Temperature-dependent diffusivity

Ma is the Markstein number, of order unity, which for temperature-dependent diffusivities is now given by... 

The second approach employs a detailed reaction model as well as the diffusion of EG in solid PET [98, 121-123], Commonly, a Fick diffusion concept is used, equivalent to the description of diffusion in the melt-phase polycondensation. Constant diffusion coefficients lying in the order of Deg, pet (220 °C) = 2-4 x 10 10 m2/s are used, as well as temperature-dependent diffusion coefficients, with an activation energy for the diffusion of approximately 124kJ/mol. 

The numerical jet model [9-11] is based on the numerical solution of the time-dependent, compressible flow conservation equations for total mass, energy, momentum, and chemical species number densities, with appropriate in-flow/outfiow open-boundary conditions and an ideal gas equation of state. In the reactive simulations, multispecies temperature-dependent diffusion and thermal conduction processes [11, 12] are calculated explicitly using central difference approximations and coupled to chemical kinetics and convection using timestep-splitting techniques [13]. Global models for hydrogen [14] and propane chemistry [15] have been used in the 3D, time-dependent reactive jet simulations. Extensive comparisons with laboratory experiments have been reported for non-reactive jets [9, 16] validation of the reactive/diffusive models is discussed in [14]. 

TEMPERATURE DEPENDENCE, DIFFUSION HEAD SENSOR CELL... 

Denh is expressed in square centimeters per second. The dose dependence of Denh has been verified for implants in the range from 5 X 1012 to 1 X 1016/cm2. The calculated profiles in Figures 21 and 22 are based on this model, with Denh used as an additive term to the normal temperature-dependent diffusion. 

Fig. 4.23 also indicates a slight decrease of the signal plateau which, at a first glance, was unexpected. In the following, a reactive dispersion model given in ref. [37] is applied to deduce rate constants for different reaction temperatures. A trapezoidal response function will be used. The temperature-dependent diffusion coefficient was calculated according to a prescription by Hirschfelder (e.g., [80], p. 68 or [79], p. 104] derived from the Chapman-Enskog theory. For the dimensionless formulation, the equation is divided by M/A (with M the injected mass and A the cross-section area). This analytical function is compared in Fig. 4.24 with the experimental values for three different temperatures. The qualitative behavior of the measured pulses is well met especially the observed decrease of the plateau is reproduced. The overall fit is less accurate than for the non-reactive case but is sufficient to now evaluate the rate constant. 

The pressure and temperature dependent diffusion coefficient of the adsorbate in the carrier gas is approximated according to Gilliland [18] ... 

In 2001, Sun and Wang were probably the first to report on diffusion coefficients of [emim]BF4 measured by NMR [26], They observed temperature-dependent diffusion radii below 330 K they found a diffusion radius of 2.79 A while it was 1.90 A above 335 K. The authors concluded that ion pairing must take place at lower temperatures while at elevated temperature individual ions are predominantly present. 

With the value of e obtained from the analysis of isotherm data, it was possible to obtain temperature dependent diffusion coefficients in the Henry s Law region for CH4 in silica gel that are in fair agreement with experiment [17]. 

Table 12.1 Material constants for temperature dependent diffusion...

Figure 7.14 Arrhenius plots of temperature-dependent diffusivity coefficients of C6 alkanes within silicalite indicate that diffusion is increasingly hindered in the medium-pore channels as the degree of branching increases. Cyclohexane also diffuses very slowly. [Reproduced from reference 133 with permission. Copyright 1995 American Chemical Society.]...

Figure 10.16 shows the Arrhenius plots with the temperature-dependent diffusion coefficients of several solids. The differences can be considerable. For some applications good ionic conductivity is required while other materials are chosen because they are good diffusion barriers. 

Of course, these results are of value only if the temperature-dependent diffusivity follows the law selected in Chapter 3. 

This nudged elastic band result was compared with other N diffusion paths and mechanisms, and was determined to have unmatched agreement with experimental results. It was also shown that careful consideration of total energy corrections and the use of a fully temperature-dependent diffusion pre-factor had modest but important effects upon the calculation of diffusivities for paired and interstitial N. N.Stoddard, P.Pichler, G.Duscher, W.Windl Physical Review Letters, 2005, 95[2], 025901... 

The electrical and optical characteristics of Pt diffusion in n-type GaN film were investigated. The diffusion extent was characterized by secondary ion mass spectrometry. The temperature-dependent diffusion coefficients of Pt in n-GaN were 4.158 X 10-4, 1 572 x 10 3 and 3.216 x 10-3cm2/s at 650, 750 and 850C, respectively. The data could be described by ... 

Two separate samples of NasCgo were prepared by direct reaction of Ceo with sodium metal vapor, and subjected to different annealing times of 10 16 days. C and Na solid-state NMR, along with elemental analysis, powder XRD and Raman spectroscopy, were used to characterise both samples. Na and C solid-state NMR spectra of the two samples are significantly different, suggesting a relationship between annealing times and the final structure of the alkali fulleride. Na VTMAS NMR experiments reveal the existence of two or three distinct Na species and reversible temperature-dependent diffusion of sodium ions between octahedral and tetrahedral interstitial sites. C MAS NMR experiments are used to identify resonances corresponding to free Ceo and fulleride species. ... 

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