Modified Kelvin-Thomson equation considering ion-dipole interaction: Comparison with observed ion-clustering enthalpies and entropies

The classical Kelvin-Thomson (CKT) equation does not consider the interaction of condensing molecules with the ions and hence is not able to treat polar and nonpolar molecules differently. The ion-clustering enthalpy and entropy changes predicted by CKT equation for small ions are known to be significantly less negative than those observed. In this paper, we derive a modified Kelvin-Thomson (MKT) equation, which considers the effect of dipole-ion interaction, by taking into account the kinetic energy change of condensing polar ligands as they approach the ions or the extra energy needed for dipole molecules to escape from the ion cluster. The clustering enthalpies and entropies for protonated clusters (H ⁺L _n, with L=H ₂O, NH ₃, CH ₃OH, and C ₅H ₅N) are calculated based on MKT equation and compared with experimental data. Our calculations indicate that enthalpy values given by MKT equation are in very good agreement with experimental results for small ions (n≤5) of all four species investigated. MKT predictions appear to be consistent with observed enthalpies for CH ₃OH at n≥6 and for H ₂O at n=14-25, however, MKT equation cannot reproduce the observed discontinuous transition in enthalpy changes at n=6 for NH ₃ and at n=7-13 for H ₂O which is probably associated with the formation of inner shell. The stepwise entropy changes for small ions are 5-15 cal mol ^-1 K ^-1 more negative when the effect of dipole-ion interaction is considered, which suggests that the ordered structure of the cluster ions can somewhat be accounted for by the dipole-ion interaction term.