Exploring Ionic Motion and Conductivity Enhancement in PEO:NaI:MnO₂ Polymer Electrolytes with DEC Plasticizer

MeenakshiRay¹1

AmitSaxena²1

BhaskarBhattacharya¹1✉Emailbhaskar.phys@bhu.ac.in

BhaskarBhattacharya1Emailbhaskarmiet@gmail.com

1Department of PhysicsMMV, Banaras Hindu University221005VaranasiINDIA

2Department of PhysicsOriental UniversityIndoreINDIA

Meenakshi Ray¹, Amit Saxena², Bhaskar Bhattacharya¹*

¹Department of Physics, MMV, Banaras Hindu University, Varanasi 221005, INDIA

² Department of Physics, Oriental University, Indore, INDIA

*Corresponding Author: bhaskar.phys@bhu.ac.in, bhaskarmiet@gmail.com

Abstract

This study investigates the effect of diethyl carbonate (DEC) plasticizers on ionic conductivity. Additionally, the research investigated the mobility and concentration of charge carriers in (PEO:NaI:MnO₂) + DEC wt% polymer electrolytes using theoretical models (Trukhan and Schutt & Gerdes models). Here, the thin films were synthesised using solution casting techniques with varying DEC concentrations (0–100 wt%) and characterised using impedance spectroscopy. The results indicate that ionic conductivity greatly depends on the amount of DEC, and we got the highest conductivity of 8.72 x 10 − 4 S/cm at 60 wt% of DEC. This increase in conductivity is expected due to an increase in amorphous nature, ion separation, and the formation of a percolation pathway that offers improved ion transport. At the higher concentration of DEC, conductivity declined due to phase separation and dilution effects. To gain a more profound understanding of how ions move with frequency, the Distribution of Relaxation Times (DRT) for the 60 wt% DEC was calculated. This calculation was performed under a temperature-dependent environment and reveals that relaxation time (τ) is inversely proportional to the rate of a process. A shorter time constant means a faster process, which offers the higher conductivity. Additional studies that looked at temperature effects confirmed Arrhenius-type behavior and found an activation energy of 0.51 eV. Charge carrier and concentrations analysis using the Trukhan and Schutt & Gerdes models showed that the Trukhan model provided a more accurate description of ion transport in the amorphous matrix compared to the Schutt & Gerdes model. The findings of this study demonstrate that optimizing plasticizer concentration is critical for achieving high-performance polymer electrolytes, which is helpful in the design of next-generation energy storage devices.

Keywords:

Ionic Conductivity

Distribution of Relaxation Times (DRT)

Trukhan Model

Schutt & Gerdes model

1. Introduction

As a result of the demand for electrochemical devices in our daily lives, research has recently concentrated on the development of the fields of energy storage and conversion[1]. A key component in these devices is the electrolyte, which facilitates ion transport between electrodes and plays a crucial role in determining the overall performance, efficiency, and stability of the system. Depending on the application, electrolytes can be liquid, solid, or gel-based, each offering unique advantages in terms of conductivity, safety, and compatibility with electrode materials. Liquid electrolytes, commonly used in batteries and supercapacitors, offer high ionic conductivity and efficient charge transport, enabling fast electrochemical reactions. Because liquid electrolytes have some disadvantages, such as the possibility of leakage, internal electrode shorting, and explosion, polymer electrolytes (PE) have been employed as potential separators in energy storage devices[2]. PE serves as a separator to prevent contact between the electrodes and conduction of ions through this electrolyte, showing the fundamental design of solar cells, batteries, supercapacitors, and electrochemical devices. Researchers from all around the world are experimenting with different techniques to increase the conductivity of polymer electrolytes in thin films. One method that is frequently employed is the use of plasticizers[1]–[4] such as PC (polycarboxylate), DEC (diethyl carbonate), DMC (dimethyl carbonate), and EC (ethyl carbonate).

In the current study, we combined a PEO:NaI (polyethylene oxide:sodium iodide) matrix with DEC as a plasticizer and MnO₂ (magnesium oxide) as a filler[5], [6]. We investigated the effects of different DEC concentrations dispersed within the PEO:NaI matrix with MnO₂ filler. Extensive computations were performed to analyze the concentration and mobility of charge carriers in thin films. While conductivity enhancement is often emphasized in the literature as a key factor, it is equally important to examine the microscopic interactions occurring within the composite matrix. However, in addition to the increase in conductivity, it is also crucial to take into account the microscopic events occurring within the composite matrix. The general observation of the percolation threshold was extended from crystal-crystal composite[7] to polymer crystal composites[8]. Further variation in terms of percolation, viz., surface percolation, volume percolation, or the formation of only space charge, has been made to justify the change in conductivity.

In this study, we sought to compute two parameters, n and µ, using accepted theories of ion conduction in a glassy matrix, crystalline superionic conductors, and the space charge model[9]–[11]. We first determined the conductivity and dielectric constant of the PE thin films in order to comprehend the theory behind these theoretical models. An important fraction of the mobile anions and cations in polymer electrolytes are bound by ion pairs or clusters. Based on the available ions, whether they are mobile or imprisoned inside the coil cage, the total number of charge carriers can be calculated. The Trukhan model, which applies the Nernst-Planck equations of electro-diffusion in a medium with a certain dielectric constant between the two blocking electrodes, can be used to compute this. The value of tan δ is then used to calculate the diffusion coefficients and mobile ion concentrations, where δ represents the phase angle[12].

To determine the number of charge carriers using the Trukhan model, we first calculated the value of tan δ. We have calculated the charge density (D) using Eq. 1.

D =

$\:\frac{2\pi\:f\text{max}{d}^{2}}{32{\left(\text{tan}\delta\:\right)}^{3}\text{m}\text{a}\text{x}}$

---------------------------------------(1)

Here, d stands for the thickness of the sample, while the values for f_max and (tanδ) _max are taken from the tan δ plot.

Further, the concentration of charge carriers through the Trukhan model is calculated with Eq. 2.

n =

$\:\frac{{{\upsigma\:}}_{d\text{C}}\text{k}\text{T}}{{\text{D}}^{{\text{e}}^{2}}}$

------------------------------------------------(2)

Here,

$\:{\sigma\:}_{dc}$

is the conductivity, k is the Boltzmann constant, and T is the temperature.

According to the Schutt and Gerdes (S and G) model, the charge carriers in the matrix move as a result of the influence of an electric field. It primarily depends on the frequency of the measurements and the dielectric constant[13]. The concentration of free charge carriers

$\:(\:{\eta\:}_{SG}$

) is extracted from the impedance spectroscopy spectrum with the help of Eq. 3.

$\:{\eta\:}_{sG}={\left[\frac{\sigma\:}{3{ϵ}_{0}{ϵ}_{s}^{{\prime\:}}{\omega\:}_{x}}\right]}^{4}\frac{{ϵ}_{s}^{{\prime\:}}{ϵ}_{0}{k}_{B}T}{{e}^{2}{d}^{2}}$

--------------------------------(3)

Where σ stands for dc conductivity,

$\:{ϵ}_{s}$

is a real part of permittivity at high frequency,

$\:{k}_{B}$

stands for Boltzmann constant,

$\:{ϵ}_{0}$

is permittivity in vaccum, and d is thickness. Here,

$\:{ϵ}_{s}$

is dielectric permittivity (real part) in the region of high frequency and

$\:{\omega\:}_{x}$

stands for angular frequency where

$\:ϵ\left({\omega\:}_{x}\right)=10{ϵ}_{s}$

It's vital to consider the contribution of the crystalline areas relative to the amorphous region in order to comprehend how the crystalline regions impact the conductivity. The Rice and Roth model is currently being investigated for this purpose[14], [15]. This model is based on the hypothesis that a transition from one site to another occurs within a predetermined length of time during a thermally active process. This procedure establishes the mean free path, or the distance between two sites, as well as the hopping frequency.

The charge carriers are determined by Eq. 4.

$\:\sigma\:=\frac{2}{3}\left[\frac{{\left(ze\right)}^{2}}{{k}_{B}Tm}\right]{n}_{RR}{E}_{a}\tau\:\text{exp}\left[\begin{array}{c}-{E}_{a}\\\:\stackrel{-}{{k}_{B}T}\end{array}\right]$

---------------------------(4)

Where Z stands for valency of charge, m for conducting ion’s mass, n for mobile ion concentration, K_B for Boltzmann constant,

$\:{E}_{a}$

is an activation energy and

$\:\tau\:$

is the free ion lifetime.

2. Experimental Section

We used the traditional solution casting method to prepare the thin film, where PEO and NaI were dissolved in acetonitrile using a fixed ratio of 90:10, and after that, we added 0.5 wt% of MnO₂.. The solution was agitated for 10–12 hours to produce a homogenous mixture before being placed onto a polypropylene Petri dish. At room temperature, the solution was allowed to gently evaporate, resulting in self-supporting films. From this initial film, we obtained the reference polymer electrolyte film, which was used to analyze the changes caused by the addition of DEC to subsequent thin films. To make the DEC-dispersed thin films, we repeated the process as mentioned above and added various wt% of DEC to the PEO:NaI:MnO₂ mixture. We prepared different DEC-dispersed thin films with a weight percentage ranging from 0 to 100%. Impedance measurements were carried out using a CHI 660E electrochemical workstation in the frequency range of 10²–10⁵ Hz at room temperature. Ionic conductivity, ionic concentration, and ion mobility within the polymer matrix were evaluated based on impedance spectroscopy data.

3. Results and Discussions

3.1 Electrical Studies

3.1.1 Conductivity: At Room Temperature

The conductivity profile of the PEO:NaI:MnO₂ polymer electrolyte system incorporating varying weight percentages of DEC demonstrates a pronounced dependence on DEC concentration (Fig. 1). Initially, at lower DEC content (0–40 wt%), the ionic conductivity remains modest but shows a gradual upward trend. This increase can be attributed to the progressive disruption of PEO crystallinity by DEC, which promotes enhanced polymer segmental motion and thus facilitates ion transport. Nevertheless, ion dissociation remains somewhat constrained by intermolecular interactions within the polymer matrix, resulting in only moderate improvements in conductivity.

In the intermediate DEC concentration range (40–60 wt%), a sharp increase in conductivity is observed, reaching a distinct maximum of 8.72 x 10^− 4 S/cm at approximately 60 wt% DEC. This pronounced enhancement is likely due to a synergistic effect where optimal polymer flexibility, increased NaI salt dissociation, and the formation of efficient percolation pathways collectively promote superior ionic mobility. The emergence of a percolation threshold at this composition may be critical in establishing continuous conduction channels throughout the matrix.

Beyond the optimal point (≥ 60 wt% DEC), conductivity exhibits a marked decline. This decrease can be ascribed to several potential factors, including phase separation, dilution of the conducting species due to excessive DEC, and diminished structural integrity of the polymer matrix—all of which compromise ion hopping efficiency. At the highest DEC loadings (80–100 wt%), conductivity stabilizes at values below the observed maximum, indicating that further addition of DEC does not restore or enhance ionic transport. This plateau suggests that DEC functions primarily as a plasticizer at these concentrations, without contributing significantly to the formation of new conduction pathways[16].

Fig. 1

Variation of conductivity with different wt% of DEC

3.1.2 Conductivity: Variation with Temperature

Since 60 wt% DEC dispersed film offered the highest conductivity, to understand more about the conductivity behavior with the variation of temperature, we performed the temperature-based conductivity.The sample was investigated in the temperature range of 30–110°C (i.e., from room temperature to above melting point; for PEO, typically this value is 65–70°C). Variation of conductivity with temperature is shown in Fig. 2. In the temperature range of 30–60°C, the ionic conductivity of the (PEO:NaI:MnO₂) + DEC thin film remains almost constant at a low value (10⁻³–10⁻² S/cm).

This is because, at low temperatures, the PEO chains are relatively rigid, and the segmental motion required for ion transport is restricted, which limits ionic mobility. As the temperature increases to the 60–80°C range, the conductivity starts to rise (~ 10⁻² S/cm). In this region, the polymer chains begin to soften as the material approaches its melting transition, while the DEC plasticizer reduces crystallinity, making it easier for ions to move. Beyond 80°C, a sharp increase in conductivity is observed (up to ~ 4.8×10⁻² S/cm at 100°C). This is due to the polymer becoming more amorphous, which greatly enhances chain flexibility and facilitates ion hopping and segmental motion, leading to an Arrhenius-type conduction behavior.

To calculate the activation energy, we have taken the slope of the curve at the temperature region 70–100°C. The process is as follows:

$\:Slope\:=m=\frac{{\Delta\:}y}{{\Delta\:}x}=\frac{-3.03-\left(-3.91\right)}{2.68-2.83}=\frac{0.88}{-0.15}=-5.87$

So,

$\:\frac{{E}_{a}}{{k}_{B}}=-m\Rightarrow\:Ea=\left(5.87\right)\left({K}_{B}\right)$

Here

$\:{k}_{B}=8.617\times\:{10}^{-5}\hspace{0.17em}\text{eV}\text{/}\text{K}$

$\:Ea=5.87\times\:8.617\times\:{10}^{-5}eV\times\:1000=0.51eV$

So the final calculated value of the activation energy from the plot is 0.51 eV. The hopping of ions through interchain is improved, and interchain movement of ions also increases as the temperature rises because the polymer chains acquire faster internal modes of vibration and enable polymer chain segmental motion, and so the ionic conductivity rises with an increase in temperature[15], [17].

Fig. 2

Variation of conductivity with temperature for 60% of DEC.

3.1.3 Temperature dependent Distribution of Relaxation Times (DRT)

Distribution of Relaxation Times (DRT) is one of the important tools to understand the data of Electrostatic Impedance Spectroscopy (EIS)[18], [19]. It gives the deeper understanding of overlapping ionic motion with respect to the frequency applied during the characterization of the samples. Here, in this work we have calculated and interpreted the DRT of 60wt DEC dispersed samples (since it offers the highest conductivity) with temperatures variation from 40 to 110 ⁰C. Figure 3 shows the DRT peak corresponding to the ion motions at different temperature. Relaxation time (τ) is inversely proportional to the rate of a process. A shorter time constant means a faster process. Electrochemical processes like ion conduction and charge transfer are thermally activated. Increasing the temperature provides more thermal energy, which excites the polymer chains (increasing mobility), accelerates ion movement, and speeds up the electrochemical reactions at the interfaces. Therefore, all processes become kinetically faster at higher temperatures. The relaxation time is a direct reflection of the energy required for the process. Higher is the Relaxation time, lower energy is required to activate the process. As the temperature is increased, the energy of the system (kT) becomes high and hence ion hopping requires less energy. Also, the since the matrix becomes more amorphous due to the melting of crystalline pockets, it requires lesser energy for ion migration and hence the higher Relaxation time is observed (Fig. 3).

Fig. 3

Temperature dependent DRT study with frequency for 60wt% of DEC

3.1.4 Fractional numbers of mobile charge carriers (n/n₀)

Fractional numbers of dissociated mobile charge carriers are calculated using the following relation:

$\:\frac{\text{n}}{{\text{n}}_{0}}=\text{exp}\left[\frac{-\text{U}}{2\in\:{\text{k}}_{\text{B}}\text{T}}\right]$

Where n is the dissociated number of charge carriers, n₀ is the total number of charge carriers, U is the dissociated energy of the salt (for NaI, U = 3.1 eV), ε is the dielectric constant of the matrix, and kʙ is the Boltzmann constant (eV/K).

At low DEC content (10–20 wt%), few ions are free, which shows that some ions remain bound as pairs and do not contribute to conductivity. As the DEC content increases to 30–60 wt%, the fraction of free ions rises sharply, to about 99.8%. This happens because DEC works as a plasticizer and high-dielectric medium, which weakens ion–ion interactions and allows more ions to move freely. However, at very high DEC levels (70–90 wt%), the fraction of free ions shows a slight decrease, likely due to dilution of the conducting pathways or clustering effects when excess plasticizer is present. Figure 4 shows the variation of the dissociated number of charge carriers with different wt% of DEC, and we observed the highest value of 0.998 at 60 wt% of DEC and the lowest of 0.975 at 10 wt% of DEC.

Fig. 4

Variation in the dissociated number of charge carriers with different wt% of DEC.

3.1.5 Concentration and Mobility at Room Temperature

The mobility and concentration of charge carriers play a crucial role in determining the overall conductivity of polymer electrolytes. Charge carrier concentration depends on the availability of dissociated ions, while mobility is influenced by the interaction of these ions with the polymer matrix. In a semicrystalline system, as described by the Trukhan model, ion transport is governed by both the crystalline and amorphous regions, where the amorphous phase facilitates higher mobility due to reduced ion trapping. Similarly, the Schutt and Gerdes model considers charge transport in an amorphous medium, where mobility is affected by the dielectric constant and frequency-dependent polarization effects.

3.1.6 Schutt and Gerdes Model

Fig. 5

Variation of mobility and charge carriers with different wt% of DEC according to the Schutt and Gerdes model.

As we can see in Fig. 5, when we add more DEC, the number of charge carriers increases, and this matches the rise in conductivity. The S and G theory is based on purely glassy materials, but our sample is amorphous, meaning it has a disordered structure rather than a rigid glassy network. Because of the difference, the S and G theory does not fully capture the behavior of our material. Specifically, in the S and G theory, the charge carrier mobility becomes constant after a certain point, assuming that the material is fully glassy and the polymer chains are completely stretched out. However, this assumption does not hold true for amorphous materials, where disorder and chain flexibility affect charge transport differently. At the beginning, mobility changes because charges can move easily through special pathways created by the interaction between the added DEC particles and the base material. These pathways allow ions to move freely, whether their concentration is low or high^17,18. Due to these reasons, we apply the Trukhan model, which better accounts for the amorphous nature of our films and the gradual changes in mobility and conductivity with increasing DEC concentration. Disadvantages of the S&G theory include its limitation to purely glassy materials, inability to describe materials with significant amorphous or disordered phases, and the oversimplified assumption that mobility quickly reaches a steady value. These shortcomings make it less suitable for explaining charge transport in our samples.

3.1.7 Trukhan Model

Fig. 6

Variation of mobility and charge carriers with different wt.% of DEC according to the Trukhan model.

Figure 6 shows that the conductivity exhibits two distinct behaviors as the DEC content increases. Initially, conductivity varies primarily due to changes in charge carrier mobility, up to approximately 60 wt% DEC. Beyond this concentration, conductivity is influenced more significantly by the charge carrier concentration. The decrease in carrier concentration with increasing DEC content is attributed to the plasticizer’s effect on the polymer’s crystallinity. The addition of DEC disrupts the crystalline regions within the polymer-salt complex, increasing the amorphous phase. This increase in amorphicity exposes more polymer segments and ionic sites, facilitating greater ion dissociation and mobility. Consequently, despite the reduction in crystallinity, the number of free charge carriers increases, enhancing the overall conductivity^19,20.

3.1.8 Temperature-based concentration and mobility of

In our current study, we found that the concentration and mobility calculated using the Trukhan model best fit the conductivity pattern, so we calculated the temperature-dependent concentration and mobility of charge carriers based on this model. We conducted this study using a sample with 60 wt% DEC, as this composition exhibited the highest conductivity at room temperature (RT). Figure 7 shows the concentration and mobility of charge carrier variations with temperature.

Fig. 7

Temperature-dependent mobility and concentration of charge carriers at 60 wt.% of DEC by the Trukhan model.

The graph shows that at lower temperatures (300–340 K), the concentration is low, approximately in the range of ~ 10¹⁹–10²¹ cm⁻³.As the temperature increases, the concentration rises sharply and approaches the order of 10³¹–10³³ cm⁻³ after 370K. This sudden change in the concentration of charge carriers is attributed to the enhanced ion dissociation of NaI salt. Also, the 60 wt% of MnO₂ might offer more ionic sites, helping with dissociation and increasing the number of charge carriers. The graph indicates that the mobility of the charge carrier is relatively high at lower temperatures, but as the temperature increases, it drops sharply to around ~ 10⁻¹⁰–10⁻¹¹ cm²/V·s at ~ 370 K. With increasing temperature, although ion concentration rises, the segmental dynamics of the polymer matrix become more disordered, and these higher ion-ion interactions and increased ion-polymer coupling may hinder the drift mobility of individual ions. Thus, it can be analyzed that the mobility decreases due to ion clustering, increased collisions, and structural relaxation limitations. The overall ionic conductivity is thus governed by the dominance of concentration at higher temperatures.

4. Conclusion

In this study, we systematically investigated the effects of DEC plasticizer on the conductivity, charge carrier concentration, and mobility of PEO:NaI:MnO₂ polymer electrolytes. The results demonstrate that DEC plays a crucial role in enhancing ionic conductivity by increasing the amorphous nature of the polymer matrix, reducing crystallinity, lowering Tg, and facilitating ion transport. The conductivity initially rises with increasing DEC concentration, reaching a peak at 60 wt% DEC before declining due to phase separation and dilution effects.

The charge carrier concentration and mobility, analyzed using the Trukhan and Schutt & Gerdes models, revealed that at lower DEC concentrations, conductivity is primarily influenced by mobility, while at higher concentrations, the number of charge carriers becomes the dominant factor. The Trukhan model provided a more accurate representation of charge transport in the amorphous polymer matrix compared to the Schutt & Gerdes model, which assumes a glassy system. The temperature-dependent study of the concentration and mobility of charge carriers through the Trukhan model shows that the overall ionic conductivity is thus governed by the dominance of concentration at higher temperatures.

Furthermore, the temperature-dependent conductivity studies also confirmed that increasing temperature enhances ion mobility and conductivity due to improved polymer chain segmental motion. Overall, these findings highlight the significance of optimizing plasticizer concentration (DEC) to achieve maximum conductivity in polymer electrolytes (PEO:NaI:MnO₂), which provides insights for the development of high-performance energy storage devices.

AUTHOR INFORMATION

Corresponding Author

Bhaskar Bhattacharya − Department of Physics, MMV, Banaras Hindu University, Varanasi 221005, India;

Email: bhaskar.phys@bhu.ac.in, bhaskarmiet@gmail.com

Authors

Meenakshi Ray − Department of Physics, MMV, Banaras Hindu University, Varanasi 221005, INDIA

Amit Saxena—Department of Physics, Oriental University, Indore, INDIA

Notes

The authors declare no competing financial interest.

Conflict of Interest

Authors declare that there is no conflict of interest.

Acknowledgement

The authors express their gratitude for the financial support provided as an incentive grant to senior faculty members (6532) by the Institute of Eminence at BHU.

Author Contribution

Meenakshi: Methodology, formal analysis and investigations, writing original draft preparationsAmit Saxena: Methodology, formal analysis, editing the draft, calculations and figure analysisBhaskar Bhattacharya: Conceptualization, review and editing, resources, Supervision

References

D. Saikia and A. Kumar, “Ionic conduction in P(VDF-HFP)/PVDF-(PC + DEC)-LiClO4 polymer gel electrolytes,” Electrochim. Acta, vol. 49, no. 16, pp. 2581–2589, 2004, doi: 10.1016/j.electacta.2004.01.029.

R. Yu et al., “Solid polymer electrolyte based on thermoplastic polyurethane and its application in all-solid-state lithium ion batteries,” Solid State Ionics, vol. 309, no. March, pp. 15–21, 2017, doi: 10.1016/j.ssi.2017.06.013.

J. Park, Y. Liu, H. B. Lim, and J.-K. Kim, “Effect of plasticizers on the electrochemical performance of PEO-based solid polymer electrolytes for rechargeable lithium batteries,” J. Ind. Eng. Chem., Sep. 2025, doi: 10.1016/j.jiec.2025.09.010.

M. F. Aziz, A. A. Rahim, E. S. A. Razak, S. N. A. Jaaffar, M. H. Buraidah, and M. F. Shukur, “Enhanced ion transport and structural dynamics in gel polymer electrolytes containing a plasticizer prospect for DSSC application,” Ionics (Kiel)., vol. 31, no. 6, pp. 6103–6115, Jun. 2025, doi: 10.1007/s11581-025-06270-9.

Meenakshi, A. Saxena, and B. Bhattacharya, “Investigating Theoretical Frameworks: Comprehending the Relationship between σ, n, and µ in MnO2 Dispersed Films,” ACS Omega, vol. 8, no. 38, pp. 35256–35265, Sep. 2023, doi: 10.1021/acsomega.3c05006.

S. Kumar, R. Raghupathy, and M. Vittadello, “Sodium Polymer Electrolytes: A Review,” Batter. 2024, Vol. 10, Page 73, vol. 10, no. 3, p. 73, Feb. 2024, doi: 10.3390/BATTERIES10030073.

C. C. Liang, A. V. Joshi, and N. E. Hamilton, “Solid-state storage batteries,” J. Appl. Electrochem., vol. 8, no. 5, pp. 445–454, 1978, doi: 10.1007/BF00615840.

A. Saxena and B. Bhattacharya, “Studies on CuI Dispersed Mixed (Ion + Electron) Conducting Composite Polymer Electrolyte System,” J. Electron. Mater., vol. 47, no. 10, pp. 6163–6170, Oct. 2018, doi: 10.1007/s11664-018-6508-y.

H. J. Schütt and E. Gerdes, “Space-charge relaxation in ionicly conducting oxide glasses. I. Model and frequency response,” J. Non. Cryst. Solids, vol. 144, no. C, pp. 1–13, 1992, doi: 10.1016/S0022-3093(05)80377-1.

10.

M. J. Rice and W. L. Roth, “Ionic transport in super ionic conductors: a theoretical model,” J. Solid State Chem., vol. 4, no. 2, pp. 294–310, 1972, doi: 10.1016/0022-4596(72)90121-1.

11.

R. J. Klein, S. Zhang, S. Dou, B. H. Jones, R. H. Colby, and J. Runt, “Modeling electrode polarization in dielectric spectroscopy: Ion mobility and mobile ion concentration of single-ion polymer electrolytes,” J. Chem. Phys., vol. 124, no. 14, 2006, doi: 10.1063/1.2186638.

12.

M. A. Brza and S. B. Aziz, “The study of ion transport parameters using two models in plasticized sodium ion conducting polymer blend electrolytes,” Polym. Bull., vol. 81, no. 4, pp. 3021–3042, Feb. 2024, doi: 10.1007/s00289-023-04846-x.

13.

E. Schütt, H. J.;Gerdes, “Effect of composition on electrical relaxation in potassium borosilicate glasses,” J. Non-cryst. Solids, vol. 68, pp. 175–191, 1984.

14.

P. G. Bruce, J. Evans, and C. A. Vincent, “Conductivity and transference number measurements on polymer electrolytes,” Solid State Ionics, vol. 28–30, no. PART 2, pp. 918–922, 1988, doi: 10.1016/0167-2738(88)90304-9.

15.

R. Kumar, B. Singh, and S. S. Sekhon, “Effect of dielectric constant of solvent on the conductivity behavior of polymer gel electrolytes,” J. Mater. Sci., vol. 40, no. 5, pp. 1273–1275, 2005, doi: 10.1007/s10853-005-6950-0.

16.

S. B. Aziz et al., “Design of potassium ion conducting PVA based polymer electrolyte with improved ion transport properties for EDLC device application,” J. Mater. Res. Technol., vol. 13, pp. 933–946, 2021, doi: https://doi.org/10.1016/j.jmrt.2021.05.017.

17.

K. Gohel and D. K. Kanchan, “Effect of PC:DEC plasticizers on structural and electrical properties of PVDF–HFP:PMMA based gel polymer electrolyte system,” J. Mater. Sci. Mater. Electron., vol. 30, no. 13, pp. 12260–12268, 2019, doi: 10.1007/s10854-019-01585-6.

18.

P. O. Hama, M. A. Brza, H. B. Tahir, S. B. Aziz, B. A. Al-Asbahi, and A. A. A. Ahmed, “Simulated EIS and Trukhan model to study the ion transport parameters associated with Li + ion dynamics in CS based polymer blends inserted with lithium nitrate salt,” Results Phys., vol. 46, p. 106262, Mar. 2023, doi: 10.1016/J.RINP.2023.106262.

19.

A.-L. Chan, H. Yu, K. S. Reeves, and S. M. Alia, “Identifying electrochemical processes by distribution of relaxation times in proton exchange membrane electrolyzers,” J. Power Sources, vol. 628, p. 235850, Feb. 2025, doi: 10.1016/j.jpowsour.2024.235850.

Yes