## 3 Results and Discussion
### Thermal Behaviour Analysis  
Differential Scanning Calorimetry (DSC) analysis was conducted to determine the thermal parameters of the samples, including T\({}_{\text{m}}\) (melting temperature), T\({}_{\text{c}}\) (crystallisation temperature), \(\Delta\text{H}_{\text{m}}\) (melting enthalpy), and \(\Delta\text{H}_{\text{c}}\) (crystallisation enthalpy). These values were extracted from the DSC cooling and second heating thermograms of the neat PBAT polymer and alum sludge/PBAT composites with various alum sludge concentrations, as illustrated in Figures 5a and 5b, respectively, and are summarised in Table 1. The degree of crystallinity was calculated using Equation (1). \[\text{X}_{\text{c}}(\%)=\frac{\Delta\text{H}_{\text{m}}}{1-\alpha\times \Delta\text{H}_{\text{m}0}}\times 100 \tag{1}\]  
where \(\Delta\text{H}_{\text{m}0}\) is the crystallisation enthalpy of 100% PBAT, taken as 114 J/g [34], and \(\alpha\) is the alum sludge content in the composite. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Sample** & **T\({}_{\text{c}}\) (\({}^{\circ}\)C)** & \(\Delta\text{H}_{\text{c}}\) (\(\
icefrac{{\text{1}}}{{\text{g}}}\)) & **T\({}_{\text{m}}\) (\({}^{\circ}\)C)** & \(\Delta\text{H}_{\text{m}}\) (\(\
icefrac{{\text{1}}}{{\text{g}}}\)) & **X\({}_{\text{c}}\) (\%)** \\ \hline Neat & 74.58 & 11.11 & 129.15 & 18.51 & 16.24 \\ \cline{3-6}
5 wt.\% & 74.38 & 14.44 & 121.92 & 15.49 & 14.30 \\ \cline{3-6}
10 wt.\% & 74.68 & 12.12 & 121.61 & 13.77 & 13.42 \\ \cline{3-6}
20 wt.\% & 74.43 & 11.94 & 119.56 & 13.85 & 15.19 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: DSC analysis for thermal properties of alum sludge/PBAT composites. Figure 5: DSC analysis of (**a**) crystallisation exotherms during the first cooling cycle and (**b**) melting endotherms during the second heating cycle for neat PBAT and alum sludge/PBAT composites. The incorporation of alum sludge into the PBAT matrix resulted in a reduction in the melting temperature of the composites, with the decrease becoming progressively more pronounced as the sludge concentration increased. For instance, the 20 wt.% sludge sample exhibited a T\({}_{\text{m}}\) reduction of approximately 20% compared to the neat PBAT polymer. A similar trend was observed for the melting enthalpy and degree of crystallinity, both of which decreased as the filler concentration increased. These reductions could be attributed to the disruption of the crystalline structure in the PBAT matrix. Since alum sludge is amorphous and has a low crystallinity, its distribution in the PBAT matrix decreases the amount of polymer available to form crystalline regions, thereby lowering the melting temperature. Secondly, the presence of sludge may interfere with polymer chain alignment, further reducing the extent of crystallinity and the thermal energy required for melting. Figure 5 shows the crystallisation exotherms and melting endotherms for all samples. In Figure 5a, the crystallisation exotherms become broader as the alum sludge concentration increases. This broadening suggests that the sludge, with its low molecular mobility, acts as a physical battier, hindering the crystallisation of PBAT and slowing the rate of crystallisation [35]. The small peaks (119-120 \({}^{\circ}\)C) and big peaks (~74 \({}^{\circ}\)C) could be attributed to the crystalline regions of the butylene adipate (BA) and the crystalline phase of poly butylene terephthalate, respectively [36; 37]. The melting endotherms in Figure 5b become progressively broader with increasing alum sludge concentrations. In contrast, composites with lower sludge concentrations exhibit a sharper rise in heat flow after the melting peak (T\({}_{\text{m}}\)), closely resembling the behaviour of neat PBAT. This suggests that higher filler concentrations may impede the flow of the molten composite, likely due to sludge particles disrupting polymer chain mobility.