Aliphatic polyesters as models for relaxation processes in crystalline polymers: 3. Mechanical relaxation in copolymers of adipic acid with 1,6 and 2,5-hexanediols

The shear moduli of a series of the title polyesters spanning a crystallinity range of 0–60% have been measured as a function of temperature at ≈1 Hz using a torsion pendulum. The experimental isochronal temperature scans of G′ and G″ are fitted to phenomenological equations. With only minor adjustments, the same relaxation spectrum parameters as found dielectrically for these polymers (relaxation shape, central relaxation times) fit the mechanical data. Thus, for the β (glass—rubber) relaxation in the amorphous fraction the broadness is very sensitive to the presence of the crystal fraction and becomes increasingly broad as the degree of crystallinity increases. In contrast, the γ process dynamic behaviour is insensitive to the presence of and degree of crystallinity. Unrelaxed and relaxed moduli values are determined for the γ and β processes. A composite model approach is used to determine bounds on the amorphous-phase unrelaxed and relaxed γ and β moduli from the bulk specimen values. As was the case dielectrically, the γ process, in addition to being assigned to the amorphous fraction, has a strength that depends on the diol composition also. The relaxed (γ + β) amorphous-phase rubbery shear modulus is bound reasonably well from application of the composite model to the bulk specimen values and is assigned the value 100 ± 20 MPa at 250 K. It decreases relatively strongly with increasing temperature.     

A dielectric study of the crystal and amorphous fractions in oriented polyethylenes

Polyethylenes have relaxation processes separately assignable to the crystal and amorphous components. The possibility thus presents itself for studying the interaction between the two phases by investigating the anisotropy of the separate relaxation processes induced by overall orientation of the material. Such a study was carried out here by the dielectric method on samples rendered dielectrically active by the introduction of a few carbonyl groups by oxidation. In addition to the usual advantage of ease of frequency variation, the dielectric method in this case has a very great advantage in interpretation resulting from the similarity of dielectric constants of the two phases. In specimens oriented by solid-state extrusion, it was found that the crystalline relaxation process (α) develops the expected anisotropy resulting from dipoles normal to C-axis alignment in the extrusion direction. In branched polyethylene (BPE) no accompanying anisotropy of the amorphous β and γ processes was observed. Since the extrusion was carried out well above the glass temperature of the amorphous component, this indicates that constraints from the crystal phase are not sufficient to prevent dissipation of amorphous orientation by segmental motion. However in linear polyethylene (LPE) (where there is no well-developed β process) some anisotropy of the γ process was observed. It is proposed that a higher degree of constraint of the amorphous component by the crystals in LPE results in suppression of the glass-rubber (β) relaxation and permits amorphous orientation to accompany crystal orientation.     

Aliphatic polyesters as models for relaxation processes in crystalline polymers: 2. Dielectric relaxation in copolymers of adipic acid with 1,6 and 2,5-hexanediols

Linear aliphatic polyesters are interesting model systems for studying relaxation processes in crystalline polymers because they show both γ and β relaxations in a prominent way whereas in many highly crystalline linear polymers (LPE, POM etc.) the β process is suppressed and, unlike branched polyethylene which also has a prominent β process, the polyesters have no chemical structural complications due to branches. To study the hypothesis that variations in the appearance of the β (glass-rubber) relaxation are due to varying degrees of immobilization of long-range segmental motion in the amorphous fraction by the presence of the crystal phase measurements are made of dielectric relaxation in a series of the title copolymers that span the crystallinity range of zero (homopolymer with 2,5-hexanediol) to ≈60% (homopolymer with 1,6-hexanediol). The data are analysed in terms of the effect of degree of crystallinity on both kinetic parameters (activation energies and relaxation width) and equilibrium parameters (dipole correlation factor deduced from relaxation strength). In the latter case special care is taken to properly assess composite mixture effects on the relaxation strength. The shape of the β process is extremely sensitive to the degree of crystallinity, broadening greatly with the onset of the presence of crystallinity and increasing in broadness with increasing degree of crystallinity. Although less sensitive than the width, the β relaxation dipole correlation factor depends on crystallinity also, the availability of chain configurations within the amorphous fraction being noticeably reduced in the crystalline specimens. The γ process kinetic parameters are relatively insensitive to the presence of the crystal phase, a behaviour consistent with a localized motion mechanism. The γ relaxation strength correlates with the process having an amorphous phase origin if it is assumed that the 2,5 diol units contribute less to relaxation strength than the 1,6 diol units; a result also consistent with the localized motion concept.     

Nuclear magnetic relaxation in linear and branched polyethylene

An assessment is made of the information provided by n.m.r. second moment, fourth moment and T₂ measurements on oriented samples of branched and linear polyethylene. Detailed theoretical comparisons are made with the previously reported experimental results of a number of workers in order to derive information about the molecular motions which underlie the α, β and γ relaxations in the two forms of the polymer. Plausible motional models are presented in each case. Particular attention has been given to the β relaxation which is explained in terms of lamellar fold motion. The relative sensitivity of the various n.m.r. measurements to molecular anisotropy and motion in the polymer is discussed.     

Local dynamics in epoxy coatings containing iron oxide nanoparticles by dielectric relaxation spectroscopy

Nanocomposites of photocurable epoxy resin and epoxy‐modified iron oxide magnetic nanoparticles were analyzed by dielectric relaxation spectroscopy to study the local dynamics at temperatures well below the glass‐transition temperature. Two secondary processes were detected, β and γ processes, but the second one was just detected at lower temperatures in the high‐frequency part of the spectra and moved out of the frequency range at higher temperatures. Data were fitted to the Havriliak–Negami and Arrhenius models, and the obtained parameters were analyzed. Relaxation times of the β secondary relaxation did not change with the nanoparticle content, but the relaxation strength increased. The increase could not be explained when we took into account the molecular origin of the relaxation. The presence of ferromagnetic nanoparticles enhanced the internal field and increased the relaxation strengths. Transmission electron microscopy images showed that the nanoparticles were well dispersed in the matrix, without magnetic agglomerates. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci 2008     

Mechanical anisotropy in oriented polychlorotrifluoroethylene

The dynamic tensile modulus (E) and loss (tan δ) of various oriented samples of polychlorotrifluoroethylene have been measured at 0°, 45° and 90° to the draw direction over the range of ? 100 to 160°C. For the cold-drawn samples the mechanical anisotropy at the lowest temperature is determined by the overall chain orientation resulting in E₀ >E₄₅ >E₉₀. Above the γ relaxation (20°C) a shear process is activated leading to a change in the anisotropy pattern to E₀ >E₉₀ >E₄₅. Cold-drawing followed by annealing gives rise to further changes so that E₉₀ >E₀ >E₄₅ above the β relaxation (120°C). The effect of annealing has been attributed to the relaxation of the amorphous regions and the development of lamellar texture, and the anisotropy in tan $\text{δ}\text{E}$ at the β relaxation is found to be consistent with the interlamellar shear model.     

Viscoelastic characteristics of chain extended/branched and linear polyethylene terephthalate resins

Two chemically modified chain extended/branched polyethylene terephthalate (PET) resins and one unmodified resin, considered to be linear, were characterized in terms of their melt flow, die swell, and viscoelastic properties. The three resins had reportedly similar nominal intrinsic viscosities but exhibited different viscoelastic behavior. The modified resins had lower melt flow index, higher die swell, higher complex viscosity and higher storage modulus than the unmodified one. The Cole–Cole plots of the resins were independent of temperature, and the data for modified resins formed a group that lay below the data group for the unmodified PET. The distribution of relaxation times was determined. The modified resins had higher relaxation strength, G_i, especially at high relaxation times, λ_i. The mean relaxation times of the chain extended/branched resins were approximately an order of magnitude higher than that of the unmodified resin, implying pronounced elastic character. The modified resins had better foaming characteristics in extrusion foam processing than the unmodified one owing to their elastic nature. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 75: 1371–1377, 2000     

Dielectric relaxation spectra of chemically treated woods

The changes in the dielectric properties of absolutely dried Sitka spruce (Picea sitchensis Carr.) wood caused by chemical treatments were investigated. Eight kinds of chemical treatments with various levels of weight percentage gain (WPG) were performed. Through the application of the Cole–Cole circular arc law to the results of the dielectric measurements in the frequency range of 1 kHz to 1 MHz at ?60°C, the relaxation spectrum was calculated. The relaxation magnitude (ε₀ ? ε_∞) was reduced by formalization, acetylation, propylene oxide, and phenol–formaldehyde resin treatments, in which chemical reactions occurred between the OH groups in the cell wall and the added reagents. On the other hand, the generalized relaxation time (τ_m) decreased with increasing WPG, except for acetylation, for which τ_m decreased up to a WPG level of 20% and then increased. In poly(ethylene glycol) impregnation, (ε₀ ? ε_∞) decreased with increasing WPG up to about 50% and then increased, whereas τ_m linearly decreased with increasing WPG. No significant changes in these parameters were recognized for the wood methyl methacrylate composite and heat treatment. With the steam treatment, τ_m increased. The distribution of the relaxation times was broad in acetylation and narrow in propylene oxide treatment and poly(ethylene glycol) impregnation. However, it remained almost unchanged in the other treatments. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 96: 37–43, 2005     

Mechanical relaxation processes of wood in the low-temperature range

The dynamic viscoelastic properties of untreated and chemically modified wood specimens were determined in the temperature range 123 to 293 K and at constant frequencies. Absolutely dry wood specimens exhibited one relaxation process labeled γ at around 180 K, being attributed to the motions of methylol groups in the amorphous region of the wood constituents. The changes in the γ process due to the chemical modifications were explained by the reduction in the original γ loss peak due to the decrease of methylol groups, and an additional relaxation induced by the other groups introduced. With moisture adsorption, an additional relaxation labeled β was induced at 220–240 K. It appeared only when the wood adsorbed moisture irrespective of chemical modifications, and its characteristics were not affected by the formaldehyde and PEG treatments involving the remarkable changes in the mobility of amorphous molecules. These results suggested that the dominant mechanism of β relaxation was not the segmental motions of the main chain, but the motion of the adsorbed water molecules. The positive activation entropy of the β relaxation was interpreted to reflect rearrangement of the adsorption sites required for the rotation of the adsorbed water molecules. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 81: 3338–3347, 2001     

Relaxation mechanism in several kinds of polyethylene estimated by dynamic mechanical measurements, positron annihilation, X-ray and C solid-state NMR

Relaxation processes of several kinds of polyethylene films and fibers with different molecular orientational degrees and crystallinities were extensively investigated by the dynamic mechanical relaxation, positron annihilation and ¹³C nuclear magnetic relaxation (¹³C NMR). From complex dynamic tensile modulus, the activation energies of α₁ and α₂ relaxations were determined to be 97-118 and 141-176 kJ/mol, respectively. The activation energy of β relaxation was 114-115 kJ/mol. These values were similar to those of α₁ relaxation reported already. For γ relaxation mechanisms, there existed two mechanisms, γ₁ and γ₂, the activation energies being 9-11 and 23-25 kJ/mol, respectively. The values were independent of the molecular orientation and crystallinity. The two local motions indicate that non-crystalline phase composes of two regions of non-crystalline phase, rubber-like amorphous phase and interfacial-like amorphous phase. From ¹³C NMR measurements of ¹³C longitudinal relaxation time for the non-crystalline phase, the activation energy was 20.7 kJ/mol. This value is close to the activation energy (23-25 kJ/mol) of the γ₂ relaxation estimated by the dynamic mechanical measurement. The result by ¹³C NMR did not provide two kinds of activation energy, indicating combined influence of the two correlation times. Even so, the activation energies obtained by ¹³C NMR indicated that the γ₂ relaxation mainly is due to the motion of the C-C central bond of a short segment (e.g. three to four CH₂) within interfacial-like amorphous phase. The γ and β relaxation peaks by the dynamic mechanical measurements corresponded to the first and second lifetime transition of ortho-positronium indicating, in turn, a drastic change in free volume by local mode relaxation.     

N.m.r. study of molecular dynamics in chemically crosslinked polyethylene

Results of measurements of the proton spin-lattice relaxation time T₁ in chemically crosslinked low-pressure polyethylene are presented. The dicumyl peroxide used for crosslinking changed the α-process dynamics without disturbing the β -process or the motion of the methyl groups. Classical relaxation processes (which are analogous to the case of pure polyethylene) have been observed for samples with 0.5–2.5 wt% crosslinking.     

Dynamic relaxation characteristics of Matrimid polyimide

The dynamic relaxation characteristics of Matrimid^® (BTDA-DAPI) polyimide have been investigated using dynamic mechanical and dielectric methods. Matrimid exhibits three motional processes with increasing temperature: two sub-glass relaxations (γ and β transitions), and the glass—rubber (α) transition. The low-temperature γ transition is purely non-cooperative, and displays an identical time-temperature response to both the dynamic mechanical and the dielectric probes with a corresponding activation energy, E_A = 43 kJ/mol. The β sub-glass transition shows a more cooperative character as assessed via the Starkweather method. Comparison of dynamic mechanical and dielectric data for the β process suggests that the dynamic mechanical test (E_A = 156 kJ/mol) is sensitive to a broader, more strongly correlated range of sub-glass motions as compared to the dielectric probe (E_A = 99 kJ/mol). Time-temperature superposition was used to establish mechanical master curves across the glass-rubber (α) relaxation, and these data could be described using the Kohlrausch-Williams-Watts function with an exponent value, β_KWW = 0.34. The corresponding shift factors were used as the basis of a cooperativity plot for the determination of dynamic fragility. The relation between fragility index (m = 115) and β_KWW for the Matrimid polyimide was in good agreement with the wide correlation reported in the literature.     

Studies on dielectric relaxation in ceramic multiferroic Gd1−xYxMnO3

Dielectric study over a broadband was carried out from 10 to 70 K on ceramic Gd_1?xY_xMnO₃ (x=0.2, 0.3 and 0.4). For all the compositions, a prominent sharp peak about ~18 K was observed in the temperature dependence of both ε′(T) and ε″(T) at all frequencies, indicating a long‐range ferroelectric (FE) transition. Using Cole‐Cole fit to the permittivity data, the relaxation time τ and the dielectric strength ?ε were estimated. Temperature variation of τ(T) in the Arrhenius representation is found to be nonlinear (non‐Debyean relaxation), with increasing barrier‐activation energy over successive temperature‐windows. Interestingly, for all the compositions, we witness a jump in τ(T) about the ferroelectric transition temperature, concurred by a broad‐maximum in ?ε(T),signifying the critical slow down of relaxations near long‐range FE‐correlations.     

The effects of deposition temperature on structure and dielectric properties of Ba0.6Sr0.4TiO3 thin films produced by pulsed laser deposition

The effects of deposition temperature on orientation, surface morphology and dielectric properties of the thin films for Ba_0.6Sr_0.4TiO₃ thin films deposited on Pt/Ti/SiO₂/Si substrates by pulsed laser deposition were investigated. X-ray diffraction patterns revealed a (2 1 0) preferred orientation for all the films. With rising substrate temperature from 650 °C to 700 °C, the crystallinity and crystal grain size of the films increase, the relative dielectric constant increases, but the dielectric losses have not obvious difference. The film deposited at 350 °C and annealed at 700 °C has strongly improved roughness and dielectric permittivity compared with the film only deposited directly at 700 °C. Three distinct relaxation processes within tan(δ) were found for the Ba_xSr_1?xTiO₃ film: a broadened process of the film relaxation, an intermediate peak which originates from Maxwell–Wagner–Sillars polarization, and an extremely slow process ascribed to leak current. The complex dielectric permittivity and loss can be fitted by an improved Cole–Cole model corresponding to a stretched relaxation function.     

An investigation of 1H and 13C longitudinal relaxation and relaxation in the rotating frame in solid poly(N‐vinylcarbazole)

¹H and ¹³C longitudinal relaxation times (T₁) and relaxation times in the rotating frame (T_1ρ) have been measured for poly(N‐vinylcarbazole) in the solid state in air and nitrogen atmospheres in an attempt to elucidate molecular motions. In air, the T₁ relaxation of both ¹H and ¹³C was dominated by interaction with absorbed paramagnetic oxygen. In nitrogen, the ¹³C T₁ relaxation times were long (>300 s) and were averaged by ¹³C–¹³C spin diffusion. The ¹³C T_1ρ relaxation times showed an exponential dependence on the strength of the rotating ¹³C magnetic field and were thus controlled by spin–spin processes rather than spin–lattice processes. © 2001 Society of Chemical Industry     

Mechanical relaxations in polybutene-1 and poly-4-methylpentene-1

Dynamic mechanical measurements between — 180°C and 180°C were made on both isotropic and drawn samples of polybutene-1 (PB-1) and poly-4-methylpentene-1 (P4MB1) over a wide frequency range by the use of a torsional pendulum (0.3–3 Hz), a viscoelastic spectrometer (5–90 Hz) and ultrasonic technique (3 MHz). The relaxation peaks were identified and the associated activation energies determined from Arrhenius plots. For PB-1 it was observed that orientation reduces the height and shifts up the temperature of the α_a-peak associated with large scale main-chain motion in the amorphous regions, but has little effect on the β-peak associated with side-group motion. In addition to the α_a and β relaxations a high-temperature crystalline relaxation (α_c) is also observed in P4MP1. For both the α_c and β relaxations the mechanical loss at 45° to the draw direction is much larger than that at 90°, which indicates that shear processes are involved in these relaxations.     

Dynamic mechanical and dielectric relaxation characteristics of poly(trimethylene terephthalate)

The dynamic mechanical and dielectric relaxation properties of a commercial poly(trimethylene terephthalate) [PTT] have been investigated for both quenched and isothermally melt-crystallized specimen films. The relaxation characteristics of PTT were consistent with those of other low-crystallinity semiflexible polymers, e.g. PET and PEEK. While the sub-glass relaxation was largely unperturbed by the presence of the crystalline phase, both calorimetric and broadband dielectric measurements across the glass transition indicated the existence of a sizeable rigid amorphous phase (RAP) fraction in melt-crystallized PTT owing to the constraining influence of the crystal surfaces over the crystal-amorphous interphase region. A strong increase in measured dielectric relaxation intensity (Δ?) with temperature above T_g indicated the progressive mobilization of the RAP material, as well as an overall loss of correlation amongst the responding dipoles.     

Enhancement of magnetic relaxation behavior by texturing in Bi-2212 superconducting rods

Time decay of magnetization, known as magnetic relaxation, is crucial for both fundamental and applied point of view in bulk high temperature superconductors (HTS) by setting the limits to the HTS devices stability. Melt-processed Bi₂Sr₂Ca₁Cu_2−xGa_xO_8+δ rods (Bi-2212, x=0, 0.1) were used to study the effect of both grain alignment and substitution on the samples critical current density, relaxation and pinning behavior. The magnetic field has been applied both perpendicular and parallel to the rods growth axis to determine the effect of grain alignment. It has been found that Ga substitution reduces grains orientation and sizes leading to lower magnetic properties. The peaks of the curves, which indicate the temperature dependence of the samples magnetic relaxation rate (S), have been observed in the 7–35 K temperature range. Characteristic pinning energy (U_e/k_B) of samples was determined using the formalism developed by Maley. The change of pinning energy as a function of magnetization has been found to be exponential between 3 and 60 K, which is in agreement with the collective creep theory.     

N.m.r. study of cellulose-water systems: Water proton spin-lattice relaxation in the rotating reference frame

A pulsed n.m.r. study of relaxation in the rotating reference frame was performed on cellulose samples with moisture contents (MC) ranging from 20.5% to 218%. The dependence of the spin-lattice relaxation time (T_1ρ) in the rotating frame on temperature in a sample hydrated to approximately the fibre saturation point (FSP) indicates that in this case water exists in two different environments or phases. The first phase consists of a small number of water molecules (<1% of adsorbed water molecules in sample) tightly bonded to cellulose whereas the second phase consists of the remaining adsorbed water molecules which are more loosely attached. At room temperature exchange occurs between these phases at an intermediate exchange rate. For samples with MC >FSP a third water phase was identified. From the dependence of T_1ρ on the rotating field strength information about water molecule dynamics was deduced.