Diffusion predicting

Organic molecules Energy barrier (kcal/mol) Maximum energy (kcal) Diffusion prediction... 

If Fick s equation is used and the diffusivities of the ion pair DAb and DBa are assumed to be equal, as for binary gas diffusivities, predicted exchange rates are the same, regardless of direction of diffusion. Thus, the newer theory taking into account the electric potential is clearly an improvement over the Fick s law approach. However, if an empirical view of this simple theory is used, allowing each diffusivity to assume a... 

As knowledge concerning diffusion processes in molecular sieve zeolites broadens, it becomes increasingly clear that development of a truly generalizable model for diffusivity prediction in such adsorbents is not likely in the immediate future ... 

In polymers, it is always observed that a packet of carriers spreads faster with time than predicted by Eq. (30). Thus, the spatial variance of the packet yields an apparent diffusivily that exceeds the zero-field diffusivity predicted by the Einstein relationship. Further, the pholocurrent transients frequently do not show a region in which the photocurrent is independent of time. As a result, inflection points, indicative of the arrival of the carrier packet at an electrode, can only be observed by plotting the time variance of the photocurrent in double logarithmic representation. The explanation of this behavior, as originally proposed by Scher and Lax (1972, 1973) and Scher and Montroll (1975), is that the carrier mean velocity decreases continuously and the packet spreads anomalously with time, if the time required to establish dynamic equilibrium exceeds the average transit time. Under these conditions, the transport is described as dispersive. There have been many models proposed to describe dispersive transport. Of these, the formalism of Scher and Montroll has been the most widely used. 

In the case of thick samples (typically few mm thick), oxidation is restricted to superficial layers. As a result, O2 concentration in an elementary sublayer, located at a depth x beneath the sample surface, is all the more so small since this sublayer is deeper. The spatial distribution (in the sample thickness) of O2 concentration has been predicted from a balance equation expressing that [O2] variation in an elementary sublayer is equal to the O2 supply by diffusion (predicted by the classical Pick s second law) minus its consumption by the chemical reaction ... 

Other promising separation data. Porous BaTiOs membranes have been prepared on alpha-alumina supports. A CO2 to N2 separation factor of 1.2 at 500 C which is higher than the Knudsen diffusion prediction of 0.8 has been obtained. If there had not been pinholes on the order of 100 nm in the membranes, the separation factor would have been higher [Kusakabe and Morooka, 1994]. The maximum CO2 permeance through the BaTiOs membranes is very high at 1.1x10 cm (STP)/s-cm -cm Hg. 

Here Dr is the rotary diffusivity predicted for a rod in an isotropic solution of like rods from the theory of Doi and Edwards (1986) for semidilnte solutions, namely. 

Using the diffusivities predicted by the Doi-Edwards theory [11] and the homogeneous rate constant given by - 7.5 1/mol s, Agarwal and Khakhar... 

The final properties of latex coatings are dependent on the mechanism of film formation and how the film forms. For example, the development of mechanical strength is a direct consequence of polymer chain inter-diffusion. Prediction of this strength is only possible from an understanding of the transformations occurring on the particle length scale. Here, the three major transformations in latex film formation are briefly outlined. 

DM, direct measure DP, diffusion predicted PP, production predicted. 

All direct measure estimates of Fe flux are corrected for precipitation loss in the flux cores (see Section 5.4) DM, direct measure DP, diffusion predicted. 

When the quantities in parentheses are assigned numerical values, the Mathcad routine yields the value of the diffusivity predicted by the Hayduk and Minhas equation, in units of cm2/s. 

D. Consequently, the errors arising from several diffusing species only become significant if one or more species exhibit abnormal diffusivities. In fact, diffusivity is only weakly dependent on the molecular weight, so it is useful to estimate the diffusivity of a solute from that of a suitable standard of known diffusivity under the same conditions. In most cases, the diffusivity predictions agree quite well with those obtained experimentally [80]. 

Recognizing the surface diffusivity predicted by eq.(7.9-20) becomes infinite at monolayer coverage, the theory of Higashi et al. was later modified by Yang et al. (1973) to allow for the second layer adsorption to rid of this deficiency. Yang et al. obtained the following equation for the surface diffusivity ... 

Organic Molecules Energy Barrier (kcal/mol) Maximum Energy (kcal) Diffusion Prediction... 

We show in Sec. Ill that the pore space of colloidal aggregates can be analyzed to yield diffusivity predictions for large molecules. It is hoped that similar models can be produced for the wider variety of materials just discussed. 

Adsorption-Reaction and Reaction-Diffusion Predictions. Next, in order to investigate adsorption and reaction effects more fully, let us consider Z and Z p in normalized form. It is straightforward to show that... 

Figure 3 Comparison of diffusion predictions with observed results from type I and type III systems.

The data consisted of values of grain boundary groove widths at several times at each of several temperatures. Mullins theory of grooving by surface diffusion ( ) predicts that the groove width w will grow with time t according to the relation... 

Fig. 7.5-2. Binary diffusion predicted from tracer diffusion. In general, binary diffusion cannot be predicted from tracer diffusion and activity data using empirical relations like Eq. 7.5-8. The data, for chloroform-carbon tetrachloride at 25 °C, are square centimeters per second. [From Kelly, Wirth, and Anderson (1971), with permission.]...

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