Analysis of permeation transients of pure gases through dense polymeric membranes measured by a new permeation apparatus
Introduction
Gas transport through dense polymeric membranes is commonly analyzed in terms of equilibrium sorption between a gas phase and a solid polymer followed by the bulk diffusion of the sorbed gas molecules within the solid [1]. Gas permeabilities are still widely evaluated with a constant-volume apparatus employing the time-lag technique [2] in which permeant gas accumulates in a pre-evacuated downstream volume. The standard mathematical analysis underlying the basic technique assumes that the diffusion coefficient is constant throughout the permeation process from initiation to steady state permeation. However, for those permeation processes in which condensable or interactive gases are common components the time-lag technique is prone to cumulative error arising from (1) vacuum leaks and system outgassing, (2) permeate adsorption to the walls of the down stream system, and (3) non-constant diffusion coefficient through the permeation process. Especially, the experimental difficulty encountered in the quantitative measurement of the condensable gas permeation because of the propensity of the gas to readily adsorb in large quantities to all available surface; such gas is then not detected by the pressure gauge used in the time-lag technique. Thus, this difficult experimental situation has resulted in the determination of so-called apparent diffusion coefficients, these quantities being inferred from steady-state permeation data, together with equilibrium sorption isotherms.
The foreknowledge of the diffusion of a permeant through a membrane requires properly understanding of the transient permeation behaviour of the permeant [3], [4]. Permeation transient data in the beginning stage of the permeation will minimize such cumulative error. A continuous-flow technique [4], [5] was employed for the direct measurement of the dynamic permeation which gives permeation transients. In the technique, the downstream is continuously pumped and then permeation transients are immediately yielded. Felder and Huward [5] designed a continuous-flow permeation cell to avoid the adsorption effect, but it is also subject to error arising from the flow time delay between the downstream face of the membrane and the detector. Watson and Baron [4] devised a continuous-flow vacuum permeation cell in which the downstream is evacuated continuously to high vacuum during permeation, and the downstream pressure is changed correspondingly when the membrane flux occurs. The result can be affected by the vacuum pump condition or an electricity fluctuation. Also a low-pressure vacuum should be maintained in the downstream for an accurate measurement of the dynamic permeation.
In the previous work [6], we had developed a novel permeation apparatus which could measure precisely the permeation transients of liquid permeants. Development of the apparatus was motivated by the desire to measure flux transients, directly, rapidly and precisely. The validity of the apparatus was proved through the successful measurement of the permeation properties of liquid permeants.
This study is a continuation of the previous work which dealt with the development of a permeation apparatus for precisely measuring permeation properties. We improved the permeation apparatus to be suitable for the measurement of gas flux transients and to solve the problems associated with the drawbacks in the existing continuous-flow technique. The measurement of flux transients is essential to study the permeation behaviour and kinetics of permeants through membrane. The apparatus was designed for the measurement to be quickly made in a simple way. In this study, in order to illustrate the performance of the new apparatus, permeations of pure gases through both glassy and rubbery membranes, i.e. 2,2-bis(3,4-dicarboxyphenyl) hexafluoropropane dianhydrade (6FDA)-based polyimides and polydimethylsiloxane (PDMS) membrane were conducted to measure flux transients, respectively. From the flux transients, permeability, diffusion and solubility coefficient, and apparent activation energies, were evaluated and compared with the values published in literatures, respectively. Also, the analysis of the permeation transients obtained was carried out for the close investigation of the permeation behaviors of gases through membrane. The emphasis in this study is put on the validity of the permeation apparatus by illustrating its performance through the determination of permeation characteristics.
Section snippets
Materials
The monomers used in this study were 2,2-bis(3,4-dicarboxyphenyl) hexafluoropropane dianhydrade (6FDA) which was obtained from Hoechst and diamino mesitylene(DAM) and 4,4-oxydianiline(ODA) which were obtained from Tokyo Chemical. The diamines were recrystallized with ethanol and tetrahydrofuran, respectively while the dianhydride was used as received. The solvent which was used in the polymerization, N,N-dimethylacetamide (DMAc), was purchased from Junsei Chemical and was dehydrated with well
Comparison of permeation properties determined by the continuous-flow technique with the literature values
Fig. 4 shows the flux transients of the pure gases N2, O2, CO2 through PDMS membrane, respectively, measured in on-line mode by the new permeation apparatus based on the continuous-flow technique. They are the typical flux transients which can be obtained by the permeation apparatus. Usually, the time-lag technique requires several hours for a measurement, but in this study, each measurement could be made quickly within 30 min because evacuating of downstream volume up to high degree of vacuum
Conclusions
A novel permeation apparatus has been developed that allows precise permeation transients to be quickly and directly measured. The apparatus also includes the on-line measurement of the composition of permeate. The performance of the apparatus has been illustrated using gas permeation through both the glassy 6FDA-based polyimide membranes and the rubbery poly(dimethylsiloxane) membrane. In the permeations, the flux transients were rapidly determined within 20 min. From the flux determined with
List of symbols
- C
permeant concentration in a membrane (g/m3)
- C1
permeant concentrations at the feed side interface of a membrane (g/m3)
- D
diffusion coefficient of permeant (m2/s)
- Ds, D1/2
diffusion coefficients determined from response times ts, t1/2, respectively (m2/s)
- Ep, Ed
permeation and diffusion activation energies of water, respectively (kcal/mol)
- J
flux at time t (g/m2 h)
- Js
flux at steady state condition (g/m2 h)
- l
membrane thickness (m)
- Qt
permeating amount per unit area for a given period of time (g/m2)
- t
operating
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