The anomalously high mobility of hydroxide and hydronium ions in aqueous solutions is related to proton transfer and structural diffusion. The role of counterions in these solutions, however, is often considered to be negligible. Herein, we explore the impact of alkali metal counter cations on hydroxide solvation and mobility. Impedance measurements demonstrate that hydroxide mobility is attenuated by lithium relative to sodium and potassium. These results are explained by ab initio molecular dynamics simulations and experimental vibrational hydration shell spectroscopy, which reveal substantially stronger ion pairing between OH– and Li+ than with other cations. Hydration shell spectra and theoretical vibrational frequency calculations together imply that lithium and sodium cations have different effects on the delocalization of water protons donating a hydrogen bond to hydroxide. Specifically, lithium leads to enhanced proton delocalization compared with sodium. However, proton delocalization and the overall diffusion process are not necessarily correlated.
The structures of the ion-pairs formed in aqueous NaOH and LiOH solutions are elucidated by combining Raman multivariate curve resolution (Raman-MCR) experiments and ab initio molecular dynamics (AIMD) simulations. The results extend prior findings to reveal that the initially formed ion-pairs are predominantly water-shared, with the hydroxide ion retaining its full first hydration-shell, while direct contact ion-pairing only becomes significant at higher concentrations. Our results confirm previous experiments and simulations indicating greater ion-pairing in aqueous LiOH than NaOH as well as at high temperatures. Our results further imply that NaOH and LiOH ion-pairing free energies have an approximately linear (rather than square-root) dependence on ion concentration (in the molar range), with positive enthalpies and entropies that increase with concentration, thus implying that water-mediated interactions enthalpically disfavor and entropically favor ion-pair formation.
The structure, dynamics, and vibrational spectroscopy of dilute HOD, methanol, and ethanol in the 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide, [emim][NTf2], ionic liquid (IL) are investigated with molecular dynamics (MD) simulations. The structure of the ILs around the solutes is qualitatively similar, where the OD bond of the deuterated alcohols donates an interaction to an [NTf2] anion and the [emim] cations interact with the oxygen atom of the OD group. The slowest time scale for the reorientational dynamics of the OD bond varied considerably for HOD, methanol, and ethanol (27, 71, and 87 ps, respectively). In contrast, the slowest time scales for spectral diffusion of the OD vibrational frequency were 11 ps for each of the three solutes, which indicates that the dynamics of the IL is relatively unchanged by the presence of the alcohols at dilute concentration. The theoretical results for the reorientational and spectral diffusion dynamics compare favorably with prior two-dimensional infrared (2D IR) spectroscopic measurements.
This manuscript presents an exercise that utilizes mathematical software to explore Fourier transforms in the context of model quantum mechanical systems, thus providing a deeper mathematical understanding of relevant information often introduced and treated as a "black-box" in analytical chemistry courses. The exercise is given to undergraduate students in their third year during physical chemistry, thus providing a theoretical foundation for the subsequent introduction of such material in analytical instrumentation courses. With the reinforcement of familiar concepts such as the Heisenberg Uncertainty Principle, classical correspondence, and linear combinations in the context of both position and momentum space for a particle in a box, a better understanding of the mathematical implications of the Fourier transform is fostered. Subsequent analysis of a time-dependent function constructed via a linear combination and its transformation to the frequency domain provides a practical example relating to the Fourier processes applied in analytical spectroscopy. The final portion of the exercise returns to the position/momentum conjugate pair and explores how the construction of a narrow wavepacket via a sum of cosines illustrates the Uncertainty Principle once the probability density functions of each coordinate are analyzed. This exercise has been shown to not only reinforce fundamental concepts necessary for a true appreciation of quantum mechanics, but also help demystify the Fourier transform process for students taking analytical chemistry.
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