Correlation constant permeabilities

However, before proceeding with the description of simulation data, we would like to comment the theoretical background. Similarly to the previous example, in order to obtain the pair correlation function of matrix spheres we solve the common Ornstein-Zernike equation complemented by the PY closure. Next, we would like to consider the adsorption of a hard sphere fluid in a microporous environment provided by a disordered matrix of permeable species. The fluid to be adsorbed is considered at density pj = pj-Of. The equilibrium between an adsorbed fluid and its bulk counterpart (i.e., in the absence of the matrix) occurs at constant chemical potential. However, in the theoretical procedure we need to choose the value for the fluid density first, and calculate the chemical potential afterwards. The ROZ equations, (22) and (23), are applied to decribe the fluid-matrix and fluid-fluid correlations. These correlations are considered by using the PY closure, such that the ROZ equations take the Madden-Glandt form as in the previous example. The structural properties in terms of the pair correlation functions (the fluid-matrix function is of special interest for models with permeabihty) cannot represent the only issue to investigate. Moreover, to perform comparisons of the structure under different conditions we need to calculate the adsorption isotherms pf jSpf). The chemical potential of a... 

The constant of proportionality is K/fx, where K is the permeability and is Newtonian viscosity. The dielectric properties of the resin are also measured using sensors. These measurements were correlated with viscosity and used as a part of the FRTM control system. 

The sizes and concentration of the free-volume cells in a polyimide film can be measured by PALS. The positrons injected into polymeric material combine with electrons to form positroniums. The lifetime (nanoseconds) of the trapped positronium in the film is related to the free-volume radius (few angstroms) and the free-volume fraction in the polyimide can be calculated.136 This technique allows a calculation of the dielectric constant in good agreement with the experimental value.137 An interesting correlation was found between the lifetime of the positronium and the diffusion coefficient of gas in polyimide.138,139 High permeabilities are associated with high intensities and long lifetime for positron annihilation. 

In rat liver mitochondria, in state 4, the AP was estimated to be about 220 mV, with the membrane potential representing about 90% of this (Nicholls, 1974 Appendix 3). Similar values have been reported for human and rat skeletal muscle mitochondria in state 4 (Stumpf et al., 1982). The control of the rate of electron transport is not only determined by the availability of ADP, but also of Pj oxidizable substrates, and oxygen. There is evidence for futile cycling of protons in intact normal rat hepatocytes (Brand et al., 1993). Recently, Porter and Brand (1993) found a correlation between the proton permeability of the inner membrane of liver mitochondria and body size in animals from the mouse (20 g) to horses (150 kg) with a decrease in permeability with increasing weight of several-fold at a constant... 

Results from constant differential pressure filtration tests have been analyzed according to traditional filtration science techniques with some modifications to account for the cross-flow filter arrangement.11 Resistivity of the filter medium may vary over time due to the infiltration of the ultrafine catalyst particles within the media matrix. Flow resistance through the filter cake can be measured and correlated to changes in the activation procedure and to the chemical and physical properties of the catalyst particles. The clean medium permeability must be determined before the slurries are filtered. The general filtration equation or the Darcy equation for the clean medium is defined as... 

The substance-specific kinetic constants, kx and k2, and partition coefficient Ksw (see Equations 3.1 and 3.2) can be determined in two ways. In theory, kinetic parameters characterizing the uptake of analytes can be estimated using semiempirical correlations employing mass transfer coefficients, physicochemical properties (mainly diffusivities and permeabilities in various media), and hydro-dynamic parameters.38 39 However, because of the complexity of the flow of water around passive sampling devices (usually nonstreamlined objects) during field exposures, it is difficult to estimate uptake parameters from first principles. In most cases, laboratory experiments are needed for the calibration of both equilibrium and kinetic samplers. 

When a saturable transporter is involved in the permeation process, the permeability is no longer a constant value but is dependent on the concentration of the substrate. In that case it is necessary to characterize the parameters of the carrier-mediated process, Km, the Michaelis-Menten constant related with the affinity by the substrate and Vmax, the maximal velocity of transport. If a passive diffusion process occurs simultaneously to the active transport pathway then it is necessary to evaluate the contribution of each transport mechanism. An example of how to characterize the parameters in two experimental systems and how to correlate them are described in the next section. 

In an in vitro experiment using Fischer 344 rat skin, the partition coefficient for skin air was determined for benzene at 203 ppm (Mattie et al. 1994). The partition coefficient of a chemical in skin is an indicator of the capacity of the skin for the chemical, and may reflect the rate at which a chemical is absorbed through the skin and enters the circulation. Results indicated a partition coefficient of 35, with an equilibration time of 4 hours. This value more closely correlates with the permeability constant of 1.5 derived by McDougal et al. (1990), than does the commonly used octanol/water partition coefficient of 134.9, as derived by Leo et al. (1971). The skin air partition coefficient is necessary for developing the dermal compartment of a PBPK model. 

Siegel studied the permeability of the oral mucosa. He found that in a homologous series, an increase in lipid solubility resulted in an increased permeability of the oral mucosa. His permeation constants correlate exactly with Kow values J7 8 ... 

There are many empirical correlations and theoretical treatments for predicting solubility, diffusivity, and permeability constants. Table 2 shows the permeability and solubility data for gases in polystyrene and low-density polyethylene. In the extrusion process. 

Ecoh is also useful in correlating or predicting many other important properties of a polymer, such as its glass transition temperature (Chapter 6), surface tension (Chapter 7), dielectric constant (Chapter 9), mechanical properties (Chapter 11), and permeability to small molecules (Chapter 15). 

The rates of change (slopes of the curves) of many important properties (such as the refractive index, surface tension, and gas permeabilities) as a function of temperature, the value of the dielectric constant, and many other optical and electrical properties, often change considerably at Tg. These changes enable the measurement of Tg by using techniques such as refractometry and dielectric relaxation spectroscopy. Refractometry provides results which are similar to those obtained from dilatometry, because of the correlation between the rates of change of the specific volume and of the refractive index with temperature. Dielectric relaxation spectroscopy is based on general physical principles which are similar to those in dynamic mechanical spectroscopy, the main difference being in its use of an electrical rather than a mechanical stimulus. 

Closed-form expressions from composite theory are also useful in correlating and predicting the transport properties (dielectric constant, electrical conductivity, magnetic susceptibility, thermal conductivity, gas diffusivity and gas permeability) of multiphase materials. The models lor these properties often utilize mathematical treatments [54,55] which are similar to those used for the thermoelastic properties, once the appropriate mathematical analogies [56,57] are made. Such analogies and the resulting composite models have been pursued quite extensively for both particulate-reinforced and fiber-reinforced composites where the filler phase consists of discrete entities dispersed within a continuous polymeric matrix. 

Compared to such correlations based on stratum comeum permeability studies, IPPSF profiles may have additional parameters related to penetrant interactions with nonlipid components of the skin. Earlier exploratory analyses indicated that the d parameter in the above model was most closely correlated to E = 0.67), suggesting it is a parameter related to stratum comeum permeability. Note, however, that in a pharmacokinetic model, the epidermal permeability coefficient is not a single rate constant but rather would be a microconstant defined by the model s differential eqnations. This is a limitation of using the empirical A,b,d modeling approach. 

Figure 14.5 depicts the predicted vs. observed permeability constants (log Kp) for all 288 treatment combinations studied without taking into account the specific mixtures at which these chemicals were dosed. The residuals of this model showed no further correlation to penetrant properties. However, when vehicle/mixture component properties were analyzed, trends in residuals became evident. An excellent single parameter explaining some variability of this residual pattern (R of 0.44) was log (1 /Henry constant) (1/HC). Figure 14.6 depicts the modified LFER model including an MF = log (1/HC). 

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