## 2 Materials and Methods
### Adsorption-Regeneration Cycles  
The ACF was subjected to subsequent adsorption-regeneration cycles.  
The adsorption step began by placing 0.18 g of the ACF into a home-made sample holder consisting of a cylindrical tube made of Hastelloy (5 cm in length, \(\frac{1}{4}^{\prime\prime}\) OD), which was immersed in a thermostat at 27 \({}^{\circ}\)C. A HPLC (high performance liquid chromatography) pump model LC-10 AS (Shimadzu, Kyoto, Japan) pumped a flow of 4.0 cm\({}^{3}\cdot\)min\({}^{-1}\) of a \(5.35\times 10^{-4}\) M phenol solution through the ACF during 240 min. The effluent stream was monitored continuously with a spectrophotometer model UV-1603 supplied by Shimadzu, at a wavelength of 270 nm to obtain the phenol breakthrough curve. The amount of phenol adsorbed could be determined in two ways. On one hand, by integrating the breakthrough curve; on the other hand, by collecting all of the effluent stream and analyzing the amount of phenol contained in it. Both procedures led to the same result. The original ACF retained 162.7 \(\pm\) 19.5 mg\({}_{\text{phenol}}\cdot\)g\({}_{\text{ACF}}\)\({}^{-1}\) during this adsorption step.  
Once the adsorption step had been completed, the regeneration step began. Figure 1 shows the schematic of the installation used for the SCCO\({}_{2}\) regeneration experiments.  
The sample holder was placed into the regeneration reactor, a cylindrical tube made of Hastelloy (50 cm in length, 2 cm OD), which was placed in the middle of a cylindrical induction coil. Then, the regenerating fluid was pumped through the exhausted ACF. Liquid cooled CO\({}_{2}\) at 50 bar and \(-4\)\({}^{\circ}\)C was pumped by a High Pressure P-Series Pump (Thar Technologies, Pittsburgh, PA, USA), a device designed to pump pressurized liquids. The effluent stream was discharged through an automatic pressure-regulating valve, which was used to control the regeneration pressure. Once the pressure had been attained, the reactor was heated by inductive heating. A generator of alternating current model Power Cube 90/180 (CEIA, Viciomaggio, Arezzo, Italy) circulated an electrical current through the coin. The magnetic field generated within the coin rapidly heated the reactor and allowed reaching the desired regeneration temperature in a few seconds. The hot effluent stream proceeding from the reactor went through a heat exchanger, where it was cooled to ambient temperature before reaching the pressure-regulating valve. This design allowed the ACF to remain into the sample holder at any time, thus avoiding any mass loss.  
In SCCO\({}_{2}\) regeneration, the temperature, time, pressure, and flow rate ranges investigated were 200-400 \({}^{\circ}\)C, 10-35 min, 100-225 bar, and 1-15 cm\({}^{3}\cdot\)min\({}^{-1}\), respectively. The SCCO\({}_{2}\) flow rate was referred to the conditions at which the fluid was pumped (\(\rho_{\text{CO2}}\) = 0.96 g\(\cdot\)cm\({}^{-3}\)), so that the volumetric and mass flow rates essentially agreed.  
The installation used for the SCW regeneration experiments was the same; in those experiments, CO\({}_{2}\) was replaced by water and the fluid was pumped by a HPLC pump model K-501 (Knauer, Hamburg, Germany). The SCW regeneration experiments were carried out at 300 bar and 425 \({}^{\circ}\)C with a water flow of 3 cm\({}^{3}\cdot\)min\({}^{-1}\). The time range investigated was 5-15 min.  
Once the ACF had been regenerated, it was exposed to a subsequent adsorption step. RE (regeneration efficiency) was calculated as follows, Equation (1):  
\[\text{RE }(\%)\ =\left(\frac{\text{phenol adsorbed by the regenerated ACF}}{\text{phenol adsorbed by the original ACF}}\right)\cdot 100 \tag{1}\]  
Figure 1: Schematic of the installation used for the supercritical CO\({}_{2}\) (SCCO\({}_{2}\)) regeneration experiments.