Coupled Ion Conduction Mechanism and Dielectric Relaxation

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Article

Coupled Ion Conduction Mechanism and Dielectric Relaxation Phenomena in PEO -LiCFSO Based Ion Conducting Polymer Nano-Composite Electrolytes 20

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Tapabrata Dam, Sidhartha S. Jena, and Dillip Kumar Pradhan J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b11112 • Publication Date (Web): 07 Feb 2018 Downloaded from http://pubs.acs.org on February 12, 2018

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The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

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The Journal of Physical Chemistry

Coupled Ion Conduction Mechanism and Dielectric Relaxation Phenomena in PEO20 -LiCF3 SO3 Based Ion Conducting Polymer Nano-Composite Electrolytes ∗,†,‡

Tapabrata Dam,

†

Sidhartha S. Jena,

and Dillip K Pradhan

∗,†

†Department of Physics & Astronomy, National Institute of Technology Rourkela, Odisha-769008, India

‡Current address:Department of Solid State Physics, Indian Association for the Cultivation of Science, Kolkata-700032, India E-mail: [email protected](TD); [email protected](DKP)

Phone: +91 (0)661 2462729. Fax: +91 (0)661 4445557

Abstract This study focuses on the eect of anatase titania acting as nono-ller on the relaxation dynamics and ionic conductivity behaviour in polymer nano-composite electrolyte based on PEO20 -LiCF3 SO3 -TiO2 . Using broadband dielectric spectroscopy , dynamics of ion transport mechanism is studied over a wide range of temperature and frequency. Polymer salt complex exhibit dc conductivity σdc = 3.760 × 10−7 S cm−1 at 303 K. But with the addition of 8 wt.% TiO2 an increase in two order of magnitude of dc conductivity value is observed at same temperature. Ion conduction mechanism is analyzed employing complex relative permittivity as well as modulus formalisms. Isotherms of real part of conductivity spectra and dielectric loss spectra are analyzed to explain the 1

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observed rst and second universalities in ion conduction mechanism. Kramer-Krönig approach is used to discuss the crossover between the two universalities. Ratner's classical approach in combination with modied Nernst-Einstein relation is used to correlate the coupling nature of polymer segmental relaxation and ionic transport mechanism. Successful scaling of conductivity spectra using Summereld approach and imaginary modulus spectra using maxima normalization approach indicate ionic transport mechanism is thermally activated temperature independent phenomena. Temperature dependent dc conductivity is explained using mismatch generated relaxation for the accommodation and transport of ions concept as well as Vogel-Tammann-Fulcher relation to get a better insight of ion conduction mechanism. With comprehensive study of relaxation events and ionic conductivity, a close coupling between polymer segmental relaxation and ionic conduction in polymer nano-composite electrolytes is observed.

Introduction Back in 1973 P.V. Wright et. al for the rst time demonstrated, the ion conduction capabilities in polymer salt complex (PSC), formed by complexation of alkali metal salt with polyethylene oxide. Since then, a great deal of interest is shown by various research groups across the globe to explore and rene the properties of solid polymer electrolytes for the technological importance in dierent energy storage/conversion devices, electro-chromic devices, solar cells, gas sensors etc. 14 One of the major challenge for PSCs is to replace the organic carbonate based liquid electrolytes, which are currently being used to prepare the commercial batteries. Some of the distinct advantages of PSCs over its liquid counterpart are low ammability, high gravimetric and volumetric energy density, good mechanical, thermal and electrochemical stability, processablity, resistance to dendrite formation in electrode electrolyte inter-phase and leakage. 5 However, at room temperature, conventional PSCs show a very poor ionic conductivity of around 10−9 S cm−1 to 10−7 S cm−1 as compared to organic liquid based electrolytes. This is a major drawback for its eminent application in practical 2


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devices. 6 For successful utilization of PSC in energy storage/conversion devices, its ambient temperature ionic conductivity needs to be enhanced to the order of 10−3 S cm−1 . Literature based on NMR studies on PSC reveal that ion conduction occur mostly through the amorphous regions of the conventional polymer electrolyte or PSC. 7,8 To increase the amorphosity and hence the ionic conductivity of polymer electrolytes, usually two dierent approaches are undertaken. Either by incorporating a low molecular weight organic carbonate liquid plasticizers; such as propylene carbonate, ethylene carbonate, poly ethylene glycol, diethyl carbonate etc. or by induction of ionic liquids into the host polymer matrix. 911 These class of electrolytes are termed as plasticized polymer electrolytes. Although, with this method the ionic conductivity can be increased but on the expense of signicant deterioration in mechanical and electrochemical stability which are essential requirement for device application. In second process modied layered clay or ceramic nano-llers such as SiO2 , TiO2 , ZrO2 , Al2 O3 etc. are added to conventional PSC. 1215 These class of electrolytes are termed as polymer nano-composite electrolyte (PNCE). Though, PNCEs posses good thermal, mechanical, electrochemical and inter-facial stability, the increase in ionic conductivity of these class of electrolytes are only two orders of magnitude higher than that of PSC. As far as, the mechanism to elevate ionic conductivity of PNCE is concerned there are two possible explanations. Incorporation of ceramic nano-ller which introduce a grain boundary eect between polymer and ceramic nano-particles. This region is higly amorphous in nature, which helps in easy movement of ions hence increases the ionic conductivity of PNCEs. Nano-ller also disturb the interaction between cation and coordinating host polymer. It helps in easy dissociation of salt, which in turn increase the ionic conductivity. 16 From the viewpoint of PNCEs (made of ternary system such as polymer, salt and ller), ion conduction mechanism is very complex in nature. 8 Apart from ion hopping and relaxation of polymer host, there exist polymer-polymer, polymer-salt, ller-polymer, ller- salt interactions, which make the system very complex to investigate. 17 Till date universal acceptance on the ion dynamics and conduction mechanism at microscopic level is not reached, which could be 3



one of the reasons for not obtaining the ionic conductivity at the desired level of 10−3 S cm−1 at ambient temperature. Over the years the ion conduction mechanism in PNCEs is explained by using various phenomenological equations and ion conduction mechanism models has been developed and demonstrated. These are Jonscher's Power law, Double Power Law, Almond-West formalism, Deithrich's counter ion model, Monte Carlo Simulation by Bunde and his co-workers, Random free energy barrier model developed by Dyre and his co-workers, Dynamic bond percolation, Jump relaxation model (JRM) developed by Funke and his co-workers etc. 1826 Among these above-mentioned formalisms, Jonscher's Power law, Double Power Law and Almond-West formalism are based on phenomenological concepts. 4,27,28 Though these are widely used to explain conductivity isotherms but the physical phenomena associated to various events in ionic conductors at molecular level are not well explained using these equations. Moreover these equations also do not hold linear response theory. Monte Carlo Simulation by Bunde and his co-workers, Deithrich's counter ion model, Dynamic bond percolation has not tried to explain the temperature dependent behavior of ionic conductors. 29,30 Random free energy barrier model is very successful in case of glass based ionic conductors or xed lattice position based ionic conductors, but in case of polymer based system where favorable site do change its location as a function of time, this model do not yield good results in terms of conductivity isotherms. 31,32 Among all the physical models JRM, developed by K. Funke et. al. tried to explain the ion conduction mechanism in ionic conductors. "MIsmatch Generated Relaxation for the Accommodation and Transport of IONs (MIGRATION)" model is a rened concept primarily based of JRM. It addresses the conductivity behaviors as a function of frequency as well as temperature. It also tried to map the outcome of Ngai Coupling model and elucidate that there exist a common ion conduction mechanism in case of ionic conductors. 3336 In the present investigation; focus will be given on analyzing ac conductivity spectra, electrical modulus, coupling and temperature dependent ionic conductivity of the samples under investigation. Apart from these, the behaviour of temperature dependent dc conductivity is also discussed using 4


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conventional VTF equation and MIGRATION concept. The, motivation behind this study are as follows (i) investigation of the ion conduction mechanism and existence of coupling between segmental relaxation with ionic transport phenomenon, (ii) nding probable explanation for the experimentally observed universalities found in the dielectric spectra of ionic conductors and (iii) explanation of temperature dependent dc conductivity of PNCEs using the outcome of MIGRATION concept. Knowledge about the above mentioned queries may help us to prepare better PNCEs, which can eventually take a big stride in replacing presently used liquid electrolytes in commercial Li-Ion batteries. This will reduce to great extent the safety concerns associated to liquid electrolytes. For the present study, a series of PNCEs is prepared using polyethylene oxide (PEO) as host polymer and lithium triuoromethanesulfonate (LiCF3 SO3 ) as salt by using solution casting technique and keeping the O/Li+ value at 20. Anatase phased titania TiO2 is used as ller. Analyzing ac conductivity spectra ion diusion coecient is evaluated to understand the observed relaxations processes and ionic transport phenomena in PNCEs. Electrode polarization (EP) is carefully studied to evaluate ion diusion coecient. Relaxation processes are studied using complex dielectric formalism along with electrical modulus formalism. To understand the universalities observed in PSC and PNCEs, conductivity isotherms are studied carefully. Employing Kramer-Krönig formalism observed second universality in dielectric loss spectra is analyzed. 37 Coupling between host polymer segmental relaxation and ionic transport mechanism is investigated using a combined theory of modied Stokes-Einstein relation and Ratner's approach. 3,38 Phenomenological Vogel-Tammann-Fulcher equation along with MIGRATION model based approach are used to explain the temperature dependent dc conductivity behaviour of PNCEs under investigation.

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Experimental Technique & Theoretical Background Sample Preparation and Characterization Polyethylene oxide of molecular weight, Mw = 6 × 105 , lithium triuoromethanesulfonate, tetragonal phased anatase titanium dioxide (TiO2 ) and analytical grade acetonitrile are used for preparation of PSC and a series of PNCE having compositions PEO20 -LiFC3 SO3 -

xwt.% TiO2 (x= 2, 3, 5, 8, 10 & 15). Prepared TiO2 is used as ller and acetonitrile is used as common solvent. X-ray diraction (XRD) is performed using Rigaku Ultima-IV X-ray diractometer. The operating condition for XRD system are 40 mA and 40 kV with scanning step of of 0.002° and scanning rate of 3° per minute. Dielectric measurements are taken with Novo-Control GMBH Alpha impedance analyzer over a frequency range from

10−1 to 106 Hz and excitation potential of 10 mV. Novo-Control Quattro Cryo-system is used to control the temperature of the samples under investigation in a liquid nitrogen gas based sample holding assembly. Details of material synthesis and characterization are given in supplementary material.

Coupled Ionic Transport Mechanism Broadband dielectric spectroscopy, which is a powerful experimental tool related to dielectric analysis, can be used to investigate the relaxation dynamics and ion conduction mechanism of disordered ionic conductors. 39 Figure 1(a) show a representative complex dielectric spectra of PEO20 -LiFC3 SO3 -3wt.% TiO2 at T = 268 K . The eects of electrode polarization (EP), ionic conductivity and polymer chain relaxation is observed in the above-mentioned gure. Various physical parameters can be obtained from complex relative permittivity spectra using the following relations. Complex ac conductivity and relative permittivity are related with the following expression σ ∗ (f ) = σ 0 (f ) − jσ 00 (f ) = j2πf ε0 (ε0 − jε00 ). The electric modulus

M ∗ = M 0 + jM 00 can be expressed in form of complex relative permittivity given by the √ equation, M ∗ (f ) = 1/ε∗ (f ) = ε00 /(ε02 +ε002 )+jε0 /(ε02 +ε002 ). 39 Here, j = −1 and ε0 is the free 6


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6

10 '

4

*

Electrode

10

Polarization

3

10

10

Relaxation

6

5

4

0.75

10

0.70

3

0.99

2

10 10

7

der

10

0.99

10

''

HN Fitting

Ionic

10

5

Conduction

10

''

der

10

2

1

10

1

(a) 10

0

10

10

-5

0

(b)

* (S cm

-1

)

'

10

10

10

''

-6

-7

-8

Onset of Electrode Polarization

10 30

-9

(c)

T = 268K

tan

20

tan

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


''

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max

tan

10

fmax

0

10

-1

10

0

10

1

10

2

10

3

10

4

10

5

10

6

frequency (Hz)

Figure 1: Frequency dependent (a)real and imaginary part of dielectric spectra and derived dielectric loss (εder ), (b) Complex ac conductivity spectra (σ ∗ ) and (c) loss tangent (tan δ ) for 3 wt.% TiO2 PNCE composition at T = 268 K . space permittivity. In general for ionic conductors, high value of ionic conductivity masks the segmental relaxation dynamics phenomena. Therefore, dc conduction free dielectric loss ε00der formalism is used to study the relaxation dynamics and evaluate the segmental relaxation time. It is dened as the negative logarithm for the derivative of real part of dielectric constant as a function of angular frequency given by the following equation. 40

ε00der = −

∂ε0 (ω) π × ≈ ε00 2 ∂(lnω)

(1)

Segmental relaxation and EP are observed at high and low frequency regions of complex relative permittivity isothermal spectra respectively. Havriliak-Negami (HN) approach, 41 is used to investigate ε00der spectra to obtain more information related to the relaxation events associated with the eects of EP and segmental motion of polymer host. Along with the

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nature of relaxation events, information about time scale, strength of relaxation can also be found using HN approach shown in equation (2). 41

ε00der =

π αγ∆ε(ωτ )α cos[απ/2 − (1 + γ)tan−1 [sin(πα/2)/((ωτ )−α + cos(πα/2))]] × 2 [1 + 2(ωτ )α cos(πa/2) + (ωτ )2α ](α+γ)/2

(2)

here, τ represents relaxation time, α and γ are the shape parameters. α and γ should satisfy the following conditions 0 < α ≤ 1 and αγ ≤ 1. 41 The shape parameters for EP relaxation obtained from HN analysis are found very close to unity and thereby the relaxation events are approximated as a non interacting Debye type relaxation. To nd ion diusivity MacdonaldTrukhan approach is used. 3 On the other hand for segmental relaxation, shape parameter values are found around 0.7 − 0.75, which suggest the relaxation events are non-Debye type. Figure 1 represents the relaxation dynamics of 3 wt.% TiO2 PNCE composition at T = 268 K. The values of shape parameters are given in gure 1(a). As the shape parameters are vely close to unity it suggests Macdonald-Trukhan approach can be used to determine ion diusivity of PSC and PNCEs. Eect of EP is best represented using complex electrical conductivity spectra. In gure 1(b), onset of EP eect and its full development is shown. Onset frequency of EP is found in correspondence to the peak frequency of tan δ isotherm spectra. In gure 1(c) loss tangent maxima, tan δmax and frequency corresponding to the maxima, fmax are represented for 3 wt.% TiO2 PNCE composition at T = 268 K. The detailed theoretical background has already been discussed in our previous publication. 32 However, the condition to examine the coupled ion conduction process are represented in form of mathematical expression below.

D∝

1 ⇒ Dτs = constant τs

(3)

and

σdc τs T = constant

8


(4)

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here, D is diusivity, τs is segmental relaxation time and T is temperature in absolute scale. Therefore equation (3) and equation (4) should be satised to conrm that ion conduction mechanism and polymer segmental relaxation are coupled event.

Result and Discussion TiO 2

(101)

Intensity (arb. units)

X-Ray Diraction

Intensity (arb. units)

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


15

30 2

45

60

(degree)

15 wt.% 10 wt.% 8 wt.% 5 wt.% 3 wt.% 2 wt.% PSC PEO

5

10

15

20

25

2

30

35

40

45

(degree)

Figure 2: X-Ray diraction patterns of PEO, PSC and dierent compositions of PNCEs represented as PEO20 -LiCF3 SO3 - x wt.% TiO2 (x = 2, 3, 5, 8, 10&15). Inset shows XRD pattern of anatase phased TiO2 used as ller for preparing the PNCEs. A dotted set of lines are used as a guide to eye for amorphous hump present in the samples. Polymer salt complexation, composite formation and crystalline-amorphous nature of the prepared samples are studied using XRD technique. The observed XRD patterns of PEO, PSC and PNCE compositions are presented in gure 2. Inset of gure 2 shows the XRD 9



pattern of tetragonal phased anatase TiO2 (JCPDF NO: 21-1272) synthesized using polymer template technique. Co-existence of an amorphous hump from 15° to 28° along with several characteristic crystalline peaks can be observed in the XRD patterns of the samples (a set of dotted lines are used as a guide to eye to show amorphous hump). Therefore it can be concluded that the samples are semi-crystalline in nature. XRD pattern of PEO lm show characteristic crystalline peaks at 2θ = 19.2°, 23.4°, 26.3° and 27°, corresponding to the (120), (112)/(032), (21 1) and (040) planes respectively. 32 The characteristic crystalline peaks of PEO mentioned here can be observed in PSC as well as in all compositions of PNCEs. The nature of these reections do not undergo any signicant change with the addition of LiFC3 SO3 or anatase TiO2 into host polymer of PEO. It indicates that, structure of host polymer remain unaected during polymer-salt complex formation or composite electrolyte formation. 28 On comparison of XRD pattern of PEO, PSC and PNCEs, it can be observed that no additional reection arises due to LiFC3 SO3 (JCPDF NO: 81-0813) in PSC and PNCEs. This indicates a proper dissolution of LiFC3 SO3 into host polymer PEO. 17,42 Characteristic peaks of TiO2 can be observed in the XRD patterns of PNCEs with its most prominent peak (101) at 2θ = 25° and its intensity tend to increase with increase in concentration of TiO2 . Since the characteristic signature of both PEO and TiO2 are found in the XRD patterns of PNCEs, it can be safely concluded that the prepared PNCEs are showing composite behaviour.

FTIR Study Infrared (IR) spectroscopy is used to study interactions between the ions and host polymer. FTIR spectra help to study the eect of additive concentration on polymer-salt complex. The characteristic bands of PSC and PNCEs are indexed as follows; band around 638 cm−1 corresponds to cis C-H wagging mode, 842 cm−1 corresponds to cis C-H2 wagging, 962 cm−1 corresponds to stretching of ether bond (C-O) of polymer, 1032 cm−1 corresponds to symmetric stretch SO3 vibration of LiCF3 SO3 , 1100 cm−1 corresponds to stretching of ether 10


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638

757

842

962

1032

1100

1055

1242

1350

1282

x = 15

absorptance (arb. unit)

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


1467

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x = 10

x = 8

x = 5

x = 3

x = 2

x = 0

1600

1400

1200

1000

wavenumber (cm

800 -1

600

)

Figure 3: FTIR spectra of polymer salt complex (composition x = 0) and polymer composite electrolytes having composition PEO20 -LiCF3 SO3 - x wt.% TiO2 , with x = 2, 3, 5, 8, 10 and 15. bond (C-O) of polymer, 1242 cm−1 corresponds to C-F and CF2 - stretching, 1282 cm−1 corresponds to CH2 twisting vibration of polymer and 1467 cm−1 corresponds to CH2 scissoring mode. 43,44 With varying concentration of ceramic additives focus is to be given on 1032 cm−1 and 1055 cm−1 bands. These bands correspond to symmetric stretch SO3 vibration of LiCF3 SO3 under complexation. 45 Band around 1032 cm−1 represents free anions and solvent separated pair vibrations whereas around 1055 cm−1 represents Li2 CF3 SO3 + aggregates. 46 The presence of both the bands can be observed in all these IR spectra, which suggests that dissociated ions do take part in enhancing the ionic conductivity of the composite electrolytes. No signicant change in the position of various bands can be observed in dierent composite samples. However, small changes in the relative intensity of dierent bands can be observed, which suggests that the local environment of PSC, at the microscopic level, is

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modied with the addition of ller. 47 The modication of local environment at molecular dimension is also represented using complex modulus spectra.

AC Conductivity Study

10-3

(a)

T = 323K

10-9 10-12 10-15

T = 203K ∆T = 10K AW Fit

10

-18

σdc (S cm-1)

σ' (S cm-1)

10-6

10-4 10-5 10-6 10-7

T = 303K

0

5

10 15

TiO2 Percentage

10-1 100 101 102 103 104 105 106

frequency (Hz) 103 101

(b)

T = 223K

∆T = 10K

10-1

105 T = 223K 2 10 ∆T = 10K 10-1 T = 323K 10-4 -1 10 103 10710111015

σ'/σdc

σ'/σdc

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

Page 12 of 33

10-3 T = 323K 10-5 10-1

103

f/Tσdc

107

f/Tσdc

1011

1015

Figure 4: (a) Frequency dependent real part of ac conductivity (σ 0 ) for 8 wt.% TiO2 PNCE, at temperatures ranging from 203 K to 323 K with an interval of 10 K between each isothermal spectrum. The variation of dc conductivity as a function of ller concentration at T = 303 K is shown as inset. (b) Scaled real part of conductivity spectra with inset showing the scaled imaginary part of conductivity spectra using Summereld scaling approach for 8 wt.% TiO2 PNCE composition, at temperature ranging from 223 K to 323 K with an interval of 10 K between each isotherms. Ion dynamics of the PSC and PNCEs have been investigated using complex electrical conductivity spectra. Figure 4(a) represents the real part of ac conductivity, σ 0 , as a function of frequency over a temperature range from 323 K to 203 K with 10 K interval for 8 12


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wt.% TiO2 PNCE composition. It can be observed that σ 0 (f ) show three distinct regions at ambient temperature, (i) high frequency dispersion region representing short range ion hopping, (ii) frequency independent plateau region representing long range ionic motion which also reect dc conductivity (σdc ) and (iii) low frequency dispersion arising due to fast ion migration. 28 With decrease in temperature, the overall ac conductivity decreases and high frequency dispersive region is found to cover a larger part of the frequency range of investigation. Here the cross-over frequency between high frequency dispersive region and frequency independent plateau region which also marks the onset of conductivity relaxation is termed as hopping crossover frequency. Hopping cross-over frequency is observed to be shifted towards lower values with decreasing temperature. While temperature is decreased, at rst low frequency dispersive region go below the frequency range of investigation, then plateau region and nally around 203 K only high frequency dispersive region prevail throughout the experimental frequency range. Therefore a strong frequency dependence of σ 0 isotherms can be observed with varying temperature. A quantitative description of ion conduction process can be presented analyzing the high frequency dispersion and frequency independent plateau regions of real part of ac conductivity isotherms. At relatively high temperature and/or low frequency, σ 0 is represented by single power law in Almond-West formalism given by the following equation 4

σ 0 = σdc [1 + (f /fc )n ]

(5)

where, σdc is the dc conductivity, f is frequency and n is power law exponent having value within 0 < n < 1. For ionic conductors, in general the value of 0 n0 is found between 0.4 and

0.7. 28 For the temperature range 323 K to 233 K a reasonably good t is observed when the experimentally obtained data is tted with equation(5). This kind of behaviour is found in most of the disordered materials hence termed as universal dielectric response (UDR) or rst universality. At very low temperature it can be observed that conductivity isotherms become

13



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nearly linear in nature, and using equation(5) a good tting can not be achieved. In low temperature regime another term, which is having nearly linear dependence on frequency is added to AW power law. Modied Almond-West equation is given below, 24

σ 0 = σdc [1 + (f /fc )n ] + Af

(6)

where, A is weakly temperature dependent parameter. This added term in the isothermal spectra of real part of ac conductivity corresponds to frequency independent dielectric loss. We found that in the present study, below 233 K, σ 0 (f ) spectra give a reasonably good t only with equation(6). Inset of gure 4(a) shows the variation of dc conductivity at T = 303 K as a function of ller concentration. This plot indicate that with the addition of TiO2 ller initially σdc increases upto 8 wt.% of TiO2 PNCE composition and thereafter it decreases. For pure PSC, at T = 303 K, σdc value is found 3.760 × 10−7 S cm−1 , whereas at the same temperature for 8 wt.% of TiO2 PNCE composition obtained σdc value is 3.174 × 10−5 S cm−1 . Hence, in terms of dc conductivity, an increase in nearly two orders of magnitude can be observed when 8 wt.% of TiO2 is added to PSC. The conductivity isotherms may be scaled using time temperature superposition principle, as it can be observed from gure 4(a), that the complex ionic conductivity exhibit a temperature independent prole. 48 For ionic conduction, the process of conductivity scaling indicates a common physical mechanism irrespective of various intrinsic physical parameters associated with it like temperature. Scaling procedure in general can be represented by the following equation 49

σ 0 /σdc = F (f /f ∗ )

(7)

where, the scaling parameter is represented by f ∗ . Here, Summereld scaling approach is used which indicates that the scaling parameter will assume the values f ∗ = σdc T . This scaling approach is very much straight forward as directly accessible physical parameters such as σdc and temperature is used to perform this time temperature superposition prin14


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ciple based conductivity scaling. Superimposed master curve using Summereld scaling for PEO20 -LiCF3 SO3 - 8 wt.% TiO2 PNCE is given in Fig.4(b). Summereld scaling indicates although, there exist a strong temperature dependence for the crossover between diusive to sub-diusive ionic conduction phenomenon, as a whole the ion conduction process is temperature independent.

Relaxation Dynamics and Electrical Modulus Formalism 0.3

0.075

HN Fitting

(a)

(c)

T = 10K

263K

213 K

0.050

0.2

M'

M''

213 K

0.025

0.1

T = 10K

0.000 KWW Fitting

0.0

263K 10

213 K

-1

10

1

10

3

10

T = 243K

1.0

M''/M''

0.5

0.75

0.0 10

-5

1

10

3

10

5

10

-7

10

-3

-1

10

3

0.25

max

T = 5K

10

10

f/f

T = 263K

-1

0.50

PSC

0.025

0.000

1.00

8 wt.%

max

(d) 0.050

10

5

frequency (Hz)

263K

max

T = 10K

M''/M''

(b)

M''

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


10

1

10

f/f

frequency (Hz)

0.00

T = 213K

5

10

9

10

13

max

Figure 5: (a) Real and (b) imaginary component of electrical modulus analyzed with Havriliak-Negami formalism, having ∆ T = 10 K between each isotherms. (c) Imaginary part of electrical modulus analysed with Bergman modied Kohlarsch-William-Watts (KWW) approach, having ∆ T = 10 K between each isotherms. (d) Scaled imaginary component of electrical modulus for the PNCE composition PEO20 -LiCF3 SO3 - 8 wt.% TiO2 , having temperature interval ∆ T = 5 K. Inset of (d) showing the scaling of PSC and 8 wt.% TiO2 PNCE composition at T = 243 K. It is mentioned earlier in section of ac conductivity study, that complex electrical modulus, M ∗ and complex relative permittivity, ε∗ are having inverse relationship. Using M ∗ spectra, conductivity relaxation phenomenon is studied. In gure 5 complex electrical modulus spectra as a function of frequency (gure 5(a) real part M 0 and gure 5(b) imaginary part M 00 ) are represented from temperature 263 K to 213 K for 8 wt.% TiO2 PNCE composition. From gure 5(a), it can be observed that with increase in frequency, there is a 15



Page 16 of 33

gradual increase in M 0 isotherm. At high frequencies of our experimental setup, M 0 tend to get saturated but due to experimental constraint of frequency range proper saturation of M 0 spectra is not observed at ambient temperature. However, at low temperatures a near saturation behaviour can be observed for M 0 isotherms. When imaginary part of M ∗ isotherms are considered, relaxation peaks are observed as shown in gure 5. These peaks indicate that with decreasing frequency there exist a transition from short to long range ion mobility. The observed peak frequency of M 00 spectra is representing conductivity relaxation frequency fc . Using this frequency one can obtain the associated conductivity relaxation time using the relation τc = 1/2πfc . Observed peaks found in M 00 isotherms are skewed towards high frequency values and are asymmetric in nature. With increase in temperature, peak of M 00 spectra is observed to shift towards high frequency values. This suggests a decreased relaxation time with fast ionic motion and making ion conduction mechanism in polymer electrolytes a thermally activated phenomena. 50 Due to broad nature of M 00 peaks, it is quite evident that conductivity relaxation are non-Debye type in nature. However, for better understanding frequency dependent complex modulus spectra are analyzed using Havriliak-Negami (HN) formalism as well as modied Kohlrausch-Williams-Watts (KWW) equation by Bergmann. Havriliak-Negami (HN) function is represented by the following equation 50,51

M ∗ = M∞ +

(Ms − M∞ ) [1 + (jωτ )αHN ]γHN

(8)

here, Ms and M∞ respectively representing low and high frequency limits of electrical modulus spectra. Again αHN , γHN are the shape parameters and τ corresponds to the relaxation time. In general shape parameters, i.e. αHN and γHN , has to satisfy the following relations

0 < αHN ≤ 1 and 0 < αHN γHN ≤ 1. 50 In case of ideal Debye type relaxation both the shape parameters should be 1 and in case of non-Debye type relaxation these deviate from unity.

16


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On the other hand, the KWW approach is represented by the equation is given below 4 00 Mmax

M 00 = (1 − βKW W )

βKW W 1+βKW W

[βKW W (fmax /f ) + (f /fmax

)βKW W ]

(9)

00 here, Mmax , βKW W and fmax are the maxima of spectra, KWW shape parameter and fre-

quency corresponding to the observed M 00 maxima respectively. In gure 5(a) and (b) HN analyzed results of real and imaginary component of electrical modulus are shown by using solid lines. From the tted results, the value of αHN and γHN are evaluated and found less than unity. It suggests that the relaxation events occurring at microscopic level are of non-Debye type. On the other hand KWW analyzed M 00 isotherms are shown in gure 5(c). The value of βKW W obtained from the tting formalism is found between 0.45 to 0.55, which infer a non-Debye type behaviour of relaxation events as also found in HN analysis of M ∗ (f ). Low values of βKW W suggest that the conductivity relaxation events are non-exponential in nature and Li+ ion transport can not be considered as an isolated event rather it is a cooperative phenomena. 50 HN and modied KWW analysis techniques can be considered equivalent if HN and KWW tting parameters are linked by 50 1.23 In the present investigation we observed that the following expression βKW W = αHN γHN .

the above mentioned relation holds true for the obtained tting parameters. Therefore any one of these representations can be used to analyze the frequency dependent complex modulus spectra. Both these formalism bear the same physical interpretation to ion conduction mechanism. Scaling is performed to investigate the common underlying physical phenomena of ion conduction mechanism. It is already represented that using Summereld conductivity scaling approach, conductivity isotherms can be scaled. Here the scaled M 00 spectra are shown in gure 5(d) for PEO20 -LiCF3 SO3 - 8 wt.% TiO2 PNCE composition. A single master curve can be formed over a wide range of temperature using maxima normalization technique. 32 This property suggest that conductivity relaxation phenomena and ion conduction mechanism are thermally activated dynamic process but they remain independent of tem-

17



perature of the sample. Inset of gure 5(d) show the process of scaling for PSC and 8 wt.% TiO2 PNCE composition at T = 243 K. These two M 00 isotherms are found not to superpose well to form a single master curve, hence using maxima normalization technique M 00 (f ) spectra can not be scaled. It reects that with the addition of TiO2 ller, local environment at molecular dimension has changed due to ller-polymer and ller-salt interactions. 4

Relaxations Dynamics and Universalities T = 323 K T = 203 K

10

10

10 10

10

(a)

(c)

(b)

(d)

10 7

T = 323 K

10

7

q

'f

10

f

3

T = 203K

'f

1

10

10

3

q = 0.9988

T = 203 K

-1

10

T = 203 K

10

5

3

10

10

7

5

10 10

9

T = 323 K

10 10

-1

T = 203 K

-1

10

1

1

T = 203 K

10

3

3

'f (Hz)

'

10

5

der

5

T = 323 K

10

7

Electrode Polarization

''

T = 323 K

Segmental

10

T = 10 K

7

Relaxation

10

''

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

Page 18 of 33

-1

10 10

NCL

-2

10

1

10

4

10

10 10

-1

10

0

10

1

10

2

10

3

10

4

10

5

10

6

10

-1

10

frequency (Hz)

0

10

1

10

2

10

3

10

4

10

5

-1

7

frequency (Hz)

-3

1

10

-3

6

frequency (Hz)

Figure 6: Frequency dependent (a) real part and (b) imaginary component of complex relative permittivity, (c) derived dielectric loss and (d) ε0 f with inset showing the tted results at T = 203 K for the 5 wt.% TiO2 PNCE composition. Temperature interval between each isothermal spectra is ∆ T = 10 K. The process of relaxation dynamics and ionic conductivity in PSC and PNCEs can be studied form complex relative permittivity spectra. Complex relative permittivity isotherms are shown in gure 6(a) and (b) respectively for

5 wt.% TiO2 PNCE composition, over a temperature range of 323 K to 203 K with interval of 10 K. At high frequency regions real part of relative permittivity, ε0 , become nearly constant and it is observed to increase with decreasing frequency. With decreasing frequency initially ε00 decreases monotonically. Thereafter in mid fre18


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quency region ε00 tends to follow the relation, ε00 ∝ f −1 , which indicate that the observation is related to dc conductivity. 28 Due to the eects of EP at low frequency regions ε00 show sudden increase in magnitude. At very low temperature, T= 203 K, ε00 is found to assume nearly constant values, which indicate the existence of NCL or second universality in PSC and PNCE. The dominance of UDR and NCL over each other will be discussed using Kramer-Krönig formalism. From complex relative permittivity isotherms the segmental relaxation phenomena are not very clear. High value of ionic conductivity in PNCEs masks the relaxation events. Therefore, to study segmental relaxation, dc conduction free dielectric loss parameter is used. The dc conduction free dielectric loss parameter clearly show both segmental relaxation and EP at high and low frequency regime respectively presented in gure 6(c). Segmental relaxation time can be calculated from each isotherms of dc conduction free dielectric loss spectra using the relation τs = 1/2πfs , where fs is the peak frequency of segmental relaxation. For detailed analysis of NCL eect, Kramer-Krönig formalism is followed. The mathematical expression for the approach is given by the following equation 37

ε0 f = Bf q

(10)

where, q is the exponent. The exponent q should be 1, if ion conduction process is dominated by second universality and not by rst universality. In gure 6(d) ε0 f (f ) is shown at dierent temperatures. Over the entire frequency range of investigation ε0 f becomes nearly linear at very low temperatures. This behaviour show the dominance of second universality over rst universality at low temperature regime. The linear region is found to shift towards high frequency regions with increasing temperature. Fitted results at T = 203 K using equation (10) is shown in gure 6(d) inset. Detailed analysis show near unity value of the exponent q = 0.998 which indicates that ion conduction process at low temperatures is governed by second universality. Exponent q value also

19



decrease with increasing temperature which suggest that with increasing temperature UDR dominates over NCL. 37 In conclusion ion conduction mechanism in PSCs and PNCEs can only be explained by simultaneous application of both UDR and NCL formalism. The cause behind observing the NCL phenomena is considered to be the caged ion dynamics of the mobile ions. At suciently low temperature and high frequency there exists very small probability for the mobile ions to hop towards a favourable neighbouring site and leave the cage like potential landscape created at microscopic level. On the other hand when temperature increases or at low frequencies, these caged ion become mobile and contribute to ion conduction process which is attributed as UDR.

Relaxation Mapping 10

10

10

1

2 wt. % TiO

0

8wt. % TiO 2

2

15 wt. % TiO

-1

2

10

-2

10

-3

10

10

-5

10

-6

10

-1

-2

-3

s

10

10

-4

0

(Sec)

(Sec)

VTF Fitted Results

10

c

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

Page 20 of 33

10

-7

10

10

10

10 3.2

3.4

3.6

3.8

4.0

1000/T (K

4.2 -1

4.4

4.6

-4

-5

-6

-7

4.8

)

Figure 7: Variation of relaxation time (conductivity and segmental) for the PNCE compositions, PEO20 -LiCF3 SO3 - x wt.% TiO2 (x = 2, 8, &15). Solid lines represent VTF tted results. Reciprocal of angular frequency for the observed relaxation event is dened as its relaxation time. Segmental relaxation time (τs ) and conductivity relaxation time ( τc ) for dierent temperatures are obtained from frequency dependent εder and M 00 spectra respectively. Both

τs and τc are shown as a function of temperature in form of a relaxation map in gure 7. It can be found that both τs and τc follow Vogel-Tammann-Fulcher (VTF) relation given by

20


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the following expression. 52

τ = τ0 exp

Ea kB (T − T0 )

(11)

where, τ , τ0 , Ea , kB , T and T0 are relaxation time, pre-exponential tting parameter, pseudo activation energy, Boltzmann's constant, absolute temperature and Vogel temperature respectively. Though VTF equation is an empirical relation, at present it is one of the widely accepted relation. Vogel temperature is considered as the temperature at which all molecular motion cease or excess conguration entropy becomes zero. Generally in literature its range is found following the relation 60 K≤ Tg − T0 ≤ 50 K, where Tg is equilibrium glass transition temperature. 28 Detailed tting parameters are given in supplementary material. A close correlation can be observed between experimentally obtained and tted results, which suggest the ionic transport mechanism and polymer segmental relaxation dynamics in PSC and PNCEs are coupled in nature. As τc and τs are following VTF relation, therefore it can be considered that there exist a coupling between ionic conduction and segmental relaxation processes found in this class of materials.

Coupling To explain the coupling between ionic conduction and segmental relaxation process as indicated by relaxation time mapping and dierent scaling approaches, Ratner's approach is used. The theoretical background of this analysis has been discussed in coupled ionic transport mechanism section earlier. It can be observed from equation (3) that for a coupled system − log σdc and log τs should follow similar behaviour. Figure 8(a) represent − log σdc and log τs as a function of temperature for the PNCE composition, PEO20 -LiCF3 SO3 - 8 wt.% TiO2 . For all other compositions in the present investigation a similar trend can be observed (not shown here). σdc and τs follow VTF behaviour and the tted spectra are shown in form of solid lines in the plot. In this context we have also examined Dτs and σ Tτs . For coupled system these two entities should remain constant as discussed earlier. These two parameters

21



2

16

(a)

-log

(

dc

14 log (

s

)

VTF Fit

0

)

s

-2

10 8

-4

log (

-log (

dc

)

)

12

6 -6 4 -8

2 3.5

4.0

1000/T (K

5.0

)

6

10

-6

10

5

10 4

s

10 10

10

-8

3

D

2

10

s

dc

10

-7

s

T

1

10

10 -7

10

-6

-9

dc

2

(nm )

10

-1

(b)

s

10

4.5 -1

T (S K s cm )

3.0

D

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

Page 22 of 33

10

-5

10

s

-4

10

-3

10

-2

10

-10

-1

(s)

Figure 8: (a) Negative logarithm of dc conductivity and segmental relaxation time as a function of temperature in inverse scale for 8 wt.% TiO2 PNCE composition. Solid lines represent VTF tted results. (b) variation of Dτs and σDτs as a function of τs for 8 wt.% TiO2 PNCE composition. has been represented in gure 8(b). Only one order of change in magnitude can be found in these plots for the entire range of investigation. This clearly indicates that, ion conduction mechanism is a cooperative phenomena of polymer segmental motion and thermally activated ion hopping. Hence ionic transport and segmental relaxation phenomena are closely coupled.

Theoretical Model Analyzed DC Conductivity Results. As described earlier MIsmatch Generated Relaxation for the Accommodation and Transport of IONs concept based theoretical approach is getting more and more attention due to its conceptual representation of the whole ion conduction process. MIGRATION is a rened concept of jump relaxation and mismatch and relaxation models. 53 MIGRATION is a ion hopping based model for structurally disordered materials, specially in cases where ion conduction phenomena is a coupled process like the present investigation. So far VTF equation is used to describe temperature dependent dc conductivity which is an empirical relation and also posses a divergence at T = T0 , where T0 is the Vogel temperature. According to this 22


Page 23 of 33

10

10

-1

-3

-5

(S cm

-1

)

10

dc

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


10

-7

dc

10

10

-9

VTF MIGRATION

-11

HF

10

10

-13

HF

Arrhenius

-15

3.0

3.5

4.0

1000/T (K

4.5 -1

5.0

)

Figure 9: Study of temperature dependent dc conductivity using MIGRATION and VTF model approach for the PNCE composition PEO20 -LiCF3 SO3 - 8 wt.% TiO2 . model a short time ion hopping is always considered successful and termed as high frequency conductivity. Ion hopping can be considered as a collection of successful as well as unsuccessful forward-backward hopping over a larger period of time. 54 This forward-backward ion hopping is the cause behind the observed dispersion in the complex conductivity isotherms. Eventually only a small fraction of these ion hopping become successful and contribute towards dc conductivity. 55 According to this mechanism beyond dispersive regime the observed constancy in the crossover angular frequency is causing the non-Arrhenius behaviour of the dc conductivity. According to this model dc conductivity, σdc is expressed by the following expression 56

∗ E∗ E α − γ exp σdc (T ) = exp − τ kB T 2kB T

(12)

where, α and γ are the pre-exponential factors, E ∗ is the elementary displacive step activation energy. Figure 9 shows a comparative study between VTF and MIGRATION based concepts for PEO20 -LiCF3 SO3 -8 wt.% TiO2 PNCE composition. A close agreement can be observed between experimentally obtained data and theoretically predicted results. Using VTF equation one can extract the information about the activation energy of ionic conductivity as well as Vogel temperature. At Vogel temperature it is considered that molecular motion cease. Unlike VTF equation, MIGRATION concept do not have any singularity at temperature scale. MIGRATION based model is successfully reproducing the temperature 23



dependent behaviour of dc conductivity and there exist no divergence temperature. Figure 9 also represents the evaluated ion hopping conductivity at high frequency range σHF . It can be observed from the plot that obtained σHF is Arrhenius activated. This σHF marks the transition from NCL to UDR as per the mapping of MIGRATION model to Ngai coupling model. A large displacive activation energy, obtained from tted results E ∗ (0.1151 eV) represents the existence of coupling between segmental motion of polymer host and ionic conduction. Observed dc conductivity behaviour as a function of temperature for the ion conducting PNCEs can be explained using MIGRATION model. It also supports the coupled nature of ion conduction mechanism as discussed in section describing coupling using modied Ratner's approach.

Conclusion Using conventional solution casting technique a series of ion conducting polymer nanocomposite electrolyte is prepared. Polymer salt complex formation, phase formation of ller and composite nature of the proposed electrolytes are conrmed using XRD analysis. At ambient temperature (T = 303 K) the maximum dc conductivity (σdc ) is found for 8 wt.% TiO2 PNCE composition and its value is to be 3.174 × 10−5 S cm−1 . Conductivity isotherms are analysed using modied AW formalism. FTIR suggests there exist a variation of free ion concentration for dierent ller composition. DC conductivity, conductivity and segmental relaxation time represented as a function of temperature is following VTF behaviour, inferring coupling between polymer segmental relaxation and ion conduction phenomena. Existence of both the rst and second universalities are shown using frequency dependent ac conductivity spectra. Dielectric loss spectra are also used to discuss these universalities. Kramer-Krönig approach explained that at low temperature NCL dominates over UDR and with increasing temperature UDR become more prominent than NCL. Summereld conductivity scaling approach and scaled electrical modulus spectra suggest that ion conduction

24


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process in PNCEs under investigation is a thermally activated and temperature independent dynamic process. With Ratner's approach the coupled nature of polymer segmental motion and ion conduction mechanism is analysed to nd the cause behind the occurrence in NCL at low temperature regime. Comparative study for dc conductivity is carried out using VTF and MIGRATION model proposed theories. A close agreement is observed between the experimentally obtained data and MIGRATION model predicted results. High value of displacive activation energy, E ∗ , also represents the existence of coupling between segmental motion of polymer host with that of ionic motion. Finally segmental relaxation and ion conduction are coupled phenomena and spatial reorganization of host polymer chains at molecular dimension of PSC and PNCEs favour ionic transport phenomena.

Supporting Information Anatase phase of titanium dioxide preparation using acrylamide gel template method, polymer nanocomposite electrolyte preparation and characterization conditions are described.

Acknowledgement T.D. acknowledge Central facility Metallurgical Engineering and Materials Science Department, IIT Bombay, India for allowing the use of Broadband Dielectric Spectrometer to carry out the experiments.

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Coupled Ion Conduction Mechanism and Dielectric Relaxation

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