A conceptual review on polymer electrolytes and ion transport models

Author links open overlay panel

, , ,

https://doi.org/10.1016/j.jsamd.2018.01.002Get rights and content

Under a Creative Commons license

open access

Abstract

This review article provides a deep insight into the ion conduction mechanism in polymer electrolytes (PEs). The concepts of different categories of polymer electrolytes are discussed. The significance of the existence of functional (polar) groups on the backbone of host polymers, which are used in polymer electrolytes, is well explained. The working principle of electrical impedance spectroscopy (EIS) is overviewed. The relationship between impedance plots and equivalent circuits, which are crucial for electrical characterization, is extensively interpreted. Based on the patterns of dc conductivity (σdc) versus 1000/T, the ion transport models of Arrhenius and Vogel–Tammann–Fulcher (VTF) are discussed. Effects of coupling and decoupling between ionic motion and polymer segmental relaxation are analyzed. The important role of dielectric constant on cationic transport in PEs is also explained. The relationships existing between electrical and dielectric parameters are elucidated, which help interpret and understand the ion conduction mechanism. From the reported empirical curves of dc conductivity vs. dielectric constant, the reformulated Arrhenius

equation is proposed. Finally, other important phenomena, occurring in polymer electrolytes, are shown to be understandable from the dielectric constant studies.. Introduction Various sources of alternative energy are continuously evolving to reduce the long-term dependence on oil, nuclear and other fossil fuels. The other environmentally friendly fuel cells, such as batteries, super capacitors and dye sensitized solar cells, are strong candidates for this reason [1]. The conception of polymer electrolytes (PEs) is a highly specialized and multidisciplinary field that covers the disciplines of electrochemistry, polymer science, organic and inorganic chemistry [2]. Dry solid polymer electrolytes (SPEs) have attracted great attention as safer alternatives to liquid electrolytes [3]. In the field of SPEs, a pioneering work was carried out by Wright et al. and cited by Singh and Bhat [4]. In their work, the dc conductivity of order of 10−5 S/cm at 330 K in highly crystalline polyethylene oxide-sodium thiocyanate (PEO–NaSCN) complexes was reported [4], [5]. The SPEs are formed by inorganic salts dissolution in a polar polymer matrix. The choice of PEs in modern applications, such as high energy density batteries, electrochromic devices, sensors and fuel cells, was justified by studying their structural, morphological and electrical properties [6], [7]. On the other hand, the choice of polymer hosts for PEs largely depends on two factors: first, the existence of polar (functional) groups with a large power of sufficient electron donor to form coordination with cations and, second, a low hindrance to bond rotation [2]. Fig. 1 shows the chemical structures of some important polymers that are widely used as host polymers in PEs. 📷Download : Download high-res image (268KB) Download : Download full-size image Fig. 1. Chemical structures of some polar polymers widely used for polymer electrolytes: (a) Poly (ethylene oxide) (PEO), (b) Poly(vinyl alcohol) (PVA), (c) Poly(methyl methacrylate) (PMMA), (d) Poly(ɛ-caprolactone) (PCL), (e) Chitosan (CS), (f) Poly(vinylpyrrolidone) (PVP), (g) Poly(vinyl chloride) (PVC), and (h) Poly(vinylidene fluoride) (PVDF).The good mechanical strength, ease of thin film fabrication with desirable shapes and the ability of forming good electrode/electrolyte contact are the main advantages of dry SPEs [6], [8], [9]. From the economical and commercial viewpoints, a low-cost membrane with good ionic conductivity, enhanced dimensional and mechanical stabilities are recent challenges to be invented. The main drawbacks of SPEs are their high crystallinity and low ionic conductivity [10]. Polymer electrolytes comprise both crystalline and amorphous regions. It has been well reported that the ion transport occurs mainly in the amorphous region rather than the crystalline region, but the polymers host materials that used in PEs are often semi-crystalline [4], [11]. Thus, to overcome the disadvantages and improve SPEs' conductivity, plasticizer, as one mostly applied method, has to be added to improve the ambient ionic conductivity. Through using plasticizers, the amorphous region and ion aggregates in PEs can be increased and dissociated, respectively, causing the dc electrical conductivity of SPE to be improved [12]. It has been established that the ionic conductivity in plasticized polymer electrolytes can be increased at the expense of decreased mechanical strength and vice versa [4], [13]. In addition to high conductivity and a broad electrochemical stability window, PEs must exhibit good thermal and mechanical properties. These performances can be achieved by dispersing nanosized fillers into polymer electrolyte. Following the creative work of Weston and Steele [4], [14], who have improved the ionic conductivity and mechanical stability of polymer electrolytes by adding Al2O3 particles, nanocomposite SPEs have been broadly studied. A complete understanding of the effects of inorganic fillers on the ion transport, thermal, mechanical and electrochemical properties of PEs is still not reached [15]. From the above survey, it is clear that the dc electrical conductivity can be improved by incorporating the plasticizer or inorganic fillers into the SPEs. But yet, the ion conduction mechanism in solid plasticized and composite polymer electrolytes is not fully understood [4]. The main goal of this review article is to shed light on different types of PEs and ion transport models. Additionally, the necessary of reformulation of Arrhenius equation based on recent experimental achievements in this field is elucidated.

2. Classifications of polymer electrolyte Polymer electrolytes have been proved to be promising materials in the research and development of electrochemical devices. Most of the research activities are devoted in the field of solid state electrochemistry, in which high ion-conducting materials are considered to be developed for the energy conversion and storage applications [16]. In this sense, PEs are a class of materials, which have been witnessed in the last 20 years by massive research efforts, to achieve systems with a good conductivity and an electrochemical stability [16], [17]. On the basis of materials, the polymer electrolytes have been categorized into dry solid polymer electrolyte, plasticized polymer electrolytes, gel polymer electrolytes, and composite polymer electrolytes [18]. 2.1. Polymer-salt complex or dry solid polymer electrolyte (DSPE) The concept of dissolving inorganic salts in functional (polar) polymer, thus creating an ion conducting solid electrolyte is known as a solid polymer electrolyte (SPE) [19]. The interactions of metal ions with polar groups of polymers are mainly resulting from electrostatic forces and accordingly the formation of coordinating bonds [20], [21]. There are some important factors that may have effect on the polymer-metal ion interactions, such as nature of the functional groups attached to the polymer backbone, compositions and distance between functional groups, molecular weight, degree of branching, nature and charge of metal cation, and counter ions [21]. The cations can transfer from one coordinated site to another when subjected to an electric field. This is due to the weak coordinate of the cations to sites along the polymer chain. For a better understanding of these technologically important materials, further study has to be conducted in this field, with a particular emphasis on their complex chemistry and ionic transport properties [19]. 2.2. Plasticized polymer electrolyte (PPEs) Plasticized polymer electrolytes, which are a branch of PEs, are prepared by incorporating the polymer host with low molecular weight compounds, such as ethylene carbonate, propylene carbonate and poly ethylene glycol (PEG) [22]. Plasticizers can reduce the number of active centers and thus weaken the intermolecular and intramolecular forces between the polymer chains [23]. Consequently, they result in lessening the rigidity of the three dimensional structure formed on drying, and changing the mechanical and thermo-mechanical properties of the prepared films [23], [24]. Therefore, the addition of low molecular weight plasticizers decreases the glass transition temperature of the PE system. Hence, the reduction of crystallinity and increment in salt dissociation capability are guaranteed, by which the enhancement of charge carrier transport is achieved. However, the resulting polymer electrolytes are predicted to obtain a low mechanical strength [25]. Recent studies have confirmed that the amorphous fraction of composite polymer electrolytes can be increased due to the plasticizers. It has been reported in ref. [26] that the crystallinity can be decreased when the plasticizer (PEG200) is added to the polyethylene oxide (PEO) based nanocomposite polymer electrolytes, as shown in Fig. 2b and c. It is obvious that the micrograph of PEO25-NaClO4 + 5 wt. % DMMT complex system [see Fig. 2a] shows the presence of spherulites. The boundary between the spherulites can be attributed to the presence of amorphous fraction. The surface roughness in Fig. 2a was ascribed to the existence of large amount of crystalline fraction in the PEO based polymer electrolyte. It was observed that the surface roughness was decreased upon the addition of plasticizer [see Fig. 2b and c], exhibiting a smooth surface texture. These changes could be attributed to the effect of plasticization that resulted in the reduction of crystallinity of the host polymer PEO and the enhancement of the overall amorphous fraction in the materials. 📷Download : Download high-res image (639KB) Download : Download full-size image Fig. 2. Optical micrographs of PPNCEs thin films of (PEO)25-NaClO4 + 5 wt.% DMMT + x wt.%PEG200 with different concentrations of x (i.e., (a) x = 0, (b) x = 10, and (c) x = 50) [26].From the above discussion, it is understood that the increase of SPE conductivity by addition of plasticizer at room temperature results in the loss of mechanical strength. Furthermore, plasticized polymer electrolytes exhibit a number of drawbacks, such as inadequate mechanical properties at high level of plasticization, reactivity of the polar solvents with lithium electrode and solvent volatility [22], [27]. 2.3. Gel polymer electrolytes (GPEs) Recently, a substantial effort in the field of polymer electrolytes has been given to gel-type polymer electrolyte (GPE). This is due to the fact that the advantages of liquid-type electrolytes, such as high ionic conductivity, and solid-state electrolytes, such as high safety, can be combined. In gel-type PE, polymer as a host matrix has been used to trap the liquid constituents. Therefore, the GPE based products are considered to be much safer than liquid-based electrolyte products, particularly, when it is used in lithium ion (Li-ion) batteries [28]. In the preparation of gel electrolytes, a large amount of organic solvent or plasticizer must be added into the polymer host [29]. The incorporated plasticizer molecules can form a wide network whereby the ion conduction takes place along with the host polymer, which principally provides structural support. Gel electrolytes can exhibit high ambient conductivities, but still undergo some other disadvantages as mentioned in the plasticized polymer electrolytes, such as the release of volatiles and increased reactivity towards the metal electrode [30]. Scheme 1 shows the influence of plasticizer on the percolative behavior of ion transport. It is clear that the portion of amorphous regions is well below a percolation threshold at room temperature (See the left hand side of Scheme. 1), resulting in the poor ionic conductivity. Plasticized polymer electrolytes with suitable liquid solvents that have high dielectric constant, ε, and low viscosity, η, are desired to form gel polymer electrolytes. Therefore, the amorphous regions grow larger in number and size, owing to the adsorption of liquid. This ultimately leads the percolation threshold to be accomplished at ambient temperature. The connected network of amorphous regions provides fast ion conducting pathways, which acts upon enhancing the ion mobility and hence the higher ionic conductivity [31]. 📷Download : Download high-res image (627KB) Download : Download full-size image Scheme 1. Transformation of a soft matter solid electrolyte such as polymer electrolyte with a non-percolative arrangement of highly disordered (higher ion mobility) regions to a percolative arrangement of disordered regions as in gel electrolytes. Percolative network of disordered regions provides fast ion transport pathways for the mobile ion [31]. 2.4. Composite polymer electrolytes (CPEs) One of the major reasons behind the poor ionic conductivity of polymer electrolytes has been attributed to the presence of ion-pairs (or ion-association) and ion triplets. This is due to weak dielectric constant of the host polymers [32]. Many approaches have been developed to avoid the occurrence of ion–ion association in polymer electrolytes. To solve these difficulties and improve the qualities of SPEs, inorganic inert fillers with high dielectric constant has been lately suggested to be dispersed in PEs [33]. Dielectric permittivity can be properly adjusted, simply by controlling the type and the amount of incorporated inorganic filler material. Ceramic materials, which are classified as inorganic fillers, are typically fragile and possess low dielectric strength [34]. Though, polymers have relatively low dielectric permittivity, they can undergo high fields, they are also flexible and easy to be processed. Therefore, by combining the advantages of these two materials, i.e., ceramic filler and polymer material, new hybrid composite materials with high dielectric constants can be fabricated [35]. When the size of these inorganic fillers is in the nano-dimension, the newly formed composites are called nanocomposite polymer electrolyte (NCPE) [10], [33]. Composite polymeric materials containing fine ceramic particles are considered as heterogeneously disordered systems [34], [36]. Their electrical property depends on the dielectric constant and their constituents' conductivity. Additionally, the volume fraction, size and shape of the added filler particles have impacts on the electrical performance of composite materials [34]. Li et al. [37] have successfully investigated the effect of in situ synthesized TiO2 on the morphology of poly (vinylidene difluoride-co-hexa fluoro propylene) (PVDF-co-HFP)) complexed with LiPF6. The surface and cross-section morphology of the PVDF-co-HFP polymer incorporated with different amounts of in situ synthesized TiO2 nanoparticles have been studied. They have observed many closed pores on the surface of the samples. They have found that the connected spherical pores are crucial in enhancing the ion mobility and ionic conductivity.

3. Electrochemical impedance spectroscopy (EIS) technique Electrochemical impedance spectroscopy (EIS) is a technique currently used to study the electrical properties of the bulk materials and their interfaces (i.e., electrode–electrolyte interfaces) over a wide range of frequency and temperature. It is also known as ac impedance spectroscopy (or dielectric spectroscopy). The bulk and interface contributions can be separated by using this technique. It can also be used to study the ion conduction mechanism and dielectric relaxation in PEs. 3.1. Origin of EIS theory Electrical charge displacements in a bulk material produce two distinct physical phenomena: (i) if the charge motion in a localized volume of the matter is strictly confined then a polarization phenomenon takes place or (ii) if the electrical charges in the materials are collectively diffused over long distances then diffusion is possible and a dc conductivity, σdc, is established [38]. In order to identify and overcome the effect of space charge polarization at the electrode/solid electrolyte interface, it is crucial to carry out the ac conductivity measurements by means of complex impedance spectroscopy (CIS), i.e., using an ac electric field [39]. It is established that, dielectric spectroscopy depends on the tendency of ions and dipoles to orient along the electric field direction [40]. When an ac electric field is applied to a parallel plate capacitor sandwich with polymeric materials, four categories of polarization are taken place, which are known as electronic, atomic, dipolar and migrating charge polarizations [41]. Ions often originate as impurities in the raw materials. Dipoles result from atoms with unequal electro negativities, which are attached to each other on the backbone of polymeric materials [40]. The dielectric relaxation processes are usually correlated to one or more polarization processes of the studied material. Dipolar polarization and polarization due to charge migration are the two main components of the dielectric responses in polymers. Dipolar and charge migration polarizations can be detected at frequencies less than 109 Hz [41]. If the electric field is reversed in sign (or direction), the dipoles will realigned with the applied field and the ions start to diffuse (or migrate) to the other electrode. As the frequency of field reversal increases, the ions and dipoles become increasingly difficult to keep up with the field changes. In addition to that the functional groups with larger sizes will be much harder to be reorienting with the field [40]. The investigation of conduction and different dielectric polarizations can eventually lead us to achieve more information on the dynamic behavior with regard to relaxation processes. 3.2. Complex impedance spectroscopy Characterization of heterogeneous and disorder materials requires non-destructive measurements. Dielectric impedance spectroscopy that measures the conductivity and permittivity as functions of frequency at different temperatures can provide insights into the electrical and structural properties of heterogeneous systems at both microscopic (molecular) and macroscopic levels [42]. The complex impedance spectroscopy (CIS) is a powerful experimental technique that provides several benefits, such as the calculation of relaxation frequency and separation of electrode (at low frequency spike) and bulk (at high frequency semicircular region) effects. Through using the CIS technique, the real (Z′) and imaginary (Z″) parts of impedance can be obtained over a wide range of frequency. Recently, this technique has been used successfully to evaluate the DC ionic conductivity and activation energy of ionic conductors [43]. In CIS measurements, an alternating voltage over a broad range of frequencies must be applied to an electrochemical sample holder [44]. Typically, the applied voltage (V) is a sinusoidal wave waveform that varies with time (t), defined as(1)

where V0 is the maximum voltage intensity and ω is the angular frequency. Likewise, the resulting electrical current (I) is a sinusoidal waveform with a phase difference (φ):(2)where Io is the maximum current intensity and φ is the phase angle between the applied voltage and current waveforms. The electrical impedance parameter, Z(ω), which defines the ratio between the applied voltage and the resulting electric current, , is expressed as(3)where and are the real and imaginary parts of the electrical impedance data, respectively, and they can be determined at a given frequency by [45],(4)(5)

The impedance experimental data can be analyzed by plotting the imaginary part

versus the real part

.

3.3. Impedance plots and equivalent circuits The direct relationship between the responses of a system under test and the proposed electrical equivalent circuit is considered to be an important characteristic of complex impedance spectroscopy (CIS) [46]. From the physics viewpoint, a resistance R is assigned to stand for the dissipative part of the dielectric response and a capacitance (C) is taken to denote the storage part of the dielectric material [46], [47]. From the electrical impedance spectroscopy (EIS) outputs, an impedance graph (imaginary part versus real part) can be plotted and thus information regarding an expected equivalent circuit can be extracted. Fig. 3 shows a typical example of EIS graphs and equivalent circuits. The real and imaginary parts of the impedance are associated with the existence of resistor and capacitor, which are in- and out-of-phases with the applied AC signal, respectively. They are generally represented by R or ZR or Z′ or Zreal and X or Zc or Z″ or Zimg, respectively. The imaginary part, which is also known as reactance, is given by [48],(6)

📷Download : Download high-res image (159KB) Download : Download full-size image Fig. 3. Cole–Cole plots and their equivalent circuits for (a) a pure resistor, (b) a pure capacitor, (c) a capacitor and a resistor in series, (d) a capacitor and a resistor in the parallel combination, and (e) a leaky system [48]. Resistor is represented by the symbol📷 and capacitor represented by📷 .

The demonstration of these simple elements on the complex impedance plane is called an “Argand diagram” as illustrated in Fig. 3a and b. The imaginary part of the impedance, reactance, is plotted against the real part, resistance, over a range of frequency [48]. If there is a resistor connected in series with a capacitor, the total impedance ZRC becomes [48],(7)

The complex impedance plot corresponding to Eq. (7) is illustrated in Fig. 3c. The impedance plot of a parallel combination of a single resistor and a capacitor, ZR−C, has a semicircular shape on the complex impedance plane, as shown in Fig. 3d. Qualitatively, this behavior can be easily understood. The impedance of the capacitor at very low frequencies becomes very large. Thus the majority of the current is flown through the resistor, causing its properties to be dominated. On the other hand, the impedance of the capacitor at very high frequencies becomes very small, such that the resistor is effectively shorted out and gives rise to zero net impedance [48]. Experimental evidence reveals that in complex impedance plane plots the low frequency tail is not truly vertical as illustrated schematically in Fig. 3e. Fig. 4 shows an experimental data example of this behavior. Most commonly, it is impossible for the ac response to be described by using simple ideal circuits. The semicircles showing in the complex (Z″-Z′) plane are often widened and deformed to asymmetrical arcs [49]. One can see in Fig. 4 that the center of the semicircles lies below the real Z′ axis. 📷Download : Download high-res image (179KB) Download : Download full-size image Fig. 4. Impedance plot of PVA:AgNt (75:25) at 303 K [50].The impedance response of PVA:AgNt (75:25) reveals the semicircular and spike regions at high and low frequencies, respectively. The semicircle at high frequency indicates the bulk response of the sample, whereas the spike at low frequency can be attributed to the accumulated double layer charges at the solid polymer electrolyte/electrodes interfaces. At low frequencies, the impedance plots should expose a straight line parallel with the imaginary axis; though the electrode polarization effect (double layer capacitance) at the blocking electrodes induces a curvature [50], [51], [52].

3.4. Impedance-related functions The electrical impedance spectroscopy (EIS) has become an important tool for characterizing the electrical properties of various materials, such as glasses, amorphous semiconductors, electronically conducting polymers, ion conducting polymers and transition metal oxides [53], [54]. There are several other derived or measured quantities associated with the impedance, which are important in the EIS. The electrical impedance (Z*), admittance (Y*), modulus (M*) and permittivity (ε*) are the four important impedance-related functions, which can be measured, analyzed and plotted in the complex plane in the EIS [55]. Dielectric permittivity (ε*) measurements, such as dielectric constant (ε′) and dielectric loss (ε″), can reveal significant information regarding the chemical and structural characteristics of polymers. It is established that these polymer characteristics can be drastically affected by the existence of other dopants in the polymer [56]. The detailed investigations of the dielectric parameters and electrode and interfacial polarization effects of polymers are of great importance [57]. On the other hand, the study of conductivity relaxation behavior in conducting polymer materials has become an interesting area of active research in condensed matter physics due to their potential applications in electrochemical solid state devices [58], [59]. It has been reported that electric modulus (M*) formalism can be used as an effective tool to predict the relaxation behavior of ion conducting polymeric materials. Through the spectrum of electric modulus, conductivity and its associated relaxation in polymers can be possibly investigated [59], [60]. The two essential quantities in dielectric relaxation spectroscopy are the complex dielectric constant or the dielectric permittivity

and the modulus function . In these expressions, is the capacitance of the empty measuring cell, where A and d refer to the area and separation length of the electrode. The quantity

is the dielectric permittivity of free space, which is equal to 8.854 × 10−12 Fm−1. Table 1 summarizes the interrelations between the four immittance functions [55].

Table 1. Relations between the four basic impedance functions [55].

Functions

μμμ−1μ−1μμμ−1μ−1

, where Co is the capacitance of the empty cell, Y∗ is admittance.

4. Ion transport models for polymer electrolytes A crucial feature that distinguishes ion conducting polymer electrolytes from other ionic conductors is that polymer electrolytes are formed by dissolving low lattice energy salts in a polar polymer matrix. For this reason, the cations are found to be responsible for the dc ionic conductivity. In agreement with the theories of cationic transport in high molar mass polymer electrolytes, long range cation transport only takes place by dissociative steps, in which cations can move between neighboring coordinating sites, whether situated on the host molecule or on a nearby host molecule [61]. It might therefore be predicted that cations, forming non-labile bonds with polar groups of the host polymer, would not promote the dc conductivity of a polymer electrolyte [61]. Fig. 5 shows the ionic motion of a lithium ion in a PEO-host. 📷Download : Download high-res image (61KB) Download : Download full-size image Fig. 5. Cartoon of ion motion in a polymer host [62].It has been established that polymer electrolytes comprise both amorphous and crystalline fractions at room temperature. It is known that ion transport principally occurs in the amorphous regions. Despite the fact that the conduction mechanisms are not fully understood yet, it is widely recognized that cations, which are interconnected with functional groups of the host polymer chains, can move through re-coordination along the polymer backbone [63]. Based on recent review works, the polymer chains are reported to be folded to form cylindrical tunnels, in which the cations are located and coordinated by the functional groups [64], [65]. These cylindrical tunnels create channels, providing a pathway for the movement of cations. The study of dc conductivity vs 1000/T can be conducted to identify the crystalline and amorphous nature of solid polymer electrolytes as can be seen in later sections. This is related to the fact that the result of this investigation can be interpreted in terms of one of the following models: 4.1. Arrhenius model for ion transport The characteristic advantage of selecting solid polymer electrolytes in a particular application of electrochemical device is basically resulting from the value of dc conductivity. In this section, the relationship between the dc conductivity and temperature is explained in accordance with the well-known Arrhenius model, given by the equation:(8)

where σo, Ea and kB are the pre-exponential factor, activation energy and Boltzmann constant, respectively. The Arrhenius-like relationship reported in Ref. [66] represents the fact that the motion of cations does not arise from the molecular motion of polymer host. Therefore, as soon as the data of temperature and ionic conductivity obeys the Arrhenius relationship, the mechanism of cation transport can be associated with that occurring in ionic crystals where ions jump to the nearest vacant sites, causing the dc ionic conductivity to increase to a higher value [67]. Recently, Ravi et al. [68], have observed the Arrhenius relationship between the dc conductivity and 1000/T for a solid polymer electrolyte system based on poly (vinyl pyrrolidone) (PVP) complexed with KClO4 as shown in Fig. 6. Similar Arrhenius behavior has been reported by Baskaran et al. [69] and by Kadir et al. [70] for PVA:LiClO4 and chitosan-PVA:NH4NO3 polymer electrolytes, respectively. 📷Download : Download high-res image (289KB) Download : Download full-size image Fig. 6. Arrhenius plots for PVP:KClO4 polymer electrolyte with different concentrations of KClO4 salt [68].Most of polar polymers used in the preparation of polymer electrolytes are semicrystalline polymers, i.e., containing both crystalline and amorphous phases. For instance, host polymer PEO has a glass transition temperature, Tg, of −67 and melting temperature, Tm, of about 68 °C. The existence of a high crystallinity fraction of PEO below Tm, can prevent the movement of small chain segments (i.e., segmental motion) in the PEO polymer. However, the crystalline regions are completely absent above the melting temperature (Tm) and hence a relatively high extent of segmental motion would be expected, and result in a high dc conductivity [71]. The two regions for the plot of dc conductivity versus inverse temperature (1000/T) have been outlined for the PEO based polymer electrolytes as can be seen in Fig. 7. At temperature below Tm (i.e., in region I), the dc conductivity was observed to increase gradually with the temperature up to 70 °C, as depicted in Fig. 7. On the other hand, above the Tm temperature (i.e., in region II), the conductivity was noticed to abruptly increase with temperature compared to that of region I. This is due to that, at high temperature, the energy would be large enough to overcome the potential barriers that created between the sites and thus leads to increase the free volume in the system, which facilitates the segmental motion of ionic charge carriers [72]. Therefore, the segmental motion either allows the ions to be hoped from one site to another site or offers a pathway for ions to be moved [71], [72]. It is therefore understood that, in polymer electrolytes, the ionic motion can takes place through the transitional motion/hopping and dynamic segmental motion of the host polymer [72], [73]. As the amorphous phase progressively swells at high temperature (i.e., region II), the polymer chain gains faster internal modes in which bond rotation creates segmental motion. This, successively, favors the inter-chain and intra-chain ion hopping of ion movements and the conductivity of the polymer electrolyte accordingly becomes higher [73], [74]. 📷Download : Download high-res image (561KB) Download : Download full-size image Fig. 7. Temperature dependence of dc conductivity of (a) pure PEO, (b) (PEO + NaClO3) (90:10), (c) (PEO + NaClO3) (80:20), and (d) (PEO + NaClO3) (70:30) [72].

4.2. Vogel–Tammann–Fulcher (VTF) model for ion transport Another important empirical model used to study the ion transport in polymer electrolytes is the Vogel–Tammann–Fulcher (VTF) model. In this model, a strong inter-relation between the conductivity and segmental relaxation in polymers is anticipated [75]. The non-linear Arrhenius plot of temperature-dependent dc conductivity data can be accurately described by the VTF equation [76] as follows:(9)

where, A is the pre-exponential factor related to the number charge ions, kB is the Boltzmann constant, B is the pseudo-activation energy associated with the polymer segmental motion and To (To = Tg − 50 K) is the temperature corresponding zero configurational entropy. In Ref. [77], the authors studied the VTF behavior of polymer electrolytes based on (x)PVAc–(1−x)PVdF: LiClO4, as shown in Fig. 8. They ascribed the non-linearity behavior of dc ionic conductivity to the fact that ion transport is assisted by the polymer segmental motion. Based on the VTF model, the curvature behavior of the Arrhenius plots has been attributed to the presence of strong inter-relation between the ionic motion and polymer segmental relaxation as mentioned earlier. This also implies that the polymer segmental relaxation and ionic motion are well coupled with each other.

📷Download : Download high-res image (195KB) Download : Download full-size image Fig. 8. Temperature dependence of ionic conductivity for PVAc:PVdF:LiClO4 polymer electrolytes containing various blend ratios [77].

Furthermore, Kim et al. [78] and Uma et al. [79] have explained the curvature feature of dc conductivity versus inverse temperature. They have confirmed that the VTF behavior can still be retained, in which the ion transport is correlated with the polymer segmental motion. However, in Ref. [80], the coupling between cation transport and segmental motion of the polymer has been demonstrated by the curvature of dc ionic conductivity versus 1000/T. As earlier mentioned, the free volume model can be used to understand the correlation between ion transport and segmental mobility. The extensive and intensive survey of literature revealed that most of researchers have applied the free volume model to interpret the abrupt increase in the dc conductivity at high temperatures (Arrhenius or VTF behavior). This agrees with the explanation that the polymer will expand and produce free volume as the temperature increases. Therefore, through the produced free volume, the polymer segments, ions or solvated molecules can easily move. Consequently, increased values are expected in ion and segmental mobility, which will assist the ion transport [81]. The question is, despite the existence of polymer segmental motion, why does still the Arrhenius conductivity linearly behave at higher temperatures? This can be explained by the fact that, at higher temperature, the increase in conductivity can be attributed to the vibrational dynamics of the polymer backbone and side chains. The increase of vibrational amplitude can bring the coordination sites closer together and enable the ions to hop from their occupied site to an adjacent empty site, using less energy [8]. In other words, the polymer segmental motion is decoupled completely from the ionic motion, i.e., the polymer segmental motion just brings the coordination sites closer together and hence ions can be easily hopped from one site to another. The pattern of dc conductivity versus 1000/T as a result becomes linear as occurred for ionic crystals. From the above discussion, it is understood that the linear and curvature behaviors of dc conductivity can be ascribed to the coupling and decoupling mechanisms between the ionic and polymer segmental motions, respectively.

It is understood from the above discussions on Arrhenius and VTF models that the increase of ion conductivity can be attributed to the hopping rate and segmental mobility increments, respectively. In addition to these models upon ion transport and conductivity behavior, ion dissociation energy and dielectric constant also have a great influence on the conductivity behavior of a polymer electrolyte. It has been reported that the dielectric relaxation study in ion conducting polymer electrolytes provides information with regard to the characteristics of ionic and molecular interactions [82]. Recently, many researchers have considered the dielectric analysis in their studies to understand and explain the conductivity behavior of solid and nanocomposite polymer electrolytes [4], [12], [83], [84], [85], [86]. Ion transport study is the subject of investigation by many researchers and various articles have been published previously on different polymer electrolytes/nano-composites and most of them interpreted the conduction mechanism based on VTF and Arrhenius models without deep insights [87], [88], [89], [90], [91], [92], [93], [94], [95], [96]. The focus of researchers on SPEs and nanocomposites is related to that fact that SPEs are light weight, flexible and they are important for power storage technologies such as super-capacitors and lithium-ion batteries [89], [91], [92], [93], [94], [95], [96]. Petrowsky and Frech in their recent works [97], [98] have hypothesized that the dc conductivity is not only temperature-dependent, but is also a function of the dielectric constant in organic liquid electrolytes. They have also explained the curvature feature of dc conductivity due to the dependency of pre-exponential factor, σo, on the dielectric constant,

.

4.3. Role of dielectric constant on ion conduction mechanism The concentration of ionic species in polymer electrolyte depends on the dielectric constant of the host polymer and the lattice energy of the salt. In other words, the higher the dielectric constant of the host polymer and/or the lower the lattice energy of the added salt, the higher the charge carrier concentration [99], [100]. The dc ionic conductivity, σ, of an electrolyte can be given as [100]:(10)

where ni is the charge carriers concentration, q is the electron charge and μi is the ions mobility, where i refers to the type of the ions [4]. It is clear from Eq. (10) that the ionic conductivity (σ) can be increased by increasing either the charge carrier concentration (n) or the ionic species mobility in the system. It has also been reported that the carrier density, n, relies mainly on both dissociation energy (U) and dielectric permittivity (ε′) of the host material as given below [101], [102]:(11)

where kB and T refer to the Boltzmann constant and absolute temperature, respectively. However, due to the presence of direct link between dielectric permittivity (ε′) and charge carriers, the increase of dielectric constant could be interpreted as a fractional increase in charge concentrations in the electrolyte. This is due to the fact that dielectric constant is related to the ratio of the material capacitance (C) to the capacitance of the empty cell (Co) (ε׳ = C/Co) while the capacitance is also related to the amount of stored charge (C = Q/V), where Q is the total charge and V is applied voltage. As it is stated in Eq. (10), conductivity (σ) depends on the amount of charge carrier concentration (n) and the mobility of the ionic species in the system [103]. However, from Eq. (11), charge carrier concentration (n) can be increased by increasing the dielectric constant. Therefore, the conductivity increases with the increase of dielectric constant based on Eqs. (10), (11). The above equations indicate the fact that the dielectric analysis is an informative approach to study the conductivity behavior of polymer electrolytes [4]. Thus, from the models presented in previous sections regarding the ion transport and the correlation between dc conductivity and dielectric constant ε′, it is understood that ion transport in polymer electrolytes is a complicated subject [104]. The incomplete understanding of the cation transport mechanism in polymer electrolytes is believed to be one of the main obstacles in fulfilling a high conducting polymer electrolyte at room temperature [105], [106]. Ramesh et al. [107] have used dielectric constant to study the conductivity behavior of non-plasticized and plasticized PVC-PMMA-LiCF3SO3 polymer electrolyte, in which the increase of the dielectric constant of the plasticized system is attributed to the increase of charge carrier density.

In Ref. [108], the effect of ethylene carbonate (EC) on the dielectric properties of PVA:LiBr:H2SO4 polymer electrolyte was studied. It was shown that the increment of storage charge was attributed to the increase of dielectric constant in the material, owing to the ion dissociation in the EC plasticized polymer system. Ethylene carbonate (EC) plasticizer has been shown that to have higher dielectric constant, PVA and thus more salts can be dissociated. This is consistent with those obtained from Eq. (11) as mentioned earlier. Various researches have been conducted to study the dielectric properties of polymer electrolytes and nanocomposite polymer electrolytes [50], [109], [110], [111], [112]. It is commonly recognized that the electrical impedance spectroscopy is an essential experimental technique for studying the dynamics of ion transport. An ac device has been used to measure the capacitive (imaginary) and resistive (real) component as a function of frequency for the sample inserted between two electronically conducting electrodes [113].

From the above surveys, it is clear that the ion carrier concentration and segmental mobility are not the only factors that determine the conductivity behavior of polymer electrolyte, but the dielectric constant and ion dissociation energy are just as important for ion transport. In our recent works, the role of dielectric constant on the dc ionic conductivity in solid and nanocomposite polymer electrolytes has been established. Similar trends were observed in the data sets of dc ionic conductivity (see Fig. 9) and dielectric constant (see Fig. 10) obtained for the PCL based electrolyte with LiBOB concentrations, in which a strong correlation between these two parameters has been revealed [2]. They were found to be increased with increasing LiBOB concentrations up to 4 wt. % and then dropped with further addition of LiBOB salt. In another work, a further confirmation of the influence of dc conductivity on dielectric constant has been made for chitosan complexed with 10 wt. % of NaTf salt, as can be seen in Fig. 11a [11]. The increase of dc conductivity (see Fig. 11) at higher temperatures has been ascribed to the increase of dielectric constant at higher temperatures (see Fig. 11). The smooth curve shown in Fig. 11 can be regarded as an empirical description of the dependence of σdc on the dielectric constant (ε′) at different temperatures [5]. This dependency in polymer electrolytes can be explained as follows. In polar polymers, as the temperature increases, the dielectric constant also increases, owing to the facilitation of dipole orientation. Consequently, this leads the degree of salt dissociation and re-dissociation of ion aggregates to be increased and the number of free ions or charge carrier density to be increased [11]. Therefore, this implies that the higher free ions, the higher the dc conductivity. In addition to that, the smooth curve obtained between the dc conductivity and dielectric constant for the nano-composite system (see Fig. 11b) validates the requirement of reformulation of Arrhenius equation. The dependence of dc conductivity on dielectric constant (see Fig. 11c) has also been reported for the chitosan:AgTf (90:10) system [104]. The recently reported results and achievements reveal that the study of dc conductivity and dielectric permittivity (ɛ*) are significant in understanding the ion conduction mechanism in polymer electrolytes [2]. Recently, the reformulated Arrhenius equation for CS:LiTf (90:10) solid polymer electrolyte has been satisfied. The activation energy, estimated from the reformulated Arrhenius equation (

), was found to be Ea = 1.36 eV and greater (see Fig. 12b) than that obtained from Arrhenius equation (Ea = 1.15 eV) (see Fig. 12a) [114]. It has been concluded that polymer electrolytes with low dc conductivity (≈10−10 S/cm) requires the activation energy for ion hopping to be large [114]. Therefore, the activation energy obtained from the reformulated Arrhenius equation is more satisfactory. However, further study in this field is required to show the validity of the dc conductivity dependence on dielectric constant in solid and nanocomposite polymer electrolytes, thus reformulating the Arrhenius equation. 📷Download : Download high-res image (113KB) Download : Download full-size image Fig. 9. dc ionic conductivity of PCL with various concentrations of LiBOB salt [2]. 📷Download : Download high-res image (100KB) Download : Download full-size image Fig. 10. Composition dependence of dielectric constant (at 1 kHz) for PCL as a function of LiBOB concentration (wt.%) at room temperature [2]. 📷Download : Download high-res image (365KB) Download : Download full-size image Fig. 11. dc conductivity dependence on dielectric constant for (a) chitosan:NaTf (90:10) CS10 sample (ɛʹ at 10 kHz) [11] at (1) 303, (2) 313, (3) 323, (4) 333, (5) 343, and (6) 353 K, (b) CSNB2 system [4] at (1) 303, (2) 308, (3) 313, (4) 318, (5) 323, (6) 328, and (7) 333 K, and (c) chitosan:AgTf (90:10) sample [104] at (1) 303, (2) 308, (3) 313, (4) 318, (5) 323, (6) 333, (7) 338 and (8) 343 K. 📷Download : Download high-res image (328KB) Download : Download full-size image Fig. 12. Temperature dependence of dc conductivity using (a) Arrhenius and (b) Reformulated Arrhenius equations [114].Several important phenomena in polymer electrolytes can be identified by studying their dielectric constant. In our previous work [8], the dc conductivity for the chitosan:AgTf solid polymer electrolyte at higher temperatures has been found to be decreasing due to the reduction of silver ions to silver particles. This silver ions (Ag+) transformation to silver particles (Ago) means reducing the number of involving silver ions in the conduction of charge as expected from Eq. (10). The existence of such silver particles induces grain boundaries and thus increases the resistance within the bulk of the material [8]. In our previously reported study on dielectric constant for the chitosan:AgTf system at high temperatures (see Fig. 13), this transformation phenomenon and its effects on dc conductivity have been confirmed [115]. Evidence for this transformation and its effects on the dc conductivity and dielectric constant in the chitosan:AgTf system has been given in detail in the Refs. [8] and [115]. Moreover, in another recent work, we have demonstrated the importance of the dielectric constant study in understanding the electrical percolation phenomenon in ion conducting solid polymer composites (see Fig. 14) [116]. Therefore, from the above reviews and findings, it can be noted that the study of dielectric constant is a viable informative technique to predict the conductivity behavior of polymer electrolytes and other physical phenomena as mentioned above. 📷Download : Download high-res image (228KB) Download : Download full-size image Fig. 13. Temperature dependence of dielectric constant (ε′) at different frequencies for the chitosan:AgTf (90:10) SPE6 [115]. 📷Download : Download high-res image (164KB) Download : Download full-size image Fig. 14. Bulk dielectric constant (ɛʹ at 1 MHz) and dc conductivity of chitosan (CS) as a function of AgI concentration [116].

5. Concluding remarks The concepts of different categories of polymer electrolytes have been discussed. Different materials' design in polymer electrolytes, such as plasticized polymer electrolytes (PPEs), gel polymer electrolytes (GPEs) and composite polymer electrolytes (CPEs), has been mainly aimed at developing dry solid polymer electrolytes (DSPEs) with a high amorphous content, in which a higher ion transmission can be provided. The significance of presence of functional (polar) groups on the backbone of host polymers, which are used in polymer electrolytes, has been revealed. A comprehensive explanation has been given on the working principle of electrical impedance spectroscopy, which is an important technique for electrical characterization of polymer electrolytes. The relationship between impedance plots and equivalent circuits, which are crucial for electrical characterization, has been analyzed in detail. The Arrhenius and Vogel–Tammann–Fulcher (VTF) models for ion transport have been shown to be inadequate in interpreting the ion conduction mechanism. It has been pointed out that the crystalline phases have a great influence on lowering the dc ionic conductivity in polymer electrolytes. Therefore, the researchers are encouraged to redirect their intention of research towards the development of new polar polymers with high amorphous contents. Effects of coupling and decoupling between the ionic motion and polymer segmental relaxation on the pattern of dc conductivity have been elucidated. In reference to our recent publications, the role of dielectric constant on cationic transport in polymer electrolytes has been shown to be crucial. The importance of the electrical and dielectric parameters relationships has been emphasized to understand the ion conduction mechanism. The presence of an empirical smooth curve between the dc conductivity and dielectric constant has revealed that the ion conduction mechanism in condensed matter physics is not a straightforward subject and the current ion transport models have to be reformulated. Some other important physics phenomena occurring in polymer electrolytes can be understood from the dielectric constant studies.

Acknowledgements The author gratefully acknowledges the financial support from the Ministry of Higher Education and Scientific Research-Kurdistan Regional Government- University of Sulaimani, College of Science-Department of Physics and University of Malaya for this research. The financial support from Komar Research Center (KRC) at Komar University of Science and Technology for this study is greatly acknowledged.

References [1]E.P. Chávez, R. Oviedo-Roa, G. Contreras-Pèrez, J.M. Martínez-Magadán, F.L. Castillo-AlvaradobTheoretical studies of ionic conductivity of crosslinked chitosan membranesInt. J. Hydrogen Energy, 35 (2010), pp. 12141-12146

View PDFView articleView in ScopusGoogle Scholar[2]

S.B. Aziz

Li+ ion conduction mechanism in poly (e-caprolactone)-based polymer electrolyte

Iran. Polym. J., 22 (2013), pp. 877-883

CrossRef

View in ScopusGoogle Scholar[3]

T. Itoh, Y. Mitsuda, T. Ebina, T. Uno, M. Kubo

Solid polymer electrolytes composed of polyanionic lithium salts and polyethers

J. Power Sources, 189 (2009), pp. 531-535

View PDFView articleView in ScopusGoogle Scholar[4]

S.B. Aziz, Z.H.Z. Abidin

Ion-transport study in nanocomposite solid polymer electrolytes based on chitosan: electrical and dielectric analysis

J. Appl. Polym. Sci. (2015), 10.1002/APP.41774

Google Scholar

[5]

T.H.J. Singh, S.V. Bhat

Morphology and conductivity studies of a new solid polymer electrolyte: (PEG)xLiClO4

Bull. Mater. Sci., 26 (2003), pp. 707-714

View in Scopus

Google Scholar[6]

S.B. Aziz, Z.H.Z. Abidin

Innovative method to avoid the reduction of silver ions to silver nanoparticles (Ag+→Ago) in silver ion conducting based polymer electrolytes

Phys. Scripta, 90 (2015), p. 035808

CrossRef

View in ScopusGoogle Scholar[7]

L. Zang, J. Luo, J. Guo, H. Liu, J. Ru

Preparation and characterization of poly(ethylene glycol)/organo-vermiculite nanocomposite polymer electrolytes

Polym. Bull., 65 (2010), pp. 669-680

CrossRef

View in ScopusGoogle Scholar[8]

S.B. Aziz, Z.H.Z. Abidin, A.K. Arof

Effect of silver nanoparticles on the DC conductivity in chitosan-silver triflate polymer electrolyte

Physica B, 405 (2010), pp. 4429-4433

View PDFView articleView in ScopusGoogle Scholar[9]

M. Hema, S. Selvasekarapandian, G. Hirankumar, A. Sakunthala, D. Arunkumar, H. Nithya

Structural and thermal studies of PVA: NH4I

J. Phys. Chem. Solid., 70 (2009), pp. 1098-1103

View PDFView articleView in ScopusGoogle Scholar[10]

M.M. Borgohain, T. Joykumar, S.V. Bhat

Studies on a nanocomposite solid polymer electrolyte with hydrotalcite as filler

Solid State Ionics, 181 (2010), pp. 964-970

View PDFView articleView in ScopusGoogle Scholar[11]

S.B. Aziz, Z.H.Z. Abidin

Electrical conduction mechanism in solid polymer electrolytes: new concepts to Arrhenius equation

J. Soft Matter, 2013 (2013), p. 8, 10.1155/2013/323868

323868

Google Scholar

[12]

D.K. Pradhan, R.N.P. Choudhary, B.K. Samantaray

Studies of dielectric and electrical properties of plasticized polymer nanocomposite electrolytes

Mater. Chem. Phys., 115 (2009), pp. 557-561

View PDFView articleView in ScopusGoogle Scholar[13]

M. Deka, A. Kumar

Electrical and electrochemical studies of poly(vinylidene fluoride)–clay nanocomposite gel polymer electrolytes for Li-ion batteries

J. Power Sources, 196 (2011), pp. 1358-1364

View PDFView articleView in ScopusGoogle Scholar[14]

J.E. Weston, B.C.H. Steele

Effects of inert fillers on the mechanical and electrochemical properties of lithium salt-poly(ethylene oxide) polymer electrolytes

Solid State Ionics, 7 (1982), pp. 75-79

View PDFView articleView in ScopusGoogle Scholar[15]

F. Alloin, A.D.’ Aprea, N. El-Kissi, A. Dufresne, F. Bossard

Nanocomposite polymer electrolyte based on whisker or microfibrils polyoxyethylene nanocomposites

Electrochim. Acta, 55 (2010), pp. 5186-5194

View PDFView articleView in ScopusGoogle Scholar

• [16]V.D. Noto, E. Negro, S. Lavina, M.V. DelloHybrid Inorganic–Organic Polymer ElectrolytesWoodhead Publishing Limited (2010)Google Scholar

[17]

J. Muldoon, C.B. Bucur, N. Boaretto, Th. Gregory, V. Di Noto

Polymers: opening doors to future batteries

Polym. Rev., 55 (2015), pp. 208-246

CrossRef

View in ScopusGoogle Scholar

• [18]V.D. Noto, B. ScrosatiPolymer electrolytes: present, past and futureElectrochim. Acta, 57 (2011), pp. 4-13Google Scholar

[19]

L. Edman, M.M. Doeff, A. Ferry, J. Kerr, L.C. De Jonghe

Transport properties of the solid polymer electrolyte system P(EO)n LiTFSI

J. Phys. Chem. B, 104 (2000), pp. 3476-3480

View in Scopus

Google Scholar[20]

B.L. Rivas, A. Maureira, C. Guzmán, M.A. Mondaca

Poly(2-acrylamido glycolic acid-co-2-acrylamido-2-methyl-1-propane sulfonic acid): synthesis, characterization, and retention properties for environmentally impacting metal ions

J. Appl. Polym. Sci., 111 (2009), pp. 78-86

CrossRef

View in ScopusGoogle Scholar[21]

B.L. Rivas, E.D. Pereira, I. Moreno-Villoslada

Water-soluble polymer–metal ion interactions

Prog. Polym. Sci., 28 (2003), pp. 173-208

View PDFView articleView in ScopusGoogle Scholar[22]

A.M. Stephan, T.P. Kumar, M.A. Kulandainathan, N.A. Lakshmi

Chitin-incorporated poly (ethylene oxide)-based nanocomposite electrolytes for lithium batteries

J. Phys. Chem. B, 113 (2009), pp. 1963-1971

CrossRef

View in ScopusGoogle Scholar[23]

S. Honary, H. Orafai

The effect of different plasticizer molecular weights and concentrations on mechanical and thermomechanical properties of free films,

Drug Dev. Ind. Pharm., 28 (2002), pp. 711-715

View in Scopus

Google Scholar[24]

S. Honary, M. Golkar

Effect of polymer grade and plasticizer molecular weights on viscoelastic behavior of coating solutions

Iran. J. Pharm. Res., 2 (2003), pp. 125-127

View in Scopus

Google Scholar

• [25]M.A.S. Samir, A.M. Mateos, F. Alloin, J.-Y. Sanchez, A. DufresnePlasticized nanocomposite polymer electrolytes based on poly(oxyethylene) and cellulose whiskersElectrochim. Acta, 49 (2004), pp. 4667-4677Google Scholar

[26]

D.K. Pradhan, R.N.P. Choudhary, B.K. Samantaray

Studies of dielectric relaxation and AC conductivity behavior of plasticized polymer nanocomposite electrolytes

Int. J. Electrochem. Sci., 3 (2008), pp. 597-608

View PDFView articleView in ScopusGoogle Scholar[27]

D. Saikia, H.-Y. Wu, Y.-C. Pan, C.-P. Lin, K.-P. Huang, K.-N. Chen, G.T.K. Fey, H.-M. Kao

Highly conductive and electrochemically stable plasticized blend polymer electrolytes based on PVdF-HFP and triblock copolymer PPG-PEG-PPG diamine for Li-ion batteries

J. Power Sources, 196 (2011), pp. 2826-2834

View PDFView articleView in ScopusGoogle Scholar[28]

Y.H. Liao, M.M. Rao, W.S. Li, L.T. Yang, B.K. Zhu, R. Xu, C.H. Fu

Fumed silica-doped poly(butyl methacrylate-styrene)-based gel polymer electrolyte for lithium ion battery

J. Membr. Sci., 352 (2010), pp. 95-99

View PDFView articleView in ScopusGoogle Scholar[29]

R.C. Agrawal, G.P. Pandey

Solid polymer electrolytes: materials designing and all-solid-state battery applications: an overview

J. Phys. D Appl. Phys., 41 (2008), p. 223001

CrossRef

View in ScopusGoogle Scholar

• [30]M.M.E. Jacob, E. Hackett, E.P. GiannelisFrom nanocomposite to nanogel polymer electrolytesJ. Mater. Chem., 13 (2002), pp. 1-5Google Scholar

[31]

M. Patel, K.G. Chandrappa, A.J. Bhattacharyya

Increasing ionic conductivity of polymer–sodium salt complex by addition of a non-ionic plastic crystal

Solid State Ionics, 181 (2010), pp. 844-848

View PDFView articleView in ScopusGoogle Scholar[32]

S.R. Mohapatra, A.K. Thakur, R.N.P. Choudhary

Effect of nanoscopic confinement on improvement in ion conduction and stability properties of an intercalated polymer nanocomposite electrolyte for energy storage applications

J. Power Sources, 191 (2009), pp. 601-613

View PDFView articleView in ScopusGoogle Scholar[33]

S. Mulmi, C.H. Park, H.K. Kim, C.H. Lee, H.B. Park, Y.M. Lee

Surfactant-assisted polymer electrolyte nanocomposite membranes for fuel cells

J. Membr. Sci., 344 (2009), pp. 288-296

View PDFView articleView in ScopusGoogle Scholar[34]

G.A. Kontos, A.L. Soulintzis, P.K. Karahaliou, G.C. Psarras, S.N. Georga, C.A. Krontiras, M.N. Pisanias

Electrical relaxation dynamics in TiO2 – polymer matrix composites

Express Polym. Lett., 1 (2007), pp. 781-789

CrossRef

View in ScopusGoogle Scholar[35]

P. Thomas, S. Satapathy, K. Dwarakanath, K.B.R. Varma

Dielectric properties of poly(vinylidene fluoride)/CaCu3Ti4O12 nanocrystal composite thick films

Express Polym. Lett., 4 (2010), pp. 632-643

CrossRef

View in ScopusGoogle Scholar[36]

A. Soulintzis, G. Kontos, P. Karahaliou, G.C. Psarras, S.N. Georga, C.A. Krontiras

Dielectric relaxation processes in epoxy resin—ZnO composites

J. Polym. Sci. BPolym. Phys., 47 (2009), pp. 445-454

CrossRef

View in ScopusGoogle Scholar[37]

Z.H. Li, H.P. Zhang, P. Zhang, G.C. Li, Y.P. Wu, X.D. Zhou

Effects of the porous structure on conductivity of nanocomposite polymer electrolyte for lithium ion batteries

J. Membr. Sci., 322 (2008), pp. 416-422

View PDFView articleView in ScopusGoogle Scholar[38]

S.B. Aziz

Occurrence of electrical percolation threshold and observation of phase transition in chitosan(1−x):AgI x(0.05 ≤ x ≤ 0.2)-based ion-conducting solid polymer composites

Appl. Phys. A, 122 (2016), p. 706

View in Scopus

Google Scholar[39]

F. Henn, C. Durand, A. Cerepi, E. Brosse, J.C. Giuntini

DC conductivity, cationic exchange capacity, and specific surface area related to chemical composition of pore lining chlorites

J. Colloid Interface Sci., 311 (2007), pp. 571-578

View PDFView articleView in ScopusGoogle Scholar[40]

S.H. Nahm

Use of dielectric spectroscopy for real-time in-situ reaction monitoring

JCT Res., 3 (2006), pp. 257-265

CrossRef

View in ScopusGoogle Scholar[41]

A. Nicolau, A.M. Nucci, E.M.A. Martini, D. Samios

Electrical impedance spectroscopy of epoxy systems II: molar fraction variation, resistivity, capacitance and relaxation processes of 1,4-butanediol diglycidyl ether/succinic anhydride and triethylamine as initiator

Eur. Polym. J., 43 (2007), pp. 2708-2717

View PDFView articleView in ScopusGoogle Scholar[42]

K. Asami

Characterization of heterogeneous systems by dielectric spectroscopy

Prog. Polym. Sci., 27 (2002), pp. 1617-1659

View PDFView articleView in ScopusGoogle Scholar[43]

D.K. Mahato, A. Dutta, T.P. Sinha

Impedance spectroscopy analysis of double perovskite Ho2NiTiO6

J. Mater. Sci., 45 (2010), pp. 6757-6762

CrossRef

View in ScopusGoogle Scholar[44]

R. Fortunato, L.C. Branco, C.A.M. Afonso, J. Benavente, J.G. Crespo

Electrical impedance spectroscopy characterisation of supported ionic liquid membranes

J. Membr. Sci., 270 (2006), pp. 42-49

View PDFView articleView in ScopusGoogle Scholar

• [45]Z. Maoxu, X. Hongsen, G. Jie, B. Wuming, X. ZumingImpedance spectroscopy analysis on electrical properties of serpentine at high pressure and high temperatureSci. China Earth Sci., 44 (2001), pp. 337-345Google Scholar

[46]

J. Benavente, M.G. Jose, R. Riley, A.E. Lozano, J. Abajo

Sulfonated poly(ether sulfones) characterization and study of dielectrical properties by impedance spectroscopy

J. Membr. Sci., 175 (2000), pp. 43-52

View PDFView articleView in ScopusGoogle Scholar[47]

J. Benavente, X. Zhang, R.G. Valls

Modification of polysulfone membranes with polyethylene glycol and lignosulfate: electrical characterization by impedance spectroscopy measurements

J. Colloid Interface Sci., 285 (2005), pp. 273-280

View PDFView articleView in ScopusGoogle Scholar[48]

R.A. Huggins

Simple method to determine electronic conductivity in mixed and ionic components of the conductors

Ionics, 8 (2002), pp. 300-313

View in Scopus

Google Scholar[49]

A.H. Eid, S. Mahmoud

The A.C. impedance of polycrystalline CuInS2 thin films

J. Mater. Sci. Mater. Electron., 8 (1997), pp. 259-264

View in Scopus

Google Scholar[50]

S.B. Aziz, R.M. Abdullah, M.A. Rasheed, H.M. Ahmed

Role of ion dissociation on DC conductivity and silver nanoparticle formation in PVA: AgNt based polymer electrolytes: deep insights to ion transport mechanism

Polymers, 9 (8) (2017), p. 338, 10.3390/polym9080338

View in ScopusGoogle Scholar[51]

M.M.E. Jacob, S.R.S. Prabaharan, S. Radhakrishna

Effect of PEO addition on the electrolytic and thermal properties of PVDF-LiClO4 polymer electrolytes

Solid State Ionics, 104 (1997), pp. 267-276

View PDFView articleView in ScopusGoogle Scholar[52]

S. Ibrahim, S.M.M. Yasin, M.N. Ng, R. Ahmad, M.R. Johan

Impedance spectroscopy of carbon nanotube/solid polymer electrolyte composites

Solid State Commun., 151 (2011), pp. 1828-1832

View PDFView articleView in ScopusGoogle Scholar[53]

S. Chakraborty, A. Sen, H.S. Maiti

Complex plane impedance plot as a figure of merit for tin dioxide-based methane sensors

Sens. Actuators B, 119 (2006), pp. 431-434

View PDFView articleView in ScopusGoogle Scholar[54]

S.B. Aziz, O. Gh. Abdullah, M.A. Rasheed, H.M. Ahmed

Effect of high salt concentration (HSC) on structural, morphological, and electrical characteristics of chitosan based solid polymer electrolytes

Polymers, 9 (6) (2017), p. 187, 10.3390/polym9060187

Google Scholar

[55]

E. Barsoukov, J.R. Macdonald

Impedance Spectroscopy, Theory, Experiment, and Application, Copyright © 2005

John Wiley & Sons, Inc. (2005), p. 7,, 10.1002/0471716243

Google Scholar

[56]

V. Rao, P.V. Ashokan, M.H. Shridhar

Studies of dielectric relaxation and a.c. conductivity in cellulose acetate hydrogen phthalate–poly(methyl methacrylate) blends

Mater. Sci. Eng. A, 281 (2000), pp. 213-220

View PDFView articleView in ScopusGoogle Scholar[57]

P. Dutta, S. Biswas, S. Kumar

Dielectric relaxation in polyaniline-polyvinyl alcohol composites

Mater. Res. Bull., 37 (2002), pp. 193-200

View PDFView articleView in ScopusGoogle Scholar[58]

S.B. Aziz, O. Gh. Abdullah, M.A. Rasheed

Structural and electrical characteristics of PVA: NaTf based solid polymer electrolytes: role of lattice energy of salts on electrical DC conductivity

J. Mater. Sci. Mater. Electron., 28 (2017), pp. 12873-12884

CrossRef

View in ScopusGoogle Scholar[59]

M.D. Migahed, M. Ishra, T. Fahmy, A. Barakat

Electric modulus and AC conductivity studies in conducting PPy composite films at low temperature

J. Phys. Chem. Solid., 65 (2004), pp. 1121-1125

View PDFView articleView in ScopusGoogle Scholar[60]

N.I. Harun, R.M. Ali, A.M.M. Ali, M.Z.A. Yahya

Dielectric behavior of cellulose acetate-based polymer electrolytes

Ionics, 18 (2012), pp. 599-606

CrossRef

View in ScopusGoogle Scholar[61]

C.A. Vincent

Ion transport in polymer electrolytes

Electrochim. Acta, 40 (1995), pp. 2035-2040

View PDFView articleView in ScopusGoogle Scholar[62]

A.M. Stephan

Review on gel polymer electrolytes for lithium batteries

Eur. Polym. J., 42 (2006), pp. 21-42

View in Scopus

Google Scholar[63]

G. Mao, R.F. Perea, W.S. Howells, D.L. Price, M.-L. Saboungi

Relaxation in polymer electrolytes on the nanosecond timescale

Nature, 405 (2000), pp. 163-165

View in Scopus

Google Scholar[64]

D. Golodnitsky, E. Strauss, E. Peled, S. Greenbaum

Review—on order and disorder in polymer electrolytes

J. Electrochem. Soc., 162 (14) (2015), pp. A2551-A2566

CrossRef

View in ScopusGoogle Scholar

• [65]L. Long, S. Wang, M. Xiao, Y. MengPolymer electrolytes for lithium polymer batteriesJ. Mater. Chem. A, 4 (2016), pp. 10038-10069Google Scholar

[66]

L.M. Carvalho, P. Gueágan, H. Cheradame, A.S. Gomes

Variation of the mesh size of PEO-based networks filled with TFSILi: from an Arrhenius to WLF type conductivity behavior

Eur. Polym. J., 36 (2000), pp. 401-409

View PDFView articleView in ScopusGoogle Scholar[67]

L. Othman, K.W. Chew, Z. Osman

Impedance spectroscopy studies of poly(methyl methacrylate)-lithium salts polymer electrolyte systems

Ionics, 13 (2007), pp. 337-342

CrossRef

View in ScopusGoogle Scholar[68]

M. Ravi, Y. Pavani, S. Bhavani, A.K. Sharma, V.V.R.N. Rao

Investigations on structural and electrical properties of KClO4 complexed PVP polymer electrolyte films

Int. J. Polym. Mater., 61 (2012), pp. 309-322

CrossRef

View in ScopusGoogle Scholar[69]

R. Baskaran, S. Selvasekarapandian, N. Kuwata, J. Kawamura, T. Hattori

Structure, thermal and transport properties of PVAc–LiClO4 solid polymer electrolytes

J. Phys. Chem. Solid., 68 (2007), pp. 407-412

View PDFView articleView in ScopusGoogle Scholar[70]

M.F.Z. Kadir, S.R. Majid, A.K. Arof

Plasticized chitosan–PVA blend polymer electrolyte based proton battery

Electrochim. Acta, 55 (2010), pp. 1475-1482

View PDFView articleView in ScopusGoogle Scholar

• [71]M.Z.A. Munshi, Handbook of Solid State Batteries & Capacitors, World Scientific, ISBN 981-02-1794-3, doi: 10.1002/adma.19960081028.Google Scholar
• [72]J.S. Kumar, A.R. Subrahmanyam, M.J. Reddy, U.V.S. RaoPreparation and study of properties of polymer electrolyte system (PEO+NaClO3)Mater. Lett., 60 (2006), pp. 3346-3349Google Scholar

[73]

M.J. Reddy, T. Sreekanth, U.V.S. Rao

Study of the plasticizer effect on a (PEO+NaYF4) polymer electrolyte and its use in an electrochemical cell

Solid State Ionics, 126 (1999), pp. 55-63

View in Scopus

Google Scholar[74]

T. Sreekanth, M.J. Reddy, S. Ramalingaiah, U.V.S. Rao

Ion-conducting polymer electrolyte based on poly ethylene oxide complexed with NaNO3 salt-application as an electrochemical cell

J. Power Sources, 79 (1999), pp. 105-110

View PDFView articleView in ScopusGoogle Scholar[75]

I.J.A. Mertens, M. Wübbenhorst, W.D. Oosterbaan, L.W. Jenneskens, J. van Turnhout

Novel polymer electrolytes based on amorphous poly(ether-ester)s containing 1,4,7-trioxanonyl main chain units. Ionic conductivity versus polymer chain mobility

Macromolecules, 32 (1999), pp. 3314-3324

View in Scopus

Google Scholar[76]

R.S. Bobade, S.V. Pakade, S.P. Yawale

Electrical investigation of polythiophene–poly (vinyl acetate) composite films via VTF and impedance spectroscopy

J. Non-Cryst. Solids, 355 (2009), pp. 2410-2414

View PDFView articleView in ScopusGoogle Scholar[77]

R. Baskaran, S. Selvasekarapandian, N. Kuwata, J. Kawamura, T. Hattori

Ac impedance, DSC and FT-IR investigations on (x)PVAc–(1−x)PVdF blends with LiClO4

Mater. Chem. Phys., 98 (2006), pp. 55-61

View PDFView articleView in ScopusGoogle Scholar[78]

J.Y. Kim, S.H. Kim

Ionic conduction behavior of network polymer electrolytes based on phosphate and polyether copolymers

Solid State Ionics, 124 (1999), pp. 91-99

View PDFView articleView in ScopusGoogle Scholar[79]

T. Uma, T. Mahalingam, U. Stimming

Conductivity studies on poly(methyl methacrylate)–Li2SO4 polymer electrolyte systems

Mater. Chem. Phys., 90 (2005), pp. 245-249

View PDFView articleView in ScopusGoogle Scholar

• [80]K. Ping-Lin, L. Wuu-Jyh, C. Ting-YenSolid polymer electrolytes V: microstructure and ionic conductivity of epoxide-crosslinked polyether networks doped with LiClO4Polymers, 44 (2003), pp. 2957-2964Google Scholar

[81]

T. Uma, T. Mahalingam, U. Stimming

Solid polymer electrolytes based on poly(vinylchloride)–lithium sulfate

Mater. Chem. Phys., 90 (2005), pp. 245-249

View PDFView articleView in ScopusGoogle Scholar[82]

K.P. Singh, P.N. Gupta

Study of dielectric relaxation in polymer electrolytes

Eur. Polym. J., 37 (1998), pp. 1023-1029

View PDFView articleView in ScopusGoogle Scholar[83]

J. Malathi, M. Kumaravadivel, G.M. Brahmanandhan, M. Hema, R. Baskaran, S. Selvasekarapandian

Structural, thermal and electrical properties of PVA–LiCF3SO3 polymer electrolyte

J. Non-Cryst. Solids, 356 (2010), pp. 2277-2281

View PDFView articleView in ScopusGoogle Scholar[84]

G.K. Prajapati, R. Roshan, P.N. Gupta

Effect of plasticizer on ionic transport and dielectric properties of PVA–H3PO4 proton conducting polymeric electrolytes

J. Phys. Chem. Solid., 71 (2010), pp. 1717-1723

View PDFView articleView in ScopusGoogle Scholar[85]

D.K. Pradhan, R.N.P. Choudhary, B.K. Samantaray

Studies of structural, thermal and electrical behavior of polymer nanocomposite electrolytes

Express Polym. Lett., 2 (2008), pp. 630-638

CrossRef

View in ScopusGoogle Scholar[86]

R.J. Sengwa, S. Choudhary, S. Sankhla

Dielectric properties of montmorillonite clay filled poly(vinyl alcohol)/poly(ethylene oxide) blend nanocomposites

Compos. Sci. Technol., 70 (2010), pp. 1621-1627

View PDFView articleView in ScopusGoogle Scholar

• [87]L. Chen, Y. Li, S.-P. Li, L.-Z. Fan, J.B. Goodenough, PEO/garnet composite electrolytes for solid-state lithium batteries: from “Ceramic-in-Polymer” to “Polymer-in-Ceramic”. Nano Energy, 10.1016/j.nanoen.2017.12.037.Google Scholar
• [88]W. Jiaa, Z. Lia, Z. Wua, L. Wanga, B. Wua, Y. Wangb, Y. Caoc, J. LiGraphene oxide as a filler to improve the performance of PAN-LiClO4 flexible solid polymer electrolyteSolid State Ionics, 315 (2018), pp. 7-13Google Scholar
• [89]J. Mindemark, M.J. Lacey, T. Bowden, D. Brandell, Beyond PEO—alternative host materials for Li+-Conducting solid polymer electrolytes. Prog. Polym. Sci., doi: 10.1016/j.progpolymsci.2017.12.004.Google Scholar

[90]

Y.-C. Lin, K. Ito, H. Yokoyama

Solid polymer electrolyte based on crosslinked polyrotaxane

Polymer, 136 (2018), pp. 121-127

View PDFView articleView in ScopusGoogle Scholar[91]

J. Shim, L. Kim, H.J. Kim, D. Jeong, J.H. Lee, J.-C. Lee

All-solid-state lithium metal battery with solid polymer electrolytes based on polysiloxane crosslinked by modified natural gallic acid

Polymer, 122 (2017), pp. 222-231

View PDFView articleView in ScopusGoogle Scholar[92]

W. Li, L. Chen, Y. Sun, C. Wang, Y. Wang, Y. Xia

All-solid-state secondary lithium battery using solid polymer electrolyte and anthraquinone cathode

Solid State Ionics, 300 (2017), pp. 114-119

View PDFView articleView in ScopusGoogle Scholar[93]

S. Popa, S. Iliescu, G. Ilia, N. Plesu, A. Popa, A. Visa, L. Macarie

Solid polymer electrolytes based on phosphorus containing polymers for lithium polymer batteries

Eur. Polym. J., 94 (2017), pp. 286-298

View PDFView articleView in ScopusGoogle Scholar[94]

Y. Kim, S.J. Kwon, H.-k. Jang, B.M. Jung, S.B. Lee, U.H. Choi

High ion conducting nanohybrid solid polymer electrolytes via single-ion conducting mesoporous organosilica in poly(ethylene oxide)

Chem. Mater., 29 (2017), pp. 4401-4410

CrossRef

View in ScopusGoogle Scholar[95]

Q. Zhang, K. Liu, F. Ding, X. Liu

Recent advances in solid polymer electrolytes for lithium batteries

Nano Rev., 10 (2017), pp. 4139-4174

CrossRef

View in ScopusGoogle Scholar[96]

H. Zhang, C. Li, M. Piszcz, E. Coya, T. Rojo, L.M. Rodriguez-Martinez, M. Armand, Z. Zhou

Single lithium-ion conducting solid polymer electrolytes: advances and perspectives

Chem. Soc. Rev., 46 (2017), pp. 797-815

CrossRef

View in ScopusGoogle Scholar[97]

M. Petrowsky, R. Frech

Temperature dependence of ion transport: the compensated Arrhenius equation

J. Phys. Chem. B (2009), pp. 5996-6000

CrossRef

View in ScopusGoogle Scholar[98]

M. Petrowsky, R. Frech

Salt concentration dependence of the compensated Arrhenius equation for alcohol-based electrolytes

Electrochim. Acta, 55 (2010), pp. 1285-1288

View PDFView articleView in ScopusGoogle Scholar

• [99]M.F. Shukura, M.F.Z. KadirHydrogen ion conducting starch-chitosan blend based electrolyte for application in electrochemical devicesElectrochim. Acta, 158 (2015), pp. 152-165Google Scholar
• [100]A.B. Samui, P. SivaramanSolid Polymer Electrolytes for SupercapacitorsWoodhead Publishing Limited (2010)Google Scholar

[101]

A. Awadhia, S.L. Agrawal

Structural, thermal and electrical characterizations of PVA: DMSO:NH4SCN gel electrolytes

Solid State Ionics, 178 (2007), pp. 951-958

View PDFView articleView in ScopusGoogle Scholar[102]

C.S. Ramya, S. Selvasekarapandian, G. Hirankumar, T. Savitha, P.C. Angelo

Investigation on dielectric relaxations of PVP–NH4SCN polymer electrolyte

J. Non-Cryst. Solids, 354 (2008), pp. 1494-1502

View PDFView articleView in ScopusGoogle Scholar[103]

A.R. Polu, R. Kumar

Preparation and characterization of PEG–Mg(CH3COO)2–CeO2 composite polymer electrolytes for battery application

Bull. Mater. Sci., 37 (2014), pp. 309-314

CrossRef

View in ScopusGoogle Scholar

• [104]S.B. AzizElectrical and Dielectric Properties of Solid and Nanocomposite Polymer Electrolytes Based on ChitosanPhD ThesisUniversity of Malaya (2012)Google Scholar

[105]

B. Natesan, N.K. Karan, R.S. Katiyar

Ion relaxation dynamics and nearly constant loss behavior in polymer electrolyte

Phys. Rev. E Stat. Nonlinear Soft Matter Phys., 74 (2006), p. 042801

CrossRef

View in ScopusGoogle Scholar[106]

B. Natesan, N.K. Karan, M.B. Rivera, F.M. Aliev, R.S. Katiyar

Segmental relaxation and ion transport in polymer electrolyte films by dielectric spectroscopy

J. Non-Cryst. Solids, 352 (2006), pp. 5205-5209

View PDFView articleView in ScopusGoogle Scholar[107]

S. Ramesh, A.H. Yahaya, A.K. Arof

Dielectric behavior of PVC-based polymer electrolytes

Solid State Ionics, 152 – 153 (2002), pp. 291-294

View PDFView articleView in ScopusGoogle Scholar[108]

E. Sheha

Ionic conductivity and dielectric properties of plasticized PVA 0.7 (LiBr) 0.3(H2SO4)2.7M solid acid membrane and its performance in a magnesium battery

Solid State Ionics, 180 (2009), pp. 1575-1579

View PDFView articleView in ScopusGoogle Scholar[109]

S. Selvasekarapandian, R. Baskaran, M. Hema

Complex AC impedance, transference number and vibrational spectroscopy studies of proton conducting PVAc–NH4SCN polymer electrolytes

Physica B, 357 (2005), pp. 412-419

View PDFView articleView in ScopusGoogle Scholar[110]

S. Ramesh, M.F. Chai

Conductivity, dielectric behavior and FTIR studies of high molecular weight poly(vinylchloride)–lithium triflate polymer electrolytes

Mater. Sci. Eng. B, 139 (2007), pp. 240-245

View PDFView articleView in ScopusGoogle Scholar[111]

M. Hema, S. Selvasekarapandian, D. Arunkuma, A. Sakunthala, H. Nithya

FTIR, XRD and ac impedance spectroscopic study on PVA based polymer electrolyte doped with NH4X (X = Cl, Br, I)

J. Non-Cryst. Solids, 355 (2009), pp. 84-90

View PDFView articleView in ScopusGoogle Scholar[112]

H. Nithya, S. Selvasekarapandian, K.D. Arun, A. Sakunthala, M. Hema, P. Christopherselvin, J. Kawamura, R. Baskaran, C. Sanjeeviraja

Thermal and dielectric studies of polymer electrolyte based on P(ECH-EO)

Mater. Chem. Phys., 126 (2011), pp. 404-408

View PDFView articleView in ScopusGoogle Scholar[113]

I.M. Hodge, K.L. Ngai, C.T. Moynihan

Comments on the electric modulus function

J. Non-Cryst. Solids, 351 (2005), pp. 104-115

View PDFView articleView in ScopusGoogle Scholar[114]

S.B. Aziz, M.F.Z. Kadir, Z.H.Z. Abidin

Structural, morphological and electrochemical impedance study of CS:LiTf based solid polymer electrolyte: reformulated Arrhenius equation for ion transport study

Int. J. Electrochem. Sci., 11 (2016), pp. 9228-9244

View PDFView articleView in ScopusGoogle Scholar[115]

S.B. Aziz, Z.H.Z. Abidin

Electrical and morphological analysis of chitosan:AgTf solid electrolyte

Mater. Chem. Phys., 144 (2014), pp. 280-286

View PDFView articleView in ScopusGoogle Scholar[116]

S.B. Aziz

Study of electrical percolation phenomenon from the dielectric and electric modulus analysis

Bull. Mater. Sci., 38 (2015), pp. 1597-1602

CrossRef

View in ScopusGoogle Scholar

Cited by (560) Inherent thermal-responsive strategies for safe lithium batteries 2024, Journal of Energy Chemistry

• Steps towards the ideal CV and GCD results with biodegradable polymer electrolytes: Plasticized MC based green electrolyte for EDLC application 2024, Journal of Energy Storage
• Dielectric and thermal behavior investigation of Mn-Zn nano ferrite-fluid for transformer oil applications 2024, Arabian Journal of Chemistry
• Investigation on electrical and electrochemical behaviour of cellulose acetate: Ammonium iodide: Silica composite biopolymer electrolyte for proton exchange membrane (PEM) fuel cell performance 2024, Materials Letters
• Effect of dopant on ion-dynamics of sodium ion-based flexible polyblend electrolyte for electrochemical device application 2024, Materials Research Bulletin
• A review on ion transport pathways and coordination chemistry between ions and electrolytes in energy storage devices 2023, Journal of Energy Storage

View all citing articles on Scopus

Peer review under responsibility of Vietnam National University, Hanoi.© 2018 The Authors. Publishing services by Elsevier B.V. on behalf of Vietnam National University, Hanoi.

• Theoretical estimation on the percolation threshold for polymer matrix composites with hybrid fillers Composite Structures, Volume 124, 2015, pp. 292-299Yuli Chen, …, Jianyu Zhang
• Flexible fiber-shaped supercapacitors: Design, fabrication, and multi-functionalities Energy Storage Materials, Volume 8, 2017, pp. 85-109Fancheng Meng, …, Lianxi Zheng
• The compatibility of chitosan with divalent salts over monovalent salts for the preparation of solid polymer electrolytes Results in Physics, Volume 11, 2018, pp. 826-836Shujahadeen B. Aziz, …, O. Gh. Abdullah
• View PDF

Citations

• Citation Indexes: 539

Captures

• Readers: 833

Mentions

• References: 2

View details📷

• Previous article

Simply plot log(σ) vs 1/T and find the slope.

Доброго дня Леш ;)

Нет, именно для полимеров там все сложнее, ибо там вклад свободного объема

Вот смотри

S. N. Shkerin

Сергей, привет!

Рад тебя видеть!

Please, add citation to this equation.