## 2 Materials and Methods
### Batch Adsorption Study  
Adsorption isotherms of MB onto both raw and KOH-modified hydrocarbons were determined by adding 10-16 mg of absorbent to 25 mL stoppered glass bottles containing 4 mL of MB solution with various initial concentrations ranging between 10 and 300 mg L\({}^{-1}\). The bottles were agitated with a magnetic stirrer at 250 rpm and were kept at 20 \(\pm\) 2 \({}^{\circ}\)C for 48 h. The pH of the MB solutions was evaluated using a portable pH meter (pH 3110 ProfiLine with SenTix41 probe, WTW, Milan, Italy). Then, the obtained solutions were centrifuged at 3000 rpm for 5 min and the MB concentrations were measured from the calibration curve of MB solutions at 665 nm using a UV-visible spectrophotometer (Model V-3250, Jasco Europe, Lecco, Italy). The adsorption capacity at equilibrium q\({}_{\rm e}\) (mg g\({}^{-1}\)) and the percentage removal of MB were evaluated by Equations (1) and (2), respectively [27; 28]:  
\[\rm{q_{e}=(C_{o}-C_{e})V/W} \tag{1}\]  
\[\rm{\%~{}removal=((C_{o}-C_{e})/C_{0})100\%} \tag{2}\]  
where C\({}_{\rm e}\) and C\({}_{0}\) are, respectively, the equilibrium and initial MB concentration (mg L\({}^{-1}\)), V is the solution volume (L) and W is the adsorbent mass used (g).  
To investigate the mechanisms of adsorption, three well-known adsorption isotherms, Langmuir, Freundlich and Tempkin-type curves, were adopted. The Langmuir sorption isotherm is applied to equilibrium sorption assuming monolayer sorption on a surface with a finite number of identical sites. The linear Langmuir equation is expressed as Equation (3) [29]:  
\[\rm{q_{e}=(K_{L}~{}q_{m}~{}C_{e})/(1+K_{L}~{}C_{e})} \tag{3}\]  
where K\({}_{L}\) is the Langmuir constant (L mg\({}^{-1}\)) related to the affinity of binding sites and the free energy of sorption, and q\({}_{m}\) is the maximum adsorption capacity when a monolayer forms on the hydrochar (mg g\({}^{-1}\)).  
The Freundlich equation describes heterogeneous surface energy systems and is expressed as Equation (4) [30]:  
\[\rm{q_{e}=K_{F}~{}C_{e}^{(1/n)}} \tag{4}\]  
where K\({}_{F}\) and 1/n are the Freundlich constants, determined from the plot of q\({}_{e}\) versus C\({}_{e}\). The parameters K\({}_{F}\) and 1/n are related to the sorption capacity and the sorption intensity of the system. The magnitude of the term 1/n gives an indication of the affinity of the sorbent/adsorbate systems [31].  
The Tempkin equation is given by the following Equation (5) [32]:  
\[\rm{q_{e}=B~{}ln~{}(K~{}C_{e})} \tag{5}\]where B = (R T)/b, T is the absolute temperature in Kelvin, R is the universal gas constant (8.314 J mol\({}^{-1}\) K\({}^{-1}\)), b and K are Tempkin constants related to the heat of sorption (J mol\({}^{-1}\)) and to the equilibrium binding (L g\({}^{-1}\)), respectively.  
The kinetics of MB adsorption on the raw and KOH-modified hydrocarbons were examined by adding 90 mg of each hydrochar to 150 mL glass bottles containing 50 mL of MB solution with a concentration of 100 mg L\({}^{-1}\). The glass bottles were then shaken at 250 rpm under a magnetic stirrer for 24 h. At different time intervals, the samples were centrifuged at 3000 rpm for 5 min and the residual MB concentration was measured by the UV-visible spectrophotometer (Model V-3250, Jasco Europe, Lecco, Italy) through the calibration curve.  
The kinetics of the MB adsorption process was evaluated using pseudo-first order and pseudo-second-order kinetic models. The kinetic equations for these models are expressed by Equations (6) [33] and (7) [34], respectively:  
\[\ln(\mathrm{q_{e}}-\mathrm{q_{f}})=\ln\mathrm{q_{e}}-\mathrm{k_{1}}\mathrm{t} \tag{6}\]  
\[\mathrm{t/q_{f}}=\mathrm{t/q_{e}}+1/(\mathrm{k_{2}}\mathrm{q_{e}}^{2}) \tag{7}\]  
where \(\mathrm{q_{e}}\) (mg g\({}^{-1}\)) and \(\mathrm{q_{f}}\) (mg g\({}^{-1}\)) denote the MB sorption at equilibrium and time t (min), respectively, and k\({}_{1}\) (min\({}^{-1}\)) and k\({}_{2}\) (g mg\({}^{-1}\) min\({}^{-1}\)) represent, respectively, the pseudo-first and pseudo-second order adsorption rate constants.