# Kinetics and Thermodynamics of Efficient Phosphorus Removal by a Composite Fiber
## 3 Results and Discussion
### Experiment on Static Adsorption and Phosphorus Removal
#### 3.1.2 Adsorption Kinetics  
Adsorption Kinetics at Different Initial Concentrations  
The adsorption rate was fast after the start of adsorption, and gradually became slower with time until the adsorption equilibrium was reached (Figure 4). When the adsorption time was the same, the higher the initial concentration, the larger the adsorbed amount of phosphorus. The initial concentration affected the phosphorus removal performance mainly in two aspects: First, the higher the initial concentration, the denser the phosphorus in the solution, and the easier it was to collide with the surface of the composite fiber to be adsorbed. Second, higher concentration led to greater concentration difference between the liquid film on the surface of the composite fiber and phosphorus. It also increased the driving force for the diffusion of phosphorus to the surface of the composite fiber. It can also be seen from the trend of the curve that the higher the initial concentration, the longer the time required for the adsorption to reach equilibrium. For example, when the initial concentration was 5 mg/L, the composite fiber reached the adsorption equilibrium after 18 h; while when the initial concentration was 20 mg/L, it took more than 48 h. The experimental data were put into pseudo-first-order and pseudo-second-order kinetic equations, and the relevant parameters were obtained (as described in Table 3).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Temperature (K)** & \(\Delta\)**G\({}^{\textbf{0}}\) (kJ/mol)** & \(\Delta\)**H\({}^{\textbf{0}}\) (kJ/mol)** & \(\Delta\)**S\({}^{\textbf{0}}\) (kJ/mol-K)** \\ \hline
288 & \(-\)17.861 & 44.721 & 0.218 \\
298 & \(-\)20.220 & 44.721 & 0.218 \\
308 & \(-\)22.203 & 44.721 & 0.218 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Thermodynamic parameters of phosphorus adsorption.  
Figure 4: Adsorption kinetic curve of ZSFB composite fiber at different initial concentrations.  
The fitting results show that the pseudo-second-order kinetic model can accurately describe the adsorption kinetics, and the value of R\({}^{2}\) > 0.99, indicating that the adsorption of phosphorus by the composite fiber, was mainly the chemical adsorption process [23]. At the initial concentrations of 5, 10, 15 and 20 mg/L, the R\({}^{2}\) of the pseudo-second-order kinetic model was higher than that of the pseudo-first-order kinetic model. It was found that the adsorption rate constant \(K_{2}\) decreased as the initial concentration increased, as the surface area and the adsorption sites of the adsorbent were constant when the amount of the adsorbent was constant. When the solution concentration increased, the total amount of the adsorbate increased, which reduced the probability of a single adsorbate binding to the adsorbent site, and thus \(K_{2}\) decreased [24]. Using the pseudo-second-order kinetic model, the equilibrium adsorption capacity \(Q_{e}\) at initial concentrations of 5, 10, 15 and 20 mg/L was 0.452, 0.918, 1.395 and 1.826 mg/g, respectively. It shows that increasing the concentration can increase the adsorption capacity of the composite fiber.