Havriliak-Negami Function Research Articles

Dielectric study of the antiplasticization of trehalose by glycerol

Recent measurements have suggested that the antiplasticizing effect of glycerol on trehalose can significantly increase the preservation times of proteins stored in this type of preservative formulation. In order to better understand the physical origin of this phenomenon, we examine the nature of antiplasticization in trehalose-glycerol mixtures by dielectric spectroscopy. These measurements cover a broad frequency range between 40 Hz to 18 GHz (covering the secondary relaxation range of the fragile glass-former trehalose and the primary relaxation range of the strong glass-former glycerol) and a temperature (T) range bracketing room temperature (220 K to 350 K). The Havriliak-Negami function precisely fits our relaxation data and allows us to determine the temperature and composition dependence of the relaxation time tau describing a relative fast dielectric relaxation process appropriate to the characterization of antiplasticization. We observe that increasing the glycerol concentration at fixed T increases tau (i.e., the extent of antiplasticization) until a temperature dependent critical "plasticization concentration" xwp is reached. At a fixed concentration, we find a temperature at which antiplasticization first occurs upon cooling and we designate this as the "antiplasticization temperature," Tant. The ratio of the tau values for the mixture and pure trehalose is found to provide a useful measure of the extent of antiplasticization, and we explore other potential measures of antiplasticization relating to the dielectric strength.

Electrode polarization for nylon 1010 with dielectric relaxation spectroscopy

AbstractElectrode polarization arising from charge carriers accumulating at the interface between an electrode and nylon 1010 was investigated with dielectric relaxation spectroscopy. In the frequency spectra of nylon 1010, the dielectric permittivity showed high values in the region of low frequencies and high temperatures. With the Havriliak–Negami function used to fit the experimental spectra, the result revealed that the high values originated from electrode polarization and direct‐current conductivity. For electrode polarization, the dielectric strength, independent of the temperature, was about 1150, and the temperature dependence of the relaxation time followed the Vogel–Tammann–Fulcher equation. Fitting with the Vogel–Tammann–Fulcher equation, the parameters τ0 = 1.33 × 10−10 s and T0 = 303.2 K were proposed (where τ0 is the relaxation time at a very high temperature and T0 is the temperature at which the relaxation time becomes extremely large), and they suggested that the motion of the polymeric chains was one of the factors leading to charge‐carrier transport at temperatures higher than the glass‐transition temperature. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102: 3590–3596, 2006

Dielectric and interaction behavior of chitosan/polyvinyl alcohol and chitosan/polyvinyl pyrrolidone blends with some antimicrobial activities

The blends of chitosan, polyvinyl alcohol and chitosan polyvinyl pyrrolidone in dilute acetic acid were found to be compatible by viscosity measurements. The dielectric behavior of the investigated blends were studied using frequency response analyzer covering a frequency range from 10 2 to 10 6 Hz and in a wide range of temperature. The permittivity ε′ was found to decrease by increasing the frequency showing an anomalous dispersion. The dielectric loss ε″ data on the frequency domain were found to be broad indicating that more than one relaxation mechanism is present. The data for the whole investigated systems were fitted using Fröhlich and/or Havriliak–Negami functions in addition to the conductivity term. The function detected below T g could be ascribed to an orientation movement related to the side chain. A second function in the lower frequency range could be ascribed as a Maxwell Wagner effect which arises from the interfacial polarization caused by the multi-constituents of the investigated systems. The biological activity of such investigated systems was tested against a representative number of pathogenic organisms by determining the minimum inhibitory concentration (MIC). The activity was found to increase by increasing the amount of CS in the blend.

Mechanical and electrical properties of paper sheets treated with chitosan and its derivatives

This work focused on studying the dependence of paper sheet strength properties on the composition of additives, namely chitosan, cyanoethyl and carboxymethyl chitosan. Chitosan and its derivatives enhanced the strength properties of unagged and aged paper sheets. Also, cyanoethyl chitosan improved the dielectric properties of the treated paper sheets. The dielectric study was carried out over a frequency range from 100 Hz to 100 kHz at temperature range from 20 to 140 °C. The variations of permittivity ε′ versus the cyanoethyl chitosan content at three different temperatures show the highest dielectric properties at cyanoethyl chitosan of 0.3%. The variation of ε″ versus the applied frequency was fitted by a superposition of Fröhlich and Havriliak–Negami functions in addition to the conductivity term. These functions could be ascribed by the Maxwell–Wagner effect and the orientation of the large aggregates formed by the addition of chitosan to the paper sheet.

Relaxation processes in the coloration of amorphous WO3 thin films studied by combined impedance and electro-optical measurements

We introduce in this paper a phenomenological model (Havriliak-Negami function) to describe the relaxation of the intercalated Li ions into amorphous WO3 electrochromic films. Kinetic behavior of intercalation was analyzed by a combined measurement of electrochemical impedance and modulated transmittance. The frequency-dependent capacitance and modulated transmittance show the processes of ion diffusion and rearrangement towards equilibrium in the stationary sites of the structure. In case of Li-doped samples, capacitance and transmittance spectra overlap along a wide interval of frequencies, thus indicating that ion diffusion does not play a central role within the measuring frequency range employed, so that the kinetics of coloring mechanism can be wholly described by HN relaxation. The rates of the coloring process are located near 100 mHz, although their probability decays slowly towards very low frequencies.

Relationships between conductivity and local topology in heterocyclic polymer networks.

The low frequency complex dielectric relaxation above the glass transition temperature T(g) for a series of well-characterized heterocyclic polymer networks has been analyzed in terms of the electric moduli formalism. It was established that the contribution of ionic conductivity to the electric modulus can be quantitatively separated from the alpha relaxation by using a combination of two Havriliak-Negami (HN) functions. A strong correlation between the mechanisms of both conductivity and segmental mobility was inferred from the similarity of the shape of the HN function for conductivity relaxation to those for the main relaxation. This correlation is further supported by the similarity of the temperature dependencies of the relevant relaxation times corresponding to both processes. The overwhelming contribution of the preexponents D0 in the Arrhenius behavior of the apparent diffusion coefficients can be explained by considering a model implying decreased mean free paths of the diffusing elements and lower activation entropies of diffusion for polymer networks with higher apparent network densities.

Modeling complex permittivity of an epoxy-amine system using simultaneous kinetic and microdielectric studies

A reactive epoxy-amine system based on digly-cidyl ether of bisphenol A (DGEBA) with 4,4'-diaminodi-phenylsulfone (DDS) was studied during isothermal curing at 140°C and 160°C using simultaneous kinetic and microdieletric studies to establish simple models to describe the changes in the dipole component of the permittivity, e*, as a function of Tg and reaction advancement x(t). Having found that a simple relationship exists between the logarithm of the relaxation time τ and the glass transition temperature Tg, it is shown, that log τ follows the Di Benedetto equation's predicting dependence of Tg on reaction advancement as revisited by Pascault and Williams. Using this equation relating Tg and reaction advancement, the reaction advancement can be monitored directly by dielectric sensing of the changing value of the relaxation time. This equation has advantages over the WLF relationship, as in place of the fitting parameters C 1 and C 2 there is only one parameter, λ, and it is independently experimentally determined. The complex permittivity, e*, was fit to the Havriliak-Negami function. The unrelaxed permittivity at high frequency e u is assumed to be constant and the skewness parameter β was found to be independent on the temperature, the frequency, and the time while the width of the distribution decreased with time as characterized by α. During isothermal cure, the measurements made at different frequencies give the static permittivity e s versus curing time t. As the reaction proceeds, the disappearance of epoxy and amine functions is responsible for a decrease in the effective moment of the dipoles, as characterized by e s , and of the diminution of the width of the distribution of relaxation times characterized by an increase in α. It is shown that the decrease in e s with cure time can also be used to monitor the extent of reaction advancement. Thus, in addition to cure monitoring measurements based on conductivity, dielectric measurements of the changes in the dipolar relaxation time, τ, and the low frequency static dipole polarization e s can be quantitatively used to monitor reaction advancement.

Relaxation Behavior of Poly(ester carbonate) Block Copolymer Across the Melting Region

The dielectric behavior of a family of block copolymers based on poly(butylene terephthalate) (PBT) and aliphatic polycarbonate (PC), with the composition of PBT varying from 100 wt.-% to 40 wt.-%, has been investigated by broad-band dielectric spectroscopy in the frequency range from 10–1 to 109 Hz. At temperatures above the glass transition, the merging of local γ process and the cooperative β process was studied for PBT and 40/60 and 60/40 PBT-PC copolymers. The experimental data can be satisfactorily analyzed considering a sum of two Havriliak-Negami functions indicating that both β and γ relaxations can be treated as independent processes. Dielectric measurements for the 40/60 copolymer were extended over and above the melting region to characterize the influence of crystal melting on the dynamic behavior. It is shown that the progressive loss of the crystalline lamellar stack microstructure, as characterized by differential scanning calorimetry and small- and wide-angle X-ray scattering, provokes a dramatic change in the dynamic behavior of both the β and γ process.

Dipolar relaxations in an epoxy–amine system

Abstract Dipolar relaxations in a reactive epoxy–amine system based on diglycidyl ether of bisphenol A with 4,4′-diaminodiphenylsulfone were studied with the Havriliak–Negami function. The system was cured isothermally at 140 °C using simultaneous kinetic and microdielectric studies. The relaxation time was calculated from the frequency fmax of the peak of the loss factor e′′ versus frequency f. A linear relation exists between the logarithm of the relaxation time τ and the glass transition temperature Tg. Then, logτ follows the Di Benedetto equation revisited by Pascault and Williams allowing the prediction of the relaxation time τ during cure. The unrelaxed permittivity at high frequency eu, the relaxed or static permittivity es and the skewness parameter β were found independent on the conversion or the curing time. The distribution parameter α decreases as curing time t increases. The difficulty of orientation of dipoles in the electric field due to vitrification is responsible of these behaviours.

Dielectric relaxation in liquid crystalline dimers

Dielectric measurements are reported for liquid crystalline dimers consisting of two mesogenic groups joined through ether links by a flexible alkyl chain. Results are presented for the odd-symmetric dimer, α,ω-bis[(4-cyanobiphenyl)-4′-yloxy]undecane (BCB.O11), and the odd-asymmetric dimer, α-[(4-cyanobiphenyl)-4′-yloxy]-ω-(4-decylanilinebenzylidene-4′-oxy) nonane (CB.O9O.10). The real and imaginary parts of the electric permittivities of aligned samples were measured as functions of frequency over the range 102–109 Hz at temperatures throughout the nematic phase. Measurements were fitted as a function of frequency to the Havriliak–Negami function, and yielded relaxation times and dielectric strengths for the relaxations at each of the temperatures studied. The static dielectric anisotropy for both materials was positive. For BCB.O11, the parallel and perpendicular components of the permittivity exhibited one low frequency and one high frequency relaxation, while the parallel component of the permittivity for CB.O9O.10 showed three relaxations, which were well-separated in frequency. A generic model of liquid crystalline dimers based on mixtures of linear and bent conformers with the tetrahedral angle has been proposed [A. Ferrarini et al., Chem. Phys. Lett. 214, 409 (1993)]. This model is used to provide a qualitative interpretation of the dielectric measurements reported. To obtain a satisfactory explanation of the results, it is necessary to include additional conformers having either a hairpin shape or a bent shape with an angle of 180° minus the tetrahedral angle. The temperature dependence measured for the strengths of the dielectric relaxations is explained in terms of changes of the order parameter and changes in the relative probabilities of different shaped conformers.

Investigation on dielectric properties of the polyetherketone nanocomposite with lead titanate ultrafines

The dielectric properties of polymer composites with inorganic nanoparticles were investigated. In the demonstration of the dielectric constant expression of the nanocomposite polymer, the dielectric contributions of the displacement polarization, the orientation polarization, and the space polarization in the nanocomposite polymer were all considered. In the demonstration, two dielectric relaxation models were used, that of Debye for inorganic nanoparticles and the Havriliak–Negami function model for polymers. Then the expression of the complex dielectric constant of the nanocomposite polymer was obtained by using Onsager's local field theory. Furthermore, the nanocomposite polymer thin films that consist of PbTiO3 nanoparticles and polyetherketone were prepared. The real parts of the dielectric constants were measured and calculated, respectively. It was found that our calculated results are in good agreement with our measured results. PACS Nos.: 77.20, 77.55, 81.20T

Relaxation time distribution function

The distribution function of relaxation time in disordered dielectrics has been calculated in the random field theory framework. For this purpose, we first consider the dynamics of single two-orientable electric dipole in a random electric field E in a disordered ferroelectric. The obtained dependence τ(E) made it possible to express the relaxation time distribution function F(τ) via the random field distribution function f(E). This function has been calculated self-consistently in the random field theory framework. Nonlinear random field contribution and effects of spatial correlations between the dipoles have also been taken into account. It was shown that nonlinear contribution of random field gives asymmetric shape of F(τ), while in linear case it is symmetric. Comparison of calculated F(τ) curves with those extracted from empirical Cole-Cole (CC), Davidson-Cole (DC), Kohlrausch-William-Watts (KWW) and Havriliak-Negami (HN) functions had shown, that they correspond to mixed ferroelectric-dipole glass (ferro-glass) phase with coexistence of short and long-range order. Different forms of F(τ) are determined by linear (CC) or nonlinear (DC, KWW, HN) contributions of random field.

Scaling behavior of the α relaxation in fragile glass-forming liquids under conditions of high compression

The effect of pressure variation on dynamics of alpha relaxation process in poly[(phenyl glycidyl ether)-co-formaldehyde] has been investigated both under isothermal (T=293 K) and isobaric (P=0.1, 60, 120, 180, and 240 MPa) conditions using broad band dielectric spectroscopy (10(-2) to 10(6) Hz). The alpha relaxation is analyzed by means of the Havriliak-Negami relaxation function which has two shape parameters (alpha and gamma) to characterize non-Debye behavior. As a result we found that the shape parameters of the dielectric function collected for different pressures fall on master curves constructed by plotting alpha and alphagamma against the logarithm of relaxation time. The scaling of shape parameters for different pressure stems from pressure independence of fragility. This provides strong experimental evidence supporting correlation of non-Debye behavior with non-Arrhenius relaxation under high pressure. From an analysis of the shape parameters of relaxation function, in terms of the Schonhals and Schlosser model, we drew conclusions that the molecular mobility of PPG is controlled in the same way by temperature and pressure. The relaxation times exhibit a clear non-Arrhenius behavior under isothermal and isobaric condition.

Modeling and scaling of chielectric relaxation of nonlinear optical polymers in frequency domain

chielectric relaxation theory was demonstrated. chielectric relaxation that selectively probes chromophore reorientation in the frequency domain was described by the Havriliak Negami (HN) function. chielectric spectra of several nonlinear optical (NLO) polymers were fitted well by the HN function. To describe the scaling of chromophore reorientation relaxation in frequency domain, two-shape parameters m and n describing the low- and high- frequency wings of the chielectric spectra need to be specified, besides the chielectric characteristic relaxation time τ and the chielectric strength Δχ(2). From the temperature dependences of m and n of NLO polymers, the relations between the chromophore relaxation and the α relaxation of the polymer host have been revealed.

Calorimetric and dielectric study of a blend containing a conductive polymer: poly(3-octylthiophene)+poly(ethylene-co-vinylacetate)

The phase diagram of the binary system poly(3-octylthiophene)+poly(ethylene-co-vinylacetate), P3OT+EVA was studied by Differential Scanning Calorimetry (DSC). The blends of low and high content of P3OT were found to be homogeneous. The system was also studied by a dielectric relaxation technique in the frequency range 20Hz–100kHz. The complex electric modulus M* is discussed in terms of the well-known Havriliak–Negami function. We also obtained the spectrum of relaxation times using a regularization technique. The spectra allowed us to calculate the d.c. conductivity. A low frequency contribution to the dielectric loss found in two-phase samples was attributed to interface polarisation effects.

Dielectric relaxation spectra in ferroelectric P(VDF-TrFE) copolymers

Dielectric spectroscopy (DS) and Thermally Stimulated Current (TSC) are employed to study the dynamics of Poly(VinyliDene Fluoride-TriFluoroEthylene) copolymers. Dielectric spectra reveal the existence of three relaxation processes: the β relaxation or the glass transition relaxation, the secondary γ relaxation present in the glassy phase and the Curie transition well characterized by a thermal hysteresis. TSC spectra are in good agreement with DS results and resolve the well known in semi-crystalline polymers αc relaxation process, as well as observed by Differential Scanning Calorimetry. The experimental DS data are analyzed using empirical Havriliak Negami function while TSC spectra are described in terms of compensation law and Hoffmann Williams Passaglia model of relaxation by means of fractional polarization technique. Curie - Weiss temperature To = 26 °C is determined by DS spectroscopy and the Curie transition is well described by a compensation law at Tc = 121 °C.

Dynamics of epoxies: a full dielectric analysis by wideband spectroscopy

The dynamics of monoepoxide (CGE) and diepoxide (DGEBA) compounds, investigated by wideband (10 2–10 10 Hz) dielectric spectroscopy from below to above the glass transition temperature in the range 130–360 K, shows a bimodal relaxation and the presence of a dc conductivity contribution. The fitting of the data by the Havriliak–Negami function provided the temperature behaviour of conductivity, relaxation times, dielectric strengths and shape parameters. The glass transition phenomenon was detected by the changes of both the relaxation strength and the low frequency slope of the secondary relaxation, and a transition temperature T B > T g between two different relaxation regimes, coincident with the splitting temperature of the systems, was also recognised. The comparative analysis of the results draws an overall picture which improves our information on the dynamics of the systems and also supports some recent ideas on the splitting between main and secondary relaxations.

Comparison of ultrasonic shear wave and dynamic-mechanical measurements in acrylic-type copolymers

An ultrasonic shear wave reflection method was applied to study film formation and temperature dependence of the complex shear modulus (G*G′ + iG″) in different amorphous films made of aqueous dispersions of acrylic-type copolymers. The data are compared with dynamic-mechanical measurements in the low frequency range. It is shown that the temperature dependence of the storage (G′) and the loss modulus (G″) for both methods can be fitted by the same set of parameters using the Havriliak–Negami function incorporating the Vogel–Fulcher–Tamman–Hesse equation for the temperature dependence of relaxation times. The temperature dependence of the relaxation times obtained from the fits to the ultrasonic shear modulus is compared to the shift factors of the dynamic-mechanical measurements. The agreement between both methods is good. This suggests an almost thermorheological simplicity of the samples for the main glass–rubber relaxation and demonstrates the capacity of the ultrasonic rheometer. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1703–1711, 1998

Nonlinear susceptibilities and polydispersivity in dipolar glasses

The dipolar glass system D-BP40BPI60 was investigated using broadband dielectric spectroscopy over 12 decades in frequency and temperatures between 4K < T < 300 K. The complex dielectric constant reveals increasing polydispersivity with decreasing temperatures. However, no criticality can be detected in the linear components of the susceptibility: the distribution of relaxation times, as well as the mean relaxation time become infinite at T = 0 only. The nonlinear susceptibility was followed over 4 decades of frequency. Again the mean relaxation times follow a pure Arrhenius-type behavior. However, from the extrapolation of the quasistatic nonlinear susceptibility a glass transition temperature of 30 K can be deduced in reasonable agreement with the AlmeidaThouless line determined from measurements of the FC/ZFC-susceptibilities. The frequency dependence of the real and imaginary parts of the third-order susceptibility cannot be described using simple extensions from Cole-Cole or Havriliak-Negami functions.

A rigorous comparison of theoretical autocorrelation functions with dielectric relaxation parameters for the alpha process of polymers

Recently, tables of parameters used to represent experimental dielectric relaxation data as well as autocorrelation functions have become available. The experimental and autocorrelation function data were represented with the Havriliak–Negami function using rigorous statistical techniques. These tables include not only parameters and their temperature dependencies, but also the confidence intervals for all of the parameters. The important parameters for this work are the two shape parameters, α and β, which represent the width and skewness of the relaxation process, respectively. A comparison is made between the experimental data and several autocorrelation functions by calculating the minimum distance (in units of standard deviations) between the experimental values of αβ parameters for a specific polymer and the αβ parameters corresponding to the autocorrelation functions reported in these tables. Quantities derived from these minimum distances (a distribution function and an error function) are reported for each of the autocorrelation functions. These results are discussed in terms of the basic assumptions of the mode coupling theory. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1887–1897, 1997