# Effect of Bounds

The effect of the value of bounds on RMSD values has been considered and shown in Table 7.9 for the UNIQUAC model and Table 7.10 for the NRTL model for System 1. A population size of 20 was used for the benchmarking system. Maximum number of iterations, that is, 2000, was used as the stopping condition. Based on the recommendations of Yang and Deb (2009), *p _{a }*of 0.25 was used. For each bound, 30 numerical trials have been carried out with random initial values of interaction parameters. It can be inferred from Tables 7.9 and 7.10 that the RMSD values are minimum at a bound of -1000 to +1000 for the UNIQUAC model and -100 to +100 for the NRTL model. All the parameters were found to lie within the same range. Keeping this in mind, we have chosen the lower and the upper bounds for the estimation of interaction parameters for all the systems.

# Maximum Number of Iterations and Population Size

The effect of the maximum number of iterations and the population size on RMSD values has been considered and shown in Figure 7.4a and b. For the UNIQUAC model, the population size of 20 and maximum iterations of 1000 are sufficient to give a very good RMSD value. A further increase in

Abbreviation and Full Name of Ionic Liquids Used in This Work along with UNIQUAC Volume and Surface Area Structural Parameters

TABLE 7.7

Abbreviation |
Full Name of Ionic Liquid |
r |
q |

[OMIM][Cl] |
1-octyl-3-methylimidazolium chloride |
11.993 |
7.886 |

[BMIM][TfO] |
1-butyl-3-methylimidazolium trifluoromethanesulfonate |
12.460 |
7.518 |

[OMIM][BF |
1-octyl-3-methylimidazolium tetrafluoroborate |
13.187 |
8.357 |

[HMIM][BF |
1-hexyl-3-methylimidazolium tetrafluoroborate |
11.658 |
7.388 |

[HMIM][PF |
1-hexyl-3-methylimidazolium hexafluorophosphate |
12.869 |
8.166 |

[BMIM][BF |
1-Butyl-3-methylimidazolium tetrafluoroborate |
10.057 |
6.368 |

[TDTHP][DCA] |
Trihexyl(tetradecyl)-phosphonium dicyanamide |
8.37 |
5.81 |

[TDTHP][DEC] |
Trihexyl(tetradecyl)-phosphonium decanoate |
8.77 |
5.96 |

[TDTHP][Phosph] |
Trihexyl(tetradecyl)-phosphonium bis(2,4,4- trimethylpentyl) phosphinate |
9.834 |
6.258 |

[BMIM][Tf2N] |
1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide |
11.964 |
9.753 |

[EMIM][ESO |
1-ethyl-3-methylimidazolium Ethylsulfate |
8.3927 |
6.6260 |

[EMIM][TfO] |
1-ethyl-3-methylimidazolium trifluoromethanesulfonate |
7.6193 |
6.075 |

^{a} Data from Banerjee, T. et al., *Fluid Phase Equilib.,* 234, 64-76, 2005. ^{b} Data from Rabari, D. and Banerjee, T. *Ind. Eng. Chem. Res.,* 53, 18935-18942, 2014. ^{c} Data from Rabari, D. and Banerjee, T. *Fluid Phase Equilib,* 355, 26-33, 2013. ^{d} Data from Bharti, A. and Banerjee, T. *Fluid Phase Equilib.,* 400, 27-37, 2015. ^{e} Data from Varma, N. R. et al., *Chem. Eng. J.,* 166, 30-39, 2011. ^{f} Data from Santiago, R. S. et al., *Fluid Phase Equilib.,* 278, 54-61, 2009.

the population size and the number of iterations was not able to improve the solution (Figure 7.4a). For the NRTL model, the population size of 20 and maximum iterations of 1500 were able to give a very high RMSD value (Figure 7.4b). Keeping this in mind, we have chosen 20 as the population size for all systems and 1000 and 1500 as the maximum number of iterations, respectively, for the UNIQUAC and the NRTL models to estimate the interaction parameters in all systems. After the benchmarking with the above system, CS has been applied on the other ternary systems. For each system, 30 trials have been carried out with random initial values of population and the lowest RMSD along with the corresponding interaction parameters was then selected as the final result.