Noura Dawass

4 76 S URFACE E FFECTS The differences between the estimation methods can be further demon- strated by using a system of LJ particles at ρ = 0.4, which is more difficult to sam- ple compared to the previously studied system. In Figure 4.5, RDFs of systems of varying sizes of a LJ fluid at ρ = 0.4 and T = 2 are shown. In Table 4.4, KBIs G ∞ computed using the RDFs in Figure 4.5 are provided. The scaling of G V with 1/ L is shown in Figure 4.6. For this method, a linear range is not obtained for all system sizes. Systems with at least N = 1000 particles can be used to extrapolate to the thermodynamic limit. In Figure 4.7, G 2 is plotted as a function of the size of the subvolume L . The figure shows that even larger systems are needed to find a reasonable estimate of G ∞ using G 2 . Figure 4.7 (b) shows that a plateau is only achieved for large systems where N equals to or larger than 5000. For this system (LJ fluid at ρ = 0.4), it is possible to use the scaling of LG V with L to compute KBIs from small sizes. Figure 4.8 demonstrates that straight lines that are easily fitted are achieved when using the scaling of LG V with L , even for sizes where an estimation can not be made with the other two methods.