Collisional frequency

As long as the collisional frequency measured by 1/tj is less than this value, i.e. 

The results from the Arrhenius analyses indicate that the CO2/CH3OH system has a higher activation barrier (74.2 7.7 kJ/mol) for the solvation process compared to C02/CH3CN (43.3 18 kJ/mol). However, C02/CH30H has a faster solvation rate. The reason for this fast solvation rate lies in the collisional or Arrhenius frequency factor. The collisional frequency factor for C02/CH30H and C02/CH3CN are (1.6 0.3) x 1014 10 M1 s1 and (4.2 0.8) x 108 M1 s1, respectively. 

The reason for the faster rate of solvation for C[Pg.108]

Precise data on the collisional shifts in In+ are presently not available and an estimate can only be based on data from comparable atomic systems. Assuming a shift coefficient of 10-10 cm3/s and ultrahigh vacuum conditions (5 10-8 Pa), the collisional frequency shift would be 1 10-18. 

The streaming frequencies and in Eq. (1.14) are related to the inertial motions of body 1 and body 2, respectively (i.e., they are the inverses of the correlation times for the deterministic motion of the two bodies). The collisional frequencies w) and w2 are a measure of the direct coupling with the stochastic environment, that is, of the dissipative contribution to the dynamics. An analogous interpretation may hold for the frequencies and related to the streaming and stochastic drift of the field. 

But the major contribution of the projected fast field to the resulting operator is given by a new frictional tensor (or collisional frequency tensor), which includes coupling terms between body 1 and 2 that are of a purely dynamic nature that is, they do not affect the final equilibrium distribution. The collisional matrices, modified by the averaged action of the fast field, may be expressed in the following way ... 

The same definition and properties of the torque vectors holds as in Eq. (2.17) V, and V2 are the gradient operators acting respectively in the subspaces L, and L2. The frequency parameter w] is the streaming frequency it is the characteristic frequency for the deterministic motion of body 1 and it is inversely proportional to the square root of the moment of inertia /,. w) is the collisional frequency of body 1, and it is a direct measure of the dissipative effect due to the solvent, since it is proportional to the friction exerted by the medium on the body. Analogous parameters Wj >2 defined for body 2. See Table I for the explicit definitions. 

The streaming operator is substantially unchanged compared to Eq. (2.58) (except for an additional contribution to the first rank interaction potential). TTie collisional operator is defined in terms of an orientational dependent friction matrix (or collisional frequency matrix in the present dimensionless formulation) as... 

The source term G-L stands for generation minus losses. Diffusion coefficients can be estimated as a function of thermal velocity, mean free path, and collisional frequency... 

The collisional frequency is lelated to the tumolecular quenching constant by the quenching efficiency... 

The meaning of the bimoleculat quenching constant can be understood in terms of the frequency of collisions between freely diSiising molecules. The collisional frequency (2) of a fluorcrphore with a quencher is given by... 

Z (collisional frequency, fluorophore-quendter), 241 Zener dtode, 151 ZiiK-fingcr peptide, 88-89,416 Z-scale, 193... 

Tiesinga E, Crampton SB, Verhaar BJ, Stoof HTC. (1993) Collisional frequency shifts and line broadening in the cryogenic deuterium maser. Phys. Rev. A 47 4342-4347. 

The analysis of the three-monomer contribution is based on exact results for hard spheres (Sengers et al. 1978). Its evaluation to a good approximation for realistic potentials was carried out by Hoffman Curtiss (1965) and by Friend (1983). The effect of a third monomer on the collisional frequency of two monomers - the so-called excluded volume effect - leads to identical expressions for B and BfJ, which again depend upon complicated integrals that are not reproduced here. 

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