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Batteries 2022, 8, 108 11 of 16 −1 −1◦ FigureFi7g.uNrey7q. NuiysqtupisltoptslootsfoHf CHCelelcectrtrode aftteerrddififfefrernetntumnubmersboefrscyocflecsyactl1e0s0amtA10g0 m(Aa) 1g0 (Ca,) 10 °C, ◦◦◦ 25 °C,(b(c) )2540C°,C(c)a4n0d C(da)n8d0(d°)C8.0 C. In the low frequency part of the data, the Warburg impedance corresponding to In the low frequency part of the data, the Warburg impedance corresponding to sodium ion diffusion and its diffusion coefficient (DNa+) could be calculated with the dium ion diffusion and its diffusion coefficient (𝐷 ) could be calculated with the follo following equation [43]: ing equation [43]: D = R2T2/2A2n4F4C2σW2 where σ is the Warburg factor, which is related to the real part of the impedance (Z W 𝐷 𝑅𝑇⁄2𝐴𝑛𝐹𝐶𝜎 re is a function of square root of frequency (ω is a function of square root of frequency (ω −1/2) expressed as: At the beginning of the galvanostatic cycling, SEI layers are gradually built up, −1/2 ) expressed as: re where σW is the Warburg factor, which is related to the real part of the impedance (Zre). Zre =Rs+Rct+σWω−1/2 (5) 𝑍 𝑅 𝑅 𝜎 𝜔/ which will affect diffusion (FiguresS13 and S14). After19 galvanostatic cycles, the bat- teries become stable and their sodium ion diffusion coefficients from 10 to 80 ◦C are Ashtotwhne ibneFgiginunreinS1g5o. Wf thenginaclvreansionsgttahteictecmypcleirnagtu,rSe,EtIhelaayversagaereDgradinucraelalysebs ufriolmt up, wh Na+ 1.14 × 10−12 cm2 s−1 at 10 ◦C to 4.62 × 10−12 cm2 s−1 at 80 ◦C. Furthermore, D + and will affect diffusion (Figures S13 and S14). After 19 galvanostatic cycles,Ntha e batteries thermal activities can be described with the Arrhenius equation [44]: come stable and their sodium ion diffusion coefficients from 10 to 80 °C are shown Figure S15. When increasing the temperature, the average 𝐷 increases from 1.14 × 1 DNa+ = D0exp(−Ea/RT) (6) cm2 s−1 at 10 °C to 4.62 × 10−12 cm2 s−1 at 80 °C. Furthermore, 𝐷 and thermal activit where D is the exponential prefactor and E is the activation energy. Overall, ln(D + ) and 0 a Na can be described with the Arrhenius equation [44]: the reciprocal of temperature exhibit a linear relationship (R2 = 0.983) in Figures 8 and S16, −1 ◦ ◦ with 16.13 kJ mol activation energy. Although the electrolyte precipitates EC below 𝐷 𝐷𝑒𝑥𝑝𝐸⁄𝑅𝑇 25 C and degrades above 50 C, it does not affect DNa+ , which related to the temperature. wherMe oDre0oivsert,hlaergeexDpon+epnrtoiavlidpesrefafsatcetroNraantrdanEspa oisrt tahned caacntievnahtaioncne ethneecragpya.ciOtyvweirtahlal, ln(𝐷 Na+ large current rate at high temperature. 2 andthereciprocaloftemperatureexhibitalinearrelationship(R =0.983)inFigures8a Figure 9a shows the HC electrode galvanostatic oxidation capacity with multiple S16, with 16.13 kJ mol−1 activation energy. Although the electrolyte precipitates EC bel current rates at 25, 40 and 60 ◦C (reduction in Figure S17). After stabilising at 100 mA g−1 25 °C and degrades above 50 °C, it does not affect 𝐷 , which re−l1ated to the temperat current density for 20 cycles, it exhibits 240, 205, 112, 55 and 41 mA h g specific capacity for 50, 100, 200, 500 and 1000 mA g−1 current density at 25 ◦C, respectively. The battery tested at 40 ◦C shows the highest capacity at 50 and 100 mA g−1 (260 and 240 mA h g−1) and increases of 80 and 10 mA h g−1 in the capacity at 200 mA g−1 and 500 mA g−1 compared with the battery at 25 ◦C (respectively). Moreover, even though the battery at 60 ◦C shows less specific capacity with 50 and 100 mA g−1 currents compared with at 40 ◦C, it displays the highest capacity at a large current rate (200, 120 and 55 for 200, 500 and (4) ). Z s i b 0 o uPDF Image | Temperature Dependence of Hard Carbon Sodium Half-Cells
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