Gas transport coefficients of phthalide-containing high-Tg glassy polymers determined by gas-flux and NMR measurements

Article abstract of DOI:10.1021/acs.macromol.5b00183

The synthesis of three aromatic polymers containing phthalide cardo groups having high inherent viscosities is described. Polyimides PIC-6F and PIC-TB were prepared from a cardo diamine and two different dianhydrides, and poly(phthalidylidenearylene) (PPDAr) was prepared by a precipitative Friedel-Crafts homopolycondensation of 3-(4-biphenylyl)-3-chlorophthalide. All polymers presented high glass transition temperatures varying between 600 and 690 K. Dense membranes prepared by casting from N,N-dimethylacetamide solutions exhibited good mechanical properties and decomposition temperatures over 770 K under a N₂ atmosphere. Results of gas transport measurements of O₂, N₂, and CO₂ were comparatively analyzed based on the chemical structure of the polymers. Additionally, the solubility, diffusion, and permeability coefficients of [¹³C]O₂ in these membranes were determined by ¹³C NMR spectroscopy and pulsed-field gradient NMR measurements, and the results were in good agreement with those determined with pressure-driven measurements. It was found that membranes of PPDAr exhibited the highest permeability and CO₂/N₂ and CO₂/O₂ permselectivities.

Full text of DOI:10.1021/acs.macromol.5b00183

Article
pubs.acs.org/Macromolecules
Gas Transport Coefficients of Phthalide-Containing High‑Tg Glassy
Polymers Determined by Gas-Flux and NMR Measurements
†
†,∥,⊥
́
Carolina García, Angel E. Lozano,
Jose G. de la Campa,† Yakov Vygoskii,‡ Mihail Zolotukhin,§
́
Javier de Abajo,†,∥ Leoncio Garrido,*,† and Julio Guzman*,†
†Instituto de Ciencia y Tecnología de Polímeros, Consejo Superior de Investigaciones Científicas (ICTP-CSIC), Juan de la Cierva 3,
́
28006 Madrid, Spain
‡Nesmeyanov Institute of Organoelement Compounds, Russian Academy of Sciences, ul Vavilova 28, Moscow, 119991 Russia
§Instituto de Investigaciones en Materiales, Universidad Nacional Auton
́ ́ ́
oma de Mexico, Apartado Postal 70-360, CU, Coyoacan
́ ́
04510 Mexico City, D.F. Mexico
∥Group of Porous Materials and Surfaces, UVa-CSIC Research Unit, SMAP, 47011 Valladolid, Spain
⊥IU CINQUIMA, Facultad de Ciencias, Universidad de Valladolid, E-47071 Valladolid, Spain
ABSTRACT: The synthesis of three aromatic polymers contain-
ing phthalide cardo groups having high inherent viscosities is
described. Polyimides PIC-6F and PIC-TB were prepared from a
cardo diamine and two different dianhydrides, and poly-
(phthalidylidenearylene) (PPDAr) was prepared by a precipitative
Friedel−Crafts homopolycondensation of 3-(4-biphenylyl)-3-
chlorophthalide. All polymers presented high glass transition
temperatures varying between 600 and 690 K. Dense membranes
prepared by casting from N,N-dimethylacetamide solutions
exhibited good mechanical properties and decomposition temper-
atures over 770 K under a N2 atmosphere. Results of gas transport
measurements of O2, N2, and CO2 were comparatively analyzed
based on the chemical structure of the polymers. Additionally, the
solubility, diffusion, and permeability coefficients of [13C]O2 in
these membranes were determined by 13C NMR spectroscopy and pulsed-field gradient NMR measurements, and the results
were in good agreement with those determined with pressure-driven measurements. It was found that membranes of PPDAr
exhibited the highest permeability and CO2/N2 and CO2/O2 permselectivities.
The solution-diffusion mechanism involves molecular scale
interactions of the permeating gas with the polymer membrane;
thus, it can be expressed in terms of the transport and sorption
coefficients for the individual polymer and gas. A more common
way of expressing this relation is
INTRODUCTION
■
Gas separation by polymer membranes is a growing field of
application that is rapidly gaining technological importance. In
fact, gas separation membranes are useful for a variety of
industrial operations, such as nitrogen and oxygen enrichment,
stripping of carbon dioxide from natural gas, hydrogen recovery
from petrochemical recycling and purge gas streams, water vapor
removal from air, recovering of volatile organic compounds and
monomers, etc.1−3 Unlike classical methods for gas separation
and purification, membrane separation technologies have the
advantages of energy efficiency, simplicity, and low cost.
However, wider commercial utilization would still require the
development of membranes with higher permeant fluxes and
higher transport selectivity. The membranes currently used in
most commercial applications are solution-diffusion membranes
because transportation of gas molecules is mainly achieved by the
solution and diffusion mechanism. The gas dissolves at the
surface of the membrane and diffuses through by a series of
activated steps. As the last step, the gas desorbs at the low-
pressure side.
(1)
P = DS
The quantity S, solubility, is thermodynamic in nature and is
affected by polymer−penetrant interactions as well as excess
interchain gaps in glassy polymers, whereas the average diffusion
coefficient, D, is kinetic in nature and determined mainly by the
molecular size of the penetrant and polymer−penetrant
dynamics.4
Significant progress in membrane separation technology
depends on the explanation of the mechanism for gas transport.
An insufficient understanding of the relationship between the
chemical structure of a polymer and its gas transport properties
Received: January 27, 2015
Revised: March 31, 2015
Published: April 8, 2015
© 2015 American Chemical Society
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may hinder this progress. Because of the more restricted
segmental motions in glassy polymers, these materials offer
enhanced selectivity of gas components according to their
diffusion characteristics as compared to rubbery polymers. An
upper limit of performance for polymeric membranes has been
noted for the industrially important separation of gas pairs, such
as oxygen/nitrogen, hydrogen/methane, carbon dioxide/meth-
ane, or carbon dioxide/nitrogen. This observation was based on a
comprehensive review of the gas transport properties of
hundreds of commercial and experimental polymers. The
conclusion was that in order to find new polymer materials
that could eventually surpass the so-called Robeson upper limit,
structural changes should be made, to control simultaneously
polymer packing and rigidity. The best way to accomplish that
seems to be a change in the primary chemical composition of the
polymers, by introducing groups and moieties able to control
both aspects.5,6 Many attempts in this direction have already
been made trying to properly combine the many factors related
to the chemical structure of polymer affecting the membrane
performance.7−10
It has been suggested that it is desirable to accomplish two
aims simultaneously when varying the structure within a family of
polymers: inhibit molecular packing while hindering the
backbone mobility. The inhibition of molecular packing will
increase the fractional free volume (FFV) of the polymer matrix,
and this will translate into higher permeability. Hindering
segmental mobility will lead to higher rigidity and higher glass
transition temperatures (Tg), and these will turn to better
selectivity. A number of studies have demonstrated that both
permeability and permselectivity may be enhanced by incorpo-
rating bulky pendent groups in membrane-forming polymers,
which simultaneously decrease chain packing efficiency and
hinder torsional mobility. In this context, many data on
structure−properties relationships have been reported for
families of aromatic glassy polymers, such as polyamides,11,12
polysulfones,13−15 polycarbonates,16,17 poly(aryl ether ke-
tones),18,19 polyimides,20−23 and other polyheterocycles, includ-
ing polymers of intrinsic microporosity (PIMs) and thermally
rearranged polymers (TRs).24−28
The present study focuses on the effect of a systematic
variation of the chemical structure on the gas permeability of
three experimental aromatic polymers containing the phthalide
moiety as a side group. Phthalide containing monomers are a
class among the so-called cardo condensation monomers, and
they were introduced at the beginning of the 1960s.29 It has been
shown that the presence of cardo groups in chains of different
polymers hinders molecular attraction forces but at the same
time greatly inhibits segmental mobility, with an overall result of
rising the Tg and improving the solubility. Simultaneously, cardo
groups in aromatic polymers twist the phenylene moieties of the
main chain out of a planar conformation, thereby causing an
increase in free volume. These characteristics make aromatic
cardo polymers suitable candidates for gas separation applica-
tions.
Previous studies on gas membranes based on polymers
containing cardo groups have shown that introducing these bulky
monomers in polyesters,30 polysulfones,31 or poly(ether
ketones)32−34 greatly improved the permeation characteristics
in comparison with those of analogous classical polymers.
The present report describes, for the first time, the synthesis of
selected polyimides containing phthalide groups with the aim of
obtaining polymer membranes having superior thermal resist-
ance (service temperature approaching 300 °C) and mechanical
behavior. The properties of these polymers are compared with
those of previously reported polymers containing phthalide
groups. Among these is poly[3,3-bis(4-phenylene)phthalide]
(PPDAr), which has been newly synthesized for the present work
and its permeation properties evaluated.
In addition, 13C NMR spectroscopy and pulsed field gradient
(PFG) NMR were used to determine all the gas transport
coefficients and assess the appropriateness of the method by
comparing the results with those attained by direct permeation
measurements using the traditional barometric method.
EXPERIMENTAL PART
■
Materials. Starting reactants and commercially available solvents
were used as received unless otherwise indicated. 2,2′-Hexafluoroiso-
propylidene diphthalic anhydride (6FDA, Chriskev, Kansas, USA) and
anhydrous AlCl3 (Sigma-Aldrich) were purified by sublimation. 5′-tert-
Butyl-m-terphenyl-3,4,3″,4″-tetracarboxylic acid dianhydride (TBDA)
was prepared in high yield (over 90%) by a synthetic method reported
elsewhere35 (mp 305 °C; lit. 304 °C).
Analysis for TBDA (C26H18O6): Calcd C, 73.23; H, 4.25. Found: C,
1
73.00; H, 4.26. H NMR (DMSO-d6, ppm): 8.62 (d, 2H); 8.48 (dd,
2H); 8.16 (d, 2H,); 8.09 (t, 1H); 7.92 (d, 2H). 13C NMR with proton
decoupling (DMSO-d6, ppm): 163.15; 163.01; 153.01; 147.88; 138.43;
135.04; 132.20; 129.86; 125.78; 125.23; 124.02.
The cardo diamine 3,3-bis(4-aminophenyl)isobenzofuran-1-(3H)-
one (PHDA) was prepared and purified in accordance with a known
procedure.36,37 After recrystallization from ethanol, the melting point
was 204−205 °C.
Analysis for PHDA (C20H16N2O2): Calcd C, 75.93; H, 5.10; N, 8.85.
Found: C, 75.93; H, 5.39; N, 8.58.
The monomer 3-(4-biphenylyl)-3-chlorophthalide, 1, was prepared
by treatment of 2-(4-phenylbenzoyl)benzoic acid with an excess of
thionyl chloride (mp 166.5−167.5 °C) according to the published
method.37
Polymer Synthesis. Polydiphenylene Phthalide Synthesis. A 100
mL flask with reflux condenser was charged under a nitrogen
atmosphere with 3.20 g of 1 (0.01 mol) and 50 mL of dichloroethane.
To the obtained transparent solution, 1.86 g of AlCl3 (0.014 mol) was
added. The purple mixture was stirred rapidly for 12 h at room
temperature. Afterward, the resulting suspension was filtered. Black
particles on the filter were carefully washed with methanol, water, and
acetone. The yield after drying in vacuum was 2.58 g (91%).
The reaction mass was dissolved in chloroform and precipitated in
methanol; the precipitate was filtered off, washed with methanol and
acetone, and dried at 120 °C.
Polyimide Synthesis. 5.0 mmol of diamine was dissolved in 20 mL of
m-cresol in a 100 mL three-necked flask. 5.0 mmol of dianhydride was
added, and the mixture warmed to 80 °C under a dry nitrogen
atmosphere until total solution and then pyridine (0.3 mL) was added.
The solution was maintained at that temperature for 1 h, and then
benzoic acid (1 mmol) was added. The solution was heated to 190 °C,
and the reaction proceeded for 6 h. After cooling, the very viscous
solution was poured slowly into a mixture 1:2 (v/v) of water/ethanol,
forming a white, fibrous precipitate that was filtered off, washed
thoroughly with a mixture 1:1 (v/v) of water/ethanol, extracted with
ethanol in a Soxhlet apparatus, and dried in a vacuum oven at 100 °C
overnight. The yields were nearly quantitative.
Polymer Characterization. Inherent viscosities were determined at
25 °C with an Ubbelohde viscometer using N-methyl-2-pyrrolidinone
(NMP) as a solvent with 0.5 g/dL polymer solutions. 1H and 13C with
proton decoupling NMR spectra were recorded on a Varian Innova 300
1
spectrometer operating at H and 13C Larmor frequencies of 300 and
75.43 MHz, respectively. Fourier transform infrared (FT-IR) spectra
were obtained on a PerkinElmer RX-1 FT-IR spectrometer, fitted with
an ATR dispositive. Qualitative solubility was determined using 10 mg
of polymer in 1 mL of solvent at room temperature. Samples that did not
dissolve after stirring at room temperature for 24 h were heated up to the
boiling temperature of the solvent.
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Differential scanning calorimetry (DSC) analyses were performed on
a PerkinElmer DSC7 calorimeter at a heating rate of 20 K/min under
nitrogen. Thermogravimetric analyses (TGA) were performed on a TA
Instruments Q500 thermobalance heating at 10 K/min under controlled
flux of nitrogen (60 mL/min). Wide-angle X-ray scattering difracto-
grams were performed at room temperature on a Bruker D8 Advance
system provided with a Vantec 1 detector, using radiation Cu Kα of 1.54
Å at 40 kV/40 mA.
times, T1, of sorbed gas. Solubility measurements were performed by
acquiring 13C NMR spectra of samples using a single pulse excitation
sequence with a repetition rate of 14 s. For diffusion measurements, a
pulsed field gradient stimulated spin echo pulse sequence was used. The
echo time between the first two 90° rf pulses, τ1, was 2.11 ms. The
apparent diffusion coefficient of [13C]O2, D, was measured at diffusion
times, Δ, of 240 ms. The length of the field gradient pulses, δ, was 1 ms,
and the amplitude of the gradient pulses, g, varied from 1.7 up to a
maximum value of 20 T m−1. The repetition rate was 14 s. The total
acquisition time for these experiments ranged from 3.5 to 87 h. Self-
diffusion coefficients may be calculated by fitting the experimental data
to the corresponding exponential function,43 but, as it will be shown
later, two decreasing exponential functions were used. This approach
allows the calculation of two diffusion coefficients that represent more
adequately the behavior of glassy polymer membranes.
Polymer density was measured on films by the flotation method. The
density data were used to evaluate chain packing by calculating the
fractional free volume (FFV) using the relation
FFV = (V − 1.3Vw)/V
(2)
where V is the polymer specific volume and Vw is the specific van der
Waals volume. The van der Waals volume was estimated by several
approximations, including the traditional method of Bondi38 and the
Hyperchem computer program,39 version 7.51. Hyperchem employs a
grid method based on the work of Bodor et al.,40 using the atomic radii
supplied by Gavezotti.41 Moreover, the computer-based method can
estimate van der Waals volume for structural units not included in the
tables typically used by the Bondi method.
Film Preparation. Membranes were prepared by casting a 6−8%
(w/v) solution in N,N-dimethylacetamide (DMA) on a balanced glass
plate fixed to a heating plate. The films were dried at 80 °C/24 h,
stripped off from the glass plate, and treated in a vacuum oven at 180 °C
for 24 h and then 6 h at 250 °C, both under vacuum. As a result, a
negligible amount of solvent remained, as confirmed by thermogravi-
metric analysis (TGA).
Permeation Measurements. A laboratory-made permeator,
described elsewhere,42 was used for permeation measurements. Briefly,
it consists of a gas cell in which the polymer membrane is placed in the
center, separating the high-pressure 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 to
reaching a low pressure of about 10−6 bar, and the whole arrangement
was thermostatically controlled at 30 °C by means of a water bath.
Subsequently, the gas contained in the high pressure chamber 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 and was varied between 0.1 and 5 bar in this work.
Three independent experiments were undertaken for each membrane
and gas.
All 13C NMR spectra were referenced to [13C(1)] acetic acid (178.1
ppm), secondary to tetramethylsilane (0.0 ppm).
Previous to these measurements, the field gradient was calibrated
following the spectrometer manufacturer’s protocol at 25 0.5 °C,
using a sample of water doped with CuSO4 at 1.0 g/L and a value of the
water diffusion coefficient equal to 2.3 × 10−5 cm2/s. Furthermore, the
calibration was verified at the range of gradient values used
experimentally by measuring the diffusion coefficient of dry glycerol.
A value of D = 2.23 × 10−8 cm2/s was found, in good agreement with the
results reported for this parameter elsewhere.44 Also, diffusion
measurements for these two liquids were performed over a wide range
of diffusion times to assess the stability of the gradients and whether
artifacts due to eddy (Foucault) currents could affect the measurements.
The temperature at the sample volume in the probe head was
determined by measuring the difference between the proton chemical
shifts of a solution of ethylene glycol at 80% v/v in deuterated dimethyl
sulfoxide.
With the experimental system indicated above and by using the
internal standard concentration, it was possible to determine both the
solubility and diffusion coefficients of the gas in the polyimide
membranes and, consequently, the corresponding permeability
coefficients.
RESULTS AND DISCUSSION
■
Polymer Preparation and Characterization. Noncom-
mercial monomers were prepared for this work following the
synthetic routes previously outlined by the authors.36,37 Thus, 5-
tert-Butyl-m-terphenyltetracarboxylic acid dianhydride (TBDA)
was synthesized by an improved, high yield method starting from
3,5-dibromo-5-tert-butylbenzene and 3,4-dimethylphenylbor-
onic acid. 1-Oxo-3,3-bis(4-aminophenyl)dihydrobenzofuran
(PHDA) was prepared by Friedel−Crafts condensation of
phthaloyl chloride and carbanilide promoted by AlCl3, with
subsequent hydrolysis in the presence of acid (H2SO4) for
PHDA. Commercial and noncommercial monomers could be
conveniently purified by recrystallization from suitable solvents
to polycondensation grade.
The permeability and diffusivity coefficients were calculated from the
curves measuring the pressure increase at the downstream side, recorded
at intervals of 1 s.
The tested gases employed in the transport measurements, all with
purity higher than 99%, were nitrogen, oxygen, and carbon dioxide.
Solubility and Diffusion Measurements by 13C NMR.
Membrane strips less than 2 mm wide and approximately 1 cm long
were placed inside a 10 mm o.d. NMR tube designed for NMR studies of
moderately pressurized gases. In addition, a standard consisting of a
sealed glass capillary with a known amount of [13C(1)] labeled (99.9%,
Euriso-top, Gif-sur-Yvette, France) acetic acid was placed in the tube.
Prior to filling the tube at a given pressure with [13C]O2 (99%,
Cambridge Isotopes Laboratories, Andover, MA) or nonlabeled CO2,
the air was removed by vacuum. Unless indicated otherwise, the gas
pressure used in these experiments was in the range of 2−5 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 diffusion coefficient of
the gas in the membranes was estimated by a spin-echo type of radio-
frequency (rf) pulse sequence, as shown by Stejskal et al.43 The
measurements were performed on a Bruker Avance 400 spectrometer
equipped with a 89 mm wide bore and a 9.4 T superconducting magnet
(13C Larmor frequency at 100.61 MHz). The reported data were
acquired at 30 0.5 °C with a Bruker diffusion probe head (Diff60)
using 90° 13C rf pulse length of about 12 μs. An inversion−recovery
pulse sequence was used to estimate the 13C longitudinal relaxation
Polyimide synthesis was accomplished by the method of high-
temperature one-step polyimidation in m-cresol solution. Using
this method, two polyimides containing cardo groups were
prepared and isolated in virtually quantitative yield.
Poly(phthalidylidenearylene) (PPDAr) was prepared by a
precipitative Friedel−Crafts homopolycondensation of 3-(4-
biphenylil)-3-chlorophthalide. The preparation of polymers
performed by precipitative electrophilic polycondensation allows
the synthesis of high molecular weight polymers in particle form.
To carry out a precipitative homopolycondensation of PPDAr,
the same reaction conditions described in the precipitative
polyketone synthesis frequently reported (dichloroethane as a
solvent, AlCl3 as catalyst, and room temperature) were used.45
The yield of PPDAr synthesis was 90%.
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All the three polymers were purified and subjected to the
common identification techniques. The chemical structures of
the repeating units are given in Scheme 1.
asymmetric stretching of imide carbonyls, as well as a strong,
sharp band around 725 cm−1 (peak at 713 cm−1) associated with
skeletal vibration of the imide ring, which overlaps with the
stretching vibration of C−F bonds. The carbonyl CO band of
the cyclic lactone, which should appear at about 1710 cm−1, is
overlapped with the imide band of 1719 cm−1. The band at 1365
cm−1 could be attributed to the C−N−C stretching. Figure 2
Scheme 1. Repeating Unit of Polymers
1
illustrates the H NMR and 13C with proton decoupling NMR
spectra of polymer PIC-6FDA, where all the signals could be
assigned readily to the protons and carbons of the polymer.
The two polyimides, PIC-6FDA and PIC-TBDA, were soluble
in organic aprotic solvents such as DMA, NMP, or DMSO, while
PPDAr was soluble also in common solvents like chloroform.
Nonetheless, polymer films were prepared by casting from DMA
solutions in all cases. Inherent viscosities in the range 0.46−0.85
dL/g indicated high molecular weight for these polymers, and
this assumption is in agreement with the excellent mechanical
properties exhibited by all materials (tensile strength over 80
MPa and modulus over 2.7 GPa).
The composition of these polymers was determined by
elemental analysis, FT-IR spectroscopy, and NMR spectroscopy.
As an example, the FT-IR spectrum of polymer PIC-6FDA is
shown in Figure 1. The most characteristic absorption bands
appeared at 1774 and 1719 cm−1, attributable to symmetric and
Figure 2. (a) 1H NMR (CDCl3, ppm): 7.52 (dd 4H); 7.70 (m 2H); 7.87
(d 1H); 7.92 (dd 1H); 7.97 (dd 1H); 8.08 (d 1H); 8.16 (d 1H). (b) 13C
with proton decoupling NMR (CDCl3, ppm): 169.4 (Cw); 166.1 (Cg);
165.9 (Ch); 151.2 (Cq); 140.7 (Cd); 139.5 (Cc); 136.3 (Cm y Cj); 132.7
(Cs); 134.4 (Ca); 131.9 (Cb); 130.1 (Cr); 128.3 (Cl y Cn) 126.6 (Ck y
Co); 126.5 (Cx); 125.6 (Ce); 125.0 (Ct); 124.5 (Cu); 124.4 (Cv); 90.8
(Cp); 77.5 (Ci).
Glass transition (Tg) and initial decomposition (Td) temper-
atures were determined by DSC and by TGA, respectively. DSC
curves, recorded from 323 to 703 K, showed only one inflection,
which was attributed to the Tg. No exotherm or endotherm
peaks, indicative of crystallization or melting, were detected in
any case. Tg values ranging from 603 to 683 K were measured
(Table 1). Decomposition temperatures (taken as the temper-
ature of the initial weight loss onset in the TGA curves) were
above 770 K for all of the polymers, as it could be expected for
aromatic polymers. The values of Tg and Td determined for
PPDAr were similar to those found previously.46
Figure 1. FT-IR spectrum of polymer PIC-6FDA.
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the diffusion coefficient, the value of P in barrer (1 barrer [10−10
Table 1. Inherent Viscosities, Specific Volumes, Glass
Transition Temperatures, Thermal Degradation
Temperatures, and Fractional Free Volume of Polymer
Membranes
cm3(STP) cm/(cm2 s cmHg)]) could be obtained from eq 5
⎛
⎜
⎞
dp(t)
dt
VL
pAT
Ω
p
P = 3.59
lim
=
⎟
⎠
t→∞
⎝
(5)
polymer
ηinh, dL/g
V, cm3/g
Tg, K
Td, K
FFV
where limt→∞(dp(t)/dt) is the stationary flux in the downstream
chamber and Ω = 3.59(VL/AT) limt→∞(dp(t)/dt). In Figure 4,
PPDAr
0.81
0.46
0.85
0.827
0.736
0.819
683
603
659
773
805
779
0.182
0.214
0.171
PIC-6FDA
PIC-TBDA
Permeability, Diffusion, and Solubility Coefficients. To
determine the transport coefficients of the membranes, several
measurements of the gas flux through the polyimide membranes
were performed using the pressure device described in the
Experimental Part. The time dependence of the gas pressure in
the downstream chamber is calculated by the integration of Fick’s
second law, and with appropriate boundary conditions, one
obtains when steady-state conditions are reached that the time
dependence of the pressure of the downstream chamber can be
written as47,48
⎛
⎜
⎞
⎟
pALST
V
Dt
L
1
6
p(t) = 0.2786
−
2
⎝
⎠
(3)
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, V the volume of the
downstream chamber in cm3, and D and S are the diffusion and
solubility coefficients in cm2/s and cm3 gas (STP)/(cm3 polymer
cmHg), respectively.
As an example, illustrative plots of the variation of pressure
with time in the downstream chamber for the permeation of CO2
in a polymer membrane of PPDAr are shown in Figure 3.
Figure 4. Ω vs p (gas pressure) for CO2 (red squares), oxygen (green
circles), and nitrogen (blue triangles) on PPDAr at 30 °C.
graphs corresponding to the permeation experiments of CO2, N2,
and O2 on PPDAr performed at different pressures and expressed
in the form of Ω vs p are depicted. It can be seen that straight lines
are obtained, and from their slopes the values of the permeability
are calculated. The obtained straight lines indicate that, in the
range of pressures studied, the permeability is constant, and
similar results were obtained for the other gases studied: oxygen
and nitrogen.
Once the permeability and diffusion coefficients are
determined, the solubility coefficients can be calculated directly
from the P/D ratio, and the results obtained for the transport
coefficients of the gases in the three polymers are shown in
Tables 2 and 3.
The comparative analysis of the transport coefficients of the
three polymers clearly indicates that the highest permeability to
CO2 corresponds to membranes of PPDAr with a value of 94
barrer while membranes PIC-6FDA and PIC-TBDA showed
values of 67 and 48 barrer, respectively. This behavior could be
attributed to the higher fraction of nonequilibrium excess free
volume in the glassy state for the PPDAr membranes that permits
higher gas adsorption in the Langmuir sites and consequently
higher solubility coefficients in the case of more condensable
gases, such as CO2.
On the contrary, the permeabilities to oxygen of the three
membranes are almost the same, which is the origin of the high
permselectivity of membrane PPDAr as is shown in Table 3.
Concerning the permeability to nitrogen, the variation is
between 2.0 and 2.5 barrer, with the lower and higher values
corresponding to the PIC-TBDA and PPDAr, respectively.
Recently, we have described49 the application of NMR
spectroscopy to the determination of all the three gas transport
coefficients through liquids and polymers. In the following, we
describe the use of this technique to determine the solubility,
diffusion, and permeability coefficients of [13C]O2 in the
membranes described in this work.
Figure 3. Variation of pressure in the downstream chamber for the
permeation of CO2 in a membrane of PPDAr, thickness of 90 μm, at
pressures in the upstream chamber between 0.14 and 3.12 bar (the low,
intermediate, and high values are indicated).
These plots in the steady state are straight lines intercepting
the abscissa axis at
L2
6θ
D =
(4)
where θ is the time lag and, therefore, the diffusion coefficient can
be obtained from eq 4. Assuming that the permeability
coefficient, P, is the product of the solubility coefficient and
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Table 2. Permeability, Diffusion, and Solubility Coefficients of Carbon Dioxide in Membranes at 30 °C, Measured with the
Pressure and NMR Methods
membrane
PPDAr
method
pressure
p, bar
0−3.2
P, barrer
D × 108, cm2/s
2.5−3.5
S, cm3 (STP)/(cm3 cmHg)
94
2
0.40−0.25
0.185
NMR (CO2)
NMR ([13C]O2)
pressure
4.06
1.73−4.24
0−4.7
3.96
91
67
6
3
4.0−5.3
1.26−2.1
0.23−0.16
0.62−0.31
0.218
PIC-6FDA
PIC-TBDA
NMR (CO2)
NMR ([13C]O2)
pressure
1.66−4.07
0−5.3
4.12
63 10
2.2−2.8
3−4.2
0.32−0.19
0.15−0.12
0.169
48
2
NMR (CO2)
NMR ([13C]O2)
1.54−4.02
45
7
2.0−2.8
0.24−0.15
Table 3. Permeability and Diffusion Coefficients of O2, N2, and CO2 and CO2/O2 and CO2/N2 Permselectivities in Cardo Polymer
Membranes at 30 °C and 1 bar
membrane
PO , barrer
PN , barrer
PCO , barrer
DO × 108, cm2/s
DN × 108, cm2/s
DCO × 108, cm2/s
α (CO2/O2)
α (CO2/N2)
2
2
2
2
2
2
PPDAr
11.8
11.6
10.0
2.5
2.2
2.0
94
67
48
7.74
5.04
5.67
2.7
2.6
1.4
3.1
7.97
5.77
4.8
37.6
30.5
24
PIC-6FDA
PIC-TBDA
1.27
1.42
The 13C NMR spectra of these type of samples with the
standard labeled 13C(1) acetic acid showed three peaks as
In Figure 5, it can be seen that the solubility coefficients of
[13C]O2 and CO2 measured by NMR at low pressures are similar
to those determined by permeation experiments, whereas at
relatively high pressures, some differences occur. This could be
due to the high rate of permeation observed for CO2 (see Figure
3) in the barometric measurements that precludes an accurate
determination of the diffusion and solubility coefficients,
although the permeability coefficients can be accurately
determined even at high pressures. In this regard, the
measurement of D and S with the NMR method, at equilibrium,
could be less prone to uncertainties in membranes exhibiting
high permeability.
illustrated in earlier work:49 one peak corresponding to the 13
C
signal of the carboxyl group of acetic acid at 178.1 ppm and two
peaks associated with the [13C]O2 in the membranes, centered at
128.4 and 125.6 ppm.49 These two peaks reflect the existence of
two populations of [13C]O2 corresponding respectively to the
nonsorbed (free) and sorbed (in the membrane) gas fractions, in
a slow exchange regime. The estimated spin−lattice relaxation
times, T1, of sorbed gas in the membranes were ∼2.3 s. The free
gas exhibits T1 values in the range of 50−65 ms.
The diffusion coefficient of CO2 in the membranes was also
measured with NMR. For illustrative purposes, 13C PFG NMR
spectra corresponding to [13C]O2 sorbed in PPDAr, at p of 3.24
bar, are shown as a function of the amplitude of the field gradient
in Figure 6.
After reaching equilibrium conditions, the solubility of
[13C]O2 in the membranes was determined by comparing the
areas of the peaks associated with the reference compound
(acetic acid) and the sorbed gas in the corresponding 13C NMR
spectra. The results are comparatively analyzed with those
obtained by permeation measurements as it is shown in Figure 5
for the solubility of CO2 and [13C]O2 in PPDAr membranes, and
all the results are summarized in Table 2.
For diffusion in liquid media or in nonglassy polymer
membranes, the echo attenuation can be written as43
A(g) = A(0) exp[−(bNMRD)]
(6)
Figure 6. 13C PFG NMR spectra corresponding to [13C]O2 sorbed in
PPDAr obtained at 30 °C and a gas pressure of 3.24 bar. The duration, δ,
of the gradient pulse was 1 ms, and the diffusion time, Δ, was 240 ms.
The gradient amplitude, g, was incremented in 12 consecutive steps of
1.70 T/m from an initial value of 1.70 T/m.
Figure 5. Variation of the concentration of CO2 in a membrane of
PPDAr as indirectly measured by pressure method (red squares) and
directly measured ([13C]O2, NMR method) (green circles). The blue
triangle corresponds to a measure by NMR with unlabeled CO2.
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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,
b
nucleus being observed, and the others as previously defined.
Figure 7 illustrates the attenuation of the echo intensity with
Table 4. Summary of Results Obtained by NMR Spectroscopy
and PFG NMR for the Transport Coefficients of [13C]O2 in
Cardo Polymer Membranes at 30 °C
NMR = (γgδ)2(Δ − δ/3) where γ is the gyromagnetic ratio of the
S, cm3
STP/
DD
×
DH
108,
cm2/s barrer cm2/s
×
DM
×
(cm3
cmHg)
108,
P,
108,
sample
PPDAr
p, bar
cm2/s
φ
1.73
2.19
3.24
4.24
1.66
2.28
3.26
4.07
1.54
2.42
2.96
4.02
0.230
0.207
0.178
0.163
0.318
0.275
0.202
0.193
0.237
0.188
0.169
0.145
9.9
11.1
8.5
0.31
0.36
0.51
0.57
0.23
0.19
0.27
0.22
0.05
0.19
0.13
0.34
1.3
91
99
87
86
69
73
56
54
47
52
48
35
3.97
4.76
4.87
5.26
2.16
2.65
2.76
2.78
1.98
2.74
2.83
2.40
1.2
1.1
8.4
1.1
PIC-6FDA
PIC-TBDA
8.2
0.36
0.74
0.56
1.0
10.8
8.7
9.1
18.7
11.7
14.4
5.9
1.1
0.64
1.1
0.60
Figure 7. Plot of the normalized echo intensities vs the field gradient
parameter bNMR corresponding to a membrane of PPDAr loaded with
[13C]O2 at 3.24 bar and 30 °C. The closed circles represent the
experimental data points, and the solid and dashed lines represent the
fits to eqs 6 and 9, respectively.
P = S[φDD + (1 − φ)DH]
(10)
With the values of permeability thus obtained and the
solubility coefficients, we also obtain a mean diffusion coefficient
DM that should be equivalent to that determined by barometric
measurements. The values of DM are shown in Table 4. A fair
agreement is observed between the results obtained by both
procedures for all the transport coefficients (see Table 2), which
clearly indicate the appropriateness of the NMR method to the
determination of gas transport in glassy membranes. Moreover,
this 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 and the corresponding NMR
spectrum is resolved.
increasing values of bNMR, keeping Δ and δ constant,
corresponding to data shown in Figure 6. It is clearly shown
that the data does not fit a monoexponential decay (eq 6).
As it is well established, the sorption isotherms in glassy
polymer membranes are well described by the dual model that
assumes two coexistent phases: one continuous where the
sorption process obeys Henry’s behavior and another discrete
with Langmuir adsorption sites. In this model the solubility
coefficient S is dependent on the gas pressure p in the form50,51
CONCLUSIONS
C′Hb
1 + bp
■
S = kD +
Two polyimides have been newly prepared that are soluble in
organic solvents and easily processable into films with good
mechanical and thermal properties. The behavior of these
polyimides was compared with that of a polymer [poly-
(phthalidylidenearylene), PPDAr] synthesized by an electro-
philic reaction and formed through the direct condensation of a
precursor derived from phthalic anhydride and biphenyl. It was
found that all polymers showed excellent thermal properties, but
the values of the transport properties of the polyimides were
lower than those of PPDAr.
(7)
where kD is Henry’s constant, C′H is the concentration of gas in
Langmuir sites, and b is an affinity gas−polymer parameter.
Therefore, the permeability of the membrane is described by
the equation
C′Hb
1 + bp
P = kDDD +
DH
(8)
The solubility and diffusion coefficients of C-13-labeled
carbon dioxide were determined with NMR methods. 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 transport coefficients of gases in glassy polymer
membranes.
where DD and DH are respectively the diffusion coefficients in the
continuous phase and Langmuir sites. This equation is really a
simplified approach because the coupling between both diffusion
modes is neglected.52
Thus, considering the dual model with two diffusion
coefficients, the NMR diffusion data were analyzed using the
sum of two decreasing exponentials according to a modification
of eq 6 in the form
A(g) = A(0)[φ exp(−bNMRDD) + (1 − φ) exp(−bNMRDH)]
AUTHOR INFORMATION
Corresponding Authors
*Tel +34 91 262 2900; Fax +34 91 564 4853; e-mail lgarrido@
cetef.csic.es (L.G.).
*Tel +34 91 262 2900; Fax +34 91 564 4853; e-mail jguzman@
ictp.csic.es (J.G.).
■
(9)
where φ is the fraction of gas in the continuous phase and (1 −
φ) represents the corresponding fraction in the Langmuir sites.
Table 4 summarizes the diffusion coefficients determined in this
manner at various pressures for all membranes. It is observed that
DD and DH differ by about 1 order of magnitude. The
permeabilities are then determined using the equation
Notes
The authors declare no competing financial interest.
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Article
(35) García, C.; Lozano, A. E.; de la Campa, J. G.; de Abajo, J.
Macromol. Rapid Commun. 2003, 24, 686−691.
ACKNOWLEDGMENTS
■
The financial support of this work by the Spanish Ministry of
Economy and Competitiveness (MAT2010-20668, MAT2013-
45071-R, and MAT 2011-29174-C02-02) and the Consejo
Superior de Investigaciones Cientıficas (CSIC) is greatly
appreciated.
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