Complex Electric Modulus Research Articles

AC CONDUCTIVITY AND DIELECTRIC PROPERTIES OF PMMA/FULLERENE COMPOSITES

Dielectric properties and electrical conductivity of different concentrations of Poly methylmethacrylate (PMMA)/fullerene C60 composites have been reported at room temperature in the frequency range from 1 kHz to 5 MHz. The frequency dependence of complex permittivity, ε*, and complex electrical modulus, M*, have been measured. Frequency dependence of dielectric constant, follows Cole–Cole dielectric relaxation equations, was investigated diagrammatically. Moreover, equations of Tsangaris et al. have been tested for our case to describe the dielectric behavior of particulate polymeric composite containing fillers which give a satisfactory agreement taking into account the variation of the aspect ratio with the volume fraction of fullerene C60 doped in the PMMA matrix.

Polymer electrolyte membranes based on p‐toluenesulfonic acid doped poly(1‐vinyl‐1,2,4‐triazole): Synthesis, thermal and proton conductivity properties

AbstractThroughout this work, the synthesis, thermal as well as proton conducting properties of acid doped heterocyclic polymer were studied under anhydrous conditions. In this context, poly(1‐vinyl‐1,2,4‐triazole), PVTri was produced by free radical polymerization of 1‐vinyl‐1,2,4‐triazole with a high yield. The structure of the homopolymer was proved by FTIR and solid state 13C CP‐MAS NMR spectroscopy. The polymer was doped with p‐toluenesulfonic acid at various molar ratios, x = 0.5, 1, 1.5, 2, with respect to polymer repeating unit. The proton transfer from p‐toluenesulfonic acid to the triazole rings was proved with FTIR spectroscopy. Thermogravimetry analysis showed that the samples are thermally stable up to ∼250 °C. Differential scanning calorimetry results illustrated that the materials are homogeneous and the dopant strongly affects the glass transition temperature of the host polymer. Cyclic voltammetry results showed that the electrochemical stability domain extends over 3 V. The proton conductivity of these materials increased with dopant concentration and the temperature. Charge transport relaxation times were derived via complex electrical modulus formalism (M*). The temperature dependence of conductivity relaxation times showed that the proton conductivity occurs via structure diffusion. In the anhydrous state, the proton conductivity of PVTri1PTSA and PVTri2PTSA was measured as 8 × 10−4 S/cm at 150 °C and 0.012 S/cm at 110 °C, respectively. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1016–1021, 2010

The synthesis and proton-conducting properties of the copolymers based on 1-vinyl-1,2,4-triazole and 2-acrylamido-2-methyl-1-propanesulfonic acid

The synthesis, thermal, electrochemical and proton-conducting properties of copolymers based on 2-acrylamido-2-methyl-1-propanesulfonic acid (AMPS) and 1-vinyl-1,2,4-triazole (VTri) were investigated. The copolymers were synthesized by free-radical copolymerization of the corresponding monomers at several monomer feed ratios to obtain poly(VTri-co-AMPS) copolymer electrolytes. The final structures of the copolymers were confirmed by FT-IR and 1H NMR methods. The composition of the copolymers was determined by elemental analysis. TGA indicates that the copolymers are thermally stable up to approximately 250 °C. The copolymer samples have higher glass transition temperatures as shown by DSC. Cyclic voltammetry results illustrated that the electrochemical stability domain extends over 3 V. Charge transport relaxation times were derived from complex electrical modulus formalism ( M *). The temperature dependence of conductivity relaxation times showed that the proton conductivity occurs by hopping mechanism via structure diffusion. In the absence of humidity, the copolymer electrolyte, poly(VTri-co-AMPS) (S2) showed proton conductivity of 2 × 10 − 3 S/cm at 130 °C, which is far higher than in imidazole based copolymers.

Dielectric relaxation and ionic conductivity studies of Ag2ZnP2O7

The complex impedance of the Ag2ZnP2O7 compound has been investigated in the temperature range 419–557 K and in the frequency range 200 Hz–5 MHz. The Z′ and Z′ versus frequency plots are well fitted to an equivalent circuit model. Dielectric data were analyzed using complex electrical modulus M* for the sample at various temperatures. The modulus plot can be characterized by full width at half-height or in terms of a non-exponential decay function $$ \phi \left( {\text{t}} \right) = \exp {\left( { - {\text{t}}/\tau } \right)^\beta } $$ . The frequency dependence of the conductivity is interpreted in terms of Jonscher’s law: $$ \sigma \left( \omega \right) = {\sigma_{\text{dc}}} + {\text{A}}{\omega^n} $$ . The conductivity σ dc follows the Arrhenius relation. The near value of activation energies obtained from the analysis of M″, conductivity data, and equivalent circuit confirms that the transport is through ion hopping mechanism dominated by the motion of the Ag+ ions in the structure of the investigated material.

Frequency dependent conductivity studies on PMMA–LiCF3SO3 polymer electrolytes

Polymer electrolytes composed of poly(methylmethacrylate) as a host polymer and lithium triflate as a salt have been prepared by solution cast technique. Polymer salt complexation has been confirmed by attenuated total reflectance Fourier transform infrared spectral studies. The ac conductivity as a function of temperatures in the frequency range 100 Hz–1 MHz has been carried out. The conductivity–temperature plots found follows the Arrhenius rule. The complex permittivity ϵ* and complex electric modulus M* have been analysed. The dispersion observe at low frequency is due to the space charge effect arising from the electrodes. The modulus spectra reveal that the dispersion deviates from the Debye behaviour. The ionic conductivity relaxation is determined from the maximum of the peaks of the dielectric loss modulus associated with the ac activation energy for ion relaxation Efp=0·337 eV, which agrees well with the dc conduction activation energy EA=0·341 eV. Thus, it is suggested that the dynamic mechanism for the ionic conduction is achieved at the same energy barrier while conducting as well as relaxing.

Dielectric properties of (1 − x)KNbO3 · xBiMg2/3Nb1/3O3 perovskite solid solutions

(1 − x)KNbO3 · xBiZn2/3Nb1/3O3 ceramic materials have been prepared by solid-state reactions. The materials with x < 0.5 have been shown to be phase-pure perovskite solid solutions. Their average lattice parameter increases linearly with x. Below 300 K, the solid solutions with 0.1 < x ≤ 0.4 are ferroelectric relaxors. M″-M′ diagrams, representing the relationship between the real and imaginary parts of the complex electric modulus, have been used to evaluate the Curie temperature of the solid solutions and the temperature of their transition to the paraelectric phase. The Arrhenius plots of dc conductivity for the solid solutions show breaks corresponding to their phase transitions. Below 400 K, the dc conductivity is low, and its contribution to the dielectric response of the solid solutions is insignificant.

Electrical and dielectric properties of Sb 2O 3–V 2O 5–K 2O glasses

Electric measurements, including temperature dependencies of direct electrical conductivity and temperature dependencies of complex electrical modulus, have been implemented using Sb 2O 3–V 2O 5–K 2O glass samples. These glasses absorb ambient humidity but their resistance to water attack depends on composition. The significant decrease of conductivity up to 100 °C can arise from water desorption. Cycling measurements of direct electrical conductivity versus temperature were also implemented. They show that the 30Sb 2O 3–30V 2O 5–40K 2O and 70Sb 2O 3–30K 2O glasses are irreversibly damaged with the formation of the hydrated layer. In addition, it was observed that the evolution of DC conductivity is ruled by Arrhenius relation, while activation energy decreases as Sb 2O 3 concentration increases.

Electrical and dielectric properties of MnF 2–ZnF 2–NaPO 3 glasses

Direct electrical conductivity and dependencies of complex electrical modulus vs. temperature and frequency have been measured on glasses from the MnF 2–ZnF 2–NaPO 3 system. These glasses are sensitive to atmospheric humidity and as a consequence, the electrical conductivity increases up to temperature of 50 °C. A hydrated layer is created by the effect of water and leads to the significant increase of the electrical conductivity in the case of 0MnF 2–20ZnF 2–80NaPO 3 glass. This behavior is governed by Arrhenius relation where the values of activation energy are increasing and values of the electrical conductivity are decreasing with the amount of MnF 2. Dielectric measurements show that a heterogeneous phase is formed in the bulk of glasses. This may be seen when plotting complex electrical modulus in the complex plane. The records made by the light microscope confirmed the occurrence of the other phase in the bulk of glasses.

Dielectric properties of BiMg1/2Ti1/2O3 and BiMg1/2Zr1/2O3 perovskite ceramics with elimination of the contribution for direct current conductivity

A technique for analysis of the electric modulus spectrum of dielectric ceramics based on the elimination of the direct current conductivity (σ dc ) contribution has been developed. Expressions are given for the real (M′ ac ) and imaginary (M′′ ac ) parts of the complex electrical modulus related only to the dielectric polarization and not containing the contribution of σ dc . The frequency dependence of M′′ ac and the M′′ ac – M′ ac diagram for BiMg1/2Ti1/2O3 and BiMg1/2Zr1/2O3 perovskite ceramics are analyzed.

Mechanical relaxation in a ternary silver borate below the glass transition temperature and corresponding features of the electrical response

Mechanical spectroscopy allows the investigation of the relaxation processes, associated with the hopping of mobile ions occurring in ionic glasses well below their glass transition temperature. In the present work we study the properties of the secondary mechanical relaxation in the fast ion conducting glass (AgI) x [(Ag 2O)· n(B 2O 3)] 1− x with n = 2 and x = 0.6 as revealed by ultrasonic measurements at MHz frequencies in a wide temperature range. We analyze the results in comparison with the features observed performing broadband dielectric measurements on the same materials. The electric response is discussed in terms of complex electric modulus. This formalism allows us to point out interesting analogies with the ultrasonic results.

Dielectric relaxation and giant dielectric constant of Nb‐doped CaCu3Ti4O12 ceramics under dc bias voltage

AbstractCaCu3Ti4–x Nbx O12 (x = 0, 0.01, 0.08, 0.2) ceramics were fabricated by a conventional solid‐state reaction method. The ceramics showed the body‐centered cubic structure without any foreign phases and the grain size decreases with Nb doping. Two Debye‐type relaxations were observed for the Nb‐doped samples at low frequency and high frequency, respectively. The complex electric modulus analysis revealed that the surface layer, grains and grain boundaries contributed to the dielectric constant. The low‐frequency dielectric constant relative to the surface layer decreased to a minimum and then increased with the dc bias voltage at 100 Hz, which were well explained in terms of a model containing two metal oxide semiconductors in series, confirming the surface layer in the ceramics. The shift voltage VB corresponding to the minimal capacitance increased with increase of the composition x. (© 2009 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Impedance spectroscopy of dielectric properties of perovskite ceramics Bi(Mg1/2Ti1/2)O3

The dielectric properties of metastable high-pressure perovskite ceramics Bi(Mg1/2Ti1/2)O3 were studied by impedance spectroscopy at frequencies of 25 Hz-1 MHz at various temperatures. It is established that, at temperatures higher than ∼450 K, the dc conductivity makes a significant contribution to the dielectric response of these ceramics. The charge-carrier activation energy ΔEdc is found from the temperature dependence of the dc conductivity σdc. As the temperature increases, the quantity ΔEdc changes in a jump from 0.12 to 1.00 eV at T ∼ 450 K. With inclusion of the contribution from σdc, the real and imaginary parts (Mac′ and Mac″) of the complex electrical modulus related only to the dielectric polarization are found. From analyzing the Mac″ − Mac′ diagrams, the contributions to the dielectric polarization from ceramic grains and their boundaries are estimated. The obtained data are interpreted in terms of the chemical composition of the ceramic compound Bi(Mg1/2Ti1/2)O3 and the existence of crystal-lattice defects formed during the synthesis under pressure. Based on an analysis of the temperature dependences of the permittivity of ceramic grains and antiparallel displacements of the Bi3+ cations, it is assumed that the dipole ordering in this perovskite compound is antiferroelectric in character.

Dielectric relaxation and dc conductivity on the PVOH-CF3COONH4 polymer system

In the present paper, the ionic conductivity and the dielectric relaxation properties on the poly(vinyl alcohol)-CF3COONH4 polymer system have been investigated by means of impedance spectroscopy measurements over wide ranges of frequencies and temperatures. The electrolyte samples were prepared by solution casting technique. The temperature dependence of the sample’s conductivity was modeled by Arrhenius and Vogel-Tammann-Fulcher (VTF) equations. The highest conductivity of the electrolyte of 3.41×10 − 3 (Ωcm) − 1 was obtained at 423 K. For these polymer system two relaxation processes are revealed in the frequency range and temperature interval of the measurements. One is the glass transition relaxation (α-relaxation) of the amorphous region at about 353 K and the other is the relaxation associated with the crystalline region at about 423 K. Dielectric relaxation has been studied using the complex electric modulus formalism. It has been observed that the conductivity relaxation in this polymer system is highly non-exponential. From the electric modulus formalism, it is concluded that the electrical relaxation mechanism is independent of temperature for the two relaxation processes, but is dependent on composition.

Synthesis of Lignin-Based Thermoplastic Copolyester Using Kraft Lignin as a Macromonomer

Lignin-based thermoplastic copolyester was synthesized for eco-friendly polymers and composite applications using lignin as a macromonomer to form a high molecular weight polymer. Kraft lignin was polymerized with sebacoyl chloride in the presence of triethylamine in N,N-dimethylacetamide (DMAc), and the molecular weight of the synthesized polymer was controlled by the polymerization temperatures and [COCl]/[OH] ratios providing up to 39 000 corresponding to 4–5 repeating units of lignin macromonomers. The glass transition temperature of the synthesized polymer was difficult to measure due to the random distribution of functional groups and irregular configurational or conformational arrangement of natural lignin. Therefore, the complex electric modulus (CEM) technique was used to determine the glass transition of the synthesized polymer to give around 70°C measured by the peak of the imaginary part of CEM. The synthesized lignin-copolyester exhibited good thermal stability up to 200°C in TGA analysis and, thus, it was possible to shape the synthesized polymer using the solvent casting or hot-melt processing techniques at 120°C–140°C without generating odor, fume or irritation. Although the molecular weight should further be increased in the future, the developed methodology may help to exploit new applications for eco-friendly sustainable materials in various fields.

Dielectric and Electric Modulus of Poly(3-hydroxybutyrate) Semi-crystalline Polymer

We present results of dielectric investigation of poly(3-hydroxybutyrate) (PHB) semi-crystalline polymer. The data obtained are treated in the view of electric modulus formalisms in order to correlate the effects of the conductivity on the net dielectric relaxation phenomena. The results reveal that the conductive relaxation processes contribution in the low frequency region is much larger than in the high frequency region. At high temperatures (above the glass transition temperature), the electrical properties are strongly influenced by the space charge. Finally the plot of the complex electric modulus for a given temperature in Argand's plane shows that the conductive processes are reflected by an arc at low frequency which agrees with the model of Coelho.

Dielectric and ac ionic conductivity investigations in the monetite

The complex impedance of the monetite has been investigated in the temperature and the frequency range 338–573 K and 200 Hz to 1 MHz, respectively. The angular frequency dependence of the conductivity is interpreted in terms of Jonscher's law and the values of the exponent n are about 0.57 ± 0.02 in all range of temperature. Dielectric data were analyzed using complex electrical modulus M* at various temperatures. The modulus plot can be characterized by full width at half height or in terms of a non-exponential decay function. Activation energy of hopping is almost close to the activation energy of conduction suggesting a hopping transport mechanism.

Dielectric properties of (1 − x)KNbO3 · xBiZn2/3Nb1/3O3 (x ≤ 0.4) perovskite solid solutions

(1 − x)KNbO3 · xBiZn2/3Nb1/3O3 ceramic materials have been prepared by solid-state reactions. The materials with x < 0.5 have been shown to be phase-pure perovskite solid solutions. Their average lattice parameter increases linearly with x. Below 300 K, the solid solutions with 0.1 < x ≤ 0.4 are ferroelectric relaxors. M″-M′ diagrams, representing the relationship between the real and imaginary parts of the complex electric modulus, have been used to evaluate the Curie temperature of the solid solutions and the temperature of their transition to the paraelectric phase. The Arrhenius plots of dc conductivity for the solid solutions show breaks corresponding to their phase transitions. Below 400 K, the dc conductivity is low, and its contribution to the dielectric response of the solid solutions is insignificant.

Electrical relaxation in the compound: LiFeVO 4

Layered ceramic oxide (LiFeVO 4) has been prepared by a standard solid-state reaction technique. LiFeVO 4 has orthorhombic crystal structure whose dielectric and electrical modulus properties were studied over a range of frequency (100 Hz–1 MHz) and temperature (298–598 K) using complex impedance spectroscopy (CIS) technique. Dielectric results suggest dielectric relaxation in the material. The presence of non-Debye type conductivity relaxation in the material has been confirmed by complex electrical modulus analysis. The activation energy calculated from electric modulus spectra is 0.237 ± 0.005 eV.

The impedance of solutions of AOT/water micelles in hexane

Broadband dielectric spectroscopy was used to study the electric properties of solutions of reverse AOT/water micelles in hexane. An analysis of the frequency dependences of the complex electric modulus allowed us to find the region of frequencies in which dc-conductivity was observed and exclude the region of electrode effects. At frequencies f of ∼ 104Hz, the field dependences of dc-conductivity changed from linear (the Ohm law) to quadratic (the Mott law) as the volume fraction of micelles increased. This was evidence of a strengthening of the effect of current limitation by a volume charge. The upper and lower limits of the drift mobility of carriers μ responsible for dc-conductivity were estimated as 0.1 cm−2 V−1 s−1 < μ < 0.3 cm−2 V−1 s−1, which was close to the mobility of electrons in hexane. This allowed us to relate the nature of current carriers to that of free electrons; the activation energy of electron creation was found to be Ea ≈ 0.41 eV. The electron lifetime up to its trapping by acceptors was estimated. The results obtained and the literature data on the rate constants of such reactions led us to conclude that micelles were capable of absorbing acceptor impurities from solvents (additional solvent purification).

Electrical conduction in (Na0·5Bi0·5)TiO3 ceramic: impedance spectroscopy analysis

Polycrystalline sample of (Na0·5Bi0·5)TiO3 was prepared using a high temperature solid-state reaction synthesis at 1070°C and subsequent sintering at 1100°C in oxygen atmosphere. X-ray diffraction (XRD) analysis of (Na0·5Bi0·5)TiO3 powder indicated the formation of a single phase rhombohedral structure. Dielectric study revealed the diffuse phase transition at 340°C. The ac conductivity data were found to obey power law and showed negative temperature coefficient of resistance character. Complex electric modulus analysis indicated non-Debye type dielectric relaxation in the system. The ac conductivity data were used to evaluate the density of states at Fermi level, minimum hopping length and activation energy of the compound. The correlated barrier hopping model was found to successfully explain the mechanism of charge transport in (Na0·5Bi0·5)TiO3.