Relaxations in thermosets. XII. Dielectric effects during curing of nonstoichiometric DGEBA-based thermosets

The dielectric permittivity ε′ and loss ε″ of diglycidyl ether of bisphenol-A thermosets cured with nonstoichiometric amounts of diamino-diphenyl methane have been measured during the course of their chemical reactions from the sol to gel to glass-formation regions. ε′ monotonically decreases with time and ε″ initially decreases, increases to a peak value, and finally decreases to extremely low values characteristic of the glassy state. The initial decrease in ε″ is due to the decrease in the dc conductivity, and the peak is due to the dipolar reorientation. The appearance of these features shifts to longer time when the thermoset is stoichiometrically starved by decreasing the amount of the curing agent and, at a molar ratio of 4 : 1 of the epoxide to diamine, the ε″ peak does not appear during the curing process. Complex plane plots of ε′ and ε″ have the shape of an arc in all cases except when the molar ratio of the epoxide to diamine is 4 : 1. The dielectric consequences of the chemical changes with time during the crosslinking of a thermoset are analogous to the frequency dependence of ε″ of a condensed phase. The time dependence of ε″ follows a stretched exponential decay, ?(t = exp ? [(t/τ)^γ], where 0 < γ < 1. The parameter decreases with decreasing amine content. ε″ has been analyzed to obtain the increase in the relaxation time as curing progresses. A representation of ε^* in terms of electrical modulus M^* shows the occurrence of, first a Maxwell relaxation due to dc conductivity, and second a dipolar relaxation, during the period of a typical isothermal cure. Changes in the features of the isothermal cure that occur on changing the amount of the curing agent are discussed in terms of network formation in the thermoset, and the change in the electrical conductivity with curing time has been analyzed in terms of both a power law for gel formation and by a new equation that suggests an approach toward a singularity.     

Relaxations in thermosets. IX. Ionic conductivity and gelation of DGEBA-based thermosets cured with pure and mixed amines

The results obtained during the isothermal curing of diglycidyl ether of bisphenol-A-based thermosets cross-linked with pure diaminodiphenyl methane and pure diaminodiphenyl sulfone and with their mixtures have been analyzed to determine how the dc conductivity changes with time during the conversion of its liquid to a gel. The complex permittivity data are first analyzed to show that ac measurements can be used to obtain the ionic conductivity over a considerable period of the curing process. The procedure allows one to obtain the dc conductivity without having data as a function of frequency. The shape of the complex plane plots of the electrical modulus are semicircles, but with small deviations that appear at long times during the curing process. The dielectric consequences of the chemical changes with time during the cross-linking of the thermoset are analogous to the frequency dependence of the complex permittivity of a liquid. The analysis shows that the dc conductivity σ_o of a thermoset during its cure follows a power law, σ_o∝ (t_g—t)^x, where t is the curing time (t < t_g). The results can also be described equally well by a new equation, σ_o ∝ exp[—B/(t_o—t)], where x, t_g, B, and t_o are empirical constants all of which vary with the temperature of the cure. t_g is close to the time for gelation known from independent studies and t_o is close to but longer than the time for vitrification. These conclusions are discussed in terms of scaling concepts for the gelation phenomenon.     

Dielectric relaxation in some polyacrylate solutions

The dielectric constant ?′ and loss factor ?″ of poly(butyl acrylate), poly(butyl methacrylate), and poly(isobutyl methacrylate) solutions are reported in the frequency region of 1 kHz to 24.42 GHz at four different temperatures of 27, 40, 50, and 60°C. Cole–Cole plots are plotted to obtain the distribution parameter and relaxation time. The activation energies are evaluated assuming dielectric relaxation to be a rate process in these solutions. A possible relaxation mechanism is discussed.     

Relaxations in thermosets. VI. Effects of crosslinking on sub-Tg relaxations during the curing and aging of epoxide-based thermosets

The dielectric permittivity and loss of diglycidyl ether of bisphenol-A-based thermosets cured with diaminodiphenyl methane and diaminodiphenyl sulfone have been measured over a temperature range 77–400 K after curing or aging for a predetermined duration. Of the two sub-T_g relaxations, the height of the γ relaxation peak monotonically decreases during both the cure and postcure periods, and the height of the β relaxation peak first increases to a maximum value and then decreases. This decrease is attributed to physical aging effects. The height of the α-relaxation peak decreases. The γ- and β-relaxation peaks become increasingly separated in temperature. A concept of accumulated equivalent curing time which is based upon known chemical kinetics has been introduced for use in both theoretical and practical aspects of the study of thermosets. It is shown that substantial curing of the sample occurs during its slow heating to the curing temperature. The use of this concept in the curing of thermosets is illustrated. A procedure for the analysis of the distribution of relaxation times from a set of results limited in both frequency and temperature range is described. The distribution parameter is 0.20 and 0.16 for the γ and β process, respectively, and remains constant with postcuring and physical aging. The distribution parameter for the α process decreases from 0.60 to 0.36 on curing.     

Relaxations of thermosets. III. Sub-Tg dielectric relaxations of bisphenol-A–based epoxide cured with different cross-linking agents

The sub-T_g relaxations of bisphenol-A–based thermosets cured with diaminodiphenyl methane and diaminodiphenyl sulfone have been studied by dielectric measurements over the frequency range 12 Hz to 200 kHz from their ungelled or “least” cured states to their fully cured states. Both thermosets show two relaxation processes, γ and β, as the temperature is increased toward their T_gs. In the ungelled states, the γ process is more prominent than the β process. As curing proceeds, the strength of the γ process decreases and reaches a limiting value, while that of the β process initially increases, reaches a maximum value, and then decreases. An increase in the chain iength and the number of crosslinks increases the number of -OH dipoles and/or degree of their motions in local regions of the network matrix. This is partly caused by the decreasing efficiency of segmental packing as the curing proceeds. The sub-T_g relaxations become increasingly more, separated from the α relaxation during curing. Physical aging causes a decrease in the strength of the β relaxation of the thermosets as a result of the collapse of loosely packed regions of low cross-linking density, and this decrease competes against an increase caused by further crosslinking during the “post-cure” process.     

Relaxations in thermosets. XIX. Dielectric effects during curing of diglycidyl ether of bisphenol-A with a catalyst and the properties of the thermoset

Changes in the dielectric permittivity ε′ and loss epsiv;″ during the curing of DGEBA catalyzed by 10 mole % dimethylbenzylamine have been studied from sol to gel to glass formation regions at different temperatures from 323 to 390 K. The ε′ monotonically decreases with time of cure, and ε″ initially decreases by several orders of magnitude and then increases to reach a peak value before finally decreasing to a low value characteristic of the glassy state. The features shift to shorter times and the peak vanishes as the curing temperature is increased. The decrease of ε″ at the initial stage of cure has been analyzed in terms of dc conductivity σ₀, which follows a power law, σ₀ ∝? (t_g–t)^x, as well as a new singularity equation, σ₀ ∝? exp[–B/(t₀–t)] where t_g, x, B, and t₀ are empirical constants that vary with the curing temperature; t_g is close to the time for gelation; and t₀ ≥ time for vitrification. The dielectric properties of the thermoset formed after different periods of cure have been studied from 77 to 325 K. Similar studies of the thermosets formed at different temperatures have been made. Increase in the curing period decreases the heights of both the γ-and α-relaxation peaks and increases their separation, while a β-relaxation peak emerges. Isothermal curing at high temperatures decreases the height of the γ peak to a vanishingly small value and increases that of the β peak from a vanishingly small value. In both the uncured and fully cured states, there is only one sub-T_g relaxation process named γ for the uncured and β for the cured state. These results are discussed in terms of our general physical concepts of local mode motions in an amorphous matrix. © 1993 John Wiley & Sons, Inc.     

Relaxations in thermosets. XVI. Dielectric studies of negative feedback during curing of an epoxide-ethylene-diamine thermoset

The complex dielectric permittivity of thermosets of diglycidly ether of bisphenol-A cured with ethylene diamine has been studied during their isothermal curing at several temperatures. As cross-linking progresses, the dc conductivity decreases. At the beginning of the cure the dc conductivity can be fitted to both the scaling laws with a critical exponent of about 4 and an equation indicating approach toward a singularity. In the later stage of the cure, the change in permittivity corresponds to dipolar relaxation of an infinitely connected network, and the Argand diagram for the complex permittivity measured at a fixed frequency obtained as the curing process proceeds at 305 K is similar to that for the complex permittivity as frequency is varied for a time-invariant system which obeys a stretched exponential relaxation function with the curing parameter or exponent, γ = 0.29. Increase in the temperature of isothermal curing lowers both γ and the net decrease in the equilibrium permittivity on curing. A plot of the calculated relaxation time with curing time is sigmoidal and shifts to shorter times on increasing the curing temperature. Measurement of the dielectric properties during the cure but for different frequencies show that the various parameters for the curing kinetics are independent of the frequency of measurement. These observations confirm the development of our concepts of thermoset curing in terms of a phenomenon of negative feedback between molecular diffusion and chemical reactions.     

Relaxations in thermosets. X. Analysis of dipolar relaxations in DGEBA-based thermosets during isothermal cure

Dielectric properties measured during isothermal curing of DGEBA-based thermosets using a mixture of aromatic amines as curing agent are analyzed. The evolution of the dielectric features of thermosets during curing and after a time when their dc conductivity has reached a negligibly small value are phenomenologically similar to the dielectric features of physically and chemically stable dipolar liquids and solids observed with increasing frequency or decreasing temperature. This equivalence is a consequence of the invariance of the dynamic behavior of dielectric susceptibility with respect to either the frequency of measurement or the relaxation time of the substance and demonstrates that crosslinking of a thermoset causes its relaxation time to increase monotonically. It is shown that the stretched exponential relaxation function formalism satisfactorily describes the dielectric results and that the value of its distribution parameter initially decreases and, after gelation, reaches a constant value, which we denote γ, in the latter part of the cure. The value of the curing parameter, γ, which lies between 0.2 and 0.4, monotonically decreases with increasing curing temperature and tends to a limiting value characteristic of a thermoset at higher temperatures. This is in contrast with the increase found in the corresponding representation in the Kohlrausch-Williams-Watts parameter β with increasing temperature. The curing time dependence of the dipolar relaxation time ι has been determined and found to have the shape of an elongated S, with a well-defined point of inflexion, as ι increases during the cure, from a value characteristic of a liquid to an ultimate value characteristic of a glass.     

The dielectric properties of polyatomic alcohols: Asymmetric dispersion in butanediols

Static permittivity ?_s, permittivity ?′, and dielectric loss ?″ were measured for 1,3-, 1,4-, and 2,3-butanediols over the frequency and temperature ranges 1 MHz-36 GHz and 293–423 K. These equilibrium properties of butanediols were analyzed using the Onsager-Kirkwood-Fröhlich theory. The correlation factor g over the temperature range was calculated. The experimental permittivity ?′ and dielectric loss ?″ values were described by the Davidson-Cole equation. The relaxation times τ_D-C and parameter β of their distribution were calculated.     

Microwave frequency dielectric properties of poly(vinylidene fluoride) films

The frequency dependence of dielectric constant ?′, dielectric loss ?″, and dielectric anisotropy were determined for poly(vinylidene fluoride) (PVDF) in microwave frequencies from 4 to 13 GHz. The ?′ and ?″ for PVDF films decreased with increasing frequency. Both ?′ and ?″ were larger in the transverse direction than in the machine direction or draw direction, but the values at 12 GHz were smaller than those observed at 4.0 GHz. The angular dependence of ?″ at microwave frequency reflects the orientational distribution of molecules in the amorphous region. The orientation function was determined to be about 0.04 and 0.01 for uniaxially and biaxially stretched PVDF, respectively. © 1995 John Wiley & Sons, Inc.     

Dielectric relaxation in styrene-related polymers at low temperatures

The complex dielectric constants ?^* = ?′ ? j?″ of each of several members of a system of copolymers of 4-chlorostyrene and 4-methylstyrene have been measured from 1.6°K to 300°K and from 0.1 kHz to 20 kHz. The principal experimental findings are: the strength of the relaxation process which occurs near 50°K at 1 kHz varies linearly with changing copolymer composition; both the apparent activation energy (H = 2.7 ± 0.7 kcal/mole) and the shape of the relaxation curve are independent of the composition variable and of the temperature (or frequency) within the ranges studied; and the ratio of the relaxation strength of poly-4-methylstyrene to that of poly-4-chlorostyrene in the 50°K process is about 25 times the corresponding ratio for the primary relaxation process that occurs in the neighborhood of the glass-transition temperature. These findings suggest that in the 50°K process the phenyl groups relax independently of one another; that the apparent activation energy and the shape of the relaxation spectrum are determined primarily by the nature of the intrachain forces; and that the strength of the relaxation process depends primarily on effects of intermolecular forces that are governed by the molar “free volume” of the copolymers.     

NMR relaxation study of thermal degradation in cured PMR polyimides

We have studied cross-linking and thermal degradation of high-performance first-and second-generation PMR-15 polyimides, both thermoset and thermoplastic versions, by performing nonspectroscopic NMR solid echo T^*₂ relaxation measurements at temperatures up to 430°C using probes built for this purpose. We employ signal averaging and automated decomposition of the relaxation decays into two Gaussian components, the slower of which gradually appears above 300°C. Tracking the molecular mobility spectrum in terms of the relative intensity of the components and their relaxation times as temperature is cycled, we detect essentially no irreversible effects below the glass transition, measure permanent mobility reductions attributable to completion of cure, and find that exposure to temperatures above 380°C on the order of 1 h is required for substantial thermal degradation to occur. These results are closely supported by thermal and mechanical measurements on parallel specimens. Second-generation PMR resins appear to have higher microscopic rigidity and reduced viscous fraction at high temperatures. ©1995 John Wiley & Sons, Inc.     

Cure behavior and thermal stability of an epoxy: new bismaleimide blends for composite matrices

A new bismaleimide (BMI) resin was synthesized to formulate epoxy(tetraglycidyl diaminodiphenyl methane; TGDDM) – bismaleimide thermoset blends for composite matrix applications. 4,4′-diaminodiphenyl methane (DDM) was used as an amine curing agent for the TGDDM. A Fourier transform infrared (FTIR) spectroscopy was employed to characterize the new BMI resin. Cure behavior of the epoxy–BMI blends was studied using a differential scanning calorimeter (DSC). DSC thermograms of the thermoset blends indicated two exothermic peaks. The glass transition temperature of the thermoset blends decreased with BMI content. Thermogravimetric analysis (TGA) was carried out to investigate thermal degradation behavior of the cured epoxy–BMI thermoset blends. The new BMI resin reacted partially with the DDM and weak intercrosslinking polymer networks were formed during cure of the thermoset blends.     

Enhanced ionic conductivity in PEO/PMMA glassy miscible blends: Role of nano‐confinement of minority component chains

AC impedance spectroscopy was used to investigate the ionic conductivity of solution cast poly(ethylene oxide) (PEO)/poly(methyl methacrylate) (PMMA) blends doped with lithium perchlorate. At low PEO contents (below overlap weight fraction w^*), ionic conductivities are almost low. This could be due to nearly distant PEO chains in blend, which means ion transportation cannot be performed adequately. However, at weight fractions well above w^*, a significant increase in ionic conductivity was observed. This enhanced ionic conductivity mimics the PEO segmental relaxation in rigid PMMA matrix, which can be attributed to the accelerated motions of confined PEO chains in PMMA matrix. At PEO content higher than 20 wt % the conductivity measured at room temperature drops due to crystallization of PEO. However by increasing temperature to temperatures well above the melting point of PEO, a sudden increase of conductivity was observed which was attributed to phase transition from crystalline to amorphous state. The results indicate that some PEO/PMMA blends with well enough PEO content, which are structurally solid, can be considered as an interesting candidate for usage as solid‐state electrolytes in Lithium batteries. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 2065–2071, 2010     

Evaluation of the relaxation modules from the response to a constant rate of strain followed by a constant strain

The stress response σ(t) to a constant rate of strain $ \dot \varepsilon $ ε during the period 0 < t ≤ t^* and to the constant strain ε^* $ ( = \dot \varepsilon t*) $ thereafter is considered in terms of the Boltzmann superposition principle. When t ≤ t^*, the data directly give the constant-rate modulus F (t) ≡ σ(t)/ε(t), which can be converted straightforwardly into the relaxation modulus E(t). Results from illustrative calculations show that a reduction in the relaxation rate effects a decrease in [σ(t^*)/ε^*]/E(t^*) and also in the time at which [σ(t)/ε^*]/E(t) becomes essentially unity. To evaluate E(t) at t > t^*, F(t) is first obtained from σ(t) and F(t ? t^*) by using a derived equation similar to that presented by Meissner. Thereafter, F(t) is transformed into E(t). For illustration, E(t) for a rubbery solid is evaluated over some 2.5 decades of time from its response to a strain rate of 0.25 min^?1 for 0.40 min and thereafter to the attained strain of 0.10 for 5.4 min.     

Dielectric spectroscopy of an antiferroelectric liquid crystal showing an antiferroelectric–ferrielectric transition

We report the dielectric relaxation behaviour in the antiferroelectric SmC_A* and ferrielectric SmC_γ* phases of the antiferroelectric liquid crystal 4-[5-(4-octloxyphenyl)-2-pyrimidinyl]phenyl 4,4,4-trifluoro-3-(methoxyphenyl)butanoate which shows an antiferroelectric transition at around 88±0.1°C. In the SmC_A* phase, two dielectric relaxation modes have been found, namely the usual antiferroelectric Goldstone mode and another arising from molecular rotation around its short axis. In the SmC_γ* phase, one dielectric relaxation mode has been observed due to the ferrielectric Goldstone mode. Dielectric increments and relaxation frequencies of the antiferroelectric and ferrielectric phases are estimated from the fits of the Cole–Cole function of the dielectric spectrum. The dependence of the bias field in the ferrielectric phase is also discussed.     

Mechanical relaxations in some ionene polymers. I. Effect of Ion concentration

Dynamic mechanical properties of m,n-ionenes, the structure of which are shown in Figure 1, were examined by torsional braid analysis. Three relaxations designated as α,β and γ were found. The α relaxation, ascribed to the primary relaxation due to an amorphous phase, was observed at 70–130°C, the temperature increasing with an increase of the ion concentration along the polymer chains. The β relaxation at around 0°C was related to the ionic portions of the polymers. The γ relaxation at around–120°C was a so-called local mode relaxation. The γ relaxation peak was split into two peaks in the very slowly cooled 12,10-ionene sample and the formation of an inhomogeneous structure in the amorphous phase is proposed.     

Interpretation of differences in temperature and pressure dependences of density and concentration fluctuations in amorphous poly(phenylmethyl siloxane)

Differences in the temperature and pressure dependences of the relaxation times of a slow diffusional process and the α structural relaxation pose an interesting problem. This feature, observed by dynamic light scattering in amorphous poly(phenylmethyl siloxane), is related to another basic feature of lack of thermorheological simplicity discovered by Plazek in polystyrene, poly(vinyl acetate), and amorphous polypropylene. A quantitative explanation based on the predictions of a general coupling theory of relaxations has been found. The coupling theory also predicts the Kohlrausch fractional exponential time correlation function exp[?(tτ^*)^1?n] at long times, as observed by photon correlation spectroscopy, and crossover to an exponential time dependence exp–(t/τ₀) at short times, as frequently assumed in Brillouin scattering. An additional relation between τ^* and τ₀ predicted by the theory is confirmed also by the experimental data.     

Relaxation spectra of concentrated polystyrene solutions

The relaxation modulus G(t) and the stress decay after cessation of steady shear flow were measured on concentrated solutions of polystyrenes in diethyl phthalate. Ranges of concentration c and molecular weight M of the polymer were from 0.112 to 0.329 g/ml and from 1.23 × 10⁶ to 7.62 × 10⁶, respectively. The relaxation spectrum H(τ) as calculated from G(t) for the solution of very high M was found to be composed of two parts. One, at relatively short times, was a broad distribution (plateau zone) with height proportional to c². The second, at the long-time end, was very sensitive to concentration and gave rise to a maximum in H(τ) for very high concentrations. The behavior of H(τ) at long times was examined quantitatively by evaluating the longest relaxation time τ₁⁰ and the corresponding relaxation strength G₁⁰ from G(t) and from the stress decay function, on the assumption of a discrete distribution of relaxation times at long times. The longest relaxation time was approximately proportional to M^3.5, even at relatively low concentrations where the zero-shear viscosity was not proportional to M^3.5. The strengths of relaxation modes with the longest few relaxation times are proportional to the third power of concentration.