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When we compare the RDFs of solute-solvent and solvent-solvent in the same graph (Figure 9-2) it is obvious that the number, Nex which gives the amount of excess molecules around a solute molecule, is negative. N (G Go ) (9.1) ex v uv vv As in our discussion in the previous chapter, we will use the shape of the radial distribution function to interpret the results. The clustering number has been estimated by integrating the radial distribution function within an appropriate range, r1 to r2 which defines the solvation shell. It is given by the following equation r2 Nclus 4g12(r)r2dr (9.2) r1 In our case, the g12 is the radial distribution function between the carbon atom of CH4 and the one from carbon dioxide. The value of r1 is equal to zero and the value of r 2 is equal to the distance where the first minimum in g(r) is being observed. In this case the upper bound for the integral in our highest densities results, the position of the minimum is around 6.68 Å. Actually, the value of r1 is not equal to zero. The value of r1 it depends on the size of the molecule and it the closest distance which two molecules can approach each other. The values r1-r2 in the integration for the calculation of the number of clustering around a methane molecule are different from the values used into the integration around a carbon dioxide molecule. So a directly comparison of the two coordination number can not be made, but a comparison with the coordination number in case that expected when we had a homogeneous fluid can be made. The isothermal compressibility expresses the gathering of an enormous number of solvent molecules. The range of gathering molecules is quite long, and becomes maximum for c. The infinite value of the isothermal compressibility near 134PDF Image | MOLECULAR SIMULATION STUDIES IN THE SUPERCRITICAL REGION
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