Diffusion correlated

The high conductivity of (3-alumina is attributed to the correlated diffusion of pairs of ions in the conduction plane. The sodium excess is accommodated by the displacement of pairs of ions onto mO sites, and these can be considered to be associated defects consisting of pairs of Na+ ions on mO sites plus a V N l on a BR site (Fig. 6.12a and 6.12b). A series of atom jumps will then allow the defect to reorient and diffuse through the crystal (Fig. 6.12c and 6.12d). Calculations suggest that this diffusion mechanism has a low activation energy, which would lead to high Na+ ion conductivity. A similar, but not identical, mechanism can be described for (3"-alumina. 

Figure 6.12 Correlated diffusion in (3-alumina (a) the Na+ positions in the conduction plane of ideal NaAlnOi7 (b) the creation of associated defects by location of pairs of Na+ ions on mO sites (c) the ionic jumps involved in diffusion of an associated defect and (d) the final position of the defect.

Othmer, D.F. and M.S. Thakar (1953), Correlating diffusion coefficients in liquids, Industrial and... 

Equation (4.70) is a starting point in the determination of diffusivities in liquid metal alloys, but in most real systems, experimental values are difficult to obtain to confirm theoretical expressions, and pair potentials and molecular interactions that exist in liquid alloys are not sufficiently quantified. Even semiempirical approaches do not fare well when applied to liquid alloy systems. There have been some attempts to correlate diffusivities with thermodynamic quantities such as partial molar enthalpy and free energy of solution, but their application has been limited to only a few systems. 

Othmer, D. F., and M. S. Thakar, Correlating Diffusion Coefficients in Liquids, Industrial and Engineering... 

Hydrocarbon molecules with an oblong shape have higher diffusion coefficients than branched or flat diene hydrocarbon molecules, and their diffusion coefficients are higher than what could be expected from the correlation. Diffusion coefficients of oblong molecules like frani-2-butene in both polymers are higher compared to branched molecules with a similar molar volume, such as cfr-2-butene or isobutylene. 

The development of mass transfer models require knowledge of three properties the diffusion coefficient of the solute, the viscosity of the SCF, and the density of the SCF phase. These properties can be used to correlate mass transfer coefficients. At 35 C and pressures lower than the critical pressure (72.83 atm for CO2) we use the diffusivity interpolated from literature diffusivity data (2,3). However, a linear relationship between log Dv and p at constant temperature has been presented by several researchers U>5) who correlated diffusivities in supercritical fluids. For pressures higher than the critical, we determined an analytical relationship using the diffusivity data obtained for the C02 naphthalene system by lomtev and Tsekhanskaya (6), at 35 C. 

Equation (31) correlates diffusion coefficients of individual components and binary diffusion coefficients also in this case as far as the order of magnitude is concerned. More complex rate laws for the exchange have certainly to be expected if the sorption of the individual components is influenced or controlled by other processes than diffusion in the solid. 

Umesi, N, O., Correlating Diffusion Coefficients in Dilute Liquid Mixtures, M.S. Thesis, Penn State University, University Park, PA, 1980,... 

Fig. 12.1. Linewidth of the EISF (see definition, p. 332) and correlated diffusion coefficient as a function of temperature, deduced from neutron scattering experiments .

Near-infrared reflectance spectroscopy (NIRS) is an analytical technique that correlates diffusely... 

In the discussions of diffusion mechanisms in Chapter 5 it was pointed out that successive jumps of tracers atoms in a solid may for some mechanisms not be completely random, but are to some extent correlated. This is, for instance, the case for the vacancy and interstitialcy mechanisms. For a correlated diffusion of a tracer atom in a cubic crystal the tracer diffusion coefficient, Dt, is related to the random diffusion coefficient for the atoms. Dr, through the correlation coefficient f ... 

The Pawlisch model [63] was applied, for example, to calculate the partition coefficient and diffusion coefficients of a series of solvents in PMMA-co-BMA (poly(methyl methacrylate-co-butyl methacrylate)) at infinite dilution [66]. Values of K and Dp that best fitted the experimental data were found, and the model predicted perfectly the system behavior. The Vrentas-Duda free volume theory was found to correctly correlate diffusion data above Tg. 

Motupally et al. (2000) proposed correlation diffusion coefficient of water in Nafion-115 as... 

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