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.     

Segmental and secondary dynamics in hydrogen‐bonded poly(4‐vinylphenol)/poly(methyl methacrylate) blends

Broadband dielectric spectroscopy was used to study the segmental (α) and secondary (β) relaxations in hydrogen‐bonded poly(4‐vinylphenol)/poly(methyl methacrylate) (PVPh/PMMA) blends with PVPh concentrations of 20–80% and at temperatures from ?30 to approximately glass‐transition temperature (T_g) + 80 °C. Miscible blends were obtained by solution casting from methyl ethyl ketone solution, as confirmed by single differential scanning calorimetry T_g and single segmental relaxation process for each blend. The β relaxation of PMMA maintains similar characteristics in blends with PVPh, compared with neat PMMA. Its relaxation time and activation energy are nearly the same in all blends. Furthermore, the dielectric relaxation strength of PMMA β process in the blends is proportional to the concentration of PMMA, suggesting that blending and intermolecular hydrogen bonding do not modify the local intramolecular motion. The α process, however, represents the segmental motions of both components and becomes slower with increasing PVPh concentration because of the higher T_g. This leads to well‐defined α and β relaxations in the blends above the corresponding T_g, which cannot be reliably resolved in neat PMMA without ambiguous curve deconvolution. The PMMA β process still follows an Arrhenius temperature dependence above T_g, but with an activation energy larger than that observed below T_g because of increased relaxation amplitude. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3405–3415, 2004     

Studies of the amorphous region of polymers. I. Relationship between the change of structure and glass-transition temperature in drawn poly(ethylene terephthalate)

The effect of drawing on the glass-transition temperature of amorphous poly(ethylene terephthalate) has been studied. The T_g decreases to a minimum at a draw ratio of 1.5, then increases to a maximum at a draw ratio of about 2.0, and again decreases with increasing draw ratio. The relationship between the change of structure and T_g is discussed in terms of the configurational entropy and the rate of molecular motion in local-mode relaxation. On the basis of configurational entropy, the decrease of T_g at the beginning of drawing depends on the increase of configurational entropy, while at draw ratios above 2.0 it depends on the increase of entropy associated with intermolecular interaction. From the point of view of molecular motion, it is concluded that the change of T_g is determined by local oscillations in the amorphous region.     

Dielectric relaxations in the liquid and glassy states of 47% polypropylene oxide in toluene as diluent

Molecular relaxations in 47-wt % polypropylene oxide of molecular weight 4000 in toluene as diluent have been studied by dielectric permittivity and loss measurements from 77 to 320 K, in the frequency range 1 Hz to 2 × 10⁵ Hz. One relaxation process (β process) is observed in the glassy state below T_g (= 148 K), and two processes are observed in the supercooled liquid at T > T_g. Relative to the amplitude of the fast relaxation process (i.e., the local segmental motions of the polymer chain), the amplitude of the slow process is increased and that of the β process decreased on dilution of the pure polymer. The β process has an Arrhenius energy of 17 kJ mol^?1. The rates of the two relaxations at T > T_g follow the Vogel–Fulcher–Tamman equation and seem to merge on cooling the liquid towards T_g. The relative temperatures at which the three relaxation processes occur at the rate of 1 kHz remain largely unaffected on dilution. The increase in static permittivity of the solution on cooling is more than anticipated from the temperature effects alone. It is suggested that the increase is due to the enhanced short-range orientational correlation of the dipoles, which may involve H bonding.     

The glass transition in linear low density polyethylene determined by thermally stimulated depolarization currents

New thermally stimulated depolarization currents (TSDC) results on LLD polyethylene functionalized with diethylmaleate polar groups are precisely computer fitted with the direct signal analysis technique. It is shown that the TSDC spectrum consists, with increasing temperatures, of a sub-γ peak, a sharp γ peak, and a β and an α relaxation. The first peak is analyzed in terms of Arrhenius relaxation times, whereas the γ and β transitions could only be fitted by using Vogel-Fulcher temperature dependence for the relaxation times. The best value for T_o obtained from both fittings is 69.7 K. This is a quantitative proof for the identification of the γ transition as one of the dielectric manifestations of the glass-rubber transition for polyethylenes, T_g = 136.5 K, which has been discussed extensively in the literature. The β relaxation, T_gβ = 237 K, has also the expected characteristic of a glass transition; the existence of two T_gs in polyethylene could explain our results. © 1996 John Wiley & Sons, Inc.     

Dielectric studies of the effects of thermal history on secondary relaxation in bisphenol-a-polycarbonate

The dielectric permittivity and loss of Bisphenol-A-polycarbonate (PC) was measured over the frequency range 100 Hz to 200 kHz and temperature range 77–383 K. One sub-T_g relaxation peak is observed which rapidly broadens with a decrease in temperature. This is attributed to a progressive separation of the γ and β peaks, which at high temperatures are merged to form one peak of high strength. The strength of the sub-T_g relaxations decreases on physical aging of PC but is increased if the sample is quenched from a temperature above its T_g. Slowly cooled PC has a lower strength of its sub-T_g relaxation than a quenched specimen. The thermal history of PC affects the magnitude of its sub-T_g relaxation.     

Effects of diluent on molecular motion and glass transitions in polymers. III. The system poly(vinyl acetate)–toluene

Dielectric measurements, differential thermal analyses (DTA), and broad-line proton magnetic resonance (NMR) measurements are reported on the system poly(vinyl acetate)–toluene. Four dielectric relaxations were observed between 80 and 400°K. From proton NMR measurements on solutions in toluene and in deuterated toluene, the relaxation processes can be assigned, respectively, to segmental motion of poly(vinyl acetate), α; motion of side group, β′ rotation of toluene, β; local motions of poly(vinyl acetate) and toluene, γ, in order of appearance with decreasing temperature. Two stepwise changes in DTA traces have been observed and can be assigned as glass transition points T_gI and T_gII. Comparison of these glass transition points with temperatures at which dielectric relaxation times for the α and β processes are 100 sec, indicate that segmental motion of poly(vinyl acetate) and rotation of toluene are frozen-in at T_gI and T_gII, respectively. Activation plots for the α process conform to the Vogel–Tamman equation. In terms of the parameters A, B, and T₀ of the equation, T_gI can be represented by an expression of the form T_gI ≈ T₀ + B/(A + 3). In the range of concentration above 50% by weight, A and B are almost independent of concentration but T₀ varies strongly. The nature of the secondary dispersions is also discussed.     

Pressure dependence of dielectric properties of chlorinated polyethylene vulcanizate. III. β relaxation

The effects of temperature and pressure on the shift factor and the dielectric increment of the β relaxation process were measured for vulcanized chlorinated polyethylene. The isobaric and isochoric activation enthalpies, H^*_P and H^*_V, the activation volume V^*, the pressure dependence of the glass–glass transition temperature, T_gβ/dP, and the apparent extinction temperature T_0β were obtained. The pressure dependences of both V^* and the dielectric increment would reach very small values near the liquid–glass transition temperature T_g, and the β process seems to be affected by the transition near T_g. The value of H^*v/H^*p for the β process is larger than that for the α process, and it is suggested that the molecular motions pertaining to the β process are more strongly restricted than those pertaining to the α process. The ratio T_0β/T₀, where T₀ is the characteristic temperature in the Vogel–Fulcher–Tammann–Hesse equation for the α process, follows the empirical relation of Matsuoka and Ishida, T_gβ/T_g ～0.75. The value of dT_gβ/dP estimated from T_g and T_0β/T₀ is consistent with the experimental value.     

A dielectric study of chain motions in poly(vinyl methyl ether)

The dielectric permittivity and loss of poly(vinyl methyl ether) (mol. wt. 30,000) have been measured from 12 Hz to 100 kHz at temperatures from 77 K to 320 K. Two relaxation processes, γ and β, are observed at T < T_g (245 K), and one above T_g. The Arrhenius plots of the γ and β processes have activation energies of 20 and 41 kJ mole^?1 respectively. The relaxation rate of the α process is described by the Vogel-Fulcher-Tamman equation or the William-Landel-Ferry equation. The relaxation rates of γ and β processes evaluated from the isochrones differ from those evaluated from the isothermal spectrum. The features of chain motions observed are similar to those in other polymer and rigid molecular glasses.     

Dielectric properties of complex zn(II) salts of ethylene-methacrylic acid copolymer with n-hexylamine

This article describes dielectric properties of complex Zn(II) salts of ethylene-methacrylic acid copolymer (5.4 mol% methacrylic acid) with n-hexylamine. In all samples, the β′ relaxation near 340 K and γ relaxation near 170 K are observed. These are assigned, respectively, to micro-Brownian molecular motion of long segments above T_g and to local molecular motion of short segments below T_g. The dielectric results indicate that ionic clusters are not formed in these systems.     

Unusual relaxation process in polybutadiene: Resolving the controversy

We report the observation of an unusual relaxation process in depolarized light scattering spectra of polybutadiene (PBD) with two different vinyl contents. The process showed up in the gigahertz frequency range with relatively mild temperature dependence and was similar to a secondary relaxation process. The most surprising observation was that the process exists even at high temperatures and does not merge with the segmental relaxation up to a temperature of 400 K (T > 2T_g). Possible mechanisms of this particular relaxation in PBD are discussed. The process is compared to the so‐called E process, double‐bond hopping process, and dielectric β process. We emphasize that this process differs from the dielectric β process, is unique for 1,4‐PBD, and has not been observed in other polymers. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 994–999, 2004     

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.     

Mechanical relaxation mechanism of epoxide resins cured with acid anhydrides. II. Effect of the chemical structure of the anhydrides on the β relaxation mechanism

The mechanism of low-temperature mechanical relaxation of acid-anhydride-cured epoxide resins has been investigated in detail. One mechanical relaxation, denoted as the β relaxation, is observed from ?80 to ?50°C for all epoxide resin systems cured with aromatic, alicyclic, and aliphatic anhydrides. The β relaxation increases in peak height and shifts to higher temperature with increasing molecular volume of the diester segments formed by the reaction of acid anhydrides. From these results, it is concluded that the β relaxation for anhydridecured systems is due to the motion of the diester segment, and that the intensity and peak position of the β relaxation depend on the molecular volume of this segment. Moreover, it was shown that the tensile impact strength of the anhydride-cured systems is governed by the intensity of the β relaxation of these systems when the parameters T_g and v of these systems are nearly constant.     

Molecular relaxation in the blends of polystyrene/poly(2,6-dimethyl-1,4-phenylene oxide) at low temperature

Molecular relaxation behavior in terms of the α, β, and γ transitions of miscible PS/PPO blends has been studied by means of DMTA and preliminary work has been carried out using DSC. From DSC and DMTA (by tan δ), the observed α relaxation (T_α or T_g) of PS, PPO, and the blends, which are intermediate between the constituents, are in good agreement with earlier reports by others. In addition, the β transition (T_β) of PS at 0.03 Hz and 1 Hz is observed at −30 and 20°C, respectively, while the γ relaxation (T_γ) is not observed at either frequency. The T_β of PPO is 30°C at 0.03 Hz and is not observed at 1 Hz, while the T_γ is −85°C at 0.03 Hz and −70°C at 1 Hz. On the other hand, blend composition-independent β or γ relaxation observed in the blends may be a consequence of the absence of intra- or intermolecular interaction between the constituents at low temperature. Thus it is suggested that at low temperature, the β relaxation of PS be influenced solely by the local motion of the phenylene ring, and that the β or γ relaxation of PPO be predominated by the local cooperative motions of several monomer units or the rotational motion of the methyl group in PPO. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1981–1986, 1998     

Diluent effects on molecular motions and glass transition in polymers. I. Polystyrene–toluene

The effects of diluent on molecular motions and glass transition in the polystyrene–toluene system was studied by means of dielectric, thermal, and NMR measurements. Three dielectric relaxations were observed between 80 and 400°K. On the basis of NMR measurements on solutions in toluene and in deuterated toluene, relaxation processes were assigned to segmental motions of polystyrene, rotations of toluene, and the local motions of polystyrene and toluene in order of appearance from the high-temperature side. The concentration dependence of the relaxation strength and of the activation energy for the primary relaxation (that at the highest temperature) show a step increment at about 50% by weight. The activation plots for the primary process were expressed by the Vogel–Tamman equation. With this equation, the temperatures at which the mean dielectric relaxation time becomes 100 sec is determined. This agrees well with the glass-transition temperature T_g and hence T_g in concentrated solution is expressed by in terms of the parameters A, B, and T₀ of the Vogel–Tamman equation. The values of A and B are, respectively, about 12 and 0.65 and independent of the concentration. The physical meaning of these parameters is discussed.     

Dielectric studies of chain dynamics in homogeneous semi‐interpenetrating polymer networks

Semi‐interpenetrating polymer networks (semi‐IPNs) were prepared from linear polyurethane (PUR) and polycyanurate (PCN) networks. Wide‐angle X‐ray scattering measurements showed that the IPNs were amorphous, and differential scanning calorimetry and small‐angle X‐ray scattering measurements suggested that they were macroscopically homogeneous. Here we report the results of detailed studies of the molecular mobility in IPNs with PUR contents greater than or equal to 50% via broadband dielectric relaxation spectroscopy (10⁻²–10⁹ Hz, 210–420 K) and thermally stimulated depolarization current techniques (77–320 K). Both techniques gave a single α relaxation in the IPNs, shifting to higher temperatures in isochronal plots with increasing PCN content, and provided measures for the glass‐transition temperature (T_g) close to and following the calorimetric T_g. The dielectric response in the IPNs was dominated by PUR. The segmental α relaxation, associated with the glass transition and, to a lesser extent, the local secondary β and γ relaxations were analyzed in detail with respect to the timescale, the shape of the response, and the relaxation strength. The α relaxation became broader with increasing PCN content, the broadening being attributed to concentration fluctuations. Fragility decreased in the IPNs in comparison with PUR, the kinetic free volume at T_g increased, and the relaxation strength of the α relaxation, normalized to the same PUR content, increased. The results are discussed in terms of the formation of chemical bonds between the components, as confirmed by IR, and the reduced packing density of PUR chains in the IPNs. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 3070–3087, 2000     

Conductance and relaxations in the glassy and rubber states of aqueous poly( vinyl pyrrolidone): A cryofixation medium

The dielectric permittivity and loss of poly(vinyl pyrrolidone), molecular weight 40,000, containing 40% (by weight) water have been measured over the temperature range 77–325 K and frequency range 12 Hz to 0.1 MHz. A prominent relaxation due to rotational diffusion of water molecules in a hydrogen-bonded structure occurs at T < T_g (237 K). The half-width of the dipolar relaxation spectra is 2.27 decades and is temperature independent, which is strikingly different from the corresponding features of pure polymers. It is concluded that H-bonded amorphous solid water persists in the glassy polymer matrix and that the H-bonded structure contains the pyrrolidone side groups of the randomly oriented chain. The relaxation peak at T near T_g is masked by a large dc conductivity which, when expressed in terms of electric modulus, has a spectrum of half-width 1.37 instead of 1.14 decades expected for dc conductivity alone. The contribution from dipolar reorientation in the glass-rubber range of the PVP-H₂O solution is smaller than that in its sub-T_g relaxation.     

Influence of the crystalline phase on the molecular mobility of PVDF

Dielectric relaxation and pyrocurrent of PVDF were studied by thermostimulated current spectroscopy. The transition spectrum of the material was investigated by differential scanning calorimetry. Two well-resolved relaxation peaks have been observed in the temperature range [?100–100°C]. The molecular mechanisms of these phenomena have been discussed, based on a comparative study of α-PVDF. and β-PVDF. The β relaxation mode is located at ?41°C in α-PVDF and is slightly shifted toward higher temperatures in the stretched material. This mode has been ascribed to the dielectric manifestation of the glass transition (T_g) of PVDF. It is comprised of two components corresponding to the free and constrained amorphous phases, respectively, in the order of increasing temperatures. The α_c transition/relaxation has been associated with molecular motions in the crystalline/amorphous interphase. At higher temperatures, a compensation phenomenon corresponding to cooperative movements liberated at the Curie transition has been observed in β-PVDF. © 1993 John Wiley & Sons, Inc.     

Properties of polyethylene modified with phosphonate side groups. II. Dynamic mechanical behavior

The viscoelastic behavior of phosphonate derivatives of phosphonylated low-density polyethylene (LDPE) was studied by dynamic mechanical techniques. The polymers investigated contained from 0.2 to 9.1 phosphonate groups per 100 carbon atoms and included the dimethyl phosphonate derivative and two derivatives for which the phosphonate ester group was an oligomer of poly(ethylene oxide) (PEO). The temperature dependences of the storage and loss moduli of the dimethyl phosphonate derivatives were qualitatively similar to those of LDPE. At low phosphonate concentrations, the α, β, and γ dispersion regions characteristic of PE were observed, while at concentrations greater than 0.5 pendent groups per 100 carbons atoms, only the β and α relaxations could be discerned. At low degrees of substitution, the temperature of the β relaxation T_β decreased from that of PE, but above a degree of substitution of 0.1, T_β increased. This behavior was attributed to the competing influences of steric effects which tend to decrease T_β and dipolar interactions between the phosphonate groups which increase T_β. For the phosphonate containing PEO, a new dispersion region designated as the β′ relaxation was observed as a low-temperature shoulder of the β relaxation. The temperature of the β′ loss was consistent with T_g(U) of the PEO oligomers as determined by differential scanning calorimetry, and it is suggested that the β′-loss process results from the relaxation of PEO domains which constitute a discrete phase within the PE matrix.     

Physical aging studies of amorphous linear polyesters. Part II. Dependence of structural relaxation parameters on the chemical structure

The enthalpy relaxation of a series of linear amorphous polyesters (poly(propylene isophthalate) (PPIP), poly(propylene terephthalate) (PPTP), poly(ethylene terephthalate) (PETP), and poly(dipropylene terephthalate) (PDPT)) has been investigated by differential scanning calorimetry (DSC). These polyesters have been annealed at equal undercooling below their respective glass transition temperatures, T_g, (T_g − 27°C, T_g − 15°C, and T_g − 9°C) for periods of time from 15 min to 480 h. The key parameters of structural relaxation, namely the apparent activation energy (Δh*), the nonlinearity parameter (x) and the nonexponentiality parameter (β), have been determined for each polyester and related to an effective relaxation rate (1/τ_eff) and to the chemical structure. We observe that the variation of the structural relaxation parameters shows a trend that is common to other polymeric systems, whereby an increase of x and β corresponds a decrease in Δh*. The comparison of these parameters in PETP and in PPTP gives information about the effect of the introduction of a methyl group pendant from the main chain; the x parameter increases (i.e., a reduced contribution of the structure to the relaxation times), β increases (i.e., a narrow distribution of relaxation times), and Δh* decreases. Additionally, enthalpy relaxation experiments show that a decrease of Δh* correlates with an increase of 1/τ_eff, when they are measured at a fixed value of the excess enthalpy, δ_H. The introduction of an isopropyl ether group in PDPT with respect to PPTP decreases both x and β, but increases Δh*, which the rate of relaxation decreases. The ring substitution in PPTP and PPIP originates less significant changes in the structural parameters. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36 : 113–126, 1998