Steady state permeation rate

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 ... 

As far as can be ascertained, no performance standards exist for this product. In the absence of such standards, the existing standards for automotive vehicles were used as guidelines. By using the most stringent standard, the SHED test, a petrol permeation rate of approximately 3.3 g/m2 for 24 h at 40°C can be estimated. With a single-fluorination treatment a pipe already exceeds this standard with a steady state permeation rate of 1.7 g/m2 per 24 h at 50°C. Since it is a known fact that permeability increases drastically with a rise in temperature, a permeability ofless than 0.17 g/m2 per 24h at 30°C is expected for a single fluorination treatment. 

Plot cumulative amount of drug in receptor versus time and calculate steady state permeation rate or flux (Jss) and lag time from the slope and x-intercept of the linear portion... 

The permeability is defined in terms of the steady state permeation rate of component i per unit area divided by the normalized partial pressure difference of component i, Ap, acting across the membrane of thickness, C (see Fig. 1) (23,24). 

Permeation Properties. The data shown in Figure 2 are the toluene permeation rates of the fluorinated and untreated containers g. toluene/container per day are plotted vs. the time of toluene exposure on a logarithmic scale. These cumulative permeation rates were calculated based on the cumulative weight loss over the time of toluene exposure, as opposed to the differential permeation rates based on the differential weight loss over each time interval. The room temperature permeation rates for the in-situ fluorinated containers were less than 0.01 g./day and, hence, have been rounded up to 0.01 g./day for illustrative purposes. In Figure 2, the,flat portion of the curves for the untreated containers yielded the steady state permeation rates. From these values, the permeability coefficients (P) for the untreated containers were calculated using Equation 1. 

A steady state permeation rate is rapidly reached. 

Slow relaxation processes appear to be the dominant factors causing the long times required to reach steady state permeation rates. Transient permeation experiments would yield incorrect diffusion coefficients for membrane materials exhibiting this behavior. Relaxation processes, highly concentration dependent diffusion coefficients and solubility coefficients, therefore, require a more detailed approach to studying transport. This paper describes a preferred method of analyzing diffusion process. 

With all aqueous systems (water and steroid/polymer/-water) the diffusion coefficients were calculated either from lag times (29) or from the steady-state permeation rate and the known saturation concentration of steroid in the polymer. For oil-water systems (sesame oil and steroid/polymer/water) the reported normalized flux is the experimentally observed value and the diffusion coefficient is derived from the lag time. 

Dt/ = 0.5 can be used to estimate the time needed for a permeant to reach the steady-state permeation rate from the moment the product containing the permeant is put in a package and immediately sealed. 

Steady state permeation rate dp/dt is obtained from the slope of p versus t plot for i> 10 0. Since the time lag is veiy short (0 < 1 min), it is difficult to determine precise diffusion coefficient. 

This approximation is valid up to / = 0.965/qo, so it is feasible to calculate the diffusivity from Eq. (18) by determining the time required to achieve a given fraction of the steady-state permeation rate. 

Measurement of water-vapour diffusion, solubility and permeability requires special techniques and care because of the unique nature of water. A number of techniques have been developed for the routine measurement of the water-vapour permeability of polymer membranes. " More accurate measurements may be obtained by using the techniques described for gases however, care must be taken to avoid the possibility of water sorbing or desorbing on to or from glass surfaces. With due caution, steady-state permeation rates may be measured in this fashion, but permeation lag-times are unreliable. 

Fig. 7.10 Long-term, steady-state permeation rate of hydrogen from ZrHi 7 layer as a function of layer temperature (Layer thickness, 0.9 cm cladding thickness, 0.376 cm)...

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