**Appendix A**

### *Appendix A.1 Specific Capacitance, Csp*

The gravimetric specific capacitance was obtained from CV according to Equation (A1)

$$\mathcal{C}\_{sp} = \frac{\int (I/m)dE}{\nu \,\Delta E} \tag{A1}$$

where *I*/*m* (mA g<sup>−</sup>1) is the voltammetric current normalized by the total mass of the composite material, ν is the scan rate (mV s<sup>−</sup>1), and Δ*E* (mV) is the potential window spanned in the CV. The reported capacitances are the average of capacitances calculated in both the anodic and cathodic branches of the voltammogram.

### *Appendix A.2 Surface Sheet Resistance, Rs*

To measure *Rs*, the electrical resistance, *R* (Ω), was first obtained from the linear slope of *V* vs. *I* plots in the range 0–10 mA. Then, *Rs* was calculated by using Equation (A2):

$$R = \frac{\rho}{t} \frac{L}{W} = R\_s \frac{L}{W} \tag{A2}$$

where ρ is the resistivity, *t* is the thickness of the probed carbon composite sheet, and *L* and *W* stand for its length and width, respectively.

### *Appendix A.3 Adsorption Isotherms and Kinetic Models*

Langmuir (Equation (A3)) and Freundlich (Equation (A4)) isotherm models were used in their linearized forms:

$$\frac{C\_{\epsilon}}{q\_{\epsilon}} = \frac{1}{bq\_{m}} + \frac{C\_{\epsilon}}{q\_{m}} \tag{A3}$$

$$
\ln q\_{\varepsilon} = \ln K\_F + \frac{1}{n} \ln \mathcal{C}\_{\varepsilon} \tag{A4}
$$

where *qe* (mg g<sup>−</sup>1) and *Ce* (mg <sup>L</sup>−1) are the adsorbate uptake and solution concentration at equilibrium; and *qm* (mg g<sup>−</sup>1) and *b* (L mg<sup>−</sup>1) are the Langmuir parameters, representing the maximum adsorption capacity and the adsorption equilibrium constant respectively [59]. In the Freundlich model, the adsorption coe fficient, *KF* (mg(1 − <sup>1</sup>/n)L1/ng−1), is related to the adsorption strength, and the exponent *n* accounts for the energetic heterogeneity of the adsorbent surface [59].

PFO (Equation (A5)) and PSO (Equation (A6)) kinetic models were used in their respective linear forms:

$$
\ln(q\_\varepsilon - q) = \ln q\_\varepsilon - k\_1 t \tag{A5}
$$

$$\frac{t}{q} = \frac{1}{k\_2 q\_c^2} + \frac{t}{q\_c} \tag{A6}$$

where *q* and *qe* (mg g<sup>−</sup>1) are the adsorption uptakes at time *t* (min) and at equilibrium respectively, and *k*1 (min−1) and *k*2 (g mg<sup>−</sup><sup>1</sup> min−1) stand for the pseudo-first and pseudo-second order rate constants. In the PSO model, the product *<sup>k</sup>*2*q*<sup>2</sup> *e*is the initial adsorption rate, *r*0.

The Vermeulen model is an approximate solution of the exact Crank equation for intraparticle di ffusion: 

$$F(t) = \sqrt{1 - \exp(-Bt)}\tag{A7}$$

where *F(t)* is the fractional uptake (*q*/*qe*) at time *t*, and *B* is the time constant (min−1) that depends on the adsorbent particle radius, *<sup>r</sup>*p, and the e ffective intraparticle di ffusion coe fficient, *D*e, as follows [72,73]:

$$B = \frac{D\_c \pi^2}{r\_p^2} \tag{A8}$$

The Vermeulen model is valid over a wide adsorption timespan and is commonly applied in the rearranged form:

$$Bt = -\ln\left(1 - F^2\right) \tag{A9}$$

Then, the product *Bt* is calculated from *F* at each contact time, and next plotted against time.

### *Appendix A.4 Average Relative Error*

The average relative error (ARE) is defined as [60]:

$$ARE = \frac{1}{N} \sum\_{i=1}^{N} \left| \frac{q\_{i,exp} - q\_{i,cal}}{q\_{i,exp}} \right| \tag{A10}$$

where the subscripts *exp* and *cal* refer to the experimental and calculated values, and *N* is the number of data points.
