Noura Dawass

A PPLICATIONS OF K IRKWOOD –B UFF I NTEGRALS 1 17 ρ G W A = ρ G WB (1.30) 1 + ρ G AA = ρ G AB (1.31) 1 + ρ G BB = ρ G AB (1.32) where ρ is the number density of the salt ( ρ A = ρ B = ρ ). Eqs. (1.30) , (1.31) and (1.32) imply that the number of molecules of species A and B cannot be varied independently. Ben-Naim [13] showed that the above constraints intro- duce a singularity to the equations relating KBIs G ∞ αβ to thermodynamic quanti- ties. It is important to note that the KB theory is general for any type of interac- tions and the issue of singularity is not due to the strong electrostatic interactions present in salt solutions. Rather, it is a result of the closure constraints imposed by Eqs. (1.30) , (1.31) and (1.32) , and it does not apply to KBIs defined in open systems [12] . Eqs. (1.30) , (1.31) and (1.32) hold for any dissociating molecule AB where the number of molecules has to be conserved simultaneously in the sys- tem, i.e. N A = N B . The approach of using KBIs of finite subvolumes of Krüger and co-workers [74, 80, 81, 84] allows KBIs of single ions to be computed from simulations in the canonical ensemble with open subvolumes embedded in the simulation box. As a result, the charge neutrality of the reservoir is maintained ( N A = N B ), while the electroneutrality condition is not applied inside the sub- volume, and therefore the grand-canonical ensemble is accessed. In the work of Schnell et al. [91] , KBIs of a sodium chloride (NaCl) solution were computed as well as partial molar volumes of water, Na + , and Cl − . The partial molar volume of Na + was reported to have a negative value [91] . In Ref. [7] , a similar observation was reported when computing the partial molar volumes of Na + and Cl − . The authors of Ref. [7] investigated the possibility of computing single-ion properties using molecular simulations by considering two methods. The first method is based on the changes in average potential energy and box volume when insert- ing an ion into a pure liquid. The second method depends on computing the reversible work associated with inserting an ion into a liquid. 1.4.3. M ASS TRANSFER IN MULTICOMPONENT LIQUIDS KBIs computed from molecular simulation can be applied to connect Fick diffusion coefficients to MS diffusivities [70, 92] . The generalized Fick’s law re- lates the molar flux, J i , to the Fick diffusivity, D i j [66, 68] , J i = − c t n − 1 X j = 1 D i j ∇ x j (1.33)