## 3 Results and Discussion
### Mathematical Modelling of Drug Release Kinetics
The \(R^{2}\) value is a measure of the goodness-of-fit of a set of data to a particular model and ranges from 0 to 1; \(R^{2}\) tending closer to 1 represents a greater goodness-of-fit and suggests the drug release kinetics can be described by that model. The standard error of estimate, \(Sy.x\), the gradient, and the \(p\) value for each nanohybrid at different conditions have also been recorded and are displayed in Table S5. The linear regression graphs for each publication that the results are based upon can be found in Figures S1-S17. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Paper**} & \multirow{2}{*}{**Nanocarrier and Release Condition**} & **Zero-Order** & **First-Order** & **Higuchi** & **Weibull** \\ \cline{3-6}  & & \(R^{2}\) & \(R^{2}\) & \(R^{2}\) & \(R^{2}\) \\ \hline \multirow{2}{*}{1} & GO-HA-RGD (pH 5.5) & 0.8597 & 0.8746 & 0.9422 & 0.9611 \\  & GO-HA-RGD (pH 7.4) & 0.7367 & 0.7390 & 0.8464 & 0.8996 \\  & GO-PAC/HEC (pH 5.0) & 0.6516 & 0.7768 & 0.8431 & 0.9694 \\  & GO-PAC/HEC (pH 7.4) & 0.6231 & 0.6409 & 0.8261 & 0.9502 \\  & NGO-PEG-DA (pH 5.0) & 0.7288 & 0.7710 & 0.8783 & 0.8823 \\  & NGO-PEG-DA (pH 6.8) & 0.9860 & 0.9869 & 0.9609 & 0.9720 \\  & NGO-PEG-DA (pH 7.4) & 0.3289 & 0.3297 & 0.4790 & 0.6881 \\  & NGO-PEG-SA (pH 5.0) & 0.8149 & 0.8389 & 0.9244 & 0.9273 \\  & NGO-PEG-SA (pH 6.8) & 0.9118 & 0.9177 & 0.9498 & 0.9488 \\  & NGO-PEG-SA (pH 7.4) & 0.4873 & 0.4875 & 0.6830 & 0.8610 \\  & GO-PEG-SS-HY (pH 5.5) & 0.7834 & 0.8080 & 0.9150 & 0.9451 \\  & GO-PEG-SS-HY (pH 7.4) & 0.8061 & 0.8158 & 0.9304 & 0.9309 \\  & GO-TD-Fe\({}_{5}\)O\({}_{4}\)-PEG (pH 5.0) & 0.8382 & 0.9618 & 0.9327 & 0.9817 \\  & GO-TD-Fe\({}_{5}\)O\({}_{4}\)-PEG (pH 6.8) & 0.8707 & 0.9491 & 0.9539 & 0.9762 \\  & GO-TD-Fe\({}_{5}\)O\({}_{4}\)-PEG (pH 7.4) & 0.8600 & 0.9315 & 0.9453 & 0.9708 \\  & Zn-d-3 rGO (pH 5.4) & 0.9085 & 0.9652 & 0.9846 & 0.9870 \\  & Zn-d-3 rGO (pH 7.4) & 0.8866 & 0.9137 & 0.9689 & 0.9749 \\  & GO (pH 5.4) & 0.5447 & 0.5871 & 0.7012 & 0.7854 \\  & GO (pH 7.4) & 0.4561 & 0.4868 & 0.6016 & 0.6859 \\  & GO/(PHEMA-g-PLA)-p-PEC-b-(-PHEMA-g-PLA) & 0.8553 & 0.8972 & 0.9515 & 0.9830 \\  & (pH 5.4) & 0.8518 & 0.6073 & 0.7737 & 0.9155 \\  & GO/(PHEMA-g-PLA)-b-PEG-b-(-PHEMA-g-PLA) & 0.85818 & 0.6073 & 0.7737 & 0.9155 \\  & (pH 7.4) & 0.7846 & 0.8607 & 0.9091 & 0.9772 \\  & FA-BSA/GO (pH 7.4) & 0.9032 & 0.9427 & 0.9747 & 0.9754 \\  & NGO-HDex (pH 5.5) & 0.9624 & 0.9755 & 0.9975 & 0.9982 \\  & NGO-HDex (pH 7.4) & 0.9914 & 0.9942 & 0.9909 & 0.9892 \\  & GO (pH 2) & 0.8323 & 0.9360 & 0.9322 & 0.9123 \\  & GO (pH 7) & 0.5794 & 0.5928 & 0.7161 & 0.6499 \\  & GO (pH 10) & 0.6437 & 0.6752 & 0.7846 & 0.7796 \\  & Fe\({}_{5}\)O\({}_{4}\)/GO/Chitosan (Normal Release) & 0.9845 & 0.9958 & 0.9990 & 0.9877 \\
11 & Fe\({}_{5}\)O\({}_{4}\)/GO/Chitosan (NIR assist) & 0.9429 & 0.9643 & 0.9690 & 0.9337 \\  & Fe\({}_{5}\)O\({}_{4}\)/GO/Chitosan (Ultrusound assist) & 0.9221 & 0.9464 & 0.9538 & 0.9096 \\  & PI27/GN (pH 5) & 0.6961 & 0.7494 & 0.8444 & 0.8964 \\
12 & PF127/GN (pH 7) & 0.5976 & 0.6186 & 0.7643 & 0.7734 \\  & PF127/GN (pH 9) & 0.6758 & 0.7080 & 0.8405 & 0.8397 \\  & GO-A-Im (pH 3.4) & 0.5645 & 0.6732 & 0.7116 & 0.8374 \\
13 & GO-A-Im (pH 5.4) & 0.6178 & 0.7175 & 0.7600 & 0.8626 \\  & GO-A-Im (pH 7.4) & 0.5040 & 0.5113 & 0.6534 & 0.8166 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The goodness-of-fit parameter \(R^{2}\) reported for the nanocarrier and different release conditions in each publication for four kinetic models. The Weibull Model showed a higher degree of correlation coefficient for 69% of the nanocarriers under any release condition, with \(R^{2}\) values ranging from 0.7734 to 0.9982. This suggests that, although the pH affects the rate of release, the mechanism of drug release is the same.