Relationship between melt viscosity and dielectric relaxation time for a series of epoxide oligomers

Melt viscosity has been investigated for a series of bisphenol-A type epoxide oligomers with different weight-average mol wts (M?_w), ranging from 388 to 2640. The temperature dependence of the melt viscosity is described by the Williams–Landel–Ferry (WLF) equation. The melt viscosity η is correlated with both the direct current (dc) conductivity σ and the dielectric relaxation time τ. The two relationships between these three properties, σ·η^κ = const (0.63 ≦ κ ≦ 1.12) and η/τ^? = const (0.73 ≦ ? ≦ 1.06), are experimentally derived. Both exponents, κ and ?, depend on the M?_w of the oligomer. The lower M?_w oligomer has the larger value of κ. The κ value is close to unity for the low M?_w oligomer, which agrees with Walden's rule, σ·.η = const, applicable to most low mol wt liquids. The ? value is near unity for the epoxide oligomer with higher M?_w than 2000, which means that the melt viscosity is proportional to the dielectric relaxation time. The low M?_w oligomer (M?_w < 2000), on the other hand, has a smaller value of ? below unity. The result indicates that the melt viscosity is not proportional to the dielectric relaxation time for the low M?_w epoxide oligomer, whose dielectric α-relaxation is not governed by the Debye equation. © 1993 John Wiley & Sons, Inc.     

Dielectric properties above the glass transition for a series of epoxide prepolymers

Dielectric properties above the glass transition have been investigated for a series of bisphenol-A type epoxide prepolymers (388 ≤ M?_w ≤ 2640). Dielectric measurements were performed over a frequency range of 50 Hz–1 MHz using a vertical parallel plate cell which was constructed in the laboratory. The dielectric α-relaxation for each prepolymer fits the empirical model of the Havriliak–Negami equation. The temperature dependence of the dielectric relaxation time τ is described by the Williams–Landel–Ferry (WLF) equation as well as that of the direct current conductivity σ, which can be measured using the same cell. The relationship between τ and σ, σ^· τ^m = const, is derived from experimental results. The exponent m, which depends on the molecular weight of the prepolymer, is considered to correspond to the ratio of the segmental mobility to ionic mobility. The dielectric loss ε″ can be used as an indicator of the direct current conduction in the temperatures where the ionic component in ε″ becomes much larger than the dipole one.     

Study of dielectric relaxation of an epoxide oligomer by a direct current transient method

Dielectric α-relaxation of a bisphenol-A type epoxide oligomer has been investigated in the vicinity of the glass transition temperature (T_g) by the direct current (DC) transient method. The logarithm of the DC transient current for the oligomer was well approximated by the third order function of the logarithm of time. The complex dielectric constant was calculated through the Fourier transformation of that approximation function according to Simpson's integration rule in a frequency range of 10^?5 ? 1 Hz. At the temperature around the T_g (45°C), the dielectric α-relaxation process of the oligomer was found to be governed by the Havriliak-Negami equation. The relationship between the DC conductivity (σ) and the dielectric relaxation time (τ), σ·τ^m = const, is valid near and above the T_g of the oligomer. The DC transient current method combined with the DC conduction and the dielectric bridge measurements is considered to be a practical tool for analyzing the dielectric α-relaxation process of the epoxide oligomer over a wide frequency and temperature range.     

Dielectric properties of bisphenol-A novolac type epoxide oligomer as a parameter for cure monitoring

Dielectric properties above the glass transition temperature (T_g) have been investigated for three bisphenol-A novolac type epoxide oligomers (PGEBANs) that have some branching in each molecule in comparison with the diglycidyl ether of bisphenol-A (DGEBA) oligomer without branching. The relationship between the dielectric relaxation time (τ) and T_g for the branched PGEBAN oligomers is expressed by a modified Williams-Landel-Ferry (WLF) equation taking T_g as a variable at fixed temperatures from 70 to 100°C. The WLF-type relationships between τ and T_g for the two types of uncured epoxide oligomers, the branched PGEBAN and the nonbranched DGEBA, were found to be useful for predicting the T_g of a branched DGEBA-alicyclic amine system during the middle stage of curing.     

Free volume and dipole mobility in an epoxide oligomer before crosslinking

The free volume of a bisphenol‐A‐type epoxide oligomer (DGEBA) was studied using Williams–Landel–Ferry parameters and thermal expansion coefficients above and below the glass transition temperature (T_g). The values of the free‐volume fraction at the T_g are around 0.02 for the DGEBA oligomers having weight‐average molecular weights (M _w's) from 1396 to 2640. The dipole mobility, which was obtained from the analysis of the temperature dependence of the dielectric relaxation time, was compared with the segment mobility in terms of the critical volume for the transport of each moving unit. The critical volume for the segment transport increases with increase of the M _w of the oligomer. The critical volume for the dipole movement, on the other hand, is not different between the oligomers studied (1396 ≤ M _w ≤ 2640), which leads to that the dipole mobility in the epoxide oligomer is smaller than is the segment mobility. The low mobility of the dipole is considered to result from the molecular interaction restricting the dipole movement, especially in a smaller M _w oligomer. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 71: 207–214, 1999     

Electrode polarization for nylon 1010 with dielectric relaxation spectroscopy

Electrode polarization arising from charge carriers accumulating at the interface between an electrode and nylon 1010 was investigated with dielectric relaxation spectroscopy. In the frequency spectra of nylon 1010, the dielectric permittivity showed high values in the region of low frequencies and high temperatures. With the Havriliak–Negami function used to fit the experimental spectra, the result revealed that the high values originated from electrode polarization and direct‐current conductivity. For electrode polarization, the dielectric strength, independent of the temperature, was about 1150, and the temperature dependence of the relaxation time followed the Vogel–Tammann–Fulcher equation. Fitting with the Vogel–Tammann–Fulcher equation, the parameters τ₀ = 1.33 × 10^?10 s and T₀ = 303.2 K were proposed (where τ₀ is the relaxation time at a very high temperature and T₀ is the temperature at which the relaxation time becomes extremely large), and they suggested that the motion of the polymeric chains was one of the factors leading to charge‐carrier transport at temperatures higher than the glass‐transition temperature. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102: 3590–3596, 2006     

Dielectric relaxation during isothermal curing of epoxy resin with an aromatic amine

The isothermal curing behavior of an epoxy resin system has been monitored by a dielectric measurement whose sensor consisted of a vertical parallel-plate cell based on a three-terminal method. The materials used in the isothermal cure were the diglycidyl ether of bisphenol-A (DGEBA), which was purified from Epon 825 by recrystallization, and 4,4′-diamino diphenyl methane (DDM). A dielectric relaxation was observed during each isothermal cure at temperatures of 70,80,90, and 100°C, which were below the glass transition temperature (T_g) of the reactive DGEBA–DDM system at the gel point. The relaxation is considered to be caused by the transformation from a liquid state to an ungelled glassy state as a result of an increase in molecular weight because gelation followed by a rubbery state did not exist in the temperature range studied. The dielectric relaxation for the DGEBA–DDM system fits the empirical model of the Havriliak–Negami equation. The T_g of the DGEBA–DDM system, which was estimated from the dielectric relaxation time, agreed with the one experimentally determined by differential scanning calorimetry (DSC).     

Modeling the dielectric response of unsaturated polyester resin during cure

The dielectric relaxation of unsaturated polyester resin during cure was modeled using a modified Williams–Watts decay function. The dielectric response was studied using dielectric measurements coupled with two dynamic mechanical measurement methods. It was found that the variation of the relaxation time during cure is a WLF process using T_g (α) (α-conversion) as the varied temperature. It was shown that this process fits the Williams-Watts decay function Φ(t)=exp(-(t/τ)^β) where τ-relaxation time and β-empirical parameter are time dependent. It was found that τ obeys a time dependent power law rule and β depends linearly on log(time). Using this modified decay function, it was shown that the experimental dielectric response measured during cure agrees well with the computed response. Relaxation times above and below the dielectric measurement system capability were computed thus, demonstrating the capability of yielding the entire relaxation times spectrum during cure, out of a single limited frequency dielectric measurement.     

Structural development in ion‐irradiated poly(ether ether ketone) as studied by dielectric relaxation spectroscopy

Structural alterations to amorphous poly(ether ether ketone) (PEEK) produced by ion irradiation (11.2 MeV H⁺ and 25.6 MeV He²⁺ ions) were investigated by dielectric relaxation spectroscopy. The analysis in terms of the Havriliak–Negami (HN) equation and the scaling model showed an increase in the intermolecular correlation with increasing irradiation dose. The dynamic fragility index (m) was estimated from Vogel–Fulcher–Tammann analysis. Ion irradiation not only elevated the glass‐transition temperature (T_g) but interestingly decreased m of the PEEK chains around T_g. This was due to increasing polar interaction and better packing efficiency of the irradiated samples compared with those of amorphous PEEK. The average size of the cooperative rearranging region decreased in line with decreasing m and indicated an increase in the rigid amorphous phase fraction after irradiation. The analysis of the direct‐current conductivity confirmed that there was a strong coupling between the macroscopic ion transport and concerted segmental motion. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2014 , 131, 39929.     

Impedance Spectroscopy,Broadband, and Microwave Dielectric Properties of Mechanically Alloyed Ba5Nb4O15 Ceramics

Ba₅Nb₄O₁₅ (BNO) ceramics were synthesized by the mechanical alloying method. The transmission electron microscope images of BNO powders revealed rod‐shaped grains. Mechanically alloyed BNO exhibited maximum density of 97.3% and is explained on the basis of Herring's scaling law. Both the dielectric constant and loss tangent show a stable response up to 0.2 GHz. Further, the dielectric response of BNO ceramics measured above 350°C shows relaxation behavior and is explained using Havriliak–Negami equation. The obtained stable dielectric response of BNO is suitable for type I capacitor and dielectric resonator applications.     

Temperature dependence of viscosity of polyurethane polyol solutions: Application of rheological models

Polyurethane polyols were synthesized by reacting the diols with polyisocyanates. Viscosity of their 50% (w/w) solutions in various solvents has been determined at different temperatures by using Haake Roto Visco RV12 Rotational Viscometer. The temperature dependence of viscosity data was solved by Levenberg Marquardt's algorithm by using nonlinear regression models based on WLF, Vogel, and Arrhenius equations. The T_g values obtained from WLF and Vogel equation are comparable to each other and these equations can be satisfactorily used for the analysis of temperature dependence of viscosity data of oligomer solutions. The residuals are random and the absolute average percentage error in analyzing the viscosity data by these equations is minimum. The values of constants in WLF equation are found to be system dependent and adjustable parameters. The predicted In η values obtained from WLF and Vogel equations fit well with the plots of experimental In η values as a function of temperature. © 1996 John Wiley & Sons, Inc.     

Flow behavior of well characterized polyethylene melts

A careful characterization and rheological study of low density polyethylene (LDPE) reveals that long-chain branching (LCB) plays a decisive role. At constant molecular weight (M?_w) higher LCB reduces the Newtonian viscosity η_o and the shear sensitivity, increases the activation energy E_o, and finally delays transition to pseudoplastic flow to higher shear rates and the onset of melt fracture to higher shear stresses (τ_d). The flow parameters η_o, \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma _{cr} $\end{document}_cr, τ_d, and the derived flow relaxation times are uniquely correlatable by means of a modified molecular weight (gM?_w) incorporating the LCB effect. High density polyethylene are less shear sensitive than their low-density counterparts, have a lower activation energy, fracture at higher shear stress levels and cannot be regarded as branchless LDPE's.     

Diffusion of m-nitroaniline into polyacylonitrile

The diffusion of nonionic penetrant, m-nitroaniline, into polyacrylonitrile was studied in detail on a range of temperature from 50.6°C to 95.0°C. The penetrant distribution in polymer is Fickian, which is different from that of cationic dye, Malachite Green reported earlier. The diffusion coefficient D increases with the rise of temperature. The sharp inflection point (72°C) of the Arrhenius plot, log D versus 1/T, corresponds to T_g of polyacrylonitrile in the presence of water, which is lower than that measured in the dry state by a dynamic mechanical testing method. The activation energy is constant below T_g (ca. 10 kcal/mole), suddenly reaches a maximum at T_g and then gradually decreases with increasing temperature. General trends of Arrhenius plot for different polymer–penetrant systems are discussed. The temperature dependence of penetrant diffusion above T_g can be described by a general form of the WLF equation, log a_T = log (D_Tg/D_T) = ? C₁^g(T ? T_g)/(C₂^g + T ? T_g), where the values of C₁^g and C₂^g were calculated to be 4.03 and 24.54, respectively. A comparison was made between m-nitroaniline and Malachite Green. The difference in the respective T_g and the constants C₁^g and C₂^g of the WLF equation in polyacrylonitrile is attributed to the size of the penetrants and their ionic character. The surface concentration increases below T_g and decreases above T_g with rise in temperature.     

Dielectric relaxation of conductive carbon black reinforced ethylene‐octene copolymer vulcanizates

The dielectric relaxation behavior of different conducting carbon black‐filled ethylene‐octene copolymer (EOC) vulcanizates prepared by melt‐mixing method has been studied as a function of frequency (100 Hz–5 MHz) over a wide range of temperatures (25–100°C). The effect of filler loading and frequency on AC conductivity, dielectric permittivity, impedance, and dielectric loss tangent (tanδ) has been studied. The nature of variation of the dielectric permittivity with the filler loadings was explained on the basis of interfacial polarization of the filler in the polymer matrix. The effect of filler loading on the real and complex part of the impedance was explained by the relaxation dynamics of the polymer chains in the vicinity of the fillers. The effect of filler and temperature on dielectric loss tangent, dielectric permittivity, AC conductivity, and Nyquist plot was also reported. The bound rubber (BR) value increases with increase in filler loading suggesting the formation of strong interphase, which is correlated with dielectric loss. Thermal activation energy (E_a) was found to be decreasing with the temperature, which follows the Arrhenius relation: τ_b = τ₀ exp(−E_a/K_BT) where τ_b is the relaxation time for the bulk material. From the plot of lnτ_b versus inverse of absolute temperature (1/T), the activation energies (E_a) were found to be 0.37 and 0.44eV, respectively. The percolation threshold was observed with 40 phr carbon black loading. POLYM. COMPOS., 37:342–352, 2016. © 2014 Society of Plastics Engineers     

Dielectric relaxation studies on thermotropic side‐chain liquid crystalline polymers

The dielectric activity of a thermotropic side‐chain liquid crystalline polymer is analysed. The sub‐glass relaxations are deconvoluted by two different empirically based equations (Fuoss–Kirkwood and Havriliak–Negami). The conductivity contributions are studied following a methodology proposed by Macdonald and Coelho. The effects of the orientation of the mesogenic group under electrical fields are also analysed. We propose a general method to estimate the curve of loss permittivity with a determined value of S_d based on the knowledge of two experimental curves, each corresponding to one well‐known orientation. © 2001 Society of Chemical Industry     

Estimation of long-chain branching in ethylene–propylene terpolymers from infinite-dilution viscoelastic properties

A method is outlined for estimation of small degrees of long-chain branching in polymers with moderately narrow molecular weight distribution (M?_w/M?_n <1.4). The storage and loss shear moduli, G′ and G″, are measured in dilute solution by the Birnboim-Schrag multiple-lumped resonator and extrapolated to infinite dilution, choosing a suitable solvent viscosity and frequency range such that the data lie in the terminal zone where G′ and G″ are proportional to the second and first powers of frequency, respectively. The intrinsic reduced steady-state shear compliance is determined from these data and corrected for moderate molecular weight heterogeneity (assuming a Gaussian distribution) from knowledge of M?_w/M?_n and the Mark-Houwink exponent a. The resulting value of S₂/S (where S₁ = Στ_p/τ₁, S₂ = Σ(τ_p/τ₁)², the τ_p's being the relaxation times and τ₁ the longest one) is compared with values calculated by the Zimm-Kilb theory as evaluated by Osaki for comb polymers of regular geometry and different numbers of branch points. The method has been illustrated by measurements on four ethylene–propylene copolymers. One containing no termonomer and one containing a saturated termonomer appeared to be linear; two containing unsaturated termonomers showed small degrees of branching. The method appears to be promising for detecting from one to four branch points per molecule.     

Craze healing in polymer glasses

Craze healing was observed in many amorphous glassy polymers. A detailed study of the kinetics of craze healing in atactic polystyrene (M_w = 255,000) was conducted. The crazes were created in 0.08 mm films in air at room temperature, T_o, and constant stress, σ_o ? 2,300 psi, healed at temperature T_h for a time, T_h, at σ = 0, and recrazed at T_o and σ_o. Nucleation times, τ₁ and τ₂, and growth rates, L₁, and L₂, for the first and second loading, respectively, were measured as a function of t_h and T_h for individual crazes using dark field optical microscopy. Complete optical and mechanical healing was observed for T_h ? 70°C(T_g ? 100°C). At constant T_h, healing progressed in five stages with increasing th as follows; (i) no healing, τ₂ = 0, L₂ ? L₁; (ii) partial healing, τ₂ <τ₁, L₂ > L₁; (iii) similar growth, τ₂ = τ₁, L₂ = L₁; (iv) slower growth, τ₂ > τ₁, L₂ < L₁; (v) disappearance, τ₂ → ∞, L₂ → 0. A craze healing envelope of T_h vs T_h was obtained for the above stages. Craze healing occurred by line mode in which uniform healing occurred along the entire length of the craze.     

Cure modeling and monitoring of epoxy/amine resin systems. II. Network formation and chemoviscosity modeling

The glass transition temperature (T_g) advancement and the chemoviscosity development under isothermal conditions have been investigated for four epoxy/amine systems, including commercial RTM6 and F934 resins. Differential scanning calorimetry (DSC) was the thermoanalytical technique used to determine the T_g advancement and rheometry the technique for the determination of the chemoviscosity profiles of these resin systems. The complex cure kinetics were correlated to the T_g advancement via an one‐to‐one relationship using Di Benedetto's formula. It was revealed that the three‐dimensional network formation follows a single activated mechanism independent of whether the cure kinetics follow a single or several activation mechanisms. The viscosity profiles showed the typical characteristics of epoxy/amine cure. A modified version of the Williams‐Landel‐Ferry equation (WLF) was adequate to model the viscosity profiles of all the resin systems, in the temperature range 130 to 170°C, with a very good degree of accuracy. The parameters of the WLF equation were found to vary in a systematic manner with cure temperature. Further correlation between T_g and viscosity showed that gelation, defined as the point where viscosity reaches 10⁴ Pas, occurs at a unique T_g value for each resin system, which is independent of the cure conditions. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 77: 2178–2188, 2000     

Effects of extrusion conditions on rheological behavior of acrylonitrile–butadiene–styrene terpolymer melt

The influence of temperatures and flow rates on the rheological behavior during extrusion of acrylonitrile–butadiene–styrene (ABS) terpolymer melt was investigated by using a Rosand capillary rheometer. It was found that the wall shear stress (τ_w) increased nonlinearly with increasing apparent shear rates and the slope of the curves changed suddenly at a shear rate of about 10³ s^?1, whereas the melt‐shear viscosity decreased quickly at a τ_w of about 200 kPa. When the temperature was fixed, the entry‐pressure drop and extensional stress increased nonlinearly with increasing τ_w, whereas it decreased with a rise of temperature at a constant level of τ_w. The relationship between the melt‐shear viscosity and temperature was consistent with an Arrhenius expression. The results showed that the effects of extrusion operation conditions on the rheological behavior of the ABS resin melt were significant and were attributable to the change of morphology of the rubber phase over a wide range of shear rates. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 85: 606–611, 2002     

Microwave dielectric properties of low temperature fired Ba5Nb4O15 ‐ BaWO4 ceramics supplemented with their own nanoparticles for LTCC applications

Polycrystalline Ba₅Nb₄O₁₅ (BNO) ‐ BaWO₄ (BWO) composite ceramics are prepared by adding their own nanoparticles as a sintering aid. The prepared samples exhibited the maximum relative density of 98.2% at 900°C. The complex dielectric response of these composite ceramics are analysed by Havriliak ‐ Negami (HN) equation. The BNO ‐ BWO composite added with x=3 wt% of their nanoparticles, fired at 900oC displayed the best microwave dielectric properties; εr=39 and Q×f0=59.8 THz at 9.44 GHz. The obtained results of BNO ‐ BWO composite makes this material as a potential candidate for LTCC applications.