Computing excess functions of ionic solutions: the smaller-ion shell model versus the primitive model. 1. Activity...

The present study compares the Monte Carlo (MC) simulation of the primitive model (PM) ( Abbas, Z. et al. J. Phys. Chem. B 2009 , 113 , 5905 ), by which activity coefficients of many binary ionic solutions have been computed through adjusting ion-size parameters (ISPs) for achieving best fit with experiment, with a parallel fit and ISP adjustment, employing the Smaller-ion Shell (SiS) treatment ( Fraenkel, D. Mol. Phys. 2010 , 108 , 1435 ), a Debye-Hückel type theory ("DH-SiS") considering counterions of unequal size. DH-SiS is analogous to the unrestricted PM (UPM), so the comparison is with the MC simulation of the UPM, "MC-UPM". Among the representative electrolytes NaCl, KCl, NaClO4, CaCl2, Ca(ClO4)2, and LaCl3, in water at 25 °C, the 1-1 electrolytes exhibit a far better fit quality for DH-SiS than for MC-UPM, and the fit extends to higher concentration. Moreover, theoretical single-ion activity coefficients derived from DH-SiS agree with experimental estimation for solutions of NaCl, CaCl2, and other electrolytes ( Fraenkel, D. J. Phys. Chem. B 2012 , 116 , 3603 ), whereas parallel MC-UPM predictions are at odds with experiment. Additional advantages of DH-SiS over MC-UPM are in (a) employing co-ion ISPs that are usually equal to the crystallographic ion diameters and (b) easily applying ISP nonadditivity in adjusting counterion ISPs.