Noura Dawass

5.2. M ETHODS 5 93 In this chapter, we aimat applying the KB theory to compute thermodynamic properties of mixtures of urea and ChCl. From MD simulations in the NPT en- semble, RDFs of mixtures of urea and ChCl are computed at T =343.15 K and P = 1 atm. Mixtures are simulated at eight different mole fractions of urea ranging from 0.20 to 0.71. At each molar concentration, KBIs of a pseudo-binary mix- ture are estimated, from which the thermodynamic factors and the partial molar volumes are computed. In addition to thermodynamic properties, transport be- haviour of mixtures of urea and ChCl are investigated at different molar concen- trations using MD simulations. The thermodynamic factors and MS diffusion coefficients are used to compute Fick diffusivities. This chapter is organized as follows. In section 5.2.1, theoretical expressions to compute RDFs of a pseudo-binary mixture with indistinguishable ions from RDFs of a ternary mixture of anions–cations–solvent are derived. In section 5.2.2, we explain how to compute MS diffusion coefficients of pseudo-binary mixtures. In section 5.2.4, the details of MD simulations and computing KBIs are provided. In section 5.3, results of the scaling of KBIs with the size of the system of mixtures of urea and ChCl are presented, along with values of the thermodynamic factor and partial molar volumes as a function of the mole fraction of urea. Transport properties of mixtures of urea and ChCl are also provided in section 5.3. In sec- tion 5.4, the main findings of this chapter are summarised. 5.2. M ETHODS To compute KBIs of mixtures of urea and ChCl, it is possible to apply expressions of ternary mixtures [13] . Alternatively, mixtures of urea and ChCl can be treated as a pseudo-binary, where the salt components (choline and chloride) are in- distinguishable. For a pseudo–binary mixture, mole fractions of urea x urea are defined as: x urea = N urea N urea + N Ch + N Cl and x ChCl = 1 − x urea (5.1) where N urea , N Ch , and N Cl are the number of molecules of urea, choline and chloride molecules, respectively. These mole fractions are used for computing thermodynamic properties of a pseudo-binary mixtures. For instance, when computing thermodynamic factors from KBIs (Eq. (1.14) ), the mole fractions are computed as in Eq. (5.1) . 5.2.1. R ADIAL DISTRIBUTION FUNCTIONS OF PSEUDO – BINARY MIXTURES In this section, we describe how to combine RDFs for components that should be treated as indistinguishable. We are specifically looking at the case where we merge the identity of two RDFs, to create a new "virtual" component. First, we