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"

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 °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 Ea. The exponential prefactor is determined by dividing the temperature-dependent diffusion coefficients by the Boltzmann term exp(−Ea/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

Applying the Compensated Arrhenius Equation to Concentrated Alcohol Electrolytes

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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