INTRODUCTION

Polyimides (PIs) occupy a special place among polymeric materials for membrane gas separation due to their thermal stability, chemical stability, mechanical strength, and high selectivity of gas separation [1–3]. Despite the fact that most PIs do not have high gas permeability, a number of PIs are materials for industrial hollow fiber gas separation membranes from companies such as Ube Industries [4], Evonik [5], and Air Liquide [6], used to separate biogas, air, evolution of hydrogen from the streams of petrochemical industries, as well as helium and CO2 from natural gas. On the Robeson diagrams [7, 8], the position of the upper boundaries in the region of low permeability and high selectivity is determined mainly by PIs. In recent decades, the most popular design elements of PIs to increase their gas permeability are hard chain breaks in diamine or dianhydride fragments [9–11] or the introduction of bulky substituents in diamine fragments [10, 12, 13], which leads to a decrease in the energy of interchain interactions, an increase in the inhibition of rotation and stiffness of the chain, and, as a consequence, an increase in the free volume and gas permeability of polymers [13, 14]. The use of a mixture of diethyl toluene diamine isomers (Table 1) with bulky side groups in the PI synthesis also leads to a sufficiently high gas permeability for PIs, which was first demonstrated [15] and confirmed [16, 17]. PIs with rigid dianhydride fragments 6FDA and BPDA on the Robeson diagrams [7, 8] occupy a position near the upper limit of 1991 [7, 15].

Table 1. Structure of the elementary unit and the glass transition temperature of the investigated polyimides (PIs) based on a mixture of diethyl toluene diamine isomers (2,4-diamino-3,5-diethyltoluene (80%) and 2,6-diamino-3,5-diethyltoluene (20%))
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The data on the gas transport characteristics of the PI-1 and PI-2 films for O2, N2, and CH4 obtained at 22°C [15] and at 35°C [16, 17] are presented in Table 2.

Table 2. Coefficients of permeability (P, Barrer), diffusion (D × 108, cm2/s), and solubility (S × 103, cm3(n. c.)/(cm3 Hg cm) of PI films
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Despite the fact that the gas transport characteristics of PI-1 and PI-2 obtained at 22°C [15] are generally higher than those reported [16, 17] for 35°C, the analysis of Table 2 reveals some regularities. Thus, the values of the permeability and diffusion coefficients for PI-1 are significantly higher than for PI-2, and the solubility coefficients of O2 and N2 for both PIs practically coincide within the error (15%), while for CO2 and CH4, the solubility coefficients for the more rigid chain and less permeable PI-2 are higher than for PI-1. This fact may indicate that the dimensions of the free volume elements in these polymers are similar and their size distribution is somewhat different. Nevertheless, the S values in [15] and [16, 17] were obtained by an indirect method from the experimental permeability and diffusion coefficients, and it is necessary to study the gas sorption in these PIs by direct methods.

On the other hand, highly permeable PIs with bulky substituents in the diamine fragment [3, 18–20] are considered promising materials for the separation of olefins and paraffins. At the same time, the transport parameters of hydrocarbons for PI based on a mixture of diethyl toluene diamine isomers have not yet been studied. Therefore, information on the gas transport parameters of С2–С4 hydrocarbons for these PIs and their comparison with highly permeable PIs similar in structure [3, 18–20] would be extremely useful for evaluating their use in similar processes.

In previous works dialed with PI, based on a mixture of diethyl toluene diamine isomers [15–17], only the transport parameters for individual gases were studied; therefore, the development of works on promising membrane materials PI-1 and PI-2 (Table 1) also involves operation with gas mixtures.

Thus, the aim of this work is to study the sorption and transport parameters of PI-1 and PI-2 for O2, N2, CO2, CH4, transport parameters for gas mixtures O2/N2 and CO2/CH4, as well as to estimate the transport parameters for hydrocarbons С2–C4.

EXPERIMENTAL

PI-1 and PI-2 were synthesized in a benzoic acid melt using a procedure similar to that reported [15]. PI films with a thickness of 25–30 μm were formed from a 5% solution in chloroform (chemical pure grade) on a cellophane substrate and dried at room temperature for 2–3 days, followed by bringing them to constant weight in vacuum. According to TGA data, there is no residual solvent in the films obtained in this way. According to the X-ray powder diffraction data, all samples of the investigated PI films were amorphous.

The permeability and diffusion coefficients of the individual gases O2, N2, CH4, C2H6, C3H8, and C4H10 for the obtained free films were obtained by the integral barometric method on a thermostated laboratory setup with MKS Baratron pressure sensors and with an air thermostat [21] at 35°С; software based on LabView was used to control the experiment. The experiments were carried out at a pressure above the membrane in the range of 0.7–0.9 atm. The pressure in the submembrane space was maintained at a level of ~1.3 × 10–7 atm; therefore, under the experimental conditions, the back diffusion of the penetrating gas was neglected. From the curve of gas leakage through the PI film into the calibrated volume, the permeability coefficients Р (by the slope of the linear dependence of the flow through the film upon reaching the stationary mass transfer mode) and the diffusion coefficients D (according to the Deines–Barrer method, taking into account the delay time θ (s): D = l 2/6θ, where l is the film thickness) were determined. The values of the diffusion coefficients of O2 and N2 for PI-1 were not determined because of the short delay times (less than 1 s). The solubility coefficients S were calculated from the experimental values of P and D using the formula S = P/D. From the data obtained, the ideal separation selectivities (α = Pi/Pj) and diffusion (αD = Di/Dj) and solubility (αS = Si/Sj) selectivities were found for different gas pairs i and j. The experimental error in measuring P and D was 5% and 10%, respectively; accordingly, in the calculation, the error in determining S, α, αD, and αS was 15, 10, 20, and 30%, respectively.

Measurement of the permeability of gas mixtures O2/N2 of composition ~29/71 (similar in composition to air) and CO2/CH4 of composition ~62/38 (composition close to biogas [22] with a high content of carbon dioxide) was carried out by the differential method on a gas chromatographic installation at temperature 20–22°С and pressure 1.15 atm. A stationary flow of a mixture of gases at atmospheric pressure washed the inlet surface of the film, while the penetrated gas flow was entrained by the carrier gas, which was helium. The partial pressure of the penetrant in the flow after the membrane was negligible compared to the pressure before the membrane. The permeability coefficients were calculated from the concentration of the penetrant in the carrier gas stream and the velocity of this stream. The penetrant concentration was determined according to the area of the characteristic peak on the chromatogram and the previously obtained calibration straight line for each of the gases.

Sorption measurements were carried out by the volumetric method with chromatographic detection using an original setup [23]. A metal tube with an inner diameter of 2 mm and a length of 90 mm was used as a sorption cell (loop), into which a polymer film of a known mass cut into strips was placed. The sorption volume was prepared by evacuating the loop. Then, the sorption volume with the polymer film was saturated with gas at a certain pressure. The moment of saturation of the sample was determined as follows: gas is supplied to the loop with the sample at a certain pressure and held for 5 min, then the amount of gas is detected in the chromatograph, the experiment is repeated, increasing the holding time by 5 min, until the chromatograph detector signal changes from increase in exposure time. After complete saturation of the sample, the amount of gas in the cell was detected using a thermal conductivity detector of a KristalLux-4000 chromatograph. The amount of gas sorbed in the polymer film was determined based on the calculations described [23]. Based on the obtained data, sorption isotherms were constructed and the solubility coefficient was calculated from the slope of the initial section of the isotherm (0.1–2 atm).

RESULTS AND DISCUSSION

Gas Transport Properties of PIs

Table 3 shows the coefficients of permeability, diffusion, and solubility for the films of the investigated PIs.

Table 3. Coefficients of permeability (P, Barrer), diffusion (D × 108, cm2/s), and solubility (S, cm3(STP)/cm3/atm)) of PI films
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According to Table 1, the permeability coefficients of O2, N2, and CH4 for both PIs obtained in this work and in [16, 17] for the same PIs and gases (Table 2) was found to be almost identical. The D and S data obtained here (Table 3) and reported [16, 17] (Table 2) for the same PIs and gases also coincide within the error. Therefore, for the PI samples studied in this work and those studied [16, 17], it is possible to check the correlations of D with the square of the effective kinetic diameter and S with the Lennard–Jones potential, which should be linear in semilogarithmic coordinates [24]. These correlations are shown in Fig. 1.

Fig. 1.
figure 1

Correlations of D with the square of the effective kinetic diameter [24] for (a) PI-1 and (b) PI-2, as well as S with the Lennard–Jones potential [24] for (c) PI-1 and (d) PI-2 in semilogarithmic coordinates.

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As can be seen from Fig. 1, for both PIs, linear correlations D with the square of the effective kinetic diameter (Figs. 1a and 1b) hold for all gases (diamonds) except for butane (squares), and linear correlations S with the Lennard–Jones potential (Figs. 1c and 1d) are valid for all gases. Consequently, the diffusion coefficient of butane for both PIs is overestimated, which is possible in the case of PI plasticization with butane, and which leads to an increase in P for butane (Table 3). At the same time, the plasticization of PI-2 is higher than that of PI-1, which is understandable given that PI-1 contains hexafluoroisopropylidene groups, since it is known that fluorine-containing polymers are significantly less plasticized by hydrocarbons and organic vapors than polymers that do not contain fluorine in the chemical structure of the elementary link [25].

The selectivity of gas separation, the selectivities of diffusion and solubility are presented in Table 4. Since the solubility of C2–C4 hydrocarbons is higher than that of methane, the corresponding solubility selectivity values are significantly less than 1.

Table 4. Selectivity of gas separation (α = Pi/Pj), selectivities of diffusion (αD = Di/Dj) and solubility (αS = Si/Sj) of various gas pairs for PI films
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As can be seen from Table 4, the gas separation selectivity for the O2/N2 gas pair coincides with the data reported [15] and [16, 17]. The diffusion selectivity for the O2/N2 gas pair for PI-2 coincides with the data reported [16, 17] and is slightly higher than the data reported [15]. The gas separation selectivity of both PIs for the CH4/C2H6 gas pair is close to 1, which is close to the data for PVTMS [26–29], while P(CH4) for PVTMS (13 Barrer) occupies an intermediate position between PI-1 and PI-2 (Tables 2, 3). The diffusion selectivity for the CH4/C2H6 gas pair, as well as the selectivity of CH4/C3H8 gas separation (Table 4), are also close to the data for PVTMS (7.7) [26–29]. At the same time, for PI based on dianhydride 6FDA and diamines with bulky substituents, such as trimethyl m‑phenylenediamine and tetramethyl p-phenylenediamine [18], at comparable (Table 3) P(C3H8) values (2.7 and 4.3, respectively) [18, 26]), the CH4/C3H8 selectivities calculated from the CH4 data of the same authors [26, 29] were found to be slightly higher (6.6 and 9.6, respectively) than for PI-1 and PI-2 (Table 4). The D(C3H8) values for the same PI based on 6FDA dianhydride and trimethyl m-phenylenediamine or tetramethyl p-phenylenediamine [18] are an order of magnitude higher (0.15 and 0.27, respectively [18, 26]) than those for PI-1 and PI-2. In this regard, the diffusion and solubility selectivities of CH4/C3H8 for PI-1 and PI-2 (Table 4) were found to be significantly higher than for structurally similar PIs calculated from the data for CH4 obtained by the same authors [26, 29].

Gas Mixtures

The data obtained for mixtures of gases and their comparison with data for individual gases are presented in Table 5.

Table 5. Permeability of mixtures of gases compared with the permeability of individual gases for polyimides PI-1 and PI-2
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As can be seen from Table 5, the data on the PI-1 permeability for the O2/N2 gas mixture do not differ from the data for individual gases obtained here (*) and reported [16, 17] (Table 2). The separation selectivity for the O2/N2 gas mixture is similar to the separation selectivity for individual gases. For PI-2, the P values for the O2/N2 gas mixture are somewhat lower than for the individual gases obtained here (*) and reported [16, 17] (Table 2). However, the separation factor for this mixture of gases remains unchanged. For PI-1, the P(CO2) values for the CO2/CH4 gas mixture are close to the data [15], but the P(CH4) values were found to be slightly lower than those obtained in this work (*) and reported [15–17], which leads to some increase in the separation factor of the CO2/CH4 gas mixture. For PI-2, the P(CO2) and P(CH4) values for the CO2/CH4 gas mixture are lower than for individual gases (Table 2). However, the relative decrease in P(CH4) is higher, which, as in the case of PI-1, leads to an increase in the selectivity of separation of the CO2/CH4 gas mixture. Possibly, in the case of a CO2/CH4 gas mixture, high CO2 solubility factors lead to competitive gas sorption, which, in turn, leads to an increase in the solubility selectivity and, consequently, to an increase in the gas separation selectivity.

Sorption of Gases

Sorption isotherms of O2, N2, and CH4 gases are shown in Fig. 2; the processing data of isotherms in comparison with the data obtained for the indirect determination of the solubility coefficients according to the equation S = P/D, are present in Table 6.

Fig. 2.
figure 2

Isotherms of sorption of O2, N2, and CH4 for PI-1 and PI-2.

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Table 6. Processing data of sorption isotherms in comparison with data obtained for indirect determination of solubility coefficients according to the equation S = P/D
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As can be seen from the sorption isotherms in the pressure range from 0 to 10 atm, the methane sorption isotherms for both polymers have a pronounced non-linear character; however, there are not enough data to process the isotherm within the framework of the double sorption model. Oxygen sorption isotherms even at pressures above 8 atm begin to deviate from linearity, and only nitrogen sorption isotherms have an obvious linear character. Perhaps this behavior is associated with the large size of the free volume elements, as evidenced by the high values of the solubility coefficients (Table 6).

As can be seen from Table 6, the values of the solubility coefficients obtained by the direct method from the sorption isotherms for both gases and polymers, within the limits of the determination error, generally coincide with the data obtained by the indirect method from the permeability and diffusion coefficients both in this work and reported [15–17]. Consequently, for PI-1 and PI-2, the values of the solubility coefficients do not depend on the method of determination and are close to equilibrium values.

CONCLUSIONS

The transport parameters of C1–C4 hydrocarbons studied in this work through films based on 6FDA-DETDA (PI-1) and BPDA-DETDA (PI-2) polyimides indicate the appearance of the effect of plasticization of polymers with butane. The effect is especially noticeable for PI-2, which may be due to the fact that, unlike polyimide PI-1, it does not contain hexafluoroisopropylidene groups.

The permeabilities of gas mixtures O2–N2 (29 : 71 vol/vol) and CO2–CH4 (62 : 38 vol/vol) were measured and no significant changes in gas separation parameters were shown as compared to individual gases. A slight increase in the separation factor for the CO2–CH4 mixture was noted, which is due to a decrease in the methane permeability coefficient. Presumably, this effect is associated with the competitive sorption of gases in this mixture.

Sorption experiments have shown that for polyimides PI-1 and PI-2, the methane sorption isotherms are of a pronounced non-linear nature, and, in addition, an insignificant non-linearity is observed for oxygen at 8 atm. This behavior of the sorption isotherms may mean that these polyimides have a large free-volume element size, which is indirectly confirmed by the values of the solubility coefficients.