Compensation temperature in amorphous polyolefins

The thermostimulated creep of two series of amorphous polyolefins, (CH₂)_mC(CH₃)₂ and (CH₂)_mC(CH₃)(CH₂CH₃) where m = 1, 2 and 3, was investigated from 77 to 350 K. The broad relaxation process observed around the glass transition in each polyolefin can be described by a distributed retardation time τ obeying a compensation law

$\text{τ=τ}{}_{\mathrm{c}}\text{exp}\text{δH}\text{k}\text{1}\text{T}\text{?}\text{1}\text{T}{}_{\mathrm{c}}$

where τ_c and T_c are characteristic of the polyolefin.     

Thermostimulated creep in amorphous polyolefins. I

The thermostimulated creep of two amorphous polyolefins having the repeating unit ─(CH₂)_mC(CH₃)2─, where m = 2 and 3, was investigated from 77° to 350°. Two relaxation processes are distinguished: a secondary relaxation is observed at 138 and 113°, respectively, for m = 2 and m = 3; a primary relaxation is found around the glass transition. These relaxations have been resolved in their elementary components. From the data acquired, the mechanical losses have been calculated and compared with data from an inverted torsional pendulum. The activation energy found for the secondary relaxation—0.26 eV at 138° K for the amorphous polyolefin with m = 2 and 0.19 eV at 113° K for the polyolefin with m = 3—confirms that this relaxation mode is associated with restricted backbone motion.     

Low-temperature relaxations in amorphous polyolefins

The dynamic mechanical relaxation behavior (1cps) of two series of amorphous polyolefins, ─(CH₂)_mC(CH₃)₂─ and ─(CH₂)_mC(CH₃)(CH₂ CH₃)─ where m = 1, 2, 3 was investigated from 4.2°K to the glass transition. Most of the polymers show a damping maximum or pleateau in the 40 to 50°K region. Various mechanisms which have been suggested for cryogenic relaxations in amorphous polymers are considered as they might relate to the polyolefins. Two secondary relaxation processes above 80°K are distinguished. A relaxation at about 160°K (β) in the second and third member of each series is associated with restricted backbone motion. This process requires a certain degree of chain flexibility since it is not observed in the first member of each series. A lower Temperature process (γ) is observed in each member of the second series and is attributed to motion of the ethyl side group.     

Ultrasound attenuation in solid CH4

We have studied the attentuation of 4 and 12 MHz longitudinal sound in polycrystalline solid CH₄ from 4 to 77°K. Just above 20·48°K, the temperature of the known upper lambda transition, a broad attenuation maximum with significant structure is observed. A sharp peak at the transition temperature is attributable to anomalous thermal conduction in small crystallites; the remainder of the absorption is described by a simple relaxation process with characteristic time τ = τ₀ exp (180/T). No attenuation anomaly was observed near the temperature of a suspected lower transition, 8°K.     

Effect of structural relaxation on low energy excitations in amorphous Zr x Cu1−x

We report on an investigation of the liquid-quenched metallic glass Zr _x Cu_1?x (0.6≦x≦0.74) subjected to heat treatments below the glass transition temperatureT _g. Annealing temperatures up to 200°C (<0.8T _g) were chosen as to achieve topological relaxation only. The superconducting transition temperaturesT _c are lowered, as already observed for other metallic glasses. Low temperature measurements of the thermal conductivity (0.5 K≦T≦15 K) and of the specific heat (0.1 K≦T≦3 K) were carried out in order to determine the effect of structural relaxation on the low energy configurational excitations characteristic of the amorphous state. The annealed samples show no detectable (<20%) change in the specific heat forT?T _c, but an increase of the thermal conductivity by a factor of 2 forT?T _c is observed. Within the tunneling model of two level systems (TLS) for the low energy excitations, this behavior can be qualitatively understood in terms of a change of the TLS relaxation time distribution upon annealing. This distribution differs from that of the commonly used standard tunneling model. The change of the phonon scattering by TLS directly observed forT?T_c is largely responsible for the enhancement of the thermal conductivity found also aboveT _c.     

Hysteresis effects at a cooperative high-spin (5T2) ⇌ low-spin (1A1) transition in dithiocyanatobis (4, 7-dimethyl-1, 10-phenanthroline) iron (II)

Hysteresis has been observed at the cooperative high-spin (⁵T₂) ? low-spin (¹A₁) transition in Fe (4, 7-(CH₃)₂-phen)₂(NCS)₂ where phen = 1, 10-phenanthroline. The transition is centered on T_c> = 121.7 K for rising and on T_c< = 118.6 K for lowering of temperature. The observations are in only qualitative agreement with the thermodynamic theory of Slichter and Drickamer.     

14N NMR study and Landau theory of phase transitions in [N(CH3)4]2ZnI4

The¹⁴N NMR spectra and spin-lattice relaxation timeT ₁ of [N(CH₃)₄]₂ZnI₄ have been studied between room temperature and 200 K. Two phase transitions atT _c 1=255 K and atT _c 1=217 K are observed. The¹⁴N NMR lineshape andT ₁ data suggest that the intermediate phase is commensurate rather than incommensurate in spite of the presence of a Lifshitz invariant in the expansion of the free energy density in powers of the order parameter. We also discuss the phenomenological theory of structural phase transitions in [N(CH₃)₄]₂ZnI₄.     

Properties of (Bi1/9Na2/3)(Mn1/3Nb2/3)O3 analysed within dielectric permittivity,conductivity, electric modulus and derivative techniques approach

The (Bi_1/9Na_2/3)(Mn_1/3Nb_2/3)O₃ ceramics with perovskite structure were sintered. The XRD test proved that the samples are cubic (a?=?3.920?±?0.001?Å). Microstructure and atomic composition were determined with a SEM (JSM-5410) equipped with energy dispersion X-ray analyser (ISIS-300). The fluctuation in the chemical composition was found indicating on local disorder. Broadband dielectric spectroscopy in the range 10^?1–3?·?10⁷?Hz was applied within the range of 100–650?K. The real, ?′(f,?T), and imaginary, ?″(f,?T), parts of complex dielectric permitivity characteristics, both in the temperature and frequency domain, show relaxation processes partially covered by electric conductivity. At high temperatures the electric conductivity exhibits a thermally activated behaviour σ(f,?T)?∝?exp(?E _a/kT) but the variable range hopping (VRH) dependence σ?∝?exp[?(T ₀/T)^1/4] is manifested at low temperatures. The derivatives technique in the frequency (??log??/??log?ω) and temperature (??log??/?T) domain enabled various relaxation processes to be distinguished. The data converted to electric modulus representation, M*(f,?T)?=?1/?*, exhibited clearly resolved relaxation peaks. The relaxation times obtained from the peaks position show a slightly non-Arrhenius temperature behaviour with the activation energy varying in 0.4–0.6?eV range and characteristic time of the electric conductivity relaxation of the order of 10^?12?s. The relaxation times can be fitted at better accuracy with the VRH dependence where T ₀ are of the order of 10⁸?K. It is shown that the low frequency ac-conductivity converges to dc-conductivity and the relation σ(0)?～?ω_m?～?τ_m ^?1 typical for the disordered solids applies. The conduction current relaxation relationship behaves in accord with the VRH system: σ_dc?∝?(T/T ₀)^q (e ²/kT) ω_c, where ω_c?=?ν_ph exp[?(T ₀/T)^1/4] is valid for the locally disordered (Bi_1/9Na_2/3)(Mn_1/3Nb_2/3)O₃ compound.     

Cl35 NQR study of the structural phase transition in (CH3NH3)HgCl3

The Cl³⁵ nuclear quadrupole resonance spectra of (CH₃NH₃)HgCl₃ have been measured between -150°C and + 100°C. The spectra clearly show that a structural phase transition of first order takes place around T_c? 60°C. The transition may be related to a disordering of the CH₃NH₃ groups which are reorienting both above and below T_c. The positive temperature coefficient of the Cl NQR frequency, dv/dT may be also explained by the CH₃NH₃ motion.     

Low temperature elastic properties of a superconducting disordered metal

We have measured the elastic properties of a glass at audiofrequencies (0.2–1.5 kHz) in the temperature interval 0.01 to 10 K. In the superducting glassy metal Cu₆₀Zr₄₀ (T_c=0.31 K) both the sound velocity and attenuation are similar to that of an insulating glass below 0.05 K. Above that temperature (T_c>T>0.05 K) the relaxation process is mainly governed by electrons which are thermally excited above the BCS gap. Above the superconducting transition we observed new features in the sound velocity which were not observed in high frequency measurements.     

The glass transition temperature of amorphous poly(ethylene terephthalate) by thermally stimulated currents

The relation between the temperature T_α of the dipolar relaxation, obtained by the technique of thermally stimulated currents (TSC) and the glass transition temperature T_g has been studied in amorphous poly(ethylene terephthalate) samples. The temperature T_α depends fundamentally on the polarization temperature T_p, the polarization time t_p, and the heating rate v. For each heating rate a maximum T_α, T_M, was obtained for an optimum polarization temperature T_po. The value of T_po is 70°C, independent of the heating rate, and very close to the glass transition temperature obtained by differential scanning calorimetry (69°C). The resulting value for T_M coincides with T_po in the limits of null heating rate and null isothermal polarization time, and, consequently, T_M gives the value of the glass transition temperature for each heating rate as a function of the isothermal dipolar contribution on polarizing at the temperature T_po.     

Proton NMR study of molecular dynamics and phase transitions in methylammonium hexachloro plumbate, [NH3CH3]2PbCl6

Proton spin lattice relaxation time (T₁), measured as a function of temperature in the range 375–77 K, shows slope changes at 333, 221 and 111 K, in addition to a first order phase transition at 150K. The observed T₁ behaviour and second moment (M₂) variation with temperature are explained on the basis of the different possible motions of CH₃ and NH₃ groups.     

Two-dimensional critical behaviour in antiferrodistortive Al ur6(CIO4)3 and Ga ur6(ClO4)3

Critical behaviour with dimensionality d = 2 has been observed for the 300 K antiferrodistortive phase transition in Al ur₆(ClO₄)₃ and Ga ur₆(ClO₄)₃ by means of the temperature dependence of the ESR parameter D. The systems exhibited d = 2 behaviour in the static critical behaviour for T<T_c?40 K for T>T_c + 40 K. From the ESR data including line width measurements the local order parameter relaxation rate ω₁ has been obtained for various temperatures above T_c, with a lowest value of ω₁ = 150 MHz at T_c + 15 K     

Central peak in the strontium titanate crystal near the tetragonal-to-cubic phase transition

Raman spectra of the SrTiO3 crystal have been measured in wide temperature (22?C316 K) and frequency (2?C1020 cm^?1) ranges. It has been shown that a central peak appears in low-frequency Raman spectra at temperatures above 70 K. In the spectral geometry with polarization rotation near the temperature T _c = 106 K of the cubic-to-tetragonal phase transition, the central peak exhibits properties of the order-disorder phase transition. Such a behavior of the central peak has been explained by the interaction of the low-frequency soft mode E _g with the relaxation mode near T _c .     

An apparent double glass transition in semicrystalline polymers

Thermal expansion and/or specific heat and/or dynamic mechanical loss data reveal the presence of two glass-like transitions in bulk crystallized polyethylene, polypropylene, polybutene-1, polypentene-1, cis-and trans-polyisoprene (natural), poly-4-methylpentene-1, isotactic polystyrene, poly(vinyl alcohol), nylon 6, the oxide polymers ?(CH₂)_nO?, with n = 1 to 4, polyethylene terephthalate, polyvinylidene fluoride, polyacrylonitrile, and polyvinylidene chloride. We designate the lower of these as T_g(L), which appears identical with the conventional T_g at zero crystallinity. The higher one, designated as T_g(U), is strongly increased with increasing levels of cystallinity. The differnece ΔT_g = T_g(U) ? T_g(L) tends to approach zero as the fractional crystallinity, X, approaches zero. For a X of 0.5 [Ptilde] 0.1, ΔT_g is about 50°C and T_g(U)/T_g(L) is about 1.2 with temperatures in °K. The increases in coefficient of thermal expansion, (Δα)_L and (Δα)_U, at these two transitions seem to depend on crystallinity and morphology in the expected manner for polyethylene and polypropylene: for × = 0.5–0.7, (Δα)_U is stronger than (Δα)_L; for X χ 0, (Δα)_L is stronger than (Δα)_U. Such data are not available for the other listed polymers. Some atactic polymers, poly-4-methylpentene-1, and polystyrene also seem to have a double T_g, the upper of which we tentatively ascribe to the presence of Geil-Yeh types of local order. Since polyethylene, polyvinylidene fluoride, and polyvinylidene chloride exhibit the apparent double T_g, tacticity, per se, is not necessary to produce it. Special care must be exercised to distinguish T_g(U) from the crystalline phase α_c relaxation occurring at temperature T_c. It is shown that T_c for well-annealed crystalline material tends to occur at about 0.83 to 0.85 T_M where T_M is the crystalline melting point in °K. Hence T_c is very close to the temperature at which rate of bulk crystallization is a maximum. While the phenomenon of a double T_g seems clear, its origin is in doubt. We suggest that T_g(L) and T_g(U) arise from tkie presence of different types of amorphous material. For example, polymer molecules not incorporated in the crystallites and/or cilia might give rise to T_g(L). Morphological entities under greater restraint, such as tie molecules or loose loops, might give rise to T_g(U). Conversely, pseudocrystalline structures (smectic or nematic) might be responsible for T_g(U), at least in polypropylene, poly-4-methylpentene-1, and possibly in some nylons.

Data available in the literature do not permit making a definite choice between different possible origins of the apparent double glass transition. Indeed, the origin may vary from polymer to polymer.     

A model for high-spin/low-spin transitions with an interpretation of thermal hysteresis effects

A model for high-spin/low-spin transitions is discussed. It can explain the temperature dependence of the high-spin fraction of the compound Fe(4, 7-(CH₃)₂-1,10-phenanthroline) (NCS)₂ and allows to interpret hysteresis effects at T_c = 120 K as a result of the existence of two minima for the free energy. The transition is assumed to take place by nucleation. The smoothness of the transition (1.5 K wide) is due to a distribution of the nucleation rate within the microcrystals of the powder sample. The distribution of the T_c is smaller 0.1 K.     

Molecular dynamics of [(CH2OH)3CNH3]2SiF6 by phase transition of 178 K

We have investigated the molecular motions of TRIS⁺ ([(CH₂OH)₃CNH₃]⁺) and ions in the [(CH₂OH)₃CNH₃]₂SiF₆ crystal below room temperature from the measurements of the spin-lattice relaxation time T₁ and the NMR absorption line of ¹H and ¹⁹F nuclei, in order to elucidate the changes of the molecular motions by the phase transition of T_c=178 K. The narrowing of the ¹⁹F-NMR line was observed around T_c=178 K and the reorientation of the anion appears above T_c. Moreover, from the analysis of the temperature dependence of T₁, we have observed that the activation energy of the reorientational motion of ions changes from 0.168 eV (T>T_c) to 0.185 eV (T<T_c). Based on these results, we found that the reorientational motion of ions is closely related to the origin of the phase transition at T_c. In addition, from the measurement of the ¹H-NMR line, we also found that the reorientational motion of H₂ in the -CH₂OH group becomes active accompanied by the phase transition.     

X-ray study of [N(CH<Subscript>3</Subscript>)<Subscript>4</Subscript>]<Subscript>2</Subscript>ZnCl<Subscript>4</Subscript> at low temperatures

The unit cell parameters a, b, and c of [N(CH₃)₄]₂ZnCl₄ have been measured by x-ray diffraction in the temperature range 80–293 K. Temperature dependences of the thermal expansion coefficients α_a, α_b, and α_c along the principal crystallographic axes and of the unit cell thermal expansion coefficient α_V were determined. It is shown that the a=f(T), b=f(T), and c=f(T) curves exhibit anomalies in the form of jumps at phase transition temperatures T₁=161 K and T₂=181 K and that the phase transition occurring at T₃=276 K manifests itself in the a=f(T) and b=f(T) curves as a break. A slight anisotropy in the coefficient of thermal expansion of the crystal was revealed. The phase transitions occurring at T₁=161 K and T₂=181 K in [N(CH₃)₄]₂ZnCl₄ were established to be first-order.     

TSC study of deuteration of polystyrene

A comparative study of natural and deuterated polysterene has been performed by thermally stimulated currents (TSC). Around the glass-rubber transition temperature (T_g a TSC peak is observed whose relaxation times obey an Arrhenius equation. At 50° above T_g another TSC peak is observed whose relaxation time obeys a Vogel equation. Deuteration is found to increase the values of T_g.     

An apparent Landau-type second order transition in the spinel CdIn2S4

Experimental evidence is given of a second order transition in the spinel CdIn₂S₄. The specific heatc _p shows a step at the transition temperature (T _c=403°K), the thermal expansion coefficientα remains unaffected. An analysis yields a critical region of this transition considerably narrower (5°K) than expected from the critical regions of transitions of a similar type (quartz: 160°K,β-brass: 250°K) and therefore the critical region has not been observed experimentally, i.e. the transition appears to follow Landau’s theory. Landau’s group theoretical analysis of second order transitions in crystals leads to a model for the transition in CdIn₂S₄ on the atomic scale. If the temperature is decreased below the critical temperature a 1:1 ordering occurs between Cd and In on the tetrahedral sites. With this model the gross features of this transition can be qualitatively understood: The unaffected thermal expansion and the long relaxation times for the establishment of equilibrium approachingT _c. Also the narrow critical region can be explained in terms of a large correlation length in CdIn₂S₄. Finally it is shown that a generalized formulation of the thermodynamic part of Landau’s theory correlates thermodynamic quantities far above and far below the critical temperature, as illustrated for CdIn₂S₄. This generalization allows also a more satisfactory determination of the critical region.