Noura Dawass

1 16 A PPLICATIONS OF K IRKWOOD –B UFF I NTEGRALS the entire volume of the simulation box was used. However, both methods were applied to compute KBIs of systems of molecules with no intramolecular degrees of freedom such as LJ fluids. 1.4. A PPLICATIONS OF K IRKWOOD –B UFF I NTEGRALS COMPUTED FROM MOLECULAR SIMULATION 1.4.1. P ARTIAL MOLAR ENTHALPIES In Ref. [89] , Schnell et al. proposed a method to compute partial molar en- thalpies from molecular simulation in the canonical ensemble. Following the SSM [16] , enthalpies ˆ H of small subvolumes embedded in a larger reservoir are used. From nanothermodynamics, an expression for the change of ˆ H with re- spect to the average number of molecules 〈 N α 〉 was derived in terms of fluctua- tions in density and energy, µ ∂ ˆ H ∂ 〈 N α 〉 ¶ T , V , µ β 6 = α = 〈 EN α 〉−〈 N α 〉〈 E 〉+〈 N α 〉 k B T 〈 N 2 α 〉−〈 N α 〉 2 (1.29) in which E is the partial energy of the subvolume. As shown in the previous sec- tion, properties of small subvolumes scale with the inverse size of the subvol- ume (1/ L ). Extrapolating the derivatives of Eq. (1.29) to the thermodynamic limit yields partial enthalpies at constant volume ³ ∂ H ∂ N α ´ T , V , N β 6 = α . To find partial molar enthalpies, ³ ∂ H ∂ N α ´ T , P , N β 6 = α , a Legendre transform was performed. To convert from enthalpies in the canonical ensemble to partial molar enthalpies, KBIs of the studied system are needed. The method of Krüger and co-workers [74, 80, 81, 84] to obtain KBIs for finite subvolumes was used. This approach was also applied by Skorpa et al. [90] to compute the heat of reaction of H 2 dissociation using a reactive force field. 1.4.2. P ROPERTIES OF SINGLE - IONS IN SALT SOLUTIONS Simulating closed and finite systems to compute KBIs has the advantage of accessing single-ion properties [91] . Essentially, to apply the KB theory to a salt solution, the systemhas to be treated as a binary mixture where ions are indistin- guishable [13] , as shown in Ref [20] . In this case, relations between KBIs and ther- modynamic properties of binary mixtures can be applied (e.g. see section 1.1) . For a ternary mixture of a dissociating monovalent substance ( AB → A + B ) and a solvent (e.g. water, W ), KBIs are subject to the following electroneutrality con- ditions,