*2.4. Phosphate Adsorption Experiments*

As a filter additive in stormwater runoff treatment, the material needs to have a certain phosphate adsorption capacity. In order to evaluate the phosphate adsorption capacity of the materials, adsorption experiments were conducted using PCB-DW and HB-DW with different concentrations of phosphate. Standard solutions of 100 mg/L Na2HPO4 were diluted to 0, 0.5, 1, 2, 5, 7 and 10 mg/L with DW and AS, respectively and AS only contained 120 mg/L CaCl2. We placed 0.2 g of PCB-DW and HB-DW into 50 mL conical flasks, added 10 mL of the above solution and oscillated the flasks for 24 h at 150 rpm at 20 ± 2 °C. The extraction method of the supernatants was the same as the leaching test and the concentrations of phosphate in the supernatants were measured. The detection method was the same as above. The experiment was repeated in 2 groups for each material. Additional conical flasks with phosphate solutions but no PCB-DW or HB-DW were used as control groups.

In order to explore the adsorption properties and capacity of phosphate, Langmuir and Freundlich models were used to fit the adsorption equilibrium quantities of phosphate after 24 h. The calculation formula of the equilibrium adsorption quantity *qe* (mg/kg) for phosphate at 24 h is [33]:

$$q\_{\varepsilon} = \frac{(\mathbb{C}\_0 - \mathbb{C}\_{\varepsilon})V}{W},\tag{1}$$

where, *C*<sup>0</sup> and *Ce* are the concentrations (mg/L) of PO4 <sup>3</sup><sup>−</sup> in the solution before and after the adsorption test; *V* is the solution volume (L); *W* is the material mass (kg).

The Freundlich model was used to fit the isothermal adsorption results [23]:

$$q\_{\ell} = K\_F \mathbb{C}e^{1/n} \,\prime \,\, \tag{2}$$

where, *KF* is the volume-affinity parameter (L/mg) of the Freundlich model, which can be regarded as the adsorption capacity at unit a concentration of *Ce*; *n* is the Freundlich characteristic constant, the value of *1/n* is generally between 0 and 1 and its value represents the influence of the concentration on the adsorption capacity. The smaller *l/n* is, the better the adsorption property is. When *1/n* is between 0.1 and 0.5, it is easy to absorb; it is difficult to adsorb when *1/n* is more than 2.

The Langmuir model of single molecular layer physical adsorption was also used to fit the isothermal adsorption results [23]:

$$q\_{\varepsilon} = q\_{\text{max}} \frac{K\_L \mathcal{C}\_{\varepsilon}}{1 + K\_L \mathcal{C}\_{\varepsilon}} \tag{3}$$

where *qmax* is the maximum adsorption capacity (mg/kg); *KL* is the affinitive parameter of the Langmuir model (L/mg), which is the equilibrium constant of adsorption, also known as the adsorption coefficient. The higher the value of *KL* is, the stronger the adsorption capacity is.

The dimensionless coefficient *RL* is used to determine whether adsorption easily occurs [34]:

$$R\_L = \frac{1}{1 + K\_L \mathcal{C}\_0} \,\mathrm{}\tag{4}$$

when 0 < *RL* < 1, adsorption easily occurs; when *RL*>1, adsorption does not easily occur; when *RL* = 0, the adsorption process is reversible. When *RL* = 1, adsorption is linear.
