Noura Dawass

1.5. S COPE OF THIS THESIS 1 21 chapter 2, a numerical method is developed to compute KBIs for subvolumes with arbitrary shapes. We show that truncating KBIs (i.e. truncating the integral of Eq. (1.3) ) is nonphysical. In chapter 3, an analytic RDF was used to investigate finite–size effects of the system and the subvolumes. RDF–related effects were studied by simulating Weeks-Chandler-Andersen (WCA) particles [112] . RDFs of systems with different sizes were corrected using three RDF correction meth- ods. When using finite systems, the method of Gaungly and van der Vegt [113] resulted in the best estimation of KBIs. Additionally, in chapter 3 it is shown that the accuracy may be affected by how KBIs of small subvolumes are extrapolated to the thermodynamic limit. If the size of the simulated system is sufficient, KBIs of small subvolumes should scale linearly with the inverse size of the subvolume. However, identifying a linear regime is not straightforward. In chapter 4, other extrapolation techniques are considered such as an expression to directly com- pute KBIs in the thermodynamic limit from RDFs of finite volumes and the scal- ing of LG V αβ with L . The scaling of KBIs depends on the size of the subvolume and a term related to surface effects. In chapter 4, different methods are used to extrapolate to KBIs in the thermodynamic limit and to compute the surface term for LJ and WCA fluids. From chapters 3 and 4, a practical method to compute KBIs using molecular simulations is established. In chapter 5, these findings are used to compute KBIs of the Deep Eutectic Solvent (DES) consisting of choline chloride and urea at various compositions. The computed KBIs are then used to obtain thermodynamic factors and partial molar volumes. The thermodynamic factors were used to examine interactions of choline chloride-urea mixtures and connect MS diffusivities with Fick diffusion coefficients. This clearly shows that the KB theory is useful for computing thermodynamic properties while avoiding insertion/deletion of molecules. However, in some cases, it is more convenient to perform molecular simulations in open ensemble. For instance, when com- puting the solubility of small gas molecules in liquid solvents. An example of this is presented in chapter 6, where the CFCMC method was used to predict the solubility of a number of gases in monoethylene glycol (MEG).