Charge carrier dynamics and relaxation in highly conducting gel polymer electrolytes added with adiponitrile and dual redox

The fundamental understanding of the relationship between ion transport and segmental dynamics of polymer chains in polymer electro-lytes is crucial for achieving high ionic conductivity at room temperature for technological applications in supercapacitors, batteries, etc. In this work, the ion dynamics and relaxation have been studied for gel polymer electrolytes (GPEs) containing P(VdF-HFP) as host polymer, adiponitrile as a plasticizer, 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide as ionic liquid, and diphenylamine and copper iodide redox additives as fillers. The crystallization temperature of the ionic liquid and the melting temperature of the plasticizer play important roles in ion dynamics. The highest room-temperature ionic conductivity (3.3 × 10 − 3 S/cm) was obtained for the GPE filled with dual redox additives. The broadband ac conductivity spectra have been analyzed by using the Universal Power law model coupled with the Poisson – Nernst – Planck (PNP) model. The solid – solid phase transition of the ionic liquid affects the grain and grain boundary regions of the GPEs due to the presence of redox fillers. The temperature dependence of the dielectric spectra of the GPEs containing redox fillers confirms the phase transition at the crystallization temperature. The electric modulus and dielectric spectra have been analyzed by using the Havrilliak – Nigami, Kohlrausch – Williams – Watts, and derivative dielectric constant functions. The scaling of ac conductivity and modulus spectra confirms a common ion conduction and relaxation mechanism for the GPEs. The influence of dual redox additives is clearly observed in the values of ionic conductivity, ion diffusivity, and relaxation time


I. INTRODUCTION
3][14][15][16] The electrochemical byproducts form an insulating layer across the electrode interface during the cycling process.Generation of heat during the charging cycle may happen due to a short circuit between two electrodes. 14][22][23] These polymers have a semi-crystalline microstructure with different thermal and mechanical stability.The PVDF has good thermal stability compared to PEO and exhibits different phase behavior at room temperature, but the β-phase shows electro-active nature. 24,25oly(vinylidene fluoride co-hexafluoropropylene) (PVDF-HFP) blend polymers facilitate the amorphous phase with high melting temperature. 26PVDF-HFP can absorb a higher amount of salt and ionic liquid in the polymer matrix, providing higher mechanical stability. 27Plasticizers play an important role in enhancing the amorphousity of the polymer electrolytes.2][33][34] Dinitrile compounds (C≡N) show metal ion bonding between the electrodes and the electrolyte surfaces that enhances the interfacial stability and long battery cycling ability. 31Nitrile-based compounds also show high oxidation stability and low flammability. 32The ADN enhances the voltage stability window as well as reduces the charge transfer resistance at the electrode-electrolyte interface. 324][35] The addition of fillers to the GPEs is another technique used for the enhancement of ionic conductivity. 35,36The size of the fillers is an important factor to form a Lewis acid-base interaction between the polymer and the filler surface. 36On the other hand, the redox-active fillers enhance significantly the specific capacitance of the supercapacitor cell. 34,37,38The electrochemical performances like lithium-ion transference number, electrochemical stability window, and compatibility with the active electrode are important parameters for device fabrication. 39,40he broadband dielectric spectroscopy has been used to study the ion transport and dielectric properties of polymer electrolytes. 41he broadband dielectric spectroscopic technique also gives information about the ion transport between intra-and inter-polymer ion hopping in the amorphous polymer matrix along with the segmental motion of the polymer chain that arises from the thermal motion.Equivalent circuit models have been used to describe the Nyquist plots that contain different circuit elements like resistors and constant phase elements (CPEs). 42,43The CPE term arises from the leaky capacitance of the double-layer space charge capacitors formed at the electrode-electrolyte interface.
In the present work, ion dynamics and relaxation properties of GPEs containing dual redox additives have been investigated.The GPEs were synthesized by a solution cast method using poly(vinylidene fluoride-co-hexafluoropropylene) (PVDF-HFP) as a host polymer matrix, ADN as a plasticizer, 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (EMIM TFSI) as an ionic liquid, and diphenylamine (DPA) and copper iodide (CuI) as redox additive fillers.
Then, appropriate amounts of ADN and ionic liquid EMIMTFSI were added to the polymer solution.The mixture of the polymer, plasticizer, and ionic liquid was stirred by a magnetic stirrer for 3 h.Then, 4 wt.% DPA and CuI redox filler were added to the polymer mixture and further stirred for 2 h to get a homogeneous viscous solution.Finally, the viscous solution was cast on a glass Petridish for solvent evaporation at room temperature.The selfstanding films were obtained after solvent evaporation and preserved in vacuum desiccators for further studies.The thickness of the GPEs was nearly equal to 0.4 mm.Five different GPEs were prepared to determine the contributions of the individual components in the dielectric and conductivity relaxation properties.The nomenclature used in this report is mentioned as GPE1: PVDF-HFP + ADN.GPE2: PVDF-HFP + ADN + EMIMTFSI, GPE3: PVDF-HFP + ADN + EMIMTFSI + DPA, GPE4: PVDF-HFP + ADN + EMIMTFSI + CuI, and GPE5: PVDF-HFP + ADN + EMIMTFSI + DPA + CuI.

B. Dielectric measurement
The broadband dielectric spectroscopy measurements were carried out using an LCR meter (HIOKI, model IM 3536 lCR) in the frequency range of 4 Hz-8 MHz.The self-standing GPEs were sandwiched between two stainless steel electrodes with a diameter of 10 mm.The cell assembly was placed in a liquid N 2 cryostat.Measurements of conductance [G(ω)] and capacitance [C(ω)] of the samples were performed in vacuum in the temperature range from 203 to 333 K with 5 K sweep and temperature stability of ±0.01 K.The real and imaginary parts of the complex impedance (Z*), ac conductivity (σ*), dielectric constant (ϵ*), and electric modulus (M*) were obtained from the following standard relations: and where l and A are the thickness and area of the sample, respectively, and ε o is the free space permittivity (8.85 × 10 −12 F/m).

III. RESULTS AND DISCUSSION
The Nyquist plots of all the GPEs are shown in Figs.1(a)-1(e) at a temperature of 233 K.The Nyquist plot of GPE1 [Fig.1(a)] shows a depressed semicircle with higher bulk resistance.But, GPE2, GPE3, and GPE4 have two depressed semicircles with smaller grain and bigger grain boundary regions of the electrolyte.The ionic liquid plays the important role to produce two different microstructures in the electrolyte below the crystallization temperature of the ionic liquid, which was obtained earlier from the DSC studies of the GPEs, ionic liquid, and plasticizer. 34But for the GPE5, two prominent depressed semicircles appear due to grain and grain boundary regions of the electrolyte.The redox additives produce two different microstructures in the electrolyte below the crystallization temperature.The influence of grain contribution becomes higher in dual redox additives-GPE compared to other GPEs at 233 K.At the crystallization temperature (∼238 K), the nature of the Nyquist plot abruptly changed for different GPEs.The grain boundary region of GPE5 fully disappears and grain resistance increases [Fig.2(a)].The redox filler plays an important role in enhancing the grain/bulk resistance in the redox-added GPEs at the crystallization temperature of ionic liquid.5][46] This microstructural phase transition at the crystallization temperature affects the bulk resistance as well as the dielectric and relaxation properties of all the redox-added GPEs (discussed later).
Figure 2(a) shows Nyquist plots of GPE5 at different temperatures.The solid lines represent the best fit to the equivalent circuit model, as shown in the inset of the figure.The Nyquist plot below the crystallization temperature contains two depressed semicircles alone with low-frequency leaky capacitive part.The equivalent circuit model contains a series and parallel combination of resistance and constant phase elements that describe the different characteristics of ion conduction of the GPEs.Here, R 1 and R 2 are the grain and grain boundary resistances, respectively, and Q 1 , Q 2 , and Q 3 are the leaky capacitances.The circuit parameters obtained from the best fits are enlisted in Tables I and II at two different temperatures (approximately below and above the crystallization temperature).It is noted that the values of R 1 and R 2 decrease with the increase in temperature, but the temperature dependence of the leaky capacitance follows the opposite trend.The ionic conductivity at different temperatures has been calculated by using the following relation: where l and A are the sample thickness and area, respectively, and R b is the bulk resistance (R 1 + R 2 ). 41Table III shows the ionic conductivity at room temperature for different GPEs obtained from Eq. ( 1).Below the melting temperature of ADN, ion dynamics follows the Arrhenius relations indicating decoupled ion motion, but above the melting temperature of ADN, the ion dynamics is described by Vogel-Tammann-Fulcher (VTF) coupled ion dynamics. 32The contribution of the segmental motion is involved in ion dynamics after the melting temperature of ADN in the GPE.Figures 2(c) and 2(d) show the frequency-dependent real [σ 0 (ω)] and imaginary [σ 00 (ω)] parts of ac conductivity, respectively, for GPE5 at different temperatures.The solid lines represent the fitted data obtained from two different ion dynamics models described below.σ 0 (ω) spectra consist of three different regions in different frequency ranges.The double-layer space charge capacitor is formed across the electrode electrolyte interface at the low frequency region. 47At the intermediate frequency, the σ 0 (ω) become frequency-independent (plateau region), where short-range ion hopping (diffusive) or successful ion hopping is prominent.The frequency independent plateau region is also known as the dc conductivity.After a crossover frequency, the long-range ion hopping or unsuccessful hopping probability increases and sub-diffusive frequency dispersion region appears. 48This crossover frequency is called hopping frequency (ω H ). The diffusive and sub-diffusive regions could be described by the universal power law (UPL) model. 49,50According to the UPL model, the real and imaginary parts of the ac conductivity can be represented as and where n and m are the power law exponents (0 < n, m < 1).
It may be noted that the low-frequency electrode polarization region cannot be analyzed by the UPL relation.2][53] According to the PNP model, the ac conductivity can be represented by where the impedance of CPE is Z CPE (ω) ¼ C À1 dl τ 1 (iωτ 1 ) Àα , with 0 < α < 1. C dl and C b are the double layer and bulk capacitance, respectively, and τ 1 is the Maxwell-Wagner relaxation time related by τ 1 ¼ R b C b .The real and imaginary parts of the ac conductivity were fitted to Eq. ( 4) coupled with Eqs. ( 2) and (3), respectively, and the fitted parameters are enlisted in Tables IV and V respectively.The UPL model provides the dc conductivity (σ dc ) and hopping frequency (ω H ), while the PNP model provides the bulk and double-layer capacitance (C b and C dl ) of the electrolyte.Tables IV and V show the dc conductivity, bulk and double-layer capacitance for the GPE5, which increase with the increase in temperature.At the crystallization temperature, the values of all those parameters show noticeable changes.
Figures 3(a) and 3(b) show the inverse temperature dependence of the dc conductivity and hopping frequency respectively for GPE5 obtained from the UPL model.The nature of the dc conductivity plot shown in Fig. 3 where σ 0 , E σ , and k B are the pre-exponential factor, activation energy, and Boltzmann constant, respectively. 54It may be noted that the plots follow two Arrhenius relation over the two temperature regions.The dual ion dynamics region appears due to the crystallization of ionic liquid in the presence of the redox filler.Similarly, the inverse temperature dependence of the hopping frequency [Fig.3(b)] also follows the Arrhenius relation represented by where ω 0 , E H , and k B are the pre-exponential factor, activation energy, and Boltzmann constant, respectively. 21Two Arrhenius where ω H is the hopping frequency.Figure 3(c) shows the scaling of the ac conductivity spectra for GPE5 at different temperatures.The superposition of all the spectra confirms that the ion conduction mechanism follows the time-temperature superposition principle 55 and a common ion dynamics follows at different temperatures.It may be noted that the ac conductivity spectra do not superpose in the low-frequency region due to the electrode polarization of space charge.Figure 4(a) shows the real part of the dielectric constant spectra of GPE5 at different temperatures.The plot contains lowfrequency electrode polarization region along with high-frequency shoulder that signifies the segmental relaxation of the polymer chain.The effect can be clearly observed in the derivative dielectric constant spectra.The derivative (ϵ 00 der ) of the dielectric spectra, obtained using Eq. ( 8) below, gives the prominent signature of segmental relaxation peak, 56 Figure 4(b) shows the ϵ 00 der spectra of GPE5 at different temperatures.The distinct segmental relaxation peaks provide the segmental relaxation time (τ s ).The inverse temperature dependence of the segmental relaxation time for different GPEs is shown in Fig. 4(c), which follows the Arrhenius relation.The redox-added GPEs have shown a sudden change of segmental relaxation time at the crystallization temperature of ionic liquid similar to the hopping frequency and the dc conductivity.
The ionic relaxation is a resultant of the segmental relaxation and the conductivity relaxation.The contribution of the conductivity relaxation can be understood from the imaginary part of the electric modulus spectra.The electric modulus is defined as the inverse of the dielectric permittivity and is represented by M * (ω) , where ε * (ω), M 0 (ω), and M 00 (ω) are the complex dielectric permittivity, real part, and imaginary part of the electric modulus, respectively. 36,57It may be noted that the low-frequency electrode polarization effect is suppressed in the modulus formalism.Figure 5(a) displays the imaginary part of modulus spectra for GPE5 at different temperatures, which exhibits distinct relaxation peaks.The peak position of M 00 (ω) spectra provides the conductivity relaxation time expressed as τ c ¼ 1 ωc .It is noted that the peak positions shift to higher frequencies with the increase in temperature.But, at the crystallization temperature of the ionic liquid, the shifting nature of the peak position suddenly changes due to the contribution of the redox fillers in the GPE5.The M 00 (ω) spectra have been analyzed using the Havriliak-Nigami (HN) model represented by 58  where M s and M 1 are the low-and high-frequency limiting values of the real part of the complex modulus [M 0 (ω)] and τ HN is the relaxation time.α HN and γ HN are the shape parameters with limiting condition 0 , α HN or γ HN , 1 and 0 , α HN :γ HN , 1.The experimental M 00 (ω) spectra have been fitted to the HN function [Eq.( 9)], and the fits (solid lines) are shown in Fig. 5(a).The values of the parameters obtained from the fits indicate non-Debye relaxation for the materials.Figure 5(b) shows that the inverse temperature dependence of the relaxation time, obtained from the fits, follows the Arrhenius relation expressed as where τ 0 , E HN , and k B are the pre-exponential factor, activation energy, and Boltzmann constant respectively. 2100 (ω) spectra also follow the universal scaling relation as shown in Fig. 5(c).The scaling relation can be represented as where ω Max is the peak frequency. 55All the M 00 (ω) spectra overlap on a single muster curve, which signifies that the M 00 (ω) spectra follow the time-temperature superposition principle and indicate a relaxation mechanism, which is independent of temperature and composition.
The modulus function can be related to the electric decay function in the time domain.The Fourier transform of the decay function can be represented as 36 where w(t) is the decay function of the applied electric field E(t), represented by The experimental decay function is obtained from the inverse Laplace transform of Eq. ( 12), represented by The shape of the decay function provides Debye or non-Debye relaxation in the SPE.The broad peak in the imaginary modulus spectra, indicating non-Debye relaxation function, can be analyzed using Kohlrausch-Williams-Watts (KWW) function represented as [50][51][52][53][54][55][56][57][58][59][60][61] where τ KWW and β are the relaxation time and stretched exponent (0 , β , 1), respectively.The experimental decay function of GPE5, obtained from Eq. ( 14), is shown in Fig. 6(a) at different temperatures.The decay function has been well fitted to the KWW function [Eq.(15)] represented by solid lines in Fig. 6  in the present samples.The values of β also confirm that the ion dynamics in the GPEs are co-operative in nature. 61he inverse temperature dependence of the KWW-relaxation time obtained from Eq. ( 15) follows the Arrhenius relation, which is represented by where τ 0 , E KWW , and k B are the pre-exponential factor, activation energy, and Boltzmann constant, respectively.The KWW-relaxation time shown in Fig. 6(c) also exhibits a similar nature to the inverse temperature-dependent relaxation spectra at the crystallization temperature of the ionic liquid.Thus, the redox contribution to the conductivity as well as relaxation dynamics was well described by different relaxation models.
It is worthy to note that the HN-function in modulus spectra and KWW-function in electric decay function is co-related by the following expression: 21,62 β ¼ (α HN γ HN ) It has been observed that the values of the stretched exponent (β) obtained from fitted parameters from Eq. ( 15) are very close to the values obtained from Eq. ( 17) using the values of parameters α HN and γ HN .
It may be mentioned that the application of the GPE with dual redox additives as supercapacitor was reported earlier. 34A symmetric activated carbon-based supercapacitor was fabricated, and its electrochemical stability window, interfacial stability, charge-discharge properties, etc., were investigated.It was observed that the specific capacitance (243 F/g) and energy density (11 Wh/

IV. CONCLUSIONS
Highly conducting gel polymer electrolytes (GPEs) have been prepared using poly (vinylidene fluoride-co-hexafluoropropylene) P(VdF-HFP) as a host polymer, adiponitrile (ADN) as a plasticizer, 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl) imide (EMIMTFSI) as an ionic liquid, and diphenylamine (DPA) and copper iodide (CuI) redox additives as fillers.The ion dynamics of these composite systems has been analyzed using broadband dielectric spectroscopy.The equivalent circuit model is used to fit the Nyquist plots.The fitted Nyquist plots signify the grain and grain boundary contributions of GPEs, and their effects become prominent in the conductivity and relaxation mechanisms.Three different ion conduction regions are observed in inverse temperature-dependent conductivity spectra due to the effect of crystallization of the ionic liquid and melting temperature of the plasticizer.The ion conduction follows the Arrhenius relation below the melting temperature of the plasticizer, and above this temperature, the ion conduction follows a different mechanism.The UPL and the PNP models describe well the electrode polarization, frequency-independent diffusive and high-frequency subdiffusive ac conductivity spectra.The contributions of the segmental relaxation and conductivity relaxation are obtained from the derivative dielectric spectra and imaginary modulus spectra, respectively.The experimental decay function is well fitted to the KWW function.The values of the stretched exponent of the KWW function confirm the non-Debye nature of the ion relaxation in the GPEs.The KWW model is also used to describe the decay function.The stretched exponent of HN-function and KWW-function is found to be co-related.The inverse temperature dependence of σ dc , ω H , τ s , and τ HN obtained from different models follows the Arrhenius relation.The values of the stretch exponent confirm the non-Debye nature of the ion relaxation.The scaling of the ac conductivity and modulus spectra depicts validity of the time-temperature superposition (TTS) principle in the investigated GPEs.The influence of dual redox additives is clearly observed in the values of ionic conductivity, which increase with the increase in dual redox additives due to the increase in ion diffusivity.
FIG. 2. (a) Nyquist plot of GPE5 at different temperatures, solid lines represent the fitted data obtained from equivalent circuit model shown in the inset.(b) Inverse temperature-dependent dc conductivity plot for different GPEs obtained from Nyquist plot.(c) and (d) Real and imaginary parts of ac conductivity spectra of GPE5 at different temperatures.The solid lines represent the best fits of the UPL and PNP models to the experimental data.
(a) is very close to the previous result [Fig.2(b)] obtained from the Nyquist plots.The inverse temperature dependence of the dc conductivity follows the Arrhenius relation represented by: ) and 3(b) conclude that the decoupled ion conduction follows in-between two individual phase transition regions below the crystallization of the ionic liquid and the melting of the plasticizer.The mechanism of the ion dynamics of the GPEs can also be studied by the scaling relation of the ac conductivity represented by Ghosh and Pan model,55

FIG. 3 .
FIG. 3. (a) and (b) The inverse temperature-dependent dc conductivity and hopping frequency plot of GPE5 obtained from the UPL model.(c) The scaling of the ac conductivity spectra of GPE5.
(a).The values of the stretched exponent β obtained from the fits are shown in Fig.6(b) as a function of temperature.It may be noted that the values are almost independent of temperature and less than unity, confirming the non-Debye relaxation

FIG. 4 .
FIG. 4. (a) Real part of the dielectric spectra of GPE5 at different temperatures.(b) Derivative dielectric constant spectra of GPE5 at different temperatures.(c) Inverse temperature dependence of the reciprocal segmental relaxation time obtained from derivative dielectric spectra.Dotted lines represent the best fits to the Arrhenius relation.

FIG. 5 .
FIG. 5. (a) Imaginary part of modulus spectra of GPE5 at different temperatures.Solid lines represent the best fit to the HN-function.(b) Inverse temperature dependence of the reciprocal conductivity relaxation time obtained from fitted HN-function.The dotted lines represent the best fits to the Arrhenius relation.(c) Imaginary modulus spectra of GPE5 scaled by the universal scaling relation.

FIG. 6 .
FIG. 6.(a) Experimental decay function in time domain for GPE5 at different temperatures.Solid lines represent the best fits to the KWW-function.(b) Inverse temperature dependence of the reciprocal KWW-relaxation time obtained from KWW-function.The dotted lines represent the best fit to the data.(c) Variation of stretched exponent (β) with temperature for different GPEs.

TABLE I .
Fitted parameters obtained from Nyquist plot of GPE5 (below the crystallization temperature) at different temperatures.

TABLE II .
Fitted parameters obtained from Nyquist plot of GPE5 (above the crystallization temperature) at different temperatures.

TABLE III .
Room-temperature dc conductivity obtained from Nyquist plot and activation energy (obtained from inverse temperature-dependent dc conductivity plot) below the crystallization temperature for different GPEs.

TABLE V .
List of parameters obtained from the fits of the PNP model to the imaginary part of complex conductivity spectra of GPE5 at different temperatures.

TABLE IV .
List of parameters obtained from the fits of the PNP model to the real part of complex conductivity spectra of GPE5 at different temperatures.