Permeation curves

Bockris and Subramanyan during studies of the permeation of hydrogen through pure Fe and Fe-SNi alloy found that a normal permeation transient was obtained (Fig. 20.21), providing the overpotential was less than a critical value, and when the overpotential was less than it was possible to reproduce the normal permeation curve, i.e. apply the polarising current at a constant rj < t , allow J to attain a steady value, switch off, reapply... 

Results of such single-molecule permeation experiments, using the MV +/ Ru(bpy)3 pair (Fig. 16), and membranes with four different nanotubule i.d.s, are shown in Fig. 17. The slopes of these permeation curves define the fluxes of and Ru(bpy)3 across the membrane. A permeation selectivity coefficient (ai)t can be obtained by dividing the flux by the Ru(bpy)3 flux. 

Since advancing and receding contact angles are likely to be different in these experiments, mercury permeation curves are expected to be different, depending on whether the mercury is being pushed in or out of the plugs. This type of hysteresis is indeed observed. We encounter another type of hysteresis associated with pore filling in Chapter 9 (Section 9.7a). 

Fig. 16. Experimental permeation curves for N, at 297 K in Membrane D of Table 5(points) and their corresponding steady-state asymptotes (lines) with Q given in dimensionless from QI45>. Absorptive permeation forward ( + X) flow reverse (—X) flow. Desorptive permeation O forward flow reverse flow. Note conformity of the data to Eqs. (68)...

In all late-time regimes notably those represented by Eqs. (60), (62), (64) and (66) ideal kinetics is obeyed 144.15°.15i.154.159.l6l) whereas this is not so in the short-time regimes presented by Eqs. (59), (63) and (65) 150 ,51 154,163,64) (which convey essentially the same information).151 The short time behaviour of lower permeation curves represented by Eq. (61) appears to occupy an intermediate position, in the sense that ideal kinetics appears to be followed only to a first approximation151. The relation between permeation and symmetrical sorption indicated by Eq. (70) is also notable. The respective kinetics become very similar at long times154 as indicated by the relevant relations151) D2M = Ds = D7 = D8 and... 

Analytic solutions to Eq. (1) subject to these auxiliary conditions can be obtained only for the special case in which D is independent of concentration. For concentration-dependent D even numerical work has not as yet been attempted. It is fortunate that without recourse to actual calculations we can deduce necessary relations and important features basic to permeation curves for systems in which D is a function of concentration alone. Those are as follows ... 

Fig. 12. Permeation curves of water for polymethyl acrylate at 20° C. Taken from unpublished experiments of Kishimoto...

Fig. 13 a and b. Anomalous permeation curves a) types ob served by Park (1952) for methylene chloride in polystyrene at 25° C. b) type found by Meares (1956b) for allyl chloride in polyvinyl acetate at 40° C. 

Equations 15.79 and 15.80 can describe the linear part of the permeation curve [116]. 

In the early potentiostatic experiments by Devanathan and Stachurski [98], the time required for the subsurface concentration to become constant, as assumed, was treated simply as a shift in the timescale at the beginning of a permeation curve. However, the permeation behavior for the constant concentration case and that in which the... 

Figure 4.8 Permeation curves of dichloromethane and methanol vapour in Hyflon AD80X membranes at 25 °C. Time lag calculation by the tangent method (top) and by a direct least squares fit of the entire permeation curve according to Eq. (4.6) (bottom). The thick dark line represents the experimental data the thin brighter line gives the tangent (top) or the least squares fit. The experimental and fitted lines superimpose completely in the case of DCM, and only one curve can be distinguished, whereas MeOH gives a poor fit. See text for further explanation...

In this work preliminary vapour permeation measurements were carried out with two different species, the rather bulky dichloromethane (DCM) molecules and the much smaller methanol molecules. Two typical permeation curves are displayed in Figure 4.8. The transport parameters, determined on the basis of the tangent method and Equations (4.9)-(4.11), are listed in Table 4.3. It contains the parameters dehned above as well as solubility C in the membrane in equilibrium with the feed pressure of penetrants. 

More careful analysis of the permeation curves show that the two vapours actually display completely different behaviour. The tangent method can be applied without problems to the DCM permeation curve, resulting in a time lag of ca. 400 s. hi contrast, this method shows that methanol has an unusually wide transient period. While the extrapo-... 

Figure 4.9 Left side Experimental permeation curve of methanol vapour in the Hyflon AD80X membrane of Figure 8 (thick dark line). The shaded areas and the thin brighter lines represent the different steps of the fitting procedure according to Eq. (4.6). Right side, B, C, D experimental data or residual experimental data (noisy dark lines), with the corresponding fit of the individual steps in the three different time intervals (thin brighter lines). The sum of the three fits coincides perfectly with the experimental data. In most cases the fit is nearly perfect and only one curve can be distinguished. See further explanation in the text...

In the experiments we were able to measure the flux and then, after integration with respect to time, we obtain a downstream permeation curve (shown in Figure 9.7) where the typical plot of versus time is presented. 

The most important parameter is the average diffusion coefficient D, calculated from the stationary permeation data. To calculate this coefficient, we have used experimental data (the thickness of membrane /, a stationary flux Js and Aco, obtained from an intercept of the asymptote to the stationary permeation curve with the axis) (Figure 9.7). 

Figure 9.7 Downstream absorption permeation curve - a schematic view. Reprinted with permission from Journal of Membrane Science, On the air enrichment by polymer magnetic membranes by A. Rybak, Z. j. Crzywna and W. Kaszuwara, 336, 1-2, 79-85, Copyright (2009) Elsevier Ltd...

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