Random Free Energy Barrier Research Articles

Translational and reorientational dynamics in deep eutectic solvents.

We performed rheological measurements of the typical deep eutectic solvents (DESs) glyceline, ethaline, and reline in a very broad temperature and dynamic range, extending from the low-viscosity to the high-viscosity supercooled-liquid regime. We find that the mechanical compliance spectra can be well described by the random free-energy barrier hopping model, while the dielectric spectra on the same materials involve significant contributions arising from reorientational dynamics. The temperature-dependent viscosity and structural relaxation time, revealing non-Arrhenius behavior typical for glassy freezing, are compared to the ionic dc conductivity and relaxation times determined by broadband dielectric spectroscopy. For glyceline and ethaline, we find essentially identical temperature dependences for all dynamic quantities. These findings point to a close coupling of the ionic and molecular translational and reorientational motions in these systems. However, for reline, the ionic charge transport appears decoupled from the structural and reorientational dynamics, following a fractional Walden rule. In particular, at low temperatures, the ionic conductivity in this DES is enhanced by about one decade compared to expectations based on the temperature dependence of the viscosity. The results for all three DESs can be understood without invoking a revolving-door mechanism previously considered as a possible charge-transport mechanism in DESs.

Exploring the universality of the alternating conductivity of disordered materials using the Gaussian distribution of activation energies

This paper presents a new approach for the analysis of AC conductivity, = + , in disordered solids which brings together the quasi-universal frequency-dependent conductivity and the idea of a Gaussian distributions of probable activation energy barriers for hopping carriers. An explicit expression for AC conductivity was obtained using a complex dielectric response function and a continuous time random walk treatment applied to a lattice obeying the Kubo’s fluctuation-dissipation theorem. This expression provides an insight into the universality of the form and (k is the dielectric constant), as well into the effect of the Gaussian disorder on exponent s. We discuss the similarities and differences with the Random Free Energy Barrier model equivalent to the long-used box model, and it brings support to an extending expression proposed by J C Dyre and one of the authors. The applicability of the model to experimental observations on poly[(2-methoxy-5-hexyloxy)-p-phenylenevinylene] reveals the dielectric constant, mean energy and variance of the Gaussian distribution for hopping carriers in this disordered conjugated polymer.

The ac conductivity of binary chalcogenide glasses $${\text {Se}}_{100-x}{\text {X}}_{x}$$ Se 100 - x X x (X = Ge, In, Te)

The random free energy barrier hopping model is used to investigate the temperature and frequency dependent ac conductivity $$\sigma _{ac}(\omega )$$ of binary chalcogenide glasses $${\text {Se}}_{100-x}{\text {X}}_{x}$$ (X = Ge, In, Te). The temperature dependent barrier height leads to Meyer–Neldel (MN) rule. The calculated MN energy $$E_{MN}$$ is in good agreement with the experimental estimates. The $$\sigma _{ac}(\omega )$$ is taken as the sum of bipolaron and single polaron hopping conductivities $$\sigma _{b}(\omega )$$ and $$\sigma _{s}(\omega ),$$ respectively. The calculated results are in close agreement with the experimental data. It is found that $$\sigma _{s}$$ is smaller by orders of magnitude than $$\sigma _{b}$$ in $${\text {Se}}_{100-x}{\text {Ge}}_{x}$$ alloys in the temperature range 250–400 K, while in $${\text {Se}}_{100-x}{\text {Te}}_{x}$$ alloys $$\sigma _{ac}(\omega )$$ is mainly due to $$\sigma _{b}$$ in the temperature range 150–250 K and $$\sigma _{s}$$ becomes significant above 250 K. However in $${\text {Se}}_{100-x}{\text {In}}_{x}$$ alloys in the temperature range 303–333 K, $$\sigma _{b}$$ is nearly temperature independent and $$\sigma _{ac}(\omega )$$ is mainly due to $$\sigma _{s}.$$ It is found that acoustic phonons assist hopping process in $${\text {Se}}_{100-x}{\text {Ge}}_{x}$$ and $${\text {Se}}_{100-x}{\text {Te}}_{x}$$ alloys, while both high energy acoustic and low energy optical phonons assist hopping process in $${\text {Se}}_{100-x}{\text {In}}_{x}$$ alloys.

Charge transport in conjugated polymer–semiconductor nanoparticle composite near the percolation threshold

This paper describes a new statistical model to predict the frequency dependence of the conductivity of conjugated polymer–semiconductor nanoparticle composites. The model considers AC conduction in an inhomogeneous medium represented by a two-dimensional model of resistor network. The conductivity between two neighboring sites in the polymer matrix and the semiconductor particles is assumed to obey the random free energy barrier model and the Drude model, respectively. The real and imaginary parts of the AC conductivity were determined using the transfer-matrix technique, and the statistical model was applied to experimental data of thin films composed of polyaniline (PANI) and indium–tin–oxide (ITO) nanoparticles. The conductivity critical exponent (s) obtained in two dimensions for PANI/ITO films below the percolation threshold was found to be 2.7, which is greater than the universal value of s described by the classical percolation theory (s = 1.3). This non-universality is explained by the existence of a local electric field distribution in the bulk of the nanocomposite. Finally, these results are discussed in terms of the distribution of potential barriers that vary according to the concentration of ITO amount in the composite.

Charge Carrier Relaxation in Different Plasticized PEO/PVDF-HFP Blend Solid Polymer Electrolytes.

In this article, we report first the effect of concentration of ethylene carbonate plasticizer on conduction and relaxation of charge carriers in PEO/PVDF-HFP-LiClO4 blend electrolytes. Second, the results for different plasticizers, such as ethylene carbonate, propylene carbonate, and dimethyle carbonate, on the conductivity and relaxation in these blend electrolytes are compared. We have followed a new approach for the analysis of the conductivity data. The frequency dependent conductivity is analyzed using random free-energy barrier model, taking into consideration the low frequency polarization effect. The temperature dependences of the ionic conductivity and the relaxation time obtained from the model exhibit Vogel-Tammann-Fulcher behavior. Using the scaling of the ac conductivity spectra it is observed that the relaxation dynamics of charge carriers in blend electrolytes are independent of temperature but depend on the nature of plasticizers. The electric modulus is studied using Havriliak-Negami function for the understanding of ionic relaxation. The modulus data are also analyzed using nonexponential Kohlrausch-Williams-Watts function. The temperature dependence of the relaxation time obtained from modulus analysis follows Vogel-Tammann-Fulcher relation for all plasticized electrolytes. It is observed that the stretched exponent is much lower than unity, which suggests that charge carrier relaxation is highly nonexponential in these plasticized electrolytes.

Molecular Dynamics and Charge Transport in Highly Conductive Polymeric Ionic Liquids

Glassy dynamics and charge transport are studied for the polymeric ionic liquid (PIL) poly[tris(2-(2-methoxyethoxy)ethyl)ammonium acryloxypropyl sulfonate] (PAAPS) with varying molecular weight (9700, 44200, 51600, and 99500 g/mol) by broadband dielectric spectroscopy (BDS) in a wide frequency (10–2–107 Hz) and temperature range (100–400 K) and by DSC- and AC-chip calorimetry. The dielectric spectra are characterized by a superposition of (i) relaxation processes, (ii) charge transport, and (iii) electrode polarization. The relaxation processes (i) are assigned to the dynamic glass transition and a secondary relaxation. Charge transport (ii) can be described by the random free-energy barrier model as worked out by Dyre et al.; the Barton–Namikawa–Nakajima (BNN) relationship is well fulfilled over more than 8 decades. Electrode polarization (iii) follows the characteristics as analyzed by Serghei et al., with deviations on the low frequency side. The proportionality between the relaxation rate of the dynamic glass transition and the charge carrier hopping rate reflects the nature of charge transport as glass transition assisted hopping. Hereby, the PIL under study exposes the highest dc-conductivity values observed for this class of materials below 100 °C, so far; and for the first time a conductivity increase by rising degree of polymerization. The comparison of the polymeric ionic liquids under study with others implies conclusions on the design of novel highly conductive PILs.

Ion dynamics in AgI doped silver selenium-tellurite mixed former glasses

The ionic conductivity and the conductivity spectra of the glass compositions xAgI-(1-x)[yAg2O-(1-y)(0.5SeO2-0.5TeO2)] have been studied at different temperatures The activation energy for the dc conduction has been analyzed using the Anderson-Stuart model, and a correlation between the dc conductivity and the doorway radius has been obtained. We have analyzed the conductivity spectra using the random free-energy barrier model, taking into account the contribution of electrode polarization. It is observed that the Barton-Nakajima-Namikawa relation between the conductivity and the relaxation time is valid for these glasses. The time-temperature superposition principle has been verified using the scaling of the conductivity spectra in the framework of the random barrier model. The charge carrier density, obtained from the Nernst-Einstein relation, is found to be almost independent of temperature, but dependent weakly on composition. We have also studied the influence of the modification of the network structure of these glasses on ion migration and correlated the conductivity with the relative strength of the structural units.

Microstructural interpretation of vibrational properties and ionic transport mechanism in Dy stabilized δ-Bi2O3

The correlation of structure and microstructure with vibrational property and ionic conduction mechanism of Bi1-xDyxO1.5-δ (0.10 ≤ x ≤ 0.40) for different doping concentration has been investigated. Room temperature δ-phase stabilization of cubic Bi2O3 has been achieved by adding Dy2O3 as the dopant, using a low temperature citrate-auto-ignition method. The Rietveld refinement of the X-ray diffraction profiles has given detailed microstructural information of the prepared samples, which corroborates with TEM study. The Raman spectroscopy study clearly indicated the structural evolution due to Dy doping. Effect of doping concentration on vibrational property of δ-Bi2O3 has been investigated in detail. Impedance spectroscopy studies of the samples exhibited thermally activated non-Debye type relaxation process. A structural model has been used to explain the ion transport mechanism in the samples. The bulk conductivity, measured from impedance spectra and frequency independent part of ac conductivity of each of these compounds show Arrhenius type behavior. The random free-energy barrier model has been utilized to analyze the frequency dependence of the conductivity. Both impedance spectroscopy and ac conductivity analysis exhibited that the composition Bi0.75Dy0.25O1.5-δ shows maximum value of conductivity. Comparable values of activation energies, obtained from different parameters, indicated that the ions follow the same type of mechanism for conduction as well as for relaxation.

Random free energy barrier hopping model for ac conduction in chalcogenide glasses

The random free energy barrier hopping model is proposed to explain the ac conductivity (σac) of chalcogenide glasses. The Coulomb correlation is consistently accounted for in the polarizability and defect distribution functions and the relaxation time is augmented to include the overlapping of hopping particle wave functions. It is observed that ac and dc conduction in chalcogenides are due to same mechanism and Meyer-Neldel (MN) rule is the consequence of temperature dependence of hopping barriers. The exponential parameter s is calculated and it is found that s is subjected to sample preparation and measurement conditions and its value can be less than or greater than one. The calculated results for a − Se, As2S3, As2Se3 and As2Te3 are found in close agreement with the experimental data. The bipolaron and single polaron hopping contributions dominates at lower and higher temperatures respectively and in addition to high energy optical phonons, low energy optical and high energy acoustic phonons also contribute to the hopping process. The variations of hopping distance with temperature is also studied. The estimated defect number density and static barrier heights are compared with other existing calculations.

Structural and electrical properties of Er doped La2Mo2O9 oxide ion conductors

We have studied structure and ionic conductivity of La2−xErxMo2O9 (0.05 ≤ x ≤ 0.25). The phase transition observed in La2Mo2O9 is suppressed in Er substituted samples. Cubic β phase in these samples is confirmed from Rietveld refinement at room temperature. The densification of the samples and grain–grain connectivity are confirmed from scanning electron microscopic study. The X-ray photoelectron microscopic analysis confirms the presence of La, Er, Mo, and O in these samples. The different vibration modes of MoO4 tetrahedral units are confirmed from Fourier transform infrared spectroscopy. The full-widths at half-maximum of all the major absorption bands show high composition dependence. The impedance spectroscopic study is presented in wide temperature and frequency ranges. The temperature dependence of the ionic conductivity is differentiated into three regimes. The effect of grain, grain boundary and electrode polarization on the conductivity is analyzed. The frequency dependence of the conductivity is analyzed using the random free-energy barrier model. The charge carrier relaxation time and its activation energy have been determined from the analysis of the conductivity spectra using the model.

The ionic transport mechanism and coupling between the ion conduction and segmental relaxation processes of PEO20-LiCF3SO3 based ion conducting polymer clay composites.

A series of ion conducting polymer-clay composites has been prepared using a solution casting technique. Relaxation dynamics and the ionic transport mechanism are systematically studied employing broadband dielectric spectroscopy over a wide frequency and temperature range. Among different phenomenological and theoretical models for ion conduction in disordered ionic conductors, conductivity isotherm spectra are analysed using the modified Almond-West and random free energy barrier model. Conductivity scaling suggests that the ionic transport mechanism is independent of temperature, and a similar inference is also obtained using scaled electrical modulus spectra. DC conductivity along with conductivity and segmental relaxation time following the Vogel-Tammann-Fulcher relationship suggests coupling between the ionic transport and segmental relaxation processes. Electrical modulus and dielectric formalism are used to understand the conductivity and segmental relaxation processes, respectively. The presence of first and second universality in the ionic transport mechanism is discussed using the real part of conductivity spectra and dielectric loss spectra. The crossover between the first and second universality is explained using the Kramer-Krönig approach. The ion diffusion coefficient is investigated using Ratner's classical approach in combination with the modified Stokes-Einstein relationship to correlate the coupled nature of the ion conduction mechanism and polymer segmental motion.

Dynamics and relaxation of charge carriers in poly(methylmethacrylate)-based polymer electrolytes embedded with ionic liquid.

In the present paper, we have studied dynamics and relaxation of the charge carriers in polymethylmethacrylate-lithium bis(trifluoromethane sulfonyl)imide polymer electrolytes embedded with 1-butyl-1-methylpyrrolidinium bis(trifluoromethylsulfonyl)imide ionic liquid. We have analyzed the frequency dependent conductivity spectra using the random free-energy barrier model coupled with the contribution of electrode polarization in the low frequency region. The temperature dependence of ionic conductivity, and relaxation time obtained from the analysis of the spectra exhibits Vogel-Tammann-Fulcher type behavior. The Barton-Nakajima-Namikawa relation is consistent with the results obtained from the random free-energy barrier model. The scaling of ac conductivity spectra has been performed to understand the effect of temperature as well as the composition on the relaxation mechanism. The analysis of the ac conductivity also clearly indicates the existence of a nearly constant loss phenomenon at low temperatures or at high frequencies.

Ionic hopping conductivity in potential batteries separator based on natural rubber–nanocellulose green nanocomposites

In this work, the electrical properties of green nanocomposites based on natural rubber (NR) had been explored. Nanocellulose was extracted from the rachis of date palm tree and used as nanofillers in two forms: nanofibrillated cellulose (NFC) and cellulose nanocrystals (CNCs). The resulting samples were characterized by dielectric spectroscopy in a board temperature range (20°C–200°C) and in the frequency range of 0.1Hz to 1MHz. The temperature and frequency dependencies of conductivity give evidence for ion transport mechanism via the occurred agreement of experimental results with the employed hopping model (Random Free-Energy Barrier model). Conductivity was found to increase highly for filled nanocomposite, especially at high CNC content. Favorable interactions between NFC and NR were evidenced and assumed to be partially responsible for the lower conductivity of NFC-filled nanocomposites. The NR–CNC green nanocomposite films had a high potential to be used for electrical applications and they should be a very promising candidate for battery separators.

Conduction mechanism in amorphous rf-sputtered TeO2+y thin films

The wide range temperature (150 K to 470 K) and frequency (100 Hz to 1 MHz) dependence of the dielectric constant and ac conductivity of rf-sputtered TeO2+y thin films (y = 0 to 1) deposited in metal–insulator–metal configuration is studied. A decrease in the value of the dc conductivity measured at room temperature was observed with increasing y, whereas the ac conductivity and dielectric constant show an increasing trend. The values of the dielectric constant for temperatures more than 340 K were found to depend intensely on the frequency because of the intrinsic behavior of the films. The dielectric distribution data have been analyzed in terms of (i) a mixed conduction model (with a spread of relaxation times) and (ii) a random free energy barrier model (which assumes that the conduction mechanism is hopping, and the dielectric spread is correlated with dc conductivity). The reason for the dielectric spread has been discussed on the basis of these models. It has been observed that the dominant transport mechanism in TeO2+y film is purely hopping in the low temperature region (<340 K) and mixed conduction at high temperature (>340 K).

AC and DC electrical conductivity in natural rubber/nanofibrillated cellulose nanocomposites

In the present study, charge transport properties of natural rubber based nanocomposites are investigated. Natural rubber is doped at various doping rates with nanofibrillated cellulose extracted from the rachis of date palm tree. The physical origin of both direct current (DC) and alternating current (AC) conductivity of polymer matrix–cellulose nanocomposites has been investigated. In fact, high activation energy values from DC measurements prove that the conductivity in the present samples is of an ionic nature. In addition, DC conductivity is more thermally activated than AC conductivity suggesting the random free-energy barrier model to explain the hopping conduction mechanism. Moreover, AC conductivity of these composites is frequency and temperature dependent, it generally follows the exponential law σAC~ωs. Exponent s lies in the range 0<s<1, characterizing an ionic hopping mechanism. Finally, using the Barton–Nakajima–Namikawa (BNN) relationship implies that the same ionic hopping mechanism is responsible for both AC and DC conduction.

Analysis of the dielectric relaxation and ac conductivity behavior of polyvinyl alcohol‐cadmium selenide nanocomposite films

We adopt an analytical approach to study the dielectric relaxation and ac conductivity behavior of the polyvinyl alcohol (PVA) ‐ Cadmium Selenide (CdSe) nanocomposite films in the frequency range 100 Hz ≤ f ≤ 1 MHz and in the temperature range 298 K ≤ T ≤ 420 K. The CdSe nanoparticles are synthesized via a simple wet chemical route and are then impregnated into the polyvinyl alcohol matrix by 0.5 wt%, 1 wt%, and 4 wt%. About 1.7 times increase in effective permittivity (at 100 KHz) for the 4 wt% nanoparticle impregnated sample is observed from the analysis of the dielectric reinforcement function, which is attributed to the occurrence of interfacial polarization. It is found that the Cole‐Cole model with a dc conductivity correction term can well fit the permittivity data. We have found that the dielectric relaxation time increases with increase in nanoinclusion into the matrix but decreases with increase in temperature. However, the space charge carrier conductivity and free charge carrier conductivity increase either with increase in nano inclusions or with increase in temperature. AC conductivity behavior have been analyzed considering the Jonscher power law and Dyre's random free energy barrier model, which reveals lowering of the maximum barrier height and correlated barrier hopping as the prevalent charge transport mechanism for the nanocomposites. Electric modulus study indicates similar conductivity relaxation dynamics for the nanocomposites but the responses deviate appreciably from the simulated ideal Debye responses. POLYM. COMPOS., 38:287–298, 2017. © 2015 Society of Plastics Engineers

Glass transition dynamics and conductivity scaling in ionic deep eutectic solvents: The case of (acetamide + lithium nitrate/sodium thiocyanate) melts

A detailed investigation on the molecular dynamics of ionic deep eutectic solvents (acetamide + lithium nitrate/sodium thiocyanate) is reported. The study was carried out employing dielectric relaxation spectroscopy covering seven decades in frequency (10(-1)-10(6) Hz) and in a wide temperature range from 373 K down to 173 K, accessing the dynamic observables both in liquid and glassy state. The dielectric response of the ionic system has been presented in the dynamic window of modulus formalism to understand the conductivity relaxation and its possible connection to the origin of localized motion. Two secondary relaxation processes appear below glass transition temperature. Our findings provide suitable interpretation on the nature of secondary Johari-Goldstein process describing the ion translation and orientation of dipoles in a combined approach using Ngai's coupling model. A nearly constant loss feature is witnessed at shorter times/lower temperatures. We also discuss the ac conductivity scaling behavior using Summerfield approach and random free energy barrier model which establish the time-temperature superposition principle. These experimental observations have fundamental importance on theoretical elucidation of the conductivity relaxation and glass transition phenomena in molten ionic conductors.

Electrical transport properties of polyvinyl alcohol–selenium nanocomposite films at and above room temperature

Here, we report the DC and AC electrical properties of polyvinyl alcohol (PVA)–selenium (Se) nanocomposite films in the temperature (T) range 298 K ≤ T ≤ 420 K and in the frequency (f) range 120 Hz ≤ f ≤ 1 MHz. The introduction of selenium nanoparticles into the PVA matrix slightly increases the values of DC conductivity whose temperature dependency obeys Vogel–Fulcher–Tammann law. The AC conductivity follows a power law with frequency in which the temperature dependence of the frequency exponent suggests that the correlated barrier hopping is the dominant charge transport mechanism for the nanocomposite films. Comparative discussions with Dyre’s random free-energy barrier model have also been made in this regard. The increase in AC conductivity with increase in nanoparticles concentration was also observed and attributed to the corresponding increase in conducting channels in the PVA matrix. The real part of the dielectric constant increases either with increase in temperature or with increase in selenium nanoparticles loading into the polymer matrix, which may be attributed to the enhancement of interfacial polarization. The frequency dispersion of the dielectric spectra has been modeled according to the modified Cole–Cole equation. Well-defined peaks were appeared in the plotting of imaginary part of electric modulus with frequency above room temperature, which was fitted with suitable equations to account for the deviations from ideal Debye-type behavior. Though the current–voltage characteristics are linear at smaller voltages, it appreciably becomes nonlinear at higher voltages. This nonlinearity has been accounted in light of Werner’s model and back to back Schottky diode model.

Ionic conductivity and dielectric relaxation in Y doped La2Mo2O9 oxide-ion conductors

In this work, we have studied electrical conductivity and dielectric properties of polycrystalline La2−xYxMo2O9 (0.05 ≤ x ≤ 0.3) compounds in the temperature range from 358 K to 1088 K and the frequency range from 10 Hz to 3 GHz. The bulk and grain boundary contributions to the overall conductivity of these compounds show Arrhenius type behavior at low temperatures. The random free-energy barrier model has been used to analyze the frequency dependence of the conductivity. The charge carrier relaxation time and its activation energy have been determined from the analysis of the conductivity spectra using this model. The results obtained from the random free-energy barrier model satisfy Barton-Nakajima-Namikawa relation. The conduction mechanism has been also predicted using random free-energy barrier model and the scaling formalism. We have observed that the dielectric relaxation peaks arise from the diffusion of oxygen ions via vacancies.

Electrical and dielectric properties of silver iodide doped selenium molybdate glassy conductors

Electrical conductivity and dielectric properties of silver iodide doped silver ion mixed-former conducting glasses have been studied in this paper. The frequency dependence of conductivity has been analyzed following the random free-energy barrier model. The charge carrier relaxation time and the activation energy for relaxation have been determined for the present glasses. The applicability of Barton-Nakajima-Namikawa relation has been tested for the present glasses using the results obtained from random free-energy barrier model. The scaling of the conductivity spectra has been performed to understand the effect of temperature as well as composition on the relaxation dynamics. The dielectric data have been analyzed employing the Cole-Cole function, and parameters such as dielectric strength and Cole-Cole exponent have been obtained. The electrode polarization phenomenon for the present glass samples has been studied depending on temperature as well as composition. The different characteristic transitions concerning electrode polarization related to the charge transport at the interface have been obtained and are correlated to the bulk behavior. An estimation of the dc conductivity has been obtained using the result obtained from electrode polarization study and is observed to be very close to the experimental values.