Meng Ruifan
Institute for Systems Rheology, School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, China.
Membranes (Basel). 2021 May 29;11(6):409. doi: 10.3390/membranes11060409.
Ferroelectric polymer composites normally show non-linear mechanical and electrical behaviors due to the viscoelastic and dielectric relaxation of polymer matrixes. In this paper, a fractional calculus approach is used to describe the non-linear behavior of ferroelectric polymer composites from both viscoelastic and dielectric perspectives. The fractional elements for viscoelasticity and dielectricity are "spring-pot" and "cap-resistor", which can capture the intermediate properties between spring and dashpot or capacitor and resistor, respectively. For modeling the viscoelastic deformation, the "spring-pot" equation is directly used as the fractional mechanical model. By contrast, for the dielectricity of ferroelectric polymer composites, which is usually characterized by dielectric constants and dielectric losses, the "cap-resistor" equation is further formulated into the frequency domain by Fourier transform to obtain the fractional order dielectric model. The comparisons with experimental results suggest that the proposed models can well describe the viscoelastic deformation as well as the frequency dependence of the dielectric constant and dielectric loss of ferroelectric polymer composites. It is noted that the fractional order dielectric model needs to be separated into two regions at low and high frequencies due to the polarization effect. Additionally, when the dipole relaxations occur at higher frequencies, the proposed model cannot describe the rise of the dielectric loss curve.
铁电聚合物复合材料通常由于聚合物基体的粘弹性和介电弛豫而呈现非线性力学和电学行为。本文采用分数阶微积分方法从粘弹性和介电两个角度描述铁电聚合物复合材料的非线性行为。粘弹性和介电性的分数阶元件分别为“弹簧 - 壶”和“电容 - 电阻”，它们能够分别捕捉弹簧与阻尼器或电容器与电阻器之间的中间特性。为了对粘弹性变形进行建模，直接将“弹簧 - 壶”方程用作分数阶力学模型。相比之下，对于通常由介电常数和介电损耗表征的铁电聚合物复合材料的介电性，通过傅里叶变换将“电容 - 电阻”方程进一步推导到频域，以获得分数阶介电模型。与实验结果的比较表明，所提出的模型能够很好地描述铁电聚合物复合材料的粘弹性变形以及介电常数和介电损耗的频率依赖性。需要注意的是，由于极化效应，分数阶介电模型在低频和高频需要分为两个区域。此外，当偶极弛豫发生在较高频率时，所提出的模型无法描述介电损耗曲线的上升。
