Diffusivity variation with temperature

With regard to the liqiiid-phase mass-transfer coefficient, Whitney and Vivian found that the effect of temperature upon coiild be explained entirely by variations in the liquid-phase viscosity and diffusion coefficient with temperature. Similarly, the oxygen-desorption data of Sherwood and Holloway [Trans. Am. Jnst. Chem. Eng., 36, 39 (1940)] show that the influence of temperature upon Hl can be explained by the effects of temperature upon the liquid-phase viscosity and diffusion coefficients. 

The mobility or diffusion of the atoms over the surface of the substrate, and over the film during its formation, will occur more rapidly as the temperature increases since epitaxy can be achieved, under condition of crystallographic similarity between the film and the substrate, when the substrate temperature is increased. It was found experimentally that surface diffusion has a closer relationship to an activation-dependent process than to the movement of atoms in gases, and the temperature dependence of the diffusion of gases. For surface diffusion the variation of the diffusion coefficient with temperature is expressed by the Arrhenius equation... 

The variation of flame speed with equivalence ratio follows the variation with temperature. Since flame temperatures for hydrocarbon-air systems peak slightly on the fuel-rich side of stoichiometric (as discussed in Chapter 1), so do the flame speeds. In the case of hydrogen-air systems, the maximum SL falls well on the fuel-rich side of stoichiometric, since excess hydrogen increases the thermal diffusivity substantially. Hydrogen gas with a maximum value of 325 cm/s has the highest flame speed in air of any other fuel. 

Figure 4.41 Variation with temperature of the diffusivity for carbon in BCC-Fe (a — Fe). Activation energy is in units of J/mol. Reprinted, by permission, from D. R. Gaskell, An Introduction to Transport Phenomena in Materials Engineering, p. 519. Copyright 1992 by Macmillan Publishing Co.

We emphasize the line shape problem perhaps a little more than usual in the spectroscopic literature. Collision-induced spectra have little structure. Yet, the diffuse line and band spectra extend over wide frequency bands and must often be subtracted, say from the complex spectra of planetary or stellar atmospheres, for a more detailed analysis of other, less well known components. The subtraction requires accurate knowledge of the profile and its variation with temperature, composition, etc., often over frequency bands of hundreds of cm-1. 

Bragg positions k+l=2n+ at room-temperature. In synthetic titanite such diffuse reflections occur in the P phase only. The diffuse reflections in natural samples have extended 2-dimensional scattering normal to the crystallographic a-axis and show strong variation with temperature (Malcherek et al. 

From a least-squares analysis, the values of n and k have been estimated and these are included in Table I, and Figure 8 represents a typical plot for benzene and toluene. The average uncertainty in the estimation of n is around 0.007. The value of n do not indicate any systematic variation with temperature. However, a general variation of n from a minimum value of 0.53 to a maximum of 0.74 indicates that the anomalous type transport mechanism is operative and the diffusion is slightly deviated from the Fickian trend. This fact can be further substantiated... 

Ifitschfelder et al. [H9] gives a generalized relation for the variation of the thermal diffusion constant with temperature for gases whose molecules interact with the so-called Lennard-Jones potential function, the difference between a repulsion energy inversely... 

In modelling crystalline solids, the MC technique is of particular value in three distinct fields. The first concerns studies of sorbed systems, e.g. micropo-rous solids loaded with organic molecules. MC techniques are particularly suitable for studying the variation with temperature of the distribution of sorbed molecules in such systems (Yashonath et al., 1988). Secondly, the method has been fruitfully applied to the study of atomic diffusion. In this case the moves are atomic jumps of defined frequencies. In complex solids (including, e.g., alloys and ionic conductors), use of the MC technique allows accurate sampling of all the different jump mechanisms contributing to the diffusion, as shown in several studies of Murch and coworkers (e.g. Murch, 1982). 

Fig. 3. Variation with temperature of the diffusion coefficients for various simulated fluids and actual laboratory fluids. Sources of data are, from left to right LJ argon, simulated Refs. 7 (DC) and 12 (C) laboratory. Ref. 41 bard spheres (for which temperature axis corresponds to pV/NkT X.50), Ref. 82 soft spheres. Ref. 20 xenon. Ref. 41 toluene. Ref. 42 methyl cyclohexane. Ref. 43 carbon tetrachloride. Ref. 44 o-terphenyl. Ref. 45 molten KQ, simulated using Tosi-Fumi (TF) potential parameters. Ref. S repellent Gaussian core particles. Ref. 21 (F. H. Stillinger kindly deduced the values his simulation results would infer for argonlike particles in familiar units) Na ions diffusing in molten 6KN03-4Ca(N0j)2 solvent medium. Ref. 46. The dashed extension of lower temperature in the case of xenon is based on the Arrhenius parameters quoted for the data. ...

Fig. S-7- The variation with temperature of the surface diffusion length /, for water molecules on the basal face of an ice crystal. The broken curve shows the conjectured behaviour of on a prism face (Mason et al. 1963).

The variation of a diffusion coefficient with temperature is given by ... 

FIGURE4.8.14. Variation of sodium ion diffusion coefficient with temperature for perfluorocaiboxylate (open symbols) and perfluorosulfonate (dark symbols) polymers in concentrated NaOH solutions [65], The concentration of NaOH in moles liter s noted in the figure. (Reproduced with permission fivm The Electrochemical Society, Inc.)... 

The self-diffusion of Ba2+ in hydrated natural mordenite was studied. From the variation of the self-diffusion coefficient with temperature, the energy of activation and the pre-exponential factor for the self-diffusion process were calculated from the Arrhenius equations ... 

Figure 8.20a shows the temperature variation of the dielectric permittivity of undoped BNT samples (curves a-c), as well as of BNT doped with 1 at% La (curve d) and 2at% La (curve e), aU sintered at 1000 C. For this, the measurement frequency was lOkHz. The dielectric permittivihes of the undoped samples varied approximately Hnearly with temperature, and hence followed the Curie-Weiss law. The low values of dielectric permittivity, and their near-linear variation with temperature, could be assigned to the deviation from the ferroelectric perovskite composihon, and the increasing presence of paraelectric contributions from the decomposition products that cause an increase in electrical conductivity. On the other hand, in concurrence with the diffuse OD phase transition from the antiferroelectric to the paraelectric phase at Tq, the dielectric permittivity of the La-doped samples reached a maximum at 350 °C. The dielectric permittivity of BNT doped with lanthanum was more than twice that of undoped BNT, and was larger for lat% La (-2300) than for 2at% La (-2000). The lower value at a higher La concentration was presumed to be related to the superposition of an increasing deformation of the rhombohedral lattice of BNT towards a (pseudo)... 

Deep freezing of concrete causes multiple processes in its structure, namely the contraction of the solid skeleton and expansion of ice in the pores. The pores are not completely filled with water, which freezes at different temperature in different sized pores. The expansion of the ice is not linear with decreasing temperature. In real situations, water filtration and diffusion continue with temperature variations. Formation of ice may disrupt certain parts of the concrete structure, but larger voids filled with ice represent hard inclusions, which increase the strength of the composite material. In general, the properties of concrete result from the amount of freezeable water in the pore system, the distribution of pore dimensions and the rate of freezing. 

This approach is widely used for the interpretation of binary diffusion data where there is just a trace of the second component (for example, Chen et al 1982 Dymond Woolf 1982 Erkey et al. 1989). The expression given for gi2(< ) is based on computer calculations. Values for the coupling factors exhibit a linear variation with temperature which gives ease of interpretation and accurate calculation of tracer diffusion at other temperatures. However, it should be noted that there are uncertainties in the computed corrections, which means that the An are not uniquely defined, though at the present time there is no a priori method for calculating these factors. 

The exponential term include the variation of diffusion coefficient with temperature beyond 30°C or 303 K. 

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