*2.2. Flocculation Experiment*

Before each assessment, a flocculant solution of 4 <sup>g</sup>·L−<sup>1</sup> was obtained by dissolving a certain amount of SF in distilled water. CuCl2•2H2O was dissolved in distilled water to afford the Cu(II) stock solution of 4 <sup>g</sup>·L−1, the pH of which was adjusted to 8.1 using NH3•H2O.

Cu(II) flocculation experiments were performed using batch assessments at room temperature. Specifically, 0.6, 1.4, 1.6, 2, 2.4, and 2.6 mL of flocculant solution were added to a glass beaker (100 mL) containing 1.2 mL Cu(II) stock solution at pH 8.1. After that, water was added to obtain a total volume of 40 mL. Finally, Cu (II) concentration was 120 mg L−1. The suspension was initiated by rapidly stirring at 300 rpm for 5 min, and then slowly mixed for 10 min at 80 rpm. The precipitate was allowed to stand for 30 min and the solution was filtered (2 μm filter paper) to obtain the filtrate for residual concentration (RC) assessments. RC of Cu(II) was estimated from the derived calibration curve (Figure S2). Jar tests were repeated at least three times, the results of which were analyzed with mean values and standard deviation. Furthermore, 2.4 mL flocculant solution was added to a glass beaker (100 mL) containing 1.2 mL Cu(II) stock solution at pH 3, 3.5, 4, 4.5, 5, 5.5, 7, and 8.5, respectively. Water was added to obtain a total volume of 40 mL. After that, the same steps above was used to conduct the remaining flocculation experiments and detection of Cu (II).

Cu(II) removal (R%; Equation (1)) and flocculation capacity (Q; Equation (2)) could be calculated as follows:

$$R = \frac{\mathbb{C}\_0 - \mathbb{C}\_f}{\mathbb{C}\_0} \times 100\% \tag{1}$$

$$Q = V \frac{\mathbb{C}\_0 - \mathbb{C}\_f}{m} \tag{2}$$

in which *C*0 and *Cf* (mg·L−1) are the initial and final concentrations of Cu(II) in the filtrate, respectively. *V* (mL) represents the volume of the solution, and *m* (mg) represents the dried mass of SF. Flocs with different Cu(II) flocculation capacities (*Q* = 0.21–0.90 mg·mg<sup>−</sup>1, *R* = 45.1–99.5%) were collected and labeled as SF-x (x = *Q* = 0.21–0.90 mg·mg<sup>−</sup>1).

#### *2.3. Fabrication of Cu-Doped Carbon Materials Using Cu(II)-Containing Sludge*

Cu-doped carbon materials (SFC) were prepared from Cu(II)-containing sludge with various flocculation capacities, i.e., 0.9 (*R* = 45.0%), 0.6 (*R* = 99.5%), and 0.25 (*R* = 45.7%) mg·mg<sup>−</sup>1, respectively. Typically, Cu(II)-containing sludge as a precursor was pyrolyzed (1 h at 300 ◦C and 2 h at 800 ◦C) under an Ar atmosphere at a rate of 5 ◦C min−1. After prolonged cooling down to room temperature, the dark powder produced was dispersed in H2O while stirring to eliminate ash and other inorganic compounds, and then denoted as SFC-x (x = 0.9, 0.6, and 0.25).

## *2.4. Characterization Methods*

The Cu(II) concentration was determined using Inductively Coupled Plasma-Atomic Emission Spectrometry (Cu: 324.754 nm, ICP-AES, Varian 710E S). The zeta potential (ZP) was assessed using a nanoplus zeta/nano particle analyzer (Otsuka Electronics) and the optical transmittance was determined by means of a UV-visible spectrophotometer (UV-6100S, METASH, Shanghai, China). X-ray diffraction (XRD, Rigaku TTR III) was used for analyzing the sample structure using Cu Kα radiation. Sample morphology was imaged using a scanning electron microscope (SEM, JEOL JSM-6490LV). Transmission electron microscopy (TEM) and high-resolution transmission electron microscopy (HRTEM) were performed using a FEI Tecnai G2 (FEI Company, Hillsboro, OR, USA). X-ray photoelectron spectroscopic (XPS) measurements were conducted on a PHI-5000C (Physical Electronics, Inc. (PHI), Chanhassen, MN, USA). A quantachrome Autosorb surface analyzer (Quantachrome Instruments, Boynton Beach, FL, USA) was used to perform BET surface area measurements at 77.3 K.

## *2.5. Electrochemical Measurements*

Working electrodes were prepared via mixing active materials (80 wt %), carbon (10 wt %), and polyvinylidene fluoride (PVDF, 10 wt %) in 1-methyl-2-pyrrolidone to form a slurry, which was then brushed onto nickel foam (active area: 1 × 1 cm2) and dried at 60 ◦C for 24 h. The active material (weight: 5 mg), a Pt foil (1 × 1 cm2), and saturated calomel electrodes (SCE) were used as working, counter, and reference electrodes, and the electrolyte was 6 M potassium hydroxide (KOH). The electrochemical performance was estimated by cyclic voltammetry (CV), galvanostatic charge/discharge (GCD) measurement, and electrochemical impedance spectroscopy (EIS) on a CHI 760E

analyzer (CH Instruments Inc., Shanghai, China). Gravimetric specific capacitance (Csp, <sup>F</sup>·g<sup>−</sup>1) for single electrodes was calculated from each galvanostatic charge/discharge curve as follows (Equation (3)):

$$\text{Cs} = \frac{\text{I} \times \Delta \text{t}}{m \times \Delta V} \tag{3}$$

where *m*: the mass of the active material, *I*: discharge current, Δ*V*: potential change after complete discharge, and Δ*t*: time for complete discharge.
