Describing Temperature-Dependent Self-Diffusion Coefficients and Fluidity of 1- and 3-Alcohols with the Compensated Arrhenius Formalism.

The location of the hydroxyl group in monohydroxy alcohols greatly affects the temperature dependence of the liquid structure due to hydrogen bonding. Temperature-dependent self-diffusion coefficients, fluidity (the inverse of viscosity), dielectric constant, and density have been measured for several 1-alcohols and 3-alcohols with varying alkyl chain lengths. The data are modeled using the compensated Arrhenius formalism (CAF). The CAF follows a modified transition state theory using an Arrhenius-like expression to describe the transport property, which consists of a Boltzmann factor containing an energy of activation, Ea, and an exponential prefactor containing the temperature-dependent solution dielectric constant, εs(T). Both 1- and 3-alcohols show the Ea of diffusion coefficients (approximately 43 kJ mol(-1)) is higher than the Ea of fluidity (approximately 35 kJ mol(-1)). The temperature dependence of the exponential prefactor in these associated liquids is explained using the dielectric constant and the Kirkwood-Frölich correlation factor, gk. It is argued that the dielectric constant must be used to account for the additional temperature dependence due to variations in the liquid structure (e.g., hydrogen bonding) for the CAF to accurately model the transport property.

Molecular model of self diffusion in polar organic liquids: implications for conductivity and fluidity in polar organic liquids and electrolytes.

Decades of studying isothermal and temperature-dependent mass and charge transport in polar organic liquids and electrolytes have resulted in two mutually incompatible models and the failure to develop a general molecular level picture. The hydrodynamic model describes conductivity, diffusion, and dielectric relaxation in terms of viscosity, while the inadequacy of the thermal activation model leads to empirical descriptions and fitting procedures whose adjustable parameters have little or no physical significance. We recently demonstrated that transport data can be characterized with a high degree of accuracy and self-consistency using the compensated Arrhenius formalism (CAF), where the transport property of interest assumes an Arrhenius-like form that also includes a dielectric constant dependence in the exponential prefactor. Here, we provide the molecular-level basis for the CAF by first modifying transition state theory, emphasizing the coupling of the diffusing molecule's motion with the dynamical motion of the surrounding matrix. We then explicitly include the polarization energy contribution from the dipolar medium. The polarization energy is related to molecular and system properties through the dipole moment and dipole density, respectively. The energy barrier for transport is coupled to the polarization energy, and we show that accounting for the role of the polarization energy leads naturally to the dielectric constant dependence in the exponential prefactor.

Mass and charge transport in 1-alkyl-3-methylimidazolium triflate ionic liquids.

Temperature-dependent transport properties in ionic liquids, such as the ionic conductivity and fluidity, are often characterized empirically through equations that require multiple adjustable fitting parameters in order to adequately describe the data. These fitting parameters offer no insight into the molecular-level mechanism of transport. Here the temperature dependence of these transport properties in 1-alkyl-3-methylimidazolium triflate ionic liquids is explained using the compensated Arrhenius formalism (CAF), where the conductivity or fluidity assumes an Arrhenius-like form that also contains a dipole density dependence in the exponential prefactor. The resulting CAF activation energies for conductivity and fluidity are much higher than those obtained from polar organic liquids and electrolytes. The CAF very accurately describes the temperature dependence of both conductivity and fluidity using only system properties (i.e., density and activation energy). These results imply that the transport mechanism in molten salts is very similar to that in polar organic liquids and electrolytes.

Application of the compensated Arrhenius formalism to explain the dielectric constant dependence of rates for Menschutkin reactions.

The dependence of the reaction rate on solvent dielectric constant is examined for the reaction of trihexylamine with 1-bromohexane in a series of 2-ketones over the temperature range 25-80 °C. The rate constant data are analyzed using the compensated Arrhenius formalism (CAF), where the rate constant assumes an Arrhenius-like equation that also contains a dielectric constant dependence in the exponential prefactor. The CAF activation energies are substantially higher than those obtained using the simple Arrhenius equation. A master curve of the data is observed by plotting the prefactors against the solvent dielectric constant. The master curve shows that the reaction rate has a weak dependence on dielectric constant for values approximately less than 10 and increases more rapidly for dielectric constant values greater than 10.

Mass and charge transport in cyclic carbonates: implications for improved lithium ion battery electrolytes.

The compensated Arrhenius formalism (CAF) is applied to conductivity and diffusion data for a family of cyclic carbonates composed of octylene carbonate, decylene carbonate, undecylene carbonate, and dodecylene carbonate. The strong intermolecular interactions in these liquids lead to diffusion activation energies that are higher than those for typical aprotic solvents. The conductivity results show that activation energies are similar between TbaTf and LiTf cyclic carbonate electrolytes. However, the conductivities of the TbaTf solutions are higher than those for the LiTf solutions, and this is attributed to the greater number of charge carriers in the TbaTf electrolytes. These CAF results are then used to give a possible explanation of why the ionic conductivity in lithium ion battery electrolytes is often optimized by mixing a cyclic carbonate with a lower viscosity liquid.

Mass and Ion Transport in Ketones and Ketone Electrolytes: Comparison with Acetate Systems.

Self-diffusion coefficient measurements were performed for pure n-alkyl ketone liquids using the pulsed field gradient NMR spin-echo technique. Ionic conductivities and dielectric constants of 0.0055 mol·L-1 tetrabutylammonium trifluoromethanesulfonate in 2-pentanone, 2-hexanone, 2-heptanone, 2-octanone, 2-nonanone, and 2-decanone were also measured. The temperature-dependent conductivities and diffusion coefficients over the range 5-80 °C can be described using the compensated Arrhenius formalism. Compensated Arrhenius equation plots were used to calculate the average activation energy for both sets of data. The average activation energy from conductivity data is approximately equal to that from diffusion data. The data for the pure ketones and ketone-based electrolytes are compared with analogous data for pure n-alkyl acetates and n-alkyl acetate-based electrolytes.

Concentration dependence of molal conductivity and dielectric constant of 1-alcohol electrolytes using the compensated arrhenius formalism.

The molal conductivity of liquid electrolytes with low static dielectric constants (ε(s) < 10) decreases to a minimum at low concentrations (region I) and increases to a maximum at higher concentrations (region II) when plotted against the square root of the concentration. This behavior is investigated by applying the compensated Arrhenius formalism (CAF) to the molal conductivity, Λ, of a family of 1-alcohol electrolytes over a broad concentration range. A scaling procedure is applied that results in an energy of activation (E(a)) and an exponential prefactor (Λ0) that are both concentration dependent. It is shown that the increasing molal conductivity in region II results from the combined effect of (1) a decrease in the energy of activation calculated from the CAF, and (2) an inherent concentration dependence in the exponential prefactor that is partly due to the dielectric constant.

Application of the compensated Arrhenius formalism to fluidity data of polar organic liquids.

The temperature dependence of viscosity (the reciprocal of fluidity) in polar liquids has been studied for over a century, but the available theoretical models have serious limitations. Consequently, the viscosity is often described with empirical equations using adjustable fitting parameters that offer no insight into the molecular mechanism of transport. We have previously reported a novel approach called the compensated Arrhenius formalism (CAF) to describe ionic conductivity, self-diffusion, and dielectric relaxation in terms of molecular and system properties. Here the CAF is applied to fluidity data of pure n-acetates, 2-ketones, n-nitriles, and n-alcohols over the temperature range 5-85 °C. The fluidity is represented as an Arrhenius-like expression that includes a static dielectric constant dependence in the exponential prefactor. The dielectric constant dependence results from the dependence of mass and charge transport on the molecular dipole moment and the solvent dipole density. The CAF is the only self-consistent description of fluid transport in polar liquids written solely in terms of molecular and system parameters. A scaling procedure is used to calculate the activation energy for transport. We find that the activation energies for fluidity of the aprotic liquids are comparable in value, whereas a higher average E(a) value is observed for the n-alcohol data. Finally, we contrast the molecular description of transport presented here with the conventional hydrodynamic model.

Ion transport with charge-protected and non-charge-protected cations using the compensated Arrhenius formalism. Part 2. Relationship between ionic conductivity and diffusion.

Temperature-dependent ionic conductivities and cation/anion self-diffusion coefficients are measured for four electrolyte families: TbaTf-linear primary alcohols, LiTf-linear primary alcohols, TbaTf-n-alkyl acetates, and LiTf-n-alkyl acetates. The Nernst-Einstein equation does not adequately describe the data. Instead, the compensated Arrhenius formalism is applied to both conductivity and diffusion data. General trends based on temperature and alkyl chain length are observed when conductivity is plotted against cation or anion diffusion coefficient, but there is no clear pattern to the data. However, plotting conductivity exponential prefactors against those for diffusion results in four distinct curves, one each for the alcohol and acetate families described above. Furthermore, the TbaTf-alcohol and TbaTf-acetate data are "in line" with each other. The conductivity prefactors for the LiTf-alcohol data are smaller than those for the TbaTf data. The LiTf-acetate data have the lowest conductivity prefactors. This trend in prefactors mirrors the observed trend in degree of ionic association for these electrolytes.

Molecular and system parameters governing mass and charge transport in polar liquids and electrolytes.

Onsager's model of the dielectric constant is used to provide a molecular-level picture of how the dielectric constant affects mass and charge transport in organic liquids and organic liquid electrolytes. Specifically, the molecular and system parameters governing transport are the molecular dipole moment µ and the solvent dipole density N. The compensated Arrhenius formalism (CAF) writes the temperature-dependent ionic conductivity or diffusion coefficient as an Arrhenius-like expression that also includes a static dielectric constant (ε(s)) dependence in the exponential prefactor. The temperature dependence of ε(s) and therefore the temperature dependence of the exponential prefactor is due to the quantity N/T, where T is the temperature. Using the procedure described in the CAF, values of the activation energy can be obtained by scaling out the N/T dependence instead of the ε(s) dependence. It has been previously shown that a plot of the prefactors versus ε(s) results in a master curve, and here it is shown that a master curve also results by plotting the prefactors against N/T. Therefore, the CAF can be applied by using temperature-dependent density data instead of temperature-dependent dielectric constant data. This application is demonstrated for diffusion data of n-nitriles, n-thiols, n-acetates, and 2-ketones, as well as conductivity data for dilute tetrabutylammonium triflate-nitrile electrolytes.

Ion transport with charge-protected and non-charge-protected cations in alcohol-based electrolytes using the compensated Arrhenius formalism. Part I: ionic conductivity and the static dielectric constant.

The temperature dependence of ionic conductivity and the static dielectric constant is examined for 0.30 m TbaTf- or LiTf-1-alcohol solutions. Above ambient temperature, the conductivity increases with temperature to a greater extent in electrolytes whose salt has a charge-protected cation. Below ambient temperature, the dielectric constant changes only slightly with temperature in electrolytes whose salt has a cation that is not charge-protected. The compensated Arrhenius formalism is used to describe the temperature-dependent conductivity in terms of the contributions from both the exponential prefactor σo and Boltzmann factor exp(-Ea/RT). This analysis explains why the conductivity decreases with increasing temperature above 65 °C for the LiTf-dodecanol electrolyte. At higher temperatures, the decrease in the exponential prefactor is greater than the increase in the Boltzmann factor.

Temperature dependence of ion transport in dilute tetrabutylammonium triflate-acetate solutions and self-diffusion in pure acetate liquids.

Conductivities and static dielectric constants for 0.0055 M tetrabutylammonium trifluoromethanesulfonate in n-butyl acetate, n-pentyl acetate, n-hexyl acetate, n-octyl acetate, and n-decyl acetate have been collected over the temperature range of 0-80 °C. Self-diffusion coefficients and static dielectric constants of pure acetates were obtained over the same temperature range. Both temperature-dependent diffusion coefficients and ionic conductivities of these pure acetates and dilute acetate solutions can be accurately described by the compensated Arrhenius formalism. Activation energies were calculated from compensated Arrhenius plots for both conductivity and diffusion data. Activation energies are higher for conductivity data of 0.0055 M TbaTf-acetates compared to diffusion data of pure acetates. The plot of the exponential prefactor versus the dielectric constant yields a single master curve for both conductivity and diffusion data. These data support the argument that mass and charge transport are thermally activated processes in the acetates, as previously observed in alcohol-based electrolytes.

Application of the compensated Arrhenius formalism to self-diffusion: implications for ionic conductivity and dielectric relaxation.

Self-diffusion coefficients are measured from -5 to 80 degrees C in a series of linear alcohols using pulsed field gradient NMR. The temperature dependence of these data is studied using a compensated Arrhenius formalism that assumes an Arrhenius-like expression for the diffusion coefficient; however, this expression includes a dielectric constant dependence in the exponential prefactor. Scaling temperature-dependent diffusion coefficients to isothermal diffusion coefficients so that the exponential prefactors cancel results in calculated energies of activation E(a). The exponential prefactor is determined by dividing the temperature-dependent diffusion coefficients by the Boltzmann term exp(-E(a)/RT). Plotting the prefactors versus the dielectric constant places the data on a single master curve. This procedure is identical to that previously used to study the temperature dependence of ionic conductivities and dielectric relaxation rate constants. The energies of activation determined from self-diffusion coefficients in the series of alcohols are strikingly similar to those calculated for the same series of alcohols from both dielectric relaxation rate constants and ionic conductivities of dilute electrolytes. The experimental results are described in terms of an activated transport mechanism that is mediated by relaxation of the solution molecules. This microscopic picture of transport is postulated to be common to diffusion, dielectric relaxation, and ionic transport.

Application of the compensated arrhenius formalism to dielectric relaxation.

The temperature dependence of the dielectric rate constant, defined as the reciprocal of the dielectric relaxation time, is examined for several groups of organic solvents. Early studies of linear alcohols using a simple Arrhenius equation found that the activation energy was dependent on the chain length of the alcohol. This paper re-examines the earlier data using a compensated Arrhenius formalism that assumes the presence of a temperature-dependent static dielectric constant in the exponential prefactor. Scaling temperature-dependent rate constants to isothermal rate constants so that the dielectric constant dependence is removed results in calculated energies of activation E(a) in which there is a small increase with chain length. These energies of activation are very similar to those calculated from ionic conductivity data using compensated Arrhenius formalism. This treatment is then extended to dielectic relaxation data for n-alkyl bromides, n-nitriles, and n-acetates. The exponential prefactor is determined by dividing the temperature-dependent rate constants by the Boltzmann term exp(-E(a)/RT). Plotting the prefactors versus the static dielectric constant places the data on a single master curve for each group of solvents.

Temperature dependence of ion transport: the compensated Arrhenius equation.

The temperature-dependent conductivity originating in a thermally activated process is often described by a simple Arrhenius expression. However, this expression provides a poor description of the data for organic liquid electrolytes and amorphous polymer electrolytes. Here, we write the temperature dependence of the conductivity as an Arrhenius expression and show that the experimentally observed non-Arrhenius behavior is due to the temperature dependence of the dielectric constant contained in the exponential prefactor. Scaling the experimentally measured conductivities to conductivities at a chosen reference temperature leads to a "compensated" Arrhenius equation that provides an excellent description of temperature-dependent conductivities. A plot of the prefactors as a function of the solvent dielectric constant results in a single master curve for each family of solvents. These data suggest that ion transport in these and related systems is governed by a single activated process differing only in the activation energy for each family of solvents. Connection is made to the shift factor used to describe electrical and mechanical relaxation in a wide range of phenomena, suggesting that this scaling procedure might have broad applications.

Concentration dependence of ionic transport in dilute organic electrolyte solutions.

Ion transport is studied in dilute organic liquid electrolyte solutions in which close cation-anion interactions are minimized either through steric hindrance imposed by the bulky tetrabutylammonium cation or by strong solvation of alkali metal cations by DMSO or 1-propanol. In these solutions, the molar conductivity does not appear to depend on either the solvent viscosity or the size of the solvated charge carrier in a manner consistent with Walden's rule. The molar conductivities plotted as a function of the solvent dielectric constant from epsilon = 5.48 to 63.5 appear to lie on a smooth curve for a set of 0.0055 M solutions of tetrabutylammonium trifluoromethanesulfonate in a variety of aprotic solvents. The molar conductivity smoothly increases with increasing dielectric constant to a maximum at roughly epsilon = 33 and then decreases with further increase of the dielectric constant. The conductivity appears to depend only on the dielectric constant and not the specific functional group in this broad family of solvents. A similar plot for a series of linear alcohols as solvents also led to a smooth curve, although the values of the molar conductivity were lower than values in the aprotic solvents by almost an order of magnitude at corresponding values of the solvent dielectric constant.

Investigation of fundamental transport properties and thermodynamics in diglyme-salt solutions.

Ionic mobility, the thermodynamics of ionic association, and the structure of associated species are studied in solutions of diglyme containing either lithium triflate or tetrabutylammonium triflate. Infrared spectroscopic, PFG NMR, thermodynamic, and crystallographic data suggest that the solute species existing in diglyme-lithium triflate are "free" ions, contact ion pairs, and dimers. Equilibrium constants, S(o), deltaH(o), and deltaG(o) are calculated for processes occurring between these species. In particular, the equilibrium constant, corrected for nonideality using a modified Debye-Hückel expression, is calculated for the dissociation of contact ion pairs into "free" cations and anions. A second equilibrium constant for the formation of dimers from contact ion pairs is also calculated; these constants do not significantly vary with salt concentration up to about 1.3 x 10(-3) mol cm(-3). The measured temperature dependence of equilibrium constants was used to calculate deltaH(o) and deltaS(o) for the two processes. The value of deltaS(o) = -102 J mol(-1) K(-1) for the dissociation of contact ion pairs shows that the large entropy decrease due to cation solvation outweighs the entropy increase due to dissociation of a contact ion pair. Ionic mobilities are calculated in lithium triflate-diglyme solutions using conductivity data in conjunction with information about the nature and concentrations of solute species obtained from IR spectroscopy. Mobilities in tetrabutlyammonium triflate-diglyme solutions are calculated directly from conductivity data. It was concluded that the concentration dependence of the molar conductivity is due in large part to the variation of the ion mobilities with concentration.