Correlations between diffusion coefficients and

FIGURE 4.8.16. Correlation between diffusion coefficient and membrane conductivity [51]. D values refer to the system 3.5 mol L NaCI/membrane/35% NaOH at 90°C and x values to 35% NaOH at W C. (With permission from Elsevier.)... 

Albert Einstein (1879-1955) was a German-bom American theoretical physicist. He was awarded the Nobel Prize in Physics in 1921. In electrochemical science, a number of equations bear Einstein s name, for example, Nemst-Einstein equation showing the relationship between conductivity and diffusion coefficient or the correlation between diffusion coefficient and viscosity, which is known as the Stokes-Einstein equation. 

Because of the correlation between rate coefficient and activation energy, the reactions which are classified as fast tend to belong to certain categories. Thus, for example, fast gas-phase reactions usually involve free radicals or atoms—a fact which increases the problems considerably since it is very difficult to generate radicals of known concentration, mix them with the other reactant and then monitor the concentrations of radicals and products at known time intervals after the start of the reaction. In solution the upper limit to the reaction velocity is governed by the rate at which the partners can diffuse together gas reactions are not so frequently diffusion-controlled because of the considerably higher diffusion coefficients in the gas phase. The fastest reaction studied in aqueous solution is the neutralization reaction, formally... 

A fair correlation has been found (Smith, 2000) between diffusion coefficients and wetting times for cotton twill tape (using a modified Draves wetting test (Chapter 6, Section IIC). 

Figure 10.3. Correlations between diffusion coefficient, configurational entropy, and tetrahedral order parameter (/h). Note that the left side of the y-axis represents the logarithm of diffusivity and the right side of ffie y-axis represents (th). The straight line fitting of the data validates the Adam-Gibbs relation between entropy and the diffusion coefficient, as discussed in the text The dashed line shows the correlation between (th) and configurational entropy. Adapted wifli permission from J. Phys. Chem. B, 114 (2010), 3633. Copyright (2010) American Chemical Society.

It is known that glassy polymer membranes can have a considerable size-sieving character, reflected mainly in the diffusive term of the transport equation. Many studies have therefore attempted to correlate the diffusion coefficient and the membrane permeability with the size of the penetrant molecules, for instance expressed in terms of the kinetic diameter, Lennard-Jones diameter or critical volume [40]. Since the transport takes place through the available free volume in the material, a correlation between the free volume fraction and transport properties should also exist. Through the years, authors have proposed different equations to correlate transport and FFV, starting with the historical model of Cohen and Turnbull for self diffusion [41], later adapted by Fujita for polymer systans [42]. Park and Paul adopted a somewhat simpler form of this equation to correlate the permeability coefficient with fractional free volume [43] ... 

Figures 3 and 4 present correlations between diffusion coefficients, log(D), and calculated CED. For all polyimides examined, including the polyimides in this study, good correlations between log(D) and CED were observed for each gas in spite of differences in measurement temperature.

This refers to the transport across the epithelial cells, which can occur by passive diffusion, carrier-mediated transport, and/or endocytic processes (e.g., transcytosis). Traditionally, the transcellular route of nasal mucosa has been simply viewed as primarily crossing the lipoidal barrier, in which the absorption of a drug is determined by the magnitude of its partition coefficient and molecular size. However, several investigators have reported the lack of linear correlation between penetrant lipophilicity and permeability [9], which implies that cell membranes of nasal epithelium cannot be regarded as a simple lipoidal barrier. Recently, compounds whose transport could not be fully explained by passive simple diffusion have been investigated to test if they could be utilized as specific substrates for various transporters which have been identified in the... 

MeOH is transported through the membrane by two modes diffusion and electro-osmotic drag. ° When MeOH comes into contact with the membrane, it diffuses through the membrane from anode to cathode and is also dragged along with the hydrated protons under the influence of current flowing across the cell. Therefore, a correlation between the MeOH diffusion coefficient and proton conductivity is observed. The diffusive mode of MeOH transport dominates when the cell is idle, whereas the electro-osmotic drag... 

The experimental diffusion parameters, D /r., at 30°C. are presented in Table II for all the coals. Clearly, no correlation exists between diffusion parameter and rank. If r<> is taken as the average particle radius for the 200 X 325 mesh samples, an upper limit to the values of diffusion coefficient, D, is obtained. The diffusion coefficient ranges from 1.92 X 10 9 sq. cm./sec. for Kelley coal to 1.41 X 10"8 sk. cm./sec. for the Dorrance anthracite. Our previous studies on the change of D /n with particle size suggested that n is not necessarily the particle radius (7) but is a smaller distance related to the average length of the micropores in the particles. That is, the calculated... 

Given information on the characteristic diffusion coefficients of the two polymers, it is then possible to estimate their relative permeabilities. The slope of the correlation line is a measure of the polarity of the polymer the lower the slope, the greater the solubility of a hydrophilic drug. The anticipated correlation between the slope and the solubility parameter of the polymer is approximately observed (cf Tables II, III). 

Third, a serious need exists for a data base containing transport properties of complex fluids, analogous to thermodynamic data for nonideal molecular systems. Most measurements of viscosities, pressure drops, etc. have little value beyond the specific conditions of the experiment because of inadequate characterization at the microscopic level. In fact, for many polydisperse or multicomponent systems sufficient characterization is not presently possible. Hence, the effort probably should begin with model materials, akin to the measurement of viscometric functions [27] and diffusion coefficients [28] for polymers of precisely tailored molecular structure. Then correlations between the transport and thermodynamic properties and key microstructural parameters, e.g., size, shape, concentration, and characteristics of interactions, could be developed through enlightened dimensional analysis or asymptotic solutions. These data would facilitate systematic... 

Tanaka, K., Kawai, T., Kita, H., Okamoto, K., Ito, Y. (2000) Correlation between gas diffusion coefficient and positron annihilation lifetime in polymers with rigid polymer chains . Macromolecules, 33, 5513. 

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