Noura Dawass

1 8 I NTRODUCTION Eq. (1.11) is close to zero. Almásy et al. [53] obtained KBIs from SANS as well as from vapor pressure data for an ionic liquid. The authors found that scattering experiments and thermodynamic data provided similar KBIs. 1.3. K IRKWOOD –B UFF I NTEGRALS FROM MOLECULAR SIMULATIONS 1.3.1. T HERMODYNAMIC PROPERTIES FROM MOLECULAR SIMULATIONS Knowledge of chemical potentials and other thermodynamic properties is of great importance for studying the phase equilibria of solutions [54] . Computing excess properties of multicomponent systems using molecular simulation is not trivial. To compute chemical potentials, a number of methods have been devel- oped and evaluated, such as thermodynamic integration [55] , and perturbation theory [56] . One of the most widely used methods is the Widom’s Test Particle Insertion (WTPI) method [57] , where a test particle is randomly inserted in the simulation box and the average Boltzmann factor of the resulting energy change is calculated. In general, molecular insertions are found to be challenging when simulating dense fluids or when strong interactions are present [58] . Recently, the Continuous Fractional Component Monte Carlo (CFCMC) method [59– 62] have been developed to improve the efficiency of molecular insertions. By vary- ing the interactions of the fractional molecule with the surrounding molecules, molecules are added/removed gradually during MC simulations. Even with ap- plying these advanced methods, simulating complex fluids such as salt solutions in open ensembles is still challenging [58] . Alternatively, excess properties of solutions can be computed using the KB theory [54] . In the previous section, we showed that KBIs relate directly to partial derivatives of the chemical po- tential with respect to composition, partial molar volumes, and the isothermal compressibility. KBIs also relate to other thermodynamic properties such as the excess Gibbs energy of mixing. Other than predicting thermodynamic proper- ties, KBIs can be used to investigate local behaviour of solutions, and to con- nect information obtained from molecular simulations to experimental mea- surements [13, 14, 63] . Knowledge of solution thermodynamics is also required when studying diffu- sion. To connect Fick diffusion coefficients, which are measured experimentally, to so–called Maxwell–Stefan (MS) diffusivities computed from MD simulations, the so–called thermodynamic factor Γ is used [16, 64, 65] . The non-ideality of solutions is also quantified by Γ [16, 66, 67] . For an n -component system, Γ αβ = δ αβ + x α µ ∂ ln γ α ∂ x β ¶ T , P , Σ (1.12)