Nano-Filler Induced Ionic Conductivity Enhancement and Relaxation

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C: Energy Conversion and Storage; Energy and Charge Transport

Nano-Filler Induced Ionic Conductivity Enhancement and Relaxation Property Analysis of Blend Polymer Electrolyte Using Non-Debye Electric Field Relaxation Function Subir Kumar Patla, Ruma Ray, Sanat Karmakar, Shantanu Das, and Sujata Tarafdar J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b10460 • Publication Date (Web): 11 Feb 2019 Downloaded from http://pubs.acs.org on February 14, 2019

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The Journal of Physical Chemistry

Nano-Filler Induced Ionic Conductivity Enhancement and Relaxation Property Analysis of Blend Polymer Electrolyte using Non-Debye Electric Field Relaxation Function Subir Kumar Patla1,2, Ruma Ray2*, Sanat Karmakar1*, Shantanu Das3, Sujata Tarafdar2 1

Condensed Matter Physics Research Centre, Department of Physics, Jadavpur University,

Kolkata - 700032, India 2

Physics Department, Gurudas College, Kolkata - 700054, India

3 Reactor

Control System Design Section (E & I Group), BARC, Mumbai - 400085, India *Emails:

[email protected] [email protected]

ABSTRACT: The enhancement of conductivity of composite polymer as a dielectric material is an essential requirement for the electrostatic storage devices. We have modified the microstructure of the polymer matrix by introducing insulating nano filler SiO2. The effect of such filler on the ionic conductivity of composite polymer electrolyte has been investigated using a variety of experimental techniques along with non-Debye type of relaxation functions. We have achieved optimum conductivity enhancement at a threshold filler concentration of 0.7 wt% in the blend polymer matrix composed of Poly (ethylene oxide) [PEO], Poly (vinilidene fluoride) [PVDF] (80:20) and salt NH4 I (35 wt%). Such an enhancement of conductivity is a result of formation of highly conducting

interphase region around the nano filler surface. The mobility of conducting species is found to increase enormously in the presence of filler. As a consequence, ionic conductivity of filler-induced blend polymer electrolyte increases three times of its magnitude (3.02 × 10-3 S/cm) compared to that without filler. The occurrence of two different activation energies which decrease with increasing filler concentration, as determined from temperature dependent conductivity, has been well explained from dynamics of free and contact ions. A non Debye behaviour of relaxation properties has been analysed using a newly approached one parameter Mittag-Lefler function. The experimental decay

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function fits very well using Mittag-Lefter function as compared to conventional non Debye Kohlrousch-Williams-Watts (KWW) function used in the literature.

1. INTRODUCTION Solid Polymer electrolytes (SPE) are widely used in charge storage devices1 due to their good thermal and electrochemical properties

2

rather than liquid electrolyte. However, SPE

suffers from poor ionic conductivity3 at room temperature. This problem was circumvented by different methods. Polymer blending is one such well-known technique4 that usually reduces the overall crystallinity of the polymer system. But some other factors arise due to polymer blending producing undesired complexity in the system. For example, miscibility of component polymers within the blend is a very important factor depending on which a composite resumes different textures. Thermal property is also improved5

by polymer

blending. Apart from using plasticizer6 for enhancement in amorphous content of the SPE, nano-filler incorporation7 also emerges as

a very useful and modern technique for

remarkable conductivity enhancement. Among different mixing techniques, like in situ mixing8,9 or mechanical mixing10 SPE films prepared by in situ mixing process comes out to be the most effective8 for conductivity enhancement. Filler size is also a very important factor for structural modification in polymer electrolyte 11,12 . Presence of active filler13-15 in polymer electrolytes followed different ion transport mechanism than that by passive fillers 16.

Different theories have been evolved so far for explaining polymer filler interaction of

which percolation and effective medium theory 17-19 is of worth mentioning. This paper reports the effect of insulating nano – filler in SPE with blend host polymer system and optimizes the filler concentration for best performance at room temperature. PEO-PVDF based blend polymer electrolyte with salt NH4I has been extensively studied in our previous work20 . Insulating silicon dioxide (SiO2) nano filler in the above mentioned


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blend SPE influences different factors like carrier mobility, polymer chain flexibility21, ion dissociation i.e. carrier concentration. In the presence of insulating nano-filler in a two – phase SPE system, a

high

conducting interphase layer is known to form around the nano filler particles22 . The area of this interphase layer is inversely proportional to the size23 of the nano filler. These two factors are responsible for structural alteration of the polymer matrix16. The interphase region formed around the nano-filler is found to be more amorphous than the rest of the polymer matrix which results in an enhancement of polymer segmental motion in the interphase region23. However, preparation of nano–composite, irrespective of any method, requires one basic criterion – uniform dispersion of filler content in the polymer system23. Nano filler creates disturbance in the polymer matrix and hence effective crystallinity of the system becomes affected. Moreover the cationic (NH4+) part of the dissociated salt interacts with ether oxygen24 of the PEO chain by hydrogen bonding. The ion-polymer interaction through hydrogen bonding exists simultaneously in both amorphous and crystalline regions20,25 , though the bond strength in amorphous region differs from that in the crystalline region. Cations, strongly coordinated with polymer chains in crystalline regions, are denoted as contact ions. These ions are responsible for short range conduction and are observed to be affected in the presence of nano-filler. In this study, FTIR results have shown contact ion band is shifted to lower wave number side with increasing nano filler concentration. Shifting of band towards low energy side signifies decrease in corresponding bond (Hydrogen bond) strength resulting in an increase in mobility of these strongly bonded cations or contact ions2628.



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2. EXPERIMENTAL 2.1. Materials PVDF (MW= 534,000), PEO (MW =105) and Nano-filler (SiO2) were obtained from Sigma Aldrich Pvt. Ltd. Ammonium Iodide (NH4I) salt was procured from MERCK. The solvent N, N-Dimethylformamide (DMF, 99.5% purity) was purchased from MERCK. 2.2. Film Preparation and Sample Nomenclature PEO-PVDF based blend polymer nano-composites were prepared by conventional solution casting technique. A mixture of dry PEO (80 wt%) and PVDF (20 wt%) powders added with requisite amount (0 – 1.3 wt%) of nano filler (SiO2) were ball milled at 300 rpm for 30 minutes, keeping the ball to sample mass ratio fixed at 16:1. The ball milled mixture was dissolved in DMF solvent after adding proportionate amount of salt (35 wt%) in it. This solution was sonicated in a bath sonicator at temperature 70 0C for 15 minutes followed by magnetic stirring for another 16 hours at room temperature. The homogeneous viscous solution was deposited in glass petri dish kept at 100 C temperature for 24 hours to produce a uniform film. To identify individual sample, a sample nomenclature scheme has been proposed in this text. 80% PEO and 20% PVDF were used to prepare this blend polymer electrolyte. Salt amount (35 %) was kept constant for all the samples while nano-filler concentration varied from 0 to 1.3 wt% with respect to total polymer. Table 1. Sample nomenclature to identify the amount of nano filler in the polymer composite based on PEO -PVDF (4:1 weight ratio) and 35 wt% of NH4 I

SiO2 (wt%)

0.0

0.3

0.7

1.3

Abbreviation

S0

S3

S7

S13

2.3. X-Ray diffraction (XRD) Miscibility of Individual polymer component in the blend was confirmed by X-Ray diffraction study. The diffraction measurement was carried out using Bruker-AXS 4 ACS Paragon Plus Environment

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diffractometer with CuKα line (1.54 Å) at an operating voltage 35 kV and current 35 mA. Scattered angle (2θ) was chosen from 10 degree to 50 degree and scan rate 3 /minute for output data collection. The sample was kept on a glass substrate whose scattered intensity is much less than the sample under study. Characteristic peaks in the XRD pattern have been characterized by using previous literature. The variation in peak position and area under the corresponding peak as a function of filler concentration have been observed to compare the filler – induced variation in effective crystallinity of the electrolyte. As the experimentally obtained diffraction pattern contains overlapped peaks, the individual peak can be extracted by deconvoluting the XRD pattern. The deconvolution was done by fitting Gaussian profiles using a software provided by ‘Originpro’. The peak position, peak width and area under the peak etc have been estimated from the fitting parameters. (Fig. S1, supplementary information).

2.4. Field Emission Scanning Electron Microscopy (FESEM) Surface morphology was investigated using Field Emission Scanning Electron Microscopy [FEIC-QUO-35357-0614]. All the sample was coated with gold by using ‘Bruker Quantax 100’ Gold coater. Operating voltage taken as 20 kV for lower magnification and 5 kV for higher magnification. Sample mounted on metal stub by using double sided carbon tape. Image taken over the broad magnification range (50X to 10000X). 2.5. Thermogravimetric Analysis (TGA) Thermal stability of individual blend component has been determined by Thermo Gravimetric Analysis (TGA), TGA/SDTA851e (Mettler Toledo AG) instruments at a constant heating rate

(100C/minute) within a temperature range of 30 0C to 700 0C under air

atmosphere. Rate of sample decomposition and exact decomposition temperature is



calculated from differential thermal analysis (DTA). DTA analysis is performed by 1st order differentiation of weight loss of the TGA data as a function of temperature. Variation of peak area in DTA plot signifies the amount of decomposition. 2.6. Differential Scanning Calorimetry (DSC) DSC measurement is done using Perkin-Elmer Diamond equipped with intracooler. The melting thermograms are taken from the 1st heating cycle within a temperature range from – 80 0C to 200 0C at a constant heating rate of 20 0C /minute under N2 gas atmosphere. Glass transition temperature (Tg) of the polymer chain and melting temperature (Tm) of giving substrate is calculated from the DSC measurement. 2.7. Fourier Transform Infrared Spectroscopy (FTIR) Vibrational spectra of different band of polymer composite film have been identified by Fourier transform infrared spectroscopy using Bruker, Tensor II in the range of wavenumber from 550 to 4000 cm

– 1.

Attenuated total reflection (ATR) mode was used to collect the

spectra in the atmospheric background. Scan rate and resolution of FTIR measurement was taken 16 and 4 cm-1 respectively. The shifting of band position and variation of intensity of vibrational bands determines the nature of chemical interaction as well as structural variation of the polymer composites. The exact significance of different bands is identified by using previous literature20 . The deconvolution of vibrational spectra as in the case of XRD profile, has been also applied for separating and estimating the contribution of individual band from the overlapping spectra. The relative area proportion of the deconvoluted bands indicates strength of the individual vibrational mode29,30. 2.8. Impedance Spectroscopy (IS): Experiment and analysis Dielectric property was measured by Agilent 4294A-Precession Impedance Analyzer. The measurement was performed with the sample sandwiched between two blocking electrodes


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(Copper) for frequencies within a range of 40 Hz to 20 MHz. Complex impedance (Z*) can be expressed as 𝑍 ∗ = 𝑍′ ― 𝑖 𝑍 "

(1)

Where Z' and Z" are the real part and imaginary part of complex impedance, respectively. Bulk resistance (𝑅𝑏) was calculated from Cole-Cole plot (Z" vs. Z'), where the imaginary part of impedance (Z") became minimum. The dc conductivity (𝝈dc ) is calculated from the following relation 𝑙

(2)

𝜎𝑑𝑐 = (𝑅𝑏.𝐴)

where A and l are the area of cross section and thickness of the sample, respectively. The complex permittivity (ε*) of a system is defined as ε ∗ = ε′ ― iε″

(3)

where ε′ and ε″ are the real and imaginary part of the permittivity respectively. Real permittivity (ε′) represents the dielectric constant of the material due to the polarization of electric dipole in the presence of external electric field. The imaginary permittivity (ε″) corresponds to the dielectric loss of electric dipoles. The ε′ and ε″ can be calculated from the following equations. ―𝑍′′

ε′ = [ωC (𝑍′2 + and

𝑍′

ε′′ = [ωC (𝑍′2 +

(4)

𝑍′′2)]

𝑍′′2)]

(5)

ω is the angular frequency. The capacitance (C) of the empty cell is given by 𝐶 = 𝜀0

𝐴

(6)

𝑙



Where ε0 is the vacuum permittivity (8.85 x 10

-14

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F/cm). The loss tangent or the dissipation

factor, tanδ is calculated using the following relation: tan δ =

ε′′

(7)

ε′

The tan δ varies with angular frequency (ω) and becomes maximum at a certain frequency (ωp) corresponding to the characteristic dielectric relaxation time (τ)31, related by the equation ωp τ = 1. If the temperature dependent dc conductivity follows the Arrhenius relation, then activation energy can be calculated by using this relation 𝐸

𝜎𝑑𝑐 = 𝜎0𝑒 ― 𝑅𝑇

(8)

where 𝜎0 is the pre-exponential factor, E is the activation energy. R is the universal gas constant and T is temperature. AC conductivity (𝜎𝑎𝑐) of the material was calculated from the following relation (9)

𝜎𝑎𝑐 = 𝜔𝜀𝑟𝜖0𝑡𝑎𝑛𝛿

where 𝜔,𝜀𝑟,𝜖0 is the angular frequency, relative permittivity and free space permittivity respectively. AC conductivity of dielectric material follows the universal power law (Jonscher’s power law). Jonscher’s power law32,33 can be written as 𝜎𝑎𝑐 = 𝜎𝑑𝑐 +𝐴𝜔𝑛

(10)

‘A’ being the pre factor depends on the material itself and n is a temperature constant. The effect of electrode polarization34 is observed at a low frequency regime due to the formation of space charge region. The study of complex electric modulus (M*) shows reduced effect of this electrode polarisation since the electric modulus is defined as the inverse of complex permittivity. 𝑀∗ =

1 Ɛ∗

= M′ + i M″

where,


(11)

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M′ = M′′ =

Ɛ′′ (Ɛ

′2

(12)

+ Ɛ′′2) Ɛ′

(Ɛ′2

(13)

+ Ɛ′′2)

Diffusion Coefficient and Carrier Concentration: Diffusion coefficient is calculated following the Trukhan Model35,36 framed with the concept of electrode polarization phenomenon and accordingly the diffusion coefficient is defined as

2𝜋𝑓𝑚𝑎𝑥𝐿2

(14)

𝐷 = 32(𝑡𝑎𝑛𝛿)2

𝑚𝑎𝑥

where L and 𝑓𝑚𝑎𝑥 are the sample thickness and relaxation frequency where loss tangent ( tan 𝛿) become maximum respectively. In this model, it is assumed that both cations and anions have the same diffusion constant. This assumption is reasonable, as there is no significant difference of the diffusion constant of both type of ions was found in earlier literatures37,38. All ions do not contribute in ion conduction process since some of them agglomerate producing aggregation of ions in the polymer matrix. Effective free carrier concentration, n, was calculated from Einstein’s equation. 𝑛=

𝜎𝑑𝑐𝑘𝑇

(15)

𝐷 𝑒2

where k is the Boltzmann constant, e is the elementary charge, T is the absolute temperature and 𝜎𝑑𝑐 represents dc conductivity. If we neglect ion-ion interaction, ionic conductivity can be expressed as (16)

𝜎 = 𝑛.𝑒.𝜇

Where 𝜇 is the mobility, calculated using equation (13).

3. RESULTS AND DISCUSSION 3.1 Surface morphology and structural variation of polymer composite 9 ACS Paragon Plus Environment


SEM micrographs (Fig. 1) show fairly uniform surface texture at lower filler concentrations (< 0.7 wt%). At 0.7 wt% filler concentration, the surface profile changes significantly with the appearance of regions of almost spherical in shape (Fig. 1). A distinct thin layer is observed around each spherical region. With further increase in the filler concentration, the individual spherical region starts to overlap or connect with neighbouring region (Fig. 1) .

Figure 1. SEM micrograph, S0, S3, S7 and S13 are the sample specification (see table 1 for composition of these specification) .

A schematic representation of these regions is shown in Fig. 2. The interphase region, around each spherical nano fillers is expected to form due to the Lewis acid-base interaction between the filler surface and the cation species of the polymer electrolyte39-41. This results in a higher conductivity of the cation – rich interphase region than the rest of polymer matrix16. The ion transport through the high conducting regions, as mentioned above can be explained using percolation model. Ion transport through a polymer composite matrix: Percolation Model :


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Percolation model, in general, is used to explain the ion transport of a composite in terms of the concentration of its constituent phases. At a critical concentration, called percolation threshold (Pc), the system undergoes a structural transition and dramatic changes are observed in the corresponding properties. In the present study the percolation model has been implemented to understand the structural variation and conductivity enhancement in the polymer electrolyte system that occurs in presence of the insulating nano-filler. We also verify the existence of finite percolation threshold (Pc) and its universal value in three dimension. The schematic representation of three phase regions is shown in Fig. 2. At low concentration of filler (Phase –I), typically below 0.7 wt%, a highly conducting phase II is formed around individual filler. The phase II is well separated by a rest of the polymer matrix (phase III). As the filler concentration is increased the region II (phase II) starts to merge with phase II of other fillers forming a well-connected conducting path (Fig. 2 b). Fig. 2(c) represents above the critical concentration when an infinite as well as continuous system – spanning cluster out of the interfacial region is formed. Accordingly the conductivity reaches maximum at a threshold concentration when connected pathways are formed throughout the sample with rare possibility of inhibition by insulating filler particles. However, for higher filler concentrations, interfacial content decreases and hence connectivity reduces due to the effect of filler aggregation, as illustrated in Fig. 2(c). The percolation threshold (fc) corresponding to the 3rd phase volume fraction was estimated when thickness of the interphase is known. The thickness of this region depends on the nano filler dimension. Previous study suggests that the thickness is chosen to be 3.5 times the filler radius16. Under this condition, the percolation threshold comes out to be 0.25 at maximum conductivity (0.7 wt% filler concentration). This value is quite close to the three dimension random percolation threshold (Pc = 0.31)42,43.

Such an enhancement of

conductivity at the threshold filler concentration has also been supported by the XRD data 11 ACS Paragon Plus Environment


(Fig. S1 and Table S1, supplementary material). Increase in the area of the diffraction profile i.e, broadening of the peak, suggests that amorphousity increases, leading to an enhancement of conductivity. This result is consistent with the percolation model. It is important to mention that the morphology of the nano-filler strongly affects the percolation threshold42. This is due to the fact that the shape of the nano-fillers, such as nanorods, nanotubes, nanosphere,

alters the connectivity as well as effective area of the interphase region.

However, we have only used amorphous powder of nano-filler SiO2 (nano-sphere).

Figure 2. Schematic representation of nano-filler induced polymer texture for three different filler concentrations. The yellow spheres correspond to nano-filler and blue regions to the interphase layers. Mobile ions (red dots) within blue region correspond to contact ions. Red dots outside the blue regions represent free ions.

3.2 Filler induced ion polymer interaction and polymer microstructure FTIR study has been employed in order gain insights into the microstructural change of polymer composites. PEO-PVDF base blend electrolyte has already been studied in our previous work20. IR spectra is normalized considering peak at 876 cm-1 as the reference band since the position of this band remains undisturbed even after the formation of composites. Two distinguished peaks (Fig. S2 in supplementary material) at 831 and 841 cm-1, corresponding to mixture of CH2 rocking and C-O-C stretching vibrations respectively have been observed. These two peaks collapse and form a single broad peak at 835 cm-1 in S7 system. These two peaks reappear separately at higher filler concentration, i.e, in sample S13. 12 ACS Paragon Plus Environment

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Another combination of two peaks are also observed in S0 system at 2868 (1st) and 2894 (2nd) cm-1 (Fig. S3) respectively. S0 system shows that the intensity of the 1st peak (2868 cm-1) is lower than the 2nd peak (2894 cm-1). However, with increase in filler concentration (upto 0.7 wt%, i.e. for S7 samples) intensity of the 1st peak remains higher than that of the 2nd peak and peak positions also shift to 2872 and 2901 cm-1 respectively. S13 system shows the opposite trend i.e. the intensity of the 1st peak gradually decreases with considerable shifting of the peak positions. After filler incorporation the positions as well as area of these bands get altered. S0 system possesses the free and contact ion peaks at 3193 and 3452 cm-1 (Fig. 3) respectively. In S7 system, the position of the free ion peak shifted to a higher wavenumber region (3198 cm-1) and contact ion peak shifted to lower wavenumber region (3441 cm-1) whereas in S13 system, both peaks shift to their initial position as found in S0. The area under free ion peak decreases at the cost of increase under the contact ion peak for filler concentration up to a 0.7 wt% (S7). Above 7 wt% The reverse trend appears for filler higher concentrations, above 7 wt%. It indicates that percentage of free ion decreases (as shown in Fig. 3) with an increase of interphase region.

Figure 3. FTIR spectra within 3100-3650 cm-1 wavenumber range. The inset table represents the percentage of free ion and contact ions respectively. These values are calculated from the area under each deconvoluted IR band. 13 ACS Paragon Plus Environment


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IR band shifting or intensity variation signifies the chemical interaction between nano filler and polymer mixture. Cations interact with the ether oxygen of Poly (ethylene oxide) through hydrogen bonding hydrogen bonding27,28.

24.

Position of –OH vibration band depends on the mode of

Free and contact ion bands were identified with two different

strengths of hydrogen bonding. Actually contact ions remain localised while the mobile free ion possesses the ability of long range hoping, with increasing filler content (to 0.7 wt %) more and more conducting cation gets trapped within the interphase layer strong

as a result of

interaction between cation and filler39,40, as already mentioned in earlier sections.

This behaviour is reflected through the increase in percentage of contact ion. The position of contact ion band shifted to lower wavenumber side (Figure 3). It is very important to note that the strength of hydrogen bonding decreases within the interphase region. As a result, the mobility of ions changes (Table 2) with filler concentration and reveals strong correlation (detailed analysis given with the impedance spectroscopy results) with the conductivity variation. 3.3 Thermal stability In order to check the thermal stability of the polymer composites with nano filler, TGA, DTA measurements have been employed. The results of these experiments have been presented in the supplementary materials (Figs. S4 and S5). Thermometric measurements indicate that the decomposition temperature as well as rate of ion interaction does not alter significantly upon incorporation of nano-filler. These results suggest the good thermal stability of the composite which indeed an essential requirement for electrochemical applications. DSC result predicts the nature of glass transition temperature (Tg) of the composite. As shown in Fig. 4, the lowest Tg has been obtained at filler concentration of 0.7 wt%. The 14 ACS Paragon Plus Environment

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most flexible mechanical property is therefore, expected at this optimum concentration. Such a low Tg of this composition is also advantageous due to negligible degradation probability at and well below room temperature47.

Figure 4. DSC plot of nano composite system. The inset table represents the Glass transition temperature varying with filler percentage, obtained from the DSC curve.

Further, low Tg value also indicates the pronounced segmental mobility of polymer chains at room temperature. Hence the incorporation of filler is expected to enhance the segmental motion of polymer chains which in turn contributes to the enhancement of ionic conductivity. This is also supported by fact that the highly amorphous and high conducting region is formed around the nano-filler due to Lewis acid base interaction between filler and the polymer matrix. In this region (Region II in Fig. 2) the enhancement of segmental motion are due to increase in flexibility and disruption of polymer chain entanglement. However, at very high concentrations of filler, one would expect the polymer being trapped inside the filler matrix, which would, in turn, restrict the polymer segmental motion. We indeed found that the increase in Tg and filler aggregation due to restriction of polymer segmental motion at higher filler concentration.



3.4 Impedance Spectroscopy 3.4.1 Dielectric properties and DC conductivity Fig. 5 depicts that dc ionic conductivity shows maximum value at 0.7 wt% of filler concentration. Similar trends has been found in the real part of the permittivity (Ɛ') at low frequency (< 102 Hz). (Fig. S6 in supplementary material). The decrease in Ɛ' at low frequency regime can be attributed to the electrode polarization effect.

Figure 5. Variation of DC conductivity (σdc ) with increasing filler concentration. Maximum of σdc was obtained at filler concentration of 0.7 wt%.

Fig. 6 shows tanδ plot with frequency, indicating the dielectric behaviour. This analysis is to determine the ion transport parameters of polymer composites. It is clearly evident from Fig. 6 that the tanδ which shows maximum for S0, decreases drastically with increasing filler concentrations. The peak position of tanδmax is also found to shift with filler concentrations.


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Figure 6. Tangent loss (Tanδ) with frequency for different composites indicated in the figure legend (see table 1 for filler concentration)

Dielectric and transport parameters, viz. diffusivity

(D), mobility (μ) and carrier

concentration (n) have been calculated using the Trukhan model35,36 and presented in Table 2. Table 2. Conductivity and calculated values of transport parameters using Trukhan model.

Sample

𝝈dc

D

μ

N

name

(S/cm)

(cm2 / sec)

(cm2 V−1 s)

(cm−3)

S0

1.01 × 10 -3

2.46×10-12

9.53×10-11

6.61×1025

S3

1.98 ×10 -3

8.96×10-10

3.47×10-8

3.56×1023

S7

3.02 × 10 -3

1.68×10-8

6.52×10-7

2.89×1022

S13

4.52 × 10 -4

4.76×10-6

1.84×10-4

1.53×1019

Fig. 7 shows the Arrhenius behaviour of DC conductivity with two different slopes at two different temperature regimes, suggesting the two different activation energies of the electrolytes with and without filler content.



Figure 7. Temperature dependent DC conductivity for S0 and S7 samples. Two different linear regions existing in each sample indicate change in activation energy.

Ɛ' value identifies the amount of electric energy stored from the external field. The maximum value of dielectric constant at lower frequencies and decrease its value at higher frequency suggests that the system behaves like a polar dielectric45-47. The increase in dielectric constant and decrease in magnitude of corresponding tangent loss of the composite in the presence of filler is due to the formation of interphase region as describes in Fig. 2. Such an interphase region enhances probability of the localized hopping instead of long range ion transportation48. As described in table 2, nano-filler also enhances the mobility of ion species which contributes predominantly for the enhancement of the effective conductivity of the system. Temperature dependent conductivity show two activation energies in this polymer matrix. Estimated activation energies, 29.58 kJ/mol and 8.18 kJ/mol for S0 system reduce to 11.22 kJ/mol and 2.35 kJ/mol, respectively for S7 system. Two activation energies found in the composite system are due to two different conducting species, such as, free ions and contact ions 49. The decrease in activation energies in the presence of filler particles largely influences the dc conductivity 8. It is known that the both free and contact ions participate in conduction process in two different ways45. In particular, free ions contribute to long rage 18 ACS Paragon Plus Environment

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hopping motion while contact ions to the short range movement. Although, we can comment the relative contribution of free and contact ions on the enhancement of conductivity, the individual or absolute contribution cannot be predicted from the present study. As has been observed from FTIR, the percentage of free ions decreases while the percentage of contact ions increases due to incorporation of filler. Therefore, the main contribution in conductivity enhancement is due to contact ions.

3.4.2 AC conductivity & Ion transport mechanism An insight into the ion transport mechanism in polymer nano-composite can be inferred from results and analysis of ac conductivity (𝝈ac) spectra and conductivity relaxation phenomenon.

Fig. 8 shows 𝝈ac as function of frequency and three distinct regions of

frequencies have been identified. The region III, as shown in Fig. 8, increases rapidly with increasing frequency is called the dispersive region.


the conductivity


Figure 8. AC conductivity spectra of polymer composites. The solid line represents the fitted curve using Jonscher’s power law and scatter plots are experimental curve.

In general, 𝝈ac can be fitted very well with the help of Jonscher’s power law (Eq. 10). The values of n decrease with increase in filler concentration (Fig. S7). However the trend changes after 0.7 wt% filler concentration and it starts to increase again. It is worth mentioning that in S3 and S7 systems only two regions (I and II) are available. Region III totally disappears in these systems. The dispersive region of AC conductivity spectrum can be explained using jump relaxation model (JRM)50. In this model, ions jump from one site to its native neighbouring available position. The jumped ion needs a second neighbour to stabilize this ion. The ion can jump back to their initial position due to unsuccessful hopping. In case of successful hopping, the ion relaxes at the second native neighbour and becomes frozen. Unsuccessful hopping eventually leads to partial relaxation of the jumped ion and hence forms dispersive region. The region II in Fig. 8 corresponding to DC conductivity arises due to short range localised successful hopping of ions45,51. On the other hand, dispersive conductivity appears when ratio of successful hopping to unsuccessful hopping decreases48,52. With the introduction of filler in the polymer matrix, the interphase region is formed (Fig. 2) which essentially enhances the localized ions (contact ion).

Therefore, the dispersive region

disappears due to increase of short range localized hopping with increasing filler concentration. 3.4.3 Modulus function and relaxation properties Fig. 9 shows a long tail behaviour of modulus function (𝑀′′) at the low frequency region. 𝑀′′ value was calculated using Eq. 15 and it shows distinct signature of dispersion with a peak at higher frequencies. Peak width decreases with an increase of filler concentration (upto 0.7wt%). At higher filler concentration (S13) it starts to increase again. 20 ACS Paragon Plus Environment

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Figure 9. Imaginary part of electrical complex modulus (𝑀′′) spectra.

Non-Debye Electric Field relaxation function The electrical modulus function M*(ω) can be written as [53,54] 1

∞

𝑀 ∗ (ω) = 𝜀 ∗ (𝜔) = 𝑀′∞[1 ― ∫0 𝑒 ―𝑖𝜔𝑡( ―

∂𝜑(𝑡) ∂𝑡

)𝑑𝑡]

(17)

Where 𝜑(𝑡) identifies the decay function of the electric field E(t) in time domain given by (18)

𝐸(𝑡) = 𝐸(0)𝜑(𝑡)

For Debye type relaxation, the decay function is exponential54. In case of Non-Debye type relaxations this function is modified by a stretched exponential function with an exponent β55-57, known as the stretching factor, whose magnitude lies between 0 to 1, (0 < 𝛽 < 1).

[

𝜑(𝑡) ≈ exp ―

( )] 𝑡

𝛽

𝜏𝐾𝑊𝑊

(19)

The above function (Eq 19) is known as Kohlrausch-Williams-Watts (KWW) function where 𝜏𝐾𝑊𝑊 is the characteristic relaxation time. For ideal Debye case, the β will be unity. Inverse Laplace transform of Eq. 17 gives us the exact form of experimental decay function in the time domain, given by 2 ∞ 𝑀′′

𝜑(𝑡) = 𝜋∫0 𝜔𝑀∞cos (𝜔𝑡)𝑑𝜔

(20)

By comparing those two equations (Eqs. 19 and 20) we can determine the stretched exponent value. Another new technique introduced by replacing the stretched exponent to MittagLefler function (Eα,β) 58 which can be written as



𝑧𝑖

∞

𝐸𝛼,𝛽(𝑧) = ∑𝑖 = 0Γ(𝑖𝛼 + 𝛽)

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(21)

The above expression is known as two parameter Mittag-Lefler function. Where α > 0 and 𝛽 > 0. Mittag-Lefler function is a generalization of the exponential function58. And one parameter Mittag-Lefler function can be written as 𝑧𝑖

∞

𝐸𝛼(𝑧) = ∑𝑖 = 0Γ(𝑖𝛼 + 1)

(22)

The behaviour of the function depends on α value. At α=0 if behaves like hyperbola and at α=1 its pure exponential decay (Debye relaxation). This function showed oscillatory behaviour within the α values of 1 and 2. Debye relaxation is shown in ordered system, many relaxing body decays with same relaxation rate. But Non-Debye relaxation occurs in disordered systems. Infinite no of bodies relaxed at a different rate and amplitude. The sum of individual body decay represents the resultant function. On the other hand Mittag-Lefler function interpolates the sum of individual disordered decays with different decay rate. Histogram function of Mittag-Lefler function showed the distribution of discrete or continuous58 Debye and Non-Debye relaxation functions. So ∞

( ― 1)𝑖𝑘𝑖𝑡𝛾𝑖

𝐸𝛼( ―𝑘𝑡𝛾) = ∑𝑖 = 0 Γ(𝑖𝛼 + 1)

(23)

Where k is a constant and 0 < γ < 1. The Eq. 23 is the another form of decay function. If we compare the experimental decay function (Eq 20) with Mittag-Lefler function (Eq 23) then we will get the fractional exponent (γ). γ=1 signifies the Debye relaxation. But our system showed Non-Debye relaxation means γ ˂ 1. If we model the Debye relaxation by equivalent circuit model, the circuit component behaves like a pure resistor and ideal capacitor. But in 22 ACS Paragon Plus Environment

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Non-Debye case the circuit components are not behaving like ideal element. The leaky capacitor nature presents in Non-Debye cases, that’s why γ value became less than one. A similar phenomenon is shown in viscoelastic material. The system is not behaving like neither elastic nor viscous. Experimental decay function (Eq 20) and theoretical decay function were fitted in broad time scale (10-9 to 10-3 sec). There are several methods available in literatures to fit the experimental decay curve56,59,60. All of these previous studies, the decay curve has been fitted successfully over a particular time domain. We have also fitted KWW function with Eq 20 as shown in Fig. 10. It is important to note that KWW function does not fit well at the higher time scale region. Therefore, it is desirable to look for different function which will be able to fit the decay curve in entire time domain. We have used, for the first time, a Mittag-Lefler function to fit the decay curve58 .

Figure 10. Best fitted Decay curve with KWW function. The black line represents the experimental curve and red line corresponds to fitted curve with KWW function.



Fig. 11 shows the fitting of experimental decay function with Mittag-Lefler function. This new function fitted well over the whole time scale region. Stretching exponents (β & γ) are calculated from individual fitting. Variation of β & γ are shown in supplementary materials (Fig. S8).

Figure 11. Decay function fitted with Mittag-Lefler function. The black line represents the experimental curve and red line corresponds to fitted (Mittag-Lefler function) curve.

As shown in Fig. 9, the peak width of the imaginary modulus function decreases with increasing filler concentration which is in consistent with variation of stretched exponents (β & γ) variation. Stretched exponent decreased with respect to filler concentration signifies the co-operative motion61 of conducting species. Segmental motion plays a prominent role in ion conduction. Jonscher’s power law exponent variation also showed the same trend (Fig. S7) similar to stretched exponent (γ). This result suggests that the probability of short range successful hopping increases due to addition of nano-filler. 4. CONCLUSION 24 ACS Paragon Plus Environment

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We have observed the nano-filler induced microstructural change, enhancement of conductivity and thermal stability etc. of composite polymer matrix (PEO-PVDF (4:1) + 35 wt% of NH4 I) using a variety of experimental techniques. The relaxation properties of the polymer composite have been analysed using non Debye type of relaxation function, namely Mittag-Lefler function. Optimum enhancement of electrical properties has been obtained at threshold filler concentration of 0.7 wt %. At a threshold filler concentration of 0.7 wt%, highly conducting interphase region around the each nano filler surface eventually connect to form an efficient conducting path for ion transport. The enhancement of DC conductivity is also caused by the rapid increase of segmental motion of polymer chain. The decrease in the glass transition temperature along with increase in mobility of ions up to the filler concentration of 0.7 wt% is consistent with the enhancement of conductivity. This blend electrolyte system shows two different activation energies due to the formation of free ions and contact ions. Tangential loss of mobile ion decreases due to enhancement of contact ions. Mittag-Lefler (single parameter) function is fitted with experimental decay function, obtained from impedance spectroscopy, over the entire time scale regime which shows excellent agreement. Variation in stretched exponents (β & γ) with filler concentration indicates cooperative motion of ions within the polymer matrix. Supporting Information : Deconvoluted XRD results, FTIR spectra, TGA and DTA plot for all composites, real part of dielectric constant spectra, variation of Jonscher’s power law exponents with filler concentration, variation of stretched exponents ( β, γ) with filler concentration.

5. ACKNOWLEDGEMENT SKP acknowledges Inter University Accelerator Centre (IUAC), New Delhi, for the research grant. Authors thank Dr. D. Mandal and Mr. K. Maity, Dept. of Physics, Jadavpur University, for providing the FTIR facility and rendering their assistance in performing the experiment. 25 ACS Paragon Plus Environment


Mr. B. Roy, Jadavpur University, Mr. D. Mandal and Mr. H. Bhunia from Indian Association for Cultivation of Science, Kolkata, are also acknowledged for their constant help in pursuing DSC experiment and for academic discussions. References (1) El-Kady, M. F.; Kaner, R. B., Scalable Fabrication of High-Power Graphene MicroSupercapacitors for Flexible and on-Chip Energy Storage. Nat. commun 2013, 4, 1475. (2) Lu, W.; Fadeev, A. G.; Qi, B.; Smela, E.; Mattes, B. R.; Ding, J.; Spinks, G. M.; Mazurkiewicz, J.; Zhou, D.; Wallace, G. G., Use of Ionic Liquids for Π-Conjugated Polymer Electrochemical Devices. Science 2002, 297, 983-987. (3) Shin, J.-H.; Henderson, W. A.; Passerini, S., Ionic Liquids to the Rescue? Overcoming the Ionic Conductivity Limitations of Polymer Electrolytes. Electrochem. Commun. 2003, 5, 1016-1020. (4) Saikia, D.; Wu, H.-Y.; Pan, Y.-C.; Lin, C.-P.; Huang, K.-P.; Chen, K.-N.; Fey, G. T.; Kao, H.-M., 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 2011, 196, 2826-2834. (5) Li, Z.; Mogensen, R.; Mindemark, J.; Bowden, T.; Brandell, D.; Tominaga, Y., Ionic Conductive and Thermal Properties of a Synergistic Poly (Ethylene Carbonate)/Poly (Trimethylene Carbonate) Blend Electrolyte. Macromol. Rapid Commun. 2018, 1800146. (6) Reddy, C. V. S.; Sharma, A.; Rao, V. N., Effect of Plasticizer on Electrical Conductivity and Cell Parameters of Pvp+ Pva+ Kclo3 Blend Polymer Electrolyte System. J. Power Sources 2002, 111, 357-360. (7) Taguet, A.; Cassagnau, P.; Lopez-Cuesta, J.-M., Structuration, Selective Dispersion and Compatibilizing Effect of (Nano) Fillers in Polymer Blends. Prog. Polym. Sci. 2014, 39, 1526-1563. (8) Lin, D.; Liu, W.; Liu, Y.; Lee, H. R.; Hsu, P.-C.; Liu, K.; Cui, Y., High Ionic Conductivity of Composite Solid Polymer Electrolyte Via in Situ Synthesis of Monodispersed Sio2 Nanospheres in Poly (Ethylene Oxide). Nano letters 2015, 16, 459-465. (9) Liu, Y.; Lee, J.; Hong, L., In Situ Preparation of Poly (Ethylene Oxide)–Sio2 Composite Polymer Electrolytes. J. Power Sources 2004, 129, 303-311. (10) Fahmi, E.; Ahmad, A.; Rahman, M. Y. A.; Hamzah, H., Effect of Nio Nanofiller Concentration on the Properties of Peo-Nio-Liclo 4 Composite Polymer Electrolyte. J. Solid State Electrochem. 2012, 16, 2487-2491. (11) Dey, A.; Ghoshal, T.; Karan, S.; De, S., Size Effect of Cubic Zro2 Nanoparticles on Ionic Conductivity of Polyethylene Oxide-Based Composite. J. Appl. Phys. 2011, 110, 043707. (12) Kumar, B.; Scanlon, L. G.; Spry, R. J., On the Origin of Conductivity Enhancement in PolymerCeramic Composite Electrolytes. J. power sources 2001, 96, 337-342. (13) Wang, X.-L.; Mei, A.; Li, M.; Lin, Y.-H.; Nan, C.-W., Polymer Composite Electrolytes Containing Ionically Active Mesoporous Sio 2 Particles. J. Appl. Phys. 2007, 102, 054907. (14) Wang, Y.-J.; Pan, Y.; Chen, L., Ion-Conducting Polymer Electrolyte Based on Poly (Ethylene Oxide) Complexed with Li1. 3al0. 3ti1. 7 (Po4) 3 Salt. Mater. Chem. Phys. 2005, 92, 354-360. (15) Liu, W.; Liu, N.; Sun, J.; Hsu, P.-C.; Li, Y.; Lee, H.-W.; Cui, Y., Ionic Conductivity Enhancement of Polymer Electrolytes with Ceramic Nanowire Fillers. Nano letters 2015, 15, 27402745. (16) Wang, W.; Yi, E.; Fici, A. J.; Laine, R. M.; Kieffer, J., Lithium Ion Conducting Poly (Ethylene Oxide)-Based Solid Electrolytes Containing Active or Passive Ceramic Nanoparticles. J. Phys. Chem. 26 ACS Paragon Plus Environment

Page 26 of 30

Page 27 of 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


C 2017, 121, 2563-2573. (17) Sandler, J.; Kirk, J.; Kinloch, I.; Shaffer, M.; Windle, A., Ultra-Low Electrical Percolation Threshold in Carbon-Nanotube-Epoxy Composites. Polymer 2003, 44, 5893-5899. (18) Wieczorek, W.; Siekierski, M., A Description of the Temperature Dependence of the Conductivity for Composite Polymeric Electrolytes by Effective Medium Theory. J. Appl. Phys. 1994, 76, 2220-2226. (19 ) Przyluski, J.; Siekierski, M.; Wieczorek, W., Effective Medium Theory in Studies of Conductivity of Composite Polymeric Electrolytes. Electrochim. Acta 1995, 40, 2101-2108. (20) Patla, S. K.; Ray, R.; Asokan, K.; Karmakar, S., Investigation of Ionic Conduction in Peo–Pvdf Based Blend Polymer Electrolytes. J. Appl. Phys. 2018, 123, 125102. (21) Croce, F.; Appetecchi, G.; Persi, L.; Scrosati, B., Nanocomposite Polymer Electrolytes for Lithium Batteries. Nature 1998, 394, 456. (22) Hamming, L. M.; Qiao, R.; Messersmith, P. B.; Brinson, L. C., Effects of Dispersion and Interfacial Modification on the Macroscale Properties of Tio2 Polymer–Matrix Nanocomposites. Compos. Sci. Technol. 2009, 69, 1880-1886. (23) Ozmusul, M.; Picu, R., Elastic Moduli of Particulate Composites with Graded Filler‐Matrix Interfaces. Polym. Compos. 2002, 23, 110-119. (24) Chintapalli, S.; Zea, C.; Frech, R., Characterization Studies on High Molecular Weight PeoAmmonium Triflate Complexes. Solid State Ionics 1996, 92, 205-212. (25) Hema, M.; Selvasekarapandian, S.; Arunkumar, D.; Sakunthala, A.; Nithya, H., Ftir, Xrd and Ac Impedance Spectroscopic Study on Pva Based Polymer Electrolyte Doped with Nh4x (X= Cl, Br, I). J. Non-Cryst. Solids 2009, 355, 84-90. (26) Gunasekaran, S.; Sailatha, E.; Seshadri, S.; Kumaresan, S., Ftir, Ft Raman Spectra and Molecular Structural Confirmation of Isoniazid. Indian J. Pure Appl. Phys. 2009, 47, 12–18 2009. (27) Hashmi, S.; Kumar, A.; Maurya, K.; Chandra, S., Proton-Conducting Polymer Electrolyte. I. The Polyethylene Oxide+ Nh4clo4 System. J. Phys. D: Appl. Phys. 1990, 23, 1307. (28) Kadir, M.; Aspanut, Z.; Majid, S.; Arof, A., Ftir Studies of Plasticized Poly (Vinyl Alcohol)– Chitosan Blend Doped with Nh4no3 Polymer Electrolyte Membrane. Spectrochim. Acta, Part A 2011, 78, 1068-1074. (29) Rahaman, M. H. A.; Khandaker, M. U.; Khan, Z. R.; Kufian, M. Z.; Noor, I. S. M.; Arof, A. K., Effect of Gamma Irradiation on Poly (Vinyledene Difluoride)–Lithium Bis (Oxalato) Borate Electrolyte. Phys. Chem. Chem. Phys. 2014, 16, 11527-11537. (30) Pal, P.; Ghosh, A., Dynamics and Relaxation of Charge Carriers in Poly (Methylmethacrylate)Lithium Salt Based Polymer Electrolytes Plasticized with Ethylene Carbonate. J. Appl. Phys. 2016, 120, 045108. (31) Bishop, A. G.; MacFarlane, D. R.; McNaughton, D.; Forsyth, M., Triflate Ion Association in Plasticized Polymer Electrolytes. Solid State Ionics 1996, 85, 129-135. (32) Jonscher, A. K., The ‘Universal’dielectric Response. nature 1977, 267, 673. (33) Jonscher, A. K., Dielectric Relaxation in Solids. J. Phys. D: Appl. Phys. 1999, 32, R57. (34) Shastry, M.; Rao, K., Ac Conductivity and Dielectric Relaxation Studies in Agi-Based Fast Ion Conducting Glasses. Solid State Ionics 1991, 44, 187-198. (35) Trukhan, E., Dispersion of the Dielectric Constant of Heterogeneous Systems. Soviet Phys.-Solid State 1963, 4, 2560-2570. (36) Wang, Y.; Agapov, A. L.; Fan, F.; Hong, K.; Yu, X.; Mays, J.; Sokolov, A. P., Decoupling of Ionic Transport from Segmental Relaxation in Polymer Electrolytes. Phys. Rev. Lett. 2012, 108, 088303. (37) Stolwijk, N.; Obeidi, S., Radiotracer Diffusion and Ionic Conduction in a Peo-Nai Polymer 27 ACS Paragon Plus Environment


Electrolyte. Phys. Rev. Lett. 2004, 93, 125901. (38) Klein, R. J.; Zhang, S.; Dou, S.; Jones, B. H.; Colby, R. H.; Runt, J., Modeling Electrode Polarization in Dielectric Spectroscopy: Ion Mobility and Mobile Ion Concentration of Single-Ion Polymer Electrolytes. J. Chem. Phys. 2006, 124, 144903. (39) Wieczorek, W.; Stevens, J.; Florjańczyk, Z., Composite Polyether Based Solid Electrolytes. The Lewis Acid-Base Approach. Solid State Ionics 1996, 85, 67-72. (40) Croce, F.; Persi, L.; Scrosati, B.; Serraino-Fiory, F.; Plichta, E.; Hendrickson, M., Role of the Ceramic Fillers in Enhancing the Transport Properties of Composite Polymer Electrolytes. Electrochim. Acta 2001, 46, 2457-2461. (41) Nan, C.-W.; Fan, L.; Lin, Y.; Cai, Q., Enhanced Ionic Conductivity of Polymer Electrolytes Containing Nanocomposite S I O 2 Particles. Phys. Rev. Lett. 2003, 91, 266104. (42) Ahrony, A.; Stauffer, D., Introduction to Percolation Theory. Taylor and Francis: 1994. (43) Jan, N.; Stauffer, D., Random Site Percolation in Three Dimensions. Int. J. Mod Phys. C 1998, 9, 341-347. (44) Reed, A.; Gilding, D., Biodegradable Polymers for Use in Surgery—Poly (Glycolic)/Poly (Iactic Acid) Homo and Copolymers: 2. In Vitro Degradation. Polymer 1981, 22, 494-498. (45) Pradhan, D. K.; Choudhary, R.; Rinaldi, C.; Katiyar, R., Effect of Mn Substitution on Electrical and Magnetic Properties of Bi 0.9 La 0.1 Feo 3. J. Appl. Phys. 2009, 106, 024102. (46) Pal, P.; Ghosh, A., Dynamics and Relaxation of Charge Carriers in Poly (Methylmethacrylate)Based Polymer Electrolytes Embedded with Ionic Liquid. Phys. Rev. E 2015, 92, 062603. (47) Patla, S. K.; Mukhopadhyay, M.; Ray, R., Ion Specificity Towards Structure-Property Correlation of Poly (Ethylene Oxide)[Peo]-Nh 4 I and Peo-Kbr Composite Solid Polymer Electrolyte. Ionics 2018, 1-13. (48) Ray, A.; Roy, A.; De, S.; Chatterjee, S.; Das, S., Frequency and Temperature Dependent Dielectric Properties of Tio2-V2o5 Nanocomposites. J. Appl. Phys. 2018, 123, 104102. (49) Mcdonald, J. R., Impedance Spectroscopy: Emphasizing Solid Materials and Systems. John Wile & Sons, New York, EUA 1987, 16. (50) Roy, A. K.; Singh, A.; Kumari, K.; Amar Nath, K.; Prasad, A.; Prasad, K., Electrical Properties and Ac Conductivity of (Bi 0.5 Na 0.5) 0.94 Ba 0.06 Tio 3 Ceramic. ISRN Ceramics 2012, 2012. (51) Pradhan, D. K.; Misra, P.; Puli, V. S.; Sahoo, S.; Pradhan, D. K.; Katiyar, R. S., Studies on Structural, Dielectric, and Transport Properties of Ni0. 65zn0. 35fe2o4. J. Appl. Phys. 2014, 115, 243904. (52) Mukherjee, S.; Chatterjee, S.; Rayaprol, S.; Kaushik, S.; Bhattacharya, S.; Jana, P., Near Room Temperature Magnetodielectric Consequence in (Li, Ti) Doped Nio Ceramic. J. Appl. Phys. 2016, 119, 134103. (53) Howell, F.; Bose, R.; Macedo, P.; Moynihan, C., Electrical Relaxation in a Glass-Forming Molten Salt. J. Phys. Chem. 1974, 78, 639-648. (54) Moynihan, C., Decay Function for the Electric Field Relaxation in Vitreous Ionic Conductors. Phys. Chem. Glasses 1973, 14, 122-125. (55) Kohlrausch, R., R. Kohlrausch, Ann. Phys.(Leipzig) 12, 393 (1847). Ann. Phys.(Leipzig) 1847, 12, 393. (56) Williams, G.; Watts, D. C., Non-Symmetrical Dielectric Relaxation Behaviour Arising from a Simple Empirical Decay Function. Transactions of the Faraday society 1970, 66, 80-85. (57) Pal, P.; Ghosh, A., Charge Carrier Dynamics in Pmma–Liclo4 Based Polymer Electrolytes Plasticized with Different Plasticizers. J. Appl. Phys. 2017, 122, 015101. (58) Das, S., Functional Fractional Calculus; Springer Science & Business Media, 2011. (59) Williams, G., The Low Frequency Dielectric Relaxation of Polyoxymethylene (Delrin) Using a Direct Current Technique. Polymer 1963, 4, 27-34. 28 ACS Paragon Plus Environment

Page 28 of 30

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(60) Hamon, B., An Approximate Method for Deducing Dielectric Loss Factor from Direct-Current Measurements. Proceedings of the IEE-Part IV: Institution Monographs 1952, 99, 151-155. (61) Ngai, K.; Mundy, J.; Jain, H.; Kanert, O.; Balzer-Jollenbeck, G., Correlation between the Activation Enthalpy and Kohlrausch Exponent for Ionic Conductivity in Alkali Aluminogermanate Glasses. Phys. Rev. B 1989, 39, 6169.



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Nano-Filler Induced Ionic Conductivity Enhancement and Relaxation

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