Density, viscosity, ionic conductivity, and self-diffusion coefficient of organic liquid electrolytes: Part I. Propylene carbonate + Li, Na, Mg and Ca cation salts

1Department of Environmental Chemistry and Chemical Engineering, School of Advanced Engineering, Kogakuin University, Hachioji-shi, Tokyo 192-0015, Japan 2Institute of Applied Physics, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan 3National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki 305-8568, Japan 4Graduate School of Science and Technology, Niigata University, Nishi-ku, Niigata 950-2181, Japan

Research and development of lithium-ion batteries (LIBs) have focused on the efficient use of energy. Application fields of LIBs are spreading from portable commercial use (mobile phone and laptop PC) to large-scale energy systems (electric vehicle and accumulator for household use). 1 Furthermore, the usages (utilities, needs, requirements and demands) of industrial-scaled electricity storage systems using LIBs are increasing for applications alongside renewable energy systems (photovoltaics and/or wind energy) and frequency regulation demands. However, resources and stock amounts of Li are limited. Another reactive cationic species, such as high Clarke number Na + (2.63, 6th) and divalent cations Mg 2+ (1.93, 8th) and Ca 2+ (3.39, 5th) have been reported as new cationic species for next-generation batteries (Li + : 0.0006, 27th). 2 The number of reports for battery operations using a Na (sodium) system is increasing, and they have focused on the research and development of electrode and electrolyte materials for, mainly, positive electrodes. [3][4][5] Because of the differences of ionic radii between Li + (60 pm) and Na + (95 pm), understanding the effects of ionic radii on electrolyte properties is important. 6,7 In addition, comparison between monovalent cations and divalent cations (Mg 2+ : 65 pm, 8 Ca 2+ : 99 pm 9 ) is also important to understand the effects of valence number of cation on the electrolyte properties. In this study, an electrolyte solutions of propylene carbonate (PC) and N(SO 2 CF 3 ) 2 − ([TFSA] − ) anion-based metal (Li, Na, Mg and Ca) salts were prepared and evaluated by measuring their physicochemical properties. We investigate the dependence of static (density) and dynamic (macroscopic fluidity: viscosity, ionic mobility: ionic conductivity and microscopic ionic diffusivity: self-diffusion coefficient) properties of electrolytes on the cationic metal species of salts (ionic radii and valence number) and salt concentrations. We also analyze the intermolecular interactions of the cations with PC and [TFSA] − by ab initio molecular orbital calculations. Using the mearurements of static and dynamic properties and analysis of interactions, the expectations of innovative next-generation battery systems are discussed.

Experimental
Materials.-PC (Kishida Chemical, battery grade) and metal cation salts (Table I) were used as the solvent and dissolved salts for electrolyte solutions, respectively. These materials were stored in a dry-argon-filled glove box. Amounts of PC and salts were weighed and mixed in a sample bottle, which allow us to obtain a homogeneous Measurements.-Density (ρ / gcm −3 ) and viscosity (η/mPas) were measured using a thermoregulated Stabinger-type viscosity and density/specific gravity meter ((Anton Paar, SVM3000G2, accuracy: 5 × 10 2 g m −3 ). The measurements were performed during cooling from 353.15 to 283.15 K at 5 K intervals with an airtight stopper to avoid moisture and air contamination. The samples were thermally equilibrated at each temperature for at least 15 min prior to the measurement.
The ionic conductivity (σ) was measured on [stainless steel (SUS)/electrolyte solution sample/SUS] hermetically sealed cells and determined by the complex impedance method using an AC impedance analyzer (Bio-Logic VSP, 200 kHz -50 mHz; impressed voltage: 10 mV) at temperatures between 353.15 and 283.15 K at 10 K intervals while cooling the samples in a thermoregulated incubator (ESPEC, SU-262). The samples were thermally equilibrated at each temperature for at least 90 min prior to the measurement.
The self-diffusion coefficient (D) was measured by a pulsedgradient spin-echo nuclear magnetic resonance (PGSE-NMR) method using a Tecmag Apollo-NTNMR and a wide-bore 6.4 T SCM equipped with a JEOL pulsed-field gradient multiprobe. The samples were inserted into a 5 mm (outer diameter) NMR microtube (BMS-005J, Shigemi). The spectra of the solvent (PC), lithium cation and various anions were measured using 1 H, 7 Li and 19 F atoms at frequencies of 270.2, 105.0 and 254.2 MHz, respectively. The attenuation of the echo signal E was obtained by varying the duration δ of the pulsed-field gradient multiprobe at a fixed amplitude g. D was determined by the regression of the Stejskal-Tanner equation 10 Computational methods.-The Gaussian 09 program 11 was used for the ab initio molecular orbital calculations with the basis sets implemented in the Gaussian program. The geometries of the complexes were fully optimized at the MP2/6-311G * * level. 12 The intermolecular interaction energies (E int ) were calculated at the MP2/6-311G * * level by the supermolecule method using the optimized geometries. The basis set superposition error (BSSE) 13 was corrected for all the interaction energy calculations using the counterpoise method. 14 15 show that the basis set effects on the calculated interaction energies of the complexes are very small if basis sets including polarization functions are used and that the effects of electron correlation beyond MP2 are negligible. Therefore, we calculated the interaction energies of the complexes at the MP2/6-311G * * level in this work. The stabilization energy for forming a complex from the isolated species (E form ) was calculated as the sum of the E int and the deformation energy (E def ), which is the sum of the increase in energy due to the deformation of the PC or [TFSA] − anion during formation of the complex. 16 Here, the E def was calculated at the MP2/6-311G * * level. The electrostatic and induction energies were calculated using ORIENT version 3.2. 17 The electrostatic energy of the complex was calculated as interactions between distributed multipoles of the molecules. Distributed multipoles 18 up to the hexadecapole on all atoms were obtained from the MP2/6-311G * * wave functions of an isolated molecule using the GDMA program. 19 The induction energy was calculated as interactions of polarizable sites with the electric field produced by the distributed multipoles of monomers. 20 The atomic polarizabilities of carbon (α = 10 au), nitrogen (α = 8 au), oxygen (α = 6 au), fluorine (α = 3 au) and sulfur (α = 20 au) were used for the calculations. 21 Distributed multipoles were used only to estimate the electrostatic and induction energies.

Results and Discussion
Static properties.-To investigate the relationships between the physicochemical properties and dissolved cation species, the temperature dependences of various physicochemical parameters were measured. Figure 1a shows the temperature dependence of the ρ for electrolyte solutions of PC and metal-containing TFSA salts at 0.5 and 1.0 mol kg −1 . Highly linear relationships (R > 0.999) with temperature were obtained for all samples in the temperature range examined in this study, and the inclination of the calculated straight line was almost similar in all electrolyte systems. The measured ρ monotonically increased in the order Li[TFSA] < Na[TFSA] < Mg[TFSA] 2 < Ca[TFSA] 2 at all temperatures with the atomic weight of cationic metals. Figure 1b shows the salt concentration dependence of the ρ at 303.15 K for electrolyte solutions of PC and metal-containing TFSA salts. The ρ showed slightly convex upward tendency with salt concentration, and the deviation of the above-mentioned order was not confirmed. Furthermore, a divalent cationic salt system standardizes a subscript by the TFSA concentration as 0.5, and also this standardization was useful for the comparison of between monovalent and divalent cation salts to normalize the amounts of total ions.  Figure 2b shows the salt concentration dependence of η at 303.15 K for    Figure 3a shows the temperature dependences of the σ for electrolyte solutions of PC and metal-containing TFSA salts at 0.5 and 1.0 mol kg −1 as Arrhenius-type plots. The obtained σ indicates similar values for all the salt systems, which is different from that of the η results. Generally, σ in a unit volume is defined as σ = j n j q j μ j , [2] where n, q and μ are the number, charge and mobility of the carrier ions in the specific volume, respectively. The suffix j corresponds to the metal cation and TFSA anion. In this case, i.e., q = 1 (Li + and Na + cation and [TFSA] − anion) or 2 (Mg 2+ cation and Ca 2+ cation), σ values should depend on n (related to the carrier density and ionic dissociation) and μ (related to the viscosity and ionic diffusion constants). Figure 3b shows the salt concentration dependence of σ at 303.15 K for electrolyte solutions of PC and metal-containing TFSA salts. The local maximum of the σ were observed for a salt concentration between 0.5 and 1.0 mol kg −1 in all electrolyte systems. Moreover, the Na[TFSA] system indicated the highest σ of all salt concentrations. The Na[TFSA] system showed the lowest η for all the salt systems ( Figure 2), therefore, it achieved the highest σ. Figure 4 shows the temperature dependences of the self-diffusion coefficients of the solvent (D PC , a), cation (D cation , lithium only, b) and anion (D TFSA , c) for electrolyte solutions of PC and TFSA salts at 1.0 and 2.0 mol kg −1 as Arrhenius-type plots. Because of the large quadrupolar constant of 23 Na, 25 Mg and 43 Ca from the viewpoint of NMR measurements, D cation was obtained only from the LiTFSA system ( 7 Li: small quadrupolar constant and high sensitivity). Ds of all diffusive species were decreased with the increase of salt concentrations, 22 and the order of the Ds were D PC > D TFSA > D cation in all electrolyte systems. The smaller D PC (Li + ) than D PC (Na + ) may be related to larger solvation energy around cation. Moreover, temperature dependences of D showed the same tendencies as those for η (inverse) and σ. The order of the D depending on the salt species is close to that of η.  as that of σ. Lager salt concentration dependence of D was observed in the solution of divalent metal cation salts compared with the solution of monovalent ones. Figure 6 shows the relationships between salt concentration and molar conductivity ( ) at 303.15 K for electrolyte solutions of PC and TFSA salts. Although the difference of the absolute value for all was very small, increased with the enlargement of cation size for both the monovalent (Li[TFSA] < Na[TFSA]) and divalent (Mg[TFSA] 2 < Ca[TFSA] 2 ) cases. Moreover, the monovalent system indicated a little higher than that of the divalent system. The is controlled by the transport properties of electrolyte systems, if the molar concentration is the same. In this study, we measured the η, σ and D of the prepared electrolyte solutions and all the observed data were affected by μ, which is strongly related with valence number and size of the metal cation. Moreover, all the electrolyte systems showed a weak electrolyte-type dissociation behavior, which rapidly decreased with the increase of salt concentration.

Diffusive properties and ionic state of electrolytes.-
To analyze the correlations between the transport and ionic conduction properties, Figure 7a shows the relationships between (a) the inverse of viscosity (fluidity: η −1 ) and ionic conductivity (σ) of   a Energy in kcal/mol. Geometries of complexes are shown in Figure S1.   In this study, we reported the measurement results and analysis of new cationic electrolyte solution including Na, Mg and Ca. There is a needed for new carrier ionic sources in next-generation batteries, and interfacial phenomena with electrodes are also important in battery technologies. We will report the analysis of electrode interfaces between electrolytes including new metal cationic salts/metallic electrodes from the viewpoint of application.

Conclusions
Density, viscosity, ionic conductivity, and self-diffusion coefficient of PC + various cation salts (cation: Li, Na, Mg, Ca; anion: TFSA) salt were measured and analyzed systematically. Density was well correlated with molecular weight and valence of the metal salt. The inverse of viscosity (macroscopic fluidity), ionic conductivity and self-diffusion coefficient were increased with cationic sizes in both monovalent and divalent systems. These values of the monovalent cationic systems were larger than those of divalent ones.