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.

Measuring the extent and width of internal energy deposition in ion activation using nanocalorimetry

“…Clusters with fewer than 55 water molecules dissociate faster than the timescale of the experiment so kinetic shift effects are negligible [25]. Because experimentally measured sequential water molecule binding energies have not been obtained for the clusters formed in these experiments, E 0 values are obtained from a discrete implementation of the Thomson liquid drop model (TLDM) [38]. Calculated sequential water molecule binding enthalpies of M(H 2 O) n 2ϩ agree with the measured binding enthalpies to within one kcal/mol for the largest clusters for which experimental binding enthalpies have been measured (n Յ 14) [38].…”

“…Because experimentally measured sequential water molecule binding energies have not been obtained for the clusters formed in these experiments, E 0 values are obtained from a discrete implementation of the Thomson liquid drop model (TLDM) [38]. Calculated sequential water molecule binding enthalpies of M(H 2 O) n 2ϩ agree with the measured binding enthalpies to within one kcal/mol for the largest clusters for which experimental binding enthalpies have been measured (n Յ 14) [38]. The values obtained from the TLDM rapidly approach the bulk heat of vaporization of water and should become increasingly accurate with increasing cluster size.…”

“…This results in a system of equations with more equations than unknowns (T ‫ء‬ values), which can readily be solved to obtain a unique set of T ‫ء‬ values for the reduced cluster and all clusters formed by water molecule loss. From these calculated effective temperatures and the sequential E 0 values obtained from a discrete implementation of the TLDM [38], the RE is obtained using eq 2. Because the RE values and calculated effective temperatures are obtained from modeling, and the accuracies of these models are not well known, uncertainty in the RE values is difficult to assess.…”

Effects of electron kinetic energy and ion-electron inelastic collisions in electron capture dissociation measured using ion nanocalorimetry

“…To obtain the RE, the threshold dissociation energy for the loss of each water molecule from the reduced precursor must be known. Values for clusters of the size typically investigated have not been measured, but these values can be obtained from the Thomson liquid drop model [28,29]. Various implementations of this model have been recently evaluated by comparison to experimental data for both monovalent and divalent ions [29].…”

“…Values for clusters of the size typically investigated have not been measured, but these values can be obtained from the Thomson liquid drop model [28,29]. Various implementations of this model have been recently evaluated by comparison to experimental data for both monovalent and divalent ions [29]. A recently introduced discrete implementation of the Thomson model that takes into account ion size appears to accurately fit most experimental and quantum chemical data [29].…”