Dielectric spectroscopy and calorimetry during postcuring of a linear chain polymer thermoset formed from a diepoxide and cyclohexylamine,and the nature of the products

The dielectric permittivity and loss spectra of an equimolar liquid mixture of diglycidyl ether of bisphenol-A and cyclohexylamine have been studied during the liquid's isothermal polymerization or curing in separate experiments at different temperatures and thereafter during the postcuring, both on rate-heating and isothermally. The spectra obtained during the growth of the linear chain polymer during the curing and postcuring show the evolution of an intermediate relaxation process whose position in the frequency plane remains relatively insensitive to the decrease in the configurational entropy during the postcuring, but whose strength increases. Postcuring ceases to occur once the calorimetric glass-liquid transition temperature of 345 K, corresponding to the ultimately formed polymeric state, has been reached. The increase in the number of covalent bonds, n, formed during curing and postcuring decreased the equilibrium dielectric permittivity, ε_s, and increased the characteristic relaxation time, τ₀, for all curing and postcuring conditions. For a fixed temperature and n, (dε_s/dT) and (dτ₀/dT), as well as the values ε_s and τ₀ of the ultimately formed state of the polymers differ significantly when the thermal history of polymerization differs. The slow dynamics in the glass-liquid transition region were analyzed in terms of the enthalpy relaxation and fictive temperature concepts. The distribution of relaxation times for these dynamics correspond to the stretched exponential parameter of 0.6, which is significantly greater than 0.39 determined for the dielectric α-relaxation spectra measured at a temperature 30 K higher. The enthalpy relaxation involves a narrower distribution of intermolecular barriers than dielectric relaxation. The results also show that the recently proposed method for determining the gelation time from the plots of the imaginary component of electrical impedance lacks scientific merit. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36 : 303–318, 1998     

Calorimetric and dielectric effects during polymerization of an elastomer‐containing mixture and liquid‐liquid phase separation

Calorimetry and dielectric spectroscopy of an elastomer, amine terminated butadiene acrylonitrile (ATBN), dissolved in a stoichiometric mixture of ethylene diamine and diglycidyl ether of bisphenol‐A, were studied in real time during the polymerization and phase separation of the mixture. In the two polymer compositions containing 8 w/w % ATBN and 20 w/w % ATBN, the total enthalpy released per mole of DGEBA's reaction was the same, indicating indetectably small changes in molecular interactions before and after the phase separation. The dielectric relaxation spectra showed no evidence for phase separation, which indicated a gradual phase separation with time and the extent of polymerization, and relatively small differences in the permittivity and conductivity between the ATBN particles and the network matrix at the time of phase separation. The equilibrium permittivity and dc conductivity showed a nonideal mixing of ATBN. The stretched exponential relaxation parameter remained at 0.36, but the characteristic dielectric relaxation time and the dc conductivity increased on addition of ATBN. An increase in the temperature had a greater effect on the relaxation time than the increase in the extent of polymerization. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1911–1919, 1999     

Steric hindrance effects on dielectric relaxation and polymerization kinetics of a monoamine–triepoxide mixture,thermochemistry, and diffusion control

Calorimetry and dielectric relaxation spectroscopy during the growth of a polymer network in the stoichiometric mixture of a triepoxide with 4-chloroaniline have been performed in separate experiments to investigate the increase in the relaxation time with the number of covalent bonds. A comparison with the corresponding study of triepoxide–aniline and triepoxide–3-chloroaniline mixtures shows that steric hindrance of the amine group by chlorine slows the molecular dynamics and the relaxation time of the state containing a fixed number of bonds. The polymerization kinetics measured during ramp heating does not yield a reliable activation energy. A recent empirical relation between the relaxation time and the extent of polymerization, and the condition for the onset of diffusion-control kinetics have been examined using the data for these three polymerizing mixtures. The results show substantial deviations from the empirical relation and appear to conflict with our basic understanding of the polymerization process. It is shown mathematically that features attributed to the onset of diffusion-controlled kinetics can arise from thermochemical behavior alone, without reference to the molecular dynamics. An earlier theory for the change in the kinetics of an addition reaction from mass control to diffusion control has been considered, and is seen as relevant to the polymerization reactions. It is argued that the dielectric relaxation rate does not directly indicate the chemical reaction rate because the reorientational motion of the dipolar entities may not be coupled to the rotational and translational diffusion that brings the sterically hindered chemically reacting sites together. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 2703–2716, 1998     

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.     

Conductivity,proton percolation,and gelation during the network growth in a flexible chain diepoxide and diamine mixture

The conductivity of a stoichiometric mixture of diglycidyl ether of 1,4‐butanediol and 1,6‐hexamethylene diamine has been studied during its polymerization at several temperatures where the ultimate product is a crosslinked gel. The decrease in the dc conductivity, σ₀, with the polymerization time, t, fits an equation for bond percolation, σ₀ ∼ [(t_gel‐t)/t_gel]^p, and yields a gelation time, t_gel which agrees with the t_gel determined from the viscosity and shear modulus measurements. It is proposed that as one covalent bond forms on chemical reaction, an indeterminable number of intermolecular H‐bonds in the structure vanish, and protonic conduction is disrupted. Thus, as the original H‐bond network gives way to a covalently bonded network, the mechanical rigidity increases, and protonic conductivity decreases. The gel point is reached when the increase in the number of covalent bonds brings the liquid's state up to its rigidity percolation threshold, and the decrease in the number of H‐bonds brings it down to its electrical percolation threshold. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 122–126, 2000     

Heteromolecular structures in aqueous solutions of dimethylformamide and tetrahydrofuran,according to molecular dynamics data

The complex dielectric permittivity of aqueous solutions of tetrahydrofuran and dimethylformamide in wide ranges of temperature (220–300 K) and pressure (0.1–12 MPa) is studied by means of molecular dynamics. The autocorrelation functions of the dipole moments of molecules are calculated. Dielectric permittivity spectra are obtained. The dielectric relaxation times are determined as functions of the tetrahydrofuran and dimethylformamide concentrations in the indicated binary mixtures. The dielectric relaxation frequency shifts toward low frequencies in the range of tetrahydrofuran and dimethylformamide concentrations x ≤ 0.5 molar fraction, due to the formation of heteromolecular structures with hydrogen bonds. This is confirmed by the negative values of the excess dielectric permittivities of binary solutions at x ～ 0.3–0.4 molar fraction.     

Dielectric Dispersion and Electric Relaxation Processes Induced by Ionic Conduction in Formamide, 2-Aminoethanol and Their Binary Mixtures

The complex dielectric permittivity, ionic conductivity, electric modulus and impedance spectra of the dipolar molecules formamide (FA), 2-aminoethanol (AE) and their binary mixtures were investigated in the frequency range from 20 Hz to 1 MHz at 303.15 K. Debye-type distributions of the frequency dependent electric modulus and complex impedance were found, corresponding to an ionic conduction relaxation process in the upper frequency regime of the spectra, whereas a spike in the impedance spectra at low frequencies confirms the contribution of an electrode polarization (EP) relaxation process induced by ionic conduction. Due to the high static permittivity of FA, its ionic conductivity was found more than one order of magnitude higher than that of the AE, which is also shown by the comparative values of their EP and ionic conductivity relaxation times. The dependences of dc ionic conductivity values of the binary mixtures on their relaxation times and static permittivity were explored. The concentration dependent static permittivity and the relaxation times led us to infer the formation of a 1:1 H-bonded stable complex between FA and AE molecules with reduction in the number of effective parallel-aligned dipoles.     

Dielectric effects of step-increased pressure on the mass- and diffusion-controlled linear chain and network macromolecules growth

The dielectric properties of four stoichiometric liquid mixtures of a diepoxide with two monoamines and two diamines have been studied in real time during the mixture's polymerization isothermally to a linear-chain polymer in two cases and a network polymer in the other two cases, at 1 and 200 bar. The pressure was applied: (a) at the beginning of polymerization, (b) after a small extent of polymerization when the viscosity was low, and (c) after a relatively large extent of polymerization when the viscosity was high. For a fixed polymerization period, pressure increased the dielectric relaxation time much more than any other quantity in all cases, without a change in the distribution of relaxation times. Contributions to the dielectric permittivity and loss from physical and chemical effects have been considered and related to the changes in the dielectric relaxation time, viscosity and polymerization-rate constant as the extent of polymerization increased with time. Pressure is expected to decrease the polymerization rate for all conditions, but the decrease is relatively insignificant at the early stage, when polymerization is mass-controlled. Here other effects override the effect of viscosity increase, and the polymerization rate instead increases. The decrease in the rate becomes significant and predominates only when polymerization becomes diffusion-controlled. Since theories of diffusion-controlled reactions do not consider the mutual slowing of the molecular diffusion and the rate of chemical reactions leading to a macromolecule's growth until its vitrification isothermally, a method for determining the onset of diffusion control was needed. It is shown that this onset can be determined from plotting the rate of polymerization against the dielectric relaxation time. Expressed in terms of the dielectric loss, these plots cross each other. The cross-over point indicates the onset of diffusion control. Thus, the effect of pressure on the dielectric behaviour can be used to determine the change from mass-controlled to diffusion-controlled kinetics.     

Limiting equivalent electrical conductivity of inorganic salt solutions and dielectric properties of a polar solvent

A relation has been found to exist between the limiting equivalent electrical conductivity of inorganic salt solutions, viscosity, temperature, and dielectric properties of the solvent. As temperature rises, the limiting equivalent electrical conductivity of aqueous solution of an inorganic salt has been shown to increase in direct proportion to the ratio of the dielectric permittivity to the dipole dielectric relaxation time, i.e., the limiting high-frequency electrical conductivity of the polar solvent. Expressions have been derived to be used in ascertaining the limiting equivalent electrical conductivities of inorganic salt solutions proceeding from the dielectric properties of the solvent.     

Effect of dielectric properties and structure of aqueous solutions of diallylammonium salts on their reactivity in radical polymerization

The complex dielectric permittivity in the frequency range 7.5–25.0 GHz and the low-frequency specific conductivity of aqueous solutions of diallylammonium salts (diallylammonium and diallylmethylammonium trifluoroacetates and diallyldimethylammonium chloride) were measured at 293–308 K over a wide concentration range. On the basis of the results, the parameters of dielectric relaxation were calculated. The number of water molecules in the solvation shell of the salts was estimated. The concentration behavior of the initial rate of radical polymerization of diallylammonium salts and the rate constant of bimolecular chain termination was correlated with the specific features of the structure of aqueous monomer solutions. The role of “free” water in the initial salt solutions was revealed, a species whose presence in the system determines the character of concentration behavior of the rate constants for the elementary steps of polymerization, such as propagation, chain transfer to the monomer, and bimolecular chain termination.     

KCl/NaCl DMSO aqueous solutions dielectric spectra and cooperative interactions

The complex permittivity spectra of KCl/NaCl DMSO aqueous solutions were measured using microwave dielectric spectroscopy. Ion–water and dipole–water cooperative interactions are investigated by using a fractional relaxation process. Only about one cooperative relaxation was found during the cut-off relaxation time interval and the relaxation time increases with concentration increasing. Ions’ concentration dependent on effective number of water molecules in the shell around ions was calculated to reveal the interactions between K⁺, Cl^?, Na⁺ ions and DMSO molecules.     

Molecular dynamics models and thermodynamic characteristics of hydrogen bonds in 1,2-ethanediol

A correlation between the lifetimes of hydrogen bonds and the thermodynamic characteristics of their formation and breaking, and the experimental relaxation times of dielectric spectra and the energy characteristics of relaxation processes, is observed via molecular dynamics (MD) simulation of the rearranging of the network structure of 1,2-ethanediol. The MD torsional frequency of the transition of gauche conformer tGg′ at 224.1 cm_?1 and the experimental frequency of the band maximum of torsional vibrations at 230 cm_?1 in the infrared spectrum correlate with the oscillation frequency of molecules at 240 cm_?1 inside clusters in the Dissado–Hill (DH) model. The MD and DH models indicate a predominantly parallel alignment of the electric dipole moments of conformers tGg′ in the three-dimensional network of hydrogen bonds of the liquid 1,2-ethanediol phase.     

Broadband dielectric spectroscopic studies of molecular motions in a Nafion® membrane vs. annealing time and temperature

The dynamics of macromolecular motions as coupled to proton migration in annealed Nafion® membranes were explored at temperatures above 100 °C using broadband dielectric spectroscopy. Loss permittivity vs. frequency spectra of both β and α relaxations showed increased relaxation times with annealing which was rationalized in terms of water de-sorption and diminished free volume. The α relaxation time increases with increased annealing temperature. A parameter N reflecting connectedness of charge hopping pathways was extracted and indicated that the conductivity network accumulates more charge traps, presumably due to free volume decrease, with increased annealing time. Conductivity increases with increased annealing time at all temperatures despite the decrease in N; this suggests a change in the nature of proton hopping on annealing at high temperatures to be between sulfonic acid groups rather than by hopping across H₂OH⁺OH₂ bonds.     

Spontaneous transformation of water's high-density amorph and a two-stage crystallization to ice VI at 1 GPa: a dielectric study

Dielectric relaxation spectra of a metastable crystal phase formed on implosive and exothermic transformation of pressure-amorphized hexagonal ice have been measured in situ at 0.97 GPa pressure over a range of temperature. The metastable phase showed no relaxation peak at 130 K and 0.97 GPa. When heated at a fixed pressure of 0.97 GPa, it began to transform at approximately 145 K exothermally to a phase whose relaxation rate and equilibrium dielectric permittivity increased. A second, but slower exothermic transformation also occurred at approximately 175 K. After keeping at 213 K, the relaxation rate and equilibrium permittivity reached the known values of these two quantities for ice VI. Thus the metastable phase transformed to ice VI in two stages. It is conjectured that the intermediate phase in this transformation could be ice XII. The rate of transformation is not determined by the reorientational relaxation rate of water molecules in the ices.     

Dielectric analysis of chitosan gel beads suspensions: influence of low crosslinking agent concentration on the dielectric behavior

Dielectric measurements were carried out for the suspensions of chitosan gel beads (CGB) crosslinked with glutaraldehyde (GA), ranging in crosslinking time from 1 to 180 min at six fixed low GA concentrations over a frequency range from 40 to 110 MHz. The distinct dielectric relaxations observed in the frequency range of 10(4)-10(5) Hz were explained by the effects of the interfacial polarization. By fitting the experimental data with Cole-Cole equation the dielectric parameters of the suspensions were obtained, and the phase parameters were calculated using Hanai's method. The influence of crosslinking on the dielectric spectra of CGB was investigated by viewing the crosslinking time dependencies of conductivity increment (Deltakappa), relaxation frequency (f(0)), permittivity of CGB (epsilon(i)), conductivity of CGB (kappa(i)) and conductivity of continuous media (kappa(a)) at six fixed GA concentrations. Some information were gained, such as, thinner electric double layer, particle with rougher surface and more compact gel backbone with increasing crosslinking time. The basic information obtained can provide valuable references for the preparation of CGB and the application to more extensive fields such as controlled-release technology of medicament.     

Dielectric spectroscopy study of cyanate ester oligomer curing kinetics

The evolution of dielectric properties during the cyanate ester oligomer curing process was studied in the electric field frequencies range of 10^–2—10⁵ Hz. The kinetic of the curing process was investigated using the acquired data for complex dielectric permittivity and conductivity. It is demonstrated that, along with the formation of the polymer network, a microphase separation of the reaction intermediate, namely carbamate, takes place during the trimerization reaction. It is manifested in the frequency spectra as the Maxwell—Wagner polarization.     

Dielectric properties of solvents and their limiting high-frequency conductivity

The behavior of the limiting high-frequency (HF) conductivity of water, methanol, ethanol, and propanol in a wide temperature range is considered. As the temperature is increased to its critical value, the static permittivity and the dipole relaxation time of the polar solvents decrease monotonically; however, the limiting HF conductivity, which is determined by their ratio, passes through a maximum. The maximum is explained by differences in the behavior of the temperature dependences of the relative temperature coefficients (RTCs) of static permittivity and the dipole relaxation time. It is shown that the maximum on the temperature dependence of the limiting HF conductivity corresponds to the equality of the RTCs of static permittivity and the dipole relaxation time. It is noted that in the temperature range corresponding to the maximum limiting HF conductivities of water and alcohols, the temperature dependences of the ion product of water and the conductivity of the considered polar solvents and solutions of inorganic salts in them also pass through maxima.     

Temperature changes of dielectric permittivity and relaxation in aqueous lithium iodide solutions

The complex permittivity of aqueous LiI solutions is studied over a wide range of concentrations at temperatures of 288–323 K in the water permittivity dispersion region at seven frequencies in the range of 7.5–25 GHz. One relaxation region describable by the Debye or Cole-Cole equation is observed in these solutions. Dielectric relaxation time τ and static permittivity ?_s are studied as dependent on temperature and concentration. The time and enthalpy of activation of dielectric relaxation decrease in going from water to solutions, which corresponds to the distortion of the initial water structure and the increasing mobility of water molecules in hydration shells of ions. In the initial concentration range, the water activity is a linear function of 1/?_s. The negative temperature dependence of ?_s disappears in going to concentrated solutions. At high concentrations, the static dielectric constant increases in response to increasing temperature. The new trends in ?_s and τ at elevated temperatures of 313–323 K are due to the formation of ion pairs and other ion-water groups having high dipole moments.     

Relaxation processes of the structural rearrangement of clusters in liquids: 1,2-ethanediol, 1,2-propanediol, and 1,2,6-hexanetriol

The dielectric relaxation spectra (DRS) of 1,2-ethanediol, 1,2-propanediol, and 1,2,6-gexanetriol are analyzed in terms of the Dissado-Hill (DH) model in a wide range of temperatures, with all parameters required for calculating the cluster dipole moments being determined within the DH molecular model itself. The dependence of the equilibrium and relaxation properties of DRS on the hydrocarbon radical length and the number of OH groups is studied. The dipole moments of the clusters are calculated. It is shown how the roles of the processes of intracluster rearrangement are redistributed due to the break of hydrogen bonds and fluctuation processes of synchronous exchange of molecules between the clusters.