Diffusion coefficient temperature variation

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 die atoms over the surface of die substrate, and over the film during its formation, will occur more rapidly as the temperature increases since epitaxy can be achieved, under condition of ctystallographic similarity between die film and the subsuate, when the substrate temperamre 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 temperamre dependence of the diffusion of gases. For surface diffusion the variation of the diffusion coefficient widr temperature is expressed by the Anhenius equation... 

From various studies" " it is becoming clear that in spite of a heat flux, the overriding parameter is the temperature at the interface between the metal electrode and the solution, which has an effect on diffusion coefficients and viscosity. If the variations of these parameters with temperature are known, then / l (and ) can be calculated from the hydrodynamic equations. 

Figure 3. Variation of the chemical diffusion coefficient with composition in the "LiAl" phase at different temperatures [35].

There is experimental evidence to suggest that anion and cation diffusion can have different mechanisms [70]. The temperature variation of the diffusion coefficients of 1,1 P and 7 Li in aPEO-LiPF6 shows quite different trends. The 31P diffusion coefficients follow a VTF-type de-... 

Fig. 3.3.4 Variation of the tortuosity x inside the catalyst pellets during coking and regeneration, obtained by measuring the self-diffusion coefficient of n-heptane at room temperature.

The terms in Eq. (6) include the gravitational constant, g, the tube radius, R, the fluid viscosity, p, the solute concentration in the donor phase, C0, and the penetration depth, The density difference between the solution and solvent (ps - p0) is critical to the calculation of a. Thus, this method is dependent upon accurate measurement of density values and close temperature control, particularly when C0 represents a dilute solution. This method has been shown to be sensitive to different diffusion coefficients for various ionic species of citrate and phosphate [5], The variability of this method in terms of the coefficient of variation ranged from 19% for glycine to 2.9% for ortho-aminobenzoic acid. 

Values for G(unknown) were experimentally determined by using the previously calibrated cells, and these data were used to calculate values for D(unknown) using the cell constants. The overall average value of D(unknown) was 1.11 x 1(T5, which compares well with a reported value of 1.1 X 10 5. The coefficient of variation associated with the diffusion coefficient was 2.7% for one cell and 1.7% for a second cell. This calibration procedure thus provided information about the accuracy and precision of the method as well as the effect of temperature and concentration on the determination of the diffusion coefficient. 

Diffusion coefficients vary considerably with temperature. This variation is generally expressed in terms of the Arrhenius equation ... 

Whatever the technique used, it is important to note that (i) only an equivalent viscosity can be determined, (ii) the response of a probe may be different in solvents of the same viscosity but of different chemical nature and structure, (iii) the measured equivalent viscosity often depends on the probe and on the fluorescence technique. Nevertheless, the relative variations of the diffusion coefficient resulting from an external perturbation are generally much less dependent on the technique and on the nature of the probe. Therefore, the fluorescence techniques are very valuable in monitoring changes in fluidity upon an external perturbation such as temperature, pressure and addition of compounds (e.g. cholesterol added to lipid vesicles alcohols and oil added to micellar systems). 

The diffusion coefficients in EFLs with alcohol/H20 mixtures were also studied [23,24]. Figure 9.3 shows the variation of the diffusion coefficient of benzene as a function of temperature (299-393 K) for EFL mixtures where the mole ratio of methanol/H20 was maintained at 0.70/0.30 and the amount of CO2 was increased from 0 to 0.40 mole fraction [23]. At 313 K, the addition of 40 mol% CO2 caused a 100% increase in the diffusion coefficient of benzene. However, increasing the temperature and the proportion of CO2 caused the largest increase in the diffusion coefficient. Over a 500% increase in the diffusion coefficient of benzene is observed when the temperature is increased to 363 K and 0.30 mole fraction CO2 is combined with the 0.70/0.30 mole ratio methanol/H20 mixture. 

Souvignet et al. [24] studied the variation of the diffusion coefficients of nonpolar compounds, such as benzene and anthracene, and polar compounds, such as m-cresol and nitrophenol, in ethanol/H20/C02 mixtures. Figure 9.4 shows the variation of benzene s diffusion coefficient in 0.61/0.39 mole ratio ethanol/H20 mixtures as a function of added CO2 (0 0 mol%) and temperature (299-333 K). For the ethanol/H20 mixture increasing the temperature from 298 to 333 K caused a 95% increase in the diffusion coefficient of benzene while adding 40 mol% CO2 to the ethanol/H20 mixtures increased the diffusion coefficient by 213%. However, the combination of both the addition of 40 mol% CO2 and increasing the temperature to 333 K provided a... 

The diffusion coefficients, as expected, increase with increasing temperature. Variation of the diffusion coefficient as a function of temperature can be expressed in terms of the Arrhenius equation, which, in logarithmic form, is... 

Following the report on The Chemistry of the Atmosphere, it appears urgent to intensify sustained observational work in order to establish facts about any eventual evolution of our global environment. Such facts need to be gathered not only for physical parameters (temperature, albedo, variations of the solar ultraviolet irradiance below 3200 A, diffusion coefficients, aerosols, etc.) but also for a growing number of chemical species whose telluric concentrations are ultimately controlling the state of that environment. In 1960, a dozen molecules were known to exist in our atmosphere by 1980, 25 more species have been added to these and experimenters are asked now to look for another 40 molecules likely to play a role in the complex aeronomical scheme outlined by Professor M. Nicolet. 

The study is performed at reduced temperature T = 0.75 and reduced density p = 0.844-0.92. This is precisely the system studied in computer simulations [102]. The variation of the self-diffusion coefficient with the solute size is shown in Fig. 8, where the size of the solute molecule has been varied from 1 to 1/20 times that of the solvent molecule. In the same figure the computer-simulated values [102] are also plotted for comparison with the calculated results. The calculated results are in good agreement with the computer simulations. Both the theoretical results and the computer simulation studies show an enhanced diffusion for size ratios TZ TZ = 01/02) between 1.5 and 15. This is due to the sharp decoupling of the solute dynamics from the solvent density mode. 

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