Noura Dawass

3 46 F INITE -S IZE E FFECTS λ G V αβ ( λ ) = λ G ∞ αβ (1 − λ 3 ) − λ 4 δ αβ ρ α + α i j V 1/3 box (3.11) by plotting λ G V αβ ( λ ) as a function of λ , one can obtain G ∞ αβ from the slope of this plot for low λ . The computed KBIs are compared to those computed by other correction methods. Details of the system studied and of the MD simulations are provided in the following section. 3.3.4. S IMULATION DETAILS To study effects resulting from computing RDFs from simulation of finite and closed systems, we examine a binary mixture interacting using the WCA poten- tial [112] where the LJ potential is shifted and truncated at 2 1/6 σ . The WCA mix- ture is simulated in the NV T ensemble using the Nose-Hoover thermostat [22] . The MD package LAMMPS [127] is used to perform the simulations, with 1 mil- lion initialization timesteps and 5 million integration timesteps for each run. A timestep of 0.001 in LJ reduced units, which are the units used for other vari- ables, are used. All simulations were performed for the same system properties with σ 11 = σ 12 = σ 22 = 1.0, ² 11 = ² 22 = 1.0, and ² 12 = 0.1. Additionally, the same thermodynamic condition was maintained for all system sizes. A mixture com- position of x 1 = 0.75 was used with the following reduced variables T ∗ = 1.8 and ρ ∗ = 0.7. The box length L box and number of molecules N were varied to obtain g 11 ( r ), g 12 ( r ), g 22 ( r ) as a function of system size. For all box sizes, g αβ ( r ) were computed up to distances of ( p 2/2) L . The RDFs are used to calculate finite sub- volumes KBIs (Eqs. (1.25) ) which are then extrapolated to the thermodynamic limit to obtain G ∞ 11 , G ∞ 12 , and G ∞ 22 , respectively. To evaluate the KBIs in the ther- modynamic limit for the system studied, simulations of a large system are per- formed. Specifically, G ∞ 11 , G ∞ 12 , and G ∞ 22 are evaluated from averaging the results of five simulations for a box with L box = 80. Each simulation was initialized with a different configuration, thus allowing for computing the standard deviations. 3.4. R ESULTS AND DISCUSSION 3.4.1. F INITE - SIZE EFFECTS OF SUBVOLUMES KBIs ( G ∞ ) are computed for the liquid with the analytic RDF model in Eq. (2.6) , using the MC algorithm discussed in section 3.2. The KBIs for finite subvolumes, G V (in this section we drop the indices αβ since a pure fluid is studied) are com- puted using simulation boxes with the following lengths, L box = 7.5, 10, 15, 20, 40 and, 50. For each box size, spherical subvolumes with R up to ( p 2/2) L box are