Diffusion coefficient from sorption

Calculation of the Diffusion Coefficient from Sorption and Desorption Kinetics in a Plane Sheet... 

D. M. Ruthven and K. F. Loughlin (University of New Brunswick, Fredericton, N. B., Canada) The data of Kondis and Dranoff illustrate a number of important points relating to the problem of calculating diffusion coefficients from sorption curves. For the analysis of sorption curves, the crystal size distribution should be expressed on a weight (or... 

Numerical solutions were applied to the dual-mode sorption and transport model for gas permeation, sorption, and desorption rate curves allowing for mobility of the Langmuir component. Satisfactory agreement is obtained between integral diffusion coefficient from sorption and desorption rate curves and apparent diffusion coefficient from permeation rate curves (time-lag method). These rate curves were also compared to the curves predicted by Fickian-type diffusion equations. 

Figure 6 shows the pressure dependence of diffusion coefficients calculated from permeation, sorption, and desorption rate curves for CO2 in PI2080. The average values of diffusion coefficients from sorption and desorption rate curves D y are in fair agreement with that from permeation rate curve D. The solid line in Figure 6 was computed from Equation 14... 

Figure 6. Pressure dependence of diffusion coefficients calcuiated from permeation ( -), sorption ((,)) and desorption (A) rate curves for CO2 in PI2080. 9 is average vaiue of diffusion coefficients from sorption and desorption rate curves at same pressure. The soiid iine is caicuiated from Equation 14 using parameters 0 in Tabie 1. The dotted line is calculated from Equation 15 using parameters in Table 1.

PI Lee. Determination of diffusion coefficients by sorption from a constant, finite volume. In RW Baker, ed. Controlled Release of Bioactive Materials. New York Academic Press, 1980, pp 255-265. 

The validity of eqn. (3) for determining the intracrystalline self-diffusion coefficients from uptake data has been shown for the sorption of benzene by... 

Diffusion coefficients for sorbed solvent and ions in Nafion have been estimated using several techniques. Yeo and Eisenberg [53] studied the sorption of water by a dry slab of Nafion (EW 1155) and estimated the interdiffusion coefficient of water in the membrane over the temperature range 0-99 °C from the water uptake dynamics. Diffusion coefficients from these measurements increased with increasing temperature over the range (1-10) x 10 cm /s with a reported activation energy of 4.5 kcal/ mol (18.8 kJ/mol). The method used to estimate the diffusion coefficients by Yeo and Eisenberg [53] was based on the dependence of the uptake in the initial portion of the uptake curve and is probably not fully appropriate [82]). 

Inverse Gas Chromatography. A technique that promises to circumvent many of the problems attendant to gravimetric sorption experiments is Inverse Gas Chromatography (IGO. Until recently, all reported applications of IGC to the measurement of diffusion coefficients have used packed chromatographic columns in which the stationary phase is supported on a granular substrate. Equations similar to those developed by van Deemter et al. (22) are used to calculate the stationary phase diffusion coefficient from the spreading of the elution profile. The equation developed by van Deemter is commonly written as... 

Studies of the diffusion of benzene in natural rubber represent some of the earliest detailed examinations of the interaction of an organic solvent with a polymer. Hayes and Park carried out measurements at low concentrations by the vapor sorption method (1), and at higher concentrations by determining the concentration distribution using an interferometric method (2). Complementary measurements by vapor transmission to determine the diffusion coefficient from time-lag data were carried out at low concentrations by Barrer and Fergusson (3). The main results of these studies have been summarized in Fujita s review (4) of organic vapor diffusion in polymers above the glass transition temperature. However, the problems with these measurements were not referenced. 

Garrido, L. Mark, J. E. Clarson, S. J. Semiyen, J. A., Studies of Cyclic and Linear Poly(dimethylsiloxanes) 15. Diffusion Coefficients from Network Sorption Measurements. Polym. Comm. 1984, 25, 218-220. 

The relationship between individual sorption states and a fully connected jump network will be discussed in Section IX. Methods for calculating a diffusion coefficient from the structure and rate constants are discussed in Section X. 

The diffusivity data were obtained by two different methods i.e. from the time-lag in the gas permeation and from the sorption kinetics. The results from both methods are plotted versus SWNT loading in Fig. 8.80. Even though the absolute values obtained from the two different methods are different, the trends observed are the same i.e., there is a significant increase in diffusion coefficient from 0 to 5 wt% loading while the diffusion coefficient either leveled off or decreased slightly by the further increase in SWNT loading. 

Diffusion-coefficients from network sorption measurements. Polymer Communications, 25,218-220. 

The cured LCER usually exhibits much lower permeability, diffusion coefficient and sorption coefficient toward permeants such as moisture, solvents as compared with cured ER (Vittoria et al. 1991 Weinkauf and Paul 1992). The results can be understood from a two-phase model, the permeant penetrates through the crystalline domains extremely slow as compared with the amorphous phase, so the permeant only diffuse predominately through the domain boundaries. The LCER is known to have aligned and densely packed crystalline domains in the cured LCER system which will result in low permeability. The Sumitomo Chemical Company has taken the advantage of this property and developed biphenyl LCER resin into the 1C packaging and encapsulation materials (Hirano et al. 1999). 

An elegant alternative method to measure sorption into polymers is the Attenuated Total Reflectance Fourier Transform Infrared (ATR-FTIR) method. It allows in situ acquisition of the kinetic data and at the same time records the changes that occur in the polymer matrix due to the influence of the diffusant. Effects such as swelling, changes in morphology and polymer solvent interactions can all be simultaneously monitored. To calculate the diffusion coefficients from ATR-FTIR data, the mass uptake equation used in gravimetric diffusion experiments has to be modified to take into account the convolution of the evanescent field with the diffusion profile. 

Pure PHEMA gel is sufficiently physically cross-linked by entanglements that it swells in water without dissolving, even without covalent cross-links. Its water sorption kinetics are Fickian over a broad temperature range. As the temperature increases, the diffusion coefficient of the sorption process rises from a value of 3.2 X 10 8 cm2/s at 4°C to 5.6 x 10 7 cm2/s at 88°C according to an Arrhenius rate law with an activation energy of 6.1 kcal/mol. At 5°C, the sample becomes completely rubbery at 60% of the equilibrium solvent uptake (q = 1.67). This transition drops steadily as Tg is approached ( 90°C), so that at 88°C the sample becomes entirely rubbery with less than 30% of the equilibrium uptake (q = 1.51) (data cited here are from Ref. 138). 

Figure 15 The sorption of acetaminophen from a solution of limited volume by 10 X 4 poly (A-isopropylacry lam idc) gel, illustrating the use of Eqs. (34) and (35) to determine the diffusion coefficient of the solute. (Data from Ref. 174.)... 

Pulsed field gradient (PFG)-NMR experiments have been employed in the groups of Zawodzinski and Kreuer to measure the self-diffusivity of water in the membrane as a function of the water content. From QENS, the typical time and length scales of the molecular motions can be evaluated. It was observed that water mobility increases with water content up to almost bulk-like values above T 10, where the water content A = nn o/ nsojH is defined as the ratio of the number of moles of water molecules per moles of acid head groups (-SO3H). In Perrin et al., QENS data for hydrated Nation were analyzed with a Gaussian model for localized translational diffusion. Typical sizes of confining domains and diffusion coefficients, as well as characteristic times for the elementary jump processes, were obtained as functions of A the results were discussed with respect to membrane structure and sorption characteristics. ... 

This equation relates the temporal concentration of a diffusing chemical to its location in space. In real soil and aquifer materials, the diffusion coefficient can be affected by the temperature and properties of the solid matrix, such as mineral composition (which affects sorption, a process that can be difficult to separate from diffusion), bulk density, and critically, water content. 

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