Penetration theory Permeability

Manson and Chin 151) reported that the addition of filler to an epoxy binder reduces the epoxy s permeability coefficient (P), as well as the solubility of water in the resin (S) and that the reduction is stronger than expected from theory 1 2). Diffusion coefficients calculated from P and S for the unfilled resin were found to be somewhat higher than those for filled resin. The difference seems to be due to the formation of ordered layers, up to 4 pm thick, around every filler particle. The layers form because of residual stresses caused by the difference between the binder and filler coefficients of thermal expansion. The effective activation energy for water to penetrate into these materials, calculated in the 0-100 °C temperature range, is 54.3 kJ/mol151). 

As a predictor of the concentration of cisplatin in normal peritoneal tissues, these data indicate a steady-state penetration depth (distance to half the surface layer concentration) of about 0.1 mm (100 tm). If this distance applied to tumor tissue, penetration even to three or four times this depth would make it difficult to effectively dose tumor nodules of 1- to 2-mm diameter. Fortunately, crude data are available from proton-induced X-ray emission studies of cisplatin transport into intraperitoneal rat tumors, indicating that the penetration into tumor is deeper and is in the range of 1-1.5 mm (10). Such distances are obtained from Equation 9.5 or 9.5 only if k is much smaller than in normal peritoneal tissues — that is, theory suggests that low permeability coefficient-surface area products in tumor (e.g., due to a developing microvasculature and a lower capillary density) may be responsible for the deeper tumor penetration. 

A phenomenological theory known as the "dual-mode sorption" model offers a satisfactory description of the dependence of diffusion coefficients, as well as of solubility and permeability coefficients, on penetrant concentration (or pressure) in glassy polymers (4-6,40-44). This model postulates that a gas dissolved in a glassy polymer consists of two distinct molecular populations ... 

Therefore, although rather cumbersome, the Tree-volume theory permits one to prepare theoretical plots of permeability as a function of temperature, penetrant pressure, and arantphous volume fraction in the rubbery polymer. 

Crete surface to the bulk of the concrete. Permeability is high (Figure 1.6) and transport processes like, e. g., capillary suction of (chloride-containing) water can take place rapidly. With decreasing porosity the capillary pore system loses its connectivity, thus transport processes are controlled by the small gel pores. As a result, water and chlorides will penetrate only a short distance into concrete. This influence of structure (geometry) on transport properties can be described with the percolation theory [8] below a critical porosity, p, the percolation threshold, the capillary pore system is not interconnected (only finite clusters are present) above p the capillary pore system is continuous (infinite clusters). The percolation theory has been used to design numerical experiments and apphed to transport processes in cement paste and mortars [9]. 

Chloride ions—and, to a lesser extent, other halogen ions—break down passivity or prevent its formation in iron, chromium, nickel, cobalt, and the stainless steels. From the perspective of the oxide-fihn theory, Cl penetrates the oxide film through pores or defects easier than do other ions, such as SOi". Alternatively, Cl may colloidally disperse the oxide film and increase its permeability. 

The structure of homogeneous PHEMA, that is materials polymerized in solutions with less than approximately 45 wt. % water in the reaction mixture 28), has been examined in greater detail. The earliest estimate of pore size in these PHEMA materials was 0.4 nm for a polymer prepared in the presence of water and ethylene glycol was provided by Refojo 29) who used the relationship between water permeability and average pore diameter developed by Ferry 30). The materials investigated by Refojo contained 39 wt. % water. This method was later applied by Haldon and Lee (57) to similar PHEMA samples of 41-42 wt. % hydration to obtain a pore radius between 0.4 and 0.8 nm. It was acknowledged that the assumptions implicit in the use of the Ferry equation resulted in underestimation of the pore size. This was highlighted by the observation that sodium fluorescein, with a radius of 0.55 nm, could readily diffuse into PHEMA. Later Kou et al. 32) demonstrated that solutes of radius 0.6 nm were able to penetrate PHEMA and copolymers of HEMA with methacrylic acid, and that the rate of diffusion was consistent with free volume theory. 

The general relationship between permeability and fugacity, as given in Eq. (35.10), can be substituted into Eq. (35.6) to estimate diffusion coefficients as a function of temperature and penetrant concentration (Merkel et al., 2000 Lin and Freeman, 2004). However, values of Pa,o and nip E are required for each gas at each temperature of interest, leading to a large number of empirical parameters needed to characterize diffusivity in a particular material (Lin and Freeman, 2006a). To address this shortcoming, a model based on ffee-volume theory was used to correlate the data, as described below. 

Penetration of a substance is measured by the permeability coefficient, P, which could be converted to a measurable diffusional coefficient, D, if Pick s law applied strictly. In the more complex situation of a membrane barrier, Kedem and Katchalsky (1958, 1961) have shown that under rigidly controlled conditions there exist at least three parameters which must be considered when characterizing the behavior of a membrane toward a particular solute (1) the interaction between membrane and solvent (2) the interaction between solute and membrane and (3) the interaction between solute and solvent. The reflection coefficient, (T, measures relative rates of solute and solvent permeabilities in the system (Staverman, 1952) and is therefore a measure of semipermeability. Lp is the mechanical coefficient of filtration or pressure filtration coefficient, and co is the solute mobility or solute diffusional coefficient. In the case of living membranes, conditions such as volume flow, osmotic gradients, and cell volume can be manipulated in order to measure the phenomenological coefficients cr, o>, and Lp. Detailed discussions of the theories, methods, and problems involved in such... 

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