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Gas permeation and positron annihilation lifetime spectroscopy of poly(ether imide)s with varying ether.


The problem of carbon dioxide removal from natural gas has highlighted two important challenges: (i) to be able to achieve good gas selectivity without sacrificing permeability and (ii) maintaining the long-term gas separation performance by overcoming the problems of aging and plasticization [1, 2], Five important classes of polymer membrane materials have been highlighted as having potential to meet this challenge: polyimides, thermally rearranged polymers (TRs), substituted polyacetylenes, polymers with intrinsic microporosity (PIM), and polyethers [3], Polyimides have been extensively investigated as gas permeability membranes and high values of selectivity have been achieved by varying the polymer structure [4-10]. Changing the polymer backbone structure will influence the accessible and inaccessible volume, the polymer dynamics, and influence the transport properties.

In a previous article, the broadband dielectric relaxation of several polyfether imides) containing different ether segments were investigated [11], Dielectric relaxation is a useful probe of the local dynamics of the polymer structure and this study indicated that librational motions occur at low temperatures associated with the imide block. Such local motions could influence gas transport through the matrix. The structure of the polyfether imide) studied are shown in Fig. I and have a common diamine block and a series of related dianhydride blocks.

The structures of the diamine; [R.sub.2] - bis(4-amino-3,5-dimethylphenyl)methane is common to this series of polymers. The dianhydride contains the diol R,, and have the structures summarized in Table 1.

Gas diffusion is commonly described by the solution--diffusion process [12, 13]. The model assumes that permeation occurs in three stages; first, gas sorption occurs on the polymer surface; second, diffusion of the gas takes place through the polymer bulk, and third, desorption takes place from the opposite face of the membrane. Permeability, P, can thus be defined as a combination of the diffusivity, D, of the gas dissolved in the polymer, and the gas solubility, S:

P = D x S (1)

At a molecular level, for most amorphous polymers, chain packing dictates free volume and its distribution which in turn determines the physical, mechanical, and transport properties of the membrane [12]. The molecular free volume is defined as the difference between the total volume and the volume occupied by the polymer molecules. The diffusing molecule can only move from one place to another when the local free volume exceeds a critical value [12, 13].

The diffusion of gas molecules through the polymer matrix will be controlled by the available free volume which may be observed directly on a nanoscale by positron annihilation lifetime spectroscopy-PALS [14-21], In systems, such as hydroxyl-containing polyimides and polybenzoxazole, thermal treatment allow further reaction and chain conformational changes which both influences the free volume distribution as determined by positron annihilation lifetime spectroscopy-PALS [15]. In certain polymer systems, water vapor can act as a plasticizer and influence gas diffusion by blocking sites by competitive sorption and as a consequence void filling inhibit diffusion [16, 17], In high barrier polymer systems, PALS indicates that the transport properties of gases can be improved by plasticization reducing chain-chain interactions and influencing the free volume hole size, fractional free volume, and solubility of the gas. Free volume measurements of polyimides characterize the ability for small molecules to permeate the polymer, but strong polymer-polymer interactions dominate properties such as the glass transition temperature ([T.sub.g]).

This study reports PALS and gas transport measurements on this previous investigated group of poly(ether imide)s [11] in order to gain an insight into the influence of molecular structure on their gas transport properties and uses carbon dioxide, oxygen, nitrogen, and argon to monitor the gas permeability.



Dianhydride synthesis has been reported previously [21, 22] and the diols incorporated in the dianhydrides are listed in Table 1.

Synthesis of Polyimides. The bis(ether anhydrides) were produced by the nitrodisplacement method from the nitrophthalodintriles by the diol [22-26] (Fig. 2). The anhydride was reacted with bis(4-amino-3,4-dimethylphenyl) by a conventional two-stage solution polymerization and imidization process. The synthesis involved 1 mmol of diamine being dissolved in 5 [cm.sup.3] of N-methylpyrrolidinone (NMP) at room temperature and an exact stoichiometric equivalence of dianhydride added with stirring.

After standing overnight, the mixtures formed a highly viscous solutions of polyfamic acid)s which was chemically imidized by the addition of 2 [cm.sup.3] of an equivolume mixture of acetic anhydride and pyridine at room temperature. After being left for several hours, the resulting polyimides were isolated by precipitation into methanol. Thin films of the polymers were produced by slow solvent evaporation from polymer solutions (3 wt%) in dichloromethane in flat bottomed Petri dishes (Anumbra). The high-molecular weight polyimides were washed with boiling methanol to remove residual solvent. Thin films of the polymers were produced by slow solvent evaporation from polymer solutions (3 wt%) in dichloromethane in flat bottomed Petri dishes (Anumbra). The transparent, yellow films, thickness 30-60 [micro]m, were annealed for 3 days at 120[degrees]C under vacuum to remove moisture.

Density and Differential Scanning Calorimetry (DSC) Measurements

Densities of the cast polyimide films were determined by a flotation method at 25[degrees]C using a saturated aqueous solution of [K.sub.2]C[O.sub.3]. The density of the salt solution was measured using an Anton Parr DM60 oscillating digital density meter connected to a DM601 density measuring cell. Measurements were performed in triplicate and the densimeter was thermostated at 25 [+ or -] 0.1 [degrees]C. The glass transition was determined using a Perkin Elmer DSC-2 with a heating rate of 10[degrees]C [min.sup.-1] under nitrogen and correspond to the onset of the [T.sub.g] process. The fractional free volume, FFV, was calculated using Eq. 2.

[V.sub.f] = ([V.sub.T] - [V.sub.0])/[V.sub.T] (2)

where [V.sub.T] is the molar volume per repeat unit of polymer at temperature T and [V.sub.0] is the volume occupied at 0 K per mole of the repeat unit and is estimated to be 1.3 times the van der Waals volume calculated from the group contribution method of Bondi [27, 28].

Positron Annihilation Lifetime Spectroscopy (PALS)

PALS measurements were performed using a fast-fast system which uses a high counting efficiency, Ba[F.sub.2] cylindrical (40 mm diameter 15 mm thick) scintillator combined with a Hamamatsu H2431 photo-multiplier tubes (PMTs) with borosilicate windows. The front face and sides of the scintillators were wrapped with PTFE tape to reduce UV reflectance and improve both time and energy resolution [29]. To avoid "pile-up" problems, the detectors were arranged to be at 90[degrees] to each other. The scintillators were coupled to the PMT's using a high viscosity (100,000 cps) silicone oil, which has low UV absorption. The rise time of the tubes, was 0.7 ns and the configuration gave count rates of 150--300 cps and an instrument resolution of 220-240 ps FWHM for a 50 [micro]Co source. The time to amplitude convertor used in the system was a Canberra 2145 instrument. A [sup.22.sub.11] [N.sup.1111] aepoxy coated Kaptan film was used as the source for the measurements. The resolution of the equipment was determined by measurement of a benzophenone single crystal. A source correction of 7.4% @ 382 ps was found and used in the analysis of all PALS spectra reported in this paper. The lifetime components were calculated using POSITRONFIT [30, 31], which minimizes the difference between the experimental data and the polymer spectrum expressed as a convolution of the instrument resolution function (symbol *) and a finite number (n) of negative exponentials:

y(t) = R(t)* ([N.sub.t] [n.sub.summation over (i=1)] [[alpha].sub.i] [[lambda].sub.i] [e.sup.-[lambda],t] + B) (3)

where y(t) is an experimental raw datum, R(t) is the instrument resolution function, [N.sub.t] is the normalized total count, B is the background, [[lambda].sub.i], is the inverse of the ith lifetime component ([[tau].sub.i]), and [[alpha].sub.i] [[lambda].sub.i], ([I.sub.i]) is its intensity. Experimental values of [[tau].sub.1] and [[tau].sub.2]

were ~0.15 ns (p-Ps) and 0.41 ns (free [e.sup.+]), respectively and these values were used in the analysis of all the samples studied. Similarly, values of [I.sub.1] and [I.sub.2] were, approximately, 19 and 65%. Third, long time exponential decay allows determination of values of [[tau].sub.3] and [I.sub.3] (o-Ps) which reflect sizes and populations of voids capable of supporting molecular diffusion.

Gas Permeability Measurements

Gas permeability's were obtained using a constant volume apparatus with 200 [cm.sup.3] downstream and upstream stainless steel chambers. Throughout the measurement, the upstream pressure was held at a constant high pressure measured using a 750B Mini Baratron transducer. The downstream pressure was monitored using a low-pressure 10 Torr MKS Baratron transducer. The polymer sample, in the form of a 7 cm diameter disc, was held between the two cylinders using two flat o-rings to ensure a good seal. The thickness of the disc was measured on 50 points using a Mitutoyo digital micrometer with a resolution of 0.1 mm. The apparatus was de-gassed for 36 h and a leak-rate measured on the downstream side of 5 mTorr per 24 h or below was considered acceptable. A gas pressure was then introduced in the upstream side and the steady state permeation rate determined by recording the downstream transducer pressure readings. The upstream driving pressures were 4 atmospheres for C[O.sub.2] and [N.sub.2], 3 atmospheres for Ar, and 2 atmospheres for [O.sub.2]. Steady-state fluxes were obtained from pressure-time curves at times greater than three to four times the time lag, [theta] [32]. Calculations of the pressure rise due to permeation were carried out using a Mathcad 6.0 program based on Eq. 4

P = Jl/A[[phi].sub.p] (4)

where, l is the membrane thickness, A is the membrane area, and [[phi].sub.p] the pressure difference across the membrane. The flux, J is defined:

J = [dp/dt] [V/T] (5)

where dp/dt is the rate of change of pressure in the downstream volume, V, as a function of time, and T is the temperature.

Effective diffusion coefficients, D, were estimated using the film thickness, l, and the time-lag, [theta], in the following relationship [33]:

[theta] = [l.sup.2]/6D (6)

The effective solubility coefficients were then estimated using Eq. 1.


Glass Transition Temperature--[T.sub.g]

The glass transition temperatures ([T.sub.g]) of the polymers studied are summarized in Table 2.

The synthesis, Fig. 1, creates a imide ring by the reaction of bis-(4-amino-3,4-dimethylphenyl) methane with the dianhydride and can adopt a series of slightly different conformations about the polymer backbone. The methyl groups in the ortho position to the imide ring twist the phenyl groups out of the plane, creating for each polymer four possible conformational preferences depending on the relative orientation methyl groups to the plane created by the imide rings; +, -: +,-: -,+:+:,-; -,+: +,-; (note shown), -,+:-, + (not shown). The four conformations will divided into two energetically degenerate sets; ; +, -:+,-; -,+:-, +; and -, + : +, -; +: +,-; Fig. 3.

The existence of two energetically different states indicates the possibility of two closely related but different relaxation processes associated with oscillatory motion about the N-C bond and is detected as a low temperature dipole relaxation [11]. These small librational motions may aid gas diffusion but are not of a sufficiently scale to allow large scale cooperative motion of the backbone associated with the glass transition.

The lowest values of the [T.sub.g] are observed with A1, A2, and A6. The propane bridge between the phenyl ether rings, Al will impose a twist on the backbone structure and this is further increased when one of the methyl groups is replaced a phenyl group in A2. The twisted backbone and the pendant phenyl group will inhibit the ability of the polymer chains to pack together and leads to the low values of [T.sub.g] which is observed The highest values of [T.sub.g] are observed when the link is simply an -O- bond, A9 or the linking unit is the rigid methyl substituted biphenyl, A12. The methyl substitution will introduce the possibility of an additional set of two conformational preferences and as a consequence an imposed twists in the backbone, A10 has the lowest density, implying that the chains are have difficult packing together. The intrinsic rigidity of the backbone in A12 inhibits free rotation up to a temperature in excess of 420[degrees]C, where upon decomposition becomes apparent. The phenyl substituted dihydroxy benzene linking group, A3, exhibits a low [T.sub.g], whereas the dihydroxynaphthalene linked polymer A7 has a higher [T.sub.g] compared with A3 although its density is almost identical. The hexafluoropropane bridge in A4 creates a [T.sub.g] which is slightly higher than for A1 but a density which is significantly higher reflecting the higher mass of the six fluorine atoms. The highly substituted phenyl in A8 raises the [T.sub.g] and has a lower density in comparison to A3 which would be consistent with the inhibiting effect of the neighboring group packing. The highly methyl substituted propane bridged biphenyl, A10 has a comparable [T.sub.g] to A8 but has the lowest density of the polymers studied. The next lowest density is observed with A11 which has a lower [T.sub.g] consistent with the less restricted methylene compared with the propane bridge demonstrated in A1. The implication is that both intra and intermolecular interactions are influencing the [T.sub.g] and the packing density in these polymers and the calculated values of FFV do not follow the variation observed in the [T.sub.g]. The smallest value of FFV is observed in A10, which has a 20[degrees]C higher value of [T.sub.g]'s than that A1, which has the next lowest density. It is clear that the [T.sub.g] is not controlled by the FFV but reflects the effects of chain--chain interactions on the ability for the polymers to undergo long range cooperative motion.

Positron Annihilation Lifetime Spectroscopy-PALS

There have been numerous studies of the correlation between positron annihilation and gas transport [[34]-[41]]. In polymers, PALS gives rise to a long-lived component, which is a consequence of ortho-positronium (o-Ps) annihilation in amorphous regions. The o-Ps species localizes itself in free volume cavities of radius 0.2-0.6 nm, a range which correlates to the non-bonded interatomic distances in polymers and the molecular radii of diffusing substances [21, 42], Analysis of the PALS data was carried out in terms of three lifetime components: [[tau].sub.1] which is attributed to parapositronium (p-Ps) annihilation; [[tau].sub.2] which is associated with free positron and positron-molecular species annihilation; and [[tau].sub.3] which is attributed to o-Ps annihilation. In molecular systems, the o-Ps localized in a cavity annihilates through an exchange process with an electron of opposite spin associated with the molecules forming the cavity wall. Each lifetime has a corresponding intensity (I) relating to the number of annihilations occurring at a particular lifetime. The long lifetime component for polymers ([[tau].sub.3], [I.sub.3]) and is related to the number and size of cavities. The average free volume size ([V.sub.Ps]) for a spherical cavity can be calculated [43,44]:

[V.sub.Ps] = 4[pi][R.sup.3]/3 (7)

where the cavity radius, R is calculated from the o-Ps lifetime: [[tau].sub.3]

[[tau].sub.3] = 1/2 [1 - R/(R + [DELTA]R) + 1/2[pi] sin[(2[pi]R/(R + [DELTA]R)).sup.-1] (8)

where, [DELTA]R represents an electron layer thickness and is estimated as 0.166 nm by fitting [[tau].sub.3] to known vacancy sizes of molecular crystals. Equation 7 can be used to calculate R from experimentally measured values of [[tau].sub.3]. The fractional free volume, f, designed as the tau x intensity product, can be found from the empirical equation:

f = [CV.sub.Ps] [I.sub.3] (9)

where, [F.sub.Ps] is in [nm.sup.3], [I.sub.3] in %, and C is an arbitrarily chosen scaling factor for a spherical cavity and is typically assigned a value of 1.5. The above equations do not allow for the effects of chemical interactions which can shorten the lifetime and reduce the measured values of [[tau].sub.3] and can reduce [I.sub.3]. However within this group of polyfether imide)s it is appropriate to look at their relative magnitudes as an indication of void size changes. The samples used for PALS, analysis were the same membranes used for the gas permeability characterization and density measurements. Polyimides are susceptible to undergoing chemical reaction with positrons and as such a contribution to quenching can arise from such processes. As a consequence, the calculated values of the radius and intensities allow comparison of the relative void characteristics for the polyfether imide)s, but should not be taken as absolute values [45, 46], Analysis of the PALS data gave the ortho lifetimes [[tau].sub.3] and intensities [I.sub.3] listed in Table 3.

Variations are observed in both the values of [[tau].sub.3], reflecting changes in the mean radius (R) and effective volumes of the cavities [V.sub.Ps]. Despite the obvious bulky nature of the side groups in A2, A3, and A8, the largest values of VPs are observed with A4 and A10. A4 contains a hexafluoropropane moiety and the incorporation of this entity in the polymer backbone is known to increase the polymer solubility (2) and in this system, appears to help create larger voids than the corresponding propane structure, A1.

Comparison of A1 and A6 in which the propane moiety is replaced by the methylene group shows that closer packing is possible in the latter and there is a corresponding decrease in the value for [V.sub.Ps], which is the smallest of the values observed with this series of polymers. A6 however has a relatively low value of [T.sub.g] which emphasizes lack of correlation between the [V.sub.Ps] and the ability for the polymer to achieve co-operative free rotation. The high [T.sub.g] materials, A11 and A12 have relatively large values of VPs but are slightly larger than for the other high [T.sub.g] material A9. Comparison of A1 and A2 indicates that the introduction of the pendant phenyl group has increased the void size. Comparison of A5, the ether link polymer with A6 the methylene link material indicates that [V.sub.Ps] is large in the ether linked material, however they have almost identical values of [T.sub.g]. As with the attempted correlation with FFV, the changes in the void size do not correlate with the variation in the [T.sub.g], indicating that the latter is strongly influenced by the strength of chain--chain interactions which are not reflected in the nanovoid size measured by FPs.

Gas Permeation Measurements

The permeation of oxygen, carbon dioxide, nitrogen and argon were measured and the values obtained are summarized in Table 4 and Fig. 4.

Glass diffusion is generally considered to be influenced by the void structure of the polymer and attempted correlations the gas transport data with the void size as measured by PALS are presented in Fig. 4B. The solubility parameter--([delta], is calculated from the group contributions using the method of Fendors [35], are presented in Fig. 4C. The permeability coefficient in the case of all the gases studied, although apparently insensitive to change in void size for value below 0.11 [nm.sup.3], follows a regular upward trend as the void size increases above this value. The radius of the diffusing molecules are, respectively; carbon dioxide, 0.165 nm; argon, 0.17; nitrogen, oxygen, 0.173 nm; nitrogen, 0.182 nm.

Carbon dioxide shows a higher than expected value of permeability for A6 and may reflect its ability to achieve plasticization through interaction with the polar entities in the backbone. Permeability is the product of the diffusion coefficient and solubility coefficient and hence the local chemical structure can play as important a role as the void size. There are no clear correlations of the variation diffusion coefficient with void size as measured on a nanoscale, although the possible void filling effect of carbon dioxide is reflected its lower values relative to those of oxygen (Fig. 4B).

There does appear to be an increase in the permeability at a value of [V.sub.Ps] of 0.12 - 0.13 nnt and this coincides with the critical diameter of the diffusing molecules being less than the measured void size. Generally, values of D for oxygen are higher than those for carbon dioxide reflecting the constraints imposed by the void size on the ability of the gas molecules to move through the matrix and the effects of local interactions on the movement of the gas molecules. A surprisingly high value of D for oxygen is observed for A6, it being the polymer with the smallest value of [V.sub.Ps]. The backbone structure in this polymer contains a bis(4'-oxyphenyl) methylene moiety and has a relatively low value of [T.sub.g], which implies weak chain-chain interactions. A7 which contains a 1,5-dioxynapthlene moiety, which would be expected to produce a significantly twist in the polymer backbone exhibits a low values of D, reflecting the influence chain-chain packing and is consistent with a high value of the [T.sub.g]. A5 exhibits a high value of D consistent with the behavior observed in its permeability.

The solubility coefficient S, does not exhibit a significant variation with solubility parameter (Fig. 4C); however, the values for carbon dioxide are significantly higher than those for oxygen which are in turn higher than those for the other gases. Carbon dioxide is clearly able to interact more strong with the polymer backbone than the other gases and reflects its known ability to plasticize polyimides. Oxygen is able to interact more strong than argon which is slightly better than nitrogen. It may be assumed that n-n and dipole induced-dipole interactions are contributing to the observed variations in the solubility coefficients and hence influence the permeability.

In many applications, it is the selectivity as reflected in the ratios of the permeability for various gas pairs that are important in the selection of materials for gas separation applications and values for these polymers are summarized in Table 5.

Comparison of the values obtained, the solubility ratios vary from a minimum of 1.3 to a maximum of 13.8, e.g., of a factor of about 10.6. The range of variation of the ratio of the diffusion coefficients covers an even larger range of 12.2, from a minimum of 0.32 to a maximum of 3.9. Accordingly, it appears that the two parameters have a similar impact on differentiating the permeability ratios. However, it is the relative values which are important and the ratio of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] varies between values of 2.2 and 3.8, indicating a low selectivity for carbon dioxide over oxygen, however values of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], in contrast vary from 6.2 to 21.3 indicating that certain of the polyfether imide)s are capable of exhibiting a high selectivity for carbon dioxide/nitrogen mixtures. Since separation of carbon dioxide from air is of current interest these values suggest that choice of the correct backbone structure is an important factor in achieving high values.

The role the diffusion coefficient plays in determining the permeability is illustrated by the variations observed for the pairs of gases studied. In the case of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], the values vary from 0.32 to 0.7 and for [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] the values vary from 1.07 to 2.08 and for [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], from 1.9 to 3.9. Clearly the void size is influencing the diffusion in certain cases but the similarity between the various ratios is consistent with the lack of trends observed in Fig. 4B. Comparison of the solubility coefficients;

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], indicates the role which solubility plays on the differentiation of gas transport in these systems. Values of the ratios ranging from 1.3 in the case of oxygen/nitrogen to 13.8 in the case of carbon dioxide/nitrogen. The solubility parameter is reflecting the ability of the more polar entities to interact with the matrix as illustrated by comparison of A6 with a value of 13.83 with A12 with a value of 4.48. The ability of the gas molecule to interact with the phenyl ring in the polymer backbone will be changed by methyl substitution in the phenyl ring and this may influence the local mobility of the gas molecules. Similar variations can be seen in the ratio of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], indicating the role of variation of the chemical structure on the solubility coefficient, which also reflects the ability of the gas molecules to interact with the polymer matrix. Comparison of the data for A11 which has a simple methyl bridge in the ether segment with A10 which has a propane bridge shows a significant increase in the permeability values and a corresponding increase in [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], which is approximately doubled and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is increased by 2.59. The methyl substitution occurring on a saturated carbon is having no effect on the polarizability of the phenyl rings but is influencing the spectrum of conformations exhibited by the polymer. Substitution of the methyl group in A1 by the fluoromethyl group in A4 increases the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], ratio by 1.23 and Dco,/Dn, by 1.54 despite a decrease in the ratio of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], by 0.78. It is clear that changes in the ability of the polymers to interact with one another are influencing the ability of the gas molecules to interact with the matrix as reflected in the solubility coefficients but are also influenced by the void structure as reflected in the changes in the values of [V.sub.Ps] and the void structure which is influencing the diffusion behavior.


While changes in the polymer structure have significant effects on the [T.sub.g], the void sizes as measured by PALS and calculated from FFV do not correlate with the observed variation in the [T.sub.g] values indicating the dominant role of chain-chain interactions in defining the temperature for the onset of mobility in these polymers. The higher solubility of C[O.sub.2] in the polyether imides compared to those for the other gases ([O.sub.2], [N.sub.2], Ar) is having a major effect on its permeability. Changing the chemical structure of the ether segment is altering the ability of the gases to diffuse through the matrix as reflected in the variation of [V.sub.Ps] and the interaction of the gas molecules with the matrix as indicated in the changes in the solubility coefficient. Substitution of protons by fluorine atoms in the bridge structure has a significant effect of the gas transport properties. This study implies that the selectivity of membranes can be influenced by careful control of both the void size and the solubility which change with the chemical structure of the ether block of the polyfether imidej's studied.

TABLE 4. Values of the permeability, diffusivity, and solubility obtained for the poly(ether imidejs.


The authors wish to acknowledge the support of the EPSRC in the form of a studentship for F.S.-M., and a post-doctoral research post for J.P., G.C. Eastmond and J. Paprotny have kindly provided the polymers used in this study and also the DSC data from which the [T.sub.g] data was obtained.


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R.A. Pethrick, F. Santamaria-Mendia

WestCHEM, Department of Pure and Applied Chemistry, Thomas Graham Building, University of Strathclyde, Glasgow, G1 1XL, UK

Correspondence to: R.A. Pethrick; e-mail:

DOI 10.1002/pen.24268

TABLE 1. Diols incorporated into the bis(ether anhydride)s to form
the polyimides.

Diol HO-RrOH forming

Name                                            Structure      Code

2,2--bis(4'-hydroxyphenyl)propane             [FORMULA NOT      A10
                                                IN ASCII]
1,1 -bis(4'-hydroxyphenyl)--1-phenyiethane    [FORMULA NOT      A2
                                                IN ASCII]
1,4-dihydroxy-2-phenylbenzene                 [FORMULA NOT      A3
                                                IN ASCII]
2,2-bis(4'-hydroxyphenyl)hexafluoropropane    [FORMULA NOT       A4
                                                IN ASCII]
di-(4-hydroxyphenyl)ether                     [FORMULA NOT       A5
                                                IN ASCII]
Bis-(4'-hydroxyphenyl (methane                [FORMULA NOT       A6
                                                IN ASCII]
1,5-dihydroxynaphthalene                      [FORMULA NOT       A7
                                                IN ASCII]
5,8-dihydroxy-1,2,3,4-tetrahydro-1,           [FORMULA NOT       A8
  4-methanonaphthalene                          REPRODUCIBLE
                                                IN ASCII]
ether link                                         -O-           A9
2,2-bis(4-hydroxy-3,5-dimethylphenyl)         [FORMULA NOT      A10
  propane                                       REPRODUCIBLE
                                                IN ASCII]
Bis(4-hydroxy-3,5-dimethylphenyl)methane      [FORMULA NOT      A11
                                                IN ASCII]
4,4'-dihydroxy-3,3',5,5'-                     [FORMULA NOT      A12
  tetramethylbiphenyl                           REPRODUCIBLE
                                                IN ASCII]

TABLE 2. Physical characteristics of some flexible polyimides;
[T.sub.g] and density at 25[degrees]C.

Polymer code               A1      A2      A3      A4      A5      A6

[T.sub.g] ([degrees]C)     245     245     249     258     256     247
Density (g [cm.sup.-3])   1.190   1.194   1.224   1.283   1.235   1.224
FFV                       0.158   0.145   0.145   0.178   0.156   0.145

Polymer code               A7      A8      A9      A10     A11     A12

[T.sub.g] ([degrees]C)     281     275    >420     274     264    >420
Density (g [cm.sup.-3])   1.225   1.214   1.231   1.140   1.153   1.162
FFV                       0.156   0.156   0.147   0.168   0.167   0.162

TABLE 3. PALS lifetime, intensity, and spherical cavity model results
for the polyimides at 298 K.

Code    [[tau].sub.3]/ns       [I.sub.3]/%              R/nm

A1     2.17 [+ or -] 0,04   19.6 [+ or -] 0.1   0.301 [+ or -] 0.005
A2     2.23 [+ or -] 0.04   19.6 [+ or -] 0.7   0.306 [+ or -] 0.005
A3     2.05 [+ or -] 0.03   17.3 [+ or -] 0.8   0.290 [+ or -] 0.004
A4     2.43 [+ or -] 0.01   20.5 [+ or -] 0.1   0.322 [+ or -] 0.001
A5     2.12 [+ or -] 0.01   18.4 [+ or -] 0.1   0.296 [+ or -] 0.001
A6     1.92 [+ or -] 0.02   16.2 [+ or -] 0.6   0.278 [+ or -] 0.003
A7     2.12 [+ or -] 0.02   19.2 [+ or -] 0.6   0.286 [+ or -] 0.003
A8     2.20 [+ or -] 0.01   18.9 [+ or -] 0.1   0.303 [+ or -] 0.001
A9     2.29 [+ or -] 0.03   15.4 [+ or -] 0.1   0.311 [+ or -] 0.004
A10    2.43 [+ or -] 0.01   21.8 [+ or -] 0.1   0.322 [+ or -] 0.001
A11    2.34 [+ or -] 0.01   22.2 [+ or -] 0.2   0.315 [+ or -] 0.001
A12    2.31 [+ or -] 0.01   19.2 [+ or -] 0.1   0.312 [+ or -] 0.001

                               [([[tau].sub.3] [I.sub.3]).sup.-1]/
Code   [V.sub.Ps]/[nm.sup.3]              [ns.sup.3] %)

A1     0.114 [+ or -] 0.003           0.0050 [+ or -] 0.0003
A2     0.120 [+ or -] 0.003           0.0046 [+ or -] 0.0003
A3     0.102 [+ or -] 0.003           0.0067 [+ or -] 0.0005
A4     0.140 [+ or -] 0.001           0.0034 [+ or -] 0.0001
A5     0.109 [+ or -] 0.001           0.0057 [+ or -] 0.0001
A6     0.090 [+ or -] 0.002           0.0087 [+ or -] 0.0005
A7     0.098 [+ or -] 0.002           0.0054 [+ or -] 0.0003
A8     0.117 [+ or -] 0.001           0.0049 [+ or -] 0.0001
A9     0.126 [+ or -] 0.003           0.0054 [+ or -] 0.0002
A10    0.140 [+ or -] 0.001           0.0032 [+ or -] 0.0001
A11    0.131 [+ or -] 0.001           0.0035 [+ or -] 0.0001
A12    0.127 [+ or -] 0.001           0.0042 [+ or -] 0.0001

TABLE 4. PALS lifetime, intensity, and spherical cavity model
results for the polyimides at 298 K.

Polyimide    IN ASCII]       IN ASCII]       IN ASCII]     [P.sub.Ar]

A1              1.52            4.00            0.30          0.61
A2              1.78            4.14            0.40          0.77
A3              1.46            4.05            0.27          0.56
A4              4.38            14.0            0.85          1.82
A5              1.70            6.26            0.30          0.59
A6              1.57            4.70            0.27          0.55
A7              1.51            3.39            0.32          0.60
A8              1.73            3.94            0.33          0.62
A9              2.38            5.11            0.55          0.96
A10             6.63            25.2            1.50          3.01
A11             3.10            6.61            1.02          1.65
A12             3.25            6.34            1.02          1.63

             IN ASCII]       IN ASCII]       IN ASCII]     [D.sub.Ar]

A1              10.9            4.4             3.6           4.6
A2              13.3            5.8             5.2           6.0
A3              14.9            5.6             5.2           6.3
A4              39.1            20.9            11.3          19.5
A5              19.7            8.5             5.3           6.6
A6              24.3            7.9             6.3           7.8
A7              11.0            4.6             4.1           4.6
A8              14.8            5.3             4.9           6.1
A9              14.5            5.7             5.4           6.1
A10             53.7            37.7            18.1          22.8
A11             16.4            9.3             8.6           9.9
A12             18.2            10.1            7.4           8.7

             IN ASCII]       IN ASCII]       IN ASCII]     [S.sub.Ar]

A1              13.9            91.7            8.1           13.3
A2              13.4            71.7            7.8           12.6
A3              9.8             73.0            5.3           8.9
A4              11.2            66.9            7.5           9.3
A5              8.7             73.5            5.6           8.9
A6              6.4             59.5            4.3           7.0
A7              13.7            74.2            7.8           13.2
A8              11.7            73.9            6.7           10.1
A9              16.4            89.1            10.1          15.8
A10             12.3            66.9            8.3           13.2
A11             19.0            70.9            11.9          16.7
A12             17.8            62.3            13.9          18.7

P is [10.sup.-10] [cm.sup.3] (STP) [cm.sup.-1] [cmHg.sup.-1], D is
[10.sup.-9] [cm.sup.2] [s.sup.-1], S is [10.sup.-3] [cm.sup.3] (STP)
[cm.sup.-3] [cmHg.sup.-1].

TABLE 5. Ratios of permeability, diffusivity, and solubility
coefficients for carbon dioxide, nitrogen, and oxygen.

Polyimide                        A1      A2      A3      A4

[MATHEMATICAL EXPRESSION NOT    2.63    2.32    2.77    3.19
[MATHEMATICAL EXPRESSION NOT    13.33   10.35   15.0    16.47
[MATHEMATICAL EXPRESSION NOT    5.06    4.45    5.40    5.15
[MATHEMATICAL EXPRESSION NOT    0.40    0.43    0.37    0.53
[MATHEMATICAL EXPRESSION NOT    1.22    1.11    1.07    1.89
[MATHEMATICAL EXPRESSION NOT     3.0     2.6     2.9     3.4
[MATHEMATICAL EXPRESSION NOT    6.59    5.35    7.44    5.97
[MATHEMATICAL EXPRESSION NOT    11.32   9.18    13.77   8.92
[MATHEMATICAL EXPRESSION NOT    1.71    1.71    1.84    1.49

Polyimide                        A5      A6      A7      A8

[MATHEMATICAL EXPRESSION NOT    3.68    2.99    2.24    2.27
[MATHEMATICAL EXPRESSION NOT    20.86   17.40   10.59   11.93
[MATHEMATICAL EXPRESSION NOT    5.66    5.81    4.71    5.24
[MATHEMATICAL EXPRESSION NOT    0.43    0.32    0.42    0.36
[MATHEMATICAL EXPRESSION NOT    1.60    1.25    1.12    1.08
[MATHEMATICAL EXPRESSION NOT     3.7     3.9     2.7     3.0
[MATHEMATICAL EXPRESSION NOT    8.44    9.29    5.41    6.31
[MATHEMATICAL EXPRESSION NOT    13.12   13.83   9.51    11.02
[MATHEMATICAL EXPRESSION NOT    1.55    1.48    1.75    1.74

Polyimide                        A9      A10     A11     A12

[MATHEMATICAL EXPRESSION NOT    2.14    3.80    2.13    1.95
[MATHEMATICAL EXPRESSION NOT    9.29    16.80   6.48    6.21
[MATHEMATICAL EXPRESSION NOT    4.32    4.42    3.03    3.18
[MATHEMATICAL EXPRESSION NOT    0.39    0.70    0.56    0.55
[MATHEMATICAL EXPRESSION NOT    1.05    2.08    1.08    1.36
[MATHEMATICAL EXPRESSION NOT     2.7     3.0     1.9     2.5
[MATHEMATICAL EXPRESSION NOT    5.43    5.44    3.73    3.51
[MATHEMATICAL EXPRESSION NOT    8.82    8.06    5.95    4.48
[MATHEMATICAL EXPRESSION NOT    1.62    1.48    1.59    1.28
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Author:Pethrick, R.A.; Santamaria-Mendia, F.
Publication:Polymer Engineering and Science
Article Type:Report
Date:Apr 1, 2016
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