Determination of the activation energy for complicated relaxation processes

Different methods are considered for analyzing the temperature dependence of the relaxation rate in the Arrhenius form. It is emphasized that the possible changes in the barrier to elementary acts with variations in temperature should be taken into account in order to determine the relaxation activation energy correctly. Changes in the barrier to elementary acts are illustrated using experimental data on the temperature-frequency dependence of the dielectric relaxation in polymers. A theoretical approach offering realistic activation energies is proposed.     

Proton longitudinal NMR relaxation of poly(p-phenylene sulfide) in the laboratory and the rotating frames reference

Spin-lattice NMR relaxation times T1 in the laboratory frame and T1rho(off) as well as T1rho(off) in the rotating frame off-resonance were employed to the study of molecular dynamics of both pristine PPS and thermally treated poly(p-phenylene sulfide) (PPS). The temperature dependence of T1 was exponential in the whole temperature range studied, whereas T1rho only in low temperatures. In the high temperature range the distribution of relaxation times T1rho and correlation times tau(c) as well as activation energy Ea was observed. The distribution of activation energy determined from T1 minima at 15 and 30 MHz and from low temperature slopes of T1rho dependence as well as from spectral density functions (estimated from proton off-resonance technique) was attributed to the reorientation of phenylene groups around the sulfur-phenyl-sulfur axis in amorphous and crystalline phases of PPS. Furthermore, it is suggested that an additional relaxation mechanism related to interactions of protons with paramagnetic centers is operative in a low temperature range. After thermal treatment of PPS the low temperature minima disappeared and the relaxation times shortened in the low temperature regime. Both these facts were attributed to an increased contribution of spin diffusion in the relaxation process.     

Ac conductivity study of lithium and potassium diphosphate LiK3P2O7 using impedance spectroscopy

In this work, a LiK₃P₂O₇ ceramic material was prepared by the solid-state reaction method and identified by X-ray diffractometry. The dielectric properties, impedance characteristics, and modulus were studied over a range of frequency (200 Hz to 5 MHz) and temperature (615–708 K). The frequency and temperature dependence of dielectric permittivity, dielectric loss, and electric modulus is studied. The frequency analysis of modulus properties showed a distribution of relaxation times. Conductivity plots against frequency at a higher frequency suggested the response obeying the universal power law. The temperature behavior of the frequency exponents shows that the correlated barrier hopping CBH model is well adapted to this material. The activation energy associated with the impedance relaxation and the electric modulus spectra is close to the activation energy for dc conductivity indicating the similar nature of relaxation and conductivity. Thermodynamic parameters such as free energy of activation, enthalpy, and entropy have been calculated.     

Low-frequency Raman scattering study of the ferroelectric phase transition in the DKDP crystal

The low-frequency Raman scattering spectra of the DKDP ferroelectric crystal are studied in the temperature range 30–393 K. At temperatures above 150 K, the Raman spectra exhibit a central peak which reflects the lattice relaxation susceptibility. The width and integrated intensity of the central peak are derived from the experimental spectra. The critical slowing down of the relaxation response predicted by the Ginzburg-Landau-Devonshire theory is observed throughout the temperature range in which the central peak persists. Its integrated intensity does not, however, follow the predictions of the theory and reveals a strong temperature dependence in the ferroelectric phase and a weaker dependence in the paraphase. It is shown that the thermal activation law describes well the temperature dependence of the intensity of the central peak. An interpretation is proposed according to which the intensity of order parameter fluctuations is related to the activation barrier whose height is proportional to the deviation from the phase transition temperature.     

Relaxation times and energy barriers of rubbing-induced birefringence in glass-forming polymers

The relaxations of rubbing-induced birefringence (RIB) in several glass-forming polymers, including polycarbonate and polystyrene (PS) derivatives with various modifications to the phenyl ring side group, are studied. Significant relaxations of RIB are observed at temperatures well below the glass transition temperature T _g . The relaxation times span a wide range from ∼ 10 s to probably geological time scale. Physical aging effects are absent in the RIB relaxations. The model proposed for the interpretation of RIB in PS describes well the RIB relaxations in all the polymers investigated here. The energy barriers are of the order of a few hundred kJ/mol and decrease with decreasing temperature, in opposition to the trend of Vogel-Fulcher form for polymer segmental relaxations above T _g . The relaxation behaviors of different polymers are qualitatively similar but somewhat different in quantitative details, such as in the values of the saturated birefringence, the shape of the initial barrier density distribution functions, the rates of barrier decrease with decreasing temperature, and the dependence of relaxation times on temperature and parameter , etc. The RIB relaxations are different from any of the other relaxations below T _g that have been reported in the literature, such as dielectric relaxations or optical probe relaxations. A microscopic model for the relaxations of RIB is much desired.     

Dependence of the longitudinal relaxation time of the polarization of cesium atoms in the ground state on the temperature of an antirelaxation coating

The dependence of the time of longitudinal relaxation of the ground-state cesium vapor on the temperature of the antirelaxation coating of the cell walls is studied experimentally. It is found that the fast component of relaxation is independent of the coating temperature, while the slow component depends on it. The temperature dependence of the slow relaxation component is used to estimate the energy of activation of desorption of cesium atoms from the antirelaxation coating, E _desorp = 0.13 eV.     

Thermostimulated current of dielectric relaxation in metal-vanadium phosphate glass-metal systems

The nature of the maxima of the thermostimulated current of dielectric relaxation in the thinfilm system metal-vanadium phosphate glass-metal is discussed. The experimental data is analyzed, taking into account the presence of a blocking barrier layer at the metalglass interface and allowing for the fact that the charge carriers in the glass have an activated mobility. The mobility of the charge carriers and their activation energy as well as the energetic position of the impurity levels and their concentration are determined from the curves of the temperature dependence of relaxation current.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 92–100, February, 1977.     

Thermoactivated molecular motions in solids and determination of the energy of their activation by NQR spectroscopy methods

The activation energy of thermoactivated molecular motions in solids is determined by examining the influence of these motions on the temperature dependence of the nuclear quadrupole spin-lattice relaxation rate and quadrupole resonance (NQR) signal intensity for chlorine-35. In the latter case, the heating of the crystals is accompanied by the fading of resonance signals, which is analyzed using a linear correlation between the activation energy of this motion and the fade-out temperature. The correlation parameters are demonstrated to be dependant on the type of molecular motion. The relaxation method is shown to be more effective in studying molecular motion and evaluating its activation energy as compared to the NQR signal fading technique.     

Investigation of the creep and glass transition of elastomers by the microindentation method: Epoxy resin and related nanocomposites

The experimental procedure and theoretical grounds of the applicability of the microindentation method as one of the effective techniques of relaxation spectrometry of solid-state polymers have been developed. It has been shown that the glass transition temperature and rheological parameters of the material (unrelaxed and relaxed elastic moduli, strain viscosity coefficients) can be determined from measurements of the temperature dependence of the microhardness of polymers in a high-elasticity state and in the glass transition region with the recording of the long-term creep under the indenter. These measurements provide sufficient information for the formulation of a rheological model of the material under investigation. The results of these measurements are supplemented by the concepts of thermally activated motion of molecular segments as the microscopic mechanism of structural relaxation in polymers, which makes it possible to obtain empirical estimates for the activation energies and vibrational frequencies of the molecular segments. The method is implemented in experiments on the microindentation of the epoxy resin and its composites with the addition of carbon nanotubes in the temperature range 230–300 K. The glass transition of these polymers has been observed at temperatures near 260 K, the unrelaxed and relaxed Young’s moduli have been measured, and two thermally activated relaxation processes determining the glass transition, as well as the shortterm and long-term creeps of these materials (α- and α′-processes), have been revealed.     

A pulse EPR study of longitudinal relaxation of the stable radical in gamma-irradiated L-alanine

The longitudinal relaxation rate of the first stable alanine radical, SAR1, was studied by employing pulse EPR technique over a wide temperature interval (5-290 K). The complex nonexponential recovery of the longitudinal magnetization in this temperature interval has been described with two characteristic relaxation times, 1/T*(1a) as the faster component and 1/T*(1b) as the slower component, respectively. It was shown that 1/T*(1a) is strongly affected by the CH(3) group dynamics of the SAR1 center. The complete temperature dependence of 1/T*(1a) was described by invoking several relaxation mechanisms that involve hindered motion of the CH(3) group from classical rotational motion to coherent rotational tunneling. It was shown that all relevant relaxation mechanisms are determined by a single correlation time with the potential barrier (Delta E/k=1570 K). On the other hand the temperature dependence of 1/T*(1b) is related to the motional dynamics of the neighborly NH(3) and CH(3) groups. We found a larger average potential barrier for this motion (Delta E/k=2150 K) corresponding to smaller tunneling frequencies of the neighbor groups.     

Parameters of LC molecules’ movement measured by dielectric spectroscopy in wide temperature range

Dielectric properties of a nematic liquid crystal (NLC) mixture ZhK-1282 were investigated in the frequency range of 10²–10⁶Hz and a temperature range of ?20 to 80?°С. On the basis of the Debye’s relaxation polarization model dielectric spectra of temperature dependence of the orientational relaxation time τ and the dielectric strength δe were numerically approximated at the parallel orientation of a molecular director relative to alternating electric field. Influence of ester components in the mixture plays crucial role in relaxation processes at low temperature and external field frequency. The activation energy of the relaxation process of a rotation of molecules around their short axis was measured in a temperature interval of ?20 to ?+15?°С in which the dispersion of a longitudinal component of the dielectric constant takes place. The energy of potential barrier for polar molecules rotation in the mesophase was calculated. The value of the transition entropy from the nematic to isotropic phase was obtained from this calculation. The values of the coefficient of molecular friction and rotational diffusion were obtained by different methods. The experimental data obtained are in a satisfactory agreement with the existing theoretical models.     

Influence of the molecular structure of components on the induction of mesophases in nematic liquid crystal systems

The dielectric properties of nematic liquid crystals (NLC) are studied in the temperature range of mesophase existence with taking into account the peculiarities of the molecular structure of components. The dependence of the ordering parameter and activation energy on the temperature and composition of an LC system are obtained and investigated by analysis of EPR spectra based on the spin relaxation theory. The values of the local viscosity of the systems are estimated within the framework of the hydrodynamic model. The appearance of induced and reentrant mesophases is established. It is shown that in NLC systems with non-center-symmetric molecules the correlation between the activation energy and thermostability should be inverse to that in the Maier-Saupe model.     

AC electrical properties of FeIn2S4

The frequency and temperature dependences of the ac capacitance and resistivity of FeIn₂S₄ semiconductors are studied. Resonances are observed at certain temperatures in the frequency range (2.5–5.0) × 10⁵ Hz. The permittivity of the crystals and the activation energy of charge carriers are determined. It is found that electrical conduction in the given temperature interval is governed by an activation mechanism. The activation energy is frequency-dependent, because the relaxation time of barrier layers decreases with rising frequency.     

Electronic relaxation of deep bulk trap and interface state in ZnO ceramics

This paper investigates the electronic relaxation of deep bulk trap and interface state in ZnO ceramics based on dielectric spectra measured in a wide range of temperature, frequency and bias, in addition to the steady state response. It discusses the nature of net current flowing over the barrier affected by interface state, and then obtains temperature-dependent barrier height by approximate calculation from steady I--V (current--voltage) characteristics. Additional conductance and capacitance arising from deep bulk trap relaxation are calculated based on the displacement of the cross point between deep bulk trap and Fermi level under small AC signal. From the resonances due to deep bulk trap relaxation on dielectric spectra, the activation energies are obtained as 0.22 eV and 0.35 eV, which are consistent with the electronic levels of the main defect interstitial Zn and vacancy oxygen in the depletion layer. Under moderate bias, another resonance due to interface relaxation is shown on the dielectric spectra. The DC-like conductance is also observed in high temperature region on dielectric spectra, and the activation energy is much smaller than the barrier height in steady state condition, which is attributed to the displacement current coming from the shallow bulk trap relaxation or other factors.     

Electronic transport mechanisms in tetraphenyleprophyrin thin films

Thermally-evaporated thin films of tetraphenylporphyrin, TPP, with thickness range from (175 to 735) nm had been prepared. Annealing temperatures ranging from (273–473) K do not influence the amorphous structure of these films. The influence of environmental conditions: film thickness, temperature and frequency on the electrical properties of TPP thin films had been reported. It was found that dc conductivity increases with increasing temperature and film thickness. The extrinsic conduction mechanism is operating in temperature range of (293–380) K with activation energy of 0.13 eV. The intrinsic one is in temperatures >380 K via phonon assisted hopping of small polaron with activation energy of 0.855 eV. The ac electrical conductivity and dielectric relaxation in the temperature range (293–473) K and in frequency range (0.1–100) kHz had been also studied. It had been shown that theoretical curves generated from correlated barrier hopping (CBH) model gives the best fitting with experimental results. Analysis of these results proved that conduction occurs at low temperatures (300–370) K by phonon assisted hopping between localized states and it is performed by single polaron hopping process at higher temperatures. The temperature and frequency dependence of both the real and imaginary parts of dielectric constant had been reported.     

Temperature effects in the liquid drop description of nuclear fission

Using recent results of the dependence of the surface tension and nuclear equilibrium density of temperature from an extended Fermi gas model the influence of temperature (compound nuclear excitation energy) on the liquid drop deformation energy and fission barrier height is studied. It is shown that increasing the temperature results in a lower fission barrier and a less constricted saddle point shape.     

Changing shapes in the nanoworld

What are the mechanisms leading to the shape relaxation of three-dimensional crystallites? Kinetic Monte Carlo simulations of fcc clusters show that the usual theories of equilibration, via atomic surface diffusion driven by curvature, are verified only at high temperatures. Below the roughening temperature, the relaxation is much slower, kinetics being governed by the nucleation of a critical germ on a facet. We show that the energy barrier for this step linearly increases with the size of the crystallite, leading to an exponential dependence of the relaxation time.     

Electron spin relaxation of radicals in γ-irradiated malonic acid and methyl malonic acid

Radicals generated by γ-irradiation of malonic acid and methyl malonic acid were studied as a function of temperature by inversion recovery, echo-detected saturation recovery and electron-electron double resonance (ELDOR) at X-band, and by continuous-wave saturation recovery at X-band and S-band. ELDOR reductions for malonic acid radical in polycrystalline and single-crystal samples indicate that nuclear spin relaxation is faster than both electron spin relaxation and cross relaxation between 93 and 233 K. Deuteration of the carboxylate protons caused the maximum ELDOR reduction to shift from about 110 to 150 K, consistent with the assignment of the rapid nuclear spin relaxation to hydrogen-bonded proton dynamics. ELDOR enhancements for both radicals formed in methyl malonic acid indicate that cross relaxation is faster than both electron spin relaxation and nuclear spin relaxation between 77 and 220 K. Enhanced cross relaxation and electron spin relaxation are attributed to the rotation of methyl groups at a rate comparable to the electron Larmor frequency. The temperature dependence of the enhancement of 1/T _1e was analyzed to determine the activation energies for methyl rotation. The same radical is formed in irradiated methyl malonic acid and L-alanine, but the barrier to rotation of the α-methyl is 500 K in the methyl malonic acid host and 1500 K in the L-alanine host, which indicates a large impact of the lattice on the barrier to rotation.     

Zur Deutung der Protonenspinrelaxation in Glycerin

In contrast with the usual assumption that proton spin relaxation in glycerol originates from rotational molecular diffusion, quantitative evaluation of the temperature and Larmor frequency dependence in the ranges ?30 °C to+70 °C and 10 kHz to 120 MHz, respectively, gives extensive agreement with Fick's translational random walk model. This observation is supported by direct measurements of the self-diffusion constant by means of the pulse gradient method, which reveals the same activation barrier as relaxation spectroscopy.     

Dielectric relaxation in nanopillar NiFe–silicon structures in high magnetic fields

We explore the dielectric relaxation properties of NiFe nanowires in a nanoporous silicon template. Dielectric data of the NiFe–silicon structure show a strong relaxation resonance near 30 K. This system shows Arrhenius type of behavior in the temperature dependence of dissipation peaks vs. frequency. We report magnetic field dependence of dipolar relaxation rate and the appearance of structure in the dielectric spectrum related to multiple relaxation rates. A magnetic field affects both the exponential prefactor in the Arrhenius formula and the activation energy. From this field dependence we derive a simple exponential field dependence for the prefactor and linear field approximation for the activation energy which describes the data. We find a significant angular dependence of the dielectric relaxation spectrum for regular silicon and nanostructured silicon vs. magnetic field direction, and describe a simple sum rule that describes this dependence. We find that although similar behavior is observed in both template and nanostructured materials, the NiFe–silicon shows a more complex, magnetic field dependent relaxation spectrum.