Article pubs.acs.org/IECR
Inverse Gas Chromatographic Study of Sorption Thermodynamics in Thermally Rearranged Polymer Based on 2,2-Bis(3-amino-4hydroxyphenyl)-hexafluoropropane and 4,4′Hexafluoroisopropylidene Diphthalic Anhydride Nikolay A. Belov,*,† Yulia A. Nizhegorodova,† Seungju Kim,‡ Sang Hoon Han,‡ Yuri P. Yampolskii,† and Young Moo Lee*,‡ †
A.V. Topchiev Institute of Petrochemical Synthesis, Russian Academy of Sciences, 29 Leninsky Pr., 119991, Moscow, Russia School of Chemical Engineering and WCU Department of Energy Engineering, College of Engineering, Hanyang University, Seoul, Republic of Korea
‡
S Supporting Information *
ABSTRACT: This work reports the first investigation using the inverse gas chromatography method of a polyimide precursor and the product of its thermal rearrangement (TR polymer), extensively studied earlier. Sorption of gases (CO2, C2H6, C3H8) was studied at the finite dilution regime, while vapors (n-alkanes C7, C8, C10, C14, C16) were investigated at infinite dilution. It was demonstrated that thermal treatment at 450 °C results in a significant increase in the solubility coefficients S for large gas molecules. The absolute values observed for the TR polymer solubility coefficients of solutes are significant and comparable with those for the polymer of intrinsic microporosity (PIM-1), the polymer known by the greatest S values among all of the polymers studied. Sorption thermodynamics in the TR polymer is distinguished by very large and negative mixing parameters: enthalpy h̅E,∞ and entropy sE,∞ . 1 1̅
1. INTRODUCTION Great achievements of membrane gas separation were based traditionally on development of polymeric membrane materials with good permeability and permselectivity.1,2 It is well-known that the permeability coefficients Pi = Di·Si, i.e., include the mobility contribution or the diffusion coefficient Di and thermodynamic contribution or solubility coefficient Si. Accordingly, in the separation factors Pi/Pj, it is possible to partition the contributions of diffusivity selectivity Di/Dj and solubility selectivity Si/Sj. To separate light gases, the diffusivity selectivity plays the most important role, while separation of hydrocarbons is governed by solubility selectivity.3 Until recently, the strategy of the search for advanced membranes implied optimization of the chemical structure of polymers. More recently, it became clear that other approaches are also possible for achieving membrane materials with advanced properties. One such approach involves the introduction of nanoparticles into polymeric matrices obtaining great improvements of the gas permeation parameters, so-called mixed matrix membranes.4 Another efficient approach is based on creation of thermally rearranged polymers (TR polymers) that exhibit extraordinary gas permeability with relevant separation performance.5−8 TR polymer membranes were prepared from precursor polyimides with functional groups at the ortho-positions that were subsequently thermally rearranged into TR polymers that included polybenzoxazoles (PBO), polybenzothiazoles (PBZ), and polybenzimidazoles (PBI). Various physicochemical methods were used to characterize TR polymers including positron annihilation lifetime spectroscopy (PALS)5 (which indicated a strong increase in free © 2013 American Chemical Society
volume in these materials), small-angle X-ray scattering (SAXS),5 BET low temperature nitrogen adsorption,5 Fourier transform infrared spectroscopy (FTIR),9 mass spectroscopy (MS),9 and electron spectroscopy for chemical analysis (ESCA)10,11 for characterization of the structure. Thermal analysis such as differential scanning calorimetry (DSC),9 thermogravimetric analysis with mass spectroscopy (TG-MS),9 and dynamic mechanical analysis (DMA)12 have been used to analyze the conversion condition from precursors into TR polymers. Molecular dynamics (MD) simulation also provided information about nanostructure of TR polymers on an atomistic level.13 Recently, the results of investigation of gas sorption in TR polymers measured using the volumetric (pressure decay) method were reported by Smith et al.14 and by Kim et al.15 Meanwhile, it will be interesting to investigate the thermodynamics of sorption in such materials by means of inverse gas chromatography (IGC). This method has never been applied to TR polymers. IGC is a versatile technique for investigation of thermodynamics of polymers16 and especially of glassy polymers with large free volume.17−19 That method allows an estimation of the solubility coefficients, enthalpies or internal energy of sorption, the activity coefficients, and excess partial Special Issue: Enrico Drioli Festschrift Received: Revised: Accepted: Published: 10467
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the pressure averaged over the length of the chromatographic column and temperature T.28 The values of Fp̅x,T are determined in the following way:
thermodynamic functions (free energy, enthalpy, and entropy), the parameters of the temperature dependence of the activity coefficients. In particular, it has been shown that in the highly permeable glassy polymers the process of mixing of penetrants is characterized by strong exothermic effects and big negative entropy of mixing.19 This method is based on the measurement of the retention times ta of solutes (gases such as CO2 or C3H8) and organic vapors in the column where the studied polymer is coated over an inert support. On the basis of the retention times, it is possible to calculate the specific retention volume Vg that is related to numerous thermodynamic parameters of the systems polymer−solute. An advantage of the IGC method, as compared to gas sorption, is that it permits the study of a range of solutes with much wider variation of the properties (e.g., critical temperature Tc). Thus, application of IGC and a wide range of the solutes indicated that the correlation ln S versus Tc widely used in the literature is only an approximation of more correct correlation ln S versus Tc2.17 From a fundamental point of view, an advantage of IGC is that it gives automatically thermodynamic parameters (e.g., solubility coefficients) at infinite dilution conditions, so no extrapolation is needed. IGC also is an express method and allows one to measure in a wide range of temperatures of sorption and permits one to work with small or brittle polymer samples. One variant of the IGC technique is capable of generating sorption isotherms of gases and vapors in polymers via the shape of a single chromatographic peak. The idea of such an approach had been proposed some time ago.20−23 In the present work, we undertook an investigation using the IGC method for sorption of gases and vapors in the precursor, OH-containing polyimide, and TR polybenzoxazoles (TR PBOs), the product of its thermal rearrangement. As is common in the IGC studies, the gases and vapor solutes are chosen as molecular probes, the term coined by the creator of this method, J. E. Guillet.16 Using a wide range of the sizes of the solutes was necessary to recognize the differences in the solubility coefficients of the TR polymer studied and other polymers.
Fp̅ , T = Fp , Ta × j32 x
K=
V2
=
V r0 m2
ρ2 = Vgρ2
S1(p0 , T 0) =
x
(3)
⎛ 2B13 − v∞ 3 ⎞ exp pin j4 ⎟ ⎜− ⎝ ⎠ RT p0 T
Vgρ2 T 0
(4)
Here, p0 = 1 atm and T0 = 273.2 K are the standard values, while the mixed virial coefficient B13 and the molar volume of the solute ν∞ at infinite dilution (usually, instead ν∞ molar volume V1 of the solute is taken) allow for the solute nonideality. These values are used in accordance with recommendations.30 The value pin is the pressure at the inlet of the column, and parameter j43 is a correction equal to the ratio between the pressure averaged over the sample retention time in the chromatographic column and the pressure at the outlet of the column.26 It is worth noting that eq 4 slightly differs from the original equation reported by Kawakami− Kagawa31 due to a new interpretation of the specific retention volume Vg.26,29 Temperature dependence of solubility coefficient or specific retention volume can be applied to estimate the internal energy of sorption US1 by the following equation: U1S = −R
∂ln Vg ∂(1/T )
(5)
A series of excess thermodynamic functions, namely, excess partial molar free energy gE,∞ , enthalpy h̅E,∞ , and entropy sE,∞ , 1̅ 1 1̅ can be found on the basis of different types of activity coefficients (see, e.g., refs 32 and 33), among which the weight 32 fraction activity coefficient Ω∞ 1 is most popular: ⎛ RT 1 ⎞ p 0 (B11 − V1) ln Ω1∞ = ln⎜⎜ · 0 ⎟⎟ − 1 RT ⎝ VgM1 p1 ⎠
(6)
where M1, p01, and B11 are molecular mass, saturated vapor pressure, and second virial coefficient of the solute. The reduced activity coefficient characterizes deviations from ideality in the polymer−solvent binary system (deviations from Raul’s law for pressure of vapor over solution). The excess thermodynamic functions can be calculated according to basic thermodynamic equations:
(1)
where Vg is the specific retention volume; m2, V2, and ρ2 are weight, volume, and density of the polymer phase, respectively, in the chromatographic column, and V0r is the corrected retention volume determined by the following equation: V r0 = (tr − ta)Fp̅ , T
T Ta
where Fp0,Ta is the volumetric flow rate of the carrier gas measured at atmospheric pressure p0 and room temperature Ta; j32 is the so-called James−Martin correction factor, which is equal to the ratio of the pressure p̅x averaged over the length of the chromatographic column and the pressure p0 at the outlet of the column.29 The IGC method can be applied to determine the solubility coefficient at infinite dilution provided quite a small amount of the solute is injected into the column:
2. BACKGROUND 2.1. Inverse Gas Chromatography at Infinite Dilution of the Solute. The IGC technique has been shown to be a powerful tool for investigation of vapor sorption behavior in various types of materials, from natural and synthetic polymers to pigments to inorganic salts and metals.24,25 The application of IGC is based on a simple expression26,27 that relates the sorption constant K, the partition coefficient of solute between gaseous and condensed (polymer) phases, and the output parameter of gas chromatographic measurement Vg: V r0
0
(2)
where tr − ta is time interval between maxima of chromatographic peaks of retained and nonretained (e.g., air) solutes, respectively, Fp̅x,T is the volumetric flow rate of the carrier gas at
g1̅ E , ∞ = RT ln Ω1∞
(7)
∂ln Ω1∞ ∂(1/T )
(8)
E ,∞
h1̅ 10468
=R
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E ,∞
where (tr)i and (tr)i+1 are retention times at i and i + 1 iterations, respectively, S(HCEG) is the area of trapezium HCEG, and β is a slope of calibration line, mol/(mV·min). Along the tail of the peak of the retained solute, the specific retention time and calculated solubility coefficient become larger. The local partial pressure also increases when the local area under the elution curve of the peak increases. The concentration of a solute in polymer phase, c1,L, is known to be determined by the following equation:
− g1̅ E , ∞ (9) T 2.2. Inverse Gas Chromatography at Finite Concentration of Solute. IGC was mainly used to monitor infinite dilution adsorption and absorption parameters of solute− polymer systems.24,25 However, the IGC technique opens another and very useful possibility for evaluation of sorption isotherms. Several methods have been proposed in order to adjust the chromatographic procedure to this task, namely, frontal analysis (i), elution at a plateau (ii), i.e., the plateau of finite concentration of a solute in the carrier gas stream, and the more traditional peak elution analysis (iii).21−23 In the present Article, we set our choice on the analysis of elution peak of solute. The theoretical background for the evaluation of the isotherms was provided by Gluekauf, 13 Conder, and Purnell21−23 and described by Kiselev and Yashin.34 Here, we will estimate the solubility coefficients,31 as a measure of partition constant (see eqs 1 and 4). Let us consider the elution peaks of nonretained (left-hand peak) and retained (right-hand peak) solutes presented in Figure 1. The letters from A to H are given to display in a visual s1̅ E , ∞ =
h1̅
c1, L =
∫0
p1
S1 dp1
(12)
where p1 is partial pressure of the solute in mobile (gaseous) phase. Here, local solubility coefficient S1 can be calculated by eq 4 on the basis of local specific retention volume Vg. Then, the concentration of the solute in the polymer, (c1,L)i,i+1, at pressure (p1)i,i+1 can be found. It corresponds to the area of a figure ABDF according to eq 12. Thus, by calculation of (c1,L)i,i+1 and (p1)i,i+1 values based on single elution peak of a solute obtained in the IGC experiment, it is possible to generate a sorption isotherm of the solute in the polymer phase under investigation. Meanwhile, it is worth noting that the above computations are valid when several assumptions are met. (i) Elution procedure performs in the quasi-equilibrium regime, i.e., in the regime when the bulk sorption in the polymer is attained; (ii) local partial pressures of the solutes in mobile phase are not higher than atmospheric pressure. Otherwise, a change of total flow rate through the column must be taken into account.21−23
3. EXPERIMENTAL SECTION 3.1. Material. Functionalized polyimide having the following structure Figure 1. Scheme of calculations of sorption isotherm by the chromatographic single elution peak.
manner the calculation of the local specific retention volume and local partial pressure for i-th and (i + 1)th iteration needed for finding the sorption isotherm. In particular, A is the abscissa of the maximum of the first peak, D is the point on the chromatogram at an average time between ti and ti+1, B is the point on the first peak that corresponds to the height D, C is the point on the chromatogram that corresponds to time ti, E is the same for the time ti+1, F is the end of the treated chromatogram, and G and H are the abscissae that correspond to E and C. The shape of the peak of the retained solute has socalled “diffuse tail”,23 and this is characteristic for the peaks observed in the present work and, more generally, for glassy polymers. One can find different retention times along the descending part of the peak: (tr)0 corresponds to the maximum and (tr)i > (tr)0 can be found for different parts of its “tail”. At each iteration region, for example i and (i + 1), local specific retention volume (Vg)i,i+1 and local partial pressure (p1)i,i+1 are determined according to the following expressions: (Vg )i , i + 1
( =
(p1 )i , i + 1 =
(tr )i + (tr )i + 1 2
m2
)F
− ta
px̅ , T
S(HCEG) ·β ·RT Fp̅ , T ((tr )i + 1 − (tr )i ) x
used as a precursor and TR polymer obtained after its thermal imidization and subsequent thermal treatment at 450 °C for 1 h were studied. The densities of the precursor and TR polymer were as follows: 1.536 and 1.293 g/cm3, respectively, according to Park et al.8 The regime of the thermal treatment is described in section 3.3.1. A set of accurately selected solutes was used in this study. They included vapors of different n-alkanes C7, C8, C10, C12, C14, and C16 as well as the gases CO2, C2H6, and C3H8. All the solutes studied had not less than 98% purity. A single peak retention time was measured in the chromatographic experiments. 3.2. Sorption Measurement by Pressure Decay. Gas solubility for small gas molecules such as CO2 and CH4 was determined by the pressure decay method using a dual-volume, dual-transducer system.35,36 The apparatus consisted of two chambers, a sample chamber and a reference volume chamber, calibrated from the Burnett method.37 Gas solubility was calculated on the basis of the Soave−Redlich−Kwong (SRK) equation of state from the measured pressure decay.38 We measured the gas solubility of TR polymer at the elevated pressure up to approximately 23 atm and obtained the curve of solubility concave to pressure axis. 3.3. Chromatographic Procedure. 3.3.1. IGC at Infinite Dilution Condition. The polyimide precursor was deposited on
(10)
(11) 10469
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examples in Figure 3). It means that the specific retention volume of each sorbate at each temperature depends on the size
a macroporous support Inerton AW (0.16−0.20 mm) with surface area about 0.5 m2/g from its tetrahydrofuran solution (5 wt %). The weight fraction of the polymer on the inert support was 9.3 ± 0.1%. The chromatographic phase was split into two parts. One was kept for the study of sorption thermodynamics in the precursor. Another was subjected to thermal treatment. The protocol of the thermal treatment in the atmosphere of nitrogen was the same as described previously6 (heating (5 °C/ min) up to 300 °C, keeping the sample for 1 h at this temperature, heating (5 °C/min) up to 450 °C, keeping the sample for 1 h at this temperature and cooling to the ambient temperature). Sorption of n-heptane and n-octane in the precursor was studied in the temperature range of 60−90 °C, whereas sorption of n-C7, n-C8, n-C10, n-C12, n-C14, and n-C16 solutes in TR polymer was investigated in the range of 195− 280 °C. A gas chromatograph with flame ionization detector was used. Helium served as a gas carrier; the peak of methane was used for estimation of ta in the experiments with vapors, while in the experiments with light gases (see section 4.2) hydrogen was used for estimation of ta. The retention time of methane was smaller than an error of the retention times of the vapors investigated. Retention time was determined via the maximum of a chromatographic peak. In order to introduce the corrections into eqs 2 and 4, the inlet pressure was checked using a high sensitivity manometer (±0.01 kPa), while the outlet pressure was taken as atmospheric. A necessary step in a study of an equilibrium chromatographic regime is the check of the range of gas carrier flow rate in which no diffusion limitations take place at different temperatures. With this aim, the determination of specific retention volume was studied as the function of gas flow rate Fpx,T .39 The flow rate in the experiments must be less than a ̅ certain limiting value such that there is no dependence of Vr0 (or Vg) on Fp̅x,T. An example of such tests is shown in Figure 2,
Figure 3. Retention times tr − ta of solutes at some temperatures vs. surface area characterizing an amount of the solute injected in chromatographic column. The gas flow rate is maintained at 10 cm3/ min over all experiments performed.
of injected sample less than 1 μmol. In such cases, the retention time tr − ta can be extrapolated to a value at zero surface area or zero concentration.40 Thus, each retention time for specific retention volume calculations was a result of the extrapolation procedure. Saturated vapor pressures of the solutes were found according to the equation ln PVP = A·lnT + B/T + C +D·T2 and/or the Antoine equation, as calculated using the KDB41 or NIST42 Databases. 3.3.2. IGC at Finite Concentration. The same packed column with TR polymer on the solid support and chromatograph with thermal conductivity detector were applied to perform chromatographic experiments at a finite concentration region. Carbon dioxide, ethane, and propane were chosen as gaseous solutes. The finite concentration chromatographic procedure differs from the previous one, and the infinite dilution technique, by the method of injection of the solute into the column. In the latter case, the probe was injected by a microsyringe while in the former technique it was done by a loop of 0.460 mL in sixth-fold valve. To vary the partial pressure of the solute in the carrier gas stream, pure gas at pressure slightly higher than atmospheric pressure and its mixtures with ratios (volume of the gas per volume of carrier gas He) 3:1, 1:1, 1:7, and 1:39 were blown through the loop. Hydrogen was a nonretained gas and was blown separately through the column in order to estimate ta time. During all the experiments, the flow rate of carrier gas was maintained at 5−6 cm3/min. All digitized chromatograms were then treated according to the procedure described in section 2.2 in order to generate the sorption isotherms of the gases.
Figure 2. Plots of specific retention volumes of n-decane in the precursor vs. gas flow rate at 210 °C.
where one can see only a slight slope of the fitted line. However, the intercept does not differ from the value at lowest flow rate if one takes into account the errors (Figure 2). Thus, the equilibrium regime of dynamic sorption is reached over the whole interval of flow rates. Therefore, the flow rate used in the experiments at this and other temperatures was chosen to be as high as 10 cm3/min. The dependencies of retention time tr − ta on an amount of a solute injected (i.e., surface area under chromatographic peak) are usually linear at all temperatures under consideration (see
4. RESULTS AND DISCUSSION 4.1. IGC Data at Infinite Dilution Condition. Retention diagrams (Figure 4) of all solutes in both the precursor and TR polymer are linear which indicates indirectly the absence of diffusion limitations in the IGC experiments. As the size of an n-alkane increases, the specific retention volume at any temperature for both polymers becomes higher in accordance with increasing boiling points and molecular masses of the 10470
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by 3 orders of magnitude (Figure 5). It is seen that, for lighter solutes such as light gases, the difference in the solubility coefficients is much smaller. Thus, pressure decay measurements reported by Kim et al.15 indicated an increase by a factor about 2. Similar effects have been observed for another polyimide and its TR polymer by Smith et al.14 The solubility coefficients of higher n-alkanes in our TR polymer are rather close to those in polymer of internal microporosity (PIM-1). It can be reminded that PIM-1 is characterized by the highest gas solubility coefficients among other polymers studied. This indicates that the thermodynamic component of permeability (solubility) can play an important role in observed strong increases in gas permeability caused by thermal rearrangement. The IGC method allowed us to estimate the intrinsic energy of sorption US1 and excess partial molar enthalpy h̅E,∞ . These 1 values (Table 1) also reveal some differences in sorption of
Figure 4. Retention diagrams of n-alkane solutes in the precursor and TR polymer. The experimental values of the specific retention volumes are tabulated in the Supporting Information.
Table 1. Thermal Properties of Sorption of n-Heptane and n-Octane in Polymers Studied by IGC
solutes in the precursor and TR polymer are summarized in two tables. Extrapolation of the temperature dependencies of specific retention volume (Vg in Figure 4) to 35 °C, the commonly used, standard temperature, allowed us to calculate solubility coefficients of the solutes needed for comparison (eq 4). The solubility coefficients of n-heptane and n-octane in the precursor (Figure 5) are relatively low and correspond to those
h̅E,∞ , kJ/mol 1
US1, kJ/mol polymer precursor TR polymer PIM-1 PTMSN
n-heptane
n-octane
n-heptane
n-octane
−46 −66 −69 −49
−45 −74 −80 −51
−18 −38 −27 −21
−9 −43 −33 −20
± ± ± ±
10 1 1 1
± ± ± ±
4 1 2 1
± ± ± ±
10 1 5 2
± ± ± ±
4 1 5 2
solutes in the precursor and TR polymers. The intrinsic energies of sorption US1 of C7 and C8 alkanes in the precursor are similar to intrinsic energies of condensation of these solutes,41,42 whereas US1 of the same solutes in TR polymer are much more negative. Moreover, while the dissolution of C7 and C8 alkanes in the precursor is only slightly exothermic, in the case of TR polymer, the excess enthalpies become strongly exothermic like in highly permeable, large free volume polymers such as PIM-1 or additive PTMSN. The values of US1 and h̅E,∞ given in this table are large and 1 negative. Such parameters are characteristic for highly permeable glassy polymers with large free volume.43 In rubbers, the US1 values correspond to internal energy of condensation, whereas excess enthalpy h̅E,∞ is close to zero and reveals 1 intermolecular interactions between solutes and polymer chains. In glassy polymers, these effects are also present but exothermic effects caused by filling the pre-existing holes overlap them; i.e., this is a manifestation of nonequilibrium state of glassy polymers.19 The large and negative values of can be considered as evidence of excess entropy s1E,∞ ̅ immobilization of solute molecules sorbed in these holes. It is reasonable to make a comparison of thermodynamic parameters of n-alkane sorption in TR polymer and AF1600 studied by us in detail using the IGC technique.19 For higher nalkanes in both cases, one observes large and negative US1 and h̅E,∞ values. However, these values are much more negative for 1 TR polymer (Table 2). The same behavior is observed for excess entropies. The fraction of nonequilibrium vacancies (FNV) in AF1600 equal to 0.12 has been reported.19 If one compares the excess entropies and enthalpies for TR polymer and AF1600, it can be concluded that the FNV value in TR polymer must be much higher than 0.12. 4.2. Sorption Isotherms of Gases in TR Polymer by IGC. Subatmospheric sorption isotherms of CO2, C2H6, and
Figure 5. Solubility coefficients of n-alkanes and light gases in the polymers vs. squared critical temperature. PIM-1 (polymer with intrinsic microporosity),43 PTMSN (additive poly(trimethylsilyl norbornene)),44 and AF160045 are taken for comparison. The IGC data correspond to the infinite dilution limit; for the gases, the initial slope of the sorption isotherms is displayed. *S0 = kD + CH′b, where [kD] = cm3(STP)/cm3/atm; [b] = 1/atm; [CH′] = cm3(STP)/cm3; S (cm3(STP)/cm3/atm) was calculated by Kim et al.15 **S = P/D; P and D values were measured via the time-lag method. For TR polymer, the value P/D corresponds to 1 bar.
in conventional glassy polymers investigated previously. The study of sorption of n-alkanes higher than C8 in the precursor can be associated with additional difficulties due to diffusion limitations. On the other hand, its thermal rearrangement has demonstrated an increase in free volume fraction and the size of free volume elements estimated by the positron annihilation method.8 Indeed, for TR polymer, we observed an increase in the solubility coefficients of the solutes such as alkanes C7−C8 10471
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Table 2. Thermodynamic Parameters of Sorption of C10, C12, C14, C16 n-Alkanes in TR Polymer and Glassy AF1600 Studied by IGC h̅E,∞ , kJ/mol 1
US1, kJ/mol solute n-C7 n-C8 n-C10 n-C12 n-C14 n-C16
TR polymer −66 −74 −84 −119 −124 −127
± ± ± ± ± ±
1 1 6 2 7 4
glassy AF1600 −47 −53 −62 −69 −76 −84
± ± ± ± ± ±
1 2 1 1 1 3
TR polymer −38 −43 −47 −67 −76 −74
± ± ± ± ± ±
1 1 5 2 7 4
C3H8 were obtained by the IGC technique with single peak analysis (Figure 6). For each solute, five chromatographic peaks were analyzed, and the plots of C vs. p were combined in one sorption isotherm. The plots are located in a rather narrow area while the curves are concave to the pressure axis. The shape of the curves is traditional for the sorption isotherms of gases in glassy polymers. The isotherms are obtained at very low pressure: it is obvious that vapor pressure of a solute in the chromatographic column corresponds to pressure close to the limit of infinite dilution. This is a peculiarity but also an advantage of this technique: it permits the determination of the initial slope of the isotherms and, hence, the solubility coefficients. In most cases, the data points form a single curve. In addition, Figure 6a shows (by the dotted line) the isotherms calculated for these, very low pressures and based on the dual-mode sorption (DMS) model as found by Kim et al.15 Note that the pressure decay method especially shows the accuracy at the high pressure range. Two points should be discussed in consideration of the results of Figure 6. First, there is satisfactory agreement between the two types of experimental isotherms for carbon dioxide. The discrepancy between the concentrations of sorbed CO2 measured by the two methods corresponds to the factor ca. 1.25. It is consistent with the differences between the sorption isotherms measured for the same polymer by different authors (see ref 46). Second, it can be noted, however, that the experimental isotherms are concave to the pressure axis, whereas the predicted one is virtually linear. A simple analysis of the dualmode sorption (DMS) model implies that at pressure p ≪ b where b (atm−1) is the affinity constant, the initial parts of the isotherms should be linear, as the dotted line in Figure 6a indicates. A possible explanation of nonlinear isotherms obtained via the IGC method can be related to the dependence of the DMS parameters on the pressure range used for drawing an isotherm. It has been shown that the DMS parameters strongly depend on the pressure range (0-p1; 0-p2; 0-p3; etc., while p3 > p2 > p1) in which the same isotherm was obtained.47 The authors of that work took a single isotherm and obtained different DMS parameters by treatment of the whole isotherm (up to 100 atm) or only its parts. It was shown that the b values strongly increase when the pressure range is getting smaller. It means that pressure 1/b at which curvature becomes more pronounced is shifted to lower pressure. It is possible that here we may encounter the same effect. In Table 3, the solubility coefficients found via different methods are compared with each other and with the S values of other polymers. The S values found by the pressure decay technique8 were calculated using the DMS parameters, so the solubility coefficient S0 was found as S0 = kD + CH′b, where kD is the Henry’s law constant, CH′ is the Langmuir capacity
sE,∞ , J/(mol·K) 1̅
glassy AF1600 −16 −17 −19 −20 −20 −20
± ± ± ± ± ±
1 1 1 1 1 3
TR polymer −82 −89 −92 −128 −143 −136
± ± ± ± ± ±
4 2 21 7 25 13
glassy AF1600 −69 −73 −84 −73 −86 −89
± ± ± ± ± ±
2 2 2 5 3 7
Figure 6. Sorption isotherms of gases in TR polymer obtained by the IGC technique. Five different amounts (1.7−20.1 μmol) of gaseous probes were injected into the chromatographic column; they are displayed by different signs in this figure. Dotted curve is plotted according to DMS parameters reported by Kim et al.15
parameter, and b is the affinity constant. These values are compared with the experimental (IGC) solubility coefficients at 10472
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Table 3. Sorption Parameters of Gases in TR Polymer by Different Techniques and for Other Polymers for Comparison TR polymer of this work gas
S0a 15
b 15
S
H2 N2 O2 CO2 CH4 C2H6 C3H8
1.57 1.53 3.02 21.1 5.98
1.1 2.2 3.8 16.5 5.9
S0 by IGC
TR 6FDA-HAB14
AF160045
S0a
S0a
S0
0.6 0.71 2.76 0.95 3.5 8.9
0.058 0.100 2.74 0.24 0.99
c
0.35 2.0 3.1 34.5 6.2
24 49.5 383
PETP48 a
EC49 S0a 0.16 0.18 1.6 3.7 11.6
S0 = kD + CH′b, where [kD] = cm3(STP)/cm3/atm; [b] = 1/atm; [CH′] = cm3(STP)/cm3; S (cm3(STP)/cm3/atm) was calculated by Kim et al.15 These data were obtained using a pressure decay method, originally described in the works by D. R. Paul and W. J. Koros.50 bS = P/D; P and D values were measured via the time-lag method. For TR polymer, the values of P/D correspond to 1 bar. cThe IGC data correspond to the infinite dilution limit; for the gases, the initial slope of the sorption isotherms is displayed. a
low pressure and with S = P/D from gas permeation studies by Kim et al.15 All the values of S presented in the first (left-hand) three columns of this table are in reasonable agreement. The same conclusion can be made by the analysis of Figure 7. All
Therefore, it can be concluded on the basis of the analysis of Table 3 and Figure 7 that great sorption capacity of the products of thermal treatment of functionalized polyimides is a general feature of these novel membrane materials.
5. CONCLUSIONS Investigation using the IGC method of sorption thermodynamics of various gases (CO2, C2H6, and C3H8) and vapors (nalkanes C7, C8, C10, C14, and C16) in the polyimide precursor and the product of its thermal treatment (TR polymer) revealed several interesting features of the TR polymer. First, it was shown that the thermal treatment results in an increase in the solubility coefficients. TR polymer has great solubility coefficients S, especially for vapors, comparable to those of PIM-1, the polymers with the highest S values among all the polymers studied. Second, TR polymer is distinguished by very large and strongly negative values of the mixing parameters h̅E,∞ 1 and sE,∞ . It indicates that the large free volume plays an 1̅ important role in sorption of gases and vapors in the TR polymer.
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Figure 7. Solubility coefficients measured by various techniques of light gases and hydrocarbons C1−C3 in TR polymers and the PI precursor of this work. *S0 = kD + CH′b, where [kD] = cm3(STP)/cm3/ atm; [b] = 1/atm; [CH′] = cm3(STP)/cm3; S (cm3(STP)/cm3/atm) was calculated by Kim et al.15 **S = P/D; P and D values were measured via the time-lag method. For TR polymer, the value P/D corresponds to 1 bar.
ASSOCIATED CONTENT
S Supporting Information *
Temperature dependencies of specific retention volume Vg (retention diagrams) of solutes. This information is available free of charge via the Internet at http://pubs.acs.org/.
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the solubility coefficients of gases in the TR polymer presented in Table 3 are plotted in the correlation shown in Figure 5. It is seen that they are on the same correlation curve as the S values for heavy hydrocarbon vapors measured by the IGC method. The solubility coefficients of light gases in the PI precursor15 are also shown in this figure. It is evident that these values are lower than those of TR polymer by a factor of 1.5−2. It is also interesting to compare the solubility coefficients of various gases measured for the TR polymer with those reported for other glassy polymers (Table 3). The value S0 found via IGC corresponds to the initial slopes of the isotherms. It can be seen that, independently of some variations of the S values found by different approaches, the solubility coefficients in the TR polymer are much larger than those in conventional glassy polymers (polyethyleneterephtalate (PETP) and ethyl cellulose (EC)) and even in amorphous Teflon AF1600. It can be added that the solubility coefficients found via the reported parameters of the DMS model for other TR polymer studied by Smith et al.14 also showed high S values (Figure 7).
AUTHOR INFORMATION
Corresponding Author
*N.A. Belov: email,
[email protected]; tel, +7 495 9554210; fax, +7 495 633 8520. Y.M. Lee: e-mail,
[email protected]; tel, 82-2-2220-0525; fax, 82-2-2291-5982. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS
We appreciate the financial support from Korea CCS R&D Center (KCRC), funded by the Ministry of Education, Science and Technology in Korea and by WCU (World Class University) program, National Research Foundation (NRF) of the Korean Ministry of Science and Technology (No. R312008-000-10092-0). The support of Russian Program of Fundamental Research OKhNM-3 for 2013 is also acknowledged. 10473
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