## 2 Methods
### Adsorption Kinetics and Isothermal Model  
The adsorption dynamic isotherms of phthalates (PAEs) were obtained by batch equilibrium experiments. The determination process was as follows: Dimethyl phthalate (DMP), diethyl phthalate (DEP), and dibutyl phthalate (DBP) were dissolved in methanol as a reserve solution and then diluted to a solution containing 0.02 mol NaCl (maintaining a constant ion concentration) and 200 mg/L NaN\({}_{3}\) (pH = 7.0 \(\pm\) 1). The percentage by volume of methanol had to be kept below the volume ratio of 0.10% to minimize the role of the cosolvent. For DMP and DEP, adsorption experiments were performed in an 8 mL glass bottle with a Teflon-lined screw cap. Adsorption kinetics was studied with the initial concentration of DMP and DEP at 10 mg/L. The adsorption kinetics of DBP was studied at an initial concentration of 4 mg/L. The solid/water ratio was 5 mg at 300 \({}^{\circ}\)C and 3 mg at 600 \({}^{\circ}\)C. Residual concentrations in a series of independent samples were measured from start to 72 h. The isotherm experiments are carried out with different solid/water ratios. For DMP and DEP, 5 mg and 3 mg biochar and 8 mL solution were added to each vial, respectively. For DBP, 5 mg and 3 mg of biocharwere added to the 15 ml vial and place in the dark. At room temperature (\(25\pm 1\)\({}^{\circ}\)C), it was shaken by a rotating shaker (rotating at 120 RPM/min) according to the balance time. During this period, all phthalates (DMP, DEP, DBP) were stable, and no significant degradation was observed. All vials were centrifuged at 2500 r/min for 10 min, and then the concentrations of DMP, DEP, and DBP of each supernatant were determined by HPLC.  
In order to provide a more in-depth and reliable basis for the study of adsorption mechanism, the adsorption equilibrium isotherm was studied in detail. The temperature in the adsorption process was mainly affected by two aspects. The first was that as the temperature increased, the viscosity of the solution decreased, and the diffusion rate of the adsorbent membrane and the internal pores of the adsorbent particles increased. The second was that changing the temperature changed the adsorption balance of a specific adsorbent [23; 24; 25]. Therefore, in order to study the isothermal adsorption characteristics of BG composites, two typical isothermal adsorption models were used to fit the isothermal adsorption data. Each experiment was repeated three times, and then the average was taken to plot a curve.  
The Langmuir isothermal model assumes that the adsorption process is adsorption in the gas-solid monolayer, and the expression is as follows:  
\[\frac{C_{e}}{q_{e}}=\frac{1}{k_{L}q_{\max}}+\frac{C_{e}}{q_{\max}^{2}} \tag{1}\]  
where \(C_{e}\) is the equilibrium concentration of phthalates; \(q_{\max}\) denotes the maximum adsorption capacity of the adsorbent on phthalate; \(q_{e}\) is the adsorption capacity of unit mass dry adsorbent to phthalate ester at adsorption equilibrium; and \(K_{L}\) represents the Langmuir constant related to the affinity of the adsorption site [26].  
The Freundlich isothermal model is a simulation of the adsorption process occurring in heterogeneous layers without considering adsorption saturation, and the expression is as follows:  
\[\ln q_{e}=\ln K_{F}+\frac{1}{N}\ln C_{e} \tag{2}\]  
where \(K_{F}\) is the Freundlich constant related to adsorption capacity, and \(N\) represents the constant related to the strength of adsorption capacity; when \(n<1\), this indicates that adsorption is very difficult; when \(1<N<2\), it indicates that adsorption is relatively difficult; when \(2<N<10\), it indicates that the adsorption strength is high and the adsorption is easy [27].