Determination of Gas Transport Coefficients of Mixed Gases in 6FDA

Article pubs.acs.org/Macromolecules

Determination of Gas Transport Coefficients of Mixed Gases in 6FDATMPDA Polyimide by NMR Spectroscopy Leoncio Garrido,* Carolina García, Mar López-González, Bibiana Comesaña-Gándara, Á ngel E. Lozano, and Julio Guzmán* Instituto de Ciencia y Tecnología de Polímeros, Consejo Superior de Investigaciones Científicas (ICTP-CSIC), Juan de la Cierva 3, 28006 Madrid, Spain ABSTRACT: The solubility and diffusion coefficients of pure carbon dioxide and its mixtures with methane, ethylene, and propylene in poly(4,4′-hexafluoroisopropylidene diphthalic anhydride-2,3,5,6-tetramethyl-1,4-phenylenediamine) (6FDA-TMPDA) membranes were determined with proton and 13C NMR spectroscopy and pulsed-field gradient NMR, respectively. In addition, the solubility and permeability of the pure gases in the polyimide membranes were also measured by sorption and permeation methods. The results showed that NMR measurements on pure gases are very reproducible and in relatively good agreement with those determined by the other methods. Furthermore, the NMR method allows the independent measurement of the solubility and diffusion coefficients for each component in mixtures of two or three gases and subsequently the gas permeability. The main conclusion of this work is that NMR spectroscopy is a suitable tool to determine all transport coefficients of multicomponent gas mixtures in polymer membranes, provided that gas molecules contain NMR observable nuclei.

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example is the flux depression of gases such as CO2 in the presence of water vapor, which behaves as a condensable gas with an outstanding solubility coefficient in most polymers.7−9 Another system which has deserved numerous studies is the pair CO2/CH4 because one of the most promising applications of polymer membranes is the separation of CO2 from natural gas and from flue gases.10 As a rule, flux and selectivity are lower for gas mixtures than those calculated from pure gases permeation measurements.11,12 The presence of other hydrocarbons, particularly aromatic hydrocarbons which are together with CH4 in the stream from gas wells, does lead to a significant drop in selectivity of CO2/CH4. In this regard, while cellulose acetate membranes undertake a low reduction of selectivity, polyimide membranes experience a great loss of selectivity for CO2/CH4 when other hydrocarbons are present.13,14 The pressure method is widely used to determine simultaneously the three transport coefficients of pure gases in polymer membranes. For mixed gases, the method requires the coupling with an analytical technique, such as mass spectrometry or gas chromatography, if values of transport coefficients for each gas are needed. NMR techniques allow the simultaneous detection of the various chemical moieties present in a sample and probe their surroundings at the molecular level. Thus, it is feasible to identify and assess the concentration of a given functional

INTRODUCTION Over the past 20 years, polymers have drawn increasing attention as materials for the fabrication of membranes required in gas separation processess.1−5 However, while they are promising materials, the design of membranes that fulfill the requirements for these applications to overcome present limitations and realize their full potential is needed. In this context, the measurement of molecular transport parameters of gas mixtures in polymer membranes would resemble more closely the membrane working conditions and may facilitate the preparation of new polymer materials for this application. Knowledge of the behavior of a gas in a mixture could provide essential information to aid molecular simulation methods and attain a better understanding of transport phenomena in these systems. Although most of the basic studies on gas polymer membranes reported so far have been conducted on single gases, it is known that results drawn out from permeation of gas mixtures through membranes compare rather poorly with those attained from single gas permeation measurements. This is because of the effect of second components on the sorption and permeation in glassy polymers.6 In fact, minor concentration of other components may influence significantly on the separation of gases by glassy polymer membranes. The presence of other components facilitates the competition of mixed penetrants for Langmuir sites or unrelaxed free volume of glassy polymers in such way that plasticization can lead to a relaxation of the glassy matrix and loss of the inherent discrimination and sieving ability of the membrane. A typical © XXXX American Chemical Society

Received: February 21, 2017 Revised: April 7, 2017

A

DOI: 10.1021/acs.macromol.7b00384 Macromolecules XXXX, XXX, XXX−XXX

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Membranes were prepared by casting filtered solutions on balanced glass plates which were fixed to a heating plate. N-Methyl-2pyrrolidinone (NMP) was used as solvent. Most solvent was removed slowly over 24 h at 80 °C. Polymer films were then stripped off, and the rest of the solvent was removed in a vacuum oven following the heating protocol: 180 °C/24 h and 24 h at 250 °C. A negligible amount of solvent remained in the membranes, as confirmed by thermogravimetric analysis (TGA). NMR Gas Solubility Measurements. To perform the NMR measurements of a given gas solubility, ∼0.1 g of polymer membrane strips less than 2 mm wide and approximately 1.5 cm long were placed inside a 5 mm o.d. NMR tube adapted for studies at moderately pressurized gases. In addition, a standard consisting of a sealed glass capillary with a known amount of labeled [13C(1)] acetic acid was placed in the tube. Prior to fill the tube at a given pressure with [13C]O2, CH4, C2H4, or C3H6, the air was removed by vacuum. For gas mixtures, the gases were loaded sequentially to specified partial and total pressures. Unless indicated otherwise, the total gas pressure used in these experiments was in the range of 1−5 bar to facilitate the measurements with adequate signal-to-noise ratio in a reasonable amount of time. The gas pressure was monitored with a transducer working in the range 0−10 bar. The NMR measurements were performed in a Bruker Avance 400 spectrometer (Bruker BioSpin GmbH, Rheinstetten, Germany) equipped with a 89 mm wide bore and a 9.4 T superconducting magnet (1H and 13C Larmor frequencies at 400.14 and 100.61 MHz, respectively). The reported data were acquired at 30 ± 0.1 °C with a Bruker diffusion probehead Diff60. Inserts for 5 and 10 mm o.d. NMR tubes tuned to proton and 13C were used, respectively. Typical 90° radio-frequency (rf) pulse lengths were 6.3 μs for protons and 12.5 μs for 13C. For each nucleus and gas, an inversion−recovery pulse sequence was used to estimate the longitudinal relaxation times, T1, of sorbed gas or gas mixture. Solubility measurements were performed as described previously.27 Briefly, 1H and 13C NMR spectra of samples were acquired using a single pulse excitation sequence with a repetition rate ≥5 × T1. The 13C NMR spectra were referenced to 13C(1) acetic acid (178.1 ppm) and the 1H NMR spectra to the methyl protons of acetic acid (2.10 ppm), secondary to tetramethylsilane (TMS, 0.0 ppm) in both cases. For each spectrum, gas peak areas were measured and normalized to the corresponding peak area of the standard (methyl protons for 1H NMR spectra and 13C(1) for 13C NMR spectra). When a spectrum showed significant peak overlap in the region of interest, spectral deconvolution was used to determine the individual peak areas. PFG NMR Measurements. The samples prepared as described above were also used to determine the diffusion coefficients of sorbed pure and mixed gases. For these measurements, a pulsed field gradient stimulated spin echo pulse sequence was used, as shown by Stejskal et al.28 The echo time between the first two 90° rf pulses, τ1, was 3.39 ms. The apparent diffusion coefficient of each gas, D, was measured at a diffusion time, tD, of 80 ms. The length of the field gradient pulses, tg, was 2 ms. For these experiments, the amplitude of the gradient pulses varied from 0 up to a maximum value of 20 T m−1. The repetition rate was ≥5 × T1, and the total acquisition time ranged from about 4 to 28 h. The diffusion coefficients were calculated by fitting the experimental data to the corresponding exponential function. Prior to these measurements, the temperature at the sample volume in the probe head and the field gradient were calibrated as described previously.24 Permeation and Sorption Measurements. In addition, permeation measurements were carried out to determine the diffusion and permeability coefficients, and the sorption method was used to assess the gas solubility coefficients at different pressures. A laboratory-made permeator, described elsewhere,29,30 was used for permeation measurements. Briefly, it consists of a gas cell in which the polymer membrane is placed in the center, separating the highpressure or upstream chamber from the low-pressure or downstream chamber. High vacuum was generated in the permeation device by means of an Edwards molecular turbo-pump, and the whole

group in a sample. 13C NMR has been used to determine the solubility of CO2 in aqueous solutions.15,16 Moreover, pulsedfield gradient (PFG) NMR methods have been extensively used to investigate molecular diffusion in a wide variety of systems17−20 and, in particular, in polymer membranes.21−25 Therefore, NMR permits the direct determination of gas solubility (S) and diffusion (D) coefficients in different media and since the permeability (P) is defined as the product between both coefficients; all the gas transport coefficients could be determined from NMR measurements. This has been demonstrated in our previous work26,27 for a pure gas, C-13labeled carbon dioxide, in membranes consisting of glassy, semicrystalline, and amorphous polymers. However, the actual working conditions of membranes in gas industrial separation processes involve gas mixtures. Therefore, we considered expanding the initial work and test the NMR method with mixtures that include other gases of interest, such as hydrocarbons. The main goal of this work is to determine by NMR spectroscopy the individual gas transport coefficients of gas mixtures in polymer membranes. Specifically, the solubility, diffusion, and permeability coefficients of pure carbon dioxide and its mixtures with methane, ethylene, and propylene in 6FDA-TMPDA polyimide membranes were evaluated. Polyimides exhibit good gas separation properties, and in particular, 6FDA-TMPDA is a high-performance polyimide having good mechanical properties, high Tg and thermal degradation temperature, and also it shows very high permeability to CO2. Thus, this polymer has been thoroughly studied in the field of gas separation membranes for several industrial applications, which facilitates the comparison between the outcome of the NMR measurements and the results obtained using absorption and permeation methods.

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EXPERIMENTAL SECTION

Materials. The [13C(1)]-labeled 99% acetic acid was of Euriso-top, Gif-sur-Yvette, France; the [13C]O2-labeled 99% was of Cambridge Isotopes Laboratories, Andover, MA; and CO2 (99.998%), methane (99.9995%), ethylene (99.95%), and propylene (99.95%) were from Praxair (Madrid, Spain). The polyimide membranes were prepared as described elsewhere.26 Briefly, the polyimide, whose chemical structure is given in Scheme 1,

Scheme 1. Repeating Unit Chemical Structure of the Polyimide 6FDA-TMPDA

was synthesized from hexafluoroisopropylidene diphthalic anhydride (6FDA) and 2,3,5,6-tetramethyl-p-phenylenediamine (3,6-diaminodurene, TMPDA) by the general two-step polyimidation procedure. The inherent viscosity of the polyimide (η = 0.93 dL/g) was determined at 25 °C with an Ubbelhode viscometer in N-methyl-2-pyrrolidinone (NMP) solutions at a concentration of 0.5 g/dL. Gel permeation chromatography analyses were carried out with a device equipped with Resipore (250 × 4.6 mm, 3 μm nominal particle size) Polymer Laboratories columns. DMF containing 0.1% LiBr was used as solvent. Measurements were performed at 70 °C at a flow rate of 0.3 mL/min using an IR detector. The number-average molecular weight, Mn, of the polyimide was 72,300 with a polydispersity index of 2.8, using polystyrene standards as reference. B

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Macromolecules arrangement was thermostatically controlled at 30 °C by means of a water bath. Before performing the measurements, vacuum was maintained overnight in the permeation device to remove the last traces of solvent and gas in the membrane and to reach a low pressure (about 10−6 bar). Subsequently, gas contained in a reservoir was allowed to flow into the downstream chamber, and the evolution of the pressure of the gas in this chamber was monitored with a MKS Baratron type 627B absolute pressure transducer working in the pressure range 10−4−1 mmHg. Pressure in the upstream chamber was measured with a Gometrics transducer of 0−10 bar range to control the gas pressures at which the experiments are performed, which varied between 0.1 and 5 bar in this work. For each gas, three independent experiments were performed. Membranes with thickness of 160 ± 5 μm were used. The permeability and diffusivity coefficients were calculated from the curves measuring the pressure increase at the downstream side, recorded at intervals of 1 s. For each experiment, the intake of air into the evacuated downstream chamber was measured as a function of time and subtracted from the curves representing the pressure of permeant against time. Sorption measurements were carried out at 30 °C to determine the concentration of gas in the polyimide membranes at different pressures. The experimental device used to perform these experiments has been extensively described elsewhere.26,31 An experimental device consisting of a gas reservoir separated from a sorption chamber by a valve was used.31 The reservoir and the sorption chamber equipped respectively with Gometrics (0−35 bar) and Ruska model 230 (0−35 bar) pressure sensors were immersed in a thermostat at the temperature of interest. At the beginning, the sample was placed inside the sorption chamber and exposed to vacuum overnight, at 30 °C, to remove air. Then, gas was introduced into the reservoir at a given pressure, and once it reached the temperature of interest, the valve separating the reservoir and the sorption chamber was suddenly opened and closed. The decrease of the gas pressure in the sorption chamber was recorded every second via a PC. After reaching a constant pressure, an additional amount of gas was introduced into the sorption chamber and, then, allowed to reach equilibrium again, and so forth. The sorption measurements at 30 °C and several pressures were performed. Pressure leaks and the adsorption of gas in the chamber walls were measured previously in blank experiments.

Figure 1. Sorption isotherms of CO2, CH4, CH2CH2, and CH2 CH−CH3 at 30 °C. The isotherms of carbon dioxide are obtained from permeation experiments.

The solubility of the gases (especially of the most condensing gases) is described by the well-known dual-mode model, which explains its pressure dependence31,32

C = kDp +

(2)

where C is the total concentration of gas in the membrane at pressure p, kD is the solubility coefficient of the gas in the continuous phase of the glassy material (Henry coefficient), C′H is the concentration of gas immobilized in Langmuir sites, and b is an affinity parameter accounting for the sorption/desorption ratio. The values of the different parameters for the four gases used in this study were determined by fitting eq 2 to the sorption data (Figure 1), and the obtained results are shown in Table 1. Here, it should be pointed out that the parameters Table 1. Values of kD, b, and C′H Obtained a 30 °C for the Gases Studied in 6FDA-TMPDA Membranes

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RESULTS AND DISCUSSION Solubility, Diffusion, and Permeability Coefficients by Sorption and Permeation Methods. The solubility coefficient of the different gases in the polyimide was determined from sorption measurements using the experimental device indicated above. The concentration of gas, in cm3 (STP)/cm3 of sample, is given by p⎞ 22414ρV ⎛ pi C= ⎜ − e⎟ RTm ⎝ z i ze ⎠

C H′ bp 1 + bp

gas

kD × 102 (cm3 (STP) cm−3 cmHg−1)

b × 102 (cmHg−1)

C′H (cm3 (STP) cm−3)

2.1 15.4

0.5 0.7

16.6 55.1

4.6 14.5

2.0 15.4

37.7 36.4

methane carbon dioxide ethylene propylene

corresponding to carbon dioxide sorption are determined from permeation experiments. In this case, the sorption technique is not an appropriate method since the very fast absorption of CO2 tends to underestimate the values of those parameters. Therefore, the sorption isotherms and, consequently, the parameters of the Langmuir equation are different from those we reported in a previous work.26 In the case of mixtures of n gases, the value of C for gas j, Cj, is given by

(1)

where m and ρ are respectively the mass and density of the sample, V is the unoccupied volume of the sorption chamber, R and T are the gas constant and absolute temperature, and p and z are respectively the pressure and compressibility coefficient of the gas. The subscripts i and e refer respectively to the initial and equilibrium conditions. The pressure dependence of the concentration of carbon dioxide, methane, ethylene, and propylene in 6FDA-TMPDA polyimide is shown in Figure 1. The curves exhibit the usual pattern displayed by the sorption of gases in this kind of material (glassy polymers); that is, the isotherms are concave with respect to the abscissa axis, showing a rather sharp increase with increasing pressure in the low-pressure region attenuated as pressure increases.

Cj = k Djpj +

C H′ jbjpj n

1 + ∑ j = 1 bjpj

(j = 1, 2, ..., n) (3)

where pj represents the partial pressure of gas j (j = 1, 2, ..., n) and the other symbols retain the meaning indicated above for each gas. Although, permeation measurements with mixed gases were not performed, from the results shown in Table 1 it is possible to estimate the solubility coefficients of the gases, C

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Table 2. Transport Coefficients of Carbon Dioxide, CH4, C2H4, and C3H6, at 30 °C, in 6FDA-TMPDA Membranes As Determined by Sorption, Permeation, and NMR gas

pa (bar)

S (cm3 (STP) cm−3 cmHg−1)

SNMR (cm3(STP) cm−3 cmHg−1)

D × 108 (cm2 s−1)

DNMR × 108 (cm2 s−1)

Pb (Barrer)

PNMR (Barrer)

CO2

4.01 2.37 2.23 2.23 2.12 0.48 4.24 3.72 2.17 2.16 2.12 0.48 2.30 2.20

0.277 0.325 0.330 0.330 0.335 0.461 0.053 0.055 0.066 0.067 0.067 0.091 0.214 0.355

0.229 0.271 0.273 0.279 0.300 0.454 0.049 0.046 0.060 0.050 0.063 0.076 0.161 0.266

18.0 18.2 18.1 15.6 15.4 13.7 5.9 6.7 5.6 5.6 5.6 5.4 4.7 2.0

28.3 24.1 27.3 22.4 22.9 14.1 5.5 7.0 6.8 7.0 6.2 7.0 4.4 2.2

499 591 598 515 516 632 31.1 36.9 37.2 37.3 37.5 49.2 100 70.9

648 653 745 625 687 640 27.0 32.2 40.8 35.0 39.1 53.2 70.8 58.5

CH4

C2H4 C3H6

Pressure at 30 °C; [13C]O2 was used in NMR measurements, CO2 in sorption and permeation. b1 Barrer is equivalent to 10−10 cm3 (STP) cm cm−2 s cmHg−1. a

−1

Sj = Cj/pj (j = 1, 2, ..., n), for mixtures at very different partial pressures, and the results can be compared with those determined by NMR spectroscopy. On the other hand, the pressure procedure indicated in the experimental part has been used to determine the transport coefficients of the membranes. In permeation measurements, the time dependence of the gas pressure in the downstream chamber is deduced by the integration of Fick’s second law using appropriate boundary conditions33 p(t ) = 0.2786

pALST ⎡ Dt 1 2 ⎢ − − 2 V ⎢⎣ L2 6 π

∞

∑ n=1

experiments, represented as a function of the pressure in the upstream chamber, follow straight lines for all the different gases studied, indicating the practical independence of the permeability coefficients in the range of pressures analyzed. Once permeability and diffusion coefficients are determined, the solubility coefficients can be calculated directly from the P/ D ratio. In Table 2, the values of S and P for the pure gases are shown in the third and seventh columns, respectively. The diffusion coefficients were calculated by means of the ratio between the values of P and S determined by permeation and sorption, respectively. Solubility of Pure and Mixed Gases Measured by NMR. The solubility of pure gases ([13C]O2, CH4, C2H4, and C3H6) in 6FDA-TMPDA polyimide membranes was assessed prior to study the corresponding gas mixtures. Although the measurement of the solubility of pure [13C]O2 in this polymer with NMR has been reported by us,26 it was once again determined in all the experiments carried out in this work since, as indicated earlier, the sorption method underestimates the values of the Langmuir coefficients when very fast gas sorption occurs. The 13C NMR spectra of the polymer samples loaded with [13C]O2 and acetic acid standard exhibited two peaks, as illustrated in Figure 2. One peak corresponding to the 13C signal of the carboxyl group of acetic acid at 178.1 ppm and a second peak associated with the sorbed [13C]O2 in the 6FDATMPDA membrane, centered at 125.5 ppm. The value of 13C T1 of sorbed gas in the membranes studied was ∼2.6 s. To determine the amount gas sorbed in the membrane and hence its solubility at 30 °C, the peak area of carbon dioxide (125.5 ppm) was normalized to the peak area of the carbonyl carbon of the standard. The results are shown in Table 2 (fourth column). Figure 3 shows the 1H NMR spectrum corresponding to samples of 6FDA-TMPDA polyimide loaded with pure CH4, C2H4, and C3H6 and the standard. The peaks observed are associated with the sorbed gases (methane: −0.99 (s) ppm; ethylene: 4.23 (d) ppm; and propylene: 0.55 (s) and 4.19 (m) ppm) and to the methyl protons of the standard at 2.10 (s) ppm. Free gas within the active volume of the rf coil was not detected with the experimental conditions used. Generally,

⎛ Dn2π 2t ⎞⎤ −1 exp⎜ − ⎟⎥ 2 ⎝ n L2 ⎠⎥⎦ (4)

In this equation, p(t) and p, which denote the pressures of gas in the downstream and upstream chambers, respectively, are given in cmHg; A and L represent the area and thickness of the membrane in cm2 and cm, respectively; the volume of the downstream chamber, V, in cm3, and D and S are the diffusion and solubility coefficients in cm2/s and cm3 gas (STP)/(cm3 polymer cmHg), respectively. Once steady-state conditions are reached, the time dependence of the pressure in the downstream chamber can be written as p(t ) = 0.2786

pALST ⎛ Dt 1⎞ ⎜ − ⎟ 2 V ⎝L 6⎠

(5)

Plots of p(t) against t in the steady state are straight lines intercepting the abscissa axis at D=

L2 6θ

(6)

where θ is the time lag, and therefore the diffusion coefficient can be obtained from eq 6. By assuming that the permeability coefficient, P, is the product of the solubility and the diffusion coefficients, the value of P in Barrer [1 Barrer [10−10 cm3 (STP) cm/(cm2 s cmHg)]] can be obtained from eq 7: P = 3.59

⎛ d p(t ) ⎞ VL lim ⎜ ⎟ pAT t →∞⎝ dt ⎠

(7)

where V, L, and A are given in units of the cgs system and p and p(t) in cmHg. The values of the stationary flux in the downstream chamber, limt→∞(dp(t)/dt), for the different D

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After measuring the diffusion coefficients of pure sorbed gases (results described later), the second gas was loaded up to the specified final pressure, and the measurement of the solubility and diffusion coefficients of the mixed gases in the polyimide membranes was performed at equilibrium conditions. The 1H and 13C NMR spectra of samples with the gas mixture of interest were acquired sequentially. The solubility coefficients of CH4, CH2CH2 or CH2CH−CH3, and [13C]O2 in the polyimide membranes were determined by comparing the areas of the peaks associated with the reference compound (13C(1)-labeled acetic acid) and the sorbed gases in the corresponding 1H and 13C NMR spectra. A mixture of three gases ([13C]O2, CH4, and CH2CH2) was also analyzed to show the viability of the method with more complex mixtures. The results are summarized in Table 3 (fourth column). It was observed that the outcome of the measurements was independent of the order in which the gases were loaded. The values of the solubility coefficient of gas mixtures calculated with the Langmuir coefficients (eq 3) are shown in Table 3 (third column). It is observed that in the case of highly soluble gases the solubility coefficient decreases with increasing gas partial pressure in pure gases and mixtures. In the case of pure CH4, the solubility coefficient tends to decrease with increase gas pressure while in mixtures no significant change is observed. Diffusion of Pure and Mixed Gases Measured by NMR. The diffusion coefficient of CH4, CH2CH2, CH2 CH−CH3, and [13C]O2 (pure and mixed) in 6FDA-TMPDA membranes was determined with a PFG NMR stimulated spin echo sequence.28 Briefly, in this type of NMR measurement, the magnetic labeling of nuclei is accomplished by applying two field gradient pulses spaced by the so-called diffusion time. In the absence of motion, the loss of phase coherence of the NMR signal caused by the first gradient pulse would be compensated by the second gradient pulse, but this would not be the case if molecular diffusion occurs during the diffusion time. For illustrative purposes, 1 H and 13 C PFG NMR spectra corresponding to CH4 and [13C]O2 sorbed in 6FDA-TMPDA are shown as a function of the amplitude of the field gradient in Figure 4. The echo attenuation can be written as28

Figure 2. 13C NMR spectrum corresponding to a sample of 6FDATMPDA loaded with 2.12 bar of [13C]O2 at 30 °C. In addition to the resonance associated with [13C(1)] of acetic acid (178.1 ppm), sorbed [13C]O2 is observed at 125.5 ppm.

A(g ) = A(0) exp[− (bNMR D NMR )]

(8)

where A(g) and A(0) are the amplitude of the echo in the presence of a gradient pulse with amplitude g and 0, respectively, bNMR = (γgtg)2(tD − tg/3) where γ is the gyromagnetic ratio of the nucleus being observed, tD and tg are respectively the diffusion time and the duration of the gradient pulse, and DNMR is the diffusion coefficient of the sorbed gas. This equation describes well the situations where a single diffusion mechanism occurs or those with multiple components but exhibiting similar diffusional behavior. As indicated earlier, the transport of gases in glassy polymers is interpreted according to a dual model. Thus, considering this model with two diffusion coefficients, the NMR diffusion data were analyzed using the sum of two decreasing exponentials according to a modification of eq 8 in the form

Figure 3. 1H NMR spectra corresponding to samples of 6FDATMPDA membranes in the presence of CH4 (2.12 bar), CH2CH2 (2.30 bar), and CH2CH−CH3 (2.20 bar) at 30 °C and with a standard of CH3[13C]OOH 99% labeled. The peaks in the region between −2 and 6 ppm correspond to the protons of sorbed gases: methane (−0.99 ppm), ethylene (4.23 ppm), and propylene (0.55 and 4.19 ppm); the peak at 2.10 ppm is associated with the methyl protons of the standard.

peaks of sorbed gases showed a shift of 1−1.2 ppm to higher field with respect to those of free gases. Proton T1 relaxation measurements showed the largest value for the protons of sorbed methane gas, ∼8.7 s, and the ethylene and propylene protons exhibited values of relaxation times of 5.8 s. As described previously for carbon dioxide, the peak areas of methane (−0.99 ppm), ethylene (4.23 ppm), and propylene (0.55 ppm) protons were normalized to the peak area of the methyl protons of the standard to determine the solubility of the hydrocarbons in the membranes (Table 2, fourth column).

A(g ) = A(0)[φ exp(− bNMR DD) + (1 − φ) exp(− bNMR DH)] (9)

where φ represents the fraction of gas in the continuous phase and (1 − φ) is the corresponding fraction in the Langmuir sites. E

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Macromolecules Table 3. Transport Coefficients of Gas Mixtures, at 30 °C, in 6FDA-TMPDA Membranes As Determined by NMR gas mix 13

CH4/[ C]O2

C2H4/[13C]O2 C3H6/[13C]O2 CH4/C2H4/[13C]O2 a

pa (bar)

Sb (cm3 (STP) cm−3 cmHg−1)

SNMR (cm3 (STP) cm−3 cmHg−1)

DNMR × 108 (cm2 s−1)

PNMR (Barrer)

4.24/0.40 2.15/1.37 2.14/2.23 2.12/1.97 1.39/2.12 0.48/4.01 2.30/1.29 1.82/2.37 2.20/1.46 1.92/2.23 1.12/1.01/1.24

0.050/0.291 0.054/0.306 0.049/0.283 0.050/0.289 0.052/0.299 0.046/0.270 0.191/0.228 0.196/0.231 0.349/0.168 0.372/0.170 0.043/0.254/0.261

0.041/0.453 0.040/0.311 0.038/0.275 0.032/0.285 0.046/0.267 0.045/0.216 0.122/0.273 0.141/0.196 0.301/0.199 0.291/0.158 0.033/0.214/0.285

6.4/16.4 10.3/21.6 12.5/24.8 10.3/22.4 9.8/22.7 13.4/29.5 5.7/23.3 7.2/27.2 1.8/30.6 2.4/32.2 10.5/4.3/19.5

26.2/743 41.2/672 47.5/682 33.0/638 45.1/606 60.3/637 69.5/636 102/533 54.2/609 69.8/509 34.6/92/555

Partial pressures at 30 °C. bValues of the solubility coefficient calculated with the Langmuir coefficients (eq 3).

Figure 4. 1H and 13C PFG NMR spectra corresponding to (left) CH4 and (right) [13C]O2 sorbed in a 6FDA-TMPDA membrane at 30 °C and total pressure of 4.09 bar (pCH4: 2.12 bar; p[13C]O2: 1.97 bar), obtained with a diffusion time, tD, equal to 80 ms. The duration of the gradient pulse, tg, was 2 ms. The amplitude of the field gradient, g, in T/m, was varied between 1.10 and 4.40 for proton and 0.75 and 9.00 for 13C measurements.

The value of DNMR is taken as the weighted sum of corresponding individual values, DD and DH.34 The echo attenuation plots for a mixture of CH4 and [13C]O2 in a 6FDA-TMPDA membrane are shown in Figure 5.

measurements for pure gases in 6FDA-TMPDA membranes are shown in Table 2 (sixth column), and those corresponding to mixed gases are summarized in Table 3 (fifth column). Numerous studies have shown that the dual-mode model describes satisfactorily the steady state flux in permeation measurements, but it has been recognized its limitations to describe the physical behavior of gas molecules in the Langmuir phase. Our initial results suggest that the diffusional behavior of several gases in 6FDA-TMPDA is complex, and to understand it better, additional experimental conditions (i.e., range of operating pressures and diffusion times) and polymer−gas systems should be studied, and other models or refinements of the dual-mode theory should be considered.35−37 Once the S and D coefficients were obtained, the corresponding values of P are then determined using the following equation

Figure 5. Plot of the normalized peak areas vs bNMR corresponding to (a) pure CH4 (open triangles) and mixed CH4 (closed triangles) and (b) mixed [13C]O2 (open circles) sorbed in a 6FDA-TMPDA membrane, obtained with the experimental conditions described in the legend of Figure 4. The solid line represents the fits to eq 8 ([13C]O2) and eq 9 (CH4).

P = S[φDD + (1 − φ)DH]

(10)

and the NMR results, expressed in Barrer, corresponding to pure and mixed gases are shown in the eight column of Table 2 and the sixth column of Table 3, respectively. The comparison between the results obtained with permeation and NMR methods shows a fair agreement for all the transport coefficients, which highlights the suitability of the NMR method to the determination of gas transport in glassy membranes. The approach could be also applicable to

It should be noted that the data for all gases, pure and mixed, but [13C]O2 fitted well to eq 9. In the case of [13C]O2, either pure or mixed, the 13C echo attenuation was well described with a monoexponential function, suggesting that the two components in the membranes studied were indistinguishable in the NMR experiment. The results of the diffusion F

DOI: 10.1021/acs.macromol.7b00384 Macromolecules XXXX, XXX, XXX−XXX

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membranes of semicrystalline and amorphous polymers. Moreover, the method offers the possibility of measuring D and S of each component in a gas mixture, providing that the gas molecules have an NMR observable nucleus (i.e., natural abundance: 1H and 19F; isotopically enriched: 13C and 15N), and the corresponding NMR spectrum is resolved. It should be noted that the intrinsic low sensitivity of NMR might hamper the detection of gases present at very low concentration in a mixture and, generally, in gas barrier polymer materials. Nevertheless, the measurement of solubility coefficients >10−3 cm3 (STP) cm−3 cmHg−1 and diffusion coefficients >10−10 cm2 s−1 should be feasible. The spectrum signal-to-noise ratio could be improved by averaging over increasing time periods, and the measurements could also be performed at higher magnetic fields. Also, the experimental temperature and pressure could be increased. Currently available NMR diffusion probes allow measurements between −40 and 150 °C, and thick walled glass with high-pressure valve NMR tubes enable measurements up to 20 bar. In addition to facilitating the determination of the transport coefficients for each gas in a mixture, the NMR method could provide accurate measurements in membranes with very high values of permeability (i.e., P > 103 Barrer) which may be challenging using other methods. Also, the measurements with this method are not perturbed by the presence of pinholes and other defects in the membranes, such as regional variations in thickness.

REFERENCES

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CONCLUSIONS In summary, an NMR-based method is described that allows the sequential measurement of the solubility and diffusion coefficients of pure and mixed gases in 6FDA-TMPDA membranes. The outcome of the measurements was independent of the order in which the gases were loaded. The NMR diffusion measurements were adequately described by a dual model, and the transport coefficients determined were in good agreement with those obtained by the permeation method. The results support the suitability of the NMR method to measure the separate gas transport coefficients of multicomponent mixtures of gases in glassy polymer membranes.

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Article

AUTHOR INFORMATION

Corresponding Authors

*(L.G.) Tel +34 91 5622900; Fax +34 91 5644853; E-mail [email protected]. *(J.G.) E-mail [email protected]. ORCID

Leoncio Garrido: 0000-0002-7587-1260 Present Address

B.C.-G.: EastChem, School of Chemistry, The University of Edinburgh, David Brewster Road, Edinburgh EH9 3FJ, U.K. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The financial support provided by the Ministerio de Economiá y Competitividad (MINECO) through projects MAT201345071-R and MAT2016-81001-P and the CSIC is gratefully acknowledged. G

DOI: 10.1021/acs.macromol.7b00384 Macromolecules XXXX, XXX, XXX−XXX

Article

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DOI: 10.1021/acs.macromol.7b00384 Macromolecules XXXX, XXX, XXX−XXX