Pair correlation function liquid structure simulation

Amorphous ice has been studied in some detail by both X-ray and neutron diffraction [738-740]. The O- -O pair-correlation functions are similar to those of liquid water, except that on condensing on very cold surfaces, i.e., 10 K, there is an extra sharp peak at 3.3 A. This indicates some interpenetration of the tetrahedral disordered ice-like short-range structures. It appears that none of the many proposed atom-atom potential energy functions can simulate a structure for liquid water that predicts pair-correlation functions which are a satisfactory fit to the experimental data [741, 742]. Opinions seem to differ as to whether the discrepancy is in the theory or the experiments. 

P ur correlation functions give detailed information about the structure of the liquid. The TIP4P-FQ model gives pair correlation functions that are in good agreement with the neutron diffraction results of Soper and Phillips[23]. For details see Ref. [1]. The static dielectric constant, Co, is calculated from the fluctuations in M, the tot2il dipole of the central simulation box, by... 

The strength of the water-metal interaction together with the surface corrugation gives rise to much more drastic changes in water structure than the ones observed in computer simulations of water near smooth nonmetallic surfaces. Structure in the liquid state is usually characterized by pair correlation functions (PCFs). Because of the homogeneity and isotropy of the bulk liquid phase, they become simple radial distribution functions (RDFs), which do only depend on the distance between two atoms. Near an interface, the PCF depends not only on the interatomic distance but also on the position of, say the first, atom relative to the interface and the direction of the interatomic distance vector. Hence, considerable changes in the atom-atom PCFs can be expected close to the surface. 

The first method deseribes the calculation of entropy from the structural order. As we have discussed earlier in this chapter, the more ordered the system is, the less is the entropy. This order of the system can be calculated from the MD simulation by caleulating the n-particle correlation function. According to Green s concept the total entropy of a system can be written as a sum of two entropy terms. One of them is the ideal gas entropy term and the other is termed the excess entropy term. The first is quite trivial as the ideal gas entropy is known for a state point. The exeess entropy of the system again can be written as the contribution from the n-partiele n = 2, 3,. .. N) entropy term which can be determined from the -partiele eorrelation in the liquid stmcture. The calculation of the n-particle correlation funetion for > 2 is almost impossible and thus only the contribution for n = 2 (pair correlation function as input, by using the following expression [11],... 

Readers might have seen a similar picture from a result of a molecular dynamics simulation. If you look carefully, there are places where molecules are densely crowded, while in some places molecules are scarce. If one takes the average of the number of molecules over the entire volume of the container, N/V = p, it is of course a constant, and it does not include useful information with respect to the structure and dynamics of the fluid. However, if one takes a product of densities at two different places r and r, and takes a thermal average over configurations, namely, u r)u r )) = p(r,r ), it then contains ample information about the structure and dynamics of liquids. The quantity is called density-density pair correlation function . When the fluid is uniform, the quantity can be expressed by a function of only the distance between the two places, such that p(r, F) p( r — r ). 

The structure factors, S q), and pair correlation functions, g r) of Sb2Tc3 and Sb2Te in the liquid and amorphous phases are shown in Fig. 18.2. If the overall agreement between experiment and simulation is reasonable, it is not as good as in the case of other chalcogenide glasses, such as GeSc2 [22]. It was established [23] that the discrepancy is mostly due to an over coordination of Te atoms in DFT calculations. However, AIMD simulation reproduce all trends observed experimentally. 

Fig. 18.2 Structure factors (lefi) and pair correlation functions (right) of Sb2Te and Sb2Te3 in their liquid and amorphous state. The experimental data (to be published) were recorded by neutron scattering and are shown with symbols. The thin black line corresponds to the AIMD simulation data, for which the total g(r) are computed with proper weighting of the partials by the elements neutron scattering lengths...

FIG. 62 The structure of the monolayers of polyst)rene latex particles adsorbed on mica expressed in terms of the pair-correlation function g (a) / = 10 M, = 0.24 (b) / = 10 M, = 0.24. The broken lines represent the pair-correlation function calculated from the Boltzmann distribution g = the continuous lines show the RSA simulations (smoothened) the insets show the adsorbed particles forming a two-dimensional liquid phase. 

There have been several liquid-solid interface simulations on the LJ system. These are reviewed in some detail in Ref. 3. Of these, by far the most extensive are those of Broughton and Gilmer. These studies of the structure and thermodynamics of fee [100], [110] and [111] LJ crystal-liquid interfaces were part of a six-part series on the bulk and surface properties of the LJ system. Like most of the earlier simulations, these were done under triple-point conditions. The numbers of particles for the [111], [100] and [110] simulations were 1790, 1598 and 1674, respectively. Analysis of diffusion profiles, various layer-dependent trajectory plots, pair correlation functions, nearest-neighbor fractions and angular correlations yield a width of about three atomic diameters for all three interfaces. The density profiles indicate an interface width that is larger... 

---