Permeation Steady state

The integral permeability coefficient P may be determined directly from permeation steady-state flux measurements or indirectly from sorption kinetic measurements 27 521 activity is usually replaced by gas concentration or pressure (unless the gas deviates substantially from ideal behaviour and it is desired to allow for this) and a<>, ax (p0, Pi) are the boundary high and low activities (pressures) respectively in a permeation experiment, or the final (initial) and initial (final) activities (pressures) respectively in an absorption (desorption) experiment. 

Testers are available to measure the permeabihty and compressibiUty of powders and other bulk soflds (6). Erom such tests critical, steady-state flow rates through various outlet sizes in mass flow bins can be calculated. With this information, an engineer can determine the need for changing the outlet size and/or installing an air permeation system to increase the flow rate. Furthermore, the optimum number and location of air permeation levels can be deterrnined, along with an estimate of air flow requirements. 

Table 10 contains some selected permeabiUty data including diffusion and solubiUty coefficients for flavors in polymers used in food packaging. Generally, vinyUdene chloride copolymers and glassy polymers such as polyamides and EVOH are good barriers to flavor and aroma permeation whereas the polyolefins are poor barriers. Comparison to Table 5 shows that the large molecule diffusion coefficients are 1000 or more times lower than the small molecule coefficients. The solubiUty coefficients are as much as one million times higher. Equation 7 shows how to estimate the time to reach steady-state permeation t if the diffusion coefficient and thickness of a film are known. 

Eor t7-limonene diffusion in a 50-pm thick vinyUdene chloride copolymer film, steady-state permeation is expected after 2000 days. Eor a 50- pm thick LDPE film, steady-state permeation is expected in less than one hour. If steady-state permeation is not achieved, the effective penetration depth E for simple diffusion, after time /has elapsed, can be estimated with equation 8. 

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. 

Fig. 20.21 J-l transients for the permeation of hydrogen through ferrous alloys. The normal transient enables the diffusion coefficient ) to be evaluated from the relationship /, = L /6D, where /, is the time at which J attains a value of 0-63 of the steady-state permeation J...

In Figure 23.8, the gradient of the plot at steady-state conditions gives a permeation rate which will provide coefficient Q using the general permeation equation (Section 23.4.2). 

Steady-state total mass balances can also be written for Sections 1, 2 and 3, based on the flow rates in each section and the permeation rates between sections. They are as follows... 

Thus, the rate of change for the cumulative mass of diffusant passing through a membrane per unit area, or the flux of diffusant, j, may be evaluated from the steady-state portion of the permeation profile of a drug, as shown in Eq. (3). If the donor concentration and the steady-state flux of diffusant are known, the permeability coefficient may be determined. 

This equation teaches us that the total stead-state flux (total rate of permeation across a membrane in the steady state of permeation), dM/dt, is proportional to the involved area (A) and the concentration differential expressed across the membrane, AC. In an experiment, flux is the experimentally measured parameter while A and AC are fixed in value when setting up an experiment. The value of the permeability coefficient, Ptotai, is what is calculated upon completion of an experiment using Eq. (8). The permeability coefficient, besides having the specific attributes ascribed to it, is... 

Equation (91) represents the situation where the permeation has attained a steady state so that the amount penetrating per unit time is constant. 

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 ... 

It is noted that the time required for reaching the steady state of hydrogen diffusion is stress, specimen geometry, and dimension dependent, and cannot be used to compare with the permeation data as discussed earlier, which was measured from stress- and crack-free thin membrane specimens. 

FIGURE 15.9 Variation of iron concentration in the permeate (at steady state) against concentration of added 1-dodecanol. 

The squares and full lines of Fig. 11 summarize their results. The scatter of the experimental points seems mainly due to the analysis of the transient behavior the diffusion coefficient D and hence the solubility s = P/D fluctuate much more than the steady-state permeation coefficient P. Their Arrhenius lines are described by ... 

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. 

PMMA) film is quenched by permeation of methyl ethyl ketone (MEK), a good solvent for PMMA. A steady-state MEK concentration profile has been estimated from quenching data with existing sorption and light scattering data. The profile contains all the features of Case II diffusion the Fickian precursor, the solvent front, and the plateau region. However, the solvent front is not so steep as those observed in systems where penetrant diffusion is much slower. 

In our previous paper (H), we introduced a novel experimental method to study the mechanistic details of solvent permeation into thin polymer films. This method incorporates a fluorescence quenching technique (19-20) and laser interferometry ( ). The former, in effect, monitors the movement of vanguard solvent molecules the latter monitors the dissolution process. We took the time differences between these two techniques to estimate both the nascent and the steady-state transition layer thicknesses of PMMA film undergoing dissolution in 1 1 MEK-isoproanol solution. The steady-state thickness was in good agreement with the estimate of Krasicky et al. (IS.). ... 

In this paper, to determine the steady state SCP across the transition layer, we analyze the fluorescence intensity decay of dye molecules covalently bound to the polymer chains. The decay is due to the permeation of... 

A typical time profile of the excited PMMA-Phe fluorescence intensity decay is shown in Figure 2. The MEK permeation commences at 24 sec. The SPR increases during the plasticization period until it becomes constant, the onset of the steady state. It is characterized by a linear relationship between the amount of solvent absorbed and time. It was determined from a linear regression analysis that the PMMA-Phe fluorescence intensity starts to deviate from linearity at 197 sec. This indicates a decrease in the SPR and/or the unquenched PMMA-Phe. The decrease in SPR is unexpected at this film thickness since the SPR in thicker PMMA-Phe films show no anomaly at 1 /tm. A more plausible explanation is the reduction in available PMMA-Phe, which is expected when the front end of the SCP reaches the substrate. 

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