Computing Excess Functions of Ionic Solutions: The Smaller-Ion Shell Model versus the Primitive Model. 2. Ion-Size Parameters

Abstract

A recent Monte Carlo (MC) simulation study of the primitive model (PM) of ionic solutions ( Abbas, Z. et al. J. Phys. Chem. B 2009 , 113 , 5905 ) has resulted in an extensive "mapping" of real aqueous solutions of 1-1, 2-1, and 3-1 binary electrolytes and a list of "recommended ionic radii" for many ions. For the smaller cations, the model-experiment fitting process gave much larger radii than the respective crystallographic radii, and those cations were therefore claimed to be hydrated. In Part 1 (DOI 10.1021/ct5006938 ) of the present work, the above study for the unrestricted PM - dubbed MC-UPM - has been confronted with the Smaller-ion Shell (SiS) treatment ( Fraenkel, D. Mol. Phys. 2010 , 108 , 1435 ), or "DH-SiS", by comparing the range and quality of model-experiment fits of the mean ionic activity coefficient as a function of ionic concentration. Here I compare the ion-size parameters (ISPs) of "best fit" of the two models and argue that since ISPs derived from DH-SiS are identical with (or close to) crystallographic or thermochemical ionic diameters for both cations and anions, and they do not depend on the counterion - they are more reliable, as physicochemical entities, than the PM-derived "recommended ionic radii".

Coulomb blockade model of permeation and selectivity in biological ion channels

“…The mobile sodium and calcium ions are described as charged spheres of radius R 0.1 i ≈ nm for both ions (allowing use of the implicit solvent model [64,65] with neglible ion radii), with diffusion coefficients of D 1.33 10 Na 9 = × − m 2 s −1 [15,66] and D 0.79 10 Ca 9 = × − m 2 s −1 [15], respectively. We take both the water and the protein to be homogeneous continua describable by relative permittivities 80 w ε = and 2 p ε = , respectively, together with an implicit model of ion hydration whose validity is discussed elsewhere [58].…”

Reply to “Comment on ‘Negative Deviations from the Debye–Hückel Limiting Law for High-Charge Polyvalent Electrolytes: Are They Real?’ ”

“…All those theories have various pitfalls and deficiencies of their own, which cause them to not fit with experiment at an adequate degree of accuracy (see discussion in ref , pp 407–420, on IPBE, Bjerrum, and Gronwall–La Mer–Sandved). For example, as I have mentioned previously, − and as is well-known in the literature (see cited references in ref ), the primitive model (PM) based HNC (and similarly, Outhwaite’s MPB and SPB, MSA, and other advanced integral equation theories) fails at low ionic strength and cannot be used for extrapolation to infinite dilution. HNC has been mostly shown to fit not with real electrolytes but with Monte Carlo (or molecular dynamics) simulations of electrolyte solutions, which become more inaccurate at lower ion density.…”

An integrated theoretical-experimental approach to understand facilitated proton transfer-electron transfer coupled reactions at thick-film modified electrodes

“…For charged species, Fraenkel's smaller-ion shell (SiS) model was used, [40][41][42][43][44] which consists in a generalization of the classical Debye-Hückel (DH) theory, in order to take into account the different sizes of spherically symmetric charged species to calculate their activity coefficients. The activity coefficients for the different cationic and anionic species in each phase α are given respectively by:…”