Loss Factor Peak Research Articles

Vitrification and dielectric relaxation during the isothermal curing of an epoxy–amine resin

The isothermal curing of an epoxy resin based on diglycidyl ether of bisphenol A (DGEBA) with a diamine based on 4,4′-diamino-3,3′-dimethyldicyclohexylmethane (3DCM) was analysed by dielectric relaxation spectroscopy (DRS), conventional differential scanning calorimetry (DSC) and temperature modulated DSC (TMDSC). The chemical kinetics corresponds to an autocatalytic model with an apparent activation energy of 58 kJ mol −1. The vitrification was analysed by TMDSC, between 40 and 140 °C, using the modulus of the complex heat capacity, |C p ∗|. A mobility factor based on the evolution of |C p ∗| was used to study the reaction step controlled by diffusion. The permittivity and loss factor were measured by DRS as a function of time in the frequency range between 10 Hz and 100 kHz. The dipolar relaxation, analysed by the peak of the maximum loss factor, was correlated with the vitrification determined by TMDSC. The analysis of the logarithm of the frequency against the conversion degree allows the characterisation of the molecular dynamics of the crosslinking reaction up until the vitrification of the system.

Damping Properties of Polyorganosiloxane/Poly(methyl methacrylate) Interpenetrating Networks

Interpenetrating polymer networks (IPNs) based on polyorganosiloxane/poly(methyl methacrylate) were prepared via sequential polymerization and the damping and mechanical properties of these materials were studied. The effects of crosslinking in both the first- and second-formed networks were investigated. The experimental results show that the extent of damping of the IPNs was decreased and shifted to higher temperature as the content of poly(methyl methacrylate) was increased; the mechanical properties such as tensile strength and hardness (Shore A) were increased with increasing poly(methyl methacrylate) (PMMA) content. The loss factor peak becomes narrower with increasing crosslinker level in the first-formed network (polysiloxane network), while increasing crosslinker content in the second-formed network (PMMA network) results in a broadening of the IPN transition peak and moves the IPN transition to higher temperatures as well.

LOSS FACTOR PEAK OF VISCOELASTIC MATERIALS: MAGNITUDE TO WIDTH RELATIONS

The loss factor of viscoelastic materials as a function of frequency has at least one peak. The relation between the magnitude and width of the loss factor peak is investigated in this paper by means of the fractional derivative Zener model with special reference to polymeric materials used for sound and vibration damping. It is shown that the magnitude and width are interrelated through the dispersion of dynamic modulus and the rate of frequency variation of loss factor. Moreover, it is proved that the relation between the magnitude and width of the loss factor peak is not unequivocal; either proportionality or inverse proportionality may exist between them. The important consequence of prediction on the proportionality is that, in contrast to the common belief concerning polymers, it is physically possible to increase the loss factor while simultaneously broadening the peak. The validity of model predictions is discussed and it is proved that the predictions are of a general nature, because they obey fundamental physical principles. Experimental data supporting the theoretical predictions are presented.

Vibration-induced jamming transition in granular media

The quasistatic frequency response of a granular medium is measured by a forced torsion oscillator method, with forcing frequency f(p) in the range 10(-4) Hz to 5 Hz, while weak vibrations at high-frequency f(s), in the range 50 Hz to 200 Hz, are generated by an external shaker. The intensity of vibration Gamma is below the fluidization limit. A loss factor peak is observed in the oscillator response as a function of Gamma or f(p). In a plot of ln f(p) against 1/Gamma, the position of the peak follows an Arrhenius-like behavior over four orders of magnitude in f(p). The data can be described as a stochastic hopping process involving a probability factor exp(-Gamma(j)/Gamma) with Gamma(j) a f(s)-dependent characteristic vibration intensity. An f(s)-independent description is given by exp(-tau(j)/tau), with tau(j) an intrinsic characteristic time, and tau=Gamma(n)/2pif(s), n=0.5-0.6, an empirical control parameter with unit of time. tau is seen as the effective average time during which the perturbed grains can undergo structural rearrangement. The loss factor peak appears as a crossover in the dynamic behavior of the vibrated granular system, which, at the time scale 1/f(p), is solid-like at low Gamma, and the oscillator is jammed into the granular material, and is fluid-like at high Gamma, where the oscillator can slide viscously.

The dielectric properties of glass-fibre-reinforced epoxy resin during polymerisation

The change in dielectric properties of thermosets between 10 Hz and 1 MHz allows us to monitor the cure of these materials. During the first heating phase at 80°C the resin conductivity (which is correlated with the Newtonian viscosity by a power law) decreases by several decades. In the subsequent heating phase at 140°C, the glass transition process is observed as a broad maximum of the dielectric loss factor at 30 kHz. The shift of the loss factor peak to lower frequencies with cure time marks the increasing relaxation time of the curing system. The relaxation time and the conductivity are indicators for cure monitoring that do not depend on frequency. So they are suitable for a comparison with other methods like DSC, FTIR and rheometry. The glass transition is analysed in the complex plane with a skewed arc function proposed by Havriliak and Negami (Havriliak S, Negami S. A complex plane analuysis of α-dispersions in some polymer systems. J Pol Sci C 1966;14:99–117). There is no significant change in the shape of the dielectric complex-plane plot during curing. The cure-monitoring parameters conductivity and relaxation time are not much affected by glass-fibre reinforcement. Only the relaxation strength and the maximum value of the loss factor are reduced as a result of the low loss factor of the glass fibres.

DSC and DEA studies of underfill curing kinetics

Isothermal and non-isothermal differential scanning calorimetry (DSC) and dielectric analysis (DEA) techniques were used to study the curing kinetics of an epoxy-based underfill material used in electronic packaging. Based on the phenomenological kinetic analyses, the activation energy for the curing reaction determined from the non-isothermal DSC studies is similar to that obtained from the isothermal DSC experiments. DEA and rheological analyses demonstrated that the DEA loss factor peak can be used to monitor the gelation. In addition, our results reveal that the activation energy determined by DEA experiments (both isothermal and non-isothermal) correlates well with the DSC results.

Differences in wood material responses for radial and tangential direction as measured by dynamic mechanical thermal analysis

Wood is a complex cellular structure with different properties in the radial and tangential direction. Many researchers have measured dynamic properties in the longitudinal direction and a few in the radial direction but very little data can be found in the literature on dynamic mechanical properties in the tangential direction. The purpose of the work presented in this paper was to investigate the dynamic mechanical behaviour in the radial and tangential directions of wood (Pinus sylvestris). Testing was done in tension at 1 Hz with a Dynamic Mechanical Thermal Analyser. Properties in radial and tangential direction were different. The radial direction showed a higher elastic modulus and lower loss factor levels at temperatures between −120°C and 80°C. The tangential direction had on average a higher peak temperature than the radial direction for a loss factor peak around −80°C. It is the opposite of synthetic composites where the stiffer direction has a higher peak temperature. A loss factor peak at around 0°C was seen, most significantly in the tangential direction. This peak has scarcely been reported in the literature before. The distance between annual rings did not significantly affect the dynamic behaviour in the tangential direction.

Mechanical and morphological study of polyurethane/polystyrene interpenetrating polymer networks containing ionic groups

The viscoelastic and mechanical properties and the morphology of polyurethane (PUR)/ olystyrene (PS) interpenetrating polymer networks (IPNs) containing ionic groups have been investigated. Dynamic mechanical thermal analysis (DMTA) revealed a pronounced change in the viscoelastic properties upon the introduction of ionic groups. For the 70 : 30 and 60 : 40 PUR/PS IPN compositions, the DMTA data changed from a dominant PUR to a dominant PS loss factor peak. Higher intertransition loss factor values indicated a significant improvement of IPN component mixing with increasing ionic content. The stress at break values increased only moderately, whereas sharp rises in Young's modulus and hardness values were found at 2 wt % ionic groups. At the same time, the strain at break values decreased by half. Scanning and transmission electron microscopy (TEM) indicated a grossly phase-separated morphology for the 70 : 30 PUR/PS IPN without ionic groups. With increasing methacrylic acid (MAA) content, the PS phase domain sizes decreased. At 2 wt % of ionic groups, a TEM micrograph showed interconnected PS phase domains resembling a network structure. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 67:1973–1985, 1998

Mechanical and morphological study of polyurethane/polystyrene interpenetrating polymer networks containing ionic groups

The viscoelastic and mechanical properties and the morphology of polyurethane (PUR)/ olystyrene (PS) interpenetrating polymer networks (IPNs) containing ionic groups have been investigated. Dynamic mechanical thermal analysis (DMTA) revealed a pronounced change in the viscoelastic properties upon the introduction of ionic groups. For the 70 : 30 and 60 : 40 PUR/PS IPN compositions, the DMTA data changed from a dominant PUR to a dominant PS loss factor peak. Higher intertransition loss factor values indicated a significant improvement of IPN component mixing with increasing ionic content. The stress at break values increased only moderately, whereas sharp rises in Young's modulus and hardness values were found at 2 wt % ionic groups. At the same time, the strain at break values decreased by half. Scanning and transmission electron microscopy (TEM) indicated a grossly phase-separated morphology for the 70 : 30 PUR/PS IPN without ionic groups. With increasing methacrylic acid (MAA) content, the PS phase domain sizes decreased. At 2 wt % of ionic groups, a TEM micrograph showed interconnected PS phase domains resembling a network structure. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 67:1973–1985, 1998

Relationship between interfacial phenomena and viscoelastic behavior of laminated materials

A literature review shows that the main arguments used to describe viscoelastic behavior of polymer composites are the existence of an interphase and/or physico-chemical matrix-reinforcement interactions. The purpose of this investigation was to study the influence of both of these parameters on the viscoelastic behavior of a sandwich structure. Using a theoretical approach of the mechanical coupling between phases in laminate composites, the interphase influence is shown to be negligible. In order to understand the influence of an interphase on viscoelastic features of laminates, some metal/polymer/metal laminates were processed under various conditions to obtain different degrees of metal/polymer adhesion. Dynamic mechanical spectroscopy tests reveal that both the amplitude of the main loss factor peak and the low temperature apparent modulus increase with the adhesion. Finite elements calculations show that discontinuities of displacements at the metal/polymer interface explain the loss peak changes. The continuity of displacements is ensured only from a threshold value of the peel energy.

Structural effects on dynamic features of sandwich metal/polymer/metal

A theoretical approach to the mechanical coupling between phases in metal/polymer/metal sandwich composites is developed assuming perfect interfaces. Comparisons between experimental dynamic mechanical spectroscopy and theoretical results are made with special attention to the geometrical characteristics. Unexpected results concerning the dependence on the width of the specimen are explained using the strain energy method. The polymer thickness influence is explained only by structural effects instead of the interface effects often found in the literature. The temperature of the sandwich loss factor peak is revealed to greatly depend on the specimen dimensions. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 65: 2493–2505, 1997

Structural effects on dynamic features of sandwich metal/polymer/metal

A theoretical approach to the mechanical coupling between phases in metal/polymer/metal sandwich composites is developed assuming perfect interfaces. Comparisons between experimental dynamic mechanical spectroscopy and theoretical results are made with special attention to the geometrical characteristics. Unexpected results concerning the dependence on the width of the specimen are explained using the strain energy method. The polymer thickness influence is explained only by structural effects instead of the interface effects often found in the literature. The temperature of the sandwich loss factor peak is revealed to greatly depend on the specimen dimensions. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 65: 2493–2505, 1997

EFFECT OF DIELECTRIC PROPERTY OF HYDROUS DISPERSOID ON ELECTRORHEOLOGY

The effect of the dielectric property was investigated of titania and microcrystalline cellulose particles dispersed in a silicon oil on Electrorheology(ER). A commom understanding of the mechanism of ER is the electrical interaction by the interfacial polarization of dispersed particles. Block et al. reported the relaxation frequency of ER fluids, i. e. the rate of polarization, was very important to have an appreciable ER effect. We found that the free water on the cellulose and the titania particles dispersed in the silicon oil, which is respectively dehydrated below the temperature of ca. 110 and 300 degree centigrade, was necessary for an appreciable ER effect. The relation was measured between the water content and the dielectric properties such as dielectric constant ε ’ and dielectric loss factor ε ", as the water adsorbed on the particles was estimated to alter the dielectric properties of the ER fluid. Both the dielectric constant and the relaxation frequency, which is defined by the applied frequency for a peak of the dielectric loss factor, increased with the increase of the water content The relation was discussed between the ER effect and the dielectric properties.

Field dependent temperature shift of dielectric losses peak in TGS

Abstract Dielectric constant and loss factor measurements have been performed in triglycine sulfate single crystals at the vicinity of the Curie temperature (Tc≈48.5°C) as a function of ac driving field (20≤v≤106 Hz) in a wide range of field amplitude (50≥Eo≥0.15V/cm). Well defined shifts of loss factor peak (Dmax), increasing monotonously with the field, not previously reported as far as we know, were observed and analyzed in terms of the energy dissipated within the vanishing hysteresis loops at T≈Tc corresponding to Eo≈Ec(T), coercive field.

Loss factor height and width limits for polymer relaxations

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.

Loss factor height–width tradeoffs for viscoelastic materials.

It is observed empirically that the height of the dynamic mechanical shear loss factor peak in a viscoelastic material is inversely related to the width of the peak (as a function of frequency). There is a question of whether this observation represents a fundamental limitation of nature or whether some new material might be found with a peak that is both high and broad. Starting with a single relaxation time model and progressing to the Havriliak–Negami model, the tradeoffs between height and width are pointed out. These analytical models confirm that the empirical observations represent fundamental limitations that high peaks are narrow and low peaks are broad. The height of the peak is maximized as the material approaches a single relaxation time. The width is maximized by minimizing the ratio of the relaxed modulus to the unrelaxed modulus and by minimizing the asymmetry of the relaxation. For realistic values of the parameters, a loss factor peak height of 2 can have a width of no more than about 3 decades. Conversely, a relaxation with a width of 8 decades can have a loss factor peak height of no more than 0.5.

Dielectric active defects and thermal conductivity of undoped KTaO3

Abstract It has been shown that “pure” incipient ferroelectric KTaO3 single crystals exhibit temperature size-dependent distorted micro-regions, which have been invoked to account for the sample-dependent phonon scattering observed in thermal conductivity K(T). A frequency-dependent dielectric loss peak (observed at 44 K for 1 kHz) is found to be present in all samples. The correlation between the thermal conductivity at 6.5 K and the intensity of the dielectric loss factor peak strongly supports the assumption that, below 20 K, K(T) is governed by the interaction of acoustic phonons with both the transverse optic soft mode and a dielectrically-active entity, the nature of which is still unknown.

Dynamic mechanical properties of toughened polysterene

The dynamic modulus and loss factor of various grades prepared high impact polystyrenes were measured at —140°C to 140°C. It is shown that the loss factor peak at the rubber transitional temperature increases monotonically with additional rubber content, and this can partially be correlated to the actual degree of material toughness.

Temperature-independent relaxation in a lamellar block copolymer

IT has long been assumed that all processes giving rise to stress relaxation in high polymers are very dependent on temperature. The peak in mechanical or dielectric loss factor (tanδ) can be used to characterise the most probable relaxation time of a high polymer solid. The temperature locus of this relaxation time is described by a simple Arrhenius-type law for low temperature, glassy state processes1 and by the Williams, Landel and Ferry expression2 for ‘Tg’ processes. We now report results for an elastomer exhibiting a unique relaxation process which remains essentially constant in position and magnitude over a temperature range of more than 100 K.

Dielectric Properties of Commercial Cooking Oils

SUMMARY— The finished drying of potato chips represents the first large‐scale use of microwaves in the food industry on a continuous basis. Hence it was deemed desirable to study the dielectric properties of various types of commercial cooking oils.The dielectric constant (ɛ), and loss tangent (tans) of 11 commercial fats and oils have been determined at three different temperatures and at three different frequencies in the microwave range. The differences in dielectric properties among these fats and oils appear to be attributable to the phase (solid vs. liquid) of the material and generally correspond to the degree of unsaturation as evidenced by iodine values. The differences in loss factors among these fats and oils at any given temperature and frequency (within the range at which the measurements were made) are too small to be of any practical importance in selecting any one of them for use in heating processes using microwaves or in choosing an optimal frequency (300, 1000 or 3000 megahertz, MHz).Data for one of the oils (number 9) were obtained over a wider range of frequencies and indicate that the loss factor peak(s) is/are found in the frequency range of 100 to 1000 MHz. Furthermore, from the data obtained for the other oils, it should be safe to assume that this oil is representative of dielectric properties of the entire group. The dielectric properties of bacon fat rendered by microwaves are almost identical to those of bacon fat rendered by conventional means.