Energy accommodation

Solution 6.1. The least-energy accommodation of the 0.5 A shift will be obtained by distributing it equally over the three springs. This gives AU = 3 x (30/2) x (0.166)2 — 1.2kcal/mol. A smaller value would be obtained with more springs. 

The energy of an incident molecule will not normally be the same as that of the molecule when it is scattered from the surface, i.e., ZsP Ef There will be an accommodation to the surface and an exchange of energy with the surface. Complete accommodation or equilibration with the surface would imply that the scattered molecules have the same temperature as the surface. The energy accommodation coefficient, ac, is defined for each surface involved in the problem by the expression... 

For convenience in this derivation, we assume that the energy accommodation coefficient is the same for collisions at surfaces 1 and 2. Thus, we may write... 

Table 4 Experimental Data for Energy Accommodation Coefficient...

As the pressure increases from low values, the pressure-dependent term in the denominator of Eq. (101) becomes significant, and the heat transfer is reduced from what is predicted from the free molecular flow heat transfer equation. Physically, this reduction in heat flow is a result of gas-gas collisions interfering with direct energy transfer between the gas molecules and the surfaces. If we use the heat conductivity parameters for water vapor and assume that the energy accommodation coefficient is unity, (aA0/X)dP — 150 I d cm- Thus, at a typical pressure for freeze drying of 0.1 torr, this term is unity at d 0.7 mm. Thus, gas-gas collisions reduce free molecular flow heat transfer by at least a factor of 2 for surfaces separated by less than 1 mm. Most heat transfer processes in freeze drying involve separation distances of at least a few tenths of a millimeter, so transition flow heat transfer is the most important mode of heat transfer through the gas. 

Fig. 5. The dependence of the recombination coefficient, the energy accommodation coefficient and the stationary concentration of adatoms on temperature for the hydrogen—tungsten system when P2 — 1 torr and the other parameters have the values specified in Fig. 4.

The parameter used to characterise the energy transfer to the surface is the energy accommodation coefficient (]3) which is defined as the fraction of the total energy of recombination adsorbed by the catalyst. 

One of the objectives of the following numerical exemplification of this simple model is to show that a prerequisite of any discussion of energy accommodation in the recombination process is a knowledge of its mechanism. 

Fig. 22. Temperature dependence of the energy accommodation coefficient and of the recombination coefficient for the nitrogen—tungsten system. P2 = 1 torr, a = 100. ° P> > 7 (Courtesy Halpem and Rosner [112 ].)...

The values of the energy accommodation coefficient for the recombination of H and O atoms by metals measured by Wood et al. [89] and by Melin and Madix [77] are given in Table 6. The /3(H) values of Wood et al. for nickel, platinum and tungsten are substantially higher than those reported by Melin and Madix, but no explanation appears to be forthcoming for this difference. From Table 6, it is seen that a given metal has... 

It will be clear from this account of energy accommodation during recombination that, while our simple model is just about adequate as a point of departure, the phenomenon is so diverse and complex that much more experimental evidence and theoretical analysis will be required before we can claim a real understanding of the factors involved. 

The amount of incident energy of the molecule ( incident) that is transferred to the surface can be represented by an energy accommodation coefficient y ... 

A truly quantitative theory of energy accommodation in lattice collisions is not yet available. However, model calculations have been carried out by McCarroll (73), and are summarized in Fig. 53. These... 

It can therefore be concluded that a condensation coefficient smaller than 1 usually indicates deficient energy accommodation. Quantitative... 

For an incident atom, = 0 if the kinetic energies of the incident and scattered atoms are the same incident = scauered- Conversely, = 1 if the kinetic energy of the scattered species is equal to the kinetic energy expected for desorbing from a surface of thermal energy kgT urface> since, in this circumstance, scattered = surface-For a scattered atom, the energy accommodation coefficient becomes the translational-energy accommodation coefficient. 

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