Lennard-Jones scaling factors

Typical forms of the radial distribution function are shown in Fig. 38 for a liquid of hard core and of Lennard—Jones spheres (using the Percus— Yevick approximation) [447, 449] and Fig. 44 for carbon tetrachloride [452a]. Significant departures from unity are evident over considerable distances. The successive maxima and minima in g(r) correspond to essentially contact packing, but with small-scale orientational variation and to significant voids or large-scale orientational variation in the liquid structure, respectively. Such factors influence the relative location of reactants within a solvent and make the incorporation of the potential of mean force a necessity. 

It has been discussed in the previous section that the long-time part in the memory function gives rise to the slow long-time tail in the dynamic structure factor. In the case of a hard-sphere system the short-time part is considered to be delta-correlated in time. In a Lennard-Jones system a Gaussian approximation is assumed for the short-time part. Near the glass transition the short-time part in a Lennard-Jones system can also be approximated by a delta correlation, since the time scale of decay of Tn(q, t) is very large compared to the Gaussian time scale. Thus the binary term can be written as... 

Latent heat of fusion (crystallisation), 118 Layer thickness, 698, 699 Length of folds in crystal lamellae, 727 Lennard-Jones equation, 658 scaling factors, 658 temperature, 658,661, 662,663 Leslie-Ericksen theory, 585, 587, 641 Leuco-emeraldine, 345,346 Lewis... 

The differential cross sections of argon and neon have been measured by using refinements of the modulated molecular-beam technique. From these measurements the intermolecular potentials were found. These potentials differ significantly from the Lennard-Jones potential. The neon and argon potentials have different shapes and are not related by any simple scaling factor. The macroscopic properties have been calculated and are in reasonable agreement with experiment. The face-centered cubic structure was found to be the most stable crystal lattice for neon. The effect of the argon potential on the critical properties and saturation pressures is also discussed. 

Fig. 14.2.1. Velocity-averaged correlation function. Dashed line is computed for a Lennard-Jones potential crosses are calculated from the zx spectrum scattered by CH< at 70 amagats and 20°. Notice a change of scale by a factor 10 for / > 1 psec. (From Lallemand, 1970.)...

Here U is the pair interaction potential dependent on the distance r = r we use the units with the Boltzmann constant scaled to unity /o = T In p is a reference free energy of an ideal state with interactions switched off the factor compensates counting twice the interacting molecules in each pair. A suitable interaction potential is the Lennard-Jones potential... 

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