Diffusion-limited transport

The above iso-pH measurements are based on the 2% DOPC/dodecane system (model 1.0 over pH 3-10 range). Another membrane model was also explored by us. Table 7.16 lists iso-pH effective permeability measurements using the soy lecithin (20% wt/vol in dodecane) membrane PAMPA (models 17.1, 24.1, and 25.1) The negative membrane charge, the multicomponent phospholipid mixture, and the acceptor sink condition (Table 7.1) result in different intrinsic permeabilities for the probe molecules. Figure 7.40 shows the relationship between the 2% DOPC and the 20% soy iso-pH PAMPA systems for ketoprofen. Since the intrinsic permeability of ketoprofen in the soy lecithin membrane is about 20 times greater than in DOPC membrane, the flat diffusion-limited transport region of the log Pe... 

Assumptions 1. Atomic diffusion limiting transport mechanism... 

This equation is nothing but the integrated form of (4.5.11] with respect to t), applying for diffusion-limited transport (C (0,t) 0 for all t). 

The term adsorption barrier is often used in the literature when diffusion-limited transport is observed to be slower than predicted by the appropriate equation of subsec. (ii) above. Some of the many experimental examples of such retardation are given in refs. ). However, the use of this term in the present context is not appropriate because adsorption does not retard the diffusional transport. Rather it is an independent, consecutive process. Relaxation processes preceding the diffusional transport in the bulk of the solution, may also retard the overall rate of transport, but may not be interpreted as a barrier to diffusion. For instance. 

The main processes governing the pharmacokinetics of a chemical are absorption, distribution, metabolism, and excretion. In PBPK models, distribution of a chemical is characterized by blood flow rates to each organ and tissue, and partitioning of the chemical between tissue and blood. These processes are commonly modeled using two alternative types of assumptions flow-Umited and diffusion-limited transport. The flow-limited assumption implies that equilibration between free and bound fractions in blood and tissue is rapid, and that concentrations of the chemical in the venous blood exiting a tissue and in the tissue are at equilibrium. The tissue is assumed to be a homogeneous... 

I. Determination of a (dimensionless parameter which relates diffusion-limited transport to kinetically limited transport) In general for the layer ... 

The overall mass-transfer rate can be limited by any of the diffusion resistances in the three liquid phases (diffusion-limited transport) and/or chemical reaction (complexation/decomplexation) rate resistances on the membrane-solution interfaces (reaction rate-limited transport). 

However, as pointed out by Silinsh and Capek [20], the argument does not resist further analysis because, at least for temperatures above 100 K, the mean free path calculated from Equation (2.2.5) falls below the distance between molecules in the crystal, which is not physically consistent with diffusion limited transport so the exact nature of charge transport in these crystals is still unresolved for the time being. 

Because of the low mobility of a-Si H, it is likely that many barriers will exhibit diffusion-limited transport. Here again, for cases in which nearly ideal behavior is obtained, the temperature dependence of Jq can be used to obtain the barrier height. The expression for diffusion-limited transport from Rhoderick (1978) is... 

Behr, Kirch and Lehn(9) and Fyles(Fyles, T.M. Can. J. Chem., submitted) have shown that macrocycle-mediated cation transport in many membrane systems, including ours, is diffusion limited. The parameters affecting diffusion limited transport are the diffusion coefficient and the distribution coefficient of the transported moiety. Furthermore, the diffusion coefficients of different cation-macrocycle complexes should be similar since their structures are similar. Hence, selective cation transport is basically a function of the factors affecting the distribution coefficients of the cation complexes involved in transport. 

In the steady state the left-hand side of Eq. (13) is equal to 0. Measurables are the steady state photocurrent, photovoltage, light and dark current voltage characteristics, and the quantum efficiency spectrum (or IPCE). If the physical origin of in is known, the dependence of such DC measurements on variations in intensity, wavelength, and bias, deliver the parameters controlling (for example, the values of the diffusion length and diffusion constant in the case of diffusion limited transport). 

The transport of alkali cations has been studied in single cation and competitive transport. A model has been developed which describes diffusion limited transport in terms of the extraction equilibria (K j) and the mean diffusion constants (D ). This model has also been used to predict the transport selectivity based on the differences in extraction ability... 

Theory and Mechanism. In Chapter 3, Reinhoudt and coworkers review recent mechanistic aspects of carrier-assisted transport through supported liquid membranes. Carriers for selective transport of neutral molecules, anions, cations, or zwitterionic species have been developed. Transport is described in terms of partitioning, complexation, and diffusion. Most of the mechanistic studies were focused on diffusion-limited transport, in which diffusion of the solute-carrier complex through the membrane phase is the rate-limiting step for transport. However, for some new carriers, the rate-limiting step was found to be decomplexation at the membrane phase-receiving phase interface. 

Another situation arises when the transport of the anion is assisted. In a later section, the transport of salts using an anion carrier, a mixture of a cation and anion carrier, or a ditopic carrier is discussed. Finally, the transport of neutral molecules will be described in the section on Diffusion-Limited Transport of Neutral Molecules. This is illustrated with our recent investigations on the transport of urea. 

Diffusion-Limited Transport of Salts. In the case of fast extraction equilibria for salts at the interfaces, the rate of transport is determined by diffusion of the complex through the membrane and the flux for steady state transport through an SLM is given by Equation 9. 

In fact, this equation is similar to the flux equation for neutral molecules (see section on Diffusion-Limited Transport of Neutral Molecules). 

Kinetically limited transport determination of a. In this section the influence of decomplexation kinetics in membrane transport will be discussed. An overview will be given of the different methods to distinguish diffusion-limited transport from kinetically limited transport. To illustrate these techniques, they will be applied to a diffusion limited (carrier 7) and a kinetically limited (carrier 6) transport system. A general model, that also includes the rate of cation release, was reported by Reichwein-Buitenhuis et al. (9). The flux is described by Equation 24. 

The basic transport parameters in the model given above are D, and a. The parameter a is a dimensionless number which relates diffusion limited transport to kinetically limited transport. When the transport is purely limited by diffusion (a - 0), D , and can be obtained from measurements of the flux as a function of a, (21). In principle, all parameters can be derived by measuring the flux... 

To obtain a clearer indication of the activation energy for diffusion-limited transport, the activation energy for the self-diffrision coefficient of NPOE can be measured. The activation energy for self-diffusion of a solvent often correlates well with the activation energy for diffusion of a solute species, since on a molecular level diffusion of a solute can be considered as a process in which either a solute or solvent molecule jumps from solvent cavity to cavity. Since the activation energy for self-diffusion varies with the solvent used, it is important to determine the activation energy E for the self-diffusion of NPOE first. The temperature dependency of the viscosity of organic solvents T has an Arrhenius-type behaviour. 

Parameters that Affect Diffusion-Limited Transport. Brown et aL varied the length of the alkyl chain of alkyl o-nitrophenyl ether membrane solvents and examined its influence on the proton-coupled transport of alkali metal cations by a crown ether derivative. By comparison of solvent characteristics, such as the dielectric constant, viscosity, and surface tension, they concluded that hexyl o-nitrophenyl ether is a better membrane solvent than NPOE (43), The effect of the solvent on the transport of NaC104 by carrier 4 has been studied by Visser et al (44), Transport parameters and were determined. A series of octyl phenyl ethers containing an electron withdrawing group (NO2, CN) of various positions on the phenyl ring were used. Data are presented in Table 5. 

The diffusion coefficient correlates linearly with the viscosity T as was already shown in the case of a diffusion limited transport system (Figure 14). When using the empirical Kirkwood function, a linear relationship between k and obtained. Figure 15 shows that the use of a more polar solvent slows down the rate of decomplexation. Hence, the regime of the transport can be influenced by the solvent polarity. 

Several models have been developed for the transport of different types of species through supported liquid membranes. The transport is described by subsequent partitioning, complexation and diffusion. Mechanistic studies are mainly focussed on diffusion limited transport of cations in which diffusion of the complex through the membrane phase is the rate-limiting step of the transport. Recently, kinetic aspects in membrane transport have been elucidated for new carriers with which the rate of decomplexation determines the rate of transport. 

Stability aspects of SLMs were investigated in DC18C6-facilitated, diffusion-limited transport of uranyl ion across a flat-sheet SLM. Solvent effects on the cation flux and diffusion coefficients were evaluated (44). The results of this study indicated that the stability and transmembrane fluxes depend on the physico-chemical characteristics of the carrier-diluent combination, not on the characteristics of the diluent alone. The physico-chemical properties of some diluents tested in the study are given in Table 5. Greater membrane stability was obtained with a membrane solvent of low volatility and aqueous solubility. Among the various diluents tested, a mixture of o-dichlorobenzene and toluene (3 7 by volume) gave the best combination of stability, regeneration capability, and transport rates. 

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