Ion transport in liquid electrolytes

For many years ion transport has been viewed as a hydrodynamic process where ion size and solvent viscosity are the primary factors controlling the movement of ions in solution. However, it will be shown for the electrolytes studied here that the isothermal parameters of interest are the following: (1) the concentration of "free" ions, (2) the solvent dielectric constant, and (3) the solvent functional group. The temperature dependence of ionic conductivity for liquid electrolytes and polymeric electrolytes above the glass transition temperature has also been studied for many years. These conductivities do not follow Arrhenius behavior like those which are observed for solid glassy electrolytes. Therefore, the temperature-dependent conductivities of liquid and amorphous polymer electrolytes are usually represented by empirical equations. However, an empirical representation of the data provides no insight into the fundamental aspects of ion transport. Here, for a family of liquid electrolytes, the temperature-dependent conductivity is written as an Arrhenius expression and it is shown that the experimentally observed non-Arrhenius behavior is due to the temperature dependence of the dielectric constant contained in the exponential prefactor. Scaling the temperature-dependent conductivities to conductivities at a chosen reference temperature so that the dielectric constant remains invariant leads to a "compensated" Arrhenius equation that provides an excellent description of the data, implying that ion transport is governed by a single activated process. An energy of activation Ea can be extracted from the compensated Arrhenius plot for each family of solvents. Dividing the temperature-dependent conductivities by the factor exp(-Ea/RT), where Ea is determined from the compensated Arrhenius plot, gives the prefactors. Plotting the prefactors versus the temperature-dependent solvent dielectric constant results in all of the data points falling on a single "master curve"

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

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 (<i>E</i>_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 <i>n</i>-acetates, 2-ketones, <i>n</i>-nitriles, and <i>n</i>-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 <i>E</i>_a value is observed for the <i>n</i>-alcohol data. Finally, we contrast the molecular description of transport presented here with the conventional hydrodynamic model

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

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, <i>E</i>_a, and an exponential prefactor containing the temperature-dependent solution dielectric constant, ε_s(<i>T</i>). Both 1- and 3-alcohols show the <i>E</i>_a of diffusion coefficients (approximately 43 kJ mol^–1) is higher than the <i>E</i>_a 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, <i>g</i>_k. 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