## 2 Materials and Methods
### Sample Characterization  
Fourier-transform infrared (FTIR) analysis was performed using a Jasco FTIR 4700 spectrometer (JASCO Corporation, Tokyo, Japan) equipped with a Specac MKII Golden Gate single-reflection diamond ATR system (Specac Ltd., Orpington, UK). Samples were scanned over a wavenumber range of 4000-650 cm\({}^{-1}\), and the resulting spectra were compared to identify any changes in functional groups or molecular interactions. Gel permeation chromatography (GPC) was used to assess whether the addition of nucleating agents led to any significant degradation of the polymer chains. The analysis was performed using a Shimadzu LC-8A liquid chromatographic pump controlled by LC Solution software, version 5.114 (Shimadzu Corporation, Tokyo, Japan). For each sample, 10 mg was dissolved in 1 mL of 1,1,3,3,3-hexafluoroisopropanol (HFIP) containing 0.05 M sodium trifluoroacetate (CF\({}_{3}\)COONa), which was also the eluent for the column. The flow rate was set at 1 mL/min, and the injected volume was 20 \(\mu\)L with a sample concentration of 10 mg/mL. A PL-HFIP-gel column (Agilent Technologies Deutschland GmbH, Boblingen, Germany) and detection was achieved with a Shimadzu RID-20A refractive index detector (Shimadzu Corporation, Tokyo, Japan). The molecular weights (\(M_{w}\) and \(M_{n}\)) and polydispersity index (PDI) of each sample were determined using polymethyl methacrylate standards. Thermogravimetric analysis (TGA) was performed using a Q50 thermogravimetric analyzer (TA Instruments, New Castle, DE, USA) to investigate the thermal stability of the P3 HBHHx samples in the presence of the nucleating agents. The samples were \begin{table}
\begin{tabular}{c c c} \hline \hline
**Sample Code** & **Nucleating Agent** & **Concentration (wt\%)** \\ \hline P3 HBHHx & None & 0 \\ PHH\_05 BN/PHH\_2 BN & Boron nitride & 0.5/2 \\ PHH\_05 PHB/PHH\_2 PHB & P3 HB & 0.5/2 \\ PHH\_05 Talc/PHH\_2 Talc & Talc & 0.5/2 \\ PHH\_05 LAK/PHH\_2 LAK & Organic potassium salt & 0.5/2 \\ PHH\_05 UFC/PHH\_2 UFC & Ultrafine cellulose & 0.5/2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: P3 HBHHx samples prepared with various nucleating agents at concentrations of 0.5 wt% and 2 wt%. heated from room temperature to 550 \({}^{\circ}\)C at a constant heating rate of 10 \({}^{\circ}\)C/min under a nitrogen atmosphere (flow rate: 50 mL/min) to ensure an inert environment and minimize oxidative degradation. This heating rate is commonly used in TGA protocols to evaluate the thermal stability of biodegradable polymers and aligns with the recommendations of ISO 11358-1:2022 [27; 28]. The degradation behavior was assessed by analyzing the temperatures at which specific percentages of mass loss occurred: \(T_{5\%}\) (5% mass loss), \(T_{50\%}\) (50% mass loss), and \(T_{90\%}\) (90% mass loss) temperatures. These parameters provide insights into the onset, midpoint, and extent of thermal degradation. In particular, \(T_{5\%}\) is widely used to indicate the initial degradation temperature, which is critical for assessing the thermal resistance of a material during processing. Additionally, the temperature at the maximum rate of mass loss (\(T_{\text{max}}\)) was determined from the derivative thermogravimetric (DTG) curve, which represents the point of the highest decomposition rate. These parameters together offer a comprehensive understanding of how different nucleating agents influence the thermal stability of P3 HBHHx. Differential scanning calorimetry (DSC) analysis was performed using a Q100 series DSC instrument (TA Instruments, New Castle, DE, USA) equipped with a refrigerated cooling system capable of operating within a temperature range of \(-\)90 to 550 \({}^{\circ}\)C. Each experiment was performed under a flow of dry nitrogen (flow rate: 50 mL/min) using approximately 4 mg of sample. The instrument was calibrated for both temperature and heat of fusion using an indium standard to ensure measurement accuracy and reproducibility.