Permeability, Solubility, Diffusivity, and PALS Data of Cross-linkable

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Permeability, Solubility, Diffusivity and PALS Data of Cross-linkable 6FDA-based Co-polyimides Mohammad Askari, Mei Ling Chua, and Tai-Shung Chung Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/ie403505u • Publication Date (Web): 13 Jan 2014 Downloaded from http://pubs.acs.org on January 20, 2014

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Industrial & Engineering Chemistry Research

Permeability, Solubility, Diffusivity and PALS Data of Cross-linkable 6FDA-based Co-polyimides

Mohammad Askari, Mei Ling Chua, Tai-Shung Chung*

Department of Chemical and Biomolecular Engineering National University of Singapore 10 Kent Ridge Crescent 4 Engineering Drive 4 Singapore 117576, Singapore

* Corresponding author. Tel.: +65 6516 6645; fax: +65 6779 1936. E-mail address: [email protected] (T. S. Chung).

1 ACS Paragon Plus Environment


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Abstract: The intrinsic gas transport properties of thermally treated cross-linkable 6FDA-based copolyimide membranes have been studied. Grafting various sizes of cyclodextrin (CD) to the copolyimide matrix and then thermally decomposing CD at elevated temperatures are an effective method to micro-manipulate microvoids and free volume as well as gas sorption and permeation. The pressure-dependent solubility and permeability coefficients were found to follow the dualmode sorption model and partial immobilization model, respectively. Solubility and permeability coefficients of CH4, CO2, C3H6 and C3H8 were conducted at 35 ºC for different upstream pressures. The Langmuir saturation constant, C'H, increases with an increase in annealing temperature. On the other hand, Henry’s solubility coefficient kD and Langmuir affinity constant b do not change noticeably. The CH4 permeability decreases with pressure, while some membranes exhibit serious plasticization with an increase in CO2, C3H6 and C3H8 pressures. The diffusivity coefficient of the Henry mode (DD) and Langmuir mode (DH) were calculated from the permeability and solubility data and their ratio, F, is higher for membranes thermally treated at 425 ºC than those treated at 200 ºC. Data from positron annihilation lifetime spectroscopy (PALS) confirm that free-volume and the number of micro-pores increases while the radius of pore sizes decreases during the high temperature annealing process. All CD grafted membranes thermally treated at 425 ºC have almost equal or lower solubility selectivity than the original membrane for CO2/CH4 and C3H6/C3H8 separations but the former has much higher diffusion selectivity than the latter. As a result, diffusion selectivity plays a more important role than solubility in determining the permselectivity of the CD grafted membranes thermally treated at 425 ºC.


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Keywords: Thermal cross-linkable co-polyimide, Solubility coefficient, Permeability coefficient, Dual-mode sorption model, Partial immobilization model.



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1.

Introduction

Membrane separation has received much attention, and various polymeric membrane materials have been synthesized and investigated for gas separation applications. Among them, the polyimide family is one of the most attractive and favorable materials due to its excellent properties such as high thermal stability, chemical resistance, mechanical strength, and spinnability.1-9 Within the polyimide materials, hexafluoroisopropylidene diphthalic anhydride (6FDA)-based co-polyimides are of particular interest since they often possess both high gas permeability and selectivity for CO2/CH4 and olefin/paraffin separation.4-15

In order to compete with other separation technologies, polymeric membranes must be carefully designed with consideration of particular applications. A molecular-level understanding of materials and engineering factors that govern the permeability, solubility, and diffusivity coefficient of gases across the membranes must be conducted and comprehended.1-12,16-21 Gas permeation across a polymer membrane usually follows the solution-diffusion mechanism where the permeability is a product of the solubility coefficient and diffusivity coefficient.12,16,22 In other words, gas permeation follows by gas sorption onto the membrane surface, then the gas molecules diffuse across the polymer matrix, and subsequently desorb from the other surface of the membrane. Thus, the permeation process involves in a combination of thermodynamic factors like condensability of the gas and its interaction with polymer segments plus kinetic factors that are mostly dependent on penetrant size, segment mobility and free volume.22

Usually, two out of the aforementioned three coefficients that characterize a membrane’s permeability are sufficient to understand its separation behavior. However, if the polymeric


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membrane is in the glassy state, the three coefficients may not be precise since glassy polymeric membranes are often in a non-equilibrium state. Besides, structural information on free volume and its size distribution in glassy polymers is another important factor in determining the transport properties. This is due to the fact that the intrinsic transport properties such as diffusivity and solubility are strongly related to the chemical structure and the free volume of membrane materials. The interdependencies have been well summarized in several articles.3,7,8,1315,21-25

Recently, we have developed novel 6FDA-based co-polyimides which were structurally grafted by thermally labile groups such as α, β, and γ-cyclodextrin (CD) as well as saccharides and then decomposed with the purpose to enhance gas separation performance for CO2/CH4, O2/N2 and C3H6/C3H8 separation.4,9,26,27 However, no fundamental studies have been conducted to investigate their sorption behavior and transport mechanism as a function of thermally labile group. Therefore, the purposes of this study is to comprehend these novel materials by examining the relationship between the gas permeation properties and grafted CD sizes over a wide range of pressures and annealing temperatures using the dual-mode sorption model.14,1622,28,29

In addition to using conventional permeation and sorption cells, positron annihilation life time spectroscopy (PALS) is utilized in this study.24-26,30-33 It is envisioned that this fundamental study may provide useful insights for better materials design and explore new materials for industrial gas separation.



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2. 2.1

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Background Dual-mode sorption model

Permeability, solubility, and diffusivity coefficient through glassy polymeric membranes are often described by the dual-mode sorption model. Henry sorption (CD) is the main mechanism of sorption into the matrix component, while Langmuir sorption (CH) governs the sorption into the micro-void region. Therefore, the total sorption (C) is written as: C = CD + CH = k D ⋅ p +

CH′ bp 1 + bp

(1)

where C is the concentration of the gas sorbed in the polymer with a unit of gas volume (cm3) per polymer volume (cm3), p (atm) is the pressure of the feed gas in contact with the polymer, CD and CH are the concentrations of the gas penetrant sorbed at the Henry sites and Langmuir sites, respectively, kD is the Henry’s law constant indicating gas dissolution into the equilibriumdefined polymer matrix, C'H is the Langmuir capacity of the glassy polymer that is related to the un-relaxed volume, which is a measure of the departure from equilibrium in the glassy state, and b is the Langmuir affinity parameter describing the affinity of the gas to a Langmuir site. The Langmuir capacity can be viewed as a measurement of the excess free volume of a polymer.1622,28,29,34-39

The solubility coefficient (S) of a gas in a glassy polymeric membrane is described as

the ratio of the equilibrium gas concentration to the applied gas pressure, as written in Eq. (2): S=

C C′ b = kD + H p 1 + bp

(2)

Gas sorption may display an unusual isotherm if a gas is polar in nature and highly condensable. Since one can conduct the gas sorption isotherm experimentally, the three dual-mode sorption parameters (kD, C'H, and b) can be obtained by curve fitting using a nonlinear least squares method.35-41 6 ACS Paragon Plus Environment

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2.2

The partial immobilization model

In the dual-mode sorption theory, the Langmuir mode species were originally considered not to be mobile at all.21 In contrast, the partial immobilization model is based on the independent dual diffusion of the Henry and Langmuir modes but assumes that species in the Langmuir mode can relatively mobilize in glassy polymeric membranes. Since the concentration C of gas sorption is assumed to obey the dual-mode sorption model as written by Eq. (1) and permeation flux (permeation amount per unit time) J through the glassy polymeric membrane by Eq. (3) and Eq. (4), the following equations can be derived for the average D and the average P as follows:19, 21,40

J = − D(C )

 ∂C ∂C ∂CH FK  ∂CD = − DD D − DH = − DD 1 + 2  ∂y ∂y ∂y  (1 + bp)  ∂y

FK  1+   ∂C FK  ∂CD (1 + bp ) 2  J = − D(C ) = − DD 1 + = − D D 2  K ∂y  1+  (1 + bp )  ∂y  (1 + bp ) 2 

  ∂C   ∂y  

FK    1 + (1 + bp )2    K  kD 1 + dp C 2  ∫0 DD  K FK  bp (1 + )     ∫0 D ( C ) dC  1 + (1 + bp )2   1 + (1 + bp )  −    D= = = DD  C C   K  1+ K   (1 + bp )  ∫0 dC ∫0 kD 1 + (1 + bp)2  dp  

(3)

(4)

C

−

−

P = S×D =

  C − K  − CH′ bDH FK  × D = k D 1 + = k D ⋅ DD 1 +  × D =k D ⋅ DD +  p 1 + bp  1 + bp   (1 + bp ) 

(5)

(6)

where C is the concentration of the penetrant; y is the membrane thickness; D(C) is the concentration dependent diffusion coefficient; DD is the diffusion coefficient under the Henry mode; DH is the diffusion coefficient under the Langmuir mode; F is the ratio of the two



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−

diffusion coefficients (DH/DD); K is equal to CH′ b k D ; D is the average diffusion coefficient, and −

P is the average permeability coefficient. Eq. (6) is reduced to a fully Henry mode dominant −

process if F is equal to zero. In addition, the permeability coefficient, P , decreases slowly with an increase in system pressure, and then reaches to kD DD irrespective of the F value because of the saturation of Langmuir sites. In this model, the diffusivity coefficients of the Henry mode (DD) and Langmuir mode (DH) can be readily calculated from the slope and intercept of an −

experimental plot of permeability ( P ) versus (1+bp)-1 when a straight line is obtained in the plot.

2.3

Positron annihilation lifetime spectroscopy

Gas sorption is also supported by the presence of free volume in the polymer matrix. Positron annihilation lifetime spectroscopy (PALS), can analyze the free-volume properties in the membrane structure directly at the atomic level and nanoscales.30-33,42 In this method, positronium (the bound state of positron and electron, Ps) is preferentially localized in the regions of low electron density sites, such as free volumes, holes, interfaces, and pores. The annihilation of ortho-positronium (o-Ps) in molecular substrates is by pick-off with electrons of the materials. Therefore, the intrinsic o-Ps lifetime (142 ns) is typically shortened to a few nanoseconds (1-10 ns) via two-γ annihilation processes in molecular substrates. According to the Ps-free volume theory42, the lifetime of o-Ps (τ3) is determined by the reciprocal of integral between the positron and the electron densities in the free volumes of molecular systems. Therefore, o-Ps lifetime is expected to directly correlate with the dimensions where Ps is


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localized in large holes. The intensity of o-Ps, denoted by I3, is sometimes considered to be correlated with the number of such vacancies.

Figure 1 shows the scheme of bulk positron lifetime measurements43 using a γ-ray with an energy of 1.27 MeV emitting almost simultaneously with the positron from a

22

Na source. The

positron lifetime of a single event can be measured by detecting the time difference between the birth γ-quanta (start signal) in the source and one of the annihilation γ- quanta of energy of 511 keV (stop signal). A special “sandwich” arrangement of foil source, samples, and detectors, as illustrated in Figure 1, guarantees that all positrons emitted from the source are penetrating the sample material. The γ-rays are converted by scintillator photo-multiplier detectors into analog electrical pulses. In order to obtain the complete lifetime spectrum, more than 106 annihilation events must be recorded.42 The time resolution of the spectrometer is determined mainly by the scintillator multiplier part and ranges between 180 and 280 ps.

3.

Experimental

3.1 Polymers The 6FDA-Durene/DABA (9/1) co-polyimide (referred as the original PI) was synthesized in 1methyl-2-pyrrolidone (NMP) as a solvent by a chemical imidization approach. The monomers 3, 5-diaminobenzoic acid (DABA), and 2, 3, 5, 6-Tetramethyl-1, 4-phenylenediamine (Durene diamine) were purchased from Aldrich (Singapore), and 4, 4’-(hexafluoroisopropylidene) diphthalic anhydride (6FDA) was supplied by Clariant (Germany). 1-methyl-2-pyrrolidone (NMP) purchased from Merck Chemicals (Germany), was distilled at 42 °C under 1 mbar and was dried by molecular sieve before usage.



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Other chemicals and solvents including triethylamine, methanol, p-toluenesulfonic acid, and α, β, and γ-cyclodextrin were all reagent grade or better from Aldrich (Singapore) and were used without further purification. The 6FDA-Durene/DABA co-polyimide grafted with α, β, and γcyclodextrin (referred as PI-g-CDs) was synthesized by the esterification reaction. A detailed description of the polymer synthesis can be found elsewhere.4

3.2 Dense flat membranes A solution casting method was used to prepare dense flat sheet films. Briefly, 2 wt% polymer solutions were prepared by dissolving the original PI and PI-g-CDs together in NMP with a weight ratio of 1:1. In purpose of removing a trace amount of residual solvent, the polymer casting solution was heated under vacuum at 40 ºC for 12 h, continued with 70 ºC for 24 h and 200 ºC for 24 h. Finally, films with a thickness of 50 ± 10 µm were prepared for testing and characterization in the following studies. A detailed description of the film formation can be obtained elsewhere.4

The thermal treatment of the prepared films was performed using a CenturionTM Neytech Qex vacuum furnace (Yucaipa, CA, USA). The films were vacuum heated with a heating rate of 10 °C/min from room temperature to specific temperatures such as 200, and 425 °C. The films were held for 2 hrs at the final temperatures and cooled naturally in the vacuum furnace to room temperature and used for permeation tests. For sample classification, the treated samples at 200 °C were named as ‘polyimide-grafted-α, β, or γ-CD-final treated temperature’, for example


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“PI-g-α-CD-200”. For samples treated at 425 °C, they were named as ‘partially pyrolyzed membrane-α, β, or γ-CD-425, for example,”PPM-γ-CD-425”.

3.3 Measurements of permeability and solubility The permeability coefficients of all dense films were measured at 35 ºC over a pressure range of 0-450 psi for CO2 and CH4 and 0-110 psi for C3H6 and C3H8 pure gasses by the vacuum time-lag method. The permeabilities were determined for CH4, CO2, C3H8, and C3H6 for different copolyimide membranes. Detailed experimental procedure was described elsewhere.44 Gas sorption tests were conducted using a Cahn D200 microbalance sorption cell at 35 °C over a pressure range of 0-30 atm for CO2 and CH4 and 0-7 atm for C3H6 and C3H8. A detailed description of the dual volume sorption cell has been reported elsewhere.45 For each run, films with a thickness of around 50 ± 10 µm, and a total mass of approximately 70-80 mg were cut into small pieces and placed on the sample pan. The system was evacuated for 24 h prior to testing. The gas at a specific pressure was fed into the system. The mass of gas sorbed by the membranes was recorded at equilibrium state. Subsequent sorption experiments were employed by further increasing the gas pressure. The equilibrium sorption value obtained was corrected by the buoyancy force. A dual-sorption mode written as Eq. (1) was employed to analyze the pure gas sorption in a glassy polymer.

3.4 Measurements of free volume The assembly for bulk PALS tests is illustrated in the bottom right of Figure 1 where

22

Na

isotope sealed in Kapton® films was used as the source of positrons and sandwiched by membrane samples. The flat-sheet membrane samples were cut into circle pieces with the



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diameter of 1 cm. The thickness of the membrane at each side of the source is about 0.5 mm. Positron lifetime was measured as the time difference between the 1.27 MeV γ-quanta (start signal) and the 511 keV γ-quanta (stop signal) generated by annihilation of positronium. In this experiment all PALS spectra were recorded with a counting rate of around 200 counts per second, and a total count of 106 was fixed to collect each spectrum. Positron lifetimes and their intensities were analyzed by a computer program PATFIT from PALS spectra. The o-Ps lifetime

τ3 (ns) was used to calculate the mean free-volume radius R (Å to nm) based on an established semi-empirical correlation equation from a spherical-cavity model:30, 32,42,46,47

R 1 1  2π R   τ 3 = 1 − + sin   2 R + ∆R 2π  R + ∆R   

−1 (7)



where τ3 and R are expressed in the units of ns and Å, respectively, and ∆R was determined to be 1.656 Å. The intensity I3 is directly related to the amount of free volume in the membrane since the quantity of o-Ps annihilation with electrons in micro-cavities may correlate to the free volume.

4.

Results and Discussion

4.1 Solubility coefficient of co-polyimide membranes It is well known that solubility is determined by (1) the inherent condensability of the penetrant, (2) the polymer–penetrant interactions, and (3) the amount and distribution of excess free volume in the glassy polymer.13-22,28,29,34-40,48 In this study, Figure 2 shows the sorption isotherms as a function of CH4, CO2, C3H8 and C3H6 and their pressures at 35 °C. All sorption isotherms are concave to the pressure axis, which were as expected on the basis of the typical behavior of glassy amorphous polymers and of the dual mode sorption model. Penetrants sorbed in Henry’s


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sites (CD) is believed to be same as gas dissolution in a rubbery polymer, while penetrants sorbed in Langmuir sites (CH) has a capacity limit due to a hole-filling process behavior.28,29,34-40,48,49

In the Supporting Information, Table S1 tabulates the dual sorption parameters of Eq. (1) using a nonlinear least-squares regression to fit the sorption isotherms. The sorption of CH4 is much less than that of other gases due to the lower condensability and weak interactions with the polymers. As shown in Table S1 and Figure 3, for all the penetrant gases investigated in this study, the original PI-200 has slightly lower solubility coefficients comparing with those of PI-g-CDs-200, indicating that the sorption capacity of the membranes increases after grafting various types of CD into the PI.

Figure 4 shows relative solubility coefficient of different gases for co-polyimide membranes thermally treated at 425 ºC using the original PI-200 as the control. Interestingly, after grafting CD and thermal treatment, CH4 and CO2 have higher increases in solubility coefficient than C3H8 and C3H6. This phenomenon may be due to the fact the former have smaller molecules and lower critical temperatures than the latter. One may therefore expect that the change in solubility coefficient has more effects on CH4 and CO2 permeabilities than C3H8 and C3H6 permeabilities.

Co-polyimide membranes annealed at higher temperatures have higher gas sorption amounts over the entire pressure range studied. As can be seen in Figure 5, the relative values of kD and b of all membranes thermally treated at 425 ºC do not increase as much as C'H when normalizing their values to those of the original PI-200. This observation indicates that thermal treatment has minor effects on Henry’s solubility coefficient (kD) and Langmuir affinity constant (b) because



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they are mainly determined by polymer and penetrant chemistry as well as their mutual interactions. However, the C'H values of PI-g-CDs have more increments than the original PI because the saturated Langmuir sorption capacity is related to the microvoid size which is increased with CD size and decomposition temperature. When additional free volume is created, both C'H and solubility coefficient increase because the spaces originally occupied by CD are converted to micro-pores. The degrees of increases in C'H and gas solubility generally follow the order of γ-CD > β-CD > α-CD due to different CD structures and thermal decomposition behaviors.

The PALS results give additional evidence for this conclusion. As shown in Table 1, the τ3 values of the membranes annealed at 425 ºC become smaller. This reduction is due to the crosslinking reaction at this high temperature that results in a small pore size. On the other hand, the intensity I3 increases when annealing at 425 ºC, indicating more free volume cavities are created due to the decomposition of CDs and the conversion of the CD spaces to micro-pores. Since the number of micro-pores increases faster than the reduction of pore sizes, as a result, the fractional free volume (FFV) increases with annealing temperature and CD size.

4.2 Permeability and diffusivity coefficient of co-polyimide membranes The permeabilities of CH4, CO2, C3H8 and C3H6 of the newly developed membranes were measured as a function of upstream pressure at 35°C, and the results are reported in Figure 6 and Figure 7. The CH4 permeability decreases with an increase in upstream pressure for all membranes. This phenomenon is consistent with the dual-mode model described by Eq. (6) for the gas transport in glassy polymers. As the feed pressure p increases, the last term of Eq.


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(6), 1 + FK  decreases and leads to the decline in permeability when other parameters are (1 + bp ) 



constant because of the saturation of Langmuir sorption sites. 20

For highly condensable gases such as CO2, C3H6 and C3H8, a down-and-up trend is observed for the permeability vs. pressure curves for all membranes due to the CO2 induced plasticization except PPM-g-β-CD-425 and PPM-g-γ-CD-425. As the pressure increases, the penetrant concentration becomes higher resulting in an increase in segmental mobility of polymer chains that facilitates the penetrant diffusion.

In this case, the increment in diffusion coefficient

surpasses the decrease in the term of 1 + FK  , leading to the augment in permeability at high (1 + bp ) 



pressures.50,51 The membranes PPM-β-CD-425 and PPM-γ-CD-425 are not governed by this behavior because these two membranes possess higher degrees of cross-linking which confine the movement of polymer chains.4,27

Since permeability is a product of diffusivity and solubility, the diffusivity coefficients of CH4, CO2, C3H8 and C3H6 can be calculated from the permeability and solubility data using Eq. (6) and their average values are given in the Supporting Information, Table S1. As expected, diffusivity coefficient is strongly dependent on penetrant size for all samples. Propane, the largest penetrant, has the lowest diffusivity coefficient while carbon dioxide, the smallest gas, has the highest one.

The diffusivity coefficients of CO2 and CH4 vary in much broader ranges than their solubility coefficients. As displayed in Table S1 in the Supporting Information, CO2 solubility coefficients



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of all membranes vary from 23.8 to 64.4 [cm3 (STP)/ cm3 cm-Hg] with an augment factor of 2.7 while CO2 diffusivity coefficients range from 10.3 to 104.5 [×10-8 cm2/s] with an augment factor of about 10. As a result, the enhancement in CO2 permeability of PPM-g-γ-CD-425 over PI-g-γCD-200 is a product of 2.4-time increase in solubility and 10.3-time increase in diffusivity. Similar trends are observed for C3H6 and C3H8. Clearly, in addition to annealing temperature, diffusivity contributes more significantly than solubility to the change in permeability of PI-gCDs. The grafting of CDs and the decomposition of CDs at various temperatures provide us with the tools to micro-manipulate the amount of free volume and its size as well as the solubility and diffusivity of the resultant membranes.

Eq. (6) implies that the plot of permeability vs. (1+bp)-1 should be linear if the dual sorption model is applicable and all its parameters are constant and independent of pressure. Then the two parameters DD and DH can be calculated via the permeability vs. pressure relationship. As demonstrated in Figure 8 and Figure 9, fairly good linear relations are observed for all the membranes. However, the plots for the CO2 case are slightly convex to the x-axis at high pressures due to the CO2 induced plasticization. Therefore, only the permeability values before plasticization were used to measure the slope and intercept. Table 2 summarizes the DD, DH and F values estimated from these plots. The variation of DD with annealing temperature is much greater than that of DH because weaker hydrogen bonding (for the original PI) and/or a higher amount of micro-pores and free volume (for the CD grafted PI) are created when annealing the membranes at high temperatures. A comparison of F values indicates that F values for all gasses in membranes thermally treated at 425 ºC are higher than those thermally treated at 200 ºC. This phenomenon might be due to the fact that membranes thermally treated at 200 ºC trap gas


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molecules in Langmuir sites and hence hinder gas transport across the membranes. The affinity between sorbed gas and Langmuir sites is reduced for the membranes thermally treated at 425 ºC because of weaker hydrogen bonding and/or more porous micro-pores created due to the decomposition of CDs.

4.3 Permselectivity Both solubility and diffusivity contribute to permselectivity. Table 3 tabulates their individual influences to the permselectivity of each membrane for CO2/CH4 and C3H6/C3H8 separations. The diffusion selectivity fluctuates at a wider range than the solubility selectivity for these polymers. For the CO2/CH4 separation, the diffusion selectivity varies from 2.44 to 4.86 while the solubility selectivity ranges from 6.55 to 8.58 for CO2/CH4.

All of CD grafted membranes thermally treated at 425 ºC have almost equal or lower solubility selectivity than the original PI-425 membrane for CO2/CH4 and C3H6/C3H8 separations. In addition, the former has much higher diffusion selectivity than the latter. As a result, diffusion selectivity plays a more important role than solubility in determining the permselectivity for CD grafted membranes thermally treated at 425 ºC.

4.4 Comparison of dual sorption behavior, solubility, and diffusivity coefficient of CO2 in polymeric membranes According to Table S1 in the Supporting Information, PPM-g-γ-CD-425 (the co-polyimide grafted with γ-CD and thermally treated at 425 °C) shows the best solubility and diffusivity with a CO2 solubility of 48.94 cm3 (STP)/cm3polymer ⋅ atm (64.4 × 10-2 cm3 (STP)/cm3polymer ⋅ cm-



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Hg) and a diffusivity of 104.5 ×10-8cm2/s. Since there are many literature data available on dual mode sorption parameters of CO2 in glassy polymeric membranes, Table S2 in the Supporting Information compares them and shows that the newly developed membranes (PPM-g-β-CD-425 and PPM-g-γ-CD-425) have higher Langmuir capacity and solubility with comparable diffusivity. The PIM-1 membrane had the best performance in previous literatures which has a CO2 solubility of 31.41 cm3 (STP)/cm3polymer⋅ atm and a CO2 diffusivity of 128.3×10-8cm2/s.20 However, this PIM-1 membrane showed plasticization below 15 atm of CO2 feed pressure52 and around 1 atm of C3H6 feed pressure20, while our membranes not only have comparable solubility and diffusivity coefficient but also can withstand CO2 plasticization until 30 atm and C3H6 plasticization until 7atm which could have an effect on solubility and diffusivity coefficients.

4.5 Mixed gas permeation experiments Figure 10 illustrates the mixed gas permeation of PPM-g-α-CD-425 and PPM-g-β-CD-425 membranes as a function of CO2 pressure. The mixed gas of CO2/CH4 (50/50) feed mixture was used to show the resistance of the membranes to a more aggressive condition. As shown in Figure 10, the CO2 permeability and the mixed gas CO2/CH4 selectivity of the cross-linked membranes (i.e., thermally treated at 425 ºC) decrease with an increasing in feed pressure. It is obvious that the cross-linked membranes did not show plasticization behavior even up to a feed pressure of 40 atm (585 psia) in a CO2/CH4 (50/50) mixture.

5.

Conclusion

We have characterized the intrinsic gas transport properties of cross-linkable 6FDA-based copolyimides grafted by various CDs for CO2/CH4 and C3H6/C3H8 separations. The permeability,


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solubility and diffusion coefficients over a wide range of pressure have been investigated and interpreted using the dual-mode sorption and partial immobilization model. The parameters of this model have been calculated and utilized to analyze the effects of pressure and annealing temperature on transport behavior of these membranes. The following conclusions can be drawn:

1) Sorption isotherms of all gases in these membranes exhibit the typical dual-mode sorption behavior. The dual-mode sorption parameter C'H increases with an increase in annealing temperature while the parameters kD and b do not change significantly. The C'H increment is mainly attributed to the excess free volume or micro-pores formed by the decomposition of CDs. 2) Sorption of CH4 is much less than that of other gases due to its lower condensability and weak interaction with the polymer. Comparing to the membranes thermally treated at 200 ºC, the membranes thermally treated at 425 ºC have higher percentages of increase in CH4 and CO2 solubility coefficients than C3H8 and C3H6 ones because the former have lower critical temperatures and small molecule sizes. 3) The permeability coefficients of CH4 in all membranes decrease with an increase in pressure; whereas the transport behavior of other gases is somehow different. Some membranes show significant CO2 and hydrocarbon-induced plasticization phenomena leading to permeability increases of CO2, C3H6 and C3H8 with an increase in pressure. 4) The values of DD, DH, and F are higher for membranes thermally treated at 425 ºC than those thermally treated at 200 ºC due to weaker hydrogen bonding and/or more porous micro-pores created because of the CD decomposition.



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5) CD grafted membranes thermally treated at 425 ºC have almost equal or lower solubility selectivity than the original PI-425 membrane for CO2/CH4 and C3H6/C3H8 separations. The former also has much higher diffusion selectivity than the latter. As a consequence, diffusion selectivity plays a more important role than solubility in determining the permselectivity for CD grafted membranes thermally treated at 425 ºC.

Acknowledgements The authors would like to thank the Singapore National Research Foundation (NRF) for the financial support on the Competitive Research Programs with the project entitled “New Biotechnology for Processing Metropolitan Organic Wastes into Value-Added Products” (grant number: R-279-000-311-281) for funding this research.

Supporting Information The permeability, solubility, diffusivity, and dual mode sorption parameters of different copolyimide membranes for different gases at 35 °C and 1 atm (Table S1); Comparison of dual sorption behavior, solubility, and diffusivity coefficient of CO2 in polymeric membranes (Table S2); and cited references of Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org.


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Nomenclature b: Langmuir affinity constant (atm -1) C: Total sorption amount of polymer (cm3 gas (STP) /cm3 polymer) CD: Concentrations of the penetrant sorbed at the Henry site (cm3 gas (STP) /cm3 polymer) CH: Concentrations of the penetrant sorbed at the Langmuir site (cm3 gas (STP) /cm3 polymer) C'H: Langmuir saturation constant (cm3 gas (STP) /cm3 polymer) −

D : Average diffusivity coefficient (cm2/s) D(C): Concentration dependent diffusion coefficient (cm2/s) DD: Henry’s law diffusion coefficient (cm2/s) DH: Langmuir mode diffusion coefficient (cm2/s) F: Mobile fraction of the Langmuir mode species FFV: Fractional free volume I3: Intensity of ortho-Positronium J: permeation flux (cm3 gas (STP) / s) kD: Henry’s solubility coefficient ((cm3 gas (STP)) / (cm3 polymer-atm)) p: Pressure of the feed (atm) −

P : Average permeability coefficient (Barrer) R: mean free-volume radius R (nm) S: Solubility coefficient ((cm3 gas (STP)) / (cm3 polymer-atm)) y: Polymer thickness (cm)

τ3: Ortho-Positronium lifetime (ns)



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List of Figures: Figure 1. Schematic diagram of the bulk PALS system, and the inset indicates the sample packing structure. Figure 2. Sorption isotherms of penetrants in different co-polyimide membranes at 35 ºC Figure 3. Solubility coefficient of penetrants in different co-polyimide membranes at 35 ºC Figure 4. Relative solubility coefficient of different gasses for co-polyimide membranes thermally treated at 425 ºC compared to Original PI-200 Figure 5. Relative a) kD value, b) b value, and c) C’H value of different gasses for co-polyimide membranes thermally treated at 425 ºC compared to Original PI-200 Figure 6. Permeabilities of CH4 and CO2 in different co-polyimide membranes as a function of pressure at 35 ºC Figure 7. Permeabilities of C3H8 and C3H6 for different co-polyimide membranes as a function of pressure at 35 ºC Figure 8. Plots of permeability coefficients of CH4 and CO2 against (1+bp)-1 for different copolyimide membranes Figure 9. Plots of permeability coefficients of C3H8 and C3H6 against (1+bp)-1 for different copolyimide membranes. Figure 10. Mixed gas CO2 permeability as a function of feed pressure for PPM-g-α-CD-425 and PPM-g-β-CD-425 membranes. The permeability curves obtained with CO2/CH4 (50/50) at 35 ºC.



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List of Tables: Table 1. Positron annihilation lifetime spectroscopy (PALS) data of different co-polyimide membranes Table 2. Diffusivity parameters of different co-polyimide membranes for different gasses at 35 °C Table 3. Contributions of solubility selectivity and diffusion selectivity to the permselectivity of each membrane for the CO2/CH4 and C3H6/C3H8 separations at 35 ºC and 1 atm


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Permeability, Solubility, Diffusivity and PALS Data of Cross-linkable 6FDA-based Co-polyimides

Mohammad Askari, Mei Ling Chua, Tai-Shung Chung*

Department of Chemical and Biomolecular Engineering, National University of Singapore 10 Kent Ridge Crescent 4 Engineering Drive 4 Singapore 117576, Singapore

ACS Paragon Plus Environment


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Figure 1. Schematic diagram of the bulk PALS system, and the inset indicates the sample packing structure 43

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Figure 2. Sorption isotherms of penetrants in different co-polyimide membranes at 35 ºC


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Figure 3. Solubility coefficient of penetrants in different co-polyimide membranes at 35 ºC

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ACS Paragon Plusfor Environment Figure 4. Relative solubility coefficient of different gasses co-polyimide membranes thermally treated at 425 ºC compared to Original PI-200


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a)

b)

c)


Figure 5. Relative a) kD value, b) b value, and c) C’H value of different gasses for co-polyimide membranes thermally treated at 425 ºC compared to Original PI-200

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Figure 6. Permeabilities of CH4 and CO2 in different co-polyimide membranes as a function of pressure at 35 ºC


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Figure 7. Permeabilities of C3H8 and C3H6 for different co-polyimide membranes as a function of pressure at 35 ºC

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Figure 8. Plots of permeability coefficients of CH4 and CO2 against (1+bp)-1 for different co-polyimide membranes


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Figure 9. Plots of permeability coefficients of C3H8 and C3H6 against (1+bp)-1 for different co-polyimide membranes

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Figure 10. Mixed gas CO2 permeability as aACS function of feed pressure for PPM-g-α-CD-425 and PPM-g-β-CD-425 Paragon Plus Environment membranes. The permeability curves obtained with CO2/CH4 (50/50) at 35 ºC.


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Table 1. Positron annihilation lifetime spectroscopy (PALS) data of different co-polyimide membranes I3 (%)

τ3 (ns)

R (Ǻ)

FFV (%)

Original PI-200

7.5088 ± 0.0673

3.1669 ± 0.0271

3.7479 ± 0.0118

2.9806 ± 0.0550

Original PI-425

6.4646 ± 0.0696

2.9381 ± 0.0293

3.5950 ± 0.0140

2.2646 ± 0.0509

PI-g-α-CD-200

8.0363 ± 0.0725

3.1007 ± 0.0259

3.7045 ± 0.0116

3.0805 ± 0.0568

PPM-g-α-CD-425

9.3544 ± 0.0823

2.9703 ± 0.0232

3.6170 ± 0.0109

3.3376 ± 0.0598

PI-g-β-CD-200

8.2312 ± 0.0736

3.0678 ± 0.0254

3.6827 ± 0.0115

3.0998 ± 0.0569

PPM-g-β-CD-425

9.9394 ± 0.1454

2.8925 ± 0.0209

3.5643 ± 0.0123

3.3936 ± 0.0765

PI-g-γ-CD-200

8.4443 ± 0.0733

3.1264 ± 0.0252

3.7214 ± 0.0112

3.2815 ± 0.0581

PPM-g-γ-CD-425

9.9808 ± 0.1261

2.8890 ± 0.0146

3.5672 ± 0.0085

3.4188 ± 0.0705

Membranes


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Industrial & Engineering Chemistry Research for different gasses at 35 °C Table 2. Diffusivity parameters of different co-polyimide membranes

Membrane

Original PI-200

Original PI-425

PI-g-α-CD-200

PPM-g-α-CD-425

PI-g-β-CD-200

PPM-g-β-CD-425

PI-g-γ-CD-200

PPM-g-γ-CD-425

DD*10-8 DH*10-8 2 (cm /s) (cm2/s) CH4 19.30 0.98 CO2 97.50 3.03 C3H8 0.20 0.01 C3H6 3.87 0.24 CH4 78.30 5.14 CO2 507.00 24.30 C3H8 0.79 0.04 C3H6 14.60 0.91 CH4 20.30 1.05 CO2 104.00 2.56 C3H8 0.26 0.01 C3H6 3.22 0.24 CH4 130.60 9.74 CO2 855.00 66.90 C3H8 2.63 0.13 C3H6 46.20 4.77 CH4 18.20 1.11 CO2 93.90 2.88 C3H8 0.26 0.01 C3H6 3.65 0.22 CH4 151.80 12.10 CO2 1036.00 78.10 C3H8 3.40 0.22 C3H6 69.30 6.45 CH4 19.40 1.13 CO2 96.50 2.65 C3H8 0.32 0.01 C3H6 4.26 0.32 CH4 183.80 15.40 CO2 1317.00 79.20 ACS Paragon Plus Environment C3H8 4.30 0.25 C3H6 82.10 8.32 Gas

F 0.051 0.031 0.043 0.061 0.066 0.048 0.048 0.062 0.051 0.025 0.048 0.076 0.075 0.078 0.051 0.103 0.061 0.031 0.046 0.061 0.079 0.075 0.065 0.093 0.058 0.027 0.042 0.075 0.084 0.060 0.059 0.101


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Page 44 of 44

Table 3. Contributions of solubility selectivity and diffusion selectivity to the permselectivity of each membrane for CO2/CH4 and C3H6/C3H8 separations at 35 °C and 1 atm

CO2/CH4 Membranes

C3H6/C3H8

Solubility selectivity

Diffusion selectivity

α

Solubility selectivity

Diffusion selectivity

α

Original PI-200

7.76

2.82

21.87

1.28

12.83

16.42

Original PI-425

8.02

3.06

24.58

1.50

14.13

21.20

PI-g-α-CD-200

7.96

2.44

19.42

1.34

11.91

15.94

PPM-g-α-CD-425

6.75

4.63

31.27

1.12

20.15

22.62

PI-g-β-CD-200

7.20

2.93

21.09

1.47

10.94

16.07

PPM-g-β-CD-425

7.25

4.64

33.69

1.15

19.11

22.01

PI-g-γ-CD-200

8.58

2.51

21.56

1.45

12.09

17.48

PPM-g-γ-CD-425

6.55

4.86

31.59

1.17

20.43

23.68


Permeability, Solubility, Diffusivity, and PALS Data of Cross-linkable

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