Loss factor height and width limits for polymer relaxations

Abstract

Polymer relaxations at the glass transition are often used in damping applications. Questions arise whether there is any limit to the height and width of the damping peak that can be achieved. A related question is whether there are any limits on the combination of these two properties that are achievable. This later question arises because of the experimental observation that the height of the peak is inversely related to the width of the peak. In this paper, these questions are addressed using various analytical models of polymer behavior. Starting with the single relaxation time model and progressing to the Cole–Cole model, the Davidson–Cole model, and finally the Havriliak–Negami (HN) model, height and width predictions are obtained. It is found that the HN model predicts a band of physically possible height and width combinations when using reasonable values of the model parameters. High peaks are narrow and broad peaks are low. For a loss factor peak height of 2, the half-width must be less than 3 decades; for a half-width of 8 decades, the peak height must be less than 0.5. A comparison with experimental data for polymers of widely varying properties is in good agreement with these predictions.

Ultrasonic Energy Transfer and Stress Concentrations in a Single-Fiber Composite with Absorbing Interface Layer

“…Moreover, as noted earlier, an accurate description for the frequency dependence of damping in the dissipative interphase may be provided by the Havriliak-Negami model [60]. Hartmann et al [61], reported all the input parameters necessary for a complete description of viscoelastic material properties for a set of polyurethane polymers within the context of Havriliak-Negami theory. The HN fitting parameters for two selected polymers with distinctively different damping properties in the frequency range of interest are listed in Table 2.…”

“…An appropriate description for the frequency dependence of the complex modulus of polymers in the glass transition region is given by HavriliakNegami model [60,61]. According to HN model, the real and imaginary parts of the complex modulus are given by [61]:…”

“…Our primary goal is to fill this gap. Therefore, in this paper, we employ the novel features of Havriliak-Negami model [60], which is known to be an appropriate description for the frequency dependence of the complex modulus of polymers in the glass transition region [61], along with the classical method of eigenfunction expansion and the pertinent boundary conditions to study interaction of time harmonic longitudinal and shear plane waves with a single fiber-interphase-matrix composite system. The proposed model is of noble interest basically due to its inherent value as a canonical problem in elastodynamics.…”

Smoothing, Interpolating, and Modeling Complex Modulus Data for Viscoelastic Damping Materials, Including a New Approach to Temperature Shift Functions

“…B. Hartman, G. Lee, and J. Lee [14] have had success in fitting polyurethane CM data using the polynomial…”

Loss Factor Peak of Viscoelastic Materials: Magnitude to Width Relations

“…This fact is clear from a comparison of equations (6b) and (20). The relation between the magnitude and width of the loss factor peak for the Havriliak}Negami model was investigated in the work of Hartmann et al [14]. The authors determined the conjugate values of the loss factor and half-width by varying the exponent for "xed values of G /G and , and the inverse relation between K and = E was found.…”