Effect of Relative Mass on Ion Velocity Cross-Correlations in Ionic Liquids and Molten Salts: Different Perspectives in Different Reference Frames

In electrolytes, the self- and interdiffusion coefficients, transport numbers, and electrical conductivity can be used to determine velocity cross-correlation coefficients (VCC) that are also accessible through molecular dynamics simulations. In an ionic liquid or molten salt, there are only three, corresponding to correlations between the velocities of distinct ion pairs (cation–anion, cation–cation, and anion–anion) averaged over both the ensemble and time, calculable from experimental ion self-diffusion coefficients and the electrolyte conductivity. Most usually, the mass-fixed frame of reference (with velocities relative to that of the center of mass of the system) is used to discuss the VCC and the distinct diffusion coefficients (DDC) derived from them. Recent work in the literature has suggested a dependence of the DDC on the ratio of the anion to cation mass. Here, we demonstrate, using our own and literature transport property data for a large number of ionic liquids and molten salts, that the trends observed depend on the particular choice of velocity reference frame, mass-, number-, or volume-fixed. The perception of ion–ion interactions may be distorted in the mass- and volume fixed frames when the co-ions have very different masses or volumes, particularly for systems containing light lithium ions

Revised and Extended Values for Self-Diffusion Coefficients of 1‑Alkyl-3-methylimidazolium Tetrafluoroborates and Hexafluorophosphates: Relations between the Transport Properties

Earlier measurements of the self-diffusion coefficients of 1-alkyl-3-methylimidazolium (or [RMIM], R = alkyl) tetrafluoroborates and hexafluorophosphates have been revised and extended to 90 °C. The main changes are to <i>D</i>_S+ and <i>D</i>_S– for [HMIM]­[PF₆] ([C₆C₁Im]­[PF₆]) and <i>D</i>_S– for [OMIM]­[BF₄] ([C₈C₁Im]­[BF₄]). New atmospheric pressure self-diffusion, density, and conductivity data are provided for [HMIM]­[BF₄] ([C₆C₁Im]­[BF₄]). Velocity cross-correlation, distinct diffusion, and Laity resistance coefficients have been calculated. There is no evidence for ion association. A new relation between the Nernst–Einstein deviation parameter (Δ) and resistance coefficients (<i>r</i>_<i>ij</i>) is derived; Δ tends toward 0.5 when the like-ion <i>r</i>_<i>ii</i> are much smaller than the unlike-ion <i>r</i>_<i>ij</i>, i.e., when the counterion interactions dominate. [OMIM]⁺ ion salts approach this limit. Stokes–Einstein–Sutherland and Walden plots overlap almost quantitatively for [BF₄]⁻, [PF₆]⁻, and Cl^– salts with a common [RMIM]⁺ cation. That is, in thermodynamic states that have the same viscosity, the salt molar conductivities and hence ionic electrical mobilities of, say, [BMIM]­[BF₄] and [BMIM]­[PF₆] are almost equal, as are the corresponding Brownian or diffusive mobilities, (<i>D</i>_Si/<i>RT</i>), for the cation, and also for these three small anions

Self-Diffusion Coefficients and Related Transport Properties for a Number of Fragile Ionic Liquids

Ion self-diffusion coefficients (<i>D</i>_Si) for [EMIM]­[CF₃SO₃] and [chol]­[Tf₂N] and cation self-diffusion coefficients for [CH₃SO₃]⁻, [TCB]⁻, and [FAP]⁻ salts of [EMIM]⁺ are reported together with ancillary data allowing calculation of velocity cross-correlation (VCC or <i>f</i>_ij), distinct diffusion (<i>D</i>^d_ij) and Laity resistance coefficients (<i>r</i>_ij). Comparison of ion Stokes–Einstein–Sutherland (SES) exponents is a useful test of experimental consistency. New analysis shows the viscosity (η) and molar conductivity (Λ) of [EMIM]­[CH₃SO₃] and [EMIM]­[TCB] do not show the dynamic crossovers previously reported. Nor do <i>D</i>_S and η for the comparison substance propylene carbonate. For all the ionic liquids, <i>D</i>_S+ > <i>D</i>_S‑. Data show fractional SES (<i>D</i>_Si-η, <i>D</i>^d_ij-η) and Walden (Λ–η) plots. The Nernst–Einstein parameter, Δ, for [EMIM]­[FAP] is approximately zero, implying the relative velocity of any ion pair selected randomly is uncorrelated with those of other distinct pairs. For the other ionic liquids, the relative pair velocities are anticorrelated. VCC values for the [EMIM]⁺ salts except [EMIM]­[FAP] lie in the order |<i>f</i>_+–| < |<i>f</i>₊₊| < |<i>f</i>_––|; that is, the anticorrelation is smallest for the unlike ion interactions: correspondingly, <i>r</i>₊₊ <i>< r</i>_–– <i>< r</i>_+–. For [EMIM]­[FAP], |<i>f</i>₊₊| < |<i>f</i>_+–| < |<i>f</i>_––|, with <i>f</i>_+– ∼ (<i>f</i>₊₊ + <i>f</i>_––)/2 and <i>r</i>_+–² <i>∼r</i>₊₊ <i>r</i>_{<i>––</i>}, consistent with Δ ∼ 0

Density, Viscosity, and Electrical Conductivity of Protic Amidium Bis(trifluoromethanesulfonyl)amide Ionic Liquids

We investigated the densities, viscosities, and electrical conductivities of the protic amidium-based ionic liquids with bis­(trifluoromethanesulfonyl)­amide ([TFSA]⁻). The cations were <i>N</i>,<i>N</i>-dimethylformamidium, [DMFH]⁺, <i>N</i>,<i>N</i>-dimethylacetamidium, [DMAH]⁺, and <i>N</i>,<i>N</i>-dimethylpropionamidium, [DMPH]⁺. The physical properties were measured over the temperature range from 273.15 to 363.15 K at atmospheric pressure. The densities were correlated with the linear or quadratic equations, and the transport properties were reproduced well with the Vogel–Fulcher–Tammann equation. The densities and the viscosities increased in the following order: [DMAH]­[TFSA] > [DMPH]­[TFSA] > [DMFH]­[TFSA]. The opposite trend was observed for the electrical conductivities. The empirical Walden plots gave the straight lines in all the present ionic liquids. It was found that the data points for [DMFH]­[TFSA] appreciably fall below [DMPH]­[TFSA] and [DMAH]­[TFSA] on the Walden plot

Solvation Structure of Imidazolium Cation in Mixtures of [C₄mim][TFSA] Ionic Liquid and Diglyme by NMR Measurements and MD Simulations

Interactions of 1-butyl-3-methylimidazolium cation ([C₄mim]⁺) with bis­(trifluoromethanesulfonyl)­amide anion ([TFSA]⁻) and diethyleneglycol dimethyl ether (diglyme) in mixtures of [C₄mim]­[TFSA] ionic liquid and diglyme have been investigated using ¹H and ¹³C NMR spectroscopy and molecular dynamics (MD) simulations. The results of NMR chemical shift measurements and MD simulations showed that the diglyme oxygen atoms have contact with the imidazolium hydrogen atoms of [C₄mim]⁺ in the mixtures. The contact between the hydrogen atoms of imidazolium and the oxygen atoms of [TFSA]⁻ remains even when the diglyme mole fraction (<i>x</i>_diglyme) increases up to 0.9. However, the coordination numbers of the hydrogen atoms of [C₄mim]⁺ with oxygen atoms of diglyme increase with <i>x</i>_diglyme. The [TFSA]⁻ anions around [C₄mim]⁺ are not completely replaced by diglyme even at <i>x</i>_diglyme > 0.9. The MD simulations revealed that the diglymes also have contact with the butyl group of [C₄mim]⁺. The methyl groups of diglyme prefer to have contact with the terminal methyl group of the butyl group, whereas the diglyme oxygen atoms prefer to have contact with the methylene group connected to the imidazolium ring of [C₄mim]⁺

CO₂ Solubility in Ether Functionalized Ionic Liquids on Mole Fraction and Molarity Scales

The effect of ether functional group(s) in the cation, anion, and both of the ions in ionic liquids on physical absorption of CO₂ are revisited in the present work. The solubilities of CO₂ in ether functionalized ammonium and pyrrolidinium salts, [N_211MEE]­[Tf₂N], [Pyr_1MOM]­[Tf₂N], and [Pyr_1MOM]­[FSA] were previously reported together with the corresponding alkyl analogues. In addition to such cation-modified ionic liquids, we investigate a new family of ether functionalized ionic liquids with alkoxy sulfates; [C₂mim]­[C₁(OC₂)₂SO₄], [P_444ME]­[C₆SO₄], [P_444ME]­[C₁OC₂SO₄], [P_444ME]­[C₁(OC₂)₂SO₄], and [N_221ME]­[C₁(OC₂)₂SO₄]. The CO₂ solubility data on the molarity as well as the mole fraction scales are presented in a series of ether functionalized ILs with a brief overview of the previously reported results. It has become apparent that the introduction of an ether functional group in anions more effectively improves the CO₂ solubilities on both the mole fraction and molarity scales than that in cations. The effects of the cation, anion, and dual functionalization with ether groups on the physical solubility of CO₂ are discussed with the volumetric properties in terms of the molecular structures of ILs

Temperature and Pressure Dependence of the Electrical Conductivity of 1‑Butyl-3-methylimidazolium Bis(trifluoromethanesulfonyl)amide

The electrical conductivities of the ionic liquid 1-butyl-3-methylimidazolium bis­(trifluoro­methanesulfonyl)­amide ([BMIM]­[Tf₂N]) have been determined between (273 and 353) K over an extended pressure range up to 250 MPa by both electrochemical impedance spectroscopy and conductance bridge techniques. The results obtained by the two techniques are generally in good agreement, within 3%, though the conductance bridge results yield lower values outside the experimental uncertainties at higher conductivities, that is, at higher temperature and lower pressures where the maximum deviation is −7%. The temperature and pressure dependence of both the conductivity and molar conductivity have been represented by modified Vogel–Fulcher–Tammann equations. The molar conductivity scales with the viscosity, with overlapping isobars and isotherms, so that a Walden plot, the logarithmic projection of molar conductivity versus fluidity (reciprocal viscosity), is a straight line with a similar slope (0.924) to those obtained for other 1,3-dialkylimidazolium ionic liquids

Density, Viscosity, and CO₂ Solubility in the Ionic Liquid Mixtures of [bmim][PF₆] and [bmim][TFSA] at 313.15 K

The density and viscosity of 1-butyl-3-methylimidazolium hexafluorophosphate ([bmim]­[PF₆]), 1-butyl-3-methylimidazolium bis­(trifluoromethanesulfonyl)­amide ([bmim]­[TFSA]), and their mixtures were measured at 313.15 K and at atmospheric pressure. Furthermore, the CO₂ solubilities and the CO₂-saturated densities of [bmim]­[PF₆], [bmim]­[TFSA], and their mixtures were determined at 313.15 K and pressures up to 8.5 MPa using a volume-variable high-pressure apparatus. The ionic liquid mixtures were prepared at the mole fractions of [bmim]­[PF₆] of 0.25, 0.50, and 0.75. The CO₂ solubilities in both the mole fraction and molarity scales increased with the composition of [bmim]­[TFSA], and the pressure-mole fraction curves showed a typical behavior for the physical absorption. The CO₂-saturated density of the ionic liquid phase decreased with increasing the composition of [bmim]­[PF₆] and the pressure. Excess volumetric properties were calculated from the pressure–volume–mole fraction relations

Electrical Conductivities, Viscosities, and Densities of <i>N</i>-Methoxymethyl- and <i>N</i>-Butyl-<i>N</i>-methylpyrrolidinium Ionic Liquids with the Bis(fluorosulfonyl)amide Anion

This paper reports the densities, viscosities, and electrical conductivities of the two pyrrolidinium ionic liquids, <i>N</i>-methoxymethyl-<i>N</i>-methylpyrrolidinium bis­(fluorosulfonyl)­amide ([Pyr_1,1O1]­[FSA]) and <i>N</i>-butyl-<i>N</i>-methylpyrrolidinium bis­(fluorosulfonyl)­amide ([Pyr_1,4]­[FSA]), over the temperature range <i>T</i> = (273.15 to 363.15) K at atmospheric pressure. The densities were fitted to polynominals, and the viscosities and electrical conductivities were analyzed with the Vogel–Fulcher–Tammann and Litovitz equations. The densities and electrical conductivities of [Pyr_1,1O1]­[FSA] are higher than those of [Pyr_1,4]­[FSA], while the viscosities of the former salt are smaller than those of the latter. The Walden plots (double logarithm graph of molar conductivity vs fluidity (reciprocal viscosity)) give the straight lines with the slopes being 0.91 to 0.94. The present results for [Pyr_1,1O1]­[FSA] and [Pyr_1,4]­[FSA] are compared with those for the bis­(trifluoromethanesulfonyl)­amide ([NTf₂]⁻) analogues, [Pyr_1,1O1]­[NTf₂] and [Pyr_1,4]­[NTf₂]

Temperature and Density Dependence of the Transport Properties of the Ionic Liquid Triethylpentylphosphonium Bis(trifluoromethanesulfonyl)amide, [P_222,5][Tf₂N]

Viscosities (η), conductivities (κ, Λ), and ion self-diffusion coefficients (<i>D</i>_Si) for triethylpentyl­phosphonium bis­(trifluoro­methanesulfonyl)­amide, ([P_222,5]­[Tf₂N]), have been measured as a function of temperature and pressure in the ranges ([273–363] K, 243 MPa max), ([273–353] K, 251 MPa max), and (298–363 K, 225 MPa max), respectively. <i>pVT</i> data are also reported from (298 to 353) K to 50 MPa. The ratio of the ion self-diffusion coefficients is constant, independent of temperature and pressure. The results are discussed using velocity correlation, distinct diffusion, and resistance coefficients, and the Stokes–Einstein–Sutherland (SES: relating <i>D</i>_Si and η) and Nernst–Einstein equations (NE: relating Λ and <i>D</i>_Si). As is usual for ionic liquids the SES and NE plots for high-pressure isotherms and the atmospheric pressure isobar overlap quantitatively, that is the self-diffusion and distinct diffusion coefficients, and the molar conductivity, are functions of the viscosity. This can be used for the interpolation of these quantities within the range of the pressures and temperatures employed here, and for moderate extrapolation beyond them. The resistance coefficients are positive: there is no evidence for any ion association. Density scaling using Rosenfeld reduced variables yields (2.37 ± 0.07) for the scaling parameter, γ, for the four transport properties