Liquid structure pair distribution

Of course, dielectric properties are also closely related to structural quantities [69-71]. Structure in liquids, namely pair distribution functions, g r) s, have been widely studied in simulations and compared to experimental data, also to validate the description of interaction forces adopted. 

The structure of a liquid is conventionally described by the set of distributions of relative separations of atom pairs, atom triplets, etc. The fundamental basis for X-ray and neutron diffraction studies of liquids is the observation that in the absence of multiple scattering the diffraction pattern is completely determined by the pair distribution function. 

For atomic liquids with only spherically symmetric interactions, the pair distribution function will contain no angular dependence and hence the structure in the system (at the pairwise level) is completely given by the radial distribution function, g(r), where r=lrl is simply the magnitude of the separation vector. For a molecular system, the radial distribution function is obtained from the full angle average of the pair distribution function. 

The isotropic nature of a liquid implies that any structure factor, S(k), obtained from a scattering experiment (typically X-ray or neutron) on that liquid will contain no angular dependence (of the molecules). Thus, the Fourier transform of any S(k) will yield a radial distribution function. Recently developed techniques of isotopic substitution [5-7] have been utilized in neutron diffraction experiments in order to extract site-site partial structure factors, and hence site-site radial distribution functions, gap(r). Unfortunately, because g p(r) represents integrals (convolutions) over the full pair distribution function, even a complete set of site-site radial distribution functions can not be used to reconstruct unambiguously the full molecular pair distribution function [2]. However, it should be mentioned at... 

Data available from a computer simulation is not similarly limited, as a complete description of the system, the positions and orientations of all its molecules, is immediately available therefore the full molecular pair distribution function should, in principle, be obtainable. Still the practical considerations of accumulating and presenting this 6-dimensional function have made it virtually inaccessible, despite its obvious importance. Computer simulation studies of molecular liquids and solutions have then traditionally relied almost exclusively upon radial distribution functions to provide structural information. 

In this section we will examine how spatial distribution function analysis can be used to bring new insights and a better understanding of the local structure in pure liquid systems. Implications to other properties, either determined by or related to the pair distribution function, will be discussed. 

Other workers have explored the structure in liquid water using approaches based upon more general descriptions such as the spatial or pair distribution functions. In their simulation study Laztiridis and Karplus [12] split the full pair distribution function into radial and angular contributions. They then... 

Probably the most notable work on the structure in liquid water based upon experimental data has been that of Soper and co-workers [6,8,10,30,46,55]. He has considered water under both ambient and high temperature and pressure conditions. He has employed both the spherical harmonic reconstruction technique [8,46] and empirical potential structure refinement [6,10] to extract estimates for the pair distribution function for water from site-site radial distribution functions. Both approaches must deal with the fact that the three g p(r) available from neutron scattering experiments provide an incomplete set of information for determining the six-dimensional pair distribution function. Noise in the experimental data introduces further complications, particularly in the former technique. Nonetheless, Soper has been able to extract the principal features in the pair (spatial) distribution function. Of most significance here is the fact that his findings are in qualitative agreement with those discussed above. 

The experimental and theoretical descriptions of liquid structure are most conveniently achieved in terms of distribution functions. This is because there is short-range structure in the liquid, but at large distances from the point of reference, the distribution of molecules is random. In this section, the fundamental aspects of distribution and correlation functions, especially, the pair correlation function, are outlined. 

Further studies were carried out in the quest for the double critcal point of the mixture 2-methyl-piridine(2MP)/D20. Within such studies we came across a remarkable anomaly appearing within 2MP neat liquid at applied pressures of about 200 bars. It manifests itself as a marked change of regime of the translation and rotational-diffusion coefficients versus density (pressure). To add more intrigue, the pressure range at which such an anomaly takes place basically coincides with that where the DCP was suspected to be located. In fact, the concurrent use of quasielastic neutron scattering and molecular dynamics simulations, evidenced a pronounced change of slope in the density dependence of both the translation and rotational diffusion coefficients for densities of p=0.975 g/cm. In turn, the description of the liquid structure carried out in terms of static pair distributions derived from computer simulations revealed indications of the presence of dynamical equilibria within the liquid as attested by clear isosbestic points. 

For some alloys such as Au-Sb [5.50], Fe-(Sb, Ge) [5.22] at Z = 1.8 e/a and Cu-Sn [5.51] over the whole amorphous region, this assumption has been confirmed by analysing the reduced pair-distribution function at small r-values. There are more structural similarities of the amorphous to the liquid than to the crystalline state. 

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