Deducing Proton-Bound Heterodimer Association Energies from Shifts in Ion Mobility Arrival Time Distributions

Through vapor modification of the counter-current drift gas in an atmospheric pressure drift tube ion mobility spectrometer (IMS), we demonstrate measurement of gas-phase association enthalpies and entropies for select proton-bound heterodimers formed from a phosphonic acid with 2-propanol. Previous efforts to determine gas-phase association thermodynamic properties have relied largely upon lower pressure systems and inference of the relative concentrations of m/z isolated species. In contrast, the drift tube IMS based approach developed and applied in this study leverages the explicit gas-phase equilibrium that is established within an ion mobility drift cell. The inferred enthalpies and entropies of association are based solely upon monitoring a shift in the arrival time of an ion at different temperatures (and not on the signal intensity or on external instrument drift time calibration). We specifically report the gas-phase Gibbs free energy, enthalpy, and entropy changes for the association of 2-propanol with protonated methyl, ethyl, and propyl phosphonic acid ions (MPA, EPA, PPA) across the 100-175 °C temperature range. For all of these proton-bound heterodimers, the standard enthalpies and entropies of 2-propanol association were negative and positive, respectively. These data indicate that proton-bound heterodimer formation is both enthalpically and entropically favorable, though we find that the magnitude of the standard enthalpy change for vapor association is small (near 1 kcal/mol for all examined heterodimers). Though many prior results (largely obtained with high pressure mass-spectrometry) for other proton-bound organic heterodimer complexes show larger enthalpic favorability and an entropic barrier, our results qualitatively conform to the bulk Kelvin-Thomson-Raoult (KTR) model, which is commonly utilized in describing ion-induced nucleation of a vapor onto a soluble, nanometer scale ion. The KTR model suggests that heterodimer formation due to vapor binding to an ion should be slightly enthalpically favored (due to a larger Thomson effect than the Kelvin effect) and entropically favored because of ion solvation (Raoult's effect). The method presented in this study can be applied to any static-field ion mobility spectrometer and to a wide variety of heterodimers. Due to the ease of implementation and broad applicability, this approach may find consistent use in determining the thermodynamic properties of weakly bound gas-phase heterodimer complexes which are difficult to probe via alternative techniques. Moreover, this renewed implementation of the IMS experiment is directly compatible with soft ionization sources which will enable the characterization of vapor modifier-induced mobility shift experiments for larger molecular complexes.