## 4 Physical Interpretation of Steric Parameters  
### Parameters \(n\), \(D_{m}\), and \(N_{c}\)  
The steric parameter \(n\) contributes by providing descriptive details concerning the adsorption process of dexamethasone and hydrocortisone molecules on MNIPs and MMIPs adsorbents. For example, the adsorption orientation of the dexamethasone and hydrocortisone solutions on the surfaces of the MNIPs and MMIPs is explained using this parameter. Numerous works in the literature [33; 34] have reported that three plausible manners arise for depicting the orientation of adsorption using the \(n\) values. * **Possibility 1**: for the case of \(n<0.5\), the receptor sites of the MNIP and MMIP adsorbents capture a portion of the dexamethasone and hydrocortisone molecules (i.e., the molecules are shared by two or more receptor sites), implying a parallel adsorption orientation. Therefore, the adsorption is defined as a multi-interaction process. * **Possibility 2**: for the case of \(0.5<n<1\), a mixed adsorption orientation can be observed, i.e., the molecules are captured via non-parallel and parallel orientations simultaneously, with two proportions. * **Possibility 3**: for the case of \(n\geq 1\), the receptor sites capture one or more molecules, showing a non-parallel adsorption orientation. Consequently, this adsorption is defined as a multi-molecular process. According to the numerical simulation results given in Table 2, the adsorption values of \(n\) are equal to \(2.67\) and \(3.18\) for hydrocortisone and are equal to \(2.73\) and \(3.75\) for dexamethasone on MNIP and MMIP adsorbents, respectively. These values are greater than 1, showing that the hydrocortisone and dexamethasone solutions are adsorbed in a non-parallel orientation through their interactions with the MNIP and MMIP adsorbents, which indicates that this adsorption is multi-molecular. For instance, the value of \(n\) for hydrocortisone adsorption on dual-template MMIPs is \(2.65\). This value, when examined using the equation \(2.65=2\times p+(1-p)\times 3\), indicates that the number of hydrocortisone molecules adsorbed per site ranges between two and three. This equation can be used to calculate the exact proportions, where p represents the sites binding with two molecules and \((1-p)\) represents the sites binding with three molecules. This calculation shows that \(p=0.35\), i.e., \(35\%\) of the MMIP sites adsorbed two molecules and \(65\%\) of the sites adsorbed three hydrocortisone molecules. A comparison among the two adsorption systems demonstrated that this parameter varies as follows: (hydrocortisone/MNIPs) \(<n\)(hydrocortisone/MMIPs) and \(n\)(dexamethasone/MNIPs) \(<n\)(dexamethasone/MMIPs). This difference is attributed to the complementary shape, spatial distribution, size, and molecular interactions of the imprinting sites in the MMIP cavities [21; 35]. Parameter \(D_{m}\) represents the effectually occupied density of the receptor sites per surface unit of the adsorbent. According to Table 2, it is apparent that the receptor site density of the MMIPs is higher than that of the MNIPs in the cases of dexamethasone and hydrocortisone solutions. This can be explained by the experimental results revealed in ref [21], which show that the surface polymerization preparation of dual-template MMIPs results in a larger specific surface area. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multirow{2}{*}{**adsorbate**} & \multirow{2}{*}{**adsorbent**} & \multicolumn{6}{c}{**Parameter**} \\ \cline{3-8}  & & \(n\) & \(D_{m}\) & \(N_{c}\) & \(Q_{sat}\) (mg/g) & \(C_{1}\) (mg/mL) & \(C_{2}\) (mg/mL) \\ \hline \multirow{2}{*}{**Hydrocortisone**} & **MNIPs** & 2.675 & 1.830 & 3.240 & 15.41 & 0.057 & 0.282 \\ \cline{2-8}  & **MMIPs** & 3.184 & 3.422 & 2.101 & 22.83 & 0.049 & 0.242 \\ \hline \multirow{2}{*}{**Dexamethasone**} & **MNIPs** & 2.738 & 2.084 & 3.321 & 18.70 & 0.050 & 0.281 \\ \cline{2-8}  & **MMIPs** & 3.757 & 4.373 & 2.328 & 38.01 & 0.043 & 0.238 \\ \hline \hline \end{tabular}
\end{table}