Accommodation coefficient values

Fig. 32. (top) Spatiotemporal profiles of etch rate of silicon in a chlorine plasma measured by laser interferometry. The measured Cl atom concentration is also shown (bottom) Etch rate of silicon (at the wafer center) in a chlorine plasma as a function of lime predicted by a mathematical model (solid lines) and measured under the same conditions (points). Curves a and b correspond to accommodation coefficient values of 0.50 and 0.75, respectively. After [98],... 

Figure 12.4 shows mass transfer rates as a function of particle diameter for the three approaches for accommodation coefficient values of 1, 0.1, and 0.01. 

FIGURE 12.8 Maximum molar uptake rate per ppb of gas-phase reagent as a function of cloud drop diameter, as controlled by gas-phase diffusion, or interfacial transport for various accommodation coefficient values at T = 298 K and for Dg = 0.1 cm2 s l and MA = 30 g mol""1 (Schwartz 1986). 

Some typical accommodation coefficient values for common gases at several different temperatures are presented in Table 7.3. 

In the case of polyatomic molecules, one may consider separately the accommodation coefficients for translational and for vibrational energy. Values of the latter, civ, are discussed by Nilsson and Rabinovitch [7]. 

The pressure dependence of effective viscosity obviously depends upon the value of the momentum accommodation coefficient. Momentum accommodation data are relatively rare, but some representative data are given in Table 1. Note that all values are relatively close to unity. Because of this observation, momentum accommodation coefficients are normally assumed to be unity in applications... 

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. 

Heterogeneous uptake on surfaces has also been documented for various free radicals (DeMore et al., 1994). Table 3 shows values of the gas/surface reaction probabilities (y) of the species assumed to undergo loss to aerosol surface in the model. Only the species where a reaction probability has been measured at a reasonable boundary layer temperature (i.e. >273 K) and on a suitable surface for the marine boundary layer (NaCl(s) or liquid water) have been included. Unless stated otherwise, values for uptake onto NaCl(s), the most likely aerosol surface in the MBL (Gras and Ayers, 1983), have been used. Where reaction probabilities are unavailable mass accommodation coefficients (a) have been used instead. The experimental values of the reaction probability are expected to be smaller than or equal to the mass accommodation coefficients because a is just the probability that a molecule is taken up on the particle surface, while y takes into account the uptake, the gas phase diffusion and the reaction with other species in the particle (Ravishankara, 1997). 

The accommodation coefficients for OH and HO2 in our model are parameterised as temperature dependent accommodation coefficients (Gratpanche et al., 1996) in Table 3, with no account taken of the surface characteristics. There are a few papers reporting uptake coefficients for both OH and HO2 with lower limits quoted for the HO2 coefficients due to experimental limitations, giving rise to a low confidence in current experimental values for HO2 (Cooper and Abbatt, 1996 Hanson et al., 1992). The impact of reactions on aerosol on HO2 concentrations in the remote atmosphere could be significant if the uptake coefficient was greater than 0.1, and could dominate if it was close to unity (Saylor, 1997). 

The model was run with the RASA at 5.6x 10-8 cm-1 and 4.2x 10-7 cm-1. The reaction probability for HO2 was set to values of y=0.1 and 1. The effect on concentrations of HO2 is shown in Fig. 8. It is clear that, except during the night, the modelled concentrations are much closer to the measurements when the uptake rate was set to a higher value, i.e. with an accommodation coefficient equal to unity and a surface area of 4.2x 10-7 cm-1. This emphasises the need for accurate measurements of the RASA (including chemical composition) during a campaign and better measurements of accommodation coefficients in the laboratory. 

In the creeping flow range, C is equal to the ratio of the terminal velocity to the terminal velocity in continuum flow. The value of C is sensitive to the nature of molecular reflections from the surface of the particle (E5). The accommodation coefficient, o-r, may be interpreted as the fraction of molecules undergoing diffuse reflection, the balance being specularly reflected. Typical values for lie between 0.8 and unity. For near-continuum flow. Basset (B9) showed that... 

For particles whose accommodation coefficient is known, Eq. (10-56) appears to give the most accurate estimate for drag. Since ctr is rarely known to sufficient accuracy, C may instead be estimated for spheres over the whole range of Kn by a semiempirical expression whose form was first proposed by Knudsen and Weber (K6). With the numerical values due to Davies (D2) ... 

Fast gas transport, high solubility, and/or fast reaction. In this case, 1 /ync( approaches 1/a i.e., the maximum value for the measured uptake approaches the mass accommodation coefficient. 

Use the data of Hu et al. (1995) in Fig. 5.19 to derive the second-order rate constant for the O, + I" reaction in the liquid phase assuming that solubility and gas-phase diffusion are not limiting factors. Also derive a value for the mass accommodation coefficient for O-, based on these data. The Henry s law constant for O-, can be taken to be 0.02 M atm-1, the temperature is 277 K, and the diffusion coefficient in the liquid phase 1.3 X 10-5 cm2 s-1. 

Some radioactive vapours are adsorbed or chemisorbed on surfaces so strongly that the boundary condition is Xo equal to zero. This is also true of particles in the submicrometric size range. The velocity of gas molecules perpendicular to surfaces is of order 100 ms-1, whereas the resistance of the laminar boundary layer to molecular diffusion usually restricts vg to a value of the order 0.1 m s-1 or less. Hence if the accommodation coefficient, the fraction of molecular collisions which entail sorption at the surface, exceeds about 10-3, the surface will act as a perfect sink. 

SO2 uptake was measured at total system pressures in the range of 20 to 50 Torr, consisting of 17.5 Torr H2O vapor with the balance either helium or argon. The observed mass accommodation coefficients, 74, are plotted in Figure 2 as a function of the inverse of the calculated diffusion coefficient of SO2 in each H20-He and l O-Ar mixture. The diffusion coefficients are calculated as a sum of the diffusion coefficients of SO in each component. The diffusion coefficients for SO in He and in Ar are estimated from the diffusion coefficient of SO2 in H 0 (Dg p = 0.124 (101) by multiplying this value by the quantity (mH-/mH Q)V2, anti (mAr/m 2o) 2> respectively. The curves in Figure 2 are plots ofEquation 7 with three assumed values for 7 0.08,0.11 and 0.14. The best fit to the experimental values of is provided by 7 = 0.11. Since gas uptake could be further limited by liquid phase phenomena as discussed in the following section, 7502 = 0.11 is a lower limit to the true mass accommodation coefficient for SO2 on water. 

The large S02 mass accommodation coefficient (7 - 0.11) indicates that interfacial mass transport will not limit the rate of S02 uptake into clean aqueous cloud and fog droplets. Either gas phase diffusion, Henry s law solubility, or aqueous reactivity will control the overall rate of aqueous S(IV) chemistry. This conclusion is demonstrated by modeling studies of S02 oxidation in clouds by Chamedies (3) showing that the conversion time of S(FV) to S(IV) is independent of the mass accommodation coefficient for 1 7 > 10 2 Schwartz (1 ) has also shown that, with 7 as large as our measured value, the interfacial mass transport is unlikely to inhibit the oxidation of SC by or Ho02 in cloud droplets for gas concentrations typical of non-urban industrialized regions. 

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 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... 

The values of the accommodation coefficient ]3 for the recombination over silver and gold (see Table 6) are probably high enough to be compatible with reaction between mobile adatoms, but the low value for copper is not. Once again, we face the same dilemma posed by recombination over the Group IB metals. 

Table 1 compares the dimensionless coagulation coefficient predicted by the present model with other models. Since the Hamaker constant for most of the aerosol systems is of the order of 10"12 eig, this value is used in the calculation of the lower bound. Particle diffusion coefficients based on Philips slip correction factor for an accommodation coefficient of unity are used for the calculation of the coagulation coefficients ft (the Fuchs interpolation formula) and fts (the Sitarski... 

It was assumed that the motion of the fictitious particle within the above time steps is rectilinear. This simplification, which accelerates the computer calculation of the trajectories of the fictitious particle, has been show n to be justified (9). The Philips slip correction factor for an accommodation coefficient of unity (Eq. [4]) was used in the calculation of the diffusion coefficients of particles. The values of the dimensionless coagulation coefficients % obtained by the computer simulation for different particle sizes, are given in Table I. The statistical errors of the Monte Carlo simulation were estimated by the standard 3 a method (corresponding to a probability of 0.997) (13). The number of particle pairs that must be generated in order to lower the error to a reasonable level depends both on the initial distance of separation between... 

Methods of detecting adsorbed films, which are of great value as auxiliaries to determinations of the amounts adsorbed, include the measurement of the accommodation coefficient ( 11), of the thermionic... 

Values of the accommodation coefficient must be determined from experiment, and a brief summary of such measurements is given in Table 12-1. 

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