Collision rate with surface

The least resolved measurement is determination of the isothermal rate constant k(T), where T is the isothermal temperature. Although conceptually simple, such measurements are often exceedingly difficult to perform for activated process without experimental artifact (contamination) because they require high pressures to achieve isothermal conditions. For dissociative adsorption, k(T) = kcol (T) [S (Tg = TS = T)), where kcol(T) is simply the collision rate with the surface and is readily obtainable from kinetic theory and Tg and T, are the gas and surface temperatures, respectively [107]. (S ) refers to thermal averaging. A simple Arrhenius treatment gives the effective activation energy Ea for the kinetic rate as... 

The rate at which the organic vapor condenses (redeposits) inside the source cell is given by the molecular collision rate with the surface and the molecular sticking probability, a ... 

The rate of physical adsorption may be determined by the gas kinetic surface collision frequency as modified by the variation of sticking probability with surface coverage—as in the kinetic derivation of the Langmuir equation (Section XVII-3A)—and should then be very large unless the gas pressure is small. Alternatively, the rate may be governed by boundary layer diffusion, a slower process in general. Such aspects are mentioned in Ref. 146. 

When mass transfer rates are very high, limitations may be placed on the rate at which a component may be transferred, by virtue of the limited frequency with which the molecules collide with the surface. For a gas, the collision rate can be calculated from the kinetic theory and allowance must then be made for the fact that only a fraction of these molecules may be absorbed, with the rest being reflected. Thus, when even a pure gas is brought suddenly into contact with a fresh solvent, the initial mass transfer rate may be controlled by the rate at which gas molecules can reach the surface, although the resistance to transfer rapidly builds up in the liquid phase to a level where this effect can be neglected. The point is well illustrated in Example 10.4. 

The heat transfer rate, dQ/dt, between two surfaces of area A is given by the product of the collision rate of gas molecules with the surface and the average change in energy per collision, which for the cold surface may be written as... 

Elementary reactions on solid surfaces are central to heterogeneous catalysis (Chapter 8) and gas-solid reactions (Chapter 9). This class of elementary reactions is the most complex and least understood of all those considered here. The simple quantitative theories of reaction rates on surfaces, which begin with the work of Langmuir in the 1920s, use the concept of sites, which are atomic groupings on the surface involved in bonding to other atoms or molecules. These theories treat the sites as if they are stationary gas-phase species which participate in reactive collisions in a similar manner to gas-phase reactants. 

You can also use simple collision theory to explain why increasing the surface area of a solid-phase reactant speeds up a reaction. With greater surface area, more collisions can occur. This explains why campfires are started with paper and small twigs, rather than logs. Figure 6.8 shows an example of the effect of surface area on collision rate. 

This is what we consistently find by monitoring EPR and Mossbaner spectra (cooperation with Prof. E. Miinck, Pittsburgh) of the Nia-S-CO, Nia-C " and Nia-SR states the A. vinosum enzyme produced by H2 and/or CO at pH 8. A possible explanation is to assume that the individual enzyme molecules can exchange electrons. The best suited place for this is via the distal [4Fe-4S] cluster which is located on the surface of the protein. Such an exchange would occur on a one-electron basis and wonld be much slower (depends on the collision rate of the 90kDa enzyme) than the reaction with H2 (which is extremely fast and depends on the rate of diffusion of H2 into the enzyme (Pershad et al. 1999)). Suppose that the NC-C state is initially formed with one Ee-S cluster in the oxidized state ... 

If this is multiplied by a surface area a, the result is the rate of surface collisions. Then by analogy with Equation (42), we may take ka as... 

EXAM PLE 9.6 Rate of Atomic Collisions as a Function of Pressure. Assuming 1019 atoms per square meter as a reasonable estimate of the density of atoms at a solid surface, estimate the time that elapses between collisions of gas molecules at 10 6 torr and 25°C with surface atoms. Use the kinetic molecular theory result that relates collision frequency to gas pressure through the relationship Z = 1/4 vNIV, for which the mean velocity of the molecules v = (BRTI-kM) 12 and NIV is the number density of molecules in the gas phase and equals pNJRT. Repeat the calculation at 10 8 and 10 10 torr. 

In a simple view, the rate of surface reaction is just the rate of collision with the surface times the probability that a collision results in a reaction. We denote the later term as the sticking coefficient (probability) y. 

The total number of collisions with the dead comers is proportional to the total number of drops in the surface layer opposite the dead comers and—when the theory of local isotropic turbulence holds here also—proportional to the turbulent fluctuation frequency u/d. Near the wall, however, the theory of local isotropic turbulence certainly will not hold and —more or less—stationary large scale eddies will occur. Therefore, centrifugal effects will strongly increase the collision rate when the dispersed phase... 

Vroman has shown by antibody methods that plasma interactions with solid surfaces result in a hierarchial adsorption process 98). The high concentration proteins dominate the surface at short times due to the higher collision rates. As time passes... 

The experiments discussed above were all carried out with total pressures below 10-4 Torr. However, Hori and Schmidt (187) have also reported non-stationary state experiments for total pressures of approximately 1 Torr in which the temperature of a Pt wire immersed in a CO—02 mixture was suddenly increased to a new value within a second. The rate of C02 production relaxed to a steady-state value characteristic of the higher temperature with three different characteristic relaxation times that are temperature dependent and vary between 3 and 100 seconds between 600 and 1500 K. The extremely long relaxation time compared with the inverse gas phase collision rate rule out an explanation based on changes within the chemisorption layer since this would require unreasonably small sticking coefficients or reaction probabilities of less than 10-6. The authors attribute the relaxation times to characteristic changes of surface multilayers composed of Pt, CO, and O. The effects are due to phases that are only formed at high pressures and, therefore, cannot be compared to the other experiments described here. 

The rate of aggregation of fully renneted micelles is very sensitive to temperature. At room temperature it is appreciably less than the diffusional collision rate, which led Payens (1977) to consider the possibility that only a fraction of the surface is reactive (so-called hot spots). The idea of hot spots is consistent with the low fractal dimension of micelle clusters formed during renneting and leads to only a proportion of all encounters between fully renneted micelles being successful. In effect, a statistical prefactor is included in the reaction kernel to reduce the diffusion rate to a level comparable with experiment. However, Payens developed the idea of hot spots only within his theory of the aggregation of fully renneted micelles. 

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