Extended diffusion models

From a mathematical perspective either of the two cases (correlated or non-correlated) considerably simplifies the situation [26]. Thus, it is not surprising that all non-adiabatic theories of rotational and orientational relaxation in gases are subdivided into two classes according to the type of collisions. Sack s model A [26], referred to as Langevin model in subsequent papers, falls into the first class (correlated or weak collisions process) [29, 30, 12]. The second class includes Gordon s extended diffusion model [8], [22] and Sack s model B [26], later considered as a non-correlated or strong collision process [29, 31, 32],... 

A critical comparison by van Konyenberg and Steele [230] and Jones et al. [231] of extended diffusion models with Brownian motion and other continuum models strongly favours the former treatment. More detailed analysis is given by Berne and Pecora [232]. 

In the first period, which ended with a review [18], the complex susceptibility x (0)) was expressed through the law of motion of the particles perturbed by a.c. external field E(t). The results of these calculations rigorously coincide with those obtained, for example, in Refs. 22 and 23, respectively, for the planar and spatial extended diffusion model (compare with our Ref. 18, pp. 65 and 68). The most important results of this period are (i) the planar confined rotator model [ 17, p. 70 20], which has found a number of applications in our and other [24—31] works (ii) the composite so-called confined rotator-extended diffusion model. However, this approach had no perspectives because of troublesome calculations of the susceptibility x ( )-... 

R-band characteristic for H20. Thus, it was suggested [47] that the confined rotator-extended diffusion model is capable of qualitatively describing the wideband spectra of water. 

Table 3. Comparison of T2K values calculated using extended-diffusion models (J- and M-diffiision) with the values measured for D2O molecules in CH3CN, CHCI3, and at atmospheric (0.1 MPa) and high (300 MPa) pressures.

Gordon (1966) has proposed what he calls extended diffusion models to take into account the effect of collisions. The <(F2(u(0) u(/))> calculated from these models cannot be expressed in simple analytical form, and we must content ourselves here with a description of the assumptions in the model and a description of results for a few particular systems. 

Comparisons of the extended diffusion model with experimental spectra on small molecules have been performed by Steele, who concludes that the model, although not very successful, is still superior to any other model studied (van Koynenberg and Steele, 1974 Jones, 1974). 

The extended diffusion model has been solved for linear molecules (Gordon, 1966), spherical top molecules (McClung, 1969, Fixman and Rider, 1969), and symmetric top molecules (Fixman and Rider, 1969). 

A most significant extension of the rotational diffusion theory to allow for rotational steps of arbitrary size is provided by the extended J- and M-diffusion theories described above. In contrast to some other models, the extended diffusion models can be rigorously tested since they contain no adjustable parameters or parameters which are difficult to determine. Although the extended diffusion theory is of recent date, a number of detailed experimental tests have already been reported. A pioneering work in this respect is that by Maryott et al. [55] who were the first to report accurate values for both... 

A third group of papers,probably the central one, present an analysis of spectral effects of the Coriolis interaction with the help of the J- and M- extended diffusion models. The main papers are due to Miiller and Kneubiihl (14,17,19), Muller, Etique et al. (15,16), Muller (18), Gilbert, Nectoux et al. (25), Eagles and Me Clung (20) and to Gilbert and Drifford (23). 

Leicknam JC, Guissani Y (1981) On extended diffusion-models for asymmetric-top molecules in liquids. Mol Phys 42(5) 1105-1120. doi 10.1080/00268978100100841... 

Lascombe J, Besnard M, Maraval P (1982) A new extended diffusion-model for rotational motion of symmetric-top molecules in the liquid-phase. Chem Phys 72(1-2) 177-184. doi 10.1016/0301-0104(82)87078-x... 

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