{Permeability of gas mixtures in the glassy polymers with and without plasticization} J. Serb. Chem. Soc. 86 (4) 341–353 (2021) Survey JSCS–5425 341 SURVEY Permeability of gas mixtures in glassy polymers with and without plasticization MASOUD SABERI* Department of Chemical Engineering, Bushehr Branch, Islamic Azad University, Bushehr, Iran (Received 15 July, revised 31 July, accepted 4 August 2020) Abstract: In this research, the solubility, permeability and diffusivity of gas mixtures through glassy polymers were comprehensively studied. The diffus- ivity of the components in the mixture was assumed to be a function of the concentration of all components in the mixture. Then, the permeability of pure species was expanded to the gas mixtures and to check the validity, the model was fitted to the experimental data for permeation of CO2/CH4 through differ- ent glassy membranes and the parameters of the model were calculated. After- wards, the obtained parameters were used for predicting the permeability of CO2 and CH4 in the mixture. The results showed that the solubility, diffusivity, and the permeability of CO2 in the glassy polymers are suppressed in the pre- sence of CH4 as well as plasticization. Moreover, the diffusivity (D) for pure CO2 is significantly pressure dependent in the presence of plasticization whereas with the increase in the CH4 fraction, this dependency decreases due to the reduction in the plasticization. Keywords: gas separation; membrane; plasticization; solubility; diffusivity. INTRODUCTION Polymeric membranes are widely used in the natural gas separation process. For removal of carbon dioxide (CO2), glassy polymeric membranes are often preferred over rubbery polymeric membranes because of their higher CO2/CH4 or CO2/N2 selectivity.1–6 Although some types of glassy membranes have a good performance in CO2 separation, the performance of these membranes can be hindered by the plasticization phenomenon.7–12 Therefore, CO2 permeability inc- reases with the feed pressure.7–13 On the other hand, permeability of pure inert gases, such as CH4 or N2, has a decreasing trend with the pressure.14–16 Thus, the ideal selectivity of CO2/N2 or CO2/CH4 increases with feed pressure.13–16 However, the behavior of mixed gas feeds is significantly different from pure * E-mail: msd.saberi@gmail.com https://doi.org/10.2298/JSC200715046S ________________________________________________________________________________________________________________________ (CC) 2021 SCS. Available on line at www.shd.org.rs/JSCS/ 342 SABERI species. In the presence of plasticization, the permeabilities of both CO2 and N2 or CH4 increase. But N2 or CH4 generally have larger increases than CO2, resulting in decreasing selectivity.1,10,14,17,18 Thus, the actual selectivity is lower than ideal selectivity at a special pressure.1,14,19 Raymond et al.19 reported that for mixed gas feed of CO2 and CH4 with equal composition, the actual selectivity at 5 atm* is well predicted by pure gases, whereas at 20 atm, the actual select- ivity was much lower than ideal selectivity. It was due to plasticization of mem- branes at 20 atm pressure. In addition, ideal selectivity of CO2 and CH4 for polyimide (6FDA-mPD) was reported to be about 60 at a feed pressure of 17.5 atm, whereas the actual selectivity for feed with equal composition of these gases was observed about 4.20 Therefore, for a proper prediction of transport behavior for gas mixtures, especially in the presence of plasticization, it is essential to represent accurately the experimental results. Then, an accurate and simple model is required to be used for all the different behaviors of gases in glassy polymers. Different approaches were developed to describe the solubility and transport of gases and vapors in glassy polymers. Among these models, the dual mode sorption (DMS) and non-equilibrium lattice fluid (NELF) models are well-known models. It should be mentioned that, although NELF model has been extended for all permeability behavior of gaseous in glassy polymers, it is used less than the DMS model because of its complexity and long calculation times. DMS, a model with empirical parameters, is widely used mainly due to its remarkable simplicity. Although, different models with different assumptions have been developed based on this theory to investigate the permeability of pure and mixed gases in glassy polymers, less attention has been paid for predicting permeation of mixed gases through glassy polymers in the presence of plasticization. In our previous works, we extended a model for permeation of gas mixtures in glassy polymers based on DMS model with no predictive capability.21,22 In the present study, a comprehensive model based on the DMS model was developed to pre- dict the permeation behavior of mixed gases through glassy polymers with and without plasticization using pure data for solubility and permeability. To achieve this aim, the diffusivity of all species in the mixture is assumed to be a function of the concentration of all components in the mixture. Then, for determining the parameters and evaluation of the accuracy of the model, the predictions of the model were compared against experimental data for the permeation of different groups of gas mixture in different glassy polymers. * 1 atm = 101325 Pa ________________________________________________________________________________________________________________________ (CC) 2021 SCS. Available on line at www.shd.org.rs/JSCS/ GAS PERMEABILITY IN GLASSY POLYMERS 343 THEORY AND BACKGROUND Solubility Based up on the DMS model, two mechanisms of sorption occur in glassy polymers: i) ordinary dissolution based on the Henry’s law and ii) “hole-filling” according to the Langmuir theory. The equilibrium isotherm for a pure gas A based on the DMS model is expressed as:21-23 A DA HA A 'HA A A A A/ (1 )= + = + +DAC C C k p C b p b p (1) where C is the gas concentrations in the polymer (cm3 STP/cm3 polymer), CD is the Henry’s solubility, represents ordinary dissolution, CH is Langmuir solubility, represents sorption in microvoids or holes, kD is Henry’s law solubility coefficient (cm3 STP/cm3 polymer.atm), C'H is the hole saturation constant (cm3 STP/cm3 polymer), b is the hole affinity constant (atm-1) and p is pressure (atm). The solubility coefficient of gas A in polymeric membranes is defined as:21,22 SA = CA/pA (2) Koros et al. extended the DMS model for gas mixture systems and the sorption of components A and B of a binary gas mixture is expressed as:23 A DA A 'HA A A A A B B= / (1 )+ + +C k p C b p b p b p (3) B DB B 'HB B B A A B B= / (1 )+ + +C k p C b p b p b p (4) Permeability Based on the partial immobilization model (PIM), a fraction F of the sorbed gases in the Langmuir sites are mobile and the remainder (1−F) are immobile whereas the whole gas dissolved in the Henry’s region is mobile. The total concentration of the mobile part of the adsorbed gas is Cm with a diffusion coefficient D. F is the immobilization factor and depends on the nature of penetrant–polymer system as well as the system temperature.24,25 The flux (N) of component i is expressed as follows:21 i i mi( ) ∂ = − ∂ C N D x (5) where:21 mi Di i Hi Di i 'i Hi i i i i/ (1 )= + = + +C C F C k p F C b p b p (6) For the diffusivity of species i, a simple exponential relationship with the penetrant mobile concentration was found effective and is given by:26,27 Di = Di0exp(βiCmi) (7) where Di0 is the diffusion coefficient of pure gas at zero penetrant concentration, and βi is the plasticization factor. It should be noted that Eq. (7) could be used for all gases, including plasticizer or not. In the absence of plasticization (i.e., βi = 0), diffusivity will be constant and would not change with pressure. Then, Eqs. (5)–(7) yield the following expression for the flux of the penetrant gas in glassy polymers: ( )m 2 m 1 0 m mexp dβ= −  i i Ci i i i iC D N C C l (8) ________________________________________________________________________________________________________________________ (CC) 2021 SCS. Available on line at www.shd.org.rs/JSCS/ 344 SABERI where subscripts 2 and 1 represent the upstream and downstream conditions and when the downstream pressure is considered zero, CmA1 = 0. Toni et al. considered the two mobility coefficients related to the concentration of both penetrants,28 whereas the diffusivities for components A and B in the binary gas mixture were assumed to be related to the concentration of both penetrants and obtained by: DA = DA0exp (βACmA+ βBCmB) (9) DB = DB0exp(βACmA+ βBCmB) (10) where DA0, DB0, βA and βB were obtained from pure state, and: mA DA A HA DA A A 'HA A A A A B B/ (1 )= + = + + +C C F C k p F C b p b p b p (11) mB DB B HB DB B 'B HB B B A A B B/ (1 )= + = + + +C C F C k p F C b p b p b p (12) Again, combining Eq. (5) and Eqs. (9)–(12) and integrating, yields the following exp- ression for the flux of components A and B in glassy polymers: ( )mA2 mA1 A0 A A mA B mB mAexp dβ β= − + C C D N C C C l (13) ( )mB2 mB1 B0 B A mA B mB mBexp dβ β= − + C C D N C C C l (14) It is worth mentioning that for integrating Eq. (13), CmA and CmB should be written in term pA and for Eq. (14) should be written in term pB. Furthermore, under steady state conditions, the permeability and selectivity are given by:22 2 1 = − i i i i N l P p p (15) where l is the membrane thickness. RESULTS AND DISCUSSION The mathematical procedure to predict the permeation of mixed gas through glassy polymeric membranes is as follows: 1. Calculation of parameters of the DMS model (Eq. (1)) for pure species by fitting this equation to the experimental data of the isotherms. 2. Using the obtained parameters from step 1, fitting Eq. (8) to the experi- mental data for permeability of pure species and the calculation of parameters β, F and D0 for the pure species. 3. Using the obtained parameters of steps 1 and 2 in conjunction with Eqs. (13) and (14), for the prediction of the permeability of the species in the gas mixture. It is worth noting that the parameters of the DMS model and the non-linear proposed models are obtained by the least squares regression technique using MATLAB software. To validate the model, comparing with the experimental data for the perme- ation of CO2/CH4 mixtures through different glassy membranes including poly- ________________________________________________________________________________________________________________________ (CC) 2021 SCS. Available on line at www.shd.org.rs/JSCS/ GAS PERMEABILITY IN GLASSY POLYMERS 345 sulfone (PSf), polyetherimide (PEI), polyhydroxyether (PH), polyarylate (PAr) and cellulose acetate (CA) are investigated.15,29–31 Solubility In order to study the permeability behavior of CO2/CH4 gaseous mixture, the parameters of the sorption isotherm of pure CO2 and CH4 in the glassy polymers is required. The DMS parameters for CO2 and CH4 in the different glassy poly- mers, which were obtained by fitting the DMS model to the experimental data, are reported in Table I. Then, by consideration the parameters of Table I, and using Eqs. (3) and (4), the solubility of the species in the gas mixture were pre- dicted. TABLE I. DMS parameters for pure CO2 and CH4 in the different glassy polymers at 35 °C Polymer Gas kD / (cm3 STP/(cm3 atm)) C'H / (cm3 STP/cm3) B / atm-1 Reference PSf CO2 0.664 17.91 0.326 29 CH4 0.161 9.86 0.070 PH CO2 0.289 10.01 0.184 29 CH4 0.051 2.70 0.067 PEI CO2 0.758 25.02 0.366 29 CH4 0.207 7.31 0.136 PAr CO2 0.631 22.69 0.215 29 CH4 0.181 6.45 0.100 CA CO2 1.362 22.58 0.248 15 CH4 0.190 2.504 0.132 As mentioned in a previous work,21,22 the solubility–pressure isotherm for CO2 and CH4 and their mixtures in glassy polymers, at lower pressures severely increases and with increasing pressure, a decrease in the sorption slope occurred. For higher pressures, this slope is almost constant and the sorption isotherm changes linearly, like the sorption of gases in rubbery polymers. This trend of sorption is because at low pressures, gas molecules adsorbed in the Henry and Langmuir sites and for higher pressures Langmuir sites will be occupied. For gas mixtures, the presence of the second component (i.e., CH4) inhibited the sorption of first component (CO2) by occupation of some sites of the Langmuir portion. Then, the sorption of CO2 is suppressed by the presence of CH4 in the mixture (Fig. 1). The solubility selectivity of CO2/CH4 vs. pressure is shown in Fig. 2. Solu- bility selectivity is found to be significantly higher in mixtures compared to the pure condition. This could be attributed to competitive sorption whereby the solubility of CO2 decreases in the presence of CH4 as well as CH4. It should be mentioned that the decrease in CH4 solubility is more than that of CO2 solubility due to higher hole affinity constant of CO2 (bCO2>bCH4) resulting in an increase in the solubility selectivity. As could be observed, the ideal solubility selectivity ________________________________________________________________________________________________________________________ (CC) 2021 SCS. Available on line at www.shd.org.rs/JSCS/ 346 SABERI increases with increasing CH4 fraction at constant pressure as reported by Vop- icka et al.20 Fig. 1. Solubility of: A) CO2 and B) CH4 in CA glassy polymer. Fig. 2. Solubility selectivity of CO2/CH4 in CA glassy polymer. Permeation without plasticization The permeability of pure CO2 and CH4 in different glassy polymers was fitted using experimental data from the literature30 and the parameters of the model, including β, F and D0 for CO2 and CH4, are reported in Table II (also determined in the literature30). The permeability–pressure plots have a decreas- ing and/or constant trend in all cases. In these cases, there is no plasticization (β = 0), then, the diffusivity is constant. In this case when there was no plastic- ization, the decreasing and/or constant trends for permeability is related to the solubility coefficient and is controlled by the immobilization factor (F), which shows the mobile parts of the sorbed gas in the Langmuir region. The predictions of the model for CO2 and CH4 gases of 50/50 volume ratio mixture in different glassy membranes using Eqs. (13) and (14) compared to the experimental data from the literature31 are shown in Fig. 4a and b. At a glance, almost a small suppression in permeability in gas mixture is observed compared to the pure species. As mentioned above, solubility of species in the presence of ________________________________________________________________________________________________________________________ (CC) 2021 SCS. Available on line at www.shd.org.rs/JSCS/ GAS PERMEABILITY IN GLASSY POLYMERS 347 second component is reduced compared to pure species due to occupation of Langmuir sites, which resulted in a reduction in the diffusivity as well as perme- ability. An acceptable prediction for all cases could be observed. TABLE II. Parameters of Eq. (8) for permeation without plasticization (β = 0)30 D0×108 / cm2 s-1 F Gas Polymer 4.53 0.118 CO2 PSf 0.690 0.174 CH4 0.877 0.094 CO2 PH 0.246 0.072 CH4 1.14 0.063 CO2 PEI 0.113 0.073 CH4 6.90 0.126 CO2 PAr 1.30 0.160 CH4 Fig. 3. Permeability of pure: A) CO2 and B) CH4 in different glassy polymers without plasticization (experimental data from the literature30). Fig. 4. Permeability of: A) CO2 and B) CH4 gases of 50/50 volume ratio mixture in different glassy polymers without plasticization (experimental data from the literature31). Permeation with plasticization Permeability. The permeability behavior of pure CO2 and CH4 through the CA membrane is shown in Fig. 5. These figures present experimental data from ________________________________________________________________________________________________________________________ (CC) 2021 SCS. Available on line at www.shd.org.rs/JSCS/ 348 SABERI the literature15 with predictions of the model, calculated by Eq. (8), using the parameters β, F and D0 for CO2 and CH4 listed in Table III. For pure CO2, the permeability increases with increasing pressure due to the higher degree of plas- ticization of the CA membrane. Due to the high sorption of CO2, which is a con- densable gas, the polymer matrix swells and the interaction between adjacent segments of the polymer chain reduces. Therefore, due to the increase in seg- mental mobility and the free volume of polymer matrix, the diffusivity increases with increasing pressure. On the other hand, the solubility coefficient decreases with increasing pressure. Since, the increase in the diffusivity overcomes the decrease in solubility coefficient, CO2 permeability increases with increasing pressure. For CH4, which has low solubility in the membrane, the permeability decreases with increasing pressure. In this case, plasticization does not occur, and diffusivity is constant. On the other hand, the solubility coefficient decreases with pressure. Then, the permeability decreases with increasing pressure. Fig. 5. Permeability of pure CO2 and CH4 penetrants in the CA membrane (experi- mental data from the literature15). TABLE III. Infinite dilution diffusivity and plasticization factor for the various penetrants in the CA membrane D0×107 / cm2 s-1 F β Gas Polymer 1.45 0.06 0.031 CO2 CA 0.29 0.38 0 CH4 In addition, comparing the experimental data for the permeability of CO2 in the gas mixture feed with different compositions from the literature15 and the predictions of the model using parameters from Table II is shown in Fig. 6. For a feed with 46.1 % CO2 and the rest CH4, the permeability decreases with increasing pressure up to about 30 atm and then increases and 30 atm is called the “plasticization pressure”. The aforementioned solubility coefficient decreases with increasing pressure and in the presence of CO2 as a plasticizer component, the diffusivity increases with increasing pressure. For a feed with 46.1 % CO2, at pressures lower than 30 atm, the decrease in the solubility coef- ficient overcomes the increase in the diffusivity whereas at higher pressures, the ________________________________________________________________________________________________________________________ (CC) 2021 SCS. Available on line at www.shd.org.rs/JSCS/ GAS PERMEABILITY IN GLASSY POLYMERS 349 increase in the diffusivity dominates. Indeed, by adding CH4 as the second com- ponent to the feed, some sites for sorption of CO2 are occupied by CH4 mole- cules so that the solubility of CO2 in the mixture declines compared to pure CO2. By suppression in the CO2 solubility, diffusivity of CO2 lowers at a specific pressure, consequently CO2-induced plasticization decreases. It means that CH4 in the feed acts as anti-plasticizer. For higher fractions of CH4 in the feed, the effect of anti-plasticization increases and the permeability with the increase in the pressure decreases. Therefore, by introducing CH4 to the feed, CO2-induced plas- ticization is suppressed. As can be seen, the prediction of the model for perme- ability behavior is almost acceptable. Fig. 6. Permeability of CO2 in mixtures with different compositions vs. pressure, compar- ison between the experimental data from the literature15 and the model prediction. Moreover, the experimental data and the predictions of the model for CH4 in gas mixture feeds with different compositions using parameters in Table II are compared in Fig. 7. As observed, for a feed with 53.9 % CH4, the permeability of CH4 passes through a minimum similar to the permeability of CO2 in Fig. 3. This behavior is due to the presence of CO2, which causes the membrane to plasticize. In addition, for feeds with higher fractions of CH4, plasticization decreases due to the reduction of CO2 sorption and diffusion, and hence, for feeds with the frac- tions higher than 53.9 % of CH4, the CH4 permeability decreases and/or is cons- tant with increasing in pressure. Furthermore, with increasing CH4 fraction in the feed, the CH4 permeability at specific pressures is reduced following suppression Fig. 7. Permeability of CH4 in mixtures of different compositions vs. pressure, compar- ison between the experimental data from the literature15 and the model calculation. ________________________________________________________________________________________________________________________ (CC) 2021 SCS. Available on line at www.shd.org.rs/JSCS/ 350 SABERI of plasticization. Diffusivity The estimated diffusivity vs. pressure for CO2 and CH4 in the pure state and in the gas mixture derived from Eqs. (9) and (10) using parameters from Tables I and II is illustrated in Fig. 8a and b. For pure CO2, stronger dependency of D on pressure was observed, so that D increases significantly with increasing pressure due to higher degree of plasticization. For feeds with different fractions of CH4, because of the reduction in the plasticization, the effect of pressure on D for CO2 became very weak and the dependency of D on pressure decreases with increas- ing CH4 fraction. For pure CH4, D is constant and did not change with increasing pressure. By adding 9.7 % CO2 to the feed, a very weak dependency of D on pressure was observed and this dependency increased with increasing CO2 fraction due to the increase in the plasticization, so that for feeds with 46.1 % CO2, D for CH4 inc- reased significantly. Additionally, at a specific pressure, D for CH4 decreases with increasing CH4 fraction. It should be mentioned that although with increas- ing CH4 fraction in the feed, the CH4 sorption increases, the swelling and the plasticization affect decreases due to reduction in CO2 sorption. The latter reason overcomes the results in the reduction in the diffusivity of CH4 with increasing CH4 fraction at a specific pressure. Fig. 8. Diffusivity of: A) CO2 and B) CH4 in the pure state and as mixtures in the CA membrane. CONCLUSIONS The permeation behavior of mixed gases through glassy membranes was sig- nificantly different from pure species, especially in the presence of the plasticize- ation phenomenon. The presence of the second component, such as CH4 or N2, along with CO2 in the feed led to a decrease in the CO2 solubility resulting in a decrease in diffusivity, permeability and the plasticization effect. This research was focused on gas mixtures and a model was developed for the prediction the ________________________________________________________________________________________________________________________ (CC) 2021 SCS. Available on line at www.shd.org.rs/JSCS/ GAS PERMEABILITY IN GLASSY POLYMERS 351 permeability of the species in mixed gases through glassy polymers with and without plasticization. Then, by comparing the proposed model for the experi- mental data of permeation of pure CO2 and CH4 through the different glassy polymer membranes, the parameters of the model were calculated. Then, these parameters were used for predicting the permeability of gases in the mixtures. The results showed that the presence of CH4 in the feed reduces the permeability of CO2 as well as the plasticization. Moreover, the results show that D for pure CO2 significantly changes with pressure and with the addition of CH4 to the feed, this dependency decreased. For a feed with 53.9 % CH4 (46.1 % CO2) the D value for CH4 increased with increasing pressure but for higher fractions of CH4 in the feed, this dependency almost disappeared. Acknowledgements. This research was supported by Islamic Azad University, Bushehr Branch. И З В О Д ПРОПУСТЉИВОСТ СМЕШЕ ГАСОВА КРОЗ ПОЛИМЕРЕ У СТАКЛАСТОМ СТАЊУ СА ПЛАСТИФИКАЦИЈОМ И БЕЗ ЊЕ MASOUD SABERI Department of Chemical Engineering, Bushehr Branch, Islamic Azad University, Bushehr, Iran У овом истраживању проучавана је растворљивост, пропустљивост и дифузивност смеша гасова кроз полимере у стакластом стању. Претпоставља се да је дифузивност компонената у мешавини функција концентрације свих компоненти у смеши. Затим се пропустљивост чистих компонената проширује на смеше гасова и за проверу ваљаности се проверава модел фитовањем експерименталних података за пермеабилност CO2/CH4 кроз различите мембране у стакластом стању и израчунавају се параметри модела. Након тога, тако добијени параметри се користе за предвиђање пропустљивости CO2 и CH4 у смеши. Резултати показују да су растворљивост, дифузивност, а такође и про- пустљивост CO2 кроз полимере у стакластом стању смањени у присуству CH4 и пласти- фикатора. Штавише, дифузивност за чисти CO2 значајно зависи од притиска у присуству пластификатора док се с повећањем удела CH4 та зависност смањује због смањења пластификације. (Примљено 15. јула, ревидирано 31. јула, прихваћено 5. августа 2020) REFERENCES 1. T. Visser, N. Masetto, M. Wessling, J. Memb. Sci. 306 (2007) 16 (https://doi.org/10.1016/j.memsci.2007.07.048) 2. Y. Liu, R. Wang, T. S. 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