1：Experimental Design and Method Selection:

The study used solution casting technique combined with ultrasonic dispersion to prepare composite films. Surface modification of BiFeO3 particles was performed with 2-aminoethanesulfonic acid to enhance dispersion and interface compatibility.

2：Sample Selection and Data Sources:

BiFeO3 particles were synthesized from bismuth oxide and ferric oxide via solid-state reaction. PMMA pellets were used as the polymer matrix. Samples included pure and modified BFO with varying weight percentages (e.g., 10 wt.%, 30 wt.%, 40 wt.%) in PMMA composites.

3：List of Experimental Equipment and Materials:

Equipment included agate mortar for mixing, high-purity alumina crucible for calcination, round-bottomed flask and reflux setup for modification, ultrasonic bath for dispersion, vacuum oven for drying, powder x-ray diffractometer (Rigaku Ultimate IV) for XRD, scanning electron microscope (ZEISS-EVO-18) for SEM, Nicolet Impact 5700 spectrometer for FTIR, and HIOKI 3532 LCR HiTESTER for dielectric measurements. Materials included Bi2O3, Fe2O3, ethanol, 2-aminoethanesulfonic acid, PMMA pellets, N,N-dimethylformamide (DMF), and glass plates.

4：Experimental Procedures and Operational Workflow:

BFO synthesis involved mixing oxides, calcining at 700°C. Surface modification involved dispersing BFO in ethanol, adding modifier, refluxing at 105°C for 4 hours, washing, and drying. Composite fabrication involved dissolving PMMA in DMF, dispersing modified BFO, casting on glass, and evaporating solvent in vacuum oven. Characterization included XRD, SEM, FTIR, and dielectric property measurements.

5：Data Analysis Methods:

Dielectric constant and loss were calculated from capacitance measurements. Percolation theory was applied using power law equations. Data fitting and analysis were performed to determine critical exponents and thresholds.