Noura Dawass

6 134 C ONCLUSIONS The Kirkwood-Buff (BF) theory is one of the most powerful theories connect- ing the microscopic structure of isotropic fluids to their macroscopic proper- ties. KBIs are defined either in terms of RDFs over infinite and open volumes, or in terms of density fluctuations in the grand–canonical ensemble. KBIs are re- lated to a number of thermodynamic quantities such as partial derivatives of the chemical potential with respect to composition, partial molar volumes, and the isothermal compressibility. Consequently, chemical potentials and other ther- modynamic properties can be obtained from KBIs. The main advantage of the KB theory is that it can be applied to any type of interactions, making it an attrac- tive alternative to molecular simulations in open ensembles which are usually carried out to predict phase equilibria. Molecular simulations in open ensembles require insertions/deletions of molecules, which can be challenging for dense liquids with strong molecular interactions. While KBIs are derived for open and infinitely large systems, they can be computed from molecular simulations of finite and closed systems (e.g. simulations in the NV T and NPT ensembles). Krüger and co–workers [74] derived an expression for KBIs of small and open subvolumes embedded in a larger reservoir (simulation box). These KBIs scale with the inverse size of the subvolume and extrapolating this scaling to the ther- modynamic limit yields KBIs of open and infinite systems. To accurately apply the method of Krüger and co–workers [63, 74] , a number of effects were examined. In chapter 2, the effect of the shape of the subvolume was investigated. When computing KBIs, the weight function w ( x ) is the only term in the method of Krüger and co–workers [63, 74] that depends on the shape of the subvolume. In chapter 2, a method to compute w ( x ) for subvolumes with arbitrary shape was developed. From computing w ( x ) and KBIs of various sub- volume shapes, it was demonstrated that KBIs in the thermodynamic limit are independent of the shape of the used subvolume. For small values of x and for all shapes, all functions w ( x ) can be transformed on to a universal function that only depends on the area to volume ratio of the subvolume. Using this universal expression for w ( x ), it was confirmed that the truncation of KBIs for infinitely large systems, which is the most commonly used approach to compute KBIs, is not correct and nonphysical. Two system size effects are observed in MD simu- lations: (1) effects due to the size of the simulation box and the size of the finite subvolume embedded in the simulation box, and (2) effects due to computing RDFs from a closed and finite system. In chapter 3, finite–size effects of comput- ing KBIs from molecular simulations were investigated using systems of WCA particles. It was demonstrated that calculations of KBIs should not be extended beyond half the size of the simulation box. For finite–size effects related to RDFs, the Ganguly and Van der Vegt correction [113] was found to yield the most accu- rate results. Numerical inaccuracies may also arise fromextrapolating the scaling