Ionic mobility in alcohols: From dielectric friction to the solvent–berg model

Rigid Cations Induce Enhancement of Microheterogeneity and Exhibit Anomalous Ion Diffusion in Water-Ethanol Mixtures

Because of the amphiphilic nature of ethanol in the aqueous solution, ions cause an interesting microheterogeneity where the water molecules and the hydroxy groups of ethanol preferentially solvate the ions, while the ethyl groups tend to occupy the intervening space. Using computer simulations, we study the dynamics of rigid monovalent cations (Li⁺, Na⁺, K⁺, and Cs⁺) in aqueous ethanol solutions with chloride as the counterion. We vary both the size of the ions and the composition of the mixture to explore size- and composition-dependent ion diffusion. The relative stability of enhanced microheterogeneous configurations makes ion diffusion slower than what would be surmised by using the bulk properties of the mixture, using the Stokes-Einstein relation. We study the structure through partial radial distribution functions and the stability through coordination number fluctuations. The ion diffusion coefficient exhibits sharp re-entrant behavior when plotted against viscosity varied by composition. Our studies reveal multiple anomalous features of ion motion in this mixture. We formulate a mode-coupling theory (MCT) that takes into account the interaction between different dynamical components; MCT can incorporate the effects of heterogeneous dynamics and nonlinearity in composition dependence that arise from the feedback between mutually dependent ion-solvent dynamics.

Linear and Nonlinear Infrared Spectroscopies Reveal Detailed Solute-Solvent Dynamic Interactions of a Nitrosyl Ruthenium Complex in Solution

In this work, the solvation of a nitrosyl ruthenium complex, [(CH₃)₄N][RuCl₃(qn)(NO)] (with qn = deprotonated 8-hydroxyquinoline), which is a potential NO-releasing molecule in the bio-environment, was studied in two bio-friendly solvents, namely deuterated dimethyl sulfoxide (dDMSO) and water (D₂O). A blue-shifted NO stretching frequency was observed in water with respect to that in dDMSO, which was believed to be due to ligand-solvent hydrogen-bonding interactions, one N═O···D and particularly three Ru-Cl···D, that show competing effects on the NO bond length. The dynamic differences of the NO stretch in these two solvents were further revealed by transient pump-probe IR and two-dimensional IR results: faster vibrational relaxation and faster spectral diffusion (SD) were observed in D₂O, confirming stronger solvent-solute interaction and also faster solvent structural dynamics in D₂O than in DMSO. Further, a significant non-decaying residual in the SD dynamics was observed in D₂O but not in DMSO, suggesting the formation of a stable solvation shell in water due to strong multi-site ligand-solvent hydrogen-bonding interactions, which is in agreement with the observed blue-shifted NO stretching frequency. This work demonstrates that small solvent molecules such as water can form a relatively rigid solvation shell for certain transition metal complexes due to cooperative ligand-solvent interactions and show slower dynamics.

Fluctuation enhancement of ion diffusivity in liquids

The diffusivity of ions in liquid solutions is known either to decrease with an increase in the ion size or to have a single maximum depending on the ion size. This article presents evidence for the appearance of multiple maxima and thus multiple ion sizes with enhanced diffusivity.

On the coupling of solvent characteristics to the electronic structure of solute molecules

We present the results of a theoretical investigation focusing on the solvent structure surrounding the -1, 0 and +1 charged species of F, Cl, Br and I halogen atoms and F2, Cl2, Br2 and I2 di-halogen molecules in a methanol solvent and its influence on the electronic structure of the solute molecules. Our results show a large stabilizing effect arising from the solute-solvent interactions. Well-formed first solvation shells are observed for all species, the structure of which is strongly influenced by the charge of the solute species. Detailed analysis reveals that coordination number, CN, solvent orientation, θ, and solute-solvent distance, d, are important structural characteristics which are coupled to changes in the electronic structure of the solute. We propose that the fundamental chemistry of any solute species is generally regulated by these solvent degrees of freedom.

SIZE DEPENDENCE OF SOLVATION STRUCTURE AND DYNAMICS OF IONS IN LIQUID N-METHYLACETAMIDE: A MOLECULAR DYNAMICS SIMULATION STUDY

The solvation structure and dynamics of alkali metal (Li+, Na+, K+, Rb+, Cs+) and halide (F-, Cl-, Br-, I-) ions in liquid N -methylacetamide (NMA) are calculated at two different temperatures T = 313 K and 453 K, by using classical molecular dynamics simulations. We have also considered [Formula: see text] and some larger cations such as I +, Me 4 N +, and Et4N+ in this study to investigate the size dependence solvation structure and dynamics of ions in liquid NMA. With the increase of ion size, the self-diffusion coefficients of cations are found to increase and the maximum is observed at Me4N+ , whereas for halide ions the increase of diffusion coefficient with ion size continues up to I- and no maximum is observed. However, the relative increase of the diffusion coefficients of larger ion compared to those of Li+ and F+ are found to be significantly higher at low temperature. Results are very good in agreement with experimental observation.

Anion-cation permeability correlates with hydrated counterion size in glycine receptor channels

The functional role of ligand-gated ion channels depends critically on whether they are predominantly permeable to cations or anions. However, these, and other ion channels, are not perfectly selective, allowing some counterions to also permeate. To address the mechanisms by which such counterion permeation occurs, we measured the anion-cation permeabilities of different alkali cations, Li(+) Na(+), and Cs(+), relative to either Cl(-) or NO(3)(-) anions in both a wild-type glycine receptor channel (GlyR) and a mutant GlyR with a wider pore diameter. We hypothesized and showed that counterion permeation in anionic channels correlated inversely with an equivalent or effective hydrated size of the cation relative to the channel pore radius, with larger counterion permeabilities being observed in the wider pore channel. We also showed that the anion component of conductance was independent of the nature of the cation. We suggest that anions and counterion cations can permeate through the pore as neutral ion pairs, to allow the cations to overcome the large energy barriers resulting from the positively charged selectivity filter in small GlyR channels, with the permeability of such ion pairs being dependent on the effective hydrated diameter of the ion pair relative to the pore diameter.

Hydronium ion motion in nanometer 3-methyl-pentane films

An ion soft-landing approach was applied to study the motion of hydronium (D(3)O(+)) and cesium (Cs(+)) ions from 84 to 104 K in glassy 3-methyl-pentane (3MP) films vapor deposited on Pt(111). Both ions were found to have very similar mobilities in 3MP. The span of ion mobilities probed is from approximately 10(-18) to approximately 10(-13) m(2) V(-1) s(-1). Ion transport in these films was studied as a function of film thickness and electric field strength. The drift velocity was found to be linear with applied field below about 2 x 10(8) Vm and deviated from linearity above this. To a large extent, D(3)O(+) and Cs(+) motion in 3MP was well predicted by a simple continuum-based ion mobility model in films from 25 to 20,000 ML thick (including pronounced perturbations 7 ML from both the vacuum and Pt interfaces). The mobility varied with temperature more slowly than predicted by Stokes' law, which may be due to extended inhomogeneous structures in the 3MP near its glass transition at 77 K.

Limiting ionic conductivity and solvation dynamics in formamide

A self-consistent microscopic theory has been used to calculate the limiting ionic conductivity of unipositive rigid ions in formamide at different temperatures. The calculated results are found to be in good agreement with the experimental data. The above theory can also predict successfully the experimentally observed temperature dependence of total ionic conductivity of a given uniunivalent electrolyte in formamide. The effects of dynamic polar solvent response on ionic conductivity have been investigated by studying the time dependent progress of solvation of a polarity probe dissolved in formamide. The intermolecular vibration (libration) band that is often detected in the range of 100-200 cm(-1) in formamide is found to play an important role in determining both the conductivity and the ultrafast polar solvent response in formamide. The time dependent decay of polar solvation energy in formamide has been studied at three different temperatures, namely, at 283.15, 298.15, and 328.15 K. While the predicted decay at 298.15 K is in good agreement with the available experimental data, the calculated results at the other two temperatures should be tested against experiments.

Evidence in Support of Levitation Effect as the Reason for Size Dependence of Ionic Conductivity in Water: A Molecular Dynamics Simulation

We report extensive molecular dynamics simulations of (i) model ions in water at high concentrations as a function of the size and charge of the ion as well as (ii) realistic simulation of Cl- and Br- ions at low concentrations in water at room temperature. We also analyze existing experimental data in light of the results obtained here. The halide ion simulations have been carried out using the interaction potentials of Koneshan et al. (J. Phys. Chem. B 1998, 102, 4193). We compute structural and dynamical properties of ions in water and explore their variation with size and charge of the ion. We find that ions of certain intermediate sizes exhibit a maximum in self-diffusivity in agreement with previous experimental measurements and computer simulations. We analyze molecular dynamics trajectories in light of the previous understanding of the levitation effect (LE) and the recent suggestion that ionic conductivity has its origin in LE (J. Phys. Chem. B 2005, 109, 8120). We report the distribution of void and neck radii that exist amidst water. Our analysis suggests that the ion with maximum self-diffusivity is characterized by a lower activation energy and a single-exponential decay of F(s)(k,t). The behavior of these and other related quantities of the ion with maximum self-diffusivity are characteristic of the anomalous regime of the LE. The simulation results of Br- and Cl- ions in water also yield results in agreement with the predictions of LE. A plot of experimental conductivity data in the literature for alkali ions in water by Kay and Evans (J. Phys. Chem. 1966, 70, 2325) also yields a lower activation energy for the ion with maximum conductivity in excellent agreement with the LE. To the best of our knowledge, none of the existing theories predict a lower activation energy for the ion with maximum conductivity.

Solute size effects on the solvation structure and diffusion of ions in liquid methanol under normal and cold conditions

We have performed a series of molecular dynamics simulations of alkali metal (Li+, Na+, K+, Rb+, and Cs+) and halide (F-, Cl-, Br-, and I-) ions in liquid methanol at two different temperatures to investigate the effects of ion size on the hydration structure and diffusion of ions in methanol under normal and cold conditions. Simulations are also carried out for some of the larger cations such as I+, (CH3)4N+, and (C2H5)4N+ and also neutral alkali metal atoms in methanol at both temperatures. With the increase of ion size, the diffusion coefficients of both positive and negative ions are found to show anomalous behavior. For cations, it is found that the maximum of the diffusion coefficient versus ion size curve occurs at the rather large cation of (CH3)4N+ unlike in water where the maximum occurs at the relatively smaller ion of Rb+. For halide ions, the anomalous behavior, i.e., the increase of diffusion with ion size, continues up to iodide ion and no maximum is observed. These results are in good agreement with experimental observations. The diffusion coefficients of neutral atoms are found to be greater in methanol than that in water and they decrease monotonically with solute size, whereas the diffusion coefficients of the corresponding ions are found to be smaller in methanol. Accordingly, an ion experiences a smaller Stokes friction and a higher dielectric friction in methanol than in water. These contrasting effects are believed to be responsible for the shift of the maximum of ion diffusion toward a larger ion size when compared with similar anomalous size dependence in liquid water.

Mode-coupling study on the dynamics of hydrophobic hydration II: Aqueous solutions of benzene and rare gases

The dynamic properties of both the solute and solvent of the aqueous solution of benzene, xenon and neon are calculated by the mode-coupling theory for molecular liquids based on the interaction-site model. The B-coefficients of the reorientational relaxation and the translational diffusion of the solvent are evaluated from their dependence on the concentration of the solute, and the reorientational relaxation time of water within the hydration shell is estimated based on the two-state model. The reorientational relaxation times of water in the bulk and within the hydration shell, that of solute, and the translational diffusion coefficients of solute and solvent, are calculated at 0-30 degrees C. The temperature dependence of these dynamic properties is in qualitative agreement with that of NMR experiment reported by Nakahara et al. (M. Nakahara, C. Wakai, Y. Yoshimoto and N. Matubayasi, J. Phys. Chem., 1996, 100, 1345-1349, ref. 36), although the agreement of the absolute values is not so good. The B-coefficients of the reorientational relaxation times for benzene, xenon and neon solution are correlated with the hydration number and the partial molar volume of the solute. The proportionality with the latter is better than that with the former. These results support the mechanism that the retardation of the mobility of water is caused by the cavity formation of the solute, as previously suggested by us (T. Yamaguchi, T. Matsuoka and S. Koda, J. Chem. Phys., 2004, 120, 7590-7601, ref. 34), rather than the conventional one that the rigid hydration structure formed around the hydrophobic solute reduces the mobility of water.

On the coupling between molecular diffusion and solvation shell exchange

The connection between diffusion and solvent exchanges between first and second solvation shells is studied by means of molecular dynamics simulations and analytic calculations, with detailed illustrations for water exchange for the Li(+) and Na(+) ions, and for liquid argon. First, two methods are proposed which allow, by means of simulation, to extract the quantitative speed-up in diffusion induced by the exchange events. Second, it is shown by simple kinematic considerations that the instantaneous velocity of the solute conditions to a considerable extent the character of the exchanges. Analytic formulas are derived which quantitatively estimate this effect, and which are of general applicability to molecular diffusion in any thermal fluid. Despite the simplicity of the kinematic considerations, they are shown to well describe many aspects of solvent exchange/diffusion coupling features for nontrivial systems.

Molecular dynamics simulation study on the transient response of solvation structure during the translational diffusion of solute

The transient response function of the density profile of the solvent around a solute during the translational diffusion of the solute is formulated based on the generalized Langevin formalism. The resultant theory is applied to both neat Lennard-Jones fluids and cations in liquid water, and the response functions are obtained from the analysis of the molecular dynamics simulations. In the case of the self-diffusion of Lennard-Jones fluids, the responses of the solvation structures are in harmony with conventional pictures based on the mode-coupling theory, that is, the binary collision in the low-density fluids, the backflow effect from medium to high density fluids, and the backscatter effect in the liquids near the triple point. In the case of cations in water, the qualitative behavior is strongly dependent on the size of cations. The pictures similar to simple dense liquids are obtained for the large ion and the neutral molecule, while the solvent waters within the first solvation shell of small ions show an oscillatory response in the short-time region. In particular, the oscillation is remarkably underdumped for lithium ion. The origin of the oscillation is discussed in relation to the theoretical treatment of the translational diffusion of ions in water.

Electric conductivities of 1:1 electrolytes in liquid methanol along the liquid-vapor coexistence curve up to the critical temperature. II. KBr and KI solutions

The molar conductivities Lambda of KBr and KI in dilute methanol solutions were measured along the liquid-vapor coexistence curve up to the critical temperature (240 degrees C). The concentration dependence of Lambda in each condition was analyzed by the Fuoss-Chen-Justice equation to obtain the limiting molar conductivities and the molar association constants. Using the present data together with the literature ones, the validity of the Hubbard-Onsager (HO) dielectric friction theory based on the sphere-in-continuum model was examined for the translational friction coefficients zeta of the halide ions (the Cl(-), Br(-), and I(-) ions) in methanol in the density range of 2.989rho(c)> or =rho> or =1.506rho(c), where rho(c)=0.2756 g cm(-3) is the critical density of methanol. For all the halide ions studied, the friction coefficient decreased with decreasing density at rho>2.0rho(c), while the nonviscous contribution Deltazeta/zeta increased; Deltazeta was defined as the difference between zeta and the friction coefficient estimated by the Stokes law. The density dependence of zeta and Deltazeta/zeta were well reproduced by the HO theory at rho>2.0rho(c). The HO theory also explained the ion-size dependence of Deltazeta/zeta which decreased with ion-size at rho>2.0rho(c). At rho<2.0rho(c), on the other hand, the HO theory could not explain the density and the ion-size dependences of zeta and Deltazeta/zeta. These results indicated that the application limit of the HO theory lied about rho=2.0rho(c) which is the same as the application limit observed for the alkali metal ions. The present results were also compared with the results in subcritical aqueous solutions.

Electric conductivities of 1:1 electrolytes in liquid methanol along the liquid–vapor coexistence curve up to the critical temperature. I. NaCl, KCl, and CsCl solutions

The molar conductivities Lambda of NaCl, KCl, and CsCl in liquid methanol were measured in the concentration range of (0.3-2.0) x 10(-3) mol dm(-3) and the temperature range of 60-240 degrees C along the liquid-vapor coexistence curve. The temperature range corresponds to the solvent density range of (2.78-1.55)rhoc, where rhoc = 0.2756 g cm(-3) is the critical density of methanol. The concentration dependence of Lambda at each temperature and density (pressure) has been analyzed by the Fuoss-Chen-Justice equation to obtain the limiting molar conductivity Lambda0 and the molar association constant KA. For all the electrolytes studied, Lambda0 increased almost linearly with decreasing density at densities above 2.0rhoc, while the opposite tendency was observed at lower densities. The relative contribution of the nonhydrodynamic effect on the translational friction coefficient zeta was estimated in terms of Deltazeta/zeta, where the residual friction coefficient Deltazeta is the difference between zeta and the Stokes friction coefficient zetaS. At densities above 2.0rhoc, Deltazeta/zeta increased with decreasing density though zeta and Deltazeta decrease, and the tendencies are common for all the ions studied. The density dependences of zeta and Deltazeta/zeta were explained well by the Hubbard-Onsager (HO) dielectric friction theory based on the sphere-in-continuum model. At densities below 2.0rhoc, however, the experimental results cannot be explained by the HO theory.

Capillary electrophoresis in aqueous-organic media. Ionic strength effects and limitations of the Hubbard-Onsager dielectric friction model

The mobilities of three aromatic sulfonates, ranging in charge from -1 to -3, were investigated by capillary electrophoresis using buffers containing 0 to 75% ethanol or 2-propanol. Absolute mobilities were determined by extrapolation of the effective mobilities to zero ionic strength according to the Pitts' equation. For all buffers studied, ions of higher charge experienced larger ionic strength effects. The resulting ionic strength-induced selectivity alterations were more dramatic when organic solvents were present in the media. Furthermore, for different organic modifier types and contents, the magnitude of the ionic strength effect was governed to a large extent by the 1/(eta epsilon 1/2) dependence in the electrophoretic effect of the Pitts' equation. Addition of ethanol or 2-propanol to the electrophoretic media resulted in changes in the absolute mobilities of the ions. These solvent-induced mobility changes are attributed to dielectric friction. As predicted by the Hubbard-Onsager model, dielectric friction increased with increasing organic content and with increasing analyte charge. As a result, dramatic changes in the relative absolute mobilities were observed, such as a reversal in migration order between sulfonates of -1 and -3 charge in 75% 2-propanol. Within the alcohols, the Hubbard-Onsager model was successful at predicting the relative mobility trends upon changing solvent. However, the relative trends observed between acetonitrile-water and alcohol-water media were not consistent with the model. This may be explained by the continuum nature of the model, whereby the different ion-solvent interactions characteristic to each solvent class are not taken into account.

Factors affecting selectivity of inorganic anions in capillary electrophoresis

Capillary zone electrophoretic separations of inorganic anions are largely governed by the intrinsic (infinite dilution) mobility of the anion. This in turn is a function of the hydrodynamic friction caused by the size of the ion and the dielectric friction caused by the charge density of the anion re-orienting the surrounding solvent. The influence of these factors on the mobility of anions is examined in both water and nonaqueous solvents. The influence of other experimental parameters, such as ionic strength, ion association, electroosmotic flow modifier concentration, and the addition of complexing agents such as polymeric cations, cyclodextrins, crown ethers and cryptands are also reviewed. From this discussion, some rules of thumb as to when different approaches will be most effective are drawn.