J. Chem. SOC., Faraday Trans. 1, 1986,82, 2057-2063 Mechanism of Permeation through Molecular-sieve Carbon Membrane Part 1.-The Effect of Adsorption and the Dependence on Pressure Jacob. E. Koresh* and Abraham Soffer Chemistry Division, The Nuclear Research Center, Negev, P.O. Box 9001, Beer Sheva, Israel The permeation in narrow-pore molecular-sieve carbon membranes (MSCM) is governed by adsorption and activated transport and proceeds exclusively through the ultramicropores. Contribution from the solution- desolution mechanism is unlikely. The dependence of permeabilities on pressure and extent of pore opening has been studied. On the basis of adsorption isotherms the relation between adsorption and permeation is established. It is maintained that the slope of the adsorption isotherm of the penetrant determines the concentration gradient responsible for the flow through the membrane.For weakly adsorbing gases, permeability is inde- pendent of pressure, as corresponding to a free molecule in the pore system or to a linear adsorption isotherm. For adsorbing gases permeability decreases with pressure, owing to the decrease in the slope of the type I adsorption isotherm. Gas separation processes are based mainly on fractional distillation, adsorption and selective chemical reactivity. These processes are essentially cyclic, and so relatively elaborate and energy demanding in most cases. During the last few decades the polymer membrane separation processes from liquid systems had been utilized in several industrial applications. Nowadays reverse osmosis, ultrafiltration and dialysis are well known membrane processes for liquid treatments.Although gas permeation through polymer membranes was also under current fundamental study,l it was only in 1977 that an industrial gas-separation process was introduced.2 Since then considerable efforts have been devoted to studying and utilizing polymer membranes for gas separation through this simple and energy-saving process. New polymers with better permeability-selectivity combinations are currently being developed. So far the relatively young science and technology of membrane gas separation has been combined primarily to synthetic polymer materials. During the recent years of our research on molecular-sieve carbon adsorbent~~-~ we have shown that the molecular- sieving effect of non-graphitizing carbonslO is extremely specific and adjustable by mild activation and sintering steps to the discrimination range 2.8-5.2 A.Recognizing that pyrolysis of polymers yields an exact mimic of the morphology of the parent material if it does not proceed through a melt, it took a short while to produce a carbon molecular-sieving membrane from a thermosetting polymer membrane. l1 The permeation characteristics of the MSCM can be readily varied by changing the high-temperature treatment parameters. This is in contrast to polymer membranes, where such variations frequently involve the synthesis of a new membrane material. As with carbon molecular-sieve adsorbents, the pore size will serve as a core parameter in studying the MSCM properties. Comparing carbon with polymer membranes, the former may be considered as a refractory porous solid into which the permeates are non-soluble and merely penetrate the pore system.In this sense the permeation mechanism through the MSCM is much 20572058 Molecular-sieve Carbon Membrane simpler than that of glassy polymer membranes, whereas the dissolution-diffusion- desolution mechanism may take place in addition to penetration through domains of low polymer density. Therefore the influence of adsorption of permeates on the pore walls of carbon has to be taken into consideration, especially in the case of penetrants with relatively high boiling points. As a membrane material, carbon was expected to exhibit different and unique properties as compared with synthetic polymers. These are in addition to its important advantage of high-temperature stability. In a preliminary study we demonstrated some of its unique properties, namely the molecular-sieving transport mechanism, its high- temperature stability up to 900 "C and its extraordinary high separation power PS (where P is the intrinsic permeability and S the selectivity), which is 1-2 orders of magnitudes greater than that of any known polymeric membrane.In the same paper it was shown that enlarging the pore dimensions by mild oxidation steps can be carried out with the carbon membrane in a similar manner as with the carbon molecular-sieve adsorbents. This is considered to be initial evidence for the molecular-sieving mechanism of permeation through the carbon membrane.In this paper further evidence of the molecular-sieving mechanism of permeation is given, and the dependence of permeabilities and selectivities on temperature, pressure and extent of pore opening is discussed, for both adsorbing and non-adsorbing permeates. Experiment a1 Adsorption measurements were carried on in a conventional volumetric high-vacuum system. The permeability system and the membrane cell were the same as described previously.ll Since the hollow fibres were end-sealed with epoxy resin which cannot withstand high temperatures, the heating zone skipped these ends. As a result, part of the hollow-fibre membrane was colder than the centre when it was heated to several hundred "C. Our high-temperature permeability data refer to the hottest zone.The gases studied were H,, He, N,, Ar, Xe, O,, CO,, N,O, SF, and CH,. All the permeability measurements were carried on with pure gases. The permeability unit used is the barrer, expressed as a flow of loplo cm3 (s.t.p.) s-l of a fluid passing through a membrane of 1 cm2 in surface area and 1 cm in thickness. The pressure difference across the membrane was 500 Torrf- or less. The average pressure was spanned up to 6000 Torr. Results and Discussion Permeability, Adsorbability and Pore Size We have shown in a previous study3 that degassing a molecular-sieve carbon at gradually higher temperatures enlarge the pores first, owing to abstraction of surface carbon atoms as carbon oxides. At higher temperatures, pore closure commences owing to progressive annealing.To demonstrate this trend, adsorption-rate experiments were employed. It would be of interest to find out whether permeation, like the adsorption rate, follows the same trend, A series of carbon membranes of different pore dimensions were produced by treating a carbon membrane at gradually higher temperatures. In parallel, the same polymer precursor (not necessarily in a membrane form) was treated similarly and prepared for adsorption experiments. The adsorbability data are summarised in table 1. Adsorbability is estimated using four qualitative degrees of adsorption kinetics: (i) n.a. - implies no detectable adsorption; (ii) v.s.a. - very slow adsorption, i.e. adsorption equilibrium is not attained within tens of hours; (iii) s.a. - slow adsorption; adsorption equilibrium would require few hours; (iv) a fast adsorption denoted by specifying the amount adsorbed at the plateau of the typical type I isotherm in mmol ggl.Using this qualitative scale is satisfactory, since the adsorption rate on carbon molecular sieves changes by orders of t 1 Torr = 101 325/760 Pa.J. E. Koresh and A . So@- 2059 Table 1. Adsorption data for different carbon membranes (in mmol g-') membrane CO, at H, at N, at Xe at SF, at materiala 80 "C 196 "C 196 "C 80 "C 80 "C M-300 M-400 M-500 M-600 M-700 M-SO0 M-900 M- 1 000 v.s.a. s.a. 3.6 3.4 3.4 3.4 3.0 2.6 n.a. n.a. v.s.a. n.a. s.a. 4.4 4.4 4.4 s.a. v.s.a - - - - - - n.a. n.a. n.a. > 106b 1 06b 21 n.a. ma. n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. a The membrane designations indicate the high-temperature treatment temperature.In pmol min-1. magnitude upon slight variations in pore size.3 Therefore, precise adsorption-rate data are unnecessary for a coarse adsorbability scale. The membrane designation shows the highest temperature of heat treatment. In table 1 adsorbability data are given for membrane materials that had been heated for gradually higher temperatures. Recognizing that the adsorbability sequence of the molecules in table 1 is CO, > H, > N, > Xe > SF,, it is evident that, starting from low HTT, the M-300 membrane acquires the narrowest porosity. Pore dimensions gradually increase up to the M-600 or M-700 membrane, then pore closure commences. The permeabilities of hydrogen and methane through a similar series of carbon membranes is given in fig.1. As for adsorbability, the permeability through the membrane passes through a maximum at 600-700 "C, thus furnishing further evidence for the molecular-sieving mechanism of permeation through the carbon membrane and for the simplicity of modifying its properties. Dependence of Permeability on Pressure In fig. 2 and 3 are shown the permeabilities of various gases plotted against the average pressure applied across the membrane. It is evident that, within the accuracy of the experimental results, the permeabilities of the low-boiling-point gases hydrogen, helium, oxygen and argon are independent of pressure (fig. 2). The permeability of methane, on the other hand, drops upon increasing the pressure. This drop is even more significant for the case of carbon dioxide and nitrous oxide.This trend seems to follow the sequence of intermolecular interactions i.e. adsorption of CH,, CO, and N,O impedes the permeation of these gases. These results may be interpreted as follows. The local flux, J , of a permeate through a unit membrane surface area is given by J = - P(dp/dx) ( 1 ) where P is the permeability (by definition) and dp/dx is the local pressure drop across the membrane. The pressure p in these equations is a local pressure determined as the bulk pressure that would determine the amount adsorbed locally according to an isotherm. It is an intermediate between the two bulk pressures on both sides of the membrane. Fick's first law is given by J = - D(dC/dx) (2) where D is the diffusion coefficient and dC/dx is the gradient of the local concentration of the permeate within the membrane.Combining the above two equations leads to P = D(dC/dp). (3)2060 1 2 10 g P N 1 a , 4 0 0. 0. 0. 0. 2 0. b P N I ; 0. 0. 0. 0. 1 I I I I I - - 1 . 2 1 . 4 *d 0 * - - 1 . 0 3 5 6 - - 0 . 8 ,p 2 L g - I O - 7 m Q - 0 . 6 0 - 0.4 L 2 - I I I I I ' - 0 . 2 Molecular-sieve Carbon Membrane I T/OC Fig. 1. Permeability of CH, and H, in membranes heat-treated to various temperatures: 0, CH,; 0, H,.J. E. Koresh and A. Sofler 206 1 5 - I I I I I I 4 - 33: - 3- 2 0 1 I I I I I 1 . - l-4 E P N 9 - 2 ;2- 7 - I I I I I I 0 1 2 3 4 5 6 5 3 . O 2 . 5 LI E m P 2.0 7 2 ;2 1.5 1 .o p/mTorr Fig. 3. Permeabilities of CO,, N,O and CH, plotted against the average pressure applied across the membrane.0, CH,; 0, N,O and *, CO,. LI 2 m .Q N I 2 k Fig. 4. Permeabilities of CO, plotted against the average pressure applied across the membrane at various temperatures: 0, 25; *, 100 and 0, 200 "C. To a first approximation we may assume that, at the presently encountered very low relative pressures p/po (where po is the vapour pressure of the penetrant), adsorption is low and interaction between the penetrant molecules is negligible, so that the diffusion coefficient is independent of the local concentration. Therefore the dependence of permeability on pressure should be analysed only through the derivative dC/dp in eqn (3). The local concentration C of the permeate obeys the adsorption isotherm c = F(P) (4) whereas dC/dp is its slope at a pressure p .It is well known that adsorption isotherms in molecular-sieving adsorbents are of type I, namely the isotherm slope is constant and high at low pressures and decreases upon increasing pressure. With respect to eqn (3), this readily explains the decrease in permeability upon increasing the pressure. This behaviour could be formulated mathe-2062 I I I I t I , 3 .O 2.5 h W 5 P P) 2.0 2 2 1.5 Molecular-sieve Carbon Membrane I 1 1 1 I- \ * - 1 matically by employing a type I adsorption isotherm, Let us take the Langmuir isotherm as a representative : where C, is the adsorption saturation capacity and b is an interaction parameter. By differentiating this equation and substituting in eqn (3), we obtain which shows that the permeability is a decreasing function of pressure.This is a general result of the curvature of a type I isotherm: it is not specific to the Langmuir mode. At high temperatures and the same pressure range, the interaction parameter of the Langmuir type isotherm becomes exponentially smaller,12 so that the isotherm resides at its linear portion, i.e. dC/dp is independent of pressure; therefore the decrease in the dependence of permeability on pressure at higher temperature is as shown in fig. 4 and 5. It is of interest to refer at this point to our previous work on the mechanism of penetration of an adsorbate into a particle of molecular-sieving ad~orbent.~ In that case we made use of the experimental fact that the adsorption rate in microporous media decreases upon increasing the amount adsorbed, so that a thin adsorption saturation layer is created at the outermost face of the porous adsorbent particle at the moment of exposure to the gas.Through this layer the transport rate is slowest, so that it becomes the rate-determining step for adsorption into the depth of the particle. In this work we provide an interpretation of this phenomenon, namely that it originates from the decreasing slope of the type I isotherm. Adsorption in a porous particle is a rate process, just as is penetration through a membrane. Both should essentially obey the same mechanism. However, unlike the previous adsorption study, in the present membrane study the pressure-temperature combination is such that adsorption saturation is not achieved. Therefore, the previously anticipated amplification of selectivity is not likely to occur for the case of membranes at or above room temperature.Returning to the light gases Ar, O,, H, and He, their interaction parameters which give rise to adsorption are much smaller than that of CO, for the same temperature; their adsorption isotherms are thus linear and the corresponding permeabilities are independent of pressure at lower temperatures as is observed in fig. 2. A comprehensive discussion of the permeability dependence on temperature must take into account the variation with temperature of the diffusion constant D in eqn (3). Thus a prolonged residence time of the adsorbed molecule at the pore's wall corresponds to C = Co bp/( 1 + bp) ( 5 ) P = DC, b / ( l + bp)2 (6)J . E. Koresh and A .Sofer 2063 blocking the pores with the penetrant at low temperatures, while a virtually zero residence time will approach the limiting case of Knudsen diffusion at high temperatures. This more complex situation will be discussed later. This work was supported by the Israel National Council for Research and Development. We are indebted to S. Saggi and D. Rosen for skilled technical assistance. References 1 S. A. Stern, in Membrane Separation Processes, ed. P . Meares (Elsevier, Amsterdam, 1976), chap. 8. 2 R. J. Gardner, R. A. Crane and J. F. Hannan, Chem. Eng. Progr., (Oct 1977), p. 76; J. M. S. Henis and M. K. Tripodi, Sep. Sci. Technol., 1980,15, 1059; S . G. Kimura and G. A. Walmet, Sep. Sci. Technol., 1980, 15, 11 15. 3 J. Koresh and A. Soffer, J. Chem. SOC., Faraday Trans. 1, 1980, 76, 2457. 4 J. Koresh and A. Soffer, J . Chem. Soc., Faraday Trans. 1, 1980, 76, 2472. 5 J. Koresh and A. Soffer, J. Chem. Soc., Furaday Trans. 1, 1981, 77, 3005. 6 J. Koresh, J. Colloid Interface Sci., 1982, 88, 398. 7 J. Koresh and A. Soffer, J. Colloid Interface Sci., 1983, 92, 517. 8 S. S. Barton and J. E. Koresh, J. Chem. SOC., Faraday Trans. 1, 1983, 79, 1147. 9 S . S. Barton and J. E. Koresh, J. Chem. Soc., Furaday Trans. 1, 1983, 79, 1 1 57. 10 J. Koresh and A. Soffer, J. Chem. Soc., Faraday Trans. 1 , 1980, 76, 2507. 11 J. Koresh and A. Soffer, Sep. Sci., 1983, 18, 723. 12 A. W. Adamson, in Physical Chemistry of Surfaces (Interscience, New York, 1967), p. 572. Paper 51980; Received 10th June, 1985