Dielectric relaxation in biological materials

The study of dielectric properties concerns storage and dissipation of electric and magnetic energy in materials. Dielectrics are important in order to explain various phenomena in Solid-State Physics and in Physics of Biological Materials. Indeed, during the last two centuries, many scientists have tried to explain and model the dielectric relaxation. Starting from the Kohlrausch model and passing through the ideal Debye one, they arrived at more com- plex models that try to explain the experimentally observed distributions of relaxation times, including the classical (Cole-Cole, Davidson-Cole and Havriliak-Negami) and the more recent ones (Hilfer, Jonscher, Weron, etc.). The purpose of this thesis is to discuss a variety of models carrying out the analysis both in the frequency and in the time domain. Particular attention is devoted to the three classical models, that are studied using a transcendental function known as Mittag-Leffler function. We highlight that one of the most important properties of this function, its complete monotonicity, is an essential property for the physical acceptability and realizability of the models. Lo studio delle proprietà dielettriche riguarda l’immagazzinamento e la dissipazione di energia elettrica e magnetica nei materiali. I dielettrici sono importanti al fine di spiegare vari fenomeni nell’ambito della Fisica dello Stato Solido e della Fisica dei Materiali Biologici. Infatti, durante i due secoli passati, molti scienziati hanno tentato di spiegare e modellizzare il rilassamento dielettrico. A partire dal modello di Kohlrausch e passando attraverso quello ideale di Debye, sono giunti a modelli più complessi che tentano di spiegare la distribuzione osservata sperimentalmente di tempi di rilassamento, tra i quali modelli abbiamo quelli classici (Cole-Cole, Davidson-Cole e Havriliak-Negami) e quelli più recenti (Hilfer, Jonscher, Weron, etc.). L’obiettivo di questa tesi è discutere vari modelli, conducendo l’analisi sia nel dominio delle frequenze sia in quello dei tempi. Particolare attenzione è rivolta ai tre modelli classici, i quali sono studiati utilizzando una funzione trascendente nota come funzione di Mittag-Leffler. Evidenziamo come una delle più importanti proprietà di questa funzione, la sua completa monotonia, è una proprietà essenziale per l’accettabilità fisica e la realizzabilità dei modelli.

X-Ray Diffraction, Calorimetric and Dielectric Relaxation Study of the Amorphous and Smectic States of a Main Chain Liquid Crystalline Polymer

Los polímeros cristales líquidos (LCP) son sistemas complejos que forman mesofases que presentan orden orientacional y polímeros amorfos. Con frecuencia, el estado amorfo isotrópico no puede ser estudiado debido a la rápida formación de mesofases. En este trabajo se ha sintetizado y estudiado un nuevo LCP: poli(trietilenglicol metil p, p '-bibenzoato), PTEMeB. Este polímero presenta una formación de mesofase bastante lenta haciendo posible estudiar de forma independiente tanto los estados amorfo y de cristal líquidos. La estructura y las transiciones de fase del PTEMeB han sido investigados por calorimetría (DSC), con MAXS / WAXS con temperatura variable que emplean radiación de sincrotrón y con difracción de rayos X. Estos estudios han mostrado la existencia de dos transiciones vítreas, relacionadas con las fases amorfa y cristal líquido. Se ha realizado un estudio de relajación dieléctrica en amplios intervalos de temperatura y presión. Se ha encontrado que la transición vítrea dinámica de la fase amorfa es más lenta que la del cristal líquido. El estudio de la relajación ? nos ha permitido seguir la formación isoterma de la mesofase a presión atmosférica. Además, con el estudio el comportamiento dinámico a alta presión se ha encontrado que se produce la formación rápida de la mesofase inducida por cambios bruscos de presión. Liquid crystalline polymers (LCPs) are complex systems that include features of both orientationally ordered mesophases and amorphous polymers. Frequently, the isotropic amorphous state cannot be studied due to the rapid mesophase formation. Here, a new main chain LCP, poly(triethyleneglycol methyl p,p'-bibenzoate), PTEMeB, has been synthesized. It shows a rather slow mesophase formation making possible to study independently both the amorphous and the liquid crystalline states. The structure and phase transitions of PTEMeB have been investigated by calorimetry, variable-temperature MAXS/WAXS employing synchrotron radiation, and X-ray diffraction in oriented fibers. These experiments have pointed out the presence of two glass transitions, related to the amorphous or to the liquid crystal phases. Additionally, the mesophase seems to be a coexistence of orthogonal and tilted smectic phases. A dielectric relaxation study of PTEMeB over broad ranges of temperature and pressure has been performed. The dynamic glass transition turns out to be slower for the amorphous state than for the liquid crystal. Monitoring of the α relaxation has allowed us to follow the isothermal mesophase formation at atmospheric pressure. Additionally, the dynamical behavior at high pressures has pointed out the fast formation of the mesophase induced by sudden pressure changes.

Conformational analysis and dielectric relaxation of polycarbosilanes and related materials

The conformational characteristics of poly(dimethylsilmethylene), poly(dimethylsilethene), poly(dimethylsilethane) and a related material, poly(2,2,5,5-tetramethyl-1-oxa-2,5-disilapentane), have been investigated using the method of molecular mechanics. In this method, a quantitative analysis of the factors affecting the nature and magnitude of the bond rotation potentials governing their conformational behaviour has been undertaken. Along with their structural data, the results obtained were employed to calculate a variety of conformationally-dependent properties for these polymers, including the characteristic ratio, the dipole moment ratio and the mean-square radius of gyration. In addition, the dielectric relaxation behaviour of two samples of poly(2,2,5,5-tetramethyl-1-oxa-2,5-disilapentane) with molar masses Mw = 28000 and Mw = 46000 respectively, have been studied as a function of temperature (179K-205K) and frequency (100-105Hz). Activation energies for the α-relaxation process and Davidson-Cole empirical distribution factors have been calculated.

Dielectric relaxation of polysiloxanes and kerr effect of p-phenylene vinylene oligomers

The dielectric relaxation behaviour of a series of cyclic and linear poly(dimethylsiloxanes) with overline nn in the range 28 to 99 has been studied, as a function of temperature (142.0K-157.5K) and frequency (12-105Hz). Activation energies for the -relaxation process, Davidson-Cole empirical distribution factors, , and mean-square dipole moments per repeat unit, < 2> , have been calculated. Differences in values of H_act reflected restricted dipolar rotation for the cyclic structures, compared to the linear structures, over the range of molecular weights studied. The dielectric relaxation behaviour of a series of linear oligomers of methyl phenyl siloxane, with n in the range 4 to 10, a series of linear fractions of poly(methyl phenyl siloxane), with overline n_n in the range 31 to 1370, and a cyclic oligomer of mehyl phenyl siloxane, with n = 10, has been studied as a function of temperature (155.5K-264.0K) and frequency (12-105Hz). Activation energies for the -relaxation process, Davidson-Cole and Cole-Cole empirical distribution factors, and , respectively, and mean-square dipole moments per repeat unit have been calculated. The reduced flexibility of short methyl phenyl siloxane chains, compared to dimethyl siloxane chains, was apparent from a comparison of dipole moment ratios. The dilectric relaxation behaviour of poly(methyl hydrogen siloxane) and poly(n-hexyl methyl siloxane) has been studied as a function of temperature and frequency. A polysiloxane liquid crystal has been synthesised and its dielectric relaxation behaviour has been studied, as a function of temperature and frequency, in the liquid crystalline phase and below T_g. Poly(p-phenylene vinylene) and related oligomers have been synthesised and characterised by a variety of experimental techniques. The Kerr effect of two oligomeric fractions, in solution in PPG 2025, has been measured. The electrical conductivities of the undoped and I_2-doped polymer and oligomers have been measured.

Study of thermal relaxation of Poly (HDDA-co-MMA) by temperature modulated DSC and dielectric spectroscopy

The thermal transitions in the copolymer of 1,6-hexanediol diacrylate (HDDA) and methyl methacrylate (MMA) was investigated to understand its use in microstereolithography. The glass transition temperature and the effect of interaction on this transition process was investigated by means of temperature modulated differential scanning calorimetry (TMDSC). The heat capacities were determined and PHDDA rich phases showed lower heat capacity than PMMA rich phases. The frequency dependence of glass transitions were studied by varying the modulation period of TMDSC and confirmed by dielectric relaxation spectroscopy. Vogel Fulcher Tammann Hesse (VFTH) parameters of homo and copolymers have also been reported.

On the dielectric dispersion and absorption in nanosized manganese zinc mixed ferrites

The temperature and frequency dependence of dielectric permittivity and dielectric loss of nanosized Mn1-xZnxFe2O4 (for x = 0, 0.2, 0.4, 0.6, 0.8, 1) were investigated. The impact of zinc substitution on the dielectric properties of the mixed ferrite is elucidated. Strong dielectric dispersion and broad relaxation were exhibited by Mn1-xZnxFe2O4. The variation of dielectric relaxation time with temperature suggests the involvement of multiple relaxation processes. Cole-Cole plots were employed as an effective tool for studying the observed phenomenon. The activation energies were calculated from relaxation peaks and Cole-Cole plots and found to be consistent with each other and indicative of a polaron conduction.

Influence of lanthanum doping on the dielectric, ferroelectric and relaxor behaviour of barium bismuth titanate ceramics

Barium lanthanum bismuth titanate (Ba1−(3/2)xLaxBi4Ti4O15, x = 0–0.4) ceramics were fabricated using the powders synthesized via the solid-state reaction route. X-ray powder diffraction analysis confirmed the above compositions to be monophasic and belonged to the m = 4 member of the Aurivillius family of oxides. The effect of the partial presence of La3+ on Ba2+ sites on the microstructure, dielectric and relaxor behaviour of BaBi4Ti4O15 (BBT) ceramics was investigated. For the compositions pertaining to x ≤ 0.1, the dielectric constant at both room temperature and in the vicinity of the temperature of the dielectric maximum (Tm) of the parent phase (BBT) increased significantly with an increase in x while Tm remained almost constant. Tm shifted towards lower temperatures accompanied by a decrease in the magnitude of the dielectric maximum (εm) with an increase in the lanthanum content (0.1 < x ≤ 0.4). The dielectric relaxation was modelled using the Vogel–Fulcher relation and a decrease in the activation energy for frequency dispersion with increasing x was observed. The frequency dispersion of Tm was found to decrease with an increase in lanthanum doping, and for compositions corresponding to x ≥ 0.3, Tm was frequency independent. Well-developed P(polarization)–E(electric field) hysteresis loops were observed at 150 °C for all the samples and the remanent polarization (2Pr) was improved from 6.3 µC cm−2 for pure BBT to 13.4 µC cm−2 for Ba0.7La0.2Bi4Ti4O15 ceramics. Dc conductivities and associated activation energies were evaluated using impedance spectroscopy.

A note on the evaluation of dielectric dispersion parameters of non-debije type liquids

A simple method for evaluating dielectric relaxation parameters ie given whioh can be used for analyeing the arelaxation times of a liquid into two absorptions.

Dielectric properties of Li2O-3B(2)O(3) glasses

The frequency and temperature dependences of the dielectric constant and the electrical conductivity of the transparent glasses in the composition Li2O-3B(2)O(3) were investigated in the 100 Hz-10 MHz frequency range. The dielectric constant and the loss in the low frequency regime were electrode material dependent. Dielectric and electrical relaxations were, respectively, analyzed using the Cole-Cole and electric modulus formalisms. The dielectric relaxation mechanism was discussed in the framework of electrode and charge carrier (hopping of the ions) related polarization using generalized Cole-Cole expression. The frequency dependent electrical conductivity was rationalized using Jonscher's power law. The activation energy associated with the dc conductivity was 0.80 +/- 0.02 eV, which was ascribed to the motion of Li+ ions in the glass matrix. The activation energy associated with dielectric relaxation was almost equal to that of the dc conductivity, indicating that the same species took part in both the processes. Temperature dependent behavior of the frequency exponent (n) suggested that the correlated barrier hopping model was the most apposite to rationalize the electrical transport phenomenon in Li2O-3B(2)O(3) glasses. These glasses on heating at 933 K/10 h resulted in the known nonlinear optical phase LiB3O5.

Dielectric, Ferroelectric and Relaxor Behavior of BaLaxBi4-xTi4O15 Ceramics

Monophasic BaLaxBi4-xTi4O15 (x = 0, 0.2, 0.4, 0.6 and 0.8) ceramics, fabricated from the powders synthesized via the solid-state reaction route exhibited relaxor behavior. Dielectric properties of the well sintered ceramics were measured in a wide frequency range (1 kHz-1 MHz) at different temperatures (300-750 K). The temperature of dielectri maximum (T-m) was found to decrease significantly from 696 K for an undoped sample (x = 0) to 395 K for the sample corresponding to the composition x = 0.8 accompanied by a decrease in the magnitude ofdielectric maximum (epsilon(m)). The temperature variation of the dielectric constant on the high temperature slope of the peak (T > T-m) was analyzed by using the Lorentz-ype quadratic law and the diffuseness of the peak was found to increase with increasing x. Vogel-Fulcher modelling of dielectric relaxation showed a decrease in freezing temperature (T-VF) (from 678 to 340 K) and an increase in the activation energy (5 to 24 meV) for the frequency dispersion with increase in x (La-3 divided by content). Strength of frequency dispersion of the phase transition increased with lanthanum content. Polarization (P)-electric field (E) hysteresis loops recorded at 373 showed a transition from a nearly squarish to slim loop hysteresis behavior with increasing lanthanum content.

Dielectric properties of (100-x)Li2B4O7-x(Ba5Li2Ti2Nb8O30) glasses and glass nanocrystal composites

Transparent glasses of various compositions in the system (100 -x)(Li2B4O7)-x(Ba5Li2Ti2Nb8O30) (5 <= x <= 20, in molar ratio) were fabricated by splat quenching technique. The glassy nature of the as-quenched samples was established by differential thermal analyses (DTA). X-ray powder diffraction studies confirmed the as-quenched glasses to be amorphous and the heat-treated to be nanocrystalline. Controlled heat-treatment of the as-quenched glasses at 500 degrees C for 8 h yielded nanocrystallites embedded in the glass matrix. High Resolution Transmission Electron Microscopy (HRTEM) of these samples established the size of the crystallites to be in the nano-range and confirmed the phase to be that of Ba5Li2Ti2Nb8O30 (BLTN) which was, initially, identified by X-ray powder diffraction. The frequency, temperature and compositional dependence of the dielectric constant and the electrical conductivity of the glasses and glass nanocrystal composites were investigated in the 100 Hz to 10 MHz frequency range. Electrical relaxations were analyzed using the electric modulus formalisms. The imaginary part of electric modulus spectra was modeled using an approximate solution of Kohlrausch-Williams-Watts relation. The frequency dependent electrical conductivity was rationalized using Jonscher's power law. The activation energy associated with the dc conductivity was ascribed to the motion of Li+ ions in the glass matrix. The activation energy associated with dielectric relaxation was almost equal to that of the dc conductivity, indicating that the same species took part in both the processes. (C) 2010 Elsevier B.V. All rights reserved.

A molecular theory of collective orientational relaxation in pure and binary dipolar liquids

A molecular theory of collective orientational relaxation of dipolar molecules in a dense liquid is presented. Our work is based on a generalized, nonlinear, Smoluchowski equation (GSE) that includes the effects of intermolecular interactions through a mean‐field force term. The effects of translational motion of the liquid molecules on the orientational relaxation is also included self‐consistently in the GSE. Analytic expressions for the wave‐vector‐dependent orientational correlation functions are obtained for one component, pure liquid and also for binary mixtures. We find that for a dipolar liquid of spherical molecules, the correlation function ϕ(k,t) for l=1, where l is the rank of the spherical harmonics, is biexponential. At zero wave‐vector, one time constant becomes identical with the dielectric relaxation time of the polar liquid. The second time constant is the longitudinal relaxation time, but the contribution of this second component is small. We find that polar forces do not affect the higher order correlation functions (l>1) of spherical dipolar molecules in a linearized theory. The expression of ϕ(k,t) for a binary liquid is a sum of four exponential terms. We also find that the wave‐vector‐dependent relaxation times depend strongly on the microscopic structure of the dense liquid. At intermediate wave vectors, the translational diffusion greatly accelerates the rate of orientational relaxation. The present study indicates that one must pay proper attention to the microscopic structure of the liquid while treating the translational effects. An analysis of the nonlinear terms of the GSE is also presented. An interesting coupling between the number density fluctuation and the orientational fluctuation is uncovered.

Anomalous dielectric behavior of some ferrites

The dielectric behavior of some powdered polycrystalline samples has been studied in the frequency range of 200 Hz–100 kHz. It is shown that the dielectric behavior in these systems below the Curie temperature is not purely relaxational in its character and cannot be described by any of the models of the dielectric relaxation hitherto put forward. It is also shown that ‘‘isolation’’ of the particles in the powder samples plays a very important role. The origin of this abnormality is thought to be due to the mechanical resonance arising out of the magnetostrictive property of the material.

Relationship between microscopic and macroscopic orientational relaxation times in polar liquids

Microscopic relations between single-particle orientational relaxation time (T, ) , dielectric relaxation time ( T ~ )a,n d many-body orientational relaxation time ( T ~o)f a dipolar liquid are derived. We show that both T~ and T~ are influenced significantly by many-body effects. In the present theory, these many-body effects enter through the anisotropic part of the two-particle direct correlation function of the polar liquid. We use mean-spherical approximation (MSA) for dipolar hard spheres for explicit numerical evaluation of the relaxation times. We find that, although the dipolar correlation function is biexponential, the frequency-dependent dielectric constant is of simple Debye form, with T~ equal to the transverse polarization relaxation time. The microscopic T~ falls in between Debye and Onsager-Glarum expressions at large values of the static dielectric constant.

Molecular expression for dielectric friction on a rotating dipole: Reduction to the continuum theory

Recently we presented a microscopic expression for dielectric friction on a rotating dipole. This expression has a rather curious structure, involving the contributions of the transverse polarization modes of the solvent and also of the molecular length scale processes. It is shown here that under proper limiting conditions, this expression reduces exactly to the classical continuum model expression of Nee and Zwanzig [J. Chem. Phys. 52, 6353 (1970)]. The derivation requires the use of the asymptotic form of the orientation‐dependent total pair correlation function, the neglect of the contributions of translational modes of the solvent, and also the use of the limit that the size of the solvent molecules goes to zero. Thus, the derivation can be important in understanding the validity of the continuum model and can also help in explaining the results of a recent computer simulation study of dielectric relaxation in a Brownian dipolar lattice.