Molecular modelling of polyimide membranes for gas separation

DESALINATION Desalination

144 (2002) 67-72 www.elsevier.com/locate/desal

Molecular modelling of polyimide membranes for gas separation Matthias Heuchel*“, Dieter Hofmannb GKSS Research Center; Institute of Chemistry, Kantstrasse 55, D-14513 Teltow, Germany “Tel. +49 (3328)352-465; “Tel. +49 (3328) 352-247; Fax: +49(0)3328/352-452; emails: [email protected], dietel:[email protected] Received

1 February 2002; accepted 15 February

2002

Abstract Well-equilibrated molecular packing models have been produced for seven different polyimides. For all packings the transport properties (solubility and diffusion coefficient) have been calculated for nitrogen, oxygen and carbon dioxide using the Gusev-Suter method. Comparison with experimental data allowed to validate the quality of the model structures. A significant improvement to former results could be assessed for the predicted selectivity values. Keywords: Polyimide;

Gas transport; Simulation;

Solubility;

1. Introduction Polyimides (PIs) have attracted much attention over the past years as material for gas separation membranes [l-3]. Particular PIs synthesized from 2,2’-bis(3,4-dicarboxy-phenyl) hexafluoropropane dianhydride (6FDA) show surprisingly high gas selectivities for gas pairs as 0,/N, and CO&H,. Combined with high inherent chemical and thermal stability as well as mechanical strength, these PIs have been identified as promising materials for

*Corresponding author. Presented at the International .Iu!\ 7-12, 2002.

Congress on Membranes

Diffusion;

Selectivity

applications, such as the recovery of H, from industrial gas mixtures of CO,, N, or CH,, the purification of natural gas and the enrichment of either 0, or N, from air. One stimulus for the extensive research was the observed tradeoff relationship between gas permeability and permselectivity. Over the last 2 decades, intensive investigations have been performed to study the structure property relationships of polyimides by systematically changing the diamine or dianhydride moieties [4-6]. Analysis of this immense experimental material allowed and Membrane

Processes

00 1I-9 I64/02/$- See front matter 0 2002 Elsevier Science B.V. All rights reserved PII: SOOll-9164(02)00290-4

(ICOM), Toulouse, France,

M. Heuche, D. Hofmnnn /Desalination

68

the development of empirical principles. It was found that the incorporation of bulky groups into the polymer backbone increased the permeability, whereas rigid polymeric segments tended to enhance the permselectivity. A good example is the hexafluoropropane -C(CF3)2- linkage in 6FDA-based polyimides which hinders the rotation of neighboring phenyl rings. As result the respective PIs show higher selectivity values at a specific permeability than PIs without this group [7,8]. The indications of the last paragraph concerning the possible connection between polymer structure and the transport properties of permeating gases in these structures show already the complexity of this relation. Therefore, it is highly desirable to investigate these systems also on an atomistic level. Over the past years molecular modeling investigations have already been used to gain a deeper insight into the structure and the transport behavior of nonporous amorphous polymer

I44 (2002) 67-72

membranes. General results of these investigations can be found, for example, in a number of reference and feature articles [9-121. In this article we show on seven PIs how adequate atomistic packing models can be “built” with molecular modeling techniques for such glassy, rigid, rodlike polymers. Further interpretation of the results, including the calculation of other properties [such as fractional free volume (FFV) distributions, backbone mobility, sorption data, etc.] for the PIs from the molecular packings, are presented in an extended paper that is in preparation [ 131. 2. Polyimides The investigated PIs are listed in Table 1. The left column contains our acronym for the PIs and the formula for the repeat unit. The next column to the right gives typical names of the PIs that are

Table 1 Structural and physical properties of the selected polyimides

GFDA-durene

KAP

-‘bk++ 0 0

GFDA-ODA

W&19,23, 27-2911

PMDA.ODA

[5_6,26]

1.43 fO.OO

572 fll

1.40 fO.01

622 275

4+1

0.5 f0.3

h4. Heuche,

D. Hofmann /Desalination

used in experimental investigations. Whenever possible we have averaged single experimental data from different research groups. All sources of experimental values for specific PIs used here and later for comparison of physical and transport properties with our simulation results are summarized in another column. The experimental density of the PIs was reproduced by our models with an accuracy of 0.02 g/cm”. The glass transition temperature (T,) is a good measure of the stiffness of the polymer structure. In comparison with the right column, which shows in decreasing order experimental permeability values of oxygen in the PIs, we see that no simple correlation exists to the TRvalues and that also the experimental data are often afflicted with substantial scattering. 3. Model construction For each of the polymers three independent atomistic bulk models were realized utilizing the amorphous cell module of InsightIUDiscover Software (Accelrys, Inc.) [30]. The basic techniques used are described in [ 111. The newly developed COMPASS force field of Accelrys was used [3 1,321 in all cases. The calculations were performed on two SGI Octane machines and an eight-processor SGI 2100. The model packings consist of about 4500 atoms (60-80 residues) each. For the packing procedure a new general methodology was developed consisting of four steps: (1) the “initial packing,” where the polymer chain and spacer molecules were packed in an amorphous cell at a lower density (about 10% of the final density); (2) the energy minimisation and MD runs combined with “scaling” of conformation energy terms and nonbonded interaction energy terms in the force field: (3) a set of MD runs to increase the density; and (4) longer MD runs for the final equilibration. For the PIs the initial packing procedure, step 1, was performed with an atactic chain of 60 to 80 repeat units (about 4500 atoms) at a density of 1.2 to 1.5 g/cm3. It can be assumed that, for stiff chain polymers, the effects of spatial non-

144 (2002) 67-72

69

uniformity would escape when modeling with relatively short chains. Because of it, we consider the PI chains twice as long than those which have been dealt with in some of the earlier works [ 1 I] on simulation of PIs. Since all our PIs contain cyclic subunits (here, phenylene rings) in the repeat units, the packing and equilibration stages were much more laborious and time consuming than in the ease of other polymers (e.g., ‘[ll]). For PIs the “traditional” packirrg algorithm may lead to artifacts of catenated phenylene rings or a spearing of side groups or backbone chains through ring sub-structures. Both effects are, of course, unacceptable and must be avoided. To solve this technical problem, it is usually necessary to start with a very low initial packing density (typically 0.1 g/cm3). For all PIs, this approach alone did, however, not lead to a complete avoiding of catenation and spearing events. Therefore, an additional set of small molecules (e.g., 200-500 methanol molecules or 200-300 Si atoms) was added randomly in the simulation box before the packing of the polymer was started to represent small obstacles preventing the respective growing polymer chains from ring catenations and spearings. The obstacle molecules are later, of course, to be removed again. The side lengths of the resulting packing cell were about 37-39 A. The resulting initial packing models were equilibrated according to a scaling procedure, step 2, outlined in a recent publication [33]. The individual stages lasted for 5-10 ps and were always preceded by a short energy minimization of several hundred iterations. Afterward, at step 3 of the procedure, a NpT run at a pressure 0.01 Mbar was performed to compress the packing approximately to the experimental density. This step was followed by NVT simulations at 600 and 300K to anneal the newly compressed packing. Next, at step 4, a 20-ps NpT simulation at 1 bar was performed to check the course of the density fluctuations. In some cases the density decreased more than 20% below the experimental values. In such cases, either the compression cycle was repeated or, if this procedure did not succeed, in

70

M. Heuche,

D. Hofmann /Desalination

further steps NVT simulations had to be performed (see KAP and ODA in Table 2). Finally a longer 300-ps MD run was performed for each of the models in order to further improve the equilibration. At least three independent packing models were built for every polymer. These models correspond to three different possible local chain segment assemblies of the respective PI. 4. Validation of the packing models We used the TST after Gusev and Suter [3436] to calculate for N,, 0, and CO, the diffusion constants (D) in polymer matrices and the solubility (S) of the gas in the matrix. The primary transport properties S and D for nitrogen and oxygen could be determined with the packing models within the same order of magnitude as the experiment. The results are shown in Table 2 in comparison

144 (2002) 67-72

with experimental data from the literature (for experimental references see Table 1). The deviation for 0, and N, is in general below a factor of three, except for the solubility values in KAP and ODA. This outcome for the selected PIs is in good accordance with recent simulation results for rubberlike materials and earlier simulations for PI membranes [ 111. The larger deviation for ODA and KAP is probably related to an insufficient parametrization of the ether oxygen in the diamine moieties through the COMPASS force field under Insight11 [37]. As a third permeate molecule the larger carbon dioxide was used. As can be seen from Table 2 for CO,, the simulated solubilities are always too high, and the calculated diffusion coefficients are in general one or two orders of magnitude too small. In reality, the interaction of CO, with the glassy PIs is strong and leads to structural relaxa-

Table 2 Calculated and experimental solubility (5) and diffusion coeffkient (D) for oxygen, nitrogen and carbon dioxide PI

Method

Sol, (bar)-’

(bar)-]

Experimental

Calculated

Experimental

Calculated

Experimental

1.7hO.4 2.4&l .3 1.8 0.910.2 0.9kO.3 0.5+0.1

2.4hO.2 1.9+0.0 0.8kO.l 2.OkO.3 2.3+0.2 2.4+0.1 2.OkO.3

1.2zto.2 1.5kO.6 1.5

84%7 68+5 36*12 76*10 106&18

18k15 13+7 30 -

NPT NPT NPT NPT NPT NVT NVT

3.4kO.l 2.8kO.l 1.4+0.1 2.9ztO.3 3.4kO.3 3.7+0.1 3.3kO.3

PI

Method

Do,, lo-* cm2/s

NPT NPT NPT NPT NPT NVT NVT

&,+,

Calculated PI3 PI4 T6 B4 BAAF ODA KAP

PI3 PI4 T6 B4 BAAF ODA KAP

SN2,(bar)-’

0.7&O.1 0.5kO.O 0.350.0

DN2, lo-* cm2/s

151*8 211*14

4.4hO.5 5.9+1.7 3.8*0.6

D co2, IO-’ cm*/s

Calculated

Experimental

Calculated

Experimental

Calculated

Experimental

41+20 106rt26 73+3 58*22 32*4 7.5+3.0 1.7hO.9

68+8 47*22 28 10*2 3.2*0.8 0.6*0.5

13*7 41zt8 28k4 19*9 10*2 2.OkO.8 0.4zto.3

27+12 20*8 8 3 3k2 1.0*0.2 0.2hO.2

0.5hO.3 2.8kO.5 l.ktO.9 0.5kO.3 0.2+0.1 0.03*0.02 0.004

34ztl2 34*17 9 8*3 2.2k1.5 0.5hO.3

71

M. Heuche, D. Hofmann / Desalination 144 (2002) 67-72

tions. This behavior violates the assumption of the TST after Gusev and Suter, where the dynamics of the dissolved molecules is coupled only to the elastic thermal motion of the dense polymer and can be treated separately from their structural relaxations. The results for CO, show clearly the necessity to allow in TST calculation the matrix to be locally flexible (as assumed in the methodological developments of a current EU project*). Only then will it be possible to calculate reasonable transport properties for CO, and larger permeate molecules. 5. Quantitative

prediction of 0,/N, selectivities

A significant improvement to former results could be assessed for the calculated 0,/N, selectivity values, shown in Table 3. This is probably a consequence of the application of the newest force field COMPASS. This force field seems to be better adjusted to density-related properties in polymers. With older force fields, pcff or cvff, comparable selectivity values showed at random higher or lower values relative to the experiment [ 111. In former simulation studies it was not possible to find, especially for glassy polymers, such comparatively consistent trends for the change of selectivity as now for the PIs shown in Table 3. In good accordance with the experiment, we see also from the modeled data that, with decreasing permeability P for oxygen (e.g., indicated Table 3 Calculated PI

PI3

and experimental Method

selectivity

by the PO2value in Table I), the permselectivity for oxygen over nitrogen Po2/PN2is increasing and further that this increase is a result of the different diffusivity of both compounds in the specific PIs. The diffusion selectivity D,/D, shows the same whereas variation as the permselectivity $oZIPNZ, the solubility selectivity S02/S,2 varies much less for the set of PIs. In an upcoming paper [13], the presented selectivity results will be discussed on a molecular level with the help of FFV distributions as a measure of the three-dimensional structure of the PIs and with results from long MD simulation given information about the dynamic properties of the polymer chains and the permeate molecules. Acknowledgements This research was supported by the European Commission Growth Program, PERMODMolecular modelling for the competitive molecular design of polymer materials with controlled permeability properties, Contract #GSRD-CT2000-200. References [I] D.R. Paul and Yu.P. Yampolskii, Eds., Polymeric Gas [2]

[3]

Separation Membranes, CRC Press, Boca Raton, FL, 1994. L.M. Robeson, W.F. Burgoyne, M. Langsam, AC Savoca and C.F. Tien, High performance polymers for membrane separation, Polymer, 35 (1994) 4970-4978. M. Langsam, Polyimides for gas separation, in: M.K. Ghosh and K.L. Mittal, (Eds.), Polyimides: Fundamentals and

values for O,/Nz separation on seven polyimides

so&G2

(permeability

P = S*D)

pOzfpN2

Do,&,

Calculated

Experimental

Calculated

Experimental

Calculated

Experimental

NPT

1.4+0.1

1.4*0._5

3.1zko.4

2.3kO.3

3.6zkO.4

3.5kO.3

l.SO.2

2.510.2

2.8ztO.8

3.6~0.4

3.5kO.3

3.4

4.61tO.7

4.1

4.7zt0.8

3.7

NPT

1.5*0.0

T6

NPT

1.710.1

1.2

2.7kO.5

B4

NPT

1.5*0.1

-

3.210.5

BAAF

NPT NVT

1.5kO.O

1.41tO.l

3.2kO.3

3.4*0.5

4.8kO.4

4.6&O. 1

ODA

1.5*0.1

1.7+0.5

4.0*0.8

3.5*1.4

6.kt1.2

5.5*1.1

KAP

NVT

1.710.0

1.6rtO.3

4.8*0.8

4.0*1.2

8.0&l .3

6.2&l .5

PI4

12

M. Heuche, D. Hofmann

/Desalination

applications, Marcel Dekker, New York, 1996. Y. Li, X. Wang, M. Ding and J. Xu, Effect of molecular structure at the permeability and permselectivity of aromatic polyimides, J. Appl. Polym. Sci., 61 (1996) 741-748. [51 Y. Mi. S.A. Stern and S. Trohalaki, Dependence of the gas permeability of some polyimide isomers on their intrasegmental mobility, J. Membr. Sci., 77 (1993) 41-48. [61 Y. Hirayama, T. Yoshinaga, Y. Kusuki, K. Ninomiya, T. Sakakibara and T. Tamari, Relation of gas permeability with structure of aromatic polyimides 1, J. Membr. Sci., I I I (1996) 169-182. [71 T.H. Kim. W.J. Koros, G.R. Husk and K.C. O’Brien, Relationship between gas separation properties and chemical structure in a series of aromatic polyimides, J. Membr. Sci., 37 (1988) 45-62. [81 K. Tanaka, H. Kita, M. Okano and K. Okamoto, Permeability and permselectivity of gases in fluorinated and nonfluorinated polyimides, Polymer, 33 (1992) 585-592. compu[91 F. Mtiller-Plathe, Permeation of polymers-a tational approach, Acta Polym., 45 (1994) 259-293. [lOI A.A. Gusev, F. Mtiller-Plathe, W. F. van Gunsteren and U.W. Suter, Dynamics of small molecules in bulk polymeres, Adv. Polym. Sci., 16 (1994) 207-247. [ill D. Hofmann, L. Fritz, J. Ulbrich, C. Schepers and M. Bohning, Detailed-atomistic molecular modelling of small molecule diffusion and solution processes in polymeric membrane materials, Macromol. Theor. Simul., 9 (2000) 293-327. D. Hofmann, L. Fritz, J. Ulbrich and D. Paul, Molecular simulation of small molecule diffusion and solution in dense amorphous polysiloxane and polyimides, Comput. Theor. Polym. Sci., IO (2000) 4191136. [ 131 M. Heuchel. D. Hofmann, S. Fudaley and P. Pulumbi, in preparation. [ 141 K. Tanaka, M. Okano, H. Toshino, H. Kita and K. Okamoto, Effect of methyl substituents on permeability and permselectivity of gases in polyimides prepared from methyl-substituted phenylenediamines, J. Polym. Sci. B Polym. Phys., 30 (1992) 907-914. [ 151 D. Hofmann, J. Ulbrich, D. Fritsch and D. Paul, Molecular modelling of gas transport in amorphous polyimide and poly(amide imide) membrane materials, Polymer, 37 (1996) 4773-4785. [I61 W.-H. Lin, R.H. Vora and T.-S. Chung, Gas transport properties of 6FDA-durene/l,4-phenylenediamine (pPDA) copolyimides, J. Polym. Sci. B Polym. Phys., 38 (2000) 2703327 13. 1171 R.A. Hayes, U.S. Patent 4,705,540, to DuPont (1987). [18] S. Matsui. H. Sato and T. Nakagawa, Effects of low molecular weight photosensitizer and UV irradiation on gas permeability and selectivity of polyimide membrane, J. Membr. Sci., 141 (1998) 31-43. [19] C.K.Yeom,J.M.Lee,Y.T.Hong,K.Y.ChoiandS.C.Kim, Analysis of permeation transients of pure gases through dense polymeric membranes measured by a new permeation apparatus, J. Membr. Sci., 166 (2000) 71-83. 1201 M. Al-Masri, H.R. Kricheldorf and D. Fritsch, New [41

144 (2002) 67-72

polyimides for gas separation. 1. Polyimides derived from substituted terphenylenes and 4,4’-(hexafluoroisopropylidene)diphthalic anhydride, Macro-molecules, 32 (1999) 7853-7858. [2 I] H. Tsuzumi, K. Toi, T. Ito and T. Kasai, Relationship between thermal properties and diffusion coefficients of gases for polyimide films, J. Appl. Polymer Sci., 64 (1997) 389-397. [22] M. Langsam and W.F. Burgoyne, Effect of diamine monomer structure on the gas permeability of polyimides. I. Bridged diamines, J. Polym. Sci. A Polym. Chem., 31 ( 1993) 909-921. [23] M.R. Coleman and W.J. Koros, Isomeric polyimides based on fluorinated dianhydrides and diamines for gas separation applications, J. Membr. Sci., 50 (1990) 285-297. [24] M. Mikawa, S. Nagoaka and H. Kawakami, Gas transport properties and molecular morions of 6FDA copolyimes, J. Membr. Sci., 163 (1999) 167-176. [25] K. Matsumoto, P Xu and T. Nishikimi, Gas permeation of aromatic polyimides. I. Relationship between gas permeabilities and dielectric constants, J. Membr. Sci., 81 (1993) 15-22. [26] C.M. Zimmetman, A. Singh and W.J. Koros, Diffusion in gas separation membrane materials: a comparison and analysis of experimental characterization techniques, J. Polym. Sci. B Polym. Phys., 36 (1998) 1747-1755. [27] K. Matsumoto and I? Xu, Gas permeation properties of hexafluoro aromatic polyimides, J. Appl. Polym. Sci., 47 (1993) 1961-1972. [28] S.A. Stern, Y. Mi, H. Yamamoto andA.K. St. Clan, Structure/ permeability relationship of polyimide membranes. Applications to the separation of gas mixtures, J. Polym. Sci. B Polym. Phys., 27 (1989) 1887-1909. [29] Y. Li, X. Wang, M. Ding and J. Xu, Effect of molecular structure at the permeability arrripermselectivity of aromatic polyimides, J. Appl. Polym. Sci., 61 (1996) 741-748. [30] Polymer User Guide, Amorphous Cell Section, Ver-sion 4.0.0, Molecular Simulations, San Diego, 1996. [3 l] H. Sun and D. Rigby, Polysiloxanes: Ab initio force-field and structural, conformational, and thermophysical properties, Spectrochim. Acta, 53A (1997) 1301-1323. [32] D. Rigby, H. Sun and B.E. Eichinger, Computer simulations of poly(ethylene oxide): Forcefield, PVT diagram, and cyclization behavior, Polymer Int. 44 (1997) 3 1l-330. [33] D. Hofmann, M. Heuchel, Yu. Yampolskii, V. Khotimskii and V. Shantarovich, Free volume distributions in ultra-high and lower free volume polymers: Comparison between molecular modeling and positron lifetime studies, Macromolecules, 35 (2002) 2129-214. 1341 A.A. Gusev and U.W. Suter, Theory of solubility in static systems, Phys. Rev. A, 43 (1991) 6488-6494. [35] A.A. Gusev, S. Arizzi, U.W. Suter andD.J. Mall, Dynamics of light gases in rigid matrices of dense polymers, J. Chem. Phys. 99 (1993) 2221-2227. 1361 A.A. Gusev and U.W. Suter, Dynamics of small molecules in dense polymers subject to thetmal motion, J. Chem. Phys. 99 ( 1993) 2228-2234. [37] D. Rigby, private communication.