Temperature dependence of diffusion

Cullinan presented an extension of Cussler s cluster diffusion the-oiy. His method accurately accounts for composition and temperature dependence of diffusivity. It is novel in that it contains no adjustable constants, and it relates transport properties and solution thermodynamics. This equation has been tested for six very different mixtures by Rollins and Knaebel, and it was found to agree remarkably well with data for most conditions, considering the absence of adjustable parameters. In the dilute region (of either A or B), there are systematic errors probably caused by the breakdown of certain implicit assumptions (that nevertheless appear to be generally vahd at higher concentrations). 

P. Clavin and P. Garcia. The influence of the temperature dependence of diffusivities on the dynamics of flame fronts. Journal de Mecanique Theorique et Appliquee, 2(2) 245-263, 1983. 

This situation is termed pore-mouth poisoning. As poisoning proceeds the inactive shell thickens and, under extreme conditions, the rate of the catalytic reaction may become limited by the rate of diffusion past the poisoned pore mouths. The apparent activation energy of the reaction under these extreme conditions will be typical of the temperature dependence of diffusion coefficients. If the catalyst and reaction conditions in question are characterized by a low effectiveness factor, one may find that poisoning only a small fraction of the surface gives rise to a disproportionate drop in activity. In a sense one observes a form of selective poisoning. 

EXAMPLE 2.6 Temperature Dependence of Diffusion Coefficients. Suppose the diffusion coefficient of a material is measured in an experiment (subscript ex) at some temperature Tex at which the viscosity of the solvent is qgx. Show how to correct the value of D to some standard (subscript s) conditions at which the viscosity is j s. Take 20°C as the standard condition and evaluate D°20 for a solute that displays a D° value of 4.76-10 11 m2 s 1 in water at 40°C. The viscosity of water at 20 and 40°C is 1.0050-10 2 and 0.6560 -10 2 P, respectively. 

Most probable settling velocity from sedimentation data Particle-size determination from sedimentation equation Sedimentation in an ultracentrifuge Solvation and ellipticity from sedimentation data Diffusion and Gaussian distribution Temperature-dependence of diffusion coefficients... 

A full model of the charge transport in the electrolyte would require the detailed description of the ionic transport processes inside the electrolyte. However, for the orientating study pursued in this contribution, it seems more appropriate to choose a simpler model that is able to describe the temperature dependence of the electrolyte qualitatively. The temperature dependence of diffusion coefficients in molten electrolytes can be described by an Arrhenius function [1]. Therefore, the temperature dependence of the conductivity is assumed to be of an Arrhenius type, as suggested in [6]. 

A. Kishimoto and K. Matsumoto Concentration and temperature dependence of diffusion coefficients for systems polymethyl acrylate and n-alkyl acetates. Trans. Faraday Soc. 56, 424 (1960). 

Fig. 3.112. Temperature dependence of diffusion coefficient D of surface-adsorbed 5-N-(octadecanoyl)aminofluorescein in black foam films stabilised by DLPE ( ) DMPE (A) DPPE ( ) and DOPE (+) [492],...

Figure 14 Temperature dependence of diffusion coefficients for the Cr-N system obtained from layer growth and concentration profiles, / 5-CrNi, o/ S-CrzN, A a-Cr(N)...

We have seen, by means of elementary theoretical considerations, that it is possible to deduce the activation energies for displacement of atoms or ions in a lattice from observations of the temperature dependence of diffusion and electrolytic conduction. 

If the mechanism of material transport in sintering is grain boundary diffusion, the viscosity can be expressed as a function of the temperature and the grain size. From a model for boundary diffusion controlled creep proposed by Coble [7] and the temperature dependence of diffusion coefficients, we obtain... 

D() Pre-exponential factor in equation for temperature dependence of diffusivity. 

The dififusivity of moisture in solids is a function of both temperature and moisture content. For strongly shrinking materials, the mathematical model used to define must account for the changes in diffusion path as well. The temperature dependence of diffusivity is adequately described by the Arrhenius equation as follows ... 

As can be seen from eqn (14.8), the calculation of the tensor reduces to the calculation of two-particle correlation functions. The lack of sufficiently detailed data on the exciton band structure and the exciton-phonon coupling constants considerably complicates the accurate calculation of the two-particle correlation functions and the exciton diffusion coefficients. However, the temperature dependence of this coefficient differs significantly for coherent and incoherent excitons (see below). Therefore, studying the temperature dependence of diffusion has always been an important tool to analyze the character of the energy transfer in molecular crystals. In the remainder of this chapter, we will focus on the main characteristics of the diffusion constant and its temperature dependence... 

Arrhenius plots showing the temperature dependence of diffusivity for n-butane in various 5A samples are shown in figure 4 while figure 5 shows the trend of activation energy with carbon number. For linear paraffins higher than n-butane, diffusion, even in the large 5A crystals, is too slow to measure by the NMR PFG method so it is only for butane that a direct comparison between ZLC and PFG NMR data is possible. 

Temperature dependence of diffusion coefficients in metals. Reprinted widi permission... 

Figure 7.2 Temperature dependence of diffusion coefficients for some common ceramic oxides. ...

Figure 7.3 Temperature dependence of diffusivity of Na ions in NaCl.

Examples of the temperature-dependence of diffusion in select silicate, oxide and carbonate systems are shown in Figure 23a for volume diffusion and Figure 23b for grain boundary diffusion. A comparison of diffusivities and activation data compiled in Table 2 (see Appendix) leads to the following general observations regarding diffusion behavior in crystalline-fluid (gas) systems. 

Data on the diffusion coefficients of solid solutes in liquid solvents are difficult to find and, if available, are usually found at low concentrations (or infinite dilution) at only one temperature. The concentration and temperature dependence of diffusion coef-... 

The temperature dependence of diffusivity is accounted for in lithographic simulators in terms of the Arrhenius expression ... 

Temperature Dependence of Diffusivity for Propylene and Propane in CHA Zeolites... 

P. Demontis, G. B. Suffritti, E. S. Fois, and S. Quartieri, J. Phys. Chem., 96, 1482 (1992). Molecular Dynamics Studies on Zeolites. 6. Temperature Dependence of Diffusion of Methane in Silicalite. 

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