Temperature on diffusion

The effect of temperature on diffusivities in zeolite ciystals can be expressed in terms of the Eyring equation (see Ruthven, gen. refs.). 

Lee, K., Ishihara, A., Mitsushima, S., Kamiya, N. and Ota, K. 2004. Effect of recast temperature on diffusion and dissolution of oxygen and morphological properties in recast Nafion. Journal of the Electrochemical Society 151 A639-A645. Vebrugge, M. R. 1989. Journal of the Electrochemical Society 136 417. 

Anisothermal Homogeneous Diffusion. Using the reasonable simplifications that the flow of heat is much faster than the transport of matter and that thermal kinetic effects can be neglected, we can dispense with the effect of changing temperature on diffusion within a phase simply by using a reduced time r = tD/R2. Use of a reduced radius p = r/R... 

Our last example does not involve the rate of a chemical reaction, but instead, the effect of temperature on diffusion rates [25]. One of the motivations for using microelectrodes as in the previous example is to allow fast experiments without appreciable iR drop. When used in the opposite extreme of very small scan rates, microdisk electrodes produce steady-state voltammograms that have the same sigmoidal shape as dc polarograms and RDE voltammograms (cf. Chap. 12). 

At low pressures, we use the following expression developed from a combination of kinetic theory and corresponding states approach to estimate the effect of temperature on diffusivity ... 

The influence of temperature on diffusion coefficients of solutes in liquids has been studied in less detail. Diffusion coefficients often can be estimated from viscosity measurements. Hydrodynamic theory relates self-diffusion coefficients to the viscosity by... 

Figure 2. Effect of temperature on diffusion coefficient of nitrogen (1) and ethyl alcohol (2-4) in the granule of zeolite CaA-1...

An increased temperature also has a favourable effect on diffusion rates and hence on the extraction efficiency. It is difficult to derive an exact relation for the effect of temperature on diffusion rates, especially with finite concentrations and a multicomponent system. In most systems, diffusion rates are estimated to increase by a factor of 2-10 on increasing the temperature from 25 to 150°C [12]. 

FIGURE 16.4 Effect of temperature on diffusion coefficients (D) in systems near the glass transition (Tg). (a) Experimental values and calculation according to the WLF theory for diffusion of fluorescein in a sucrose-water system. (From results by D. Champion et al. J. Phys. Chem. B 10 (1997) 10674.) (b) Diffusion of water in 81% pullulan (a polysaccharide) in water. (From results by S. Ablett et al. In J. M. V. Blanshard, P. Lillford, eds. The Glassy States in Foods. Nottingham Press, 1993, p. 189.)... 

Effect of Temperature. At pH 5.0 or less, figures 3 and 4 show that the dissolution rate increases by a factor of 1.6 to 1.8 from 25 to 55°C. This gives an activation energy of about 4 kcal/gmol, corresponding to the effect of temperature on diffusivities. 

Effect of Material Moisture Content and Temperature on Diffusivity... 

The influence of temperature on diffusion in metals AND conductivity IN SALTS... 

Write an expression for the relaxation time during diffusion of the considered species in liquids. Combine this expression with that for the effect of temperature on diffusion coefficient and obtain the dependence of relaxation time on temperature. 

The influence of temperature on diffusion should not be confused with thermal diffusion, which leads to a separation of components with different molar masses Soret effect). The theory is complicated but can be explained as follows At a warmer location, all gas molecules gain the same kinetic energy (m/2v ) but the impulse of heavier molecules is higher (mv). Thus, at collisions, they penetrate deeper into the direction of the lower temperature than lighter ones. The separation causes a concentration gradient parallel (heavy molecules) or antiparallel with respect to the temperature gradient. Thermal diffusion is very slow and mostly negligible compared to ordinary diffusion, but is relevant for polymer characterization and enrichment of isotopes, for example, for uranium isotopes. 

Figure 4.5.11 Effect of temperature on diffusion coefficients of vanadium(ll) and (III) complex ions in NaCI-KCI based melts...

The influence of temperature on diffusivity varies for the second group. This somewhat sweeping categorization can be made for almost all UP resins. Structure, crosslinking density, and degree of curing could shift the boundaries. 

Ta b I e 5.82 Influence of conditioning temperature on diffusion coefficient and equilibrium-water absorption in reinforced and non-reinforced polyamide 66 (without correction for side effects) [748]... 

Moisture uptake in epoxide demonstrating (a) effect of reiative humidity on equilibrium moisture content and (b) effect of temperature on diffusion coefficient... 

This law describes an ideal case of steady flow which is strongly influenced by the nature of polymer, crosslinks, plasticizers, fillers, nature of penetrant, and temperature. Figure 7.1.10 shows the effect of polymer crystallinity and temperature on diffusion coefficients of 1-butanol and 1-octanol in poly(ethylene terephthalate). Increase of temperature facilitates diffusion (see also Figure 7.1.1). There is also difference in diffusion between two penetrants studied. Butanol has higher diffusion rate than octanol, which is easy to understand since butanol has smaller molecular volume (see also Figirre 7.1.3). Increase in crystallinity causes decrease of diffusion rate of both solvents. ... 

The strong effect of temperature on diffusion rate is described by the following equa-... 

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