The Effectiveness of the Havriliak-Negami Model in Predicting the Master Curves of the Asphalt Blends with SBS Triblock Copolymer and Organic-Montmorillonite at Different Temperatures and Frequencies

The dynamic viscoelastic properties of asphalt AC-20 and its composites with Organic-Montmorillonite clay (OMMt) and SBS were modeled using the empirical Havriliak-Negami (HN) model, based on linear viscoelastic theory (LVE). The HN parameters, α, β, G0, G∞and τHN were determined by solving the HN equation across various temperatures and frequencies. The HN model successfully predicted the rheological behavior of the asphalt and its blends within the temperature range of 25˚C - 40˚C. However, deviations occurred between 40˚C - 75˚C, where the glass transition temperature Tg of the asphalt components and the SBS polymer are located, rendering the HN model ineffective for predicting the dynamic viscoelastic properties of composites containing OMMt under these conditions. Yet, the prediction error of the HN model dropped to 2.28% - 2.81% for asphalt and its mixtures at 100˚C, a temperature exceeding the Tg values of both polymer and asphalt, where the mixtures exhibited a liquid-like behavior. The exponent α and the relaxation time increased with temperature across all systems. Incorporating OMMt clay into the asphalt blends significantly enhanced the relaxation dynamics of the resulting composites.

一种用于水声材料设计的动态参数测试方法

针对提高水声材料设计中动态参数输入精度的问题,提出了一种复杨氏模量及泊松比准确测试方法。对于复杨氏模量测试,通过将Williams-Landel-Ferry(WLF)方程引入到Havriliak-Negami(H-N)模型中,采用信赖域反射算法对未知参数进行拟合得到材料参数宽频域主曲线。对于泊松比测试,根据同一材料不同形状因子表观杨氏模量之比与泊松比存在唯一量化关系的特性,仅通过两种不同形状因子试样的准静态有限元模拟,获得表观杨氏模量比值与泊松比量化曲线。因此,根据橡胶样品表观杨氏模量测试结果,可以直接利用局部加权回归获得其泊松比。最后,将前述材料制成直径为55 mm、厚度为50 mm的声管样品,放置在水声管中进行吸声系数测试。同时,把橡胶的复杨氏模量和泊松比的测量结果输入到水-橡胶-水分层介质模型中进行吸声系数计算。结果表明两者吻合,验证了上述测试方法的正确性和有效性。

Parameter of dielectric loss distribution in the new model for complex conductivity based on Havriliak-Negami formula

This paper is focused on the comparison of the results of various approximation models describing the frequency dependences of the dielectric constanε'/ε_(0)(f)andε"/ε_(0)(f),the tangent of the loss angle tgδ(f)T and the electrical conductivityγ'(f)T andγ"(f)T of nonlinear dielectrics.The classic ferroelectric material of the PZT system with x=0.50 was chosen as the object of study.Based on the analysis of temperature-frequency dependences of the“empirical”parametersαandβ,a regularity has been revealed that allows them to be calculated.A new relationship has been established through the parameterα,which allows to relate the temperature and frequency dependences of the complex electrical conductivity asω→∞and asω→0 in the Havriliak-Negami approximation models and in the new model for the description of the complex electrical conductivityγ*.It is shown thatαis a parameter of the temperature-frequency distribution of dielectric losses.Using the obtained expressions,a new theoretical description of experimental spectra having a relaxation character was proposed.It has been proven that the use of the new model makes it possible to accurately describe the set of studied spectra,including the high and low frequencies,in the frequency range from 10^(-3) to 10^(8) Hz.

Dielectric and piezoelectric properties of modified lead-free NaNbO_(3)-KNbO_(3)/PVDF composite ceramics

This work presents the results of study of the electrophysical properties of composite polymer ceramics(1−x)[KNN-LTSN]-xPVDF at x=25 vol.%and x=50 vol.%in the temperature range of T=20-160℃and frequency range of f=2×10^(1)-2×10^(6)Hz.The concentration dependence of piezomodules of the studied materials has been analyzed as a function of temperature.X-ray measurements have also been carried out.A model of description of revealed dielectric parameters dispersion in the material is presented.The nonclassical modified Havriliak-Negami model written for complex electrical conductivity has been used to describe the temperature-frequency properties.It is shown that the dielectric spectra of the studied composites include three relaxation processes in the temperature ranges of 40-80℃,80-120℃and 120-150℃,which were confirmed by the dynamics of changes in the dependences of g′(f),tgδ(f),M′(f),M″(f)and M″(M′).All three processes are almost exactly described by this model and well correlated with the studies by other researchers of the composites based on PVDF.The results of this work show that the use of such experimental model is suitable for describing the complex dielectric spectra of any nonlinear dielectrics including composite materials.

Studying of dielectric spectra of YCu_(0.15)Mn_(0.85)O_(3)solid solution with the use of complex conductivity

This work presents the results of studying the electrophysical properties of the YCu_(0.15)Mn_(0.85)O_(3)solid solution in the range of temperatures of T=26-400°C and frequency range of f=102-105 Hz.A model description of the revealed dispersion of dielectric parameters in the material is made.The nonclassical modified Havriliak-Negami model written for complex electrical conduc-tivity was used as an approximation model.It is shown that the application of this model almost exactly describes the frequency behavior of the dielectric constantε′/ε0(f),the dielectric loss tangent tgδ(f)as well as the real and imaginary parts of complex conductivityγ′(f)andγ′′(f).The results of this work are an important step in identifying the opportunities and understanding the applications of this model.