Noura Dawass

4 82 S URFACE E FFECTS E FFECT OF SYSTEM SIZE AND DENSITY Figure 4.9 (a) shows the effect of the size of the system on the values of G ∞ com- puted using the scaling of LG V with L . The obtained values of G ∞ are practically constant. For the LJ fluid, a weak decrease, roughly linear in N − 1/3 , is observed. Figure 4.9 (a), Table 4.3, and Table 4.4 demonstrate that statistical uncertainties are small for systems with intermediate sizes ( N = 5000 and N = 10000). Smaller systems do not provide a sufficient linear regime and very large systems require longer sampling. In Figure 4.9 (b), KBIs at different densities are shown for the LJ and WCA fluids. To estimate G ∞ , the scaling of LG V with L was used. MD sim- ulations were performed to study systems with dimensionless densities ranging from 0.1 to 0.8. The behaviour of KBIs in the limit ρ → 0 can be checked by using the fact that in this limit, the RDF is known analytically, g ( r ) = exp[ − β u ( r )], where u ( r ) is the pair potential [26] and β = 1/( k B T ). Figure 4.9 (b) shows that for both interaction potentials, the values of G ∞ computed using molecular simulation approach the correct value in the low density limit. In the high density limit, the differences between G ∞ of LJ andWCA fluids seem to disappear. At high densities, the repul- sive part of the interaction potential, which is the same for WCA and LJ, becomes more important. Hence, the two fluids are expected to behave in the same way as the density increases. This is shown in Figure 4.9 (b).