Infinite dilution diffusion coefficient

Hayduk-Laudie They presented a simple correlation for the infinite dilution diffusion coefficients of nonelectrolytes in water. It has about the same accuracy as the Wilke-Chang equation (about 5.9 percent). There is no explicit temperature dependence, but the 1.14 exponent on I compensates for the absence of T in the numerator. That exponent was misprinted (as 1.4) in the original article and has been reproduced elsewhere erroneously. 

Matthews, M.A. and Akgerman, A. Infinite dilution diffusion coefficients of methanol and 2-propanol in water. J. Chem. Eng. Data, 33(2) 122-123, 1988. 

Here D() is the infinite dilution diffusion coefficient, kd is the concentration coefficient and c is the concentration. A plot illustrating this behaviour is shown in Fig. 3.32. The concentration coefficient is given by (Vink 1985). 

Thus generally, for liquids D°AB D°BA. Different techniques with which to estimate the infinite dilution diffusion coefficient are described by Reid et al. [31]. Various correlation s (valid for an arbitrary composition of a binary mixture and for electrolytes) are also given. In the Wilke-Chang correlation for D°AB the effect of temperature has been accounted for by assuming D°AB — T. Although this approximation may be valid over small temperature ranges, it is usually preferable to assume that... 

This theory also gives good quantitative agreement with available experimental data for these properties. For example, for the non-LC backbone polymer polyisoprene [see Figure 3(a)] at infinite dilution in hexane [CHj-(Cl -CHj] in the I liquid phase at T - 293 K, the infinite dilution diffusion coefficient D g (in units of... 

As the mole fraction of either component in a binary mixture approaches unity, the thermodynamic factor E approaches unity and the Fick D and the Maxwell-Stefan D are equal. This result is shown clearly in Figures 4.1-4.3. The diffusion coefficients obtained under these conditions are the infinite dilution diffusion coefficients and given the symbol )°. 

TABLE 4.3 Infinite Dilution Diffusion Coefficients of Methanol and 2-Propanol in Water"... 

Ideally one would like to be able to predict the elements of [D] from a knowledge of the infinite dilution diffusion coefficients f)°y. A comparison of the generalized Fick s law (Eq. 3.2.5), with the Maxwell-Stefan equations (Eq. 2.2.10) shows that, for a nonideal system, the... 

M7L4 The infinite dilution diffusion coefficients >°y have been estimated as follows [10-" mVs] ... 

Carry out a review of methods for estimating infinite dilution diffusion coefficients in binary liquid mixtures. Your review should include calculations to test the accuracy of the methods that have been proposed. Fundamental data for computing the coefficients should be obtained from a single source as far as is possible we recommend the compilation by Daubert and Danner (1985). 

From the experimental data the infinite dilution diffusion coefficients can be determined as follows... 

In contrast to the case for gases, where an advanced kinetic theory to explain molecular motion is available, theories of the structure of liquids and their transport characteristics are still inadequate to allow a rigorous treatment. Liquid diffusion coefficients are several orders of magnitude smaller than gas diffiisivities, and depend on concentration due to the changes in viscosity with concentration and changes in the degree of ideality of the solution. As the mole fraction of either component in a binary mixture approaches unity, the thermodynamic factor T approaches unity and the Fick diffusivity and the MS diffusivity are equal. The diffusion coefficients obtained under these conditions are the infinite dilution diffusion coefficients and are given the symbol TP. 

Most methods for predicting D in concentrated liquid solutions attempt to combine the infinite dilution diffusion coefficients (D12)° and (D2,)° in a single function of composition. The Vignes formula is recommended by Reid et al. (1987) ... 

In electrolyte systems the components diffiise as ionic species and the effictive ionic diffiisivities are related to the nature and concentration of the other ions present. Taylor and Krishna [1993] give as an exanple the diffiision of an aqueous solution of HCl and BaCl2. The infinite dilution diffusion coefficients for the individual ions in water are ... 

Readers can choose it to be either the smallest or largest value in the infinite dilution diffusion coefficient matrix. 

A semi-empirical law, based on free volume theory [16], is usually considered to hold between the infinite dilution diffusion coefficient in the pure polymeric phase, A.p(0), and its FFV ... 

Equation (7.16) relates the apparent infinite dilution diffusion coefficient in the mixed matrix to the FFVm of the unpenetrated polymeric phase of the MMM. 

The FFV in the unpenetrated polymer phase of the MMM calculated from the sorption isotherm of the test penetrant (n-C4) throngh the NELF model can also be used to correlate the diffusivity data collected during sorption tests. The infinite dilution diffusion coefficient in the polymeric phase, T>p(0) determined from the experimental diffusivity data can be related to the FFV initially present in the polymer matrix (FFVm). As shown in Figure 7.7 for diffusion of n-bntane in AF 2400, there is a correlation between the infinite dilution diffusion coefficient and l/FFVS, that agrees with Eqnation (7.16). Similar behaviour is observed for n-Cs, with different valnes of the parameters A and B, as it can be seen from the results reported in Table 12. This is not surprising, because the values of these empirical parameters are expected to be a function of the penetrant nature and size. 

Figure 7.7 Infinite dilution diffusion coefficient of (a) n-C4 and (b) n-Cs in the polymeric phase of mixed matrices based on AF 2400 as a function of FFV. P coefficient for diffusion of (c) n-C4 and (d) n-Cs in the mixed matrices based on AF 2400 as a function of FFV...

Zhao, C. Li, J. Jiang, Z. Chen, C., Measurement of the Infinite Dilution Diffusion Coefficient of Small Molecule Solvents in Silicone Rubber by Inverse Gas Chromatography. Eur. Polym. J. 2006, 42, 615-624. 

BON Bonifaci, L. and Ravanetti, G.P., Measurement of infinite dilution diffusion coefficients of 8-caprolactam in nylon-6/solvent at elevated temperatures by inverse gas chromatography, J. Chromatogr., 607, 145, 1992. 

Zhao et al. [73] used the van Deemter equation to determine the infinite dilution diffusion coefficient for several n-alkanes in crosslinked silicone rubber. The infinite diffusion coefficient was calculated from ... 

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