Evaluation of Different Implementations of the Thomson Liquid Drop Model: Comparison to Monovalent and Divalent Cluster Ion Experimental Data

Abstract

The Thomson model, used for calculating thermodynamic properties of cluster ions from macroscopic properties, and variations of this model were compared to each other and to experimental data for both hydrated mono- and divalent ions. Previous models that used the Thomson equation to calculate sequential binding thermodynamic values of hydrated ions, either continuously or discretely including an ion-dipole interaction term, were compared to a discrete model that includes the excluded volume of an impurity ion. All models, given their limitations, provided reasonable agreement to data for monovalent ions. For divalent cluster ions, the continuous model, and a discrete model that includes the ion-exclusion volume provide significantly better agreement to both the binding enthalpy and the binding entropy data as compared to the model that includes an ion-dipole term. A systematic deviation in the continuous model resulted in significantly lower binding enthalpies than the discrete model for clusters with fewer than about nine and 19 water molecules for mono- and divalent ions, respectively, but this difference became negligible for larger clusters. Previous investigations of the various Thomson model implementations used parameters for bulk water at 313 K. Using parameters at 298 K has a negligible effect at small cluster sizes, but at larger sizes, the binding enthalpies are 0.2 kcal/mol higher than with the 313 K parameters. Although small, the effect is significant for ion nanocalorimetry experiments in which thermochemical information is obtained from the number of water molecules lost upon activating large clusters.