Rentería-Baltiérrez Flor Y, Puente-Córdova Jesús G, Mohamed-Noriega Nasser, Luna-Martínez Juan
Facultad de Ciencias Químicas, Universidad Autónoma de Nuevo León, Av. Universidad s/n, San Nicolás de los Garza 66455, Mexico.
Facultad de Ingeniería Mecánica y Eléctrica, Universidad Autónoma de Nuevo León, Av. Universidad s/n, San Nicolás de los Garza 66455, Mexico.
Polymers (Basel). 2025 Jun 20;17(13):1726. doi: 10.3390/polym17131726.
The dielectric relaxation behavior of polymeric materials is critical to their performance in electronic, insulating, and energy storage applications. This study presents an electrical fractional model (EFM) based on fractional calculus and the complex electric modulus (M*=M'+iM″) formalism to simultaneously describe two key relaxation phenomena: α-relaxation and interfacial polarization (Maxwell-Wagner-Sillars effect). The model incorporates fractional elements (cap-resistors) into a modified Debye equivalent circuit to capture polymer dynamics and energy dissipation. Fractional differential equations are derived, with fractional orders taking values between 0 and 1; the frequency and temperature responses are analyzed using Fourier transform. Two temperature-dependent behaviors are considered: the Matsuoka model, applied to α-relaxation near the glass transition, and an Arrhenius-type equation, used to describe interfacial polarization associated with thermally activated charge transport. The proposed model is validated using literature data for amorphous polymers, polyetherimide (PEI), polyvinyl chloride (PVC), and polyvinyl butyral (PVB), successfully fitting dielectric spectra and extracting meaningful physical parameters. The results demonstrate that the EFM is a robust and versatile tool for modeling complex dielectric relaxation in polymeric systems, offering improved interpretability over classical integer-order models. This approach enhances understanding of coupled relaxation mechanisms and may support the design of advanced polymer-based materials with tailored dielectric properties.
聚合物材料的介电弛豫行为对其在电子、绝缘和能量存储应用中的性能至关重要。本研究提出了一种基于分数阶微积分和复电模量（M* = M'+iM″）形式的电学分数模型（EFM），以同时描述两个关键的弛豫现象：α弛豫和界面极化（麦克斯韦-瓦格纳-西拉斯效应）。该模型将分数阶元件（电容电阻）纳入修改后的德拜等效电路，以捕捉聚合物动力学和能量耗散。推导了分数阶微分方程，分数阶取值在0到1之间；使用傅里叶变换分析频率和温度响应。考虑了两种与温度相关的行为：应用于玻璃化转变附近α弛豫的松冈模型，以及用于描述与热激活电荷传输相关的界面极化的阿累尼乌斯型方程。使用无定形聚合物、聚醚酰亚胺（PEI）、聚氯乙烯（PVC）和聚乙烯醇缩丁醛（PVB）的文献数据对所提出的模型进行了验证，成功拟合了介电谱并提取了有意义的物理参数。结果表明，EFM是一种用于模拟聚合物系统中复杂介电弛豫的强大且通用的工具，与经典整数阶模型相比具有更好的可解释性。这种方法增强了对耦合弛豫机制的理解，并可能支持设计具有定制介电性能的先进聚合物基材料。
