Compensated Arrhenius Formalism Research Articles

Effects of Methylating Imidazolium-Based Ionic Liquids on Viscosity: New Insights from the Compensated Arrhenius Formalism.

Methylation of the C(2) carbon on imidazolium-based room temperature ionic liquids (RTILs) causes an unexpected increase in viscosity when paired with the anion bis(trifluoromethylsulfonamide) [Tf2N]-, but the viscosity decreases when the methylated imidazolium is paired with a tetracyanoborate [B(CN)4]- anion. This paper investigates these different observations in viscosity using the compensated Arrhenius formalism (CAF) for fluidity (inverse viscosity), which assumes fluidity to be a thermally activated process. CAF activation energies are determined for imidazolium [Tf2N]- and methylated imidazolium [Tf2N]- and compared to imidazolium [B(CN)4]- and methylated imidazolium [B(CN)4]-. The results show that the activation energy increases with methylation for [Tf2N]-, but it decreases with methylation for [B(CN)4]-. The CAF results also yield information concerning the entropy of activation, which are compared for the two systems.

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.

Compensated Arrhenius formalism applied to a conductivity study in poly(propylene glycol) diacrylate monomers.

The temperature dependence of the ionic conductivity is studied in a series of poly(propylene glycol) diacrylate monomers. The experimental data are analyzed by means of the approach recently proposed by Petrowsky etal. [J. Phys. Chem. B. 113, 5996 (2009)10.1021/jp810095g]. This so-called compensated Arrhenius formalism (CAF) approach takes into account the influence of the dielectric permittivity on the exponential prefactor in the classical Arrhenius equation. The experimental data presented in this paper show a good agreement with the CAF; this means that the exponential prefactor is principally dielectric permittivity dependent. The compensated data revealed two conduction processes with different activation energies; they correspond to low and high temperature ranges, respectively.

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.

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.

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.Electronic supplementary materialThe online version of this article (doi:10.1007/s10953-013-9983-z) contains supplementary material, which is available to authorized users.

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 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.

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.

Extending the compensated Arrhenius formalism to concentrated alcohol electrolytes: Arrhenius vs. non-Arrhenius behavior

The compensated Arrhenius formalism is applied to ionic conductivities in alcohol-based electrolytes at concentrations where the salt makes a non-negligible contribution to the static dielectric constant of the solution. The temperature-dependent behavior of the conductivity depends on the amount of added salt. Non-Arrhenius behavior is observed for low to moderate salt concentrations, while Arrhenius behavior occurs at high concentrations. The compensated Arrhenius formalism provides insight into this behavior by analyzing the effect of salt concentration on the temperature dependence of the exponential prefactor. When the compensated Arrhenius prefactors are plotted against the solution static dielectric constants using the E a obtained from the compensated Arrhenius equation, the prefactors lie on a single master curve. In contrast, a similar plot based on the E a obtained from a simple Arrhenius plot of the same conductivity data does not yield a master curve. Application of the compensated Arrhenius formalism requires the construction of a reference curve. It is essential that the range of static dielectric constant values spanned by the reference curve encompasses the range of temperature-dependent static dielectric constant values of the selected alcohol electrolyte. This will allow an accurate interpolation to obtain the appropriate reference conductivity. A detailed description is given for the method used to construct an appropriate reference conductivity curve.

Examining the Correlation between Ionic Conductivity and Diffusion Coefficients in Organic Liquid Electrolytes Using the Compensated Arrhenius Formalism

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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.