Lennard-Jones collision frequency

From equation (2.30) it can be seen that p E, t) is dependent on cj, the form of P(EIE ) and k E). o is most often taken to be the Lennard-Jones collision frequency i.e., the hard sphere collision frequency which is rectified for the effects of intermolecular forces by the inclusion of a collision integral factor. 

With this convention, we can now classify energy transfer processes either as resonant, if IA defined in equation (A3,13,81 is small, or non-resonant, if it is large. Quite generally the rate of resonant processes can approach or even exceed the Lennard-Jones collision frequency (the latter is possible if other long-range potentials are actually applicable, such as by permanent dipole-dipole interaction). 

Resonant rotational to rotational (R-R) energy transfer may have rates exceeding the Lennard-Jones collision frequency because of long-range dipole-dipole interactions in some cases. Quasiresonant vibration to rotation transfer (V-R) has recently been discussed in the framework of a simple model [57]. 

This latest transformation is only valid with the assumption that the collision frequency oj(E) is only a weak function of E and hence can be treated as a constant. This assumption holds well if, for example, Lennard-Jones collision frequencies are used. 

Troe gives an expression for kQ in terms of factors such as the harmonic density of states, the Lennard-Jones collision frequency, the vibrational partition function, and the critical energy, Eq, as well as terms to account for anharmonicity corrections, the energy dependence of the density of states, and rotational effects. We use equation (1) of reference 76 to estimate kQ. Expressions to evaluate each of the factors in that equation are summarized in reference 75. For the purpose of this discussion, 6c =1 unimolecular dis-... 

The Lennard-Jones collision frequency LJ can be used as the overall rate coefficient for collisional energy transfer. It is given by... 

We start from a model in which collision cross sections or rate constants for energy transfer are compared with a reference quantity such as average Lennard-Jones collision cross sections or the usually cited Leimard-Jones collision frequencies [54]... 

The relative efficiency per collision for deactivation of excited molecules in thermal reactions increases with the number of atoms in the collider, but reaches a constant limit when this number exceeds about 12. This has been demonstrated for many thermal reactions by studying the low pressure fall-off. It may be noted from eqn. (10) that plots of k /k against pressure for different inert gases should comprise a set of curves dispersed along the pressure axis according to the various efficiencies of deactivation per unit pressure. The relative efficiency per collision can be derived by calculating the collision frequency, Z, with a hard sphere or Lennard—Jones model. 

Fig. 10. The densities obtained at different cooling rates at T = 0 and p = 1 for the Lennard-Jones glass. The cooling rate is the value of the stochastic collision frequency per particle, v. The number of runs employed to obtain the reported average is shown inside each point. (From Fox and Andersen (67).)...

---