Solvent Effect on Rotational Motion of Perchlorate Ion

Abstract

The rotational relaxation times of perchlorate ion, τ2r, in 15 solvents and at various temperatures were determined from the measurements of the 17O NMR spin−lattice relaxation times. The obtained τ2r values were much smaller than those predicted from the hydrodynamic model (Stokes−Einstein−Debye, SED, equation). Comparison between the observed solvent dependence of the τ2r value and those predicted by the continuum models, including the SED hydrodynamic model, the Hubbard−Onsager−Felderhof (HOF) electrohydrodynamic model, and the Alavi−Waldeck (AW) dielectric friction model for multipole rotation, demonstrated that solvent viscosity is an expedient indicator for representing the overall trend of the solvent dependence of the rotational relaxation time; the observed τ2r values showed a fractional power dependence on the viscosity (i.e., τ2r ∝ ηα, where α ∼ 0.25 and η is the solvent viscosity). Site−site interactions between the perchlorate ion and solvent molecules, however, provided a significant effect on the perchlorate rotation in some solvents with a large imbalance of the electronic donor and acceptor properties (e.g., hexamethylphosphoric triamide). The values for τ2r calculated for alcohols (methanol, ethanol, and n-propanol) according to the HOF and the AW models were appreciably overestimated to a greater degree than those in the other solvents, and this result was ascribed to a predominant contribution from the interactions with the hydroxyl groups of the alcohols. The result of the analysis for the solvent dependence of the perchlorate rotation by the electrohydrodynamic model was also compared with that for the perchlorate translation, and the difference in the validity of the continuum models for the ionic rotation and the translation was discussed.

Solvent Effect on Rotational Relaxation Time of Ammonium Ion

“…Figure shows the dependence of the T 1 (D) -1 values of the ammonium ion on the concentration in acetone. A linear concentration dependence in τ 2r was observed in some ions in the dilute solutions (0.02 − 0.1 mol L -1 ), ,, and was theoretically predicted by Ibuki et al In the present study, the effect of the perchlorate anion on the τ 2r values, i.e., the T 1 (D) -1 values below the perchlorate salt concentration of 0.015 mol L -1 was, however, not beyond 10% of the value extrapolated to infinite dilution if a linear relation was assumed to the concentration dependence of τ 2r , i.e., T 1 (D) -1 below 0.02 mol L -1 . The effect of the counteranion on τ 2r is expected to be the largest in acetone because the dielectric constant of acetone is the smallest among the solvents used in the present study.…”

“…This slowdown in the ammonium rotation may indicate the importance of the interaction between the solvent and the ionic charge or the fractional charge of the ammonium protons. This observation should be contrasted to the prediction that the relaxation is faster than that of perchlorate, since a spherical molecule (ion) with a size comparable or smaller than that of the solvent should have a more “slip” boundary condition. ,

2 Logarithm plot of the observed τ 2r values of the ammonium ion (closed circles) and of the perchlorate ion (open triangles) versus those calculated by the Stokes−Einstein−Debye equation assuming the stick hydrodynamic boundary condition at 298 K. The data for the perchlorate ion were taken from ref . Numbers in the figure indicate the solvent used: (1) nitromethane; (2) acetone; (3) acetonitrile; (4) propylene carbonate; (5) dimethylsulfoxide (DMSO); (6) N , N -dimethylformamide (DMF); (7) hexamethylphosphoric triamide (HMPA); (8) water; (9) methanol; (10) ethanol; (11) ethylene glycol; (12) benzonitrile; (13) nitrobenzene; (14) n -propanol; (15) tetramethylurea.

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“…In the present study, we examined the solvent dependence of the rotational relaxation time of ammonium ion and compared the results with that of perchlorate ion. In our previous study on the rotational motion of the perchlorate ion, it was shown that hydrodynamic or electrohydrodynamic models well represent, at least phenomelogically, the rough trend of the observed solvent dependence of the rotational relaxation times, despite the size of the ion being not large enough to regard the solvent as a hydrodynamic and/or a dielectric continuum. The ammonium ion is the smallest spherical ion that has a freedom of rotation.…”

“…Studies on ionic rotation in solution have been performed for many kinds of ions from various points of view, e.g., inorganic ions such as NO 3 - , 6-10 CO 3 2- , XO 4 n - (X = Cl, S, P), , and NH 4 + , and some metal complex ions. , On the other hand, examples for systematic experiments on the rotational motions of spherical ions in a wide variety of solvents and tests by various continuum models are very limited. Such a study is, however, indispensable to clarify the limitation to regarding the solvent as a hydrodynamic and dielectric continuum and requiring the introduction of “molecularlity” of the solvent.…”

“…0.1−1.4 mol L -1 ). As pointed out in our previous study for the solvent dependence of the rotational relaxation times of the perchlorate ion, a choice of solvents with wide variations in solvent properties is particularly effective for judging the validity of solvent continuum models. The interaction with a counteranion also disturbs the analysis of the solvent dependence; e.g., the ion-pair formation will change the rotational relaxation time. , The extent of this contribution will depend on the solvent since the formation constant depends on the solvent properties, such as the dielectric constant.…”