# Removal of Volatile Phenols From Wine Using Crosslinked Cyclodextrin Polymers
## 2 Results and Discussion
### Determination of CD Polymer Adsorption Capacity in Model Wine
In the current study, the starting and equilibrium concentrations of volatile phenols were no more than 1 mg/L, which are more reflective of concentrations observed in wine than concentrations reported in studies targeting pollutant removal from water. There is indeed limited literature reporting adsorption rates at these lower concentrations, so adsorption isotherm models were developed in the current study to predict the maximum adsorption capacity of the studied polymers. Several isotherm models have been developed to describe the adsorption of gaseous/liquid molecules onto an adsorbent surface. In the current study, Langmuir and Freundlich isotherm models were used to fit the data (Table 1). The Langmuir isotherm assumes single-layer adsorption of adsorbate onto a homogenous surface with an identical cavity [34]. It is especially useful in describing adsorption at lower pressures (concentration of adsorbate), i.e., when the adsorption capacity curve (Figure 3) appears to be close to linear [38]. It can be expressed as:  
\[\text{q}_{\text{e}}=1/\text{q}_{\text{max}}\text{ K}_{\text{L}}+\text{C}_{\text{e}}/\text{q}_{\text{max}} \tag{1}\] \begin{table}
\begin{tabular}{c l c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Langmuir Adsorption Isotherm**} & \multicolumn{3}{c}{**Freundlich Adsorption Isotherm**} \\ \cline{3-8}  & & \(\text{q}_{\text{m}}\) (mg/g) & \(\text{K}_{\text{L}}\) (L/mg) & \(\mathbf{r}\) & \(\text{K}_{\text{f}}\) & **1/n** & \(\mathbf{r}\) \\ \hline guaiacol & \(\beta\)-CD-HDI & 22.3 & 3.0 & 0.989 & 21.7 & 0.67 & 0.992 \\  & \(\gamma\)-CD-HDI & 19.6 & 5.8 & 0.992 & 22.3 & 0.56 & 0.991 \\
4-methylguaiacol & \(\beta\)-CD-HDI & 20.1 & 4.9 & 0.990 & 21.5 & 0.56 & 0.987 \\  & \(\gamma\)-CD-HDI & 21.2 & 5.8 & 0.988 & 23.5 & 0.54 & 0.995 \\
4-ethylguaiacol & \(\beta\)-CD-HDI & 20.0 & 10.4 & 0.995 & 23.9 & 0.44 & 0.968 \\  & \(\gamma\)-CD-HDI & 20.5 & 7.7 & 0.997 & 24.2 & 0.50 & 0.959 \\
4-ethylphenol & \(\beta\)-CD-HDI & 25.1 & 8.1 & 0.986 & 34.0 & 0.56 & 0.957 \\  & \(\gamma\)-CD-HDI & 20.6 & 23.1 & 0.976 & 25.9 & 0.35 & 0.985 \\ \hline \hline \end{tabular}  
* q\({}_{\text{m}}\) = the maximum adsorption capacity; K\({}_{\text{L}}\) = the Langmuir isotherm constant; r = the correlation coefficient; K\({}_{\text{f}}\) = the Freundlich constant; and n = the constant related to the adsorption intensity.  
\end{table} 
Table 1: Langmuir and Freundlich isotherms for the adsorption of volatile phenols by \(\beta\)-CD-HDI and \(\gamma\)-CD-HDI in model wine at 25 \({}^{\circ}\)C.  
where \(\rm q_{e}\) is the adsorption capacity per unit weight of the polymer, \(\rm q_{max}\) is the maximum adsorption capacity of the system, \(\rm C_{e}\) is the residual concentration of volatile phenols at equilibrium, and \(\rm K_{L}\) is the Langmuir isotherm constant. The equation can be re-arranged to give:  
\[\rm C_{e}/q_{e}=1/q_{max}^{\rm\ast}C_{e}+1/K_{L}q_{max} \tag{2}\]  
It is obvious that if \(\rm C_{e}/q_{e}\) is plotted against \(\rm C_{e}\), values of \(\rm K_{L}\) and \(\rm q_{m}\) can be calculated from the slope and intercept of the regression. In the current study, a Langmuir model fitted the data well with good linearity. The calculated values of \(\rm K_{L}\) and \(\rm q_{m}\) are shown in Table 1. The modelled maximum adsorption capacity (\(\rm q_{m}\)) for \(\rm\beta\)-CD-HDI and \(\rm\gamma\)-CD-HDI binding guaiicol, 4-methylguaiacol, 4-ethylguaiacol and 4-ethylphenol is between 19.6 mg/g (for \(\rm\gamma\)-CD-HDI adsorbing guaiacol) and 25.1 mg/g (for \(\rm\beta\)-CD-HDI adsorbing 4-ethylphenol), which falls within the ranges reported previously [31; 34; 36].