Momentum correlation time

In the impact approximation (tc = 0) this equation is identical to Eq. (1.21), angular momentum relaxation is exponential at any times and t = tj. In the non-Markovian approach there is always a difference between asymptotic decay time t and angular momentum correlation time tj defined in Eq. (1.74). In integral (memory function) theory Rotc is equal to 1/t j whereas in differential theory it is 1/t. We shall see that the difference between non-Markovian theories is not only in times but also in long-time relaxation kinetics, especially in dense media. 

Table 2.1. Angular momentum correlation times tj of various molecules in liquefied gases [93J.

The physical meaning of and f L.., is obvious they govern the relaxation of rotational energy and angular momentum, respectively. The former is also an operator of the spectral exchange between the components of the isotropic Raman Q-branch. So, equality (7.94a) holds, as the probability conservation law. In contrast, the second one, Eq. (7.94b), is wrong, because, after substitution into the definition of the angular momentum correlation time... 

Gillen K. T., Douglas D. S., Malmberg M. S., Maryott A. A. NMR relaxation study of liquid CCI3F. Reorientational and angular momentum correlation times and rotational diffusion, J. Chem. Phys. 57, 5170-9 (1972). 

Yi and Ys - gyromagnetic ratio of spin 1 and spin S nuclear spin, rJS = intemuclear distance, tr= rotational correlation time, x< = reorientation correlation time, xj = angular momentum correlation time, Cs = concentration of spin S, Cq = e2qzzQ/h = quadrupole coupling constant, qzz = the electric field gradient, Q = nuclear electric quadrupole moment in 10 24 cm2, Ceff = effective spin-rotational coupling constant, a = closest distance of appropriate of spin 1 and spin S, D = (DA+DB)/2 = mutual translational self diffusion coefficient of the molecules containing I and S, Ij = moment of inertia of the molecule, Ao = a// - ol-... 

The more obvious and consistent deviations from the hard sphere theory occur, at the low density values, due to the effects of attractive forces in the real system. We can attempt to correct for these effects using a method described previously (27-30) for the analysis of angular momentum correlation times in supercritical CFjj and CFjj mixtures with argon and neon. We replace the hard sphere radial distribution function at contact hs with a function gp (0) which uses the more realistic... 

If one corrects for the effects of attractive forces, the corrected values are much smaller than the observed values the correction overestimates the importance of attractive forces on the value of the diffusion coefficient. Although attractive forces have an effect on the diffusion coefficient at low density, they are not nearly as Important as they are in determining the value of the angular momentum correlation time. Diffusion is primarily determined by the repulsive forces between molecules, even at the lowest densities. 

The angular momentum correlation time rj is obtained from MD simulations... 

BKM-SRLS Momentum Correlation Times (Left Column) and Dominant Eigenvalues (Right Column)"... 

Both the SRLS and the FT inertial models were discussed in the context of the Hubbard-Einstein relation, that is, the relation between the momentum correlation time Tj and the rotational correlation time (second rank) for a stochastic Brownian rotator [39]. It was shown that both models can cause a substantial departure from the simple expression predicted by a one-body Fokker-Planck-Kramers equation ... 

Fig. 8. (Effective) reorienta-tional correlation times Xe and angular momentum correlation times Xj from NMR [5] and Raman spectra [8] as a function of the reciprocal temperature in the plastic crystalline and liquid phases of PH, and PD, (from [5]).

Apart from the reorientational correlation time, also the angular momentum correlation time, is of great interest in con-... 

Another possible way to investigate whether rotation is diffusive or not is to compare the reorientational correlation time with the angular momentum correlation time making use of Hubbard s relation (Eq. (2.12)). Such tests are few, mainly since Tj may often not be easily obtainable from experiment. However, for molecules such as CIO F [55], CCl F [110] and CCl [122] the Hubbard relation has been found to apply at low temperatures. 

In the last relation C is the spin rotation coupling constant 4 and I the moment of inertia of a linear molecule. Tj is the angular momentum correlation time. 

In the diffusion limit the correlation time of the spin-rotation interaction, the angular momentum correlation time Tj, is related to the orientational... 

The correlation time tj is the angular momentum correlation time, the time the molecule changes its angular momentum, usually the time between collisions. The terms C and Cj are components of the spin-rotation interaction tensor and I is the moment of inertia of the molecule. For small step diffusion, and r are connected by the Hubbard relation ... 

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