Fractional Calculus as a Tool for Modeling Electrical Relaxation Phenomena in Polymers

Area of Science:

• Materials Science
• Polymer Physics
• Dielectric Spectroscopy

Background:

• Dielectric relaxation in polymers is crucial for electronic and energy storage applications.
• Existing models often struggle to capture multiple relaxation phenomena simultaneously.
• Understanding polymer dynamics and energy dissipation is key to material performance.

Purpose of the Study:

• To develop and validate an electrical fractional model (EFM) for describing coupled dielectric relaxation in polymers.
• To simultaneously model α-relaxation and interfacial polarization (Maxwell-Wagner-Sillars effect).
• To enhance the interpretability of polymer dielectric behavior.

Main Methods:

• Utilized fractional calculus and complex electric modulus formalism.
• Incorporated fractional elements (cap-resistors) into a modified Debye equivalent circuit.
• Analyzed frequency and temperature responses using Fourier transform and temperature-dependent models (Matsuoka, Arrhenius).

Main Results:

• The EFM successfully modeled dielectric spectra for amorphous polymers, PEI, PVC, and PVB.
• The model accurately captured both α-relaxation and interfacial polarization.
• Meaningful physical parameters were extracted, demonstrating model robustness.

Conclusions:

• The EFM is a versatile and robust tool for modeling complex dielectric relaxation in polymers.
• This approach offers improved interpretability over classical integer-order models.
• The EFM aids in understanding coupled relaxation mechanisms and designing tailored polymer materials.