Permeation time lag

Most experimental determinations of Dt, D2 reported to date 13 15 16 23 26,55,56) have been obtained by the method described above but sorption kinetics 16,17,27) and permeation time lag measurements 29,57 58> have also been employed for this purpose. 

These parameters are in many ways analogous to permeation time lags but the relevant expressions for the case of S(X), DT(X) are considerably more complicated (even in the case of the First njoment which is the simplest)171> than the corresponding time lag formulae 4). Accordingly, moments represent a less efficient way of making use of the information contained in transient diffusion data than the methods discussed above. In spite of these limitations, further study of moments should prove worthwhile. 

In the second case D can be calculated from the permeation time lag by means of the equation ... 

The more conventional method for studying the energetics of diffusion in membranes is to perform permeation experiments as a function of equilibrium temperature. Figure 13 illustrates the eflEect of temperature on the apparent diflEusion coeflScient calculated from the water vapor permeation time lag established by steady-state permeation with a 75 to 0% RH gradient across the membrane. The principles of the time lag permeation method are adequately discussed elsewhere (58). The lower curve corresponds to a sample which was not mechanically supported and was observed to deform into a hemispherical shape. This deformation is the combined result of a small pressure diflEerence across the membrane and a decrease in modulus of stratum corneum as the temperature is increased. The upper curve corresponds to a supported sample. Previous to the experiment, both samples had identical thermal histories. Stresses accompanying deformation of the unsupported cor-... 

Wang, K., Suda, H. Haraya, K. (2001). Permeation Time Lag and the Concentration Dependence of the Diffusion Coefficient ofCO in a Carbon Molecular Sieve Membrane. Industrial Engineering Chemistry Research, 40(13), 2942-2946. 

Carbon Dioxide Transport. Measuring the permeation of carbon dioxide occurs far less often than measuring the permeation of oxygen or water. A variety of methods ate used however, the simplest method uses the Permatran-C instmment (Modem Controls, Inc.). In this method, air is circulated past a test film in a loop that includes an infrared detector. Carbon dioxide is appHed to the other side of the film. AH the carbon dioxide that permeates through the film is captured in the loop. As the experiment progresses, the carbon dioxide concentration increases. First, there is a transient period before the steady-state rate is achieved. The steady-state rate is achieved when the concentration of carbon dioxide increases at a constant rate. This rate is used to calculate the permeabiUty. Figure 18 shows how the diffusion coefficient can be deterrnined in this type of experiment. The time lag is substituted into equation 21. The solubiUty coefficient can be calculated with equation 2. 

The two most common temporal input profiles for dmg delivery are zero order (constant release), and half order, ie, release that decreases with the square root of time. These two profiles correspond to diffusion through a membrane and desorption from a matrix, respectively (1,2). In practice, membrane systems have a period of constant release, ie, steady-state permeation, preceded by a period of either an increasing (time lag) or decreasing (burst) flux. This initial period may affect the time of appearance of a dmg in plasma on the first dose, but may become insignificant upon multiple dosing. 

The advantage of using the time lag method is that the partition coefficient K can be determined simultaneously. However, the accuracy of this approach may be limited if the membrane swells. With D determined by Eq. (12) and the steady-state permeation rate measured experimentally, K can be calculated by Eq. (10). In the case of a variable D(c ), equations have been derived for the time lag [6,7], However, this requires that the functional dependence of D on Ci be known. Details of this approach have been discussed by Meares [7], The characteristics of systems in which permeation occurs only by diffusion can be summarized as follows ... 

Tiag = the time needed to achieve e - )le (63%) of the steady-state permeation level (time-lag method),... 

Diffusivity. Diffusivity values derived from time lag measurements of permeation (D = P/6t) vs. membrane composition of PVC/EVA show the same general tendency as the permeability-composition data. The D values are, however, less reproducible, probably owing to short time lag values, and therefore are not reported here. Solubility values can also be calculated (S = P/D), but they are not reported for the same reason. No separate solubility measurements were made. 

The gas-polymer-matrix model for sorption and transport of gases in polymers is consistent with the physical evidence that 1) there is only one population of sorbed gas molecules in polymers at any pressure, 2) the physical properties of polymers are perturbed by the presence of sorbed gas, and 3) the perturbation of the polymer matrix arises from gas-polymer interactions. Rather than treating the gas and polymer separately, as in previous theories, the present model treats sorption and transport as occurring through a gas-polymer matrix whose properties change with composition. Simple expressions for sorption, diffusion, permeation and time lag are developed and used to analyze carbon dioxide sorption and transport in polycarbonate. 

Using the dual-mode parameter values determined from sorption and permeation experiments, calculated time lags agree with the experimental data only at gas pressures above 5 atm. At lower pressures, dual-mode time lags are appreciably shorter than the observed ones, whereas time lags calculated from the matrix model by eq. (15) agree with the experimental data over the entire pressure range. 

Figure 3. Time lag for diffusion of CO at 35 °C in a U.9 mil thick polycarbonate film conditioned by prior exposure to C02 The data are from Ref. 15. Calculated time lags based on the matrix model (solid line) and the dual-mode model (broken line) use parameters determined from fitting the sorption and permeation data.

MESI operation requires processing of the whole sample to be extracted and has to reach steady-state permeation, which usually takes a long time. Thus, a new technical modification of MESI, called pulse introduction (flow injection-type) membrane extraction (PIME), has been developed, in which the sample is introduced to the membrane as a pulse pushed by a stream of eluent (usually water).55 This means that attaining a steady state is no longer crucial. PIME therefore provides not only a faster response and higher sensitivity, but also allows extraction of individual samples via discrete injections in addition to continuous on-line monitoring by sequential injection of a series of samples. Guo et al.56 described a mathematical model for the PIME permeation process, which showed that (a) there was a trade-off between the sensitivity and the time lag (the time taken to complete the permeation process) and (b) a large sample volume and a low flow rate enhance the sensitivity but also increase the time lag. 

The assumption of a steady-state profile in the oil laminates and small concentration drops in the water layers may be used to derive asymptotic solutions for the permeation problem. It may be shown that (2) for P P y and t[Pg.36]

In vitro skin permeation studies in a hydrodynamically well-calibrated skin permeation cell (Figure 4) demonstrated that simple pharmaceutical excipients, like capric acid (a saturated straight-chain fatty acid), can substantially enhance the trandermal permeation rate of progesterone. The time lag is significantly re-... 

Example 9-5. When measuring the gas permeation through a film one obtains a time-axis intercept of the steady-state permeation asymptote of 0 = 254 min using the time-lag method. The thickness of the film being studied is 75 pm. The pressure difference (Ap) between the two sides of the film remains constant at 0.2 bar and the flux through the film is 2 cwW h. Calculate the value of the solubility coefficient 5. 

Procedures to remove the restrictions of the permeation technique, also inherent in the time lag method, have been described by Grachev et al. [13] and Gibilaro et al. [14], As with the Wicke-Kallenbach method, they are based on the application of a carrier gas. Details of these methods may be found in Ref. 1. 

In the characterization of porous membranes by liquid or gaseous permeation methods, the interpretation of data by the hyperbolic model can be of interest even if the parabolic model is accepted to yield excellent results for the estimation of the diffusion coefficients in most experiments. This type of model is currently applied for the time-lag method, which is mostly used to estimate the diffusion coefficients of dense polymer membranes in this case, the porosity definition can be compared to an equivalent free volume of the polymer [4.88, 4.89]. 

This is the time lag equation which was used by Barrer for determining the diffusion coefficient using permeation measurements. The steady state permeation flux is given by the slope of the straight line, eqn 8.28 ... 

A major breakthrough in the study of gas and v or transport in polymer membranes was achieved by Daynes in 1920 He pointed out that steady-state permeability measurements could only lead to the determination of the product EMcd and not their separate values. He showed that, under boundary conditions which were easy to achieve experimentally, D is related to the time retired to achieve steady state permeation throu an initially degassed membrane. The so-called diffusion time lag , 6, is obtained by back-extrapolation to the time axis of the pseudo-steady-state portion of the pressure buildup in a low pressure downstream receiving vdume for a transient permeation experiment. As shown in Eq. (6), the time lag is quantitatively related to the diffusion coefficient and the membrane thickness, , for the simple case where both ko and D are constants. 

Since the product Dk is known from the steady state rate of permeation, kp can also be obtained. This time lag method is the basis of most of the gas and some of the vapor transport studies made today. Little application of the time lag method was made until Barter introduced the use of vacuum on the downstream side of the membrane and measured the gas permeation rate by monitoring the increase in pres-arre in a fixed downstream receiving volume Recently the original isobaric method has been reintroduced in a number of commercial permeability instruments. 

The predicted effect of du mode sorption on the time lag and permeability vras derived by Paul using the total immobilization transport model and experimentally verified by Paul and Kemp using molecular sieves embedded in a silicone mbber. This was an excellent model system which fulfilled the postulate of complete inunobilization of the Langmuirian mode penetrant. The possibility that gas molecules sorbed in the Langmuirian mode may not necessarily be completely immobilized in glassy polymers was first raised by Petropoulos in 1970 Equations were developed and the possibility of these being used to check the assumption of immobilization by sorption and permeation data were described. The relaxation of the... 

The combined procedure described above, which uses only sorption and steady state permeation data, specifies all five of the sorption and tran rt model parameters without requiring reference to the independenfly measured time lags, Com-pariscm of tiieoretically predicted time lags with flie experimentally meaaired values provides a rigorous test of the internal consistency of the transport and sorption data as well as a check of the applicability of the partial immobSization model for description of the transient processes. 

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