## 3 Results and Discussion
### Adsorption Isotherm Models
#### 3.3.1 Langmuir Model Isotherm for WPET-SiAMPy Composite Nanofibres  
Langmuir adsorption, specifically designed to describe gas-solid adsorption, is additionally used to quantify and distinguish between the adsorptive ability of more than a few adsorbents [42]. The Langmuir isotherm balances the relative costs of adsorption and desorption (dynamic equilibrium). Adsorption is proportional to the fraction of the sites of the adsorbent that are open whilst desorption is proportional to the fraction of the adsorbent sites that are blanketed [43]. The Langmuir adsorption isotherm describes the adsorption of the adsorbate on the surface of the adsorbent in three ways. First, the Langmuir adsorption isotherm states that the surface of the adsorbent is in contact with a solution containing the adsorbate which is strongly attracted to the surface. Secondly, this isotherm states that the surface has a specific number of sites where the adsorbate molecules can be adsorbed. Lastly, the Langmuir adsorption isotherm states that the adsorption involves the attachment of only one layer of molecules to the surface [32]. The Langmuir adsorption isotherm proves that a dynamic equilibrium exists between the adsorbed molecules and free molecules. This isotherm describes the isothermal variation of the free adsorbate and the vacancies on the surface of the adsorbent [44]. The adsorbent and the adsorbate are in dynamic equilibrium, and the fractional coverage of the surface depends on the concentration of the adsorbate. The extent of surface coverage is normally expressed as the fractional coverage, \(\theta\). The Langmuir isotherm was used to calculate the monolayer adsorption, which was represented by the following linearized form presented as Equation (5):  
\[q_{e}=\frac{q_{m}K_{L}C_{e}}{1+K_{L}C_{e}} \tag{5}\]  
The Langmuir Equation presents \(q_{e}\) as the amount of metal ion adsorbed on adsorbents (mg/g), \(q_{m}\) and \(K_{L}\) are the monolayer adsorption capacity (mg/g) and Langmuir equilibrium constant (L/mg) which indicates the nature of adsorption, respectively. The values of \(q_{m}\) and \(K_{L}\) were graphically determined with a plot of, \(q_{e}\) against \(C_{e}\) that gives a straight line of slope \(q_{m}K_{L}\) and the intercept is \(q_{m}\), which corresponds to the complete monolayer coverage [45]. The essential calculation of the Langmuir isotherm is expressed in terms of a dimensionless constant separation factor, \(R_{L}\)[46], which is expressed as Equation (6):  
\[R_{L}=\frac{1}{1+K_{L}C_{o}} \tag{6}\]  
where \(q_{e}\) is the equilibrium adsorption uptake of Cu\({}^{2+}\) ions, \(q_{m}\) is the maximum adsorption capacity corresponding to the complete monolayer coverage, \(K_{L}\) is the Langmuir adsorption tion, \(R_{L}=1\) indicating linear adsorption; \(R_{L}=0\) indicating irreversible adsorption and \(0<R_{L}<1\) indicating optimum/favourable adsorption. The Langmuir isotherm for the adsorption of Cu\({}^{2+}\) using WPET-SiAMPy nanofibres is indicated in Figure 9. The correlation coefficient of R\({}^{2}=0.9905\) indicated that the adsorption of Cu\({}^{2+}\) from aqueous solution using WPET-SiAMPy nanofibres as adsorbent was optimum and favourable, supported by the separation factor \(0<R_{L}<1\). WPET-SiAMPy nanofibres have shown an equilibrium trend of the Type II isotherm which represents unrestricted monolayer-multilayer adsorption, as demonstrated by IUPAC classification of isotherms [47]. The accumulation of Cu\({}^{2+}\) ion on the surface of the WPET-SiAMPy nanofibres suggests that the Cu\({}^{2+}\) ions partially saturated the sites and followed the L3 type classification proposed by [PERSON], 2001 [48]. The L3 curve presented in Figure 9 indicates that the Cu\({}^{2+}\) ions, as the adsorbate, have a high affinity such that in diluted solutions, Cu\({}^{2+}\) is completely adsorbed, or at least no measurable amount of Cu\({}^{2+}\) remained in the solution that could be further adsorbed. The initial part of the adsorption isotherm is conclusively vertical.