Transport Arrhenius plot

Figure 5.37. Arrhenius plot illustrating the effect on the apparent activation energy of pore diffusion and transport limitations through the stagnation layer surrounding a catalyst...

Describe qualitatively the consequences of transport limitations on the apparent activation energy of a catalytic process by using an Arrhenius plot. What is the best temperature to run this reaction in an industrial application ... 

An example of this approach was presented earlier in Figure 3.34, which contains Arrhenius plots (rate vs. l/T cf. Section 3.0.2) at different total pressures. Figure 3.34 clearly shows the two types of deposition rate behavior. At low temperatures (higher 1/r) the reaction kinetics are slow compared to mass transport, and the deposition rate is low. At higher temperatures (lower HT) chemical kinetic processes are rapid compared to mass transport, resulting in a distinct change in slope and a higher deposition rate. 

Measurements of the steady state phosphoprotein level at different temperatures revealed that phosphoprotein formation is accompanied by a large and constant enthalpy change of 48 kJ/mol. In contrast, the likewise quite high activation energy of phosphoprotein formation exhibits a pronounced break between 20°C and 30°C. A break in the Arrhenius plot of the calcium-dependent ATPase has been observed in the same temperature range and has been interpreted as transitions between two activity states of the enzyme. Apparently, the phosphorylation of the calcium free protein by inorganic phosphate exhibits a similar kind of activity transition as observed for the calcium-dependent interaction of the transport protein with ATP131. A similar transition phenomenon complicates the time course of phosphoprotein formation... 

Fig. 18. Arrhenius-plot of the rate constants kg for the retarded polymer transfer from the gel into the sol (full lines), and ks for the corresponding reversible-thermodynamic equilibrium in that transport (dashed lines), see Fig. 17...

Although originally derived for membrane transport phenomena, the mechanisms outlined above can also provide potential explanations for non-linear, upwardly-concave Arrhenius plots for passive diffusion (Silvius and McElhaney, 1981 Klein, 1982). Other... 

Figure 1.5 (A) Dependence of rate on contact time r W is the weight of catalyst F is the flow-rate. (B) Arrhenius plot showing change from kinetic control to mass-transport control.

Transit Pulse Shapes. Figure 3 displays the current-mode hole transit pulse shapes in PVK and in Br-substituted PVK from 264 to 490 K, together with the corresponding Arrhenius plots of mobility (34). For brominated PVK, the transit pulses remain relatively featureless over the entire experimentally accessed range. For PVK, however, the transit pulses display a well-developed shoulder above 414 K, which is characteristic of nondisper-sive transport of the photoinjected carrier sheet. 

Fundamental studies of gas transport in polymers other than rubbers began with the classical work of Meares in 1954 He was the first to demonstrate and theorize about the now well-known inflection in the Arrhenius plots of D near the ass transition temperature. He also speculated abcut two modes of sorption in glassy polymers. Later studies were initiated with many polymers by Barrer, Michaels and their coworkers together with important contributions by Brandt, Stern, Stannett and many others ... 

Careful studies with a large number of gases in pdy(ethyl methacrylate) by Stannett and Wlliams showed no break in the Ardienius plots of either P or D, even for krge penetrants. However a later study of hydrogen and deuterium transport by Zie and Eirich vrith the same polymer showed a cl break in the Arrhenius plots for Ixith permeabilities and difhisivities. In vkw of this discrepancy in such an apparendy unique system, the hydrc n transport in a sample which had been carefully armealed for two days at 10 °C above Tg, was remeasured and did... 

Figure 8. Arrhenius plot of transport difiusivities in samples A ( ), B ( ), and C(l)...

Microscopically, the activation energy ( ) is an energetic barrier for the elementary act of ion transport and, obviously, depends on the crystal structure, in particular, on the bottleneck size (see Section 7.2.2). Macroscopically, it is determined from the slope of the Arrhenius plot, assuming that the is independent of temperature. This assumption is not necessary true, especially in the vicinity of a phase transition when the structure changes rapidly. For example, dilatometric studies of Na3Zr2Si2. 

Lithium transport in all of these phases occurs via the shared faces of octahedra and tetrahedra. In normal spinels (e.g., Li2ZnCl4), wliert the tetrahedra are occupied by M, the conductivity is much louver. Diffuse order-disorder transitions in both Li2MX4 and LigMXg result in strong deviations from linearity on their Arrhenius plots. 

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