Permeation methods

The permeation method is based on the slow penetration or permeation of molecules through a polymeric membrane. The permeation rate of the compound is determined by physical characteristics of the chemical and the membrane. Permeation is pressure and temperature dependent. Higher vapor-pressure compounds will have a higher permeation rate. Similarly, high temperature will create high internal vapor pressure that leads to higher permeation rate. 

Controlled and predictable concentrations over a wide flow rate range are readily achievable. The generator uses a small diameter tube (e.g., 1/4 in. O.D.) made of a suitable membrane material such as polytetrafluoroethylene (pTFE) loaded with the liquid agent. The compound contacts the inside surface of the membrane and the vapor slowly permeates. 

When the permeation tube is held at a constant temperature, a steady flux flow of compound vapor is emitted. This output can be measured by weight loss over a period of time to determine the permeation or emission rate. The permeation rate is generally expressed as number of nanograms per minute (ng/min). Weight-loss measurements can be taken at various temperatures to produce different emission rates for the same tube. The emission can be diluted with a known flow of dilution air to achieve the desired concentration. 

The permeation rate is determined by the gravimetric method. The permeation device, after it has been assembled, is weighed and then placed in a temperature-controlled cavity with constant flow of nitrogen or clean air to sweep away the permeated chemical vapor. After a period of time, perhaps days, the tubing is weighed again and the permeation rate is determined by weight loss over elapsed time. Since 

The membrane permeation method is used to study protein diffusion through a thin membrane, from a reservoir at high concentrahon (donor 

ct is the concentration of protein at any time t, Cq is the initial protein concentration, VI is the donor cell volume, C, is the receptor cell volume, U is the overall mass-transfer coefficient, and A is the surface area of the membrane exposed to solution. 

The overall mass-transfer coefficient, U, is related to the local mass-transfer coefficients on either side of the membrane, and 2, as follows  

Finally, the permeability, P, can be described by the partition coefficient, K, the diffusion coefficient, D, and the hydrogel thickness, 5  

The partition coefficient, K, is the ratio of protein concentration located in the hydrogel, c, to the concentration of protein in solution at equilibrium. 

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For practical purposes, the mutual diffusion coefficient is the quantity commonly reported to characterize diffusional transport in pharmaceutical systems. It is thus the purpose of investigators to determine this quantity experimentally. To this end, both sorption and permeation methods are commonly used. 

Diffusion of small molecular penetrants in polymers often assumes Fickian characteristics at temperatures above Tg of the system. As such, classical diffusion theory is sufficient for describing the mass transport, and a mutual diffusion coefficient can be determined unambiguously by sorption and permeation methods. For a penetrant molecule of a size comparable to that of the monomeric unit of a polymer, diffusion requires cooperative movement of several monomeric units. The mobility of the polymer chains thus controls the rate of diffusion, and factors affecting the chain mobility will also influence the diffusion coefficient. The key factors here are temperature and concentration. Increasing temperature enhances the Brownian motion of the polymer segments the effect is to weaken the interaction between chains and thus increase the interchain distance. A similar effect can be expected upon the addition of a small molecular penetrant. 

The suitability and general applicability of an artificial membrane and PAMPA in vitro permeation methods were evaluated for their ability to predict drug absorption potential in comparison to Caco-2 cell literature data [57], A linear correlation (R2 = 0.957) was obtained between artificial membrane Papp and human absorption data, indicating the good predictive ability of the proposed method for HP compounds with greater differentiation of drugs with /a below 50% [57],... 

The diffusion coefficients of n-paraffins with 12 to 22 carbon atoms in high density (HDPE) and low density polyethylene (LDPE) have been measured by a permeation method (Koszinowski, 1986). Methanol (MeOH) and ethanol (EtOH) were used as contacting liquid phases which minimized interaction between these polar solvents and the nonpolar polymers. No interaction was observed over the investigated temperature range of 6 to 40 °C for both solvents. 

The measurement of sorption, diffusion and permeability coefficients takes place as a rule using one of three methods sorption of the gases in the polymer, permeation through a membrane (film or sheet) into a sealed container or permeation through a membrane into a gas stream. As far as possible sorption methods should be used together with permeation methods that are specific for the measured gas/polymer system in order to uncover any possible anomalies or errors in the measurements by comparison of results. 

One of the central problems in the study of diffusion is to evaluate D for a given system as a function of such parameters as penetrant concentration and temperature. For polymer-penetrant systems with which we are concerned in this article two experimental methods are typical for this purpose. They are the sorption method and the permeation method. 

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]. 

A differential permeation method was used to determine diffusion kinetics of strongly adsorbing vapors through an Ajax activated carbon (type 976) (whose physical properties [7] particle density of 733 kg/m micropore porosity 0.40, macropore porosity 0.31 and mean macropore radius 0.8 pm). An activated carbon pellet was carefully mounted in a copper block, separating two reservoirs. One reservoir is much larger in volume than the... 

Bae J.-S. and Do D. D., Study on diffusion and flow of benzene, ra-hexane and CCI4 in activated carbon by a differential permeation method. Chem. Eng. Sci. in press (2002). 

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-... 

Research on removal of noble gases by permeation method with dimethyl silicon membranes was carried out in Oak Ridge National Laboratory [160]. On the basis of experimental work, the calculations for different industrial cascades separating krypton and xenon from the space of molten salt and sodium cooled breeder reactor or from the off gas from a plant processing spent reactor fuel were performed. 

This analysis shows that permeability is a complex function of porosity and surface area, the latter being determined by the size distribution and shape of the particles. The appearance of specific surface in Eq. (20) offers a method for its measurement and provides the basis of fluid permeation methods of size analysis. This equation also applies in the studies of filtration. 

The modelling of gas permeation has been applied by several authors in the qualitative characterisation of porous structures of ceramic membranes [132-138]. Concerning the difficult case of gas transport analysis in microporous membranes, we have to notice the extensive works of A.B. Shelekhin et al. on glass membranes [139,14] as well as those more recent of R.S.A. de Lange et al. on sol-gel derived molecular sieve membranes [137,138]. The influence of errors in measured variables on the reliability of membrane structural parameters have been discussed in [136]. The accuracy of experimental data and the mutual relation between the resistance to gas flow of the separation layer and of the support are the limitations for the application of the permeation method. The interpretation of flux data must be further considered in heterogeneous media due to the effects of pore size distribution and pore connectivity. This can be conveniently done in terms of structure factors [5]. Furthermore the adsorption of gas is often considered as negligible in simple kinetic theories. Application of flow methods should always be critically examined with this in mind. 

F.W. Altena, H.A.M. Knoef, H. Heskamp, D. Bargeman and C.A. Smolders, Some comments on the applicability of gas permeation methods to characterise porous membranes based on improved experimental accuracy and data handling. /. Membr. Sci., 12 (1983) 313. 

P. Uchytil, Z. Wagner, J. Rocek and Z. Broz, Possibility of pore size determination in separation layer of ceramic membrane using permeation method. /. Membr. Sci., 103... 

Porosity can be also measured by pressure permeation methods [B.60] if the agglomerate can not be treated and submerged in a liquid without losing its integrity. 

Of all the proportioning principles already known from the production of calibration gas from permanent gas, only the permeation method can be used because the diffusion process is not bound to the gaseous state and even for the dosage of permanent gases the permeation tubes contain two-phase mixtures. This method, as well as the mixed gas cylinders, are limited to the trace domain because the tubes only contain insignificant amounts. 

Oel filtration and gel permeation methods are complementary in that gel filtration is applied to water-soluble samples and gel permeation is used for substances in less-polar organic solvents. One useful application of the size-exclusion procedure is to the separation of high-moIccular-mass, natural-product molecules from low-molccular-mass species and from salts. For example, a gel with an exclusion limit of several thousand can clearly separate proteins from amino acids and low-molecular-mass peptides. 

The alternating current technique is essentially a variant of the permeation method [48]. The current measured at the output side varies sinusoidally in response to the alternating cathodic current. The diffusivity can be determined from both the phase difference of the alternating current between the two sides and the amplitude of the alternating current at the output side. 

The most useful commercially available titanium powders are made by calcium hydride reduction, and are furnished in a variety of particle sizes, generally coarser than zirconium. The latter is made by calcium metal reduction and is of an average particle size of only 2-5 ju, measured by the permeation method, though coarser grades also exist. The differences of manufacture and grain sizes do not permit a fair comparison of the two as to intrinsic hazardousness, but at present in this country, zirconium is frequently the cause of serious accidents, while to the author s knowledge titanium rarely is. Conversely, the subsieve-sIze zirconium affords advantages in. performance that cannot be duplicated by the other metal. 

The permeation method is a steady-state method applied to a film of material. According to this method, the permeation rate of a diffusant through a material of known thickness is measured under constant, well-defined, surface concentrations. The analysis is also based on Pick s diffusion equation. 

The remainder of the book deals with various methods commonly used in the literature for the measurement of diffusivity. We start with Chapter 12 with a time lag method, which belongs to the class of permeation method, of which another method employing a diffusion cell is presented in Chapter 13. The time lag method was pioneered by Barrer in the early 50 s, and is a very useful tool to study diffusion through porous media as well as polymeric membranes. Chromatography method is presented in Chapter 14, and finally we conclude with a chapter (Chapter 15) on the analysis of batch adsorber. 

Chapters 9 to 11 deal with the dynamic analysis of a single particle exposed to a constant bulk environment. The method of differential adsorption bed discussed in Chapter 11 is suitable for the application of the single particle analysis. A permeation method called the time lag method is useful for characterisation of diffusional flow, viscous flow and surface flow of pure gas through a single pellet (Chapter 12). The diffusion cell method either in steady state mode or transient mode is useful to characterize binary diffusional systems (Chapter 13). All these methods evolve around the analysis of a single particle and they complement each other in the characterization of diffusion and adsorption characteristics of a system. From the stand point of system set-up, the time lag and diffusion cell methods require a careful mounting of a particle or particles between two chambers and extreme care is exercised to avoid any gas by-passing the particle. 

Table 13.5 CO2 and N2 permeability (P), diffusion (D) and sorption (S) coefficients obtained for three Pebax 1657-PECEPi blends by using the gas permeation method in...

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