DD0 RT
ð5Þ
This model envisions the sorption of gas in both Henry's law dissolution mode and in Langmuir ‘hole filling’ mode where p is the pressure in the gas phase and kD , C H0 , and b are Henry's law solubility, Langmuir sorption capacity, and hole affinity parameters, respectively. The temperature dependence of C H0 is related to the volume of the glass in excess of the equilibrium volume and is proportional to the distance from the glass transition temperature, i.e., Tg T, and is not related to any energetic parameters. On the other hand, the temperature dependence of kD and b can be expressed as follows [21]. ΔH D ð6Þ kD ¼ kD0 exp RT ΔH b b ¼ b0 exp RT
C C H0 b ¼ kD þ p 1 þ bp
ð8Þ
As indicated by Costello and Koros [20], the enthalpy of gas sorbed in the Langmuir sites should be less than that in Henry's
3. Experimental PIM-1 was synthesized via polycondensation reactions described in previous papers [5–7]. All gases, i.e., He, H2, N2, O2, CH4, CO2, C2H4, C2H6, C3H6 and C3H8, were purchased from Soxal (Singapore) with purities higher than 99.9%. The solvents methanol and N-methyl-2-pyrrolidione were AR grade and purchased from Merck; while HPLC grade chloroform (99.9%) and hydrochloric acid (37.5% in H2O) were purchased from Fisher Chemical. Films of PIM-1 were prepared via solvent casting from a 2 wt% polymer solution in chloroform; the detailed procedure was provided in the previous paper [18]. PIM-1 films with a thickness around 507 5 μm were used for permeation and sorption measurements. Similar to our previous paper, pure gas permeability coefficients were determined using a constant-volume permeation cell while sorption isotherms were measured using a dual-volume pressure decay system. Details of these systems and the measuring protocols were provided earlier [18,23]. Since PIM-type materials exhibit severe physical aging behavior, the gas transport properties for PIM-1 were highly affected by both the film preparation and the testing protocols. Thus, we tried to maintain and adopt an identical film preparation process for all fresh PIM-1 samples as introduced in the previous paper [18]. For gas permeation measurements, the permeability of N2 was first determined for each fresh film at 25 1C and 1 atm; if the observed value was in the
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expected range (variation o10%), then further measurements were made for this film. Each film was replaced after one day of measurement or when there was a change in the temperature. For highly condensable gases such as the hydrocarbons, the film was replaced when there was a change of gas, temperature or the testing duration was longer than one day. On the contrary, for sorption measurements, it usually took 3–5 days to obtain a sorption isotherm; thus, the PIM-1 film would only be replaced after a complete sorption isotherm was obtained.
4. Results and discussion 4.1. Gas sorption Fig. 2 shows sorption isotherms for N2, CO2 and C3H8 in PIM-1 at temperatures from 25 to 55 1C; the sorption isotherms of the other 7 gases are shown in Supporting Information. All sorption isotherms exhibit the non-linear behavior typical of glassy polymers [18]. The experimental sorption data were fitted to Eq. (5) by a non-linear routine to obtain the parameters shown in Table 1. In a few cases, a parameter range is shown when the outcome of the fitting is sensitive to the initial parameter estimated. The solid lines in all the plots of C versus p were calculated using Eq. (5) and the parameters in Table 1; these lines provide an excellent representation of the experimental data. As the temperature increases, the extent of gas sorption gradually decreases in all cases, as expected, since the sorption enthalpy is negative or exothermic. For hydrocarbons like C3H6 and C3H8, the sorption isotherms show some indications that there might be upward curvature at higher pressures as observed for methanol, heptanes and toluene in PIM-1 at 25 1C [15]. Chiou et al. [24] made a systematic study of CO2 sorption isotherms in miscible blends of poly(methyl methacrylate) and poly (vinylidene fluoride) at 35 1C and found that as the amount of the absorbed CO2 increased, the glass transition
temperature, Tg, of the polymer blend continuously decreased. At a certain CO2 pressure, when the Tg drops below 35 1C by plasticization, the CO2 sorption isotherm becomes linear, indicating the loss of the Langmuir ‘hole filling mode’ as the blend became rubbery at 35 1C. It is believed that the high levels of sorption by the highly condensable C3H6 and C3H8 gradually lowers the Tg of PIM-1; however, because of the very high Tg of PIM-1, very high pressures would be required to reduce the Tg to the range of the current measurement temperatures. Table 1 shows that the dual-mode sorption parameters kD, C H0 , and b for all gases generally decrease as the temperature increases; however, for the hydrocarbons C2H4, C2H6, C3H6 and C3H8 the trends between the temperature and sorption parameters are not always so clear owing to the more significant effects of plasticization. The degree of plasticization decreases as the temperature is raised because the extent of sorption decreases, and this will have some effect on the temperature dependence of the parameters shown in Table 1. Koros et al. [21] proposed that gas dissolved via Henry's law mode requires energy to open space to accept the gas molecules; therefore, larger gas molecules should require more energy for opening the larger space needed. Hence, the energy difference between the two sorption modes, HD HH, should be greater for larger penetrants. The values of HD HH shown in Table 2 increase in the order: C3H8 oC3H6 oC2H6 oC2H4 oCO2 oHeoH2 oCH4 oO2 oN2, which is not the order of the kinetic diameters of these penetrants. However, for the less condensable gases He, H2, O2 and N2, the values of HD HH do increase with kinetic diameter as might be expected. For the more highly condensable gases CH4, CO2, C2H4, C2H6, C3H6 and C3H8, the values of HD HH decrease in almost the same order as their critical temperatures: C3H8 4C3H6 4C2H6 4 CO2 4C2H4 4CH4. The complicating issues of plasticization coupled with the stronger interaction of these more condensable gases with the polymer make arguments about the size of the space needed to accommodate the sorbed molecule too simplistic.
180 160
35
CO2 concentration cm3 (stp)/cm3 polymer
N2 concentration cm3 (stp)/cm3 polymer
40
30 25 20 15 2
10
4 5
5 0
0
10
20
140 120 100 80 60 4 5
20 0
30
2
40
0
5
N2 pressure (atm)
10
15
20
25
30
CO2 pressure (atm)
160
C3H8 concentration cm3 (stp)/cm3 polymer
140 120 100 80 60
2
40
4 5
20 0
0
2
4
6
8
C3H8 pressure (atm) Fig. 2. Gas sorption isotherms for N2, CO2 and C3H8 in PIM-1 from 25 to 55 1C. The solid curves were generated from the dual-mode sorption model and the parameters in Table 1.
P. Li et al. / Journal of Membrane Science 450 (2014) 380–388
383
Table 1 Dual-mode sorption parameters for gases in PIM-1 at 25–55 1C. Unit (1C)
kD
C H0
b
He 25 35 45 55
0.065 0.047 70.003 0.048 0.050 7 0.004
6.60 6.58 7 0.32 5.28 4.737 0.30
0.037 0.036 7 0.002 0.036 0.026 7 0.002
H2 25 35 45 55
0.0677 0.027 0.032 7 0.005 0.029 7 0.007 0.0357 0.014
44.6 7 4.6 35.17 0.1 31.5 7 1.5 35.7 72.5
0.0137 0.001 0.0157 0.002 0.0167 0.001 0.0117 0.001
N2 25 35 45 55
0.493 0.472 0.457 0.462
31.0 30.5 30.8 28.6
0.076 0.064 0.050 0.044
O2 25 35 45 55
1.33 1.107 0.77 0.896 7 0.26 0.863 7 0.05
18.6 19.2 7 18.5 17.5 7 4.6 17.6 7 1.4
0.132 0.1057 0.03 0.0977 0.22 0.050 7 0.004
CH4 25 35 45 55
0.592 0.578 0.519 0.567
65.0 61.7 59.0 50.5
0.150 0.124 0.104 0.090
K
Unit (1C)
kD
C H0
b
K
CO2 25 35 45 55
2.35 2.01 1.54 1.16
106 96.8 92.4 92.0
0.421 0.341 0.291 0.212
19.1 16.4 17.4 16.8
C2 H 4 25 35 45 55
1.81 1.86 1.81 1.65
93.5 81.3 70.3 64.4
0.556 0.589 0.627 0.554
28.8 26.1 24.4 21.6
4.79 4.12 3.38 2.71
C2 H 6 25 35 45 55
2.76 2.49 2.00 1.58
81.1 71.6 70.4 66.4
1.09 1.13 0.827 0.745
31.9 32.5 29.2 31.6
1.85 1.83 1.89 1.02
C3H6 25 35 45 55
10.1 7.26 5.16 5.09
88.8 81.1 78.0 63.2
2.57 2.36 1.64 2.09
22.6 26.5 24.8 25.9
16.5 13.3 11.9 8.83
C3 H 8 25 35 45 55
10.5 7.82 6.40 4.89
78.1 70.4 65.5 59.3
3.43 4.03 3.52 3.05
25.4 36.2 36.0 37.1
3.76 4.67 3.91 2.37 16.0 14.7 13.8 12.1
kD [cm3 (stp)/cm3polymer atm]; C H0 [cm3(stp)/cm3polymer]; b (atm 1); K¼ C H0 b=kD .
Table 2 Sorption enthalpies Gas
He H2 CO2 O2 N2 CH4 C2H4 C2H6 C3H6 C3H8
ΔHD, ΔHb, and HD HH for gases in PIM-1.
Critical temperature Tc (K) [25]
Kinetic diameter dk (Å) [25]
ΔHD
ΔHb
(kcal/mol)
(kcal/mol)
HD HH (kcal/mol)
5.2 33.2 304.2 154.6 126.2 190.6 282.5 305.3 365.2 369.9
2.6 2.89 3.30 3.46 3.64 3.80 3.9 4.0 4.5 4.3
1.42 1.23 4.60 2.92 0.42 0.28 0.57 3.67 4.72 4.86
2.07 2.25 4.29 5.70 3.67 2.78 0.12 2.78 1.95 0.90
0.65 1.02 0.31 2.78 3.25 2.50 0.69 0.89 2.77 3.96
4.2. Gas permeation Fig. 3 shows the permeability coefficients of N2, CO2 and C3H8 in PIM-1 versus the upstream driving pressure from 25 to 55 1C; similar plots for the other 7 gases are included in Supporting Information. The permeability coefficients for He, H2, O2, N2 and CH4 increase with increasing temperature at all pressures. This is a general trend for penetrants where diffusion rather than sorption dominates the response of permeation to temperature. In these type of cases, the permeability coefficient decreases with increasing upstream pressure as expected from Eq. (11). For CO2, the permeability coefficient weakly depends on temperature, and when plotted on the expanded scale of logarithm of P versus 1/T shown in Fig. S7 of the Supporting Information, the data show a slight maximum. Consequently, the permeability shows a small decrease with increasing temperature in the higher temperature range. This is a consequence of the strong decrease in sorption with increasing temperature coupled with the weak plasticization of PIM-1 by CO2.
For the highly condensable gases including C2H4, C2H6, C3H6 and C3H8, the gas permeation isotherms cross each other at some pressure range as shown in Fig. 3(c) for C3H8 and in the Supporting Information for the other hydrocarbons. Except for the lowest pressure in Fig. 3(c), the permeability coefficient for C3H8 actually decreases with increasing temperature. Stannett et al. [26,27] reported similar behavior some time ago for the permeation of organic vapors in polymer films. This is generally the consequence of a stronger decrease in sorption with temperature than an increase in diffusion with temperature. In the case of strong plasticization, the diffusion coefficient may have an inverted temperature dependence. 4.3. Gas diffusion coefficients Effective diffusion coefficients were calculated from the experimentally measured permeability and solubility coefficients using the relation D ¼P/S where S is the secant slope of the sorption isotherm evaluated at the same pressure of the upstream gas in the permeation experiment. Fig. 4 shows these diffusion coefficients for N2, CO2, and C3H8 plotted versus pressure for each of the temperatures within the range from 25 to 55 1C; similar plots for the other 7 gases are included in the Supporting Information. For He, H2, O2, N2, CH4 and CO2, the diffusion coefficients increase more or less linearly with upstream pressure over the range from 1 to 10 atm. As discussed more fully in our previous paper [18], these trends do not stem from plasticization behavior but rather reflect the responses expected from the dual-mode sorptionmobility model summarized by Eq. (11). On the other hand, for the hydrocarbons C2H4, C2H6, C3H6 and C3H8, the plots of diffusion coefficients versus pressure exhibit similar trends as do the plots of their permeability coefficients versus pressure. At low temperatures, the diffusion coefficients increase sharply with upstream pressure due to serious plasticization of the PIM-1 film by the penetrants. However, at higher temperatures where the amount of sorption of these penetrants is less, the plasticization is also less
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6000
CO2 Permeability (barrer)
N2 permeability (barrer)
450
400
350
300
250
200
0
2
4
6
8
10
5500
5000
4500
4000
12
0
2
Pressure (atm)
4
6
8
10
12
Pressure (atm)
C3H8 Permeability (barrer)
6000 5000 4000 3000
2000 1000 0
0
2
4
6
8
10
Pressure (atm) Fig. 3. Permeability coefficients for N2, CO2 and C3H8 for pressures up to 10 atm and temperatures from 25 to 55 1C. The solid curves are to guide the eye.
0.5 CO2 Diffusion coefficient (10-5cm2/s)
N2 diffusion coefficient (10-5cm2/s)
0.25
0.2
0.15
0.1
0.05
0
2
4
6
8
10
12
0.4
0.3
0.2
0.1
0
2
Pressure (atm)
4 6 8 Pressure (atm)
10
12
C3H8 Diffusion coefficient (10-5cm2/s)
0.25
0.2
0.15
0.1
0.05
0
0
2
4
6
8
10
Pressure (atm) Fig. 4. Gas diffusion coefficients for N2, CO2 and C3H8 for pressures up to 10 atm and temperatures from 25 to 55 1C. The solid curves are to guide the eye.
P. Li et al. / Journal of Membrane Science 450 (2014) 380–388
severe. In some cases, as a result of these issues, the diffusion coefficients at high temperatures are not as great as those at low temperatures; of course, this trend is not really due to negative activation energies for diffusion as a simple phenomenological analysis would suggest. 4.4. Temperature dependence of the dual-mode model parameters: DD and DH The dual mobility model parameters DD and DH can be obtained from the slope and intercepts of plots of P versus 1/(1 þbph) as discussed previously [18]. Such plots for He, H2, O2, N2, CH4 and CO2 are shown in Supporting Information and the model parameters deduced from them are summarized in Table 3. Similar plots are not shown for the hydrocarbons C2H4, C2H6, C3H6 and C3H8 since the plots would be highly non-linear owing to the strong plasticization they exert on PIM-1 and obtaining meaningful parameters would not be possible. For the gases that do not plasticize PIM-1 significantly, both DD and DH increase with temperature as seen in Table 3. This dependence can be analyzed in terms of Eqs. (12) and (13), and the resulting activation energies are shown in Table 4 as well as the difference EDH EDD that characterizes how the parameter F depends on temperature, see Eq. (14). As noted previously, the values of F are considerably smaller for PIM-1 than for other glassy polymers that have been subjected to a similar analysis [18]. In glassy polymers, segmental rotations are highly restricted and only short-range chain motion is allowed [25], and this is especially true for PIM-1. Broadly speaking, the results in Table 4 show that the two activation energies EDH and EDD increase as the size of the penetrant molecules increase as expected for diffusion in all types of polymers according to various models [25]. Table 3 Values of DD, DH and F for gases in PIM-1 at 25–55 1C. Unit (1C)
DD
DH
F¼ DH/DD
Unit (1C)
He 25 35 45 55
150 201 215 206
177 242 215 370
0.012 0.012 0.010 0.018
O2 25 35 45 55
5.04 7.47 8.26 9.29
H2 25 35C 45 55
537 550 634 654
170 110 203 397
0.003 0.002 0.003 0.006
CH4 25 35 45 55
3.71 4.77 6.84 6.92
0.026 0.030 0.043 0.062
CO2 25 35C 45 55
N2 25 35 45 55
3.48 4.37 4.98 5.54
9.10 13.1 21.4 34.4
DD
13.0 12.2 15.2 19.7
DH
F¼DH/DD
33.8 40.3 78.5 138
0.067 0.054 0.095 0.148
3.34 4.77 10.3 15.0 34.1 65.7 90.0 120
0.009 0.010 0.015 0.022 0.026 0.054 0.059 0.061
DD 106 (cm2/s); DH 108 (cm2/s).
385
Interestingly, EDH is about 2–3 times larger than EDD for all penetrants, and their differences, EDH EDD , generally increase as the penetrant molecules get larger. It is important to note that the dual-mode sorption parameters C H0 , kD and b are needed to estimate DD and DH. The pressure range used here for measuring the sorption isotherms of H2 and O2 was 0–200 psi due to safety concerns while the range used for He, CO2, N2 and CH4 was 0– 450 psi. Barbari et al. [28] reported that the estimated dual mode sorption parameters can be somewhat dependent on the pressure range used to determine the sorption isotherms. For this and other reasons, it is important to look at only the broad trends from such an analysis and not over interpret the details.
4.5. Phenomenological analyses of the energetics of sorption, diffusion and permeation It is rather uncommon to find detailed analyses of the energetics of sorption and diffusion in glassy polymers like that presented above where the pressure dependence has been dealt with via descriptive models. More often the temperature dependence of the phenomenological parameters P, D, and S at a given pressure is analyzed in terms of Eqs. (1)–(3) to obtain effective activation energies. It is useful to examine the data reported here in this fashion at each pressure so that the current results can be compared with some of the other results reported in the literature for gas permeation in PIM-1, see Table 5. The results in Table 5 show that the activation energies for permeation of gases in PIM-1 from different research groups vary greatly. This may be due, in part, to the different thermal histories and/or different testing protocols for the PIM-1 films. It is important to remember that PIM-1 is a glassy polymer with an extraordinary high free volume, and its gas permeation behavior is highly dependent on the film preparation history. In the report by Thomas et al. [12], the PIM-1 films were soaked with methanol before the gas permeation test; while in the report by Budd et al. [17], the PIM-1 films were cast from chloroform, similar to our sample preparation procedure. Therefore, the activation energies from Budd et al. are more similar to our data except for He, CH4 and CO2. In our study, we frequently replaced the PIM-1 films during the gas permeation test to maintain a similar thermal history. While in the report by Budd et al., they did not mention the replacement of PIM-1 films during the gas permeation measurements. The different testing procedures may be responsible for the different estimated activation energies observed for He, CH4 and CO2. Table 6 compares the activation energies of permeation and diffusion and the heat of sorption of various gases in PIM-1 with those for a range of other glassy polymers: polycarbonate (PC) [29], poly[1-(trimethylsilyl)- l-propyne] (PTMSP) [30], polyimide [31], and Teflon AF 1600 [32]. For these gas/polymer pairs, the values of Hs varies over the range of 5.3 to 1.0 kcal/mol; and Table 5 Reported values of activation energies for gas permeation in PIM-1. Gas
Table 4 Activation energies for gas diffusion via Henry and Langmuir modes. Gas
He H2 CO2 O2 N2 CH4
Kinetic diameter dk (Å) [25]
EDD (kcal/mol)
E DH (kcal/mol)
EDH EDD (kcal/mol)
2.6 2.89 3.3 3.46 3.64 3.80
2.00 1.42 2.84 3.80 2.88 4.36
4.03 5.98 8.00 9.42 8.67 10.2
2.03 4.56 5.16 5.62 5.79 5.87
He H2 O2 N2 CH4 CO2
Ep (kcal/mol) Thomas et al. [12]
Budd et al. [17]
This studya
0.10 0.10 1.33 3.40 4.62 0.24
1.29 0.76 0.79 2.50 2.60 1.07
0.64 0.41 0.61 2.85 4.20 0.11
a The activation energies are estimated based on the permeability at 1 atm and the temperature range of 25–55 1C.
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P. Li et al. / Journal of Membrane Science 450 (2014) 380–388
Table 6 Activation Energies for permeation and diffusion and heat of sorption for six penetrants in polycarbonate (PC) [29], poly[1-(trimethylsilyl)-l-propyne] (PTMSP) [30], a polyimide (PI)[31], Teflon AF 1600 [32], and PIM-1. Polymer Tg FFV
PC 150 1C 0.16
PI 335 1C 0.18 [33]
PIM-1 4350 1C 0.25
Teflon AF 1600 160 1C 0.32
PTMSP 4350 1C 0.33
0.1 0.6 1.6 1.2 1.5 2.3
Ep (kcal/mol) He 4.2 H2 – O2 5.0 N2 6.0 CH4 6.2 CO2 3.0
– – 0.8 2.5 3.7 0.7
0.6 0.4 0.6 2.8 4.2 0.4
1.0 1.1 0.8 1.1 2.5 0.4
Ed (kcal/mol) He 6.7 H2 – O2 7.6 N2 9.7 10 CH4 CO2 8.3
– – 4.2 6.7 6.4 4.0
3.0 3.2 5.3 6.0 7.8 4.2
– – 2.0 2.9 4.4 3.6
Hs (kcal/mol) He 2.5 H2 – O2 2.6 N2 3.7 CH4 3.8 CO2 5.3
– – 3.4 4.2 2.6 3.3
2.4 2.8 4.7 3.1 3.7 3.8
– – 1.2 1.8 1.9 4.0
1.0 0.6 1.2 1.2 1.2 0.1 1.0 1.2 2.8 2.4 2.7 2.4
the Hs for PIM-1 seem to fall more or less in the middle of this range for most gases indicating there is nothing unusual about its energetics of sorption. The activation energy for diffusion, Ed, for the various gas/polymer pairs varies over the range of 0.6–10 kcal/ mol. Within this limited range of polymers, it seems that the higher the free volume and Tg the less gas diffusion depends on temperature; again, PIM-1 seems to fall in the middle range in line with its free volume. The activation energy for permeation, Ep, is more complex since it reflects both kinetic and thermodynamic issues. The values for PIM-1 are quite similar to those of the polyimide [31] shown in Table 6. Thus, it appears that these energetic parameters for PIM-1 are within a range that might be expected. Table 7 lists the activation energies of gas permeation and diffusion as well as the heat of sorption of all gases in PIM-1 at pressures from 1 to 10 atm. For He, H2, O2, N2, CH4, and CO2, the activation energies of diffusion decrease with increasing pressure while the heat of sorption increases (i.e., becomes less negative) with increasing pressure. The solubility coefficient, S, can be expressed in terms of the dual-sorption model as shown in Eq. (9). As seen there, the relative contribution of the Langmuir term to the total sorption amount decreases as pressure increases. The Langmuir capacity term has a strong temperature dependence owing to its connection to the excess volume of the glass that decreases as the temperature is increased [22,24]; thus, reducing its contribution via higher pressures reduces the temperature dependence of the overall solubility coefficient, S. The diffusion coefficient calculated from D ¼P/S can be expressed in terms of the dual-mode sorption-mobility model as follows [18] DðpÞ ¼
DD ð1 þ bpÞ þ KDH K ¼ DD ðDD DH Þ ð1 þ bpÞ þK ð1 þ bpÞ þ K
ð15Þ
Eq. (15) predicts that the diffusivity coefficient D increases as the upstream pressure increases, and that the phenomenological activation energy of diffusion, Ed , decreases with pressure. This is understandable by the observation that the activation energy for diffusion for Henry's law mode is less than that for the Langmuir
mode as seen in Table 4. As the pressure increases, a greater fraction of the gas is associated with Henry's law mode and a higher fraction of the diffusion occurs via this mode at higher pressures. Thus, the overall or phenomenological activation energy for diffusion is expected to decrease with pressure. For the less condensable gases He, H2, O2, N2, and CH4, the increase in the sorption energy with pressure counter-balances the decrease in the diffusion activation energy; thus, the activation energy for permeation remains a relatively constant and positive value for each gas over the range from 1 to 10 atm. However, for CO2, the diffusion activation energy and the heat of sorption are nearly equal in magnitude (but opposite in sign); thus, the activation energy for permeation of CO2 is nearly zero but the global average value over the temperature range studied appears to decrease as the pressure increases. For the hydrocarbons C2H4, C2H6, C3H6 and C3H8, the effect of temperature on P and D is quite complex (see plots in Fig. S7) due to the strong effect temperature has on the extent of sorption and its effect on diffusion via plasticization. Since PIM-1 is strongly plasticized by these hydrocarbons, DD and DH in the Eq. (11) are not constant and there is no practical way to evaluate them. Therefore, it is not appropriate to utilize the dual-mode sorptionmobility model parameters to analyze the dependence of the activation energy or heat of sorption on the pressure. Because of the strong coupling between temperature and plasticization behavior, the usual interpretations of activation energies in these systems becomes meaningless; and as a consequence no values for Ep or Ed are given in Table 7 for these penetrants.
5. Conclusions Solubility, permeability and diffusion coefficients for 10 gases were determined for films of PIM-1 at temperatures from 25 to 55 1C over a range of pressures. The following conclusions can be drawn: (1) All 10 gases exhibit typical dual-mode sorption isotherms, and the extent of sorption decreases as temperature increases. (2) The dual-mode sorption parameters kD,C H0 , and b decrease with temperature for He, H2, N2, O2, CH4 and CO2 while for the hydrocarbons C2H4, C2H6, C3H6 and C3H8 the trends are less clear owing to the varying effects of plasticization. (3) For He, H2, O2 and N2, the sorption energy difference HD HH increases as the kinetic diameter increases. For the highly condensable gases CH4, CO2, C2H4, C2H6, C3H6 and C3H8, HD HH decreases as the critical temperature increases. (4) For He, H2, O2, N2 and CH4, the permeability coefficients increase with temperature and decrease with pressure. For CO2 the activation energy for diffusion is nearly canceled by the heat of sorption so that the permeability coefficient is only weakly dependent on temperature. For C2H4, C2H6, C3H6 and C3H8, the permeability coefficients are often higher at low temperatures than high temperatures due to the effects of plasticization. (5) The diffusion coefficients of He, H2, O2, N2, CH4 and CO2 increase more or less linearly as the upstream pressure increases from 1 to 10 atm. This is not a consequence of plasticization but can be well explained by the dual-mode sorption-mobility model. However, for C2H4, C2H6, C3H6 and C3H8, plasticization causes an increase in the diffusion coefficient with pressure that is much greater than expected from the dual-mode effects. In certain cases, the diffusion coefficients of the hydrocarbons have an inverted temperature dependence, i.e., the apparent activation energy is negative, due to plasticization effects.
P. Li et al. / Journal of Membrane Science 450 (2014) 380–388
387
Table 7 Apparent Arrhenius and van't Hoff energy parameters at different pressures. Penetrant
Pressure (atm)
Ep (kcal/mol)
Hs (kcal/mol)
Ed (kcal/mol)
Penetrant
Pressure(atm)
Ep (kcal/mol)
Hs (kcal/mol)
Ed (kcal/mol)
He
1.0 2.5 5.0 7.5 10.0
0.63 0.64 0.64 0.64 0.64
2.38 2.36 2.22 2.13 2.09
3.01 2.99 2.86 2.77 2.73
CO2
1.0 2.5 5.0 7.5 10.0
0.37 0.19 0.11 0.09 0.28
3.82 3.59 2.79 2.74 2.62
4.19 3.79 2.89 2.64 2.34
H2
1.0 2.5 5.0 7.5 10.0
0.41 0.41 0.40 0.39 0.40
2.79 2.67 2.52 2.51 2.57
3.19 3.08 2.93 2.90 2.97
C2H4
1.0 2.5 5.0 7.5 10.0
– – – – –
1.96 2.17 2.64 2.09 2.05
– – – – –
O2
1.0 2.5 5.0 7.5 10.0
0.60 0.60 0.61 0.64 0.66
4.73 4.31 3.79 3.43 3.21
5.33 4.90 4.39 4.07 3.87
C2H6
1.0 2.5 5.0 7.5 10.0
– – – – –
2.03 2.30 2.17 1.86 2.24
– – – – –
N2
1.0 2.5 5.0 7.5 10.0
2.83 2.85 2.88 2.86 2.84
3.14 2.84 2.53 2.34 2.03
5.97 5.68 5.41 5.20 4.87
C3H6
1.0 2.5 5.0 7.5 10.0
– – – – –
3.67 2.51 3.67 3.27 3.44
– – – – –
CH4
1.0 2.5 5.0 7.5 10.0
4.15 4.20 4.27 4.24 4.19
3.68 3.35 2.87 2.62 2.49
7.83 7.56 7.14 6.86 6.68
C3H8
1.0 2.5 5.0 7.5
– – – –
2.98 2.91 3.22 3.11
– – – –
(6) The diffusion coefficients DD and DH and their ratio, F, increase with temperature, and their activation energies, as well as the difference,EDH EDD , generally increase as the kinetic diameters of He, H2, O2, N2, CH4 and CO2 increase. (7) For He, H2, O2, N2, and CH4, the activation energies of diffusion decrease with pressure while the heat of sorption increases; as a result, the activation energies of permeation remain nearly independent of pressure. For the hydrocarbons C2H4, C2H6, C3H6 and C3H8, activation energies for permeation and diffusion are not meaningful owing to the effects of plasticization that cause Arrhenius plots to be non-linear.
The molecular picture of the solid-state structure of high free volume polymers like PIM-1 is still emerging. Clarification of the many issues involved is well beyond the scope of this and our previous [18] paper; however, this work adds the following to this picture. While PIM-1 clearly has exceptional sorption and permeation properties stemming from its very low packing density, it does share a number of features in common with other glassy polymers. First, the sorption isotherms for all gases are well described by the dual sorption model. Second, for gases with relatively low levels of condensability like He, H2, N2, O2, CH4 and CO2, the effect of upstream pressure on permeability is well described by the dual mobility model. In a much earlier paper [34], the relationship between values of DH and DH for CO2 at 35 1C in a series of about 15 glassy polymers, including polysulfones, polycarbonates, etc., was analyzed and it was found that the mobilities for the two sorption populations are about equally influenced by changes in the polymer molecular structure and that the ratio DH/DH was on average about 0.078 with some variation about this average. The results found for PIM-1 are well within this range. It is worth noting that gas sorption and permeation in a polymer having an even higher level of free volume and permeability than PIM-1, viz., poly[1-(trimethylsilyl)-1-propyne] or TMPSP, are also well described by these models as shown by Auvil
et al. [35]. The facts available confirm that gas permeation in both PTMSP and PIM-1 occurs by a solution-diffusion mechanism, and the main reason for their high permeability is high diffusion coefficients. Furthermore, PIM-1 is significantly plasticized by more condensable species such as the C2 and C3 hydrocarbons considered in this work, which is true for other glassy polymers.
Acknowledgments The authors would like to thank Mr. Fuyun Li, and Ms. Wai Fen Yong for their help in the synthesis of PIM-1 and Ms. Xiuzhu Fu and Mr. Yihui Sim for their valuable suggestions. The authors also express appreciation for financial support from NUS grant C-279000-019-101 for appointment of Prof. D.R. Paul as the Tan Chin Tuan Centennial Professor. The authors would also like to thank the Singapore National Research Foundation (NRF) for funding the project with grant number R-279-000-311-281.
Appendix A. Supporting information Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.memsci.2013.09.030. References [1] P.M. Budd, B.S. Ghanem, S. Makhseed, N.B. Mckeown, K.J. Msayib, C. E. Tattershall, Polymers of intrinsic microporosity (PIMs): robust, solutionprocessable, organic nanoporous materials, Chem. Commun. (2004) 230–231. [2] P.M. Budd, E.S. Elabas, B.S. Ghanem, S. Makhseed, N.B. Mckeown, K.J. Msayib, C. E. Tattershall, D. Wang, Solution-processed, organophilic membrane derived from a polymer of intrinsic microporosity, Adv. Mater. 16 (2004) 456–459. [3] B.S. Ghanem, M. Hashem, K.D.M. Harris, K.J. Msayib, M. Xu, P.M. Budd, N. Chaukura, D. Book, S. Tedds, A. Walton, N.B. Mckeown, Triptycene-based polymers of intrinsic microporosity: organic materials that can be tailored for gas adsorption, Macromolecules 43 (2010) 5287–5294. [4] B.S. Ghanem, K.J. Msayib, N.B. Mckeown, K.D.M. Harris, Z. Pan, P.M. Budd, A. Butler, J. Selbie, D. Book, A. Walton, A triptycene-based polymer of intrinsic microporisity that displays enhanced surface area and hydrogen adsorption, Chem. Commun. (2007) 67–69.
388
P. Li et al. / Journal of Membrane Science 450 (2014) 380–388
[5] F.Y. Li, Y.C. Xiao, Y.K. Ong, T.-S. Chung, UV-rearranged PIM-1 polymeric membranes for advanced hydrogen purification and production, Adv. Energy Mater. 2 (2012) 1456–1466. [6] F.Y. Li, Y.C. Xiao, T.-S. Chung, S. Kawi, High-performance thermally self-crosslinked polymer of intrinsic microporosity (PIM-1) membranes for energy development, Macromolecules 45 (2012) 1427–1437. [7] W.F. Yong, F.Y. Li, Y.C. Xiao, P. Li, K.P. Pramoda, Y.W. Tong, T.-S. Chung, Molecular engineering of PIM-1/Matrimid blend membranes for gas separation, J. Membr. Sci. 407–408 (2012) 47–57. [8] N. Du, G.P. Robertson, J. Song, I. Pinnau, S. Thomas, M.D. Guiver, Polymers of intrinsic microporosity containing trifluoromethyl and phenylsulfone groups as materials for membrane gas separation, Macromolecules 41 (2008) 9656–9662. [9] D. Fritsch, P. Merten, k. Heinrich, M. Lazar, M. Prike, High performance organic solvent nanofiltration membranes: development and thorough testing of thin film composite membranes made of polymers of intrinsic microporosity (PIMs), J. Membr. Sci. 401–402 (2012) 222–231. [10] S. Tsarkov, V. Khotimskiy, P.M. Budd, V. Volkov, J. Kukushkina, A. Volkov, Solvent nanofiltration through high permeability glassy polymers: Effect of polymer and solute nature, J. Membr. Sci. 423–424 (2012) 65–72. [11] N. Du, G.P. Robertson, M.M. Dal-Cin, L. Scoles, M.D. Guiver, Polymers of intrinsic microporosity (PIMs) substituted with methyl tetrazole, Polymer 53 (2012) 4367–4372. [12] S. Thomas, I. Pinnau, N. Du, M.D. Guiver, Pure- and mixed-gas permeation properties of a microporous spirobisindane-based ladder polymer (PIM-1), J. Membr. Sci. 333 (2009) 125–131. [13] S.V. Adymkanov, Y.P. Yampol'skii, A.M. Polyakov, P.M. Budd, K.J. Reynolds, N. B. Mckeown, K.J. Msayib, Pervaporation of alcolhols through highly permeable PIM-1 polymer films, Polym. Sci. Ser. A 50 (2008) 444–450. [14] C.R. Mason, M.G. Buonomenna, G. Golemme, P.M. Budd, F. Galiano, A. Figoli, K. Friess, V. Hynek, New organophilic mixed matrix membranes derived from a polymer of intrinsic microporosity and silicalite-1, Polymer 54 (2013) 2222–2230. [15] O. Vopicka, K. Friess, V. Hynek, P. Sysel, M. Zgazar, M. Sipek, K. Pilnacek, M. Lanc, J.C. Jansen, C.R. Mason, P.M. Budd, Equilibrium and transient sorption of vapours and gases in the polymer of intrinsic microporosity PIM-1, J. Membr. Sci. 434 (2013) 148–160. [16] O. Holck, M. Bohning, M. Heuchel, M.R. Siegert, D. Hofmann, Gas sorption isotherms in swelling glassy polymers-detailed atomictic simulations, J. Membr. Sci. 428 (2013) 523–532. [17] P.M. Budd, N.B. McKeown, B.S. Ghanem, K.J. Msayib, D. Fritsch, L. Starannikova, N. Belov, O. Sanfirova, Y. Yampolskii, V. Shantarovich, Gas permeation parameters and other physicochemical properties of a polymer of intrinsic microporosity: polybenzodioxane PIM-1, J. Membr. Sci. 325 (2008) 851–860. [18] P. Li, T.S. Chung, D.R. Paul, Gas sorption and permeation in PIM-1, J. Membr. Sci. 432 (2013) 50–57. [19] K. Ghosal, B.D. Freeman, Gas separation using polymer membranes: an overview, Polym. Adv. Tech. 5 (1993) 673–697.
[20] L.M. Costello, W.J. Koros, Temperature dependence of gas sorption and transport properties in polymers: measurement and applications, Ind. Eng. Chem. Res. 31 (1992) 2708–2714. [21] W.J. Koros, D.R. Paul, G.S. Huvard, Energetics of gas sorption in glassy polymers, Polymer 20 (1979) 956–960. [22] W.J. Koros, D.R. Paul, CO2 sorption in poly(ethylene terephthalate) above and below glass transition temperature, J. Polym. Sci.: Polym. Phys. Ed. 16 (1978) 1947–1963. [23] P. Li, D.R. Paul, T.S. Chung, High performance membranes based on ionic liquid polymers for CO2 separation from the flue gas, Green Chem. 14 (4) (2012) 1052–1063. [24] J.S. Chiou, Y. Maeda, D.R. Paul, Gas and vapor sorption in polymers just below Tg, J. Appl. Polym. Sci. 30 (1985) 4019–4029. [25] S. Matteucii, Y. Yampolskii, B.D. Freeman, I. Pinnau, Transport of gases and vapors in glassy and rubber polymers, in: Y. Yampolskii, I. Pinnau, B. D. Freeman (Eds.), Materials Sciences of Membranes for Gas and Vapor Separation, John Wiley & Sons, Ltd., The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England, 2006, pp. 1–40. [26] I. Sobolev, J.A. Meyer, V. Stannett, M. Szwarc, Permeation, diffusion, and solubility of methyl bromide and isobutene in polyethylene, Ind. Eng. Chem. 49 (1957) 441–444. [27] R. Waack, N.H. Alex, H.L. Frisch, V. Stannett, M. Szwarc, Permeability of polymer films to gases and vapors, Ind. Eng. Chem. 47 (1955) 2524–2527. [28] T.A. Barbari, W.J. Koros, D.R. Paul, Gas transport in polymers based on bisphenol-A, J. Polym. Sci.: Part B: Polym. Phys. 26 (1988) 709–727. [29] L.M. Costello, W.J. Koros, Effect of structure on the temperature dependence of gas transport and sorption in a series of polycarbonates, J. Polym. Sci.: Part B: Polym. Phys. 32 (1994) 701–713. [30] T. Masuda, Y. Iguchi, B.-Z. Tang, T. Higashimura, Diffusion and solution of gases in substituted polyacetylene membranes, Polymer 29 (1988) 2041–2049. [31] T.S. Chung, C. Cao, R. Wang, Pressure and temperature dependence of the gas transport properties of dense poly[2,6-toluene-2,2-bis(3,4-dicarboxylphenyl) hexafluoropropane diimide] membranes, J. Polym. Sci.: Part B: Polym. Phys. 42 (2004) 354–364. [32] A.Y. Alentiev, V.P. Shantarovich, T.C. Merkel, V.I. Bondar, B.D. Freeman, Y. P. Yampolskii, Gas and vapor sorption, permeation, and diffusion in glassy amorphous Teflon AF 1600, Macromolecules 35 (2002) 9513–9522. [33] K. Tanaka, M. Okano, H. Toshino, H. Kita, K.-I. Okamoto, Effect of methyl substituents on permeability and permselectivity of gases in polyimides prepared from methyl-substituted phenylenediamines, J. Polym. Sci.: Part B: Polym. Phys. 30 (1992) 907–914. [34] C.L. Aitken, W.J. Koros, D.R. Paul, Transport properties of biphenol polysulfones, Macromolecules 25 (1992) 3651–3658. [35] R. Srinivasan, S.R. Auvil, P.M. Burban, Elucidating the mechanism(s) of gas transport in poly[1-(trimethylsilyl)-1-propyne] (PTMSP) membranes, J. Membr. Sci. 86 (1994) 67–86.
