Alkali-Metal Insertion Processes on Nanospheric Hard Carbon Electrodes: An Electrochemical Impedance Spectroscopy Study

In this study, we report the results of electrochemical impedance spectroscopy data modelling of various battery half-cells with different alkali metal (Li, Na, K) salts. Test results of electrochemical half-cells were evaluated for the D-glucose derived hard carbon negative electrode in 1.0 M LiPF6 + EC:DMC (1:1 volume ratio), 1.0 M NaPF6 + EC:DMC (1:1), 1.0 M NaClO4 + PC, 0.8 M KPF6 + EC:DEC (1:1) and 0.8 M KPF6 + EC:DMC (1:1) solutions at 0.5 mV s−1 potential scan rate measured within the potential region from 0.05 V to 1.2 V (vs Me/Me+) (where Me is Li, Na or K). Modelling of electrochemical impedance spectroscopy data was employed to characterize alkali metal insertion processes in/on D-glucose derived hard carbon anode. Detailed analysis of impedance data shows that Newman equivalent circuit modified with a constant phase element can be applied for calculation of impedance spectra and fitting of calculated data to experimental ones, using non-linear least square root fitting method. Equivalent circuit fit parameters depend strongly on electrolyte composition. Very slow processes have been observed for KPF6 + EC:DEC based half-cell. Comparatively quick metal-cation reduction and accumulation processes have been observed in NaClO4 + PC and LiPF6 +EC:DMC based half-cell anodes. © 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: 10.1149/2.0431711jes] All rights reserved.

Lithium-ion batteries (LIBs) are currently dominating the global portable electronics and electric vehicles market, but as the demand for LIBs rises, lithium (Li) supply might soon become the limiting factor to LIB production. 1 Li and cobalt (Co) supply are under risk according to a study by British Geological Survey. 2 The matter gets even worse as the need for grid-scale energy storage increases with the integration of intermittent renewable technologies such as photovoltaics and wind into the grid. Thus, a large-scale implementation of energy storage requires a battery technology that is based on cheap and abundant raw materials. Fortunately, potential alternatives do exist, because both sodium (Na) and potassium (K) have only slightly different electrochemical properties than Li and are 1000 times more abundant in the Earth's crust than Li. [3][4][5] While the first sodium-sulfur batteries (Na-S) date back to 1968, 6 intensive research on room-temperature sodium-ion batteries has only started in recent years. 4 Hard carbons (HCs) are currently the most promising and simplest anode materials for sodium-ion batteries (NIBs). They are extensively investigated and used in some commercial Na-ion battery cells. 7 Although, there are numerous papers analyzing the synthesis and electrochemical characterization of hard carbons in Li-, [8][9][10][11][12][13][14][15][16] Na-ion [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31] battery cells, only some papers on K-ion 32,33

battery (KIB) cells have been published.
There are no systematic studies on how the same carbon electrode performs in half-cells with all three Li + , Na + and K + cation containing electrolytes and how the metal cation properties affect the charge-transfer kinetics on/in the electrode.
Carbon anode materials are generally divided into three classes: graphite, non-graphitized glass-like carbon (hard carbon) which cannot be graphitized even when heat-treated at very high temperature, and soft carbon which can be modified with heat-treatment. 34 The theoretical capacity of Li intercalation into graphite is 372 mAh g −1 (850 mAh cm −3 ) based on the reaction to form the LiC 6 compound: Li + + 6C + e − → LiC 6 . 35 However, the electrochemical sodiation/desodiation capacity of graphite is only ∼35 mAh g −1 by forming NaC 64 . [36][37][38] As demonstrated by recent theoretical calculations, the interlayer distance of graphene layers in graphite (∼0.34 nm) is too small to accommodate the large Na + ion. A minimum interlayer distance of 0.37 nm is believed to be required for Na + intercalation into graphite-like materials. 39 Due to the large size of K-ions, 0.272 nm, it has been assumed that bulk carbon anodes could not take in K-ions electrochemically. Wang et al. reported reversible electrochemical insertion of potassium into non-graphitic carbon nanofibers at room temperature. 40 Jian and co-workers found that graphite exhibits surprisingly high capacities of 475 and 273 mAh g -1 in potassiation and depotassiation steps, respectively and the depotassiation capacity is very close to the theoretical value of 279 mAh g -1 when KC 8 forms. 41 Jian et al. investigated hard carbon microspheres (HCS) as an anode for KIBs and compared its performance to NIBs. HCS shows a high capacity of 262 mAh g −1 with 83% of capacity retention over 100 cycles in KIBs. Even at 2C and 5C charge/discharge rates, the capacity remains at 190 and 136 mAh g −1 , respectively. These results suggest that some types of hard carbon can be promising anodes not only for NIBs, but also for KIBs. 33 It is believed that the insertion of alkali metal in hard carbon electrodes corresponds to the filling of micropores (voids) and smaller mesopores in the carbon by nanoclusters of Li, Na or K. 37 Electrochemical impedance spectroscopy (EIS) is well-established as a powerful tool for investigating the mechanism of electrochemical reactions, for measuring the dielectric and transport properties of materials, for exploring the properties of porous electrodes, and for investigating passive surfaces. [43][44][45][46][47][48][49] J. Newman has conducted very detailed analysis of porous carbon electrodes in non-aqueous LIB electrolytes. [45][46][47][48][49] Some limiting cases have been demonstrated depending on the porosity (pore size distribution, electrolyte concentration, etc).
The most common and fundamental source of capacity fade in successful Li-ion batteries (which manage to resist degradation over hundreds of cycles) is the loss of lithium to the solid-electrolyte interphase (SEI), which typically forms at the negatively charged electrode during recharging. 50 NIBs and LIBs are both subject to the same limitations in the anode-electrolyte interfacial reaction; the solid electrolyte interphase (SEI) on an anode with the electrochemical potential below ∼1 V vs Na/Na + is vital to make a NIB kinetically stable. 51,52 There are good empirical reasons to suspect that the dissolution of the SEI in NIBs is more of a challenge than that in LIBs. Firstly, sodium salts can have very different solubilities than their lithium analogues in the same solvent 53,54 and secondly, there is some evidence from propylene carbonate based systems (a work by Aurbach and coworkers 55 ), where sodium perchlorate in propylene carbonate is shown to produce a substantial amount of soluble decomposition products while LiClO 4 and KClO 4 do not.
To our knowledge, EIS with equivalent circuit (EQC) modeling in a wide state-of-charge (SOC) range has only been used to characterize LIBs and NiMHs. [56][57][58][59][60] Zhang et al. employed EIS and subsequent modelling to determine how various EQC resistance components such as bulk resistance (R b ), solid-state interface resistance (R SEI ) and charge-transfer resistance (R ct ) contribute to the total cell resistance in a LIB cell 59 and how R SEI varies in according to LIB half-cell SOC in different electrolyte mixtures. 58 Greenleaf and Zheng compared two commercial 18650 LIB cells by measuring EIS at a various SOCs and then employed physical electric circuit modelling to understand which processes take place in bigger commercial cells. 60 The purpose of this article is to broaden the application of electrochemical impedance spectroscopy from LIBs to NIBs and KIBs.

Experimental
Chemicals, reagents and experimental.-The synthesis and physical characterization of the electrode material has been described in detail in our previous work. 22 The SEM image ( Fig. 1) of the synthesized powder was acquired using Helios Nanolab 600 and HR-TEM image ( Fig. 1 inset) using Tecnai 12 instrument, operated at 120 kV accelerating voltage. The electrochemically active hard carbon powder was mixed with Super P (Alfa Aesar) and polyvinylidene difluoride (PVDF) in a 75:15:10 weight ratio and stirred overnight using Nmethyl-2-pyrrolidone (NMP, Sigma-Aldrich, 99.5%) as the solvent. The resulting mixture was cast onto copper foil using the doctor blade technique. The cast electrodes were dried under vacuum at 120 • C for 24 h. The electrochemical performance of half-cells was evaluated at 23 ± 0.5 • C using EL-Cell Combi (EL-CELL GmbH) stainless steel cell. Measurements were carried out using the following electrolytes: commercially prepared solution (battery grade, Aldrich) of 1.0 M LiPF 6 in 1:1 volume ratio of ethylene carbonate (EC) and dimethyl carbonate (DMC), 1.0 M NaClO 4 (98%, Sigma-Aldrich) solution in propylene carbonate (PC, 99.7%, Sigma-Aldrich), 1.0 M NaPF 6 (99%, Alfa Aesar) or 0.8 M KPF 6 (99%, abcr GmbH) in 1:1 volume ratio of ethylene carbonate (EC, 99%, Sigma-Aldrich) and dimethyl carbonate (DMC, 99%, Sigma-Aldrich) and 0.8 M KPF 6 in EC and diethyl carbonate (DEC, 99%, Aldrich), respectively. The counter electrode in each cell was the same metal as the salt cation, i.e. Li for LiPF 6 , Na for NaClO 4 and NaPF 6 , and K for KPF 6 . A thick glass fiber separator (thickness 1.55 mm, EL-Cell GmbH) was used in all measurements to avoid cell shorting due to dendrite formation. All test cells were assembled inside an Ar-filled glove box (MBraun, O 2 < 0.1 ppm and H 2 O < 0.1 ppm).

Electrochemical experiments.-All electrochemical experiments
were carried out using potentiostat/galvanostat/frequency response analyzer PMC-1000 (Princeton Applied Research). Test cells were evaluated using cyclic voltammetry (CV), galvanostatic charging/discharging (GCD) and electrochemical impedance spectroscopy (EIS). Measurements were set up and controlled using VersaStudio 2.49 software platform. EIS spectra were acquired after 200 mV potential steps between 1.0 V and 0.4 V and after 25 mV steps between 0.4 and 0.04 V vs Me/Me + . Three charge and discharge cycles were completed in such a way. Data analysis and scripting was carried out using OriginPro 2016 software. ZView 3.5b was used for equivalent circuit fitting. Li + or Na + reduction and Li and Na oxidation peaks between 0.01 V and 0.2 V in Li-or Na-salt based electrolytes. The reduction peak is attributed to reduction of Li + or Na + and accumulation/insertion of Li or Na into the voids (porous network) in hard carbon, while the oxidation peak signifies their removal and Li + or Na + cation formation (Figs. 2a and 2b). In the case of KPF 6 , the linear carbonate composition (DMC or DEC) appears to have a strong effect on the electrochemical process at the electrode surface (Fig. 2c). With DMC there is very low electrochemical activity -current density is low throughout the CV cycle. A slight reduction peak at 0.05 V vs K/K + is visible, but no sign of oxidation on the cathodic scan. On the other hand, DEC produces much higher current densities with clearly visible reduction and oxidation peaks, although the voltage hysteresis is bigger than with Li-or Na-based half-cells and current density is lower. Such a difference between DMC and DEC could be caused by a stronger coordination between K + and DMC than between K + and DEC. For that reason, 0.8 M KPF 6 + EC:DMC electrolyte data are not used in the impedance analysis below.

Results and Discussion
Both Li-and Na-based half-cells showed high reversibility as illustrated by 1.0 M NaClO 4 + PC system in Fig. 2d.
Galvanostatic charge/discharge data (Figs. 3a-3c) highlights differences between the studied cells' efficiencies, capacities and chargestorage mechanisms. LiPF 6 + EC:DMC system produces sloping charge/discharge curves with no plateaus (Fig. 3a), which is commonly observed for hard carbon|Li cells. 38,42 Only a slight deviation from capacitor-like linear E -Q response can be observed, which suggests that the charge storage mechanism is almost purely adsorptive. The calculated capacity at 1.0 V vs Li/Li + is 180 mAh g -1 , which is a moderate value for LIB anodes based on carbon. Furthermore, the absence of any plateaus decreases its applicability as an anode in a LIB cell, since the full cell would not have a stable voltage. In addition, the capacity loss during the first cycle is 35%. Such capacity loss is often attributed to high electrolyte consumption by the SEI layer formation on amorphous carbons with high specific surface areas (SSA) and high content of surface functional groups. 61 The GDHC used in this study has a BET SSA of 200 m 2 g -1 , which is significantly more than that of graphite (≤ 10 m 2 g -1 ), commonly used in LIBs. 22,62 On the other hand, sodium based cells produce galvanostatic profiles (Fig.  3b) with a single plateau at low potential (E < 200 mV vs Na/Na + ) followed by a sloping curve up to 1.0 V vs Na/Na + . Compared to NaPF 6 + EC:DMC, NaClO 4 + PC electrolyte produces superior cell performance in all aspects -higher cumulative discharge capacity (204 vs 139 mAh g -1 ), higher capacity at E < 200 mV vs Na/Na + Figure 2. Cyclic voltammograms of the tested half-cells at fixed potential scan rate 0.5 mV s -1 , for systems based on Li (a), Na (b), K (c), the first three cycles for NaClO 4 + PC system (d).
(109 vs 63 mAh g -1 ) and lower irreversible capacity (10% vs 15%). Ideally, all of the anode capacity should come from charge storage at E < 100 mV to enable constructing a full cell with both high voltage and capacity.
Potassium-based half-cells are very different from Li and Na cells (Fig. 3c). Charge/discharge curves are sloping, there is high hysteresis of voltage between charge and discharge plateaus and capacities are low, 105 and 58 mAh g -1 , for DEC and DMC based solvent, respectively. An IR-drop of 77 mV can be observed when switching from charging to discharging mode, unlike with Li-and Na-cells, where such voltage drops are barely noticeable. The cycling performance of the studied half-cells was evaluated at current densities ranging from 25 mA g −1 to 100 mA g −1 (Fig. 3d). The specific capacity values from the first 25 discharge cycles (Fig. 3d) were highest for 1.0 M NaClO 4 + PC system with an exception at 100 mA g -1 , where LiPF 6 + EC:DMC showed better rate capability.

Electrochemical impedance spectroscopy measurements and non-linear fitting of impedance data.-Various equivalent circuits
(EQCs) have been tested for fitting the impedance data of the halfcells, but three best ones (Figs. 4a-4c) were selected for comparison ( Fig. 5 and Table I) to determine the most applicable EQC for fitting the data. We considered an EQC by Zhang et al. 58,59 (Fig. 4c) which they have used to evaluate bulk or series resistance (R s ), solid electrolyte interface resistance (R SEI ) and charge-transfer resistance (R ct ) values in LIB cells. Also, we tested EQC developed by Newman and Meyers et al. 46 (Fig. 4b) which has been proved to model the real physical processes in model porous intercalation electrodes. Since the Meyers et al. model fits impedance data at frequencies only above 0.05 Hz, it has been slightly modified (hereafter named modified Newman) by replacing the double-layer capacitance with a constant phase element (CPE) 63,64 in the equivalent circuit for analysis of double layer formation/relaxation at porous energetically heterogeneous carbon surface consisting of graphitic (sp 2 ) and amorphous sp 3 areas. In the modified Newman EQC (Fig. 4a), R s is the high-frequency resistance of the half-cell, which corresponds to the total resistance of the electrolyte, separator and electrodes; R SEI and C SEI are resistance and capacitance of the SEI, which corresponds to the semicircle at high frequencies. R ct and CPE are charge transfer resistance and distributed double layer capacitance/resistance expressed as a constant phase element, which corresponds to the semicircle at medium frequencies. Finite-length Warburg impedance (Z Ws ) is related to an effect of the diffusion of Li + , Na + or K + ions in/on the porous electrode electrolyte interfaces, respectively.
The shape of impedance spectra depends strongly on the cell potential applied and EIS spectra consists of two partially overlapped and depressed semicircles. However, at some electrode potentials the second semicircle has been screened by the Warburg-like finite-length mass-transfer impedance behavior or mixed kinetics, i.e. by finitelength adsorption and mass-transfer effects (mainly at E ≥ 0.37 V), where there are no quick faradaic processes at the electrode surface or in the porous electrode bulk. Although finite-space Warburg element would also be applicable, 65 we cannot really discriminate between finite-length and finite-space Warburg elements due to absence of well-developed semicircles. According to the fitting results of 1.0 M NaPF 6 + EC:DMC system, presented in Fig. 5 and Table I, the CPE modified Newman EQC shows the best fitting results (smaller χ 2 and error %). Therefore, only modified Newman circuit is used for fitting the impedance data in this study. Also, using the EQC given in Fig. 4a  enables better comparison with our previous data on Li + , Na + , Cs + cations based electrolyte|CDC carbon interface. 63,66,67 Table II summarizes R s values for the tested half-cells at 0.04 V and 1.0 V vs Me/Me + for three tested cycles. For consecutive cycles, R s values of each half-cell differ only slightly, which shows that all half-cells have good reversibility and therefore, only the first cycle spectra have been analyzed in detail.
The   I  II  III  I  II  III   1 Comparison of data in Figs. 6-9 shows that processes in KPF 6 electrolyte containing halfcells are noticeably slower than those for Li + or Na + cation based electrolytes and for 0.8 M KPF 6 + EC:DEC system, the very low ac frequency finite-length adsorption area (region) in log|Z |, logf plot has not been developed.
The results of non-linear regression analysis show that experimental Nyquist plots for all systems can be simulated with high accuracy and with chi-square functions (Fig. 10) χ 2 ≤ 5 × 10 −3 , with the exception of NaPF 6 based system showing χ 2 values above 0.01.
The calculated SEI resistance (R SEI ) and capacitance (C SEI ) values (Figs. 11a and 11b) for the GDHC|vLi, GDHC|Na or GDHC|K halfcells depend on the solvent system used. R SEI decreases in the order of alkali metal (Me) / GDHC half cells in the order: LiPF 6 < NaClO 4 < KPF 6 < NaPF 6 .    The constant phase element fractional exponent α CPE values ( Fig.  12a) are nearly independent of E, but α CPE ≈ 0.8 values indicate that the mixed adsorption step and mass-transfer step limited kinetics takes place within 0.4 < E < 0.04 V region. At E > 0.5 V, for NaPF 6 + EC:DMC system, α CPE → 1 indicates that adsorption step rate limited processes dominate in the system. The highest CPE constant (A) values have been calculated for the same system (Fig. 12b). Surprisingly, very low A values have been calculated for KPF 6 + EC:DEC electrolyte based half-cells.
Charge transfer resistance, R ct , values (Fig. 13a) are very high (2500-3500 cm 2 ) for 1.0 M LiPF 6 + EC:DMC (1:1) based system which can be explained with the reduction of Li + ions, as well as SEI formation on GDHC electrode porous surface. For Na-and K-salt based half-cells, the R ct values are quite small (<500 cm 2 ) because there is no formation of resistive SEI layer on the metal|electrolyte interface.
It is clear that the mass-transfer and finite length adsorption process rates, as well as faradaic electro-reduction/re-oxidation process rates depend noticeably on the electrolyte composition (Li + , Na + , K + ), solvents used and the applied electrode potential.
The diffusion resistance (R D ) values (Fig. 13b) depend noticeably on the system studied and R D values are highest for KPF 6 + EC:DEC, but lowest for LiPF 6 + EC:DMC and NaPF 6 + EC:DMC system. R D values vary in great extent for 1.0 M NaClO 4 + PC system, where the highest Warburg-like diffusion impedance fractional exponent α W ≥ 0.8 values have been calculated at different E. Surprisingly, for KPF 6 + EC:DEC and LiPF 6 + EC:DMC based systems Figure 11. Solid electrolyte interface resistance (R SEI ) (a) and solid electrolyte interface capacitance (C SEI ) vs E (b) for the tested half-cells (noted in figure). Potential values correspond to respective alkali-metal potentials (Me/Me + ).  ) unless CC License in place (see abstract). ecsdl.org/site/terms_use address. Redistribution subject to ECS terms of use (see 193.40.12.10 Downloaded on 2017-07-04 to IP α W ≈ 0.5 (characteristic of semi-infinite diffusion model) have been calculated (Fig. 13c). The very high R D and α W ≥ 0.75 values for KPF 6 + EC:DEC electrolyte based system, calculated from impedance data, are in agreement with the shape of the CVs, where very low current densities (very slow faradaic and mass-transfer processes) have been observed. The slower K + reduction and K oxidation/re-oxidation kinetics established by CV method (Fig. 2c) are in agreement with impedance data.

Conclusions
Electrochemical D-glucose derived hard carbon based half-cells were evaluated as negative electrodes in 1.0 M LiPF 6 + EC:DMC (1:1 volume ratio), 1.0 M NaPF 6 + EC:DMC (1:1), 1.0 M NaClO 4 + PC, 0.8 M KPF 6 + EC:DEC (1:1) and 0.8 M KPF 6 + EC:DMC (1:1) solutions at 0.5 mV s −1 potential scan rate, measured within the potential region from 0.05 V to 1.2 V (vs Me/Me + ) (where Me is Li, Na or K) using cyclic voltammetry, galvanostatic charging/discharging and electrochemical impedance spectroscopy methods. Modelling of electrochemical impedance spectroscopy data was employed to characterize alkali metal insertion processes in/on D-glucose derived hard carbon anode. Cyclic voltammetry data show that Li + , Na + and K + reduction intercalation kinetics depend noticeably on the solvent composition and on the applied electrode potential. At fixed E and composition, slow faradaic processes and mass-transfer processes at/in K|KPF 6 + EC:DEC interface have been observed. Using non-linear least square root fitting method detailed analysis of impedance data shows that modified Newman equivalent circuit (where C dl replaced with CPE) can be applied for calculation of impedance spectra and fitting these to the experimental ones. Equivalent circuit parameters depend on the electrolyte composition (both the salt and solvents) and very slow processes have been observed for KPF 6 + EC:DEC based half-cell. Comparatively quick metal-cation reduction and accumulation (adsorption) processes have been observed in NaClO 4 + PC and LiPF 6 + EC:DMC based half-cells.