Collision numbers, rotational

The rotational relaxation collision number Zrot is a parameter assumed to be available at 298 K. It represents the number of collisions that it takes to deactivate a rotationally excited molecule. It is generally a small number, on the order of unity, except for molecules with very small moments of inertia (e.g., Zrot for H2 is 280). The rotational relaxation collision number has a temperature dependence, for which we use an expression from Parker [306] and Brau and Jonkman [42],... 

Rotational quanta are much smaller than vibrational quanta, and rotational energy is therefore much more easily degraded to translational energy. For most molecules the collision number for rotation-translation transfer is less than 10, corresponding to relaxation times smaller than 10 9 sec at one atmosphere pressure. 

Zeleznik [54] has derived rotational collision numbers for pure polar gases from a classical perturbation theory in two dimensions, in which the polar... 

Results show that the rotational collision number increases with increasing temperature and decreasing dipole moments and moments of inertia (see Section VII.A.2). 

Figure 3.25 Rotational collision number for several diatomic molecules at room temperature as a function of AEr (see text), according to Bauer and Kosche.

Malinauskas and co-workers [204, 205] and also Healy and Storvich [206] have derived rotational collision numbers from thermal transpiration measurements, utilizing the theory developed by Mason and co-workers [149]. Values have been obtained for the gases N2, CO, 02, and C02, up to temperatures of 500°K. Collision numbers were also obtained by Healy and Storvick for H2 at 444° and for CH4 and CF4 at 366°K. The latter three cases present difficulties for this technique, and it could only be ascertained that Zr(H2) is greater than 100. For N2, 02, and C02, the values of Zr obtained were in good agreement with those derived from acoustical methods, except that the increase in Zr with increasing temperature appeared more pronounced for the thermal transpiration method. 

Figure 3.26 Comparison of the experimental dependence of rotational collision number Zf on temperature with that predicted from the theory of Parker (from ref. 125).

Figure 3.27 Comparison of experimental and theoretical temperature dependence of rotational collision numbers ZT = Mr. (a) The cases of p-H2-p-H2 and p-H2-He Half-filled circles are the data of Jonkman et al., half-filled squares are their results for p-H2-He. Open squares are from Bose et al. Room-temperature results are by Geide (open circle) and by Valley and Amme (solid symbols). Upper broken curve is based on Takayanagi (/ = 0.105), solid line based on theory of Roberts (j9 =0.113) or Davison (/S =0.108). Lower dashed line is for p-H2-He theory of Roberts (/9 = 0.30). (b) Results for />-H2-Ne (open squares, Jonkman et al. solid square, Valley and Amme) and for />-H2-Ar (open circles, Jonkman et al. solid circle, Valley and Amme). Solid line is for/>-H2-Ar based on Jonkman et al., theoretical curve (/ = 0.13) dashed line is for />-H2-Ne (fi = 0.20).

DC1, HF, and DF, rotational collision numbers appear to decrease with increasing temperature over the intervals for which data are available (see Table 3.2). His comparison of acoustic-absorption and thermal-conductivity data for both HC1 and H20 indicates consistent results for these two experimental methods and their respective interpretations. However, the apparent decrease of Zr with increasing temperature is in contradiction to Zeleznik s... 

Experimental Rotational Collision Numbers for Polar Diatomic Gases [54]. 

Effective Rotational Collision Numbers from Measurements by Hill and Winter [279]. 

Malinauskas et al. [205] derived a rotational collision number for C02, from thermal transpiration measurements, of 1.9 at a nominal temperature of 504°K. 

Fig. 12 Variation of modal temperatures of OH, initially in (v n) = (8 3) with number of collision cycles (collision number) for a 1 10 mixture of OH (8 3) in a 4 1 mixture of N2 (0 10) and 02 (0 12) at 250 K. Total number of molecules is (nominally) 8,000. Tv (squares) represents vibrational temperature, Tt (circles) rotational temperature and Tt (triangles) translational temperature throughout. For OH and N2 the symbols are black, red and green for Tv, Tt and Tt respectively and are solid for OH and open for N2. The symbols for 02 follow this same pattern but are blue for all three modal temperatures. As described in the text, the primary data are the quantum state populations. Modal temperatures are calculated assuming a Boltzmann distribution and thus Tv and Tr will not be meaningful at the outset and in the early stages of ensemble evolution...

Q is the usual partition function of the activated complex referred to the minimum in the potential of the normal molecule as the zero of energy, Q is the partition function qf the three rotations and three translations of the normal molecule, Ea IS the activation energy of the reaction as measured from the minimum of the normal molecule potential energy surface to the minimum of the activated complex, 0 is the zero-point energy of the activated complex, and the v( s are the vibrational frequencies, of the normal molecule. Moreover, A the rate of deactivation of active molecules to normal molecules, has been set equal to the collision number Z times an efficiency factor y, assumed to be isotope independent. 

Unlike the case of collision-induced vibrational energy transfer, collision induced rotational energy transfer seems to be free of strong restrictions on the changes in the rotational quantum numbers. When account is taken of the spectral widths of the excitation sources used, the nature of the rotation-vibration structure in the fluorescence and absorption spectra, and the possibility of resonant ener f transfer in the collision, it is concluded that the studies of Bj aniline are the weakest, those of B2 benzene better, and those of glyoxal the best available. With this hierarchy of quality of information kept in mind, the following weaker conclusions can also be obtained from the studies cited. 

At present the derivation of this equation from the fully quantum-mechanical theory relies upon a heuristic extension of the semiclassical treatment for rigid rotors in which the rotational heat capacity and rotational collision number are replaced by the total internal heat capacity and the internal collision number respectively. This (approximate) extension seems to be justified by a result of van den Oord Korving (1988). 

The correlation problem thus reduces to the determination of the translational-rotation interaction and the diffusion coefficient for rotational energy. The interaction can be described by a collision number for rotational relaxation, frot. which can be found from independent measurements such as sound absorption (Lambert 1977). The temperature dependence of frot is reasonably well-determined from theory (Parker 1959 Brau Jonkman 1970), and depends on T and one new parameter, the limiting high-temperature value However, this theory is valid only for the case of a single rotational degree of freedom. 

In order to perform such an analysis, equation (14.25) for (which was identified with 6 (2000)) is used as a subcorrelation. Similarly, a representation for the rotational collision number was derived based on experimental information and the Brau-Jonkman formula (Brau Jonkman 1970). Furthermore, it has been assumed that vibrational collision numbers for nitrogen are very large (order of magnitude of 10 ) and will not influence significantly the subcorrelation for 6 (0001). 

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