Rate constant crossover temperature

The two-mode model has two characteristic crossover temperatures that correspond to the freezing of each vibration. At temperatures above Tc0 = h(o0/2kB, the rate constant k(T) exhibits its ordinary Arrhenius form, in which the activation energy is determined by the effective barrier height... 

The temperature dependence of this rate constant was measured by Al-Soufi et al. [1991], and is shown in Figure 6.17. It exhibits a low-temperature limit of rate constant kc = 8x 105 s 1 and a crossover temperature 7 C = 80K. In accordance with the discussion in Section 2.5, the crossover temperature is approximately the same for hydrogen and deuterium transfer, showing that the low-temperature limit appears when the low-frequency vibrations, whose masses are independent of tunneling mass, become quantal at Tisotope effect increases with decreasing temperature in the Arrhenius region by about two orders of magnitude and approaches a constant value kH/kD = 1.5 x 103 at T[Pg.174]

The rate constant for hydrogen atom transfer (conversion II into III) spans six orders of magnitude in the range 290-80 K. The quantum limit of the rate constant and crossover temperature are 5xl0 3s 1 and 100 K, respectively. The ratio kH/ku increases from 10 to 5 x 103 as the temperature falls from 290 to 100 K. It is the H atom in position a that is transferred, since the substitution of deuterium atom at position b (R = H) does not change the rate constant. 

Hancock et al. [1989] used a version of the small curvature semiclassical adiabatic approach introduced by Truhlar et al. [1982] to calculate the temperature dependence of the rate constant, as shown in Figure 6.29. Variations in k(T) below the crossover point (25-30 K) are due to changes in the prefactor due to zero-point vibrations of the H atom in the crystal. Obviously, the gas-phase model does not take these into account. The absolute values of the rate constant differ by 1-2 orders of magnitude from the experimental ones for the same reason. 

Applied in sensors, the complex is usually immobilized in solid polymer matrices. Hence, the first two mechanisms will also play a significant role. Additionally, at higher temperatures the triplet excited state of the ligand can also be deactivated leading to a less efficient energy transfer to the lanthanide irai. The rate constants w of the crossover processes involved can be described approximatively by an Arrhenius-type equation, where the barrier height is expressed by the activation energy a [118, 119] ... 

FIGURE 5.5 Summary of the key kinetic concepts associated with active gas corrosion under the surface reaction, diffusion, and mixed-control regimes, (a) Schematic iUusIration and corrosion rate equation for active gas corrosion under surface reaction control, (b) Schematic illustration and corrosion rate equation for active gas corrosion under reactant diffusion control. (c) Schematic illustration and corrosion rate equation for active gas corrosion under mixed control, (d) Illustration of the crossover from surface-reaction-conlrolled behavior to diffusion-controlled behavior with increasing temperature. The surface reaction rate constant (k ) is exponentially temperature activated, and hence the surface reaction rate tends to increase rapidly with temperature. On the other hand, the diffusion rate inereases only weakly with temperature. The slowest process determines the overall rate. 

When 2M methanol solution is fed to the stack at a flow rate of 2 ml/min and the stack is operated at a constant voltage output of 3.8V, the transient response of the stack current density is shown in Fig. 3 varying the flow rate of air to the cathode. The stack was maintained at a temperature of 50°C throughout the experiment. As shown in the figure, while the stack current is maintained at the air flow rates higher than 2 L/min, the stack current begins unstable at the slower flow rates. A similar result is shown in Fig. 4 for varying methanol flow rate at an air flow rate of 2 lymin. At a methanol flow rate of 8 ml/min, the current density reaches initially a current density value of about 130 mA/cm and then starts to decrease probably due to medianol crossover. As the methanol flow rate decreases, the stack current density increases slowly until the methanol flow rate reaches 3 ml/min because of the reduced methanol crossover. The current density drops rapidly from the methanol flow rate of 2 ml/min. 

Temperature quenching of broad band emission is usually explained by a simple configuration coordinate model consisting of two parabolas that have been shifted with regard to each other (Fig. 6). This is called the Mott-Seitz model. Nonradiative return from the excited to the ground state is possible via the parabola crossover. Its rate can be described with an activation-energy formula Pnr = C where C is a constant of the order of 10 sec i and AE is the... 

The cumulative effect of an anodic ORR (induced by O2 crossover from the cathode to the anode) on cathode carbon catalyst-support loss (C corrosion) under fuel starved and ordinary (e.g. constant current) PEMFC operating eonditions were studied.The effects of C corrosion at constant cmrent are less severe than start-up and fiill H2 partial starvation, but they are large enough to affeet the cell performance after a long-time operation. The design factors of the MEA and operational factors such as humidity and temperature also affect carbon loss. The influence of these parameters is not always simple, and the coupling of these factors was addressed with MEMEPhy s to elucidate the rate of carbon loss under normal PEMFC operation... 

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