Diffusion overview

An overview of some basic mathematical techniques for data correlation is to be found herein together with background on several types of physical property correlating techniques and a road map for the use of selected methods. Methods are presented for the correlation of observed experimental data to physical properties such as critical properties, normal boiling point, molar volume, vapor pressure, heats of vaporization and fusion, heat capacity, surface tension, viscosity, thermal conductivity, acentric factor, flammability limits, enthalpy of formation, Gibbs energy, entropy, activity coefficients, Henry s constant, octanol—water partition coefficients, diffusion coefficients, virial coefficients, chemical reactivity, and toxicological parameters. 

The kinetics of diffusion-controlled phase transformations has long been a focus of research and it is vital information for industrial practice as well as being a fascinating theme in fundamental physical metallurgy. An early overview of the subject is by Aaronson et ai (1978). 

Heat is produced by chemical reaction in a reaction zone. The heat is transported, mainly by conduction and molecular diffusion, ahead of the reaction zone into a preheating zone in which the mixture is heated, that is, preconditioned for reaction. Since molecular diffusion is a relatively slow process, laminar flame propagation is slow. Table 3.1 gives an overview of laminar burning velocities of some of the most common hydrocarbons and hydrogen. 

The influence of interfaeial potentials (diffusion or liquid junction potentials) established at the boundary between two different electrolyte solutions (based on e.g. aqueous and nonaqueous solvents) has been investigated frequently, for a thorough overview see Jakuszewski and Woszezak [68Jak2]. Concerning the usage of absolute and international Volt see preceding chapter. 

The simple pore structure shown in Figure 2.69 allows the use of some simplified models for mass transfer in the porous medium coupled with chemical reaction kinetics. An overview of corresponding modeling approaches is given in [194]. The reaction-diffusion dynamics inside a pore can be approximated by a one-dimensional equation... 

Highly sophisticated pulse sequences have been developed for the extraction of the desired information from ID and multidimensional NMR spectra [172]. The same techniques can be used for high-resolution 1-NMR, s-NMR and NQR. Pulse experiments are commonly used for the measurement of relaxation times [173], for the study of diffusion processes [174] and for the investigation of chemical reactions [175]. Davies et al. [176] have described naming and proposed reporting of common NMR pulse sequences (IUPAC task group). An overview of pulse sequence experiments has been given [177],... 

An overview of this kind is, of necessity, limited in detail. Readers interested in a more thorough development of mass transfer principles are encouraged to consult the references listed at the end of the chapter. In particular, Cussler s excellent textbook on diffusion is an accessible introduction to the subject geared toward the physical scientist [11], Those with a more biological orientation may prefer Friedman s text on biological mass transfer [12], which is also exceptional. A classic reference in the field is Crank s Mathematics of Diffusion [13], which contains solutions to many important diffusion problems. 

While the lipid bilayer has a very low water content, and therefore behaves quite hydrophobically, especially in its core (see Chapter 2 of this volume), the cell wall is rather hydrophilic, with some 90% of water. Physicochemically, the cell wall is particularly relevant because of its high ion binding capacity and the ensuing impact on the biointerphasial electric double layer. Due to the presence of such an electric double layer, the cell wall possesses Donnan-like features, leaving only a limited part of the interphasial potential decay in the diffuse double layer in the adjacent medium. For a detailed outline, the reader is referred to recent overviews of the subject matter [1,2]. 

As described previously in this chapter, efforts have been made to develop methods for quantification of skin permeability, validation of diffusion cell setups, and correlation of in vitro data with the in vivo situation. However, the average drug permeation experiment does not provide insight into the temporal and local disposition within the tissue, that is, the skin penetration. The following discussion will give an overview of methods tackling this kind of problem. 

This chapter starts with a short introduction on the skin barrier s properties and the methods employed for analyzing experimental data. This is followed by an overview of several selected approaches to predict steady-state diffusion through the skin. Then a few approaches that approximate the structural complexity of the skin by predicting drug diffusion in biphasic or even multiphasic two-dimensional models will be presented. Finally, the chapter concludes with a short summary of the many variables possibly influencing drug permeation and penetration. 

Many drugs have been recognized to cross the intestinal epithelial cells via passive diffusion, thus their lipophilicity has been considered important. However, as described above, recent studies have demonstrated that a number of drug transporters including uptake and efflux systems determine the membrane transport process. In this chapter, we provide an overview of the basic characteristics of major drug transporters responsible not only for absorption but also for disposition and excretion in order to delineate the impact of drug transport proteins on pharmacokinetics. 

Surface diffusion has been extensively studied in literature. An overview of experimental data is given in Table 6.1. Okazaki, Tamon and Toei (1981), for example, measured the transport of propane through Vycor glass with a pore radius of 3.5 nm at 303 K and variable pressure (see Table 6.1). The corrected gas phase permeability was 0.69 m -m/m -h-bar, while the surface permeability was 0.55 m -m/m -h-bar, and so almost as large as the gas phase permeability (Table 6.1). It is clear from Table 6.1, that the effects of surface diffusion, especially at moderate temperatures, can be pronounced. At higher temperatures, adsorption decreases and it can be expected that surface diffusion will become less pronounced. 

The third and last part of the book (Chapters 12-16) deals with zeolite catalysis. Chapter 12 gives an overview of the various reactions which have been catalyzed by zeolites, serving to set the reader up for in-depth discussions on individual topics in Chapters 13-16. The main focus is on reactions of hydrocarbons catalyzed by zeolites, with some sections on oxidation catalysis. The literature review is drawn from both the patent and open literature and is presented primarily in table format. Brief notes about commonly used zeolites are provided prior to each table for each reaction type. Zeolite catalysis mechanisms are postulated in Chapter 13. The discussion includes the governing principles of performance parameters like adsorption, diffusion, acidity and how these parameters fundamentally influence zeolite catalysis. Brief descriptions of the elementary steps of hydrocarbon conversion over zeolites are also given. The intent is not to have an extensive review of the field of zeolite catalysis, but to select a sufficiently large subset of published literature through which key points can be made about reaction mechanisms and zeolitic requirements. 

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