Manifestation of liquid-state and solid-state properties in electron relaxation of paramagnetic ions in solutions: Non-Markovian processes

The linewidth δH and the spin-spin relaxation time T ₂ for Gd³⁺, Mn²⁺, and Cr³⁺ ions in aqueous, water-glycerol, and water-poly(ethylene glycol) solutions at paramagnetic ion concentrations providing the dipole-dipole mechanism of spin relaxation are measured using two independent methods, namely, electron paramagnetic resonance (EPR) and nonresonance paramagnetic absorption in parallel fields. Analysis of the experimental results indicates a gradual crossover from pure liquid-state (diffusion) to quasi-solid-state (rigid lattice) spin relaxation. It is demonstrated that the limiting cases are adequately described by standard, universally accepted formulas for dipole-dipole interactions in the liquid-state (the correlation time of translational motion satisfies the condition τ _c ?τ₂) and solid-state (τ _c ?τ₂) approximations. A complete theoretical treatment of the experimental dependences (including the observed gradual crossover of spin relaxation) is performed in the framework of the non-Markovian theory of spin relaxation in disordered media, which is proposed by one of the authors. Within this approach, the collective memory effects for spin and molecular (lattice) variables are taken into account using the first-order and second-order memory functions for spin-spin and spin-lattice interactions. A correlation between the spin magnitude and the temperature-viscosity conditions corresponding to the crossover to non-Markovian relaxation is revealed, and the situations in which structural transformations occurring in the solutions favor the crossover to solid-state spin relaxation are analyzed.     

Evidence of antiferroelectric-like ordering from the study of dielectric permittivity–voltage behavior in bent core liquid crystalline material showing B2 phase

Detailed dielectric relaxation behavior of a bent core liquid crystalline material showing B₂ phase has been investigated. Only one relaxation mode is detected in the dielectric relaxation spectrum which was attributed to the long-axis rotation process. Though the field-dependent dielectric study does not reveal any other relaxation mode, the appearance of two humps in the dielectric permittivity–voltage spectrum, similar to the antiferroelectric (AFLC) case, confirms the signature of weak AFLC ordering in the B₂ phase.     

Orbit Tracking of Quantum State for Non-Markovian Quantum System Based on Model Reference Adaptive Control

Utilizing model reference adaptive control theory and Lyapunov stability theorem, we derive the adaptive law for the model reference adaptive system. Then we design the Lyapunov control law by double control functions and investigate the orbit tracking of quantum state for non-Markovian quantum system with phase relaxation and energy dissipative relaxation. The influence of Ohmic reservoir with Lorentz-Drude regularization is numerically studied for a two-level system. The simulations show that the controlled quantum system will track the target orbit with a small oscillation due to the non-Markovian environmental memory effect, which indicates the orbit tracking of non-Markovian quantum system is incomplete.     

Optimal control-based states transfer for non-Markovian quantum system

Utilizing the method of optimal control, we investigate the tactics of state transfer in the non-Markovian quantum system with phase relaxation and energy dissipative relaxation. The influence of Ohmic reservoir with Lorentz–Drude regularization is numerically studied. Owing to the decoherence and memory effects of non-Markovian channel, the purity of quantum state attenuates damply in the free evolution. The numerical simulations indicate that arbitrary state transfer for non-Markovian system can be realized under the optimal control function by a proper external control field with a success rate of more than 98 percent. When the right control field and function is implemented, not only the decoherence is compensated completely but also the purity of quantum states are maintained in the process of state transfer.     

Dielectric anisotropy of 5CB liquid crystal in a decimeter wavelength range

Parallel and perpendicular components of the dielectric constant for 5CB nematic liquid crystal are measured in a relaxation region. Two frequencies f ₁≈30 and f ₂≈350 MHz are determined at which the inversion of the dielectric anisotropy sign is observed. It is shown that the observed sizable high-frequency shift of f ₂ with respect to the value calculated according the Debye theory is caused by the dielectric resonance near the relaxation region.     

Dielectric and thermodynamic properties of CHF3 near the critical temperature

We report here some measurements of the complex dielectric constant of CHF₃ near the critical temperature from the low pressure gas densities up to the compressed liquid ones. The behaviour of the complex dielectric constant, measured at about 10 GHz, is compared with the provisions of some recent theories. The dielectric relaxation time is derived and an interpretation of the relaxation mechanisms in the whole explored density range is proposed. The pressure second virial coefficient is also obtained.     

Gamma radiation in non-Markovian Fermi systems

The gamma-quanta emission is considered within the framework of the non-Markovian kinetic theory. It is shown that the memory effects have a strong influence on the spectral distribution of gamma quanta in the case of long-time relaxation regime. It is shown that the gamma radiation can be used as a probe for both the time-reversible hindrance force and the dissipative friction caused by the memory integral.     

Dielectric relaxation and ac conduction of AgTlTe2 amorphous semiconductor

Measurements of the dielectric properties of AgTlTe₂ in the solid and liquid states were carried out in a wide range of frequencies and temperatures. The material shows dielectric dispersion. Cole-Cole diagrams have been used to determine the distribution parameter and the molecular relaxation time. The ac conduction mechanism and dielectric loss are attributed to correlated barrier hopping in the amorphous solid.     

Changes in dynamical behavior of ionic liquid in silica nano-pores

Dielectric relaxation measurement has been carried out on an ionic liquid (1-butyl-3-methyl imidazolium hexafluorophosphate, [BMIM][PF₆]) confined in nano-porous silica matrix. Two dielectric relaxation peaks have been observed in the confined ionic liquid (IL) while there is only one relaxation peak for bulk IL. Confinement results in layering of some IL molecules near the pore wall while other molecules, less affected by pore wall interaction, remain in the central core. The two relaxation peaks are assigned to the different dynamical behaviors of the central core and layered IL molecules.     

Characteristic dielectric parameters of para-, ferro- and antiferro-electric phases of (S)-4-(1-methylheptyloxycarbonyl)phenyl-4′-(6-pentanoyloxyhex-1-oxy)biphenyl-4-carboxylate

Frequency and temperature dependence of dielectric parameters of a liquid crystalline compound (S)-4-(1-methylheptyloxycarbonyl)phenyl-4′-(6-pentanoyloxyhex-1-oxy)biphenyl-4-carboxylate under planar orientation of the molecules have been investigated in the frequency range 1 Hz-10 MHz. This compound possesses smectic paraelectric (SmA*), ferroelectric (SmC*) and antiferroelectric (SmC_A*) phases. Dielectric spectroscopy suggests the existence of a relaxation mechanism in the SmA* phase, which behaves as a soft mode. In the SmC* phase two relaxation modes are observed. One mode continues from the SmA* phase with decreasing dielectric strength and the other has characteristics of the Goldstone mode. Two dielectric relaxation modes have been observed for the SmC_A* phase. These two modes are related to the antiferroelectric ordering and the helical structure of the SmC_A* phase.     

Dielectric spectroscopy of liquid crystals. Theoretical model of ITO electrodes influence on dielectric measurements

Indium tin oxide (ITO) layers are widely used to make electrodes in measuring cells, because these layers are transparent and electrooptical investigations can be performed using such prepared cells. It was found during the dielectric spectroscopy measurements, performed for smectic liquid crystalline mixture, that it is not possible to detect some important relaxation modes in paraelectric SmA*, ferroelectric SmC*, and antiferroelectric SmC_A* phases for the frequencies higher than 300 kHz. The measuring cell does not allow to measure relaxations, because its own dielectric behaviour covers the dielectric response of a liquid crystalline medium. One can observe the spurious contribution for high frequency part of the dielectric spectrum, due to the finite resistance of ITO layers. The theoretical model was introduced, which shows how to calculate relaxations related to liquid crystals from dielectric response of the empty and filled measuring cell. The proof of strong influence of cell properties on effective (measuring) values of dielectric permittivities was shown.     

Dielectric polarization of bismuth titanate,Bi2O3·3TiO2

Experimental data describing the dielectric polarization of polycrystalline bismuth titanate, Bi₂O₃·3TiO₂, is cited, and the physical nature of its polarization discussed. We conclude that Bi₂O₃·3TiO₂ at temperatures equal to or lower than that of liquid nitrogen is a ferroelectric, while at considerably higher temperatures it is a normal relaxation process dielectric.     

Dielectric spectroscopy of liquid crystals. Electrodes resistivity and connecting wires inductance influence on dielectric measurements

Dielectric spectroscopy is a very useful experimental method for liquid crystal investigation. Electrodes made from indium tin oxide (ITO) or gold are widely used in measuring cells. During the dielectric spectroscopy measurements performed for smectic liquid crystalline mixture it was found that detection of some important relaxation modes in paraelectric SmA*, ferroelectric SmC* and antiferroelectric SmC_A* phases for frequencies higher than 0.2–0.5 MHz is not possible. The measuring setup does not allow us to measure such relaxations due to its own dielectric response covering the dielectric response of liquid crystalline medium. One can observe the spurious contribution for high frequency part of the dielectric spectrum, due to non-zero resistivity of electrode material or non-zero inductivity of connecting wires. In this paper, the new model was introduced. Its final equations show how to calculate parameters of relaxations observed in liquid crystals, from dielectric response of the empty and filled measuring cell. The experimental proof of strong influence of measuring setup properties on effective (measured) values of dielectric permittivities was shown.     

Dielectric relaxation spectrum of water studied by the site—site generalized Langevin/modified mode-coupling theory

The dielectric relaxation spectrum of water is calculated from the site-site generalized Langevin/modified mode-coupling theory. The main part of the relaxation follows the Debye-type function, and a small deviation from the Debye relaxation is found on the high-frequency side. This tendency is consistent with recent experiments, although the absolute relaxation time does not agree with the experimental value quantitatively. The time development of the longitudinal polarization function resembles the dielectric part of the memory function, and we consider that this is because the dielectric friction dominates the collective reorientation of the dipole moment of water. We performed calculations with different dielectric constants using the reference interaction-site model integral equation, and found that the large gap between the time scales of the dielectric relaxation and the longitudinal polarization relaxation causes the Debye-type dielectric relaxation in our theory when the dielectric friction is dominant in the friction on the collective reorientation of the dipole moment. Namely, the longitudinal polarization relaxation is fast enough to be considered as a white noise to the dielectric relaxation process, so that the relaxation becomes a Markov process. The large gap between the two relaxation times originates from a large local field correction owing to the large dielectric constant of water. It is also suggested that the deviation from the Debye relaxation at the high-frequency side is the manifestation of the slow memory caused by the long-time part of the longitudinal polarization relaxation in the low-wavenumber region.     

A. C. behaviour and dielectric relaxation in indium oxide films

Vacuum deposited blackish indium oxide films (In-O) as well as the oxidised films (In₂O₃) were studied for their a.c. behaviour at different temperatures and at various film thicknesses in the audio frequency region. ε of In-O films was thickness dependent and also showed dielectric relaxation at lower frequencies due to the dipolar orientation arising from their non-stoichiometric nature. However at liquid nitrogen temperature region ε was thickness independent similar to the oxidised films which neither showed any relaxation effect nor any thickness dependent ε. The results have been discussed from the classical theory of dielectric polarisation.     

Nonlinear dielectric response of antiferroelectric liquid crystals in the smectic Cα * phase

Nonlinear dielectric response of antiferroelectric liquid crystals has been studied in the smectic C_α* (SmC_α*) phase. The linear dielectric spectrum shows a single relaxation of Debye type and its relaxation frequency is as high as one hundred kHz. The profile of the third-order nonlinear dielectric spectrum varies in complex fashion with temperature. In the vicinity of the SmA-SmC_α* phase transition, experimentally obtained nonlinear spectra are well described by those calculated with phenomenological theory of Landau type. The soft mode of the SmC_α* phase shows critical slowing-down near the transition temperature. In the lower-temperature region of the SmC_α* phase, the contribution from the soft mode of the SmC_α* phase reduces and the other relaxation mode with Debye-type spectrum appears at several hundred Hz in the nonlinear spectrum. The appearance of this low-frequency mode suggests that the cooperative fluctuation of directors over long range exists in the SmC_α* phase. Received 19 April 2002 and Received in final form 23 July 2002 RID="a" ID="a"e-mail: kimura@exp.t.u-tokyo.ac.jp     

Observation of dielectric relaxation modes in chiral smectic C liquid crystal mixture

The dielectric parameters in the frequency range 50 Hz to 1 MHz have been measured in a SmC* liquid crystal mixture in planar alignment. The relaxation frequency (f_r), distribution parameter (α) and dielectric strength (δε) have been evaluated and their corresponding values were found to be 206.62 Hz, 0.06 and 114.6 respectively. The Goldstone mode, domain mode, soft mode and a new relaxation mode have been observed.     

Dielectric studies of alkyl acrylates with primary alcohols using time domain reflectometry

Binary polar–polar liquid mixtures of alkyl acrylates (methyl acrylate, ethyl acrylate and butyl acrylate) with primary alcohols (propan-1-ol, butan-1-ol and hexan-1-ol) were subjected to dielectric studies at 303?K for different concentrations using time domain reflectometry (TDR) over the frequency range from 10?MHz to 10?GHz. Static permittivity (ε₀) dielectric constant at high frequency (ε_∞) and relaxation time (τ) were found through dielectric measurements for different concentrations of each system. The Bruggeman dielectric factor, Kirkwood correlation factor and the excess inverse relaxation time were determined and discussed to yield information on the molecular interactions of the systems. Deviations from the linearity of various models suggest molecular association through hydrogen bonding between the ?OH group of alcohols and C=O group of esters. The results also show a dependence of dielectric parameters on the alkyl chain length of both the alcohols and esters.     

Influence of sintering conditions and doping on the dielectric relaxation originating from the surface layer effects in CaCu3Ti4O12 ceramics

Detailed investigations into the dielectric dispersion phenomenon in the giant dielectric constant material CaCu₃Ti₄O₁₂ (CCTO) around room temperature revealed the existence of two successive dielectric relaxations. In the temperature domain, a new dielectric relaxation was clearly observed around 250 K, in addition to the well-investigated dielectric relaxation close to 100 K. The effect of sintering and doping (La³⁺) on the strength of these dielectric relaxations were studied in detail. The sintering temperature as well as its duration was found to have tremendous influence on the dielectric relaxation that was encountered around 250 K. This Maxwell-Wagner (M-W) type of relaxation was found to be originating from the surface layer containing the Cu-rich phase, which was ascribed to the difference in the oxygen content between the surface and the interior of the sample. Interestingly, this particular additional relaxation was not observed in La_2/3Cu₃Ti₄O₁₂, a low dielectric constant member of the CCTO family, in which the segregation of Cu-rich phase on the surface was absent. Indeed the correlation between the new relaxation and the presence of Cu-rich phase in CCTO ceramics was further corroborated by the absence of the same after removing the top and bottom layers.