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.     

Calorimetric relaxation and glass transition in poly(propylene glycols) and its monomer

The glass transition temperature T_g of propylene glycol (PG) and poly(propylene glycols) (PPGs) of molecular weight up to 4000 has been measured by differential scanning calorimetry, and the activation energy and change in heat capacity ΔC_p have been determined in the glass transition range. The activation energy increases with an increase in the molecular weight of the polymer, and ΔC_p measured at a fixed heating rate decreases. The increase in T_g with molecular weight is remarkably more rapid for poly(propylene glycols) than for other polymers, and a limiting value of T_g is reached for a chain containing 20 monomer units. These results are discussed in terms of the Fox-Flory and the entropy theories. The calorimetric relaxation times are comparable with the extrapolated dielectric relaxation times. The initial increase of ΔC_p from PG to PPG 200 is attributed to the decrease of H-bonding sites from 12 in 3 monomers to 4 on polymerization to PPG 200 and further decrease with increase in molecular weight to an increasingly large amplitude of the β-process at T < T_g.     

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.     

Ion-solvent molecule interaction in nonaqueous solutions: Spin-lattice relaxation time of7Li

The spin-lattice relaxation time (T ₁) of⁷Li⁺ was measured in solutions of LiCl and LiClO₄ in protic (MeOH, EtOH,n-PrOH,i-PrOH,n-BuOH, sec-BuOH, formamide, N-methylformamide) and aprotic (MeCN, acetone, methyl ethyl ketone, propylene carbonate, dimethyl sulfoxide, dimethylformamide, hexamethylphosphotriamide) solvents and in mixtures of H₂O-formamide, H₂O–N-methylformamide, H₂O–N,N-dimethylformamide, H₂O-DMSO, H₂O-hexamethylphosphotriamide, and formamide-N,N-dimethylformamide at 25°C. The values of (1/T ₁)₀ obtained by extrapolation are discussed in terms of current theories of the magnetic relaxation of ionic nuclei. Linear correlations were found between (1/T ₁)₀ and Gutmann's donor numbers and Kosower's Z-values. These correlations indicate that relaxation of⁷Li⁺ is dominated by donor-acceptor interaction of the cation with solvent molecules. Concentration dependences of 1/T ₁ for LiCl and LiClO₄ differ from one another in a given solvent, a fact which is accounted for by a specific cation-anion short-range potential. The quantity 1/T ₁ of⁷Li⁺ atC=1 mole per 55.5 moles of mixed solvent as a function of solvent composition show characteristic features, which are discussed in terms of the relaxation mechanism proposed.     

Calorimetric and Dielectric Investigations of Glass Transition in Intermediate Glass-forming Liquid

The calorimetric glass transition and dielectric dynamics of -relaxation in propylene glycol (PG) and its five oligomers (polypropylene glycol, PPG) have been investigated by the modulated differential scanning calorimetry (MDSC) and the broadband dielectric spectroscopy. From the temperature dependence of heat capacity of PPGs, it is clarified that the glass transition temperature (T_g) and the glass transition region are affected by the heating rate. The kinetic changes of PG and PPGs near T_g strongly depend on the underlying heating rate. With increasing the molecular mass of PPGs, the fragility derived from the relaxation time against temperature also increases. The PG monomer is stronger than its oligomers, PPGs, because of the larger number density of the —OH end group which tends to construct the intermolecular network structure. Adam-Gibbs (AG) theory could still hold for MDSC results due to the fact that the dielectric relaxation time can be related to the configurational entropy.This revised version was published online in November 2005 with corrections to the Cover Date.     

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.     

Ionic conductivity of complexes of novel multiarmed polymers with phosphazene core and LiClO4

Novel multiarmed polymers with ethylene oxide units, [( CH₂CH₂O)_n : 7, n = 3; 8, n= 7.2; 9, n = 11.8, and 12, n = 11.8] were prepared from the reaction of polyethylene glycol monomethyl ethers with acid chlorides of hexakis(3,5-dicarboxyphenoxy)-( 6 ) and hexakis(4-carboxyphenoxy)cyclotriphosphazenes ( 11 ) and conductivities of their Li⁺ salt complexes were investigated. The glass transition temperatures of the salt-free polymers are in the temperature range −59 to −54°C, indicative of a high degree of reorientational mobility of the arms. When LiClO₄ was added to the multiarmed polymers, the T_g values raised monotonically. The extent of T_g elevation was affected by the length of arms and the number of oxygen atoms around cyclotriphosphazene core and increased in the order 7 > 8 > 12 > 9 . The conductivities increased in the order 9 > 8 = 12 > 7 and the maximum conductivities of 4.0 × 10⁻⁵ S/cm at 30°C and 6.0 × 10⁻⁴ S/cm at 90°C have been achieved for the 9 -Li⁺ complex with Li⁺/O = 0.03. Interestingly, the conductivity of 9 -Li⁺ complexes at constant reduced temperatures increased in the whole concentrations of LiClO₄ examined (Li⁺/O = 0.01–0.2), although the degree of increase in conductivity above Li⁺/O = 0.06 became small. From the behaviors of T_g and the conductivity of multiarmed polymer–LiClO₄ complexes, it appears that the conductivity is governed by relative concentrations of inter- and intramolecular complexes in the polymer matrix. The influence of structural change of the comb-shaped to multiarmed polymers on the conductivity is described. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35 : 1839–1847, 1997     

Segmental and crosslink point motion in networks

¹³C- and ³¹P-NMR spin lattice relaxation in the rotating frame have been measured on a series of networks prepared from monodisperse and deliberately bimodal poly(propylene glycols) (PPG) crosslinked with tris(4-isocyanatophenyl) thiophosphate. The T_1pC minima correspond to loss maxima in the DMTA (Dynamic Mechanical Testing) measured at 10Hz. The T_1p^P minima fall at higher temperatures than those of T_1p^C for the same network indicating that these crosslinks lag the segments in frequency of motion at a given temperature. The carbon relaxation is biphasic below T_g of the segments indicating two relaxation domains which we assign to bulklike PPG segments and PPG segments proximal to he crosslink. Lineshape analysis by a diffusional model indicates crosslink reorientation is not isotropic until well above T_g. Relaxation and lineshapes for the bimodal networks indicate that junctions are not uniformly plasticized by the segments.     

Solid polymer electrolytes. IV. Preparation and characterization of novel crosslinked epoxy‐siloxane polymer complexes as polymer electrolytes

Two series of novel crosslinked siloxane‐based polymers and their complexes with lithium perchlorate (LiClO₄) were prepared and characterized by Fourier transform infrared spectroscopy, solid‐state NMR (¹³C, ²⁹Si, and ⁷Li nuclei), and differential scanning calorimetry. Their thermal stability and ionic conductivity of these complexes were also investigated by thermogravimetric and AC impedance measurements. In these polymer networks, poly(propylene oxide) chains with different molecular weights were introduced through self‐synthesized epoxy‐siloxane precursors cured with two curing agents. The glass‐transition temperature (T_g) of these copolymers is dependent on the length of the ether units. The dissolution of LiClO₄ considerably increases the T_g of the polyether segments. The dependence of the ionic conductivity was investigated as a function of temperature, LiClO₄ concentration, and the molecular weight of the polyether segments. The ion‐transport behavior was affected by the combination of the ionic mobility and number of carrier ions. The ⁷Li solid‐state NMR line shapes of these polymer complexes suggest a significant interaction between Li⁺ ions and the polymer matrix, and temperature‐ and LiClO₄ concentration‐dependent chemical shifts are correlated with ionic conductivity. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 1226–1235, 2002     

Structural and dynamical aspects of PEG/LiClO4 in solvent mixtures via NMR spectroscopy

Motivated by the potential usefulness of polyethylene glycol (PEG)/Li⁺ salt mixtures in several industrial applications, we investigated the structure and dynamics of PEG/LiClO₄ mixtures in D₂O and its mixtures with CD₃CN and DMSO-d₆, in a series of PEG-based polymers with a wide variation in their molecular weights. ¹H NMR chemical shifts, T₁/T₂ relaxation rates, pulsed-field gradient NMR diffusion experiments, and 2D HOESY NMR studies have been performed to understand the structural and dynamical aspects of these mixtures. Increasing the temperature of the medium results in a significant perturbation in the H-bonded structure of PEG in its PEG/LiClO₄/D₂O mixtures as observed from the increase in chemical shifts. On the other hand, the addition of molecular cosolvents has a negligible effect. The hydrodynamic structure of PEG shows a pronounced variation at low temperature with increasing molecular weight, which, however, disappears at higher temperatures. Increasing the temperature leads to a decrease in the hydrodynamic structure of PEG, which can be explained on the basis of solvation–desolvation phenomena. The 2D HOESY NMR spectra reveal a new finding of Li⁺-water binding in the PEG/LiClO₄/D₂O mixtures with the addition of molecular solvents, suggesting that the Li⁺ cation diffuses freely in the D₂O mixtures of polymers as compared with the polymer mixtures with DMSO or CD₃CN.     

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.     

Dielectric relaxation spectroscopy of amorphous and liquid-crystalline side-chain polycarbonates

The molecular dynamics of amorphous and liquid-crystalline (LC) side-chain polycarbonates was studied by dielectric spectroscopy at frequencies from 10⁻² to 10⁶ Hz and at temperatures from −160 to 180°C. ‘Model’ compounds containing no mesogenic side-groups showed two relaxations, which originate from the carbonate group (α, β_m-relaxation). By contrast, in LC-polycarbonates bearing a mesogenic nitrostilbene side group around and above the glass transition temperature T_g up to three relaxation modes were distinguished (α-, λ₁-, λ₂-process); below T_g four secondary relaxations (γ-, β_m-, β_s-, β_sc-relaxation) were observed. The γ-relaxation was found only in compounds possessing an aliphatic spacer linked to the backbone by an ether bond. Apart from β_m-, two additional β-processes were identified as relaxations associated with the mesogenic unit in the glassy (β_s) or in the crystalline state (β_sc).     

Thermostimulated depolarization currents and thermoelectret effects in poly(methyl methacrylate)

The electrical dipole relaxation in PMMA has been studied by measuring thermostimulated depolarizing currents. A master curve for the segmental component of the dielectric constant has been constructed. The increment of the dielectric permittivity due to the α-relaxation has been determined. The distribution function of the relaxation times and the average relaxation times in the region from 70°C up to T_g = 105°C have been obtained. A way of describing the electret properties of the polymer is discussed.     

Evidence of dynamic heterogeneity as obtained from dielectric and brillouin light-scattering studies of poly(n-hexylmethacrylate)

We report dielectric relaxation and Rayleigh-Brillouin spectroscopic measurements on the side chain polymer poly(n-hexylmethacrylate), PHMA (T_g = 268 K), exhibiting a broad glass transition region. The dielectric loss curves can be represented by single Havriliak-Negami functions in the temperature range of 260–450 K. The width of the distribution relaxation function is a decreasing function of temperature up to T = 333 K ≊ 1.24 × T_g and remains virtually constant above that temperature. This is interpreted as marking the merging of the α-process with a slow β-relaxation in agreement with the value of the cooperativity length associated with the α-mode. Hence above that temperature, the relaxation times confirm well to an Arrhenius temperature dependence. The hypersonic dispersion deduced from the Brillouin spectra (210–550 K) surprisingly peaks at temperatures near T_g which bears no relation to the main α-relaxation. This structural relaxation is rather associated with the side hexyl group motion showing striking resemblance with the hypersonic dispersion in molecular liquids. It is conceivable that the observed damping in PHMA is dynamically related to the internal plasticization effect of the hexyl group. © 1996 John Wiley & Sons, Inc.     

Dielectric and conductivity relaxations in poly(hema) and of water in its hydrogel

The dielectric permittivity ε′ and loss ε″ of anhydrous poly(2-hydroxyethyl methacrylate) and its 38.6 w/w% hydrogel have been measured in the frequency range from 12 Hz to 200 kHz and the temperature range from 77 to 273 K. The former has a sub-T_g relaxation with a half-width of 4.5 decades for the loss spectra, whose strength increases with temperature, and an activation energy of 62.5 kJ/mol. The dielectric relaxation time of the α process of supercooled water in the hydrogel is 53 s at its calorimetric T_g of 135 K. The half-width of the relaxation spectrum is 2.85 decades and, in the narrow temperature range, its apparent activation energy is 60.8 kJ/mol. Heating of the hydrogel causes crystallization of water which begins at about 207 K and becomes readily detectable as a second dielectric loss peak at about 230 K. For each temperature between 207 and 267 K, supercooled water in the hydrogel coexists with its crystallized form, with the amount of the crystallized solid increasing with increasing temperature. These results are discussed in terms of “bound” and “free” states of water in the hydrogel.     

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.     

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.     

The effect of soft-segment length and concentration on phase separation in segmented polyurethanes

Three series of polyurethanes, based on three polyols, diphenylmethane diisocyanate (MDI), and three chain extenders were synthesized. Polypropylene glycol (PPG) soft-segment length (MW 1000, 2000, and 3000), soft-segment concentration (30%, 50%, and 70%), and the type of chain extender (ethylene glycol, butane diol, and hexane diol) were varied and their effect on the amount of phase separation studied. Methods for assessing phase separation quantitatively, based on shifts of the glass transition temperature T_g and the enthalpy jump at the glass transition were tested. It was shown that they give incorrect results, especially with PPG 1000 as the soft segment. Dependence of the soft segment T_g on the polyol length was explained by the “network effect.” True phase mixing was found only with PPG 1000 series at low soft-segment concentration, whereas, no clear indication of the phase mixing with PPG 2000 and PPG 3000 based polyurethanes was observed.     

Molecular dynamics of amorphous/crystalline polymer blends studied by broadband dielectric spectroscopy

The molecular dynamics of poly(vinyl acetate), PVAc, and poly(hydroxy butyrate), PHB, as an amorphous/crystalline polymer blend has been investigated using broadband dielectric spectroscopy over wide ranges of frequency (10⁻² to 10⁵ Hz), temperature, and blend composition. Two dielectric relaxation processes were detected for pure PHB at high and low frequency ranges at a given constant temperature above the T_g. These two relaxation peaks are related to the α and α′ of the amorphous and rigid amorphous regions in the sample, respectively. The α′-relaxation process was found to be temperature and composition dependent and related to the constrained amorphous region located between adjacent lamellae inside the lamellar stacks. In addition, the α′-relaxation process behaves as a typical glass relaxation process, i.e., originated from the micro-Brownian cooperative reorientation of highly constraints polymeric segments. The α-relaxation process is related to the amorphous regions located between the lamellar crystals stacks. In the PHB/PVAc blends, only one α-relaxation process has been observed for all measured blends located in the temperature ranges between the T_g’s of the pure components. This last finding suggested that the relaxation processes of the two components are coupled together due to the small difference in the T_g’s (ΔT_g = 35 °C) and the favorable thermodynamics interaction between the two polymer components and consequently less dynamic heterogeneity in the blends. The T_g’s of the blends measured by DSC were followed a linear behavior with composition indicating that the two components are miscible over the entire range of composition. The α′-relaxation process was also observed in the blends of rich PHB content up to 30 wt% PHB. The molecular dynamics of α and α′-relaxation processes were found to be greatly influenced by blending, i.e., the dielectric strength, the peak broadness, and the dielectric loss peak maximum were found to be composition dependent. The dielectric measurements also confirmed the slowing down of the crystallization process of PHB in the blends.     

Bisphenol-A polycarbonate–diluent interactions

The effect of low-molecular-weight miscible additives on the sub-T_g (β) relaxation process in bisphenol-A polycarbonate (BPAPC) was studied using high-resolution carbon-13 solid-state NMR. The trend of the spin-lattice relaxation times T₁ at 50 MHz suggests that strong intermolecular interactions occur upon mixing when BPAPC is physically stiffened by the antiplasticizing diluent, diphenylphthalate. The values of ¹³C T₁ at 15 MHz in d-chloroform solutions for similar BPAPC-diluent mixtures suggest that diluent effects on the megahertz mobility of the polymer occur exclusively in the solid state. These results are explained using equilibrium thermodynamics, in the Ehrenfest sense, at the second-order glass transition temperature T_g. Theory predicts that the temperature dependence of the Flory–Huggins interaction parameter ?χ/?T changes abruptly as the polymer-diluent blends are cooled below T_g from the molten state. The difference between ?χ/?T in the liquid and glassy states is the major factor which determines the diluent concentration dependence of T_g. A method is developed to estimate the relative magnitudes of χ for polymerdiluent blends in the glassy state.