Calculations: Single Electrode
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| Supporting Information
Scalable Self-Grown of Ni@NiO Core-Shell Electrode with Ultrahigh Capacitance and Super Long Cyclic Stability for supercapacitors Minghao Yu, Wang Wang, Cheng Li, Teng Zhai, Xihong Lu*, and Yexiang Tong* Calculations: 1. Single Electrode : Areal capacitances of the ANF electrodes were calculated from their CVs according to the following equation:  (1)
where Ca (F/cm2) is the areal capacitance, Q (C) is the average charge during the charging and discharging process, ∆V (V) is the potential window and S (cm2) is the area of ANF electrode. Alternatively, areal capacitances of electrodes were measured by galvanostatic charge/discharge method based on the following equation:
where Ca (F/cm2) is the areal capacitance, I (A) is the constant discharging current, Δt is the discharging time, ΔV (V) is the potential window, and S (cm2) is the surface area 2. ANF//Graphene@NF-ASC Devices: The cell (device) capacitance (Ccell) and volumetric capacitance of the VN-based devices were calculated from their CVs according to the following equation:  (3)
 (4)
where Q (C) is the average charge during the charging and discharging process in the applied current, V (cm3) is the volume of the whole device (The area and thickness of our ANF//Graphene@NF-ASC device is about 0.5 cm2 and 0.2 cm. Hence, the whole volume of our ANF//Graphene@NF-ASC device is about 0.1 cm3), Δt (s) is the discharging time, ΔV (V) is the voltage window. It is worth mentioning that the volumetric capacitances were calculated taking into account the volume of the device stack. This includes the electrode and the separator with electrolyte. Alternatively, the cell (device) capacitance (Ccell) and volumetric capacitance (Cv) was estimated from the slope of the discharge curve using the following equations:
where I (A) is the applied current, V (cm3) is the volume of the whole device (the whole volume of our ANF//Graphene@NF-ASC device is about 0.1 cm3, and the volume of compressed ANF//Graphene@NF-ASC device is about 0.06 cm3 ), Δt (s) is the discharging time, ΔV (V) is the voltage window. Volumetric energy density, equivalent series resistance and power density of the devices were obtained from the following equations:
where E (Wh/cm3) is the energy density, CV is the volumetric capacitance obtained from Equation (5) and ΔV (V) is the voltage window. ESR (Ω) is the internal resistance of the device. P (W/cm3) is the power density. 3. Balance the charge of electrodes in ASC device: As for a SC, the charge balance will follow the relationship q+ = q-. The charge stored by each electrode depends on the capacitance (Cs), the potential range for the charge/discharge process (  E) and the area of the electrode (A) follows the Equation (10):
q = Cs × E × m (10)
In order to get q+ =q– at 100 mV s-1, the area balancing between ANF and Graphene@NF electrode will be calculated as follow: 
The calculated CA(Graphene@NF) is 1.02 F cm-2, ∆E (Graphene@NF) is 0.8 V, CA(ANF) is 1.27 F cm-2, and ∆E (ANF) is 0.6 V. Therefore, the calculated areal ration between the ANF electrode and Graphene@NF electrode is about 1.07 : 1. 
Fig. S1. (a) Digital photos of pristine NF. (b) Digital photos of activation process of NF, insets are comparison of HCl solution before and after activation process. 
Fig. S2. XRD spectra of NF and ANF. 
Fig. S3. (a) CV curves of NF electrode collected at various scan rates. (b) Areal capacitance as a function of the scan rate of the NF and ANF electrodes. Galvanostatic charge/discharge curves collected at different current densities for (c) NF electrode and (d) ANF electrode. 
Fig. S4. (a) CV curves of ANF electrode after 30000 cycles collected at various scan rates. (b) Galvanostatic charge/discharge curves of ANF electrode after 30000 cycles collected at different current densities. 
Fig. S5. (a) SEM images of ANF electrode after 100000 cycles. (b) Raman spectra of ANF electrode after 30000 cycles and after 100000 cycles. 
Fig. S6. (a)SEM images of RGO electrode. (b) CV curves collected at various scan rates for RGO electrode. 
Fig. S7. CV curves collected for RGO and ANF after 30000 cycles CV test at 100 mV-1 electrodes collected at a scan rate of 100 mV s-1. 
Fig. S8. Cycling performance collected at a scan rate of 100 mV s-1 for the ANF//RGO-ASC device with potential windows of 0.5 V, 1.1V and 1.5 V. 
Fig. S9. (a) CV curves collected at various scan rates for ANF//RGO-ASC device electrode. (b) Volumetric capacitance as a function of the scan rate of the ANF//RGO-ASC device. Fig. S9 shows the CV curves of the as-prepared ANF//RGO-ASC device collected from 10 to 100 mV s-1. The highest volumetric capacitance obtained from CV curves reached 3.36 F cm-3 at 10 mV s-1, which is considerably higher than most of recently reported ASCs at the same scan rate, such as MnO2/RGO//RGO-ASC device (0.89 F cm-3)[1], VOx//VN-ASC device (1.30 F cm-3)[2], TiO2@MnO2//TiO2@C-ASC device (0.71 F cm-3)[3], ZnO@MnO2//RGO-ASC device (0.52 F cm-3)[4], ZnO@MnO2//GO-ASC device (0.40 F cm-3) [4].
1. T. Zhai, F. Wang, M. Yu, S. Xie, C. Liang, C. Li, F. Xiao, R. Tang, Q. Wu, X. Lu and Y. Tong, Nanoscale, 2013, 5, 6790. 2. X. Lu, M. Yu, T. Zhai, G. Wang, S. Xie, T. Liu, C. Liang, Y. Tong and Y. Li, Nano Lett., 2013, 13, 2628. 3. X. Lu, M. Yu, G. Wang, T. Zhai, S. Xie, Y. Ling, Y. Tong and Y. Li, Adv. Mater., 2013, 25, 267. 4. Z. L. Wang, Z. Zhu, J. Qiu and S. Yang, J. Mater. Chem. C, 2014, 2, 1331.
Fig. S10. Galvanostatic charge/discharge curves of compressed ANF//RGO-ASC device 
Fig. S11. (a) Volumetric capacitance for the compressed ANF//RGO-ASC device as a function of current density. (b) Comparison of the ragon plots between ANF//RGO-ASC device and compressed ANF//RGO-ASC device. The thickness of ANF//RGO-ASC device could be compressed from 0.2 cm to 0.12 cm. |
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