Noura Dawass

5 94 P ROPERTIES OF U REA -C HOLINE C HLORIDE M IXTURES show the derivation for a ternary mixture α , β and γ , where the identities of β and γ are combined to ω . Second, we will provide the expressions for the case of combining an arbitrary number of components. Finally, we show that the ob- tained RDFs converge to the correct answer in the case of an ideal gas. The radial distribution function of molecules of the same type equals [13] g ii ( r ) = n ii ( r )/ V shell ( r ) N i / V box = n ii ( r ) N i c ( r ) (5.2) where n ii ( r )/ V shell ( r ) is the local density of component i inside a small ra- dial shell with volume V shell at distance r from a central molecule of type i , N i / V box is the overall number density of component i in the system, and c ( r ) = V shell ( r )/ V box , where V box is the volume of the simulation box. In the case of molecules of two different types, RDFs are computed from g i j ( r ) = n i j ( r ) N j c ( r ) (5.3) where n i j ( r ) is the number of atoms of type j in a radial shell formed around a central molecule of type i . Based on these general expressions, we can write the following RDFs for the ternary system composed of α , β and γ : g αα ( r ) = n αα ( r ) N α c ( r ) (5.4) g ββ ( r ) = n ββ ( r ) N β c ( r ) (5.5) g γγ ( r ) = n γγ ( r ) N γ c ( r ) (5.6) g αβ ( r ) = n αβ ( r ) N β c ( r ) (5.7) g αγ ( r ) = n αγ ( r ) N γ c ( r ) (5.8) g βα ( r ) = n βα ( r ) N α c ( r ) (5.9) g γα ( r ) = n γα ( r ) N α c ( r ) (5.10) g γβ ( r ) = n γβ ( r ) N β c ( r ) (5.11)