Variation with temperature diffusion coefficient

Variation of overall diffusivity coefficient, D, with temperature. 

To test for either adsorptive or electrostatic interactions, the SEC separation is performed at a variety of temperatures. If the separation occurs by size alone, the retention coefficient R(= V0/Ve) is independent of temperature very small variations may be observed as a result of gel swelling or microstructural changes to the gel. The presence of a significant dependence of R on T indicates the presence of a mechanism other than size exclusion. While R should not vary with 7 diffusion coefficients increase with T and so zone broadening occurs, leading to decreased resolution with increasing separation temperatures. 

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. 3. Variations of the methyl pentane diffusivity coefficient at room temperature versus the AN ratio for different crystal sizes ofMFI sanities. A corresponds to the external surface of the crystdlites and 7 to their volume (from ref 46). Measurements were made by measuring weight gain rate m by gravimetry at room temperature, k is calculated with the relationship (m /m o) = (ANl /iffl t = k t, D being the diffusion coefficient.

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. 

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].

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. 

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... 

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

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. 

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... 

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. 

The metal ion uptake profiles are shown in Fig. 11.1 for variations of NaCNS concentration (Fig. 11.1a), temperature (Fig. 11.1b) and plasticisation drawing (Fig. 11.1c) of the precipitation bath for Co uptake. Similar curves were obtained with Ni. Table 11.2 shows the data for different parameters related to a fully metallised fibre obtained after metallisation of PAN fibres, produced under different experimental conditions of the precipitation bath. Despite the fact that the uptake profiles are considerably different and the data obtained (diffusion coefficient) confirms this, no remarkable changes are observed in the total amount of metal absorbed by the fibre. This means that saturation for metal uptake is obtained independently of the precipitation bath parameters. The role of these parameters is limited to the rate of metal uptake, and a choice for the optimal value of these parameters should be based on economic reasons first the consumption of chemicals and energy and, secondly, the processing time. Taking these two criteria into account, a NaCNS concentration of about 12%, a temperature of 283 K and a plasticisation drawing of 500% are further used. 

Figure 2.9 Arrhenius plot showing temperature variation of nohle gas diffusion coefficients. Samples 1-3 are glass melts 4, 5, and 14 are vitreous silica 6 is commercial glass 7 and 14 are B203 8-10 are mixtures of alkali oxides with B203, Si02, and A1203 11 and 12 are obsidians 13 and 15 are Si02. Reproduced from Hiyagon (1981).

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