High-frequency dielectric spectra from liquid crystals of series nCB and nOCB

The design of a resonant frequency-tunable high-sensitivity microstrip sensor is suggested. The permittivity dispersion of liquid crystals of two homologic series, alkylcyanobiphenyls (7CB and 8CB) and alkyloxycyanobiphenyls (7OCB and 8OCB), is studied at frequencies of 100–900 MHz. The dielectric spectra are shown to be the sum of the Debye relaxation and dielectric resonances observed at f≈160, 280, 360, 450, 550, and 650 MHz. The dielectric resonances are present in the spectra of all the samples in both the nematic and isotropic phase. The substitution of an oxygen atom (series nOCB) for a carbon atom (series nCB) in liquid crystal molecules has a minor effect on the dielectric resonance frequencies but changes the resonance intensities and splits some of the resonance lines.     

Exact solution for the extended Debye theory of dielectric relaxation of nematic liquid crystals

The exact solution for the transverse (i.e. in the direction perpendicular to the director axis) component α_⊥(ω) of a nematic liquid crystal and the corresponding correlation time T_⊥ is presented for the uniaxial potential of Martin et al. [Symp. Faraday Soc. 5 (1971) 119]. The corresponding longitudinal (i.e. parallel to the director axis) quantities α_⊥(ω), T_⊥ may be determined by simply replacing magnetic quantities by the corresponding electric ones in our previous study of the magnetic relaxation of single domain ferromagnetic particles Coffey et al. [Phys. Rev. E 49 (1994) 1869]. The calculation of α_⊥(ω) is accomplished by expanding the spatial part of the distribution function of permanent dipole moment orientations on the unit sphere in the Fokker-Planck equation in normalised spherical harmonics. This leads to a three term recurrence relation for the Laplace transform of the transverse decay functions. The recurrence relation is solved exactly in terms of continued fractions. The zero frequency limit of the solution yields an analytic formula for the transverse correlation time T_⊥ which is easily tabulated for all nematic potential barrier heights σ. A simple analytic expression for T_∥ which consists of the well known Meier-Saupe formula [Mol. Cryst. 1 (1966) 515] with a substantial correction term which yields a close approximation to the exact solution for all σ, and the correct asymptotic behaviour, is also given. The effective eigenvalue method is shown to yield a simple formula for T_⊥ which is valid for all σ. It appears that the low frequency relaxation process for both orientations of the applied field is accurately described in each case by a single Debye type mechanism with corresponding relaxation times (T_∥, T_⊥).     

Specific features of the approximation of the dielectric spectra of alkylcyanobiphenyl liquid crystals

The frequency dependences of the longitudinal and transverse permittivities of oriented nematic liquid crystals belonging to the alkylcyanobiphenyl group nCB (n=5–8) are measured in the relaxation region in the meter and decimeter wavelength ranges. It is established that the dispersion of the longitudinal permittivity is well approximated by the sum of two Debye processes with different relaxation times. The frequency dependence of the transverse permittivity is represented by the dispersion relation with a continuous distribution of relaxation times in a specified time range. It is demonstrated that, in the high-frequency range (f>200 MHz), in which the dielectric spectra exhibit a number of weakly pronounced dispersion features, the total dispersion of the permittivity is adequately described by the sum of relaxation and resonance processes.     

Temperature dependence of the dielectric characteristics of a 5CB liquid crystal within the relaxation region

The temperature dependence of the real part of the permittivity of a 4-n-pentyl-4-cyanobiphenyl liquid crystal was studied within a broad frequency range of 30–5000 MHz and in the temperature interval 20–60°C in the vicinity of the nematic-isotropic-liquid phase transition. It was established that the dispersion of the longitudinal component of the permittivity can be fitted well by a sum of two Debye terms with strongly differing relaxation times. The temperature and frequency dependence of the shorter relaxation time was determined for which the best fit between calculations and experiment was achieved.     

Investigating low-frequency dielectric properties of a composite using the distribution of relaxation times technique

The distribution of relaxation times approach, a less frequently employed dielectric data analysis technique, is utilized to better understand the relaxation characteristics of composites consisting of metal-coated, hollow glass spheres dispersed in a paraffin wax matrix. The dielectric properties of the composite samples are measured by means of impedance spectroscopy in the frequency range 0.1?mHz to 10?MHz. The application of a mixture law is not appropriate for the analysis of the frequency-dependent properties of the considered system on this broad frequency range. However, utilization of the distribution of relaxation times procedure to study the dielectric behaviour shows clear trends in the mixtures’ relaxation spectra. Relaxation processes of the paraffin wax and those specific to the composites are found from the extracted distribution of relaxation times spectra. The influence of the filler concentration, q, on the dielectric properties is examined; a relaxation with a narrow distribution at intermediate frequencies becomes broad with the addition of the filler. This relaxation, in the form of the low-frequency-dispersions (also known as constant phase angle) phenomenon, dominates the dielectric properties of the composites with high bead concentration, q>0.15. The variation in dielectric properties of individual samples whose bead concentrations q are nominally the same is discussed in terms of possible microstructural variations.     

Specific features of the dielectric spectra of the liquid crystal 5CB in the decimeter wavelength range

The dispersion and anisotropy of the permittivity of the liquid crystal 5CB in the solid, nematic, and isotropic phases are investigated at frequencies ranging from 50 to 1000 MHz using discretely tunable hybrid microstrip cavities. Resonance features which grow with increasing temperature are observed in the dielectric spectra. It is found that the section of the dispersion which is due to oriented vibrations of the mesophase molecules covers the frequency range almost up to 300 MHz, and the resonances found could be due to conformational vibrations of the molecules. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 4, 251–253 (25 August 1997)     

Determination of the two dimensional distribution of the attempt relaxation times and activation energies from temperature dependence of dielectric dispersion

We present a method for numerical calculation of two dimensional distributions of the attempt relaxation times and activation energies from the temperature dependence of the experimental dielectric permittivity dispersion. We introduce empirical attempts to account for broad and/or asymmetric dispersions with the idea of using a weighted collection of Debye relaxation times. Then we present a modification of the aforementioned idea including attempt relaxation time and activation energy using the Arrhenius law, which significantly complicates the computation of the aforementioned distribution. Incorporating the activation energy and the attempt relaxation time into the equation transforms the discretized matrix equations into tensor equations. We rework the tensor equations into simpler matrix equations, thus permitting us to solve the presented discretized integral equation by using existing Least Distance Problem solving methods. Also, we present a regularization method and a way to choose the regularization parameter based on a best fit criterion. In the end we discuss the method showing some simulated results and experimental results. We then point out some problems involved in the calculations and propose methods to reduce their significance.     

Numerical calculation of the dielectric relaxation time distribution function in polar liquids

A numerical method for calculation of the relaxation time distribution function based on the discrete Fourier transform of the dispersion part of the complex dielectric permittivity is developed. The time relaxation distribution function is found for water; its dispersion of relaxation times is narrow. This is explained by the presence of distorted hydrogen bonds (the Pople model).Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 37–40, March, 1982.     

Discotic liquid crystals of cucurbit[7]uril (CB[7])-functionalised Laponite clays

ABSTRACT

Here we demonstrate that in the presence of the small, barrel-shaped molecule cucurbit[7]uril (CB[7]) Laponite clay particles undergo a phase transition into a birefringent gel with lamellar structure and a fluid, Laponite-poor aqueous solution. We employ various characterisation methods and polarised light microscopy to study this transition and the system's structural and optical properties. Furthermore, when dried completely we obtain a layered, transparent composite film, still retaining some liquid-crystalline structure that can be rehydrated reversibly. We argue that this new system may be a model system for anisotropic patchy particles.     

Numerical elimination methods of ITO cell contribution to dielectric spectra of ferroelectric liquid crystals

Indium tin oxide (ITO) electrodes are widely used for liquid crystal applications as well as for measuring cells. Unfortunately, ITO layer possesses its own non zero resistivity R which produces (with the capacity C) the cut-off frequency f₀ of RC circuit. Dielectric spectroscopy cannot be performed for high frequencies because of high frequency losses caused by the cell behaviour. Four procedures for estimating and extracting high frequency losses in ITO cells are presented and compared in this paper. Their limitations and viability are discussed.     

Discrepancy between the times of space charge grating formation and relaxation in photorefractive crystals

A discrepancy between the times of formation and relaxation of space charge gratings is found. This effect is observed when the uniform and nonuniform parts of the optical excitation of the medium appear and disappear simultaneously. It is shown that the formation time of these gratings is always shorter than the relaxation time and the higher the light intensity, the greater the discrepancy.     

An analytical study of the dielectric relaxation mechanism in crystals with polar molecules

The kinetic equations for motion of polar vacancies, the dipole moments of which are numerically equal to the moment of a molecule in an electric field, are derived and studied. The polarization process is explained through orientation of the polar vacancies. A formula for the dielectric loss angle as a function of the frequency spectrum of external fields and temperature is derived, and using this formula calculations are performed for crystals.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 3, pp. 51–58, March, 1972.     

Segmental relaxation in semicrystalline polymers: A mean-field model for the distribution of relaxation times in confined regimes

The effect of confinement in the segmental relaxation of polymers is considered. On the basis of a thermodynamic model we discuss the emerging relevance of the fast degrees of freedom in stimulating the much slower segmental relaxation, as an effect of the constraints at the walls of the amorphous regions. In the case that confinement is due to the presence of crystalline domains, a quasi-Poissonian distribution of local constraining conditions is derived as a result of thermodynamic equilibrium. This implies that the average free-energy barrier F for conformational rearrangement is of the same order of the dispersion of the barrier heights, ( F) , around F . As an example, we apply the results to the analysis of the -relaxation as observed by dielectric broad-band spectroscopy in semicrystalline poly(ethylene terephthalate) cold-crystallized from either an isotropic or an oriented glass. It is found that in the latter case the regions of cooperative rearrangement are significantly larger than in the former.