*2.3. Characterization*

The N2 adsorption isotherms of APHS were measured with a BELSORP-max (BEL JAPAN, Toyonaka, Japan) at liquid nitrogen temperature. For pore analysis, all samples were degassed at 573 K for 6 h with the residual pressure maintained at 10−<sup>3</sup> torr, or less. The specific surface area was calculated for the relative pressure interval of 0.03–0.19 using the Brunauer-Emmett-Teller (BET) equation. [28] The total pore volume, VTotal, was calculated from N2 adsorption data as the volume of liquid N2 at a relative pressure of 0.99. The mesopore volume, VMeso, was determined by the Barrett-Joyner-Halenda (BJH) method, and the micropore volume, VMicro, was obtained by subtraction of the mesopore volume from the total pore volume. Micropore and mesopore size and distribution were calculated using the non-local density functional theory (NLDFT) [29] and BJH method [30], respectively. The microstructure of the APHS was determined using an X-ray di ffractometer (XRD, X'Pert Pro Di ffractometer, PANalytical, Almelo, The Netherlands), employing a Rigaku SmartLab X-ray di ffractor with a customized auto-mount and a Cu K α (λ = 1.5406 Å) radiation source. Di ffraction patterns were collected within the di ffraction angles from 5◦ to 90◦ at a rate of 2◦/min. The interlayer spacing (d002, d10*l*) of the samples were calculated using Bragg's Law (2dsinθ = nλ) to the position of the (002) and (10*l*) peak, respectively. The size of crystalline under the Scherrer equation [31] can be expressed as follows:

$$\mathcal{L} = \frac{\mathcal{K}\lambda}{\mathcal{B}\cos\theta} \tag{1}$$

In this equation, the constant K is 0.9 and 1.84 when calculated from crystalline height (Lc) and crystalline diameter (La), respectively. λ is the wavelength of the X-ray, and B is the full width at half maximum (FWHM) calculated from the radian.

#### *2.4. Electrochemical Measurements*

The slurry was prepared by mixing 80 wt% active materials (activated HC, APHS), 10 wt% conductive agents (carbon black, Super P, TIMCAL, Bodio, Switzerland), 10 wt% binder (carboxymethyl cellulose and styrene-butadiene rubber) dispersed in water. The slurries were coated on the aluminum foil using a doctor blade technique. The thickness of the coating layer was controlled to 127 μm. The coated foils were then first dried in an oven at 80 ◦C for over one hour. To remove any remaining water, the electrodes were further dried in a vacuum oven at 120 ◦C overnight. After the drying was completed, the electrodes were roll pressed to a thickness of less than 80 μm using a two-roll press at 80 ◦C.

For electrochemical testing, a CR2032 coin cell consisting of two punched electrodes 12 mm in diameter, punched cellulose paper separators 16 mm in diameter (NKK, Kochi, Japan), and 1M (C2H5)4NBF4/propylene carbonate (1M TEABF4/PC) were used. All cell assembly was carried out in a dry room where the dew point was below 60.0 ◦C.

The fifth cycle of galvanostatic charge/discharge (GCD) and the second cycle of cyclic voltammetry (CV) were used to evaluate the electrochemical performance of the samples. The GCD was charged at 10 mA and then discharged at 2 mA (0.1–2.4 V) for the coin cell using a charge/discharge tester (Maccor 4300 K, Maccor, Tulsa, OK, USA). CV and impedance spectrometry (EIS) were analyzed using a potentiostat (Bio-Logic VSP, Bio-Logic Science Instruments, Seyssinet-Pariset, France). CV studies were performed in the same potential range of GCD at a scan rate of 30 mV/s. The impedance Nyquist plots were recorded in the frequency range 10 mHz to 300 kHz. The cells produced were measured based on the capacitance per unit weight, and calculated only using the weight of active materials (F/g). The specific capacitance was calculated according to the GCD based on the following equation:

$$\mathbf{C}\_{\mathcal{B}} = \mathbf{i}\Delta\mathbf{t}/\mathbf{m}\Delta\mathbf{V} \tag{2}$$

where i is the discharge current (A), Δt is the discharge time (s), m is the mass of the electrode (g), and ΔV is the potential di fference (V).
