Volumetric properties and sorption behavior of perfluoropolymers with

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Cite This: Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Volumetric Properties and Sorption Behavior of Perfluoropolymers with Dioxolane Pendant Rings Yafei Li,† Milad Yavari,‡ Antonio Baldanza,§ Ernesto Di Maio,§ Yoshiyuki Okamoto,∥ Haiqing Lin,‡ and Michele Galizia*,† †

School of Chemical, Biological and Materials Engineering, University of Oklahoma, Norman, Oklahoma 73019, United States Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260, United States § Department of Chemical, Materials and Manufacturing Engineering, University of Naples, Napoli, 80125, Italy ∥ Department of Chemical and Biomolecular Engineering, New York University, Brooklyn, New York 11201, United States

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‡

S Supporting Information *

ABSTRACT: Lattice fluid theory is used to develop transport property−structure correlations for glassy perfluoropolymers with dioxolane pendant rings, a new class of membrane materials for gas separation. Poly(perfluoro-2-methylene-1,3-dioxolane) (poly(PFMD)) and poly(perfluoro-2-methylene-4-methyl-1,3-dioxolane) (poly(PFMMD)) exhibit lower permeability but much higher selectivity than commercial fluoropolymers, such as Teflons AF. Their enhanced separation performance is due to the combined effect of solubility- and diffusivity-selectivity. Moreover, poly(PFMD) and poly(PFMMD) exhibit enhanced CO2-philicity as compared to Teflons AF, which can be ascribed to the higher oxygen/carbon ratio exhibited by the former materials. To provide rational guidelines to maximize the solubility-selectivity, the enthalpic and entropic contributions to sorption coefficient were calculated and compared for several polymers of practical interest for gas separation. In the absence of localized penetrant−polymer interactions, gas sorption is controlled essentially by the free volume and solubility-selectivity is controlled by the polymer cohesive energy density.

1. INTRODUCTION

Substantial research efforts have been devoted to develop solvent-processable perfluoropolymers with higher selectivities.4−6 Recently, a new class of perfluoropolymers based on dioxolanes was reported by Okamoto and co-workers.2−6,18 Specifically, poly(perfluoro-2-methylene-1,3-dioxolane) (poly(PFMD)) and poly(perfluoro-2-methylene-4-methyl-1,3-dioxolane) (poly(PFMMD)) were synthesized via radical polymerization and exhibited performance near or above the 2008 upper bound for the separation of several gas pairs, such as He/H2, He/CH4, H2/CH4, H2/CO2, and N2/CH4.6 Interestingly, while poly(PFMD) and poly(PFMMD) exhibit lower permeability than Teflon AF, due to their lower fractional free volume, their light gas/CH4 selectivity and CO2/CH4 selectivity are much larger than that exhibited by Teflon AF.6 Although this difference has been ascribed essentially to the stronger size-sieving ability (i.e., the higher diffusivity-selectivity) exhibited by poly(PFMD) and poly-

Owing to the unique combination of physical−chemical properties, fluorinated polymers have attracted interest in the automotive, aerospace, electronics, and medical industries.1 Fluorine-containing polymers exhibit uncommon thermal and chemical stability and poor solubility in organic solvents, as well as peculiar surface, electrical, and optical properties.1−6 In the early 1990s, amorphous, solvent soluble perfluoropolymers appeared in the market.7,8 Among them, Teflon AF, Hyflon AD, and Cytop exhibit peculiar transport properties, low swelling in the presence of vapors and liquids, and superior resistance to physical aging, which makes them attractive for membrane applications.9−15 For example, the solubility of light gases and hydrocarbon vapors in amorphous perfluoropolymers is unusually low, and this feature has been ascribed to unfavorable polymer−penetrant interactions.11,16 Analogously to fluorinated liquids, perfluoropolymers exhibit low cohesive energy density, which leads to relatively high free volume fractions.11 This feature makes commercial perfluoropolymers highly permeable but moderately selective.6 Currently, these materials dominate the right-bottom part of the 2008 Robeson upper bound.6,17 © XXXX American Chemical Society

Special Issue: Donald R. Paul Festschrift Received: Revised: Accepted: Published: A

June 23, 2019 August 16, 2019 August 20, 2019 August 20, 2019 DOI: 10.1021/acs.iecr.9b03411 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research (PFMMD), we provide evidence that the latter polymers also exhibit a much larger solubility-selectivity than commercial perfluoropolymers.

T* =

ϕ2p2* T2*

(3)

where TSTP and pSTP represent the standard temperature (273.15 K) and pressure (1 bar), respectively, r0i is the number of lattice sites occupied by a molecule of pure component i, v*i represents the volume occupied by 1 mol of lattice sites of pure component i, ρ02 is the density of the unpenetrated polymer, and subscripts 1 and 2 stand for the pure penetrant and polymer species, respectively. Equation 4 allows deconvolution of the solubility coefficient into its entropic (ϕS) and enthalpic (ϕH) contributions, which represent the entropic and enthalpic contributions to the penetrant chemical potential:29 Ä ÉÑ l ÑÑ ji o oÅÅÅij v1* yz ρ2* yz| ρ20 zyz ij v1* ÑÑ jj o 0oÅ j z jj zzo Å z j z ϕS = r1 m − 1 + 1 ln 1 − + − 1 } Å Ñ j z j z j z Å Ñ 0 o o j z j z j z ÅÅ v2* ÑÑ j * * o o z ρ v ρ o o 2 Å Ñ k { k { 2 2 Ç Ö k { n ~

(1)

where subscripts 1 and 2 stand for the penetrant and polymer species, respectively, and ω1 and ω2 are the penetrant and polymer mass fractions, respectively. The mixture characteristic pressure, p*, is given by22 p* = ϕ1p1* + ϕ2p2* − ϕ1ϕ2[p1* + p2* − 2(1 − k12) p1* p2* ]

+

Small molecule solubility in a glassy polymer is calculated at any temperature and pressure by imposing the validity of the Sanchez−Lacombe equation of state for the pure penetrant in the external gas phase and by equating the penetrant chemical potential in the external gas phase to that in the polymer mixture.22,29 Equations 1, 2 and 3 must be satisfied as well, and polymer density has to be known experimentally.22,29,31,32 Relevant model parameters and equations are summarized in Table S1 of the Supporting Information. The model provides an explicit expression for the solubility coefficient in the limit of infinite dilution (i.e., at vanishing pressure):31 ÉÑ ÄÅ l ÑÑ ij T yz o yz ρ2* oÅÅÅÅijj v1* Ñ STP 0 j z zz + r1 mÅÅjj − 1zzz 0 + 1ÑÑÑ ln(Sinf ) = lnjjj o z j z ÑÑ Å * o jp Tz v ρ Å o ÑÖ { 2 k STP { nÅÇk 2 0 ij yz ρ yz ij v * lnjjjj1 − 2 zzzz + jjj 1 − 1zzz z j ρ2* z{ jk v2* { k | 0 o ρ2 T1* 2 o * * + (1 − k12) p1 p2 o } o * * o ρ2 T p1 o ~ ij T yz = lnjjjj STP zzzz + ϕS + ϕH jp Tz (4) k STP {

2. THEORETICAL BACKGROUND Due to its better predictive capability compared to semiempirical models,19−21 the nonequilibrium lattice fluid model (NELF) has been used to describe and predict gas sorption isotherms in glassy polymers and mixed matrix materials.10,22−24 It was developed by extending the lattice fluid theory originally developed by Sanchez et al. for rubbery polymers25,26 to the domain of glassy polymers. Specifically, the polymer density was assumed as an internal variable of state, since its rate of change depends on the state variables and an order parameter, as it directly quantifies the out of equilibrium degree of glassy polymers.22 The model requires, in input, three lattice fluid parameters for the pure components, T*i , p*i , and ρ*i , plus the polymer density, which is a macroscopic property and can be measured with minimal experimental effort.22 The characteristic temperature, Ti*, relates to the depth of the potential energy well of the pure component i. The characteristic pressure, p*i , is the cohesive energy density of pure component i at close packed conditions (i.e., at 0 K). Finally, the characteristic density, ρ*i , is the density of pure component i at close packed conditions (i.e., the highest density possible for the component i). The lattice fluid parameters of polymers and penetrants are determined from experimentally available volumetric data and from liquid− vapor equilibrium data, respectively.27,28 An appropriate set of mixing rules is used to calculate the lattice fluid parameters of the polymer−penetrant mixture at any given composition. Specifically, the mixture characteristic density, ρ*, is calculated as follows:22 ω ω 1 = 1 + 2 * ρ* ρ1 ρ2*

p* ϕ1p1* T1*

(5) (2)

ϕH = r10

where ϕ1 and ϕ2 are the penetrant and polymer volume fraction, respectively, and k12 is the polymer−penetrant binary interaction parameter. When k12 = 0, eq 2 degenerates into the classic Hildebrandt mixing rule, which holds true when 1−1, 2−2, and 1−2 mean field interactions are energetically equivalent. When k12 < 0, penetrant−polymer (i.e., 1−2) interactions deviate negatively from the Hildebrand rule; that is, they are more thermodynamically favorable than the 1−1 or 2−2 interactions. In contrast, when k12 > 0, penetrant− polymer (i.e., 1−2) mean field interactions are less thermodynamically favorable than the 1−1 or 2−2 interactions.22,29 The approach described above holds true in the absence of specific, localized interactions.30 Finally, the mixture characteristic temperature, T*, is given by22

ρ20 T1* 2 (1 − k12) p1* p2* ρ2* T p1*

(6)

While light gases sorption does not swell glassy polymers, matrix swelling is required to accommodate highly sorbing penetrants, such as carbon dioxide and hydrocarbon vapors. Since polymer volume dilation is approximately linear with penetrant partial pressure,33 the NELF model assumes that the polymer density decreases linearly with increasing penetrant pressure in the contiguous gas phase:31 ρ2 = ρ20 (1 − kswp)

(7)

where ρ02 is the density of the unpenetrated polymer (which is experimentally measurable), p is the pressure, and ksw is the swelling coefficient. B

DOI: 10.1021/acs.iecr.9b03411 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research Table 1. Physical Properties of Polymers Considered in This Study and Commercial Perfluoropolymers

Figure 1. pVT properties of (A) poly(PFMD) and (B) poly(PFMMD). Blue filled circles: 10 MPa; red filled squares: 20 MPa; green filled triangles: 30 MPa; blue open circles: 40 MPa; red open squares: 50 MPa; green open triangles: 60 MPa.

3. EXPERIMENTAL SECTION

4. RESULTS AND DISCUSSION 4.1. Volumetric Properties of Polymers. The specific volume of poly(PMFD) and poly(PFMMD) is reported in Figure 1 as a function of temperature and in the pressure range 10−60 MPa. To make Figure 1 readable, experimental uncertainty on pVT data was reported in Figure S1 of the Supporting Information. The isothermal compressibility of the two polymers at room temperature was calculated from the pVT data as follows:36

3.1. Membrane Synthesis and Fabrication. Poly(PFMD) and poly(PFMMD) were synthesized via radical polymerization from perfluoro-2-methylene-1,3-dioxolane and perfluoro-2-methylene-4-methyl-1,3-dioxolane, respectively.6 Details of membrane fabrication are briefly summarized in the Supporting Information. The chemical structure and relevant physical properties of poly(PFMD) and poly(PFMMD) are shown in Table 1. 3.2. Sorption Measurements. Gas sorption isotherms were measured at 35 °C and up to 15 atm using a dual chamber pressure decay device. Experimental details are provided elsewhere.6 3.3. PVT Measurements. The specific volume of poly(PFMD) and poly(PFMMD) was measured up to 300 °C and 60 MPa using a high-pressure dilatometer (Gnomix, Boulder, CO).30,34,35 Isothermal pVT measurements were run by increasing the pressure from 10 to 60 MPa. Details about the experimental protocol are provided elsewhere.30,34,35

β=−

1 ijj ∂V̂ yzz jj zz V̂ jk ∂p z{T

(8)

Experimental uncertainty on β was estimated using the Jackknife method.37 Commercial perfluoropolymers, such as Teflon AF2400 and 1600, exhibit very high compressibility relative to hydrocarbon-based polymers (cf. Table 2), which indicates that their specific volume is extremely sensitive to pressure changes.32,38 This unique feature has been ascribed to the extremely high fractional free volume (up to 33%) and the low cohesive energy density of perfluoropolymers. Poly(PFMD) and poly(PFMMD) have much lower values of β (cf. Table 2), which are comparable to those exhibited by C


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Industrial & Engineering Chemistry Research Table 2. Isothermal Compressibility of poly(PFMD), poly(PFMMD), and Other Polymers at Room Temperature polymer Poly(PFMD) Poly(PFMMD) Teflon AF2400 Teflon AF1600 Nylon-6.6 Poly(2,6-dimethyl-1,4-phenylene)oxide (PPO) PS PSF

β (10−4 MPa−1)

source

2.22 ± 0.28 2.57 ± 0.35 8.50 7.00 0.50 1.97

this study this study 38 38 39 39

3.95 2.17

39 39

Table 3. Lattice Fluid Parameters of poly(PFMD), poly(PFMMD), and Penetrantsa T* (K)

p* (MPa)

ρ* (cm3/g)

source

640 ± 3.62

300 ± 28

2.184 ± 0.006

Poly(PFMMD)

616 ± 18

250 ± 23

2.200 ± 0.010

Teflon AF2400 Hyflon AD80 HAB-6FDA polyimide PPO Ar CH4 C2H6 C2H4 CO2

624 550 720

250 180 481

2.130 2.150 1.610

this study this study 32 42 40

703 190 215 320 295 300

510 180 250 330 345 630

1.140 1.400 0.500 0.640 0.680 1.520

41 41 10 32 45 10

polymer Poly(PFMD)

hydrocarbon-based polymers.39 While this result is consistent with the much lower free volume exhibited by poly(PFMD) and poly(PFMMD) (21−23%) than commercial perfluoropolymers, it cannot be correlated with the low cohesive energy density of poly(PFMD) and poly(PFMMD). The molecular origin of this behavior is explained in section 4.2. 4.2. Estimation of Polymer Lattice Fluid Parameters. The lattice fluid parameters of poly(PFMD) and poly(PFMMD) were estimated by fitting the pVT data above Tg (i.e., in the rubbery region) to the Sanchez−Lacombe equation of state (cf. Figures 2A−B). Polymers often exhibit multiple sets of lattice fluid parameters, depending on the temperature and pressure ranges over which pVT data are fit.27 To get a more precise description of experimental sorption isotherms, it is worth to estimate the lattice fluid parameters by fitting the pVT data in a pressure range close to that where the sorption data were collected.27 Since the volumetric data for poly(PFMD) and poly(PFMMD) were available in a relatively narrow range of operative conditions, we decided to fit all data in the interval 0−60 MPa and in the rubbery region to the Sanchez− Lacombe equation of state. The lattice fluid parameters of the polymers considered in this study, and their uncertainty,37,40 are shown in Table 3, where they are compared with those of commercial perfluoropolymers and hydrocarbon-based polymers of practical interest for gas separation.32,41,42 The lattice fluid parameters estimated for poly(PFMD) and poly(PFMMD) are close to those of commercial glassy perfluoropolymers, which reflects the similarities between the polymer structures. Specifically, perfluoropolymers exhibit low p* values, which is indicative of weak interchain interactions

Lattice fluid parameters of other polymers are reported for the sake of comparison. a

(i.e., low values of cohesive energy density). In contrast, PPO and HAB-6FDA polyimide, two hydrocarbon-based polymers,43,44 exhibit much larger p* values than perfluoropolymers. This difference reflects the higher cohesive energy density of hydrocarbon-based polymers, i.e., the stronger intermolecular interactions and more closely packed structure. The characteristic pressure, p*, is inversely proportional to the isothermal compressibility, β, as both parameters are related to the polymer cohesive energy density.25,26 However, although perfluoropolymers with pendant rings exhibit lower β values than commercial perfluoropolymers, the two classes of materials exhibit similar p* values. This result is interesting and could be explained by invoking a different free volume morphology. Indeed, as reported by Yavari et al., poly(PFMD) and poly(PFMMD) exhibit lower fractional free volume than Teflons AF but larger free volume cavities.6 Apparently, the two factors offset, leading to similar p* values in these two classes of polymers. Poly(PFMD) exhibits a slightly larger p* value than commercial perfluoropolymers. As discussed in section 4.4, this fact mirrors the larger solubility-selectivity exhibited by poly(PFMD) relative to commercial perfluoropolymers. A comparison among ρ* values could be misleading. Indeed, despite exhibiting larger free volume than PPO, perfluoropol-

Figure 2. pVT properties in the rubbery region for (A) poly(PFMD) and (B) poly(PFMMD). Symbols represent experimental pVT data. Lines represent the best fit to the Sanchez−Lacombe equation of state. D


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Industrial & Engineering Chemistry Research

Figure 3. (A) Argon, (B) methane, (C) ethane, (D) ethylene, and (E) carbon dioxide sorption in poly(PFMD) (filled blue circles) and poly(PFMMD) (open red circles) at 35 °C. Symbols are the experimental data from Yavari et al.6 Lines represent the NELF best fit.

ymers have much larger ρ* values, due to the presence of bulky fluorine atoms. 4.3. Modeling Gas Sorption and Dilation Isotherms. In Figure 3, experimental methane, ethane, ethylene, carbon dioxide, and argon sorption isotherms in poly(PFMD) and poly(PFMMD) at 35 °C and up to 15 atm6 were compared with the NELF model calculations. Ethylene sorption was measured in poly(PFMMD) only.6 Argon sorption isotherms are quantitatively described by adjusting the binary parameter, k12, to the sorption data available in the low-pressure range, and assuming a constant polymer density (i.e., negligible polymer swelling). The latter assumption is physically sound, as argon is a low-sorbing gas. The obtained k12 value is 0.09 for the system poly(PFMD)/ argon and 0.07 for the system poly(PFMMD)/argon, which points out that argon interaction with perfluoropolymers with dioxolane pendant rings is weaker (i.e., less thermodynamically

favorable) than that predicted by the Hildebrand mixing rule based on the standard geometric-average, where k12 = 0. Methane and ethane sorption in poly(PFMD) was calculated with the same k12 value of 0.045, which is very close to that reported by Freeman et al. for the mixture methane/Teflon AF2400 (i.e., 0.05).32 To calculate methane solubility in poly(PFMD), the polymer density was assumed to be constant. In contrast, to get a more accurate description of the ethane sorption isotherm in poly(PFMD), the swelling coefficient was adjusted to the sorption datum available at the highest pressure. This fact is consistent with ethane being a more condensable and soluble penetrant than methane. The optimal ksw value is 0.008 MPa−1. Methane and ethane sorption in poly(PFMMD) was calculated by adjusting the binary parameter to 0.07 and 0.09, respectively, which indicates that the interaction between hydrocarbons with poly(PFMMD) is less thermodynamically E


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Industrial & Engineering Chemistry Research favorable than that with poly(PFMD). This result mirrors the higher degree of fluorination exhibited by poly(PFMMD) (over 69% on a molar basis) than poly(PFMD) (67% on a molar basis). It is well-known, indeed, that the mean field hydrocarbon−perfluorocarbon interaction is highly unfavorable, even though the molecular origin of this phenomenon is still unknown.11,13,16,46,47 Similarly, liquid perfluorocarbons are poorly soluble in their hydrocarbon-based analogs.11,16,32 Ethane is known to be a swelling penetrant. Consistently, to get a good description of the experimental sorption isotherm in poly(PFMMD), the swelling coefficient has been treated as an adjustable parameter. The optimal value of ksw, 0.007 MPa−1, is slightly lower than that obtained by fitting the ethane sorption isotherm in poly(PFMD) (i.e., 0.008 MPa−1). A comparison between the volume swelling exhibited by the two polymers will be provided later in this study. Ethylene sorption in poly(PFMMD) was calculated using a k12 value of 0.08, which is very close to that found for aliphatic hydrocarbons, and assuming negligible polymer swelling (i.e., ksw = 0). The latter result is consistent with the lower ethylene solubility in poly(PFMMD) than ethane, which, in turn, is ascribable to the lower critical temperature (i.e., condensability) of ethylene (TC = 282.5 K) than ethane (TC = 305.3 K).48 Finally, the model provides a quantitative description of carbon dioxide sorption in poly(PFMD), using two adjustable parameters. Specifically, the interaction parameter was adjusted to the sorption data in the low-pressure range (k12 = −0.04), where no swelling is expected to take place, and the swelling coefficient was optimized to the sorption datum available at the highest pressure, where swelling is likely to occur (ksw = 0.007 MPa−1). Interestingly, the optimal value of the binary parameter for the system poly(PFMD)/CO2 is negative. For the system Teflon AF2400/CO2, k12 is equal to zero.10 Therefore, the poly(PFMD)/CO2 mean field interaction is more thermodynamically favorable than the Teflon AF2400/ CO2 interaction. This difference is interesting, especially considering that the two polymers exhibit similar structures. A similar picture emerges from the analysis of the CO2 sorption isotherm in poly(PFMMD). The optimal values of k12 and ksw are −0.025 and 0.005 MPa−1, respectively. In summary, for both materials, a negative value of the binary parameter is required to get a good description of CO2 sorption isotherms. Therefore, perfluoropolymers with dioxolane pendant rings exhibit a more favorable mean field interaction with CO2 than commercial perfluoropolymers. The modeling outcomes indicate that the higher CO2/gas selectivity exhibited by poly(PFMD) and poly(PFMMD) than Teflon AF is due not only to the stronger size-sieving ability exhibited by these polymers relative to commercial perfluoropolymers but also to their larger CO2 solubility-selectivity, which, in turn, is ascribed to a favorable polymer/CO2 energetic interaction. Specifically, the CO2/CH4 solubilityselectivity exhibited by perfluoropolymers with dioxolane pendant rings is up to 65% higher than that of commercial perfluoropolymers (cf. Table 4). The uncertainty on the k12 parameter is reported in Table S2, Supporting Information. It is shown that the k12 values are statistically significant and that the negative k12 value exhibited by CO2 is not a mathematical artifact, as it provides a realistic picture of CO2 interaction with perfluoropolymers with dioxolane pendant rings.

Table 4. Permeability and Selectivity Data at 10 atm and 35 °C for Several Polymers

Poly(PFMD) Poly(PFMMD) Hyflon AD80 Teflon AF1600 Teflon AF2400 HAB-6FDA

SCO2/ SCH4

DCO2/ DCH4

PCO2 (Barrer)

SC2H6/ SCH4

3.3 2.9 2.0 2.7 2.7 3.8

14.0 9.9 7.7 2.0 2.2 10.2

5.9 58 150 520 2294 12

2.8 2.4 1.8 2.4 2.6

Source 6 6 49 9, 10 9, 10 50

To further prove the high CO2-philicity exhibited by the perfluoropolymers with dioxolane pendant rings, the polymers’ Hildebrand solubility parameter, δ2, was predicted as follows:51,52 ρ2EQ δ2 = p* ρ* 2 2

(9)

ρEQ 2

where is the equilibrium polymer density at any given temperature above Tg, which is available from pVT measurements. The average value of δ2 for poly(PFMD), poly(PFMMD), and Teflon AF2400 is 13.44 ± 0.49 MPa0.5, 12.13 ± 0.41 MPa0.5, and 10.78 ± 0.1 MP0.5, respectively. Based on the Hildebrand theory, polymer−penetrant mean field interactions are expected to be more favorable with decreasing the difference between the polymer and penetrant solubility parameters.53−55 Since the δ2 value for CO2 is 21.8 MPa0.5,6 poly(PFMD) and poly(PFMMD) are expected to be more CO2-philic than Teflon AF2400, which is consistent with the modeling results discussed above. The enhanced CO2-philicity exhibited by perfluoropolymers with dioxolane pendant rings than commercial perfluoropolymers is ascribable to their higher oxygen/carbon ratio. Specifically, the oxygen/carbon ratio is 2:4 for poly(PFMD), 2:5 for poly(PFMMD), and 2:5.3 for Teflon AF2400. It is known that polar C−O−C bonds establish polar, mean field interactions with CO2 molecules, which is consistent with the behavior observed experimentally. The CO2/poly(PFMD) binary interaction parameter is more negative than the CO2/poly(PFMMD) binary parameter, which indicates that CO2 interacts more favorably with the former polymer. This result mirrors the higher oxygen/carbon ratio and the larger δ2 value of poly(PFMD) than poly(PFMMD). Despite the fact that poly(PFMD) exhibits more thermodynamically favorable interactions with penetrant molecules, it exhibits lower sorption capacity than poly(PFMMD). This result indicates that the effect of free volume on gas sorption overwhelms the effect of mean field interactions. In Figure 4A−B, the poly(PFMD) and poly(PFMMD) swelling in the presence of CO2 and C2H6 at 35 °C is compared to that exhibited by Teflon AF2400.10 At fixed penetrant concentration, swelling systematically decreases with increasing the polymer FFV (cf. Table 1): poly(PFMD) > poly(PFMMD) > Teflon AF2400.6,10 Indeed, at any fixed penetrant concentration, the need to open gaps between polymer chains, which is ultimately responsible for polymer swelling, is significantly reduced when more free volume is available. Moreover, at a fixed penetrant concentration, the swelling induced by C2H6 sorption is higher than that induced by CO2 sorption. This result is consistent with the larger molecular size of C2H6 than CO2. F


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Figure 4. Carbon dioxide (A) and ethane (B) sorption induced swelling at 35 °C in poly(PFMD), poly(PFMMD), and Teflon AF2400. Lines represent the NELF model predictions, and symbols are experimental data. Experimental swelling measurements are not available for poly(PFMD) and poly(PFMMD).

Figure 5. Logarithm of infinite dilution solubility coefficient and its enthalpic and entropic contributions as a function of critical temperature at 35 °C: (A) poly(PFMD), (B) poly(PFMMD), (C) Hyflon AD80, (D) Teflon AF2400, and (E) HAB-6FDA polyimide.

G


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exhibited by commercial perfluoropolymers. Specifically, βH is 0.0346 K−1 for poly(PFMD) and 0.0286 K−1 for poly(PFMMD), with an average value of 0.0316 K−1. For HAB6FDA polyimide, βH is 0.0361 K−1. Therefore, the increase of ϕH with penetrant condensability in perfluoropolymers is less steep relative to hydrocarbon-based polymers. This result reflects the polymer structure and polymer−penetrant interaction pattern. Generally, perfluoropolymers exhibit (i) lower cohesive energy density (i.e., lower p2*), (ii) weaker mean field interactions with gas molecules (i.e., lower value of (1 − k12)), and (iii) higher fractional free volume than the hydrocarbon-based polymers. Based on eq 12, ϕH ∝ (1 − f)(1 − k12)√p2*, and therefore, perfluoropolymers are expected to exhibit lower ϕH values than hydrocarbon-based polymers, as well as less marked increase of ϕH with increasing penetrant critical temperature. Substantial differences are observed among perfluoropolymers. For example, despite the fact that poly(PFMMD) and Hyflon AD80 exhibit a fairly similar fractional free volume ( f ≅ 0.11) and interactional pattern with small penetrant molecules, βH is 0.021 K−1 for Hyflon AD80 and 0.029 K−1 for poly(PFMD). Their ratio, 0.72, is very close to the p* /p* ratio (i.e., 0.80, cf. eq 12), which indicates

4.4. Infinite Dilution Solubility Coefficient and the Role of Cohesive Energy Density. The logarithm of infinite dilution sorption coefficient increases linearly with penetrant critical temperature:9,56 ln(Sinf ) = α + βTC

(10)

where the slope β is a measure of polymer solubility-selectivity. Specifically, larger values of β indicate larger solubilityselectivity, and smaller values of β indicate lower solubilityselectivity. To put the data discussed in the previous sections in perspective, we will compare the slope of ln(Sinf) and its enthalpic and entropic counterparts vs TC for some important perfluoropolymers and hydrocarbon-based polymers14,50 (TeflonAF, HyflonAD80, and HAB-6FDA polyimide), with the aim of setting rational guidelines to maximize the solubilityselectivity. Equally important, while the slope of ln(Sinf) vs TC has been the subject of extensive investigation,13,47,57 the TC dependence of ϕH and ϕS is rarely reported,29,41 and to the best of our knowledge, it has never been discussed previously for perfluoropolymers. For the sake of simplicity, we will confine our discussion to the infinite dilution region, where polymer swelling is not expected to take place. Typical β values are in the range 0.019−0.022 K−1 for hydrocarbon-based polymers and 0.010−0.011 K−1 for perfluoropolymers.57 The β values exhibited by poly(PFMD) and poly(PFMMD) are consistent with those typically observed in perfluoropolymers (cf. Figure 5), although poly(PFMD) exhibits a larger β value than poly(PFMMD) (+26%). This result is consistent with the larger solubilityselectivity exhibited by the former polymer (cf. Table 4). The enthalpic (ϕH) and entropic (ϕS) contributions to the infinite dilution sorption coefficient are also shown in Figure 5. They were calculated using eqs 5−6. ϕH and ϕS can be expressed as a function of the lattice fluid definition of polymer fractional free volume, f, as follows:41 Ä ÉÑ l ÑÑ o oÅÅÅij v1* yz 1 ij v1* yz| ÑÑ 0oÅ j z jj zzo Å j z ϕS = r1 m − 1 + 1 ln( f ) + − 1 } Å Ñ j z j z Å Ñ o o j z j z Å Ñ * o o v* ÑÑÖ o {1 − f k v2 {o nÅÅÇk 2 ~ (11) ϕH = r10

2T1* (1 − f )(1 − k12) p1* p2* p1* T

Hyflon

(12)

where f is defined by f=

ρ2* − ρ20 ρ* 2

(13)

Obviously, f and FFV (i.e., FFV = (V̂ − V̂ 0)/V̂ 0, where V̂ and V̂ 0 are the polymer specific volume and the volume occupied by polymer chains, respectively) values do not match each other, since they are defined and calculated in different ways. However, as shown in Figure S2, Supporting Information, they are proportional with each other. ϕH and ϕS are linear functions of penetrant critical temperature (cf. Figure 5): ϕH = αH + βH TC

(14)

ϕS = αS + βS TC

(15)

PFMMD

that the enthalpic contribution to the solubility coefficient in Hyflon AD80 increases less than in poly(PFMMD) with increasing penetrant condensability because the former polymer exhibits lower cohesive energy density. Poly(PFMMD) and Teflon AF exhibit the same p2* value but different free volumes (f = 0.11 and 0.17, respectively). The βH ratio between the two polymers is 1.25, which is fairly close to the ratio (1 − f PFMMD)/(1 − f Hyf lon) (i.e., 1.10). Therefore, the enthalpic contribution to the solubility coefficient in Teflon AF increases less than in poly(PFMMD) with increasing the penetrant condensability because the former polymer exhibits much higher free volume. Comparison between perfluoropolymers and hydrocarbonbased polymers also discloses interesting correlations. Specifically, poly(PFMMD) and HAB-6FDA have fairly similar free volume fractions (f = 0.11 and 0.12, respectively), but the latter exhibits a much larger p2* value and more favorable energetic interactions with light gases than poly(PFMMD), which is consistent with the steeper increase of ϕH with penetrant condensability in HAB-6FDA. The discussion presented above can be summarized by noting that the βH value of perfluoropolymers with dioxolane pendant rings is larger than the commercial perfluoropolymers, and it is very close to that of the hydrodrocarbon-based polymers. The entropic contribution to the solubility coefficient depends essentially on the polymer f value (cf. eq 11), and specifically, βS becomes less negative with increasing f value. This result is consistent with the statistical interpretation of entropy, since the probability of accommodating penetrant molecules in the polymer decreases less with increasing penetrant size when more free volume is available. For Teflon AF copolymers, the average βS value is −0.013 K−1, which is about 40% lower than that observed for poly(PFMD) and poly(PFMMD). This large difference is ascribed to the much larger f values of Teflon AF than poly(PFMD) and poly(PFMMD). Poly(PFMD), poly(PFMMD), Hyflon AD80, and HAB-6FDA exhibit fairly similar f values. The βS value for Hyflon AD80 is −0.014 K−1,

βH and βS values for poly(PFMD) and poly(PFMMD) are slightly lower than those of hydrocarbon-based polymers, such as HAB-6FDA, and they are substantially higher than those H


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parameter to tailor solubility-selectivity, with all other factors (interactional pattern, free volume) being equal.

which is comparable to that of Teflon AF and HAB-6FDA and much lower than that of poly(PFMD) and poly(PFMMD). This comparison is very interesting, since it is made at fixed free volume. It indicates that the free volume morphology and accessibility in poly(PFMD) and poly(PFMMD) might be different from that of Hyflon AD80. This result is consistent with the free volume characterization discussed previously by Yavari et al.,6 which showed that poly(PFMD) and poly(PFMMD) have larger microcavities and narrower pore connections than Hyflon AD80. The presence of smaller microporous necks makes poly(PFMD) and poly(PFMMD) more size-selective and likely causes a steeper decrease of the entropic contribution to the solubility coefficient with increasing penetrant size than in Hyflon AD80. Since gas sorption is governed by its enthalpic contribution (as both of them increase with increasing TC), to maximize β (i.e., the solubility-selectivity), it is necessary to maximize the slope of ϕH vs TC. To satisfy this condition, the membrane material should exhibit, at any given fractional free volume, high values of cohesive energy density (i.e., p2*). Consistently, Lipscomb et al.58 observed that the position of the solubility/ solubility-selectivity upper bound shifts upward with increasing polymer cohesive energy density. Poly(PFMD) exhibits higher cohesive energy density (i.e., higher p2*) and lower free volume than poly(PFMMD), and therefore, it exhibits larger solubilityselectivity. HAB-6FDA exhibits the largest value of β, βH, and cohesive energy density among the polymers considered in this study and, consistently, the highest solubility-selectivity (cf. Table 4). Based on the Meares theory, small molecule permeability and diffusivity are expected to decrease with increasing polymer cohesive energy density.59 Indeed, stronger energetic interactions among polymer chains enhance the energy barrier for diffusion jumps, which translates to higher permeation and diffusion activation energies. However, as discussed by Faupel et al.,60 selectivity increases with increasing the polymer cohesive energy density. Therefore, chemical modifications to increase cohesive energy density would decrease gas permeability and increase both solubility- and diffusivityselectivity, as validated in this study. Indeed, poly(PFMD) and poly(PFMMD) are less permeable than Teflons AF, but they exhibit much larger solubility- and diffusivity-selectivity (cf. Table 4).6,18 A possible avenue to enhance the polymer cohesive energy density consists in introducing interchain hydrogen bonds, as well as promoting the formation of charge transfer complexes. Chemical cross-linking could be another way to pursue this goal. In the latter case, however, the crosslinker length and rigidity must be selected properly, to mitigate losses in permeability.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.9b03411. Membrane casting protocol, relevant NELF model equations, experimental uncertainty on pVT data, overview of k12 and ksw parameters, and FFV vs f correlation (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Ernesto Di Maio: 0000-0002-3276-174X Haiqing Lin: 0000-0001-8042-154X Michele Galizia: 0000-0001-5430-4964 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS MY and HL acknowledge the financial support from the U.S. National Science Foundation (NSF), with the award number of 1554236.

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REFERENCES

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5. CONCLUSIONS Structure−transport property correlations were developed and discussed for poly(PFMD) and poly(PFMMD), two novel glassy fluoropolymers with dioxolane pendant rings. The high selectivity exhibited by these materials is ascribed to a combination of favorable solubility- and diffusivity-selectivity. Due to the high oxygen/carbon ratio, poly(PFMD) and poly(PFMMD) exhibit enhanced CO2-philicity relative to commercial perfluoropolymers, such as Teflons AF. The NELF model provides a satisfactory quantitative description of gas solubility in poly(PFMD) and poly(PFMMD) and helps devise rational guidelines to maximize solubility-selectivity. Specifically, the polymer cohesive energy density is the key I


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