Spectroscopic and Electrochemical Analyses for Neodymium Complexes in Potassium Bis(trifluoromethylsulfonyl)amide Melts

The coordination states of the multivalent neodymium complexes in potassium bis(trifluoromethyl-sulfonyl) amide; K[TFSA] were investigated by Raman spectroscopy. The concentration dependences of deconvoluted Raman spectra were investigated for 0.23–0.45 mol kg−1 Nd(III), and mixed sample of Nd(II)/Nd(III) = 1/3 at the molar ratio in K[TFSA]. According to the conventional analysis, the solvation number; n of neodymium complexes were determined to be n = 4.06 for Nd(II), 5.02 for Nd(III). Moreover, thermodynamic properties such as isoG, isoH, and isoS for the isomerism of [TFSA]− from transto cis-coordinated isomer were evaluated from temperature dependence of Raman bands. In the first solvation sphere of Nd3+ cation, isoH(Nd) became remarkably negative, suggesting cis-[TFSA]− isomers were stabilized by enthalpic contributions. Then, isoH(Nd) contributed to the remarkable decrease in isoG(Nd), and this result clearly indicates cis-[TFSA]− conformers bound to Nd3+ cations are preferred coordination state of [Nd(III)(cis-TFSA)5]2−. Furthermore, the electrochemical analysis revealed the reduction process proceeded in two steps; [Nd(III)(TFSA)5]2− + e− → [Nd(II)(TFSA)4]2− + [TFSA]− and [Nd(III)(TFSA)5]2− + 3e− → Nd(0) + 5[TFSA]−. The diffusion coefficient of [Nd(II)(TFSA)4]2− was larger than that of [Nd(III)(TFSA)5]2− on the range of whole temperature. The activation energies of [Nd(II)(TFSA)4]2− and [Nd(III)(TFSA)5]2− were 29.5 kJ mol−1 and 49.8 kJ mol−1, respectively. © The Author(s) 2017. Published by ECS. This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 License (CC BY, http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse of the work in any medium, provided the original work is properly cited. [DOI: 10.1149/2.0361708jes] All rights reserved.

Rare earth (RE) elements have peculiar physicochemical properties and are indispensable for abrasives, catalysts, fluorescent materials and permanent magnets. [1][2][3][4] In particular, Nd-Fe-B permanent magnets have high ferromagnetic performance and it has been used for a variety of high-tech products, such as voice coil motors in hard disk drives, magnetic field sources for magnetic resonance imaging, driving motors for hybrid-type electric vehicles etc. [5][6][7] From the standpoint of energy conservation, the development of a recovery process for RE metals with reduced energy consumption is desired. In previous investigations, we demonstrated the recovery of Nd metal using low-temperature molten salts (LTMSs), 8,9 because an LTMS has many useful physicochemical properties 10,11 such as a wide electrochemical window, low liquid-phase temperature, and high ionic conductivity. From an environmental point of view, LTMSs are stable compared to organic reagents and prevent the spreading of noxious decomposition chemicals because LTMSs can be recycled back into acid production cycles and be applied repeatedly as an electrolytic bath. Potassium bis(trifluoromethylsulfonyl) amide; K[TFSA] melts consisting of a potassium cation and a bis(trifluoromethyl-sulfonyl)amide; [TFSA] anion, as shown in Fig. 1, are useful candidates for LTMSs.
In the case of the ionic liquids (ILs), it was known that the electrodeposition process was remarkably affected by the solvation structure of metal ion. It was reported that the solvation structures of various metal ions, Li, [12][13][14][15][16] Mn, 17,18 Fe, 19 Co, 17,19 Ni, 17,19 Zn, 17 Nd, 20,21 Eu 22 and Dy 23 ions in [TFSA]-based ionic liquids (ILs) were evaluated by Raman spectroscopy and DFT calculations. We also demonstrated that the solvation structures and the electrochemical behaviors of trivalent Nd and Dy cations in order to reveal the electrodeposition mechanism in our previous study. 20,24 In our findings, the reduction process of trivalent Dy cations proceeded in two steps by way of divalent of Dy cations [Dy(III) + e − → Dy(II), Dy(II) + 2e − → Dy(0)], because the [Dy (III) (TFSA) 5 ] 2− and [Dy (II) (TFSA) 4 ] 2− in ILs were confirmed by Raman spectroscopic analysis and DFT calculations. 23 However, there were no information about the detailed solvation conformations of Nd(II) and Nd(III) in K[TFSA] melts. Therefore, we have inves-tigated the solvation number and the isomeric characteristic of the [TFSA] − ligand of Nd(II) and Nd(III) complexes by means of Raman spectroscopic analysis in this study. Moreover, the activation energy of diffusion process for Nd(II) and Nd(III) in K[TFSA] melts was also investigated in this study. In this way, the methodology both spectroscopic and electrochemical analyses enables us to deeply understand the coordination states of Nd(II) and Nd(III) complexes in K[TFSA] melts.

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and 0.45 mol kg −1 , respectively. The samples containing each Nd(III) concentration were heated at 473 K before Raman spectroscopic measurement and the homogeneous liquid phase at 473 K was quenched into the quartz tube. The silver substrate with the hole on the center was used for Raman spectroscopic measurement with heating system. It is appropriate to use the silver substrate, because the thermal conductivity of silver was extremely high. The quenched Nd(III) sample was recovered and set on the center of the silver substrate in the glove box (H 2 O and O 2 <10 ppm). The heating system (LKM-10033, Japan High Tech Co., Ltd) was based on Proportional-integral-derivative (PID) control method in this study. The temperature monitoring system was used for non-contact infrared radiation thermometer. Raman spectra (NRS-4100, JUSCO Corp.) were measured at elevated temperatures using a 532-nm laser for Nd. The calibration on a Raman spectroscopic measurement was confirmed for standard Si sample each time. The focusing of a laser beam was confirmed by the position which is inside approximately 5 μm from the edge of silver substrate. The appropriate gratings for the collection of the Raman spectra were 1800 mm −1 for Nd. These conditions were adopted to prevent fluorescence of the Nd ions, and the selection of the gratings is based on the results of our recent investigations. 19,20 In order to analyze the solvation number of Nd(II) in K[TFSA], according to the previous study using ILs 23 the mixed samples of Nd(II)/Nd(III) complexes for Raman spectroscopy were prepared by the controlled potential electrolysis (CPE) method based on the electrochemically reduction reaction. The induced overpotential on the working electrode was maintained at +2.0 V vs. (K/K + ) during CPE. Pt disk electrode with surface area: 2.0 × 10 −5 m 2 was employed as a working electrode. Pt wire with 0.5 mm inside diameter was used as a quasi-reference electrode (QRE). A counter electrode of Pt wire with 0.5 mm inside diameter was isolated from the electrolyte with ceramic glass filter in order to prevent the decomposition of the bulk sample. After where f L (ν) and f G (ν) stand for the Lorentzian and Gaussian components, respectively, and the parameter γ (0 < γ < 1) is the fraction of the Lorentzian component. The intensity I of a single Raman band is evaluated according to I = γ I L + (1 -γ)I G , where I L and I G denote integrated intensities of the Lorentzian and Gaussian components, respectively. A nonlinear least square curve-fitting program was applied in this study.
Electrochemical measurement.-The K[TFSA] melts including Nd(III) (molar fraction:x Nd = 0.1) were applied as the electrolyte for the electrochemical experiment and this solution was dried at 373 K in a vacuum chamber (<0.1 MPa) for 24 h. The water content of the electrolyte was <50 ppm, as measured by a Karl-Fischer coulometric moisture titrator (MKC-610-DT, Kyoto Electronics Manufacturing Co., Ltd.). Cyclic voltammetry (CV) at different temperatures (473, 478, 483, 488 and 493 ± 1.0 K) was carried out using a cylindrical cell constituted from three-electrode system with an electrochemical analyzer (BAS Inc., ALS760D) under Ar flow. The Pt electrode (surface area: 6.91 × 10 −5 m 2 ) was selected as a working electrode that was mirror polished using alumina paste (d = 0.05 μm). Platinum wires (ϕ = 0.7 mm) were used as a counter electrode and a quasireference electrode (Q.R.E) because the potential obtained using a Pt Q.R.E was stable and exhibited a good reproducibility at medium temperatures. As a preliminary experiment, the K/K + redox peak was clearly appeared in cyclic voltammogram for K[TFSA] melts without Nd(III). The potential which the K/K + redox peak intersects y-axis; current: i(K/K + ) = 0 can conventionally determine the potential on the redox reaction K/K + couple. All the potentials reported herein were compensated for the redox reaction of K/K + couple.
Calculation methods.-DFT calculation of the anion components of the K[TFSA] was carried out using the Gaussian09 program. 25 The calculation on model of [trans-TFSA] − and [cis-TFSA] − ions were performed at the B3LYP/6-311G(d,p) level. Subsequently, frequency analysis was carried out on the optimized geometry. The hybrid functional B3LYP, which includes a mixture of Hartree-Fock exchange and DFT exchange-correlation, is Becke's three-parameter hybrid method(B3) 26 with non-local correlation provided by the Lee, Yang, and Parr (LYP) functional. 27

Results and Discussion
Analysis of the solvation number.-Theoretical Raman spectrum (red line) for the optimized geometry of [TFSA] − by DFT calculation and raw data (blue line) of Raman spectrum for Nd(III) sample at 478 K was shown in Fig. 2. It was confirmed that there was no overlapping with Raman bands from [TFSA] − . Then, the raw and deconvoluted bands of Raman spectrum for Nd(III) sample at 478 K in the frequency range of 720-770 cm −1 was shown in Fig. 3. The band at 740 cm −1 is ascribed to the coupled bending δ(CF 3 ) + stretching ν(S-N-S) vibration of free [TFSA] − , which shifts to a higher frequency upon binding of [TFSA] − to the metal ion. 28,29 The concentration dependences of the deconvoluted Raman spectra in the frequency range 720-780 cm The   In order to perform a quantitative evaluation based on thermodynamics about [TFSA] − isomers, the apparent thermodynamic quantities; iso G, iso H and T iso S were determined from van't Hoff plots analysis. 13 The parameters of iso G, iso H and T iso S from the trans-[TFSA] − to cis-[TFSA] − as a function x Nd can be defined as follows. As the first step, the apparent equilibrium constant, K iso for the [TFSA] − conformational isomerism from the trans-[TFSA] − to cis-[TFSA] − as a function x Nd was defined as K iso = c cis /c trans . Using this equilibrium constant, K iso , iso G was represented as follows.
iso G = −RT ln K iso = −RT ln (c cis /c trans ) [ 2 ] where R and T were a gas constant and an absolute temperature, respectively. In addition, iso G can be expressed as iso G = iso H − T iso S and the Raman intensity; I is I = Jc. When these two equations were substituted for iso G = −RT ln (c cis /c trans ), the following van't Hoff equation 13 was obtained.
− R ln (I cis /I trans ) = iso H/T − iso S − R ln (J cis /J trans ) [3] where Then, the value of iso S was also evaluated from the intercept of the van't Hoff plot. It is necessary to consider the J cis /J trans ratio and this value was estimated by means of the relationship of I cis = -(J cis /J trans ) I trans + J cis c T . 13 From the slope of the plots of I trans against I cis , it was experimentally determined that the value of J cis /J trans ratio was 0.68. In order to confirm the reliability of this value (0.68), the theoretical calculation for the value of J cis /J trans ratio using DFT method was carried out. The theoretical value of J cis /J trans ratio estimated by DFT method was 0.69. Thus, an experimental value was in good accordance with a theoretical value with high accuracy, so that we applied this value to evaluate the entropy term; iso S. All obtained thermodynamic quantities; iso G, iso H and T iso S were plotted against the x Nd as shown in Fig. 7. It was suggested that apparent thermodynamic quantities; iso X (X = G, H and S) existed as a function of x Nd(III) because the lin-  . That is to say, the apparent thermodynamic quantities; iso X (X = G, H and S) were expressed as the following equation. 13 iso X = nx Nd(III) iso X (Nd) + (1 − nx Nd(III) ) iso X (bulk) [4] where n stands for the solvation number of Nd(III), n = 5.02. Therefore, from the relationship of Eq. 4, the values of iso X at x Nd(III) = 0 and 0.33 are iso X(bulk) and iso X(Nd), respectively, as shown with the broken lines in Fig. 7. Thermodynamic quantities for [TFSA] − of the bulk and the first solvation sphere of Nd 3+ cation were listed in Table I Nd (III) (TFSA) 5 2− + 3e − → Nd (0) + 5[TFSA] − peak (B) [6] Regarding each peak based on the cathodic Reactions 5 and 6, it was confirmed that the plot of the cathodic peak of the current density; j p vs. the square root of the scan rate; v 1/2 showed a good linear relations. This result indicated that both of two reduction reactions were controlled by the diffusion process; the mass transport under semi-infinite linear diffusion conditions. Elucidation of the diffusion behavior of [Nd (III) (TFSA) 5 ] 2− in K[TFSA] melts as well as the reduction behavior is necessary in order to perform the electrodeposition of Nd metal; thus, we evaluated the diffusion coefficients of [Nd (III) (TFSA) 5 ] 2− in K[TFSA] melts. The diffusion coefficients were analyzed by SI and SD methods. Initially, the SI curve (solid line) was obtained from convolutional voltammogram for [Nd (III) (TFSA) 5 ] 2− (x Nd = 0.1) in K[TFSA] melts as shown in Fig. 9. The diffusion coefficients were calculated from the limiting current, m * according to the following equation: 31 where n is the number of electrons involved in the charge transfer reaction, F is the Faraday constant, A is the electrode surface area, and C * is the bulk concentration of the electroactive species. As seen from Fig. 9, SD curve (chain line) was also obtained from the voltammogram by SD method. The value of W p ; the width of a derivative neopolarographic peak at half its height, and e p ; the current semi-derivative at the peak of the derivative neopolarogram, were determined from the SD curve. The diffusion coefficients were calculated using the following equations 32 that were established in the case of the irreversible reaction: The obtained diffusion coefficients by SD analysis were relatively close to the value derived from SI analysis. This congruence suggests high reliability of the calculated diffusion coefficients of [Nd (III) (TFSA) 5 ] 2− in K[TFSA] melts derived from SI and SD analyses. Then, we evaluated the activation energy for diffusion, E A,D using the diffusion coefficients with temperature dependence. The transfer of the metallic cations in the electrolysis was generally affected by the electrostatic interaction of the ion constituting metal complexes. Therefore, the diffusion of the metallic cations in K[TFSA] melts needs the activation energy more than the dissociation energy with surrounding anions constituting the metal complexes. The value of E a,D is derived from the following Arrhenius rule: [10] where A * is the frequency factor, R the gas constant, and T the absolute temperature. Moreover, the thermodynamic stability for [TFSA] − isomerism was evaluated from the van't Hoff plots from the temperature dependence of the Raman spectra. The thermodynamic properties such as iso G, iso H and iso S for the isomerism of [TFSA] − from trans-to cis-isomer in bulk and the first solvation sphere of the centered Nd 3+ cation in K[TFSA] were calculated in the range of 298-398 K. In the first solvation sphere of Nd 3+ cation, iso H(Nd) increased to the negative value (−47.42 kJ mol −1 ) remarkably and revealed that the cis-[TFSA] − isomers were stabilized for enthalpy. iso H(Nd) contributed to the remarkable decrease in the iso G(Nd) and this result indicated that the cis-[TFSA] − bound to Nd 3+ cation was preferentially stabilized and the coordination state of [Nd (III) (cis-TFSA) 5