Noura Dawass

1 2 I NTRODUCTION A homogenous solution consists of two or more components that are uni- formly mixed. Homogenous liquid solutions are present in biological, medical, geological, and industrial applications. To design and develop industrial pro- cesses, knowledge of the thermodynamic and transport properties of solutions is essential [1– 6] . This task is not simple, especially for systems where strong inter- molecular forces are present such as aqueous solutions, ionic liquids (ILs), and deep eutectic solvents (DESs) [7– 11] . The advantage of using a molecular theory of solutions, as opposed to experiments and classical thermodynamic models, is that bulk properties are provided by directly considering molecular interac- tions and structure. In this regard, the Kirkwood–Buff (KB) theory [12] provides an important connection between the microscopic structure of fluid mixtures and the corresponding macroscopic properties. Rooted in statistical mechan- ics, the KB theory applies to any type of intermolecular interactions, making it one of the most general and important theories for homogenous solutions [12– 15] . Kirkwood and Buff [12] expressed thermodynamic quantities such as par- tial derivatives of chemical potentials with respect to composition, partial mo- lar volumes, and the isothermal compressibility in terms of integrals of radial distribution functions (RDFs) over infinite and open volumes. These integrals, which are considered the key quantity in the KB theory, are referred to as KB In- tegrals (KBIs). Alternatively, KBIs can be obtained from density fluctuations in the grand-canonical ensemble [13, 16] . The KB theory was derived in 1951, however, it has not gained much inter- est until the late 70s of the previous century after Ben–Naim [14] proposed the inversion of the KB theory. The inversion of the theory allows the calculation of KBIs from experimental data [17– 20] . Thirty years following the inversion of the KB theory, molecular simulation emerged as a powerful tool for studying pure liquids and mixtures [21] . There are two main types of molecular simulation techniques [22, 23] : Molecular Dynamics (MD), where trajectories of molecules are determined by solving Newton’s equation of motion numerically; and Monte Carlo (MC) simulations, where relevant states of the system are sampled accord- ing to their statistical weight [21– 25] . In both simulation techniques, RDFs and local density fluctuations are easily computed, thus in principle enabling the cal- culation of KBIs. Molecular simulations can be used to study closed systems with a fixed number of molecules, or open systems in which the number of molecules fluctuates [22] . It is important to note that molecular simulations can only be performed for finite systems, while the KB theory requires KBIs for infinite and open systems [12] . This disparity between the KB theory and molecular simula- tions has to be considered when computing KBIs from simulations. The focus of this thesis is to provide a framework to accurately compute KBIs using molecu- lar simulation. In this chapter, we briefly introduce the KB theory and provide