A conceptual review on polymer electrolytes and ion transport mode

Review ArticleA conceptual review on polymer electrolytes and ion transport models a Advanced Polymeric Materials Research Lab, Department of Physics, College of Science, University of S

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Review Article

A conceptual review on polymer electrolytes and ion transport models

a Advanced Polymeric Materials Research Lab, Department of Physics, College of Science, University of Sulaimani, Qlyasan Street, Sulaimani, 46001,

Kurdistan Regional Government, Iraq

b Komar Research Center (KRC), Komar University of Science and Technology, Sulaimani, 46001, Kurdistan Regional Government, Iraq

c Centre for Ionics University of Malaya (CIUM), University of Malaya, 50603 Kuala Lumpur, Malaysia

d Centre for Foundation Studies in Science, University of Malaya, 50603 Kuala Lumpur, Malaysia

a r t i c l e i n f o

Article history:

Received 14 June 2017

Received in revised form

19 January 2018

Accepted 21 January 2018

Available online 31 January 2018

Keywords:

Polar polymers

Polymer electrolytes

Electrical impedance spectroscopy

Impedance plots

Arrhenius model

VogeleTammanneFulcher (VTF) model

Reformulated Arrhenius model

a b s t r a c t

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

vs dielectric constant, the reformulated Arrhenius

sdcðTÞ ¼s0exp

E a

k B Tε0

equation is proposed Finally, other important phenomena, occurring in polymer electrolytes, are shown to be understandable from the dielectric constant studies

© 2018 The Authors Publishing services by Elsevier B.V on behalf of Vietnam National University, Hanoi This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)

1 Introduction

Various sources of alternative energy are continuously

evolving to reduce the long-term dependence on oil, nuclear and

other fossil fuels The other environmentally friendly fuel cells,

such as batteries, super capacitors and dye sensitized solar cells,

are strong candidates for this reason[1] The conception of

poly-mer electrolytes (PEs) is a highly specialized and multidisciplinary

ﬁeld that covers the disciplines of electrochemistry, polymer

sci-ence, organic and inorganic chemistry [2] Dry solid polymer

electrolytes (SPEs) have attracted great attention as safer

alter-natives to liquid electrolytes[3] In theﬁeld of SPEs, a pioneering

work was carried out by Wright et al and cited by Singh and Bhat

[4] In their work, the dc conductivity of order of 105 S/cm at

330 K in highly crystalline polyethylene oxide-sodium thiocya-nate (PEOeNaSCN) complexes was reported [4,5] The SPEs are formed by inorganic salts dissolution in a polar polymer matrix The choice of PEs in modern applications, such as high energy density batteries, electrochromic devices, sensors and fuel cells, was justified by studying their structural, morphological and electrical properties[6,7] On the other hand, the choice of poly-mer hosts for PEs largely depends on two factors:first, the exis-tence of polar (functional) groups with a large power of sufficient electron donor to form coordination with cations and, second, a low hindrance to bond rotation [2] Fig 1 shows the chemical structures of some important polymers that are widely used as host polymers in PEs

The good mechanical strength, ease of thinﬁlm fabrication with desirable shapes and the ability of forming good electrode/elec-trolyte contact are the main advantages of dry SPEs[6,8,9] From the economical and commercial viewpoints, a low-cost membrane with good ionic conductivity, enhanced dimensional and me-chanical stabilities are recent challenges to be invented The main drawbacks of SPEs are their high crystallinity and low ionic

* Corresponding author.

E-mail addresses: shujaadeen78@yahoo.com , shujahadeenaziz@gmail.com

(S.B Aziz).

Peer review under responsibility of Vietnam National University, Hanoi.

Contents lists available atScienceDirect

Journal of Science: Advanced Materials and Devices

j o u r n a l h o m e p a g e : w w w e l s e v i e r c o m / l o c a t e / j s a m d

https://doi.org/10.1016/j.jsamd.2018.01.002

Journal of Science: Advanced Materials and Devices 3 (2018) 1e17

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conductivity [10] Polymer electrolytes comprise both crystalline

and amorphous regions It has been well reported that the ion

transport occurs mainly in the amorphous region rather than the

crystalline region, but the polymers host materials that used in PEs

are often semi-crystalline[4,11] Thus, to overcome the

disadvan-tages and improve SPEs' conductivity, plasticizer, as one mostly

applied method, has to be added to improve the ambient ionic

conductivity Through using plasticizers, the amorphous region and

ion aggregates in PEs can be increased and dissociated, respectively,

causing the dc electrical conductivity of SPE to be improved[12] It

has been established that the ionic conductivity in plasticized

polymer electrolytes can be increased at the expense of decreased

mechanical strength and vice versa [4,13] In addition to high

conductivity and a broad electrochemical stability window, PEs

must exhibit good thermal and mechanical properties These

per-formances can be achieved by dispersing nanosized ﬁllers into

polymer electrolyte Following the creative work of Weston and

Steele[4,14], who have improved the ionic conductivity and

me-chanical stability of polymer electrolytes by adding Al2O3particles,

nanocomposite SPEs have been broadly studied A complete

un-derstanding of the effects of inorganicﬁllers on the ion transport,

thermal, mechanical and electrochemical properties of PEs is still

not reached [15] From the above survey, it is clear that the dc

electrical conductivity can be improved by incorporating the plas-ticizer or inorganicﬁllers into the SPEs But yet, the ion conduction mechanism in solid plasticized and composite polymer electrolytes

is not fully understood[4] The main goal of this review article is to shed light on different types of PEs and ion transport models Additionally, the necessary of reformulation of Arrhenius equation based on recent experimental achievements in this ﬁeld is elucidated

2 Classiﬁcations of polymer electrolyte Polymer electrolytes have been proved to be promising mate-rials in the research and development of electrochemical devices Most of the research activities are devoted in theﬁeld of solid state electrochemistry, in which high ion-conducting materials are considered to be developed for the energy conversion and storage applications[16] In this sense, PEs are a class of materials, which have been witnessed in the last 20 years by massive research ef-forts, to achieve systems with a good conductivity and an electro-chemical stability[16,17] On the basis of materials, the polymer electrolytes have been categorized into dry solid polymer electro-lyte, plasticized polymer electrolytes, gel polymer electrolytes, and composite polymer electrolytes[18]

Fig 1 Chemical structures of some polar polymers widely used for polymer electrolytes: (a) Poly (ethylene oxide) (PEO), (b) Poly(vinyl alcohol) (PVA), (c) Poly(methyl methacrylate) (PMMA), (d) Poly( 3 -caprolactone) (PCL), (e) Chitosan (CS), (f) Poly(vinylpyrrolidone) (PVP), (g) Poly(vinyl chloride) (PVC), and (h) Poly(vinylidene ﬂuoride) (PVDF).

S.B Aziz et al / Journal of Science: Advanced Materials and Devices 3 (2018) 1e17

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2.1 Polymer-salt complex or dry solid polymer electrolyte (DSPE)

The concept of dissolving inorganic salts in functional (polar)

polymer, thus creating an ion conducting solid electrolyte is known

as a solid polymer electrolyte (SPE)[19] The interactions of metal

ions with polar groups of polymers are mainly resulting from

electrostatic forces and accordingly the formation of coordinating

bonds [20,21] There are some important factors that may have

effect on the polymer-metal ion interactions, such as nature of the

functional groups attached to the polymer backbone, compositions

and distance between functional groups, molecular weight, degree

of branching, nature and charge of metal cation, and counter ions

[21] The cations can transfer from one coordinated site to another

when subjected to an electricﬁeld This is due to the weak

coor-dinate of the cations to sites along the polymer chain For a better

understanding of these technologically important materials,

further study has to be conducted in thisﬁeld, with a particular

emphasis on their complex chemistry and ionic transport

proper-ties[19]

2.2 Plasticized polymer electrolyte (PPEs)

Plasticized polymer electrolytes, which are a branch of PEs, are

prepared by incorporating the polymer host with low molecular

weight compounds, such as ethylene carbonate, propylene

car-bonate and poly ethylene glycol (PEG)[22] Plasticizers can reduce

the number of active centers and thus weaken the intermolecular

and intramolecular forces between the polymer chains [23]

Consequently, they result in lessening the rigidity of the three

dimensional structure formed on drying, and changing the

me-chanical and thermo-meme-chanical properties of the preparedﬁlms

[23,24] Therefore, the addition of low molecular weight

plasti-cizers decreases the glass transition temperature of the PE system

Hence, the reduction of crystallinity and increment in salt

dissoci-ation capability are guaranteed, by which the enhancement of

charge carrier transport is achieved However, the resulting poly-mer electrolytes are predicted to obtain a low mechanical strength

[25] Recent studies have conﬁrmed that the amorphous fraction of composite polymer electrolytes can be increased due to the plas-ticizers It has been reported in ref.[26]that the crystallinity can be decreased when the plasticizer (PEG200) is added to the poly-ethylene oxide (PEO) based nanocomposite polymer electrolytes, as shown inFig 2b and c It is obvious that the micrograph of PEO25-NaClO4þ 5 wt % DMMT complex system [seeFig 2a] shows the presence of spherulites The boundary between the spherulites can

be attributed to the presence of amorphous fraction The surface roughness inFig 2a was ascribed to the existence of large amount

of crystalline fraction in the PEO based polymer electrolyte It was observed that the surface roughness was decreased upon the addition of plasticizer [seeFig 2b and c], exhibiting a smooth sur-face texture These changes could be attributed to the effect of plasticization that resulted in the reduction of crystallinity of the host polymer PEO and the enhancement of the overall amorphous fraction in the materials

From the above discussion, it is understood that the increase of SPE conductivity by addition of plasticizer at room temperature results in the loss of mechanical strength Furthermore, plasticized polymer electrolytes exhibit a number of drawbacks, such as inadequate mechanical properties at high level of plasticization, reactivity of the polar solvents with lithium electrode and solvent volatility[22,27]

2.3 Gel polymer electrolytes (GPEs) Recently, a substantial effort in theﬁeld of polymer electrolytes has been given to gel-type polymer electrolyte (GPE) This is due to the fact that the advantages of liquid-type electrolytes, such as high ionic conductivity, and solid-state electrolytes, such as high safety, can be combined In gel-type PE, polymer as a host matrix has been used to trap the liquid constituents Therefore, the GPE based

ﬁlms of (PEO) þ 5 wt.% DMMT þ x wt.%PEG200 with different concentrations of x (i.e., (a) x ¼ 0, (b) x ¼ 10, and (c) x ¼ 50) S.B Aziz et al / Journal of Science: Advanced Materials and Devices 3 (2018) 1e17

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products are considered to be much safer than liquid-based

elec-trolyte products, particularly, when it is used in lithium ion (Li-ion)

batteries[28] In the preparation of gel electrolytes, a large amount

of organic solvent or plasticizer must be added into the polymer

host[29] The incorporated plasticizer molecules can form a wide

network whereby the ion conduction takes place along with the

host polymer, which principally provides structural support Gel

electrolytes can exhibit high ambient conductivities, but still

un-dergo some other disadvantages as mentioned in the plasticized

polymer electrolytes, such as the release of volatiles and increased

reactivity towards the metal electrode[30].Scheme 1shows the

inﬂuence of plasticizer on the percolative behavior of ion transport

It is clear that the portion of amorphous regions is well below a

percolation threshold at room temperature (See the left hand side

ofScheme 1), resulting in the poor ionic conductivity Plasticized

polymer electrolytes with suitable liquid solvents that have high

dielectric constant,ε, and low viscosity,h, are desired to form gel

polymer electrolytes Therefore, the amorphous regions grow

larger in number and size, owing to the adsorption of liquid This

ultimately leads the percolation threshold to be accomplished at

ambient temperature The connected network of amorphous

re-gions provides fast ion conducting pathways, which acts upon

enhancing the ion mobility and hence the higher ionic conductivity

[31]

2.4 Composite polymer electrolytes (CPEs)

One of the major reasons behind the poor ionic conductivity of

polymer electrolytes has been attributed to the presence of

ion-pairs (or ion-association) and ion triplets This is due to weak

dielectric constant of the host polymers [32] Many approaches

have been developed to avoid the occurrence of ioneion

associa-tion in polymer electrolytes To solve these difﬁculties and improve

the qualities of SPEs, inorganic inert ﬁllers with high dielectric

constant has been lately suggested to be dispersed in PEs [33]

Dielectric permittivity can be properly adjusted, simply by

con-trolling the type and the amount of incorporated inorganicﬁller

material Ceramic materials, which are classiﬁed as inorganic ﬁllers,

are typically fragile and possess low dielectric strength [34]

Though, polymers have relatively low dielectric permittivity, they

can undergo highfields, they are also flexible and easy to be pro-cessed Therefore, by combining the advantages of these two ma-terials, i.e., ceramic filler and polymer material, new hybrid composite materials with high dielectric constants can be fabri-cated[35] When the size of these inorganicfillers is in the dimension, the newly formed composites are called nano-composite polymer electrolyte (NCPE) [10,33] Composite poly-meric materials containingfine ceramic particles are considered as heterogeneously disordered systems [34,36] Their electrical property depends on the dielectric constant and their constituents' conductivity Additionally, the volume fraction, size and shape of the added filler particles have impacts on the electrical perfor-mance of composite materials[34] Li et al.[37]have successfully investigated the effect of in situ synthesized TiO2 on the morphology of poly (vinylidene difluoride-co-hexa fluoro propyl-ene) (PVDF-co-HFP)) complexed with LiPF6 The surface and cross-section morphology of the PVDF-co-HFP polymer incorporated with different amounts of in situ synthesized TiO2 nanoparticles have been studied They have observed many closed pores on the surface of the samples They have found that the connected spherical pores are crucial in enhancing the ion mobility and ionic conductivity

3 Electrochemical impedance spectroscopy (EIS) technique Electrochemical impedance spectroscopy (EIS) is a technique currently used to study the electrical properties of the bulk mate-rials and their interfaces (i.e., electrodeeelectrolyte interfaces) over

a wide range of frequency and temperature It is also known as ac impedance spectroscopy (or dielectric spectroscopy) The bulk and interface contributions can be separated by using this technique It can also be used to study the ion conduction mechanism and dielectric relaxation in PEs

3.1 Origin of EIS theory Electrical charge displacements in a bulk material produce two distinct physical phenomena: (i) if the charge motion in a localized volume of the matter is strictly conﬁned then a polarization phe-nomenon takes place or (ii) if the electrical charges in the materials

Scheme 1 Transformation of a soft matter solid electrolyte such as polymer electrolyte with a non-percolative arrangement of highly disordered (higher ion mobility) regions to a

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are collectively diffused over long distances then diffusion is

possible and a dc conductivity,sdc, is established[38] In order to

identify and overcome the effect of space charge polarization at the

electrode/solid electrolyte interface, it is crucial to carry out the ac

conductivity measurements by means of complex impedance

spectroscopy (CIS), i.e., using an ac electricﬁeld[39] It is

estab-lished that, dielectric spectroscopy depends on the tendency of ions

and dipoles to orient along the electricﬁeld direction[40] When an

ac electricﬁeld is applied to a parallel plate capacitor sandwich

with polymeric materials, four categories of polarization are taken

place, which are known as electronic, atomic, dipolar and migrating

charge polarizations[41] Ions often originate as impurities in the

raw materials Dipoles result from atoms with unequal electro

negativities, which are attached to each other on the backbone of

polymeric materials[40] The dielectric relaxation processes are

usually correlated to one or more polarization processes of the

studied material Dipolar polarization and polarization due to

charge migration are the two main components of the dielectric

responses in polymers Dipolar and charge migration polarizations

can be detected at frequencies less than 109Hz[41] If the electric

ﬁeld is reversed in sign (or direction), the dipoles will realigned

with the appliedﬁeld and the ions start to diffuse (or migrate) to

the other electrode As the frequency ofﬁeld reversal increases, the

ions and dipoles become increasingly difﬁcult to keep up with the

ﬁeld changes In addition to that the functional groups with larger

sizes will be much harder to be reorienting with theﬁeld[40] The

investigation of conduction and different dielectric polarizations

can eventually lead us to achieve more information on the dynamic

behavior with regard to relaxation processes

3.2 Complex impedance spectroscopy

Characterization of heterogeneous and disorder materials

re-quires non-destructive measurements Dielectric impedance

spec-troscopy that measures the conductivity and permittivity as

functions of frequency at different temperatures can provide

in-sights into the electrical and structural properties of heterogeneous

systems at both microscopic (molecular) and macroscopic levels

[42] The complex impedance spectroscopy (CIS) is a powerful

experimental technique that provides several beneﬁts, such as the

calculation of relaxation frequency and separation of electrode (at

low frequency spike) and bulk (at high frequency semicircular

re-gion) effects Through using the CIS technique, the real (Z0) and

imaginary (Z00) parts of impedance can be obtained over a wide

range of frequency Recently, this technique has been used

suc-cessfully to evaluate the DC ionic conductivity and activation

en-ergy of ionic conductors[43] In CIS measurements, an alternating

voltage over a broad range of frequencies must be applied to an

electrochemical sample holder[44] Typically, the applied voltage

(V) is a sinusoidal wave waveform that varies with time (t), deﬁned

as

where V0is the maximum voltage intensity anduis the angular

frequency Likewise, the resulting electrical current (I) is a

sinu-soidal waveform with a phase difference (4):

where Iois the maximum current intensity and4 is the phase angle

between the applied voltage and current waveforms The electrical

impedance parameter, Z(u), which deﬁnes the ratio between the

applied voltage and the resulting electric current, ZðuÞ ¼ VðtÞ=IðtÞ,

is expressed as

where Zrealand Zimgare the real and imaginary parts of the elec-trical impedance data, respectively, and they can be determined at a given frequency by[45],

The impedance experimental data can be analyzed by plotting the imaginary partðZimgÞ versus the real part ðZrealÞ

3.3 Impedance plots and equivalent circuits The direct relationship between the responses of a system under test and the proposed electrical equivalent circuit is considered to

be an important characteristic of complex impedance spectroscopy (CIS)[46] From the physics viewpoint, a resistance R is assigned to stand for the dissipative part of the dielectric response and a capacitance (C) is taken to denote the storage part of the dielectric material[46,47] From the electrical impedance spectroscopy (EIS) outputs, an impedance graph (imaginary part versus real part) can

be plotted and thus information regarding an expected equivalent circuit can be extracted.Fig 3shows a typical example of EIS graphs and equivalent circuits The real and imaginary parts of the impedance are associated with the existence of resistor and capacitor, which are in- and out-of-phases with the applied AC signal, respectively They are generally represented by R or ZRor Z0

or Zrealand X or Zcor Z00or Zimg, respectively The imaginary part, which is also known as reactance, is given by[48],

The demonstration of these simple elements on the complex impedance plane is called an “Argand diagram” as illustrated in

Fig 3a and b The imaginary part of the impedance, reactance, is plotted against the real part, resistance, over a range of frequency

[48] If there is a resistor connected in series with a capacitor, the total impedance ZRCbecomes[48],

The complex impedance plot corresponding to Eq (7) is illustrated inFig 3c The impedance plot of a parallel combina-tion of a single resistor and a capacitor, ZR C, has a semicircular

shape on the complex impedance plane, as shown in Fig 3d Qualitatively, this behavior can be easily understood The impedance of the capacitor at very low frequencies becomes very large Thus the majority of the current isﬂown through the resistor, causing its properties to be dominated On the other hand, the impedance of the capacitor at very high frequencies becomes very small, such that the resistor is effectively shorted out and gives rise to zero net impedance [48] Experimental evidence reveals that in complex impedance plane plots the low frequency tail is not truly vertical as illustrated schematically in

Fig 3e Fig 4 shows an experimental data example of this behavior Most commonly, it is impossible for the ac response to

be described by using simple ideal circuits The semicircles showing in the complex (Z00-Z0) plane are often widened and deformed to asymmetrical arcs[49] One can see inFig 4 that the center of the semicircles lies below the real Z0axis The impedance response of PVA:AgNt (75:25) reveals the semicircular and spike regions at high and low frequencies, respectively The semicircle at high frequency indicates the bulk S.B Aziz et al / Journal of Science: Advanced Materials and Devices 3 (2018) 1e17

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response of the sample, whereas the spike at low frequency can be

attributed to the accumulated double layer charges at the solid

polymer electrolyte/electrodes interfaces At low frequencies, the

impedance plots should expose a straight line parallel with the

imaginary axis; though the electrode polarization effect (double

layer capacitance) at the blocking electrodes induces a curvature

[50e52]

3.4 Impedance-related functions

The electrical impedance spectroscopy (EIS) has become an

important tool for characterizing the electrical properties of various

materials, such as glasses, amorphous semiconductors,

electroni-cally conducting polymers, ion conducting polymers and transition

metal oxides[53,54] There are several other derived or measured

quantities associated with the impedance, which are important in

the EIS The electrical impedance (Z*), admittance (Y*), modulus

(M*) and permittivity (ε*) are the four important

impedance-related functions, which can be measured, analyzed and plotted

in the complex plane in the EIS [55] Dielectric permittivity (ε*)

measurements, such as dielectric constant (ε0) and dielectric loss

(ε00), can reveal signiﬁcant information regarding the chemical and

structural characteristics of polymers It is established that these

polymer characteristics can be drastically affected by the existence

of other dopants in the polymer[56] The detailed investigations of

the dielectric parameters and electrode and interfacial polarization

effects of polymers are of great importance[57] On the other hand,

the study of conductivity relaxation behavior in conducting

poly-mer materials has become an interesting area of active research in

condensed matter physics due to their potential applications in electrochemical solid state devices[58,59] It has been reported that electric modulus (M*) formalism can be used as an effective tool to predict the relaxation behavior of ion conducting polymeric materials Through the spectrum of electric modulus, conductivity and its associated relaxation in polymers can be possibly investi-gated[59,60] The two essential quantities in dielectric relaxation spectroscopy are the complex dielectric constant or the dielectric permittivity ε*¼ ðjuCοZ*Þ1¼ ε0 jε00

and the modulus function

M*¼ juC0Z*¼ M0þ jM00

In these expressions, Cο¼ εοA=d is the capacitance of the empty measuring cell, where A and d refer to the area and separation length of the electrode The quantityεοis the dielectric permittivity of free space, which is equal to 8.854 1012

Fm1 Table 1 summarizes the interrelations between the four immittance functions[55]

4 Ion transport models for polymer electrolytes

A crucial feature that distinguishes ion conducting polymer electrolytes from other ionic conductors is that polymer electro-lytes are formed by dissolving low lattice energy salts in a polar polymer matrix For this reason, the cations are found to be responsible for the dc ionic conductivity In agreement with the theories of cationic transport in high molar mass polymer elec-trolytes, long range cation transport only takes place by dissociative steps, in which cations can move between neighboring coordi-nating sites, whether situated on the host molecule or on a nearby host molecule[61] It might therefore be predicted that cations,

(a)

Zreal

(b)

Zreal

(c)

Zreal

(d)

Zreal

(e)

Zreal

Fig 3 ColeeCole plots and their equivalent circuits for (a) a pure resistor, (b) a pure capacitor, (c) a capacitor and a resistor in series, (d) a capacitor and a resistor in the parallel combination, and (e) a leaky system [48] Resistor is represented by the symbol and capacitor represented by

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forming non-labile bonds with polar groups of the host polymer,

would not promote the dc conductivity of a polymer electrolyte

[61].Fig 5shows the ionic motion of a lithium ion in a PEO-host

It has been established that polymer electrolytes comprise both

amorphous and crystalline fractions at room temperature It is

known that ion transport principally occurs in the amorphous

re-gions Despite the fact that the conduction mechanisms are not

fully understood yet, it is widely recognized that cations, which are interconnected with functional groups of the host polymer chains, can move through re-coordination along the polymer backbone

[63] Based on recent review works, the polymer chains are re-ported to be folded to form cylindrical tunnels, in which the cations are located and coordinated by the functional groups[64,65] These cylindrical tunnels create channels, providing a pathway for the movement of cations The study of dc conductivity vs 1000/T can be conducted to identify the crystalline and amorphous nature of solid polymer electrolytes as can be seen in later sections This is related

to the fact that the result of this investigation can be interpreted in terms of one of the following models:

4.1 Arrhenius model for ion transport The characteristic advantage of selecting solid polymer elec-trolytes in a particular application of electrochemical device is basically resulting from the value of dc conductivity In this section, the relationship between the dc conductivity and temperature is explained in accordance with the well-known Arrhenius model, given by the equation:

sdcðTÞ ¼s0exp

Ea

kBT

(8)

whereso, Eaand kBare the pre-exponential factor, activation energy and Boltzmann constant, respectively The Arrhenius-like rela-tionship reported in Ref.[66]represents the fact that the motion of cations does not arise from the molecular motion of polymer host Therefore, as soon as the data of temperature and ionic conduc-tivity obeys the Arrhenius relationship, the mechanism of cation

0 2 4 6 8 10 12

Rb = 622 Ohm

Zr (Ohm) × 102

Zi

Fig 4 Impedance plot of PVA:AgNt (75:25) at 303 K [50]

Table 1

Relations between the four basic impedance functions [55]

m¼ juC o , where C o is the capacitance of the empty cell, Y*is admittance.

Fig 5 Cartoon of ion motion in a polymer host [62]

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transport can be associated with that occurring in ionic crystals

where ions jump to the nearest vacant sites, causing the dc ionic

conductivity to increase to a higher value[67] Recently, Ravi et al

[68], have observed the Arrhenius relationship between the dc

conductivity and 1000/T for a solid polymer electrolyte system

based on poly (vinyl pyrrolidone) (PVP) complexed with KClO4as

shown inFig 6 Similar Arrhenius behavior has been reported by

Baskaran et al [69]and by Kadir et al [70] for PVA:LiClO4 and

chitosan-PVA:NH4NO3polymer electrolytes, respectively

Most of polar polymers used in the preparation of polymer

electrolytes are semicrystalline polymers, i.e., containing both

crystalline and amorphous phases For instance, host polymer PEO

has a glass transition temperature, Tg, of 67 and melting

tem-perature, Tm, of about 68C The existence of a high crystallinity

fraction of PEO below Tm, can prevent the movement of small chain

segments (i.e., segmental motion) in the PEO polymer However,

the crystalline regions are completely absent above the melting

temperature (Tm) and hence a relatively high extent of segmental

motion would be expected, and result in a high dc conductivity[71]

The two regions for the plot of dc conductivity versus inverse

temperature (1000/T) have been outlined for the PEO based

poly-mer electrolytes as can be seen inFig 7 At temperature below Tm

(i.e., in region I), the dc conductivity was observed to increase

gradually with the temperature up to 70C, as depicted inFig 7 On

the other hand, above the Tmtemperature (i.e., in region II), the

conductivity was noticed to abruptly increase with temperature

compared to that of region I This is due to that, at high

tempera-ture, the energy would be large enough to overcome the potential

barriers that created between the sites and thus leads to increase

the free volume in the system, which facilitates the segmental

motion of ionic charge carriers [72] Therefore, the segmental

motion either allows the ions to be hoped from one site to another

site or offers a pathway for ions to be moved[71,72] It is therefore

understood that, in polymer electrolytes, the ionic motion can takes place through the transitional motion/hopping and dynamic segmental motion of the host polymer[72,73] As the amorphous phase progressively swells at high temperature (i.e., region II), the polymer chain gains faster internal modes in which bond rotation creates segmental motion This, successively, favors the inter-chain and intra-chain ion hopping of ion movements and the conduc-tivity of the polymer electrolyte accordingly becomes higher

[73,74]

4.2 VogeleTammanneFulcher (VTF) model for ion transport Another important empirical model used to study the ion transport in polymer electrolytes is the VogeleTammanneFulcher (VTF) model In this model, a strong inter-relation between the conductivity and segmental relaxation in polymers is anticipated

[75] The non-linear Arrhenius plot of temperature-dependent dc conductivity data can be accurately described by the VTF equation

[76]as follows:

sðTÞ ¼ AT1=2exp

kBðT T0Þ

(9)

where, A is the pre-exponential factor related to the number charge ions, kBis the Boltzmann constant, B is the pseudo-activation en-ergy associated with the polymer segmental motion and To

(To¼ Tg 50 K) is the temperature corresponding zero conﬁgura-tional entropy In Ref.[77], the authors studied the VTF behavior of polymer electrolytes based on (x)PVAce(1x)PVdF: LiClO4, as shown inFig 8 They ascribed the non-linearity behavior of dc ionic conductivity to the fact that ion transport is assisted by the polymer segmental motion Based on the VTF model, the curvature behavior

of the Arrhenius plots has been attributed to the presence of strong Fig 6 Arrhenius plots for PVP:KClO4 polymer electrolyte with different concentrations of KClO4 salt [68]

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inter-relation between the ionic motion and polymer segmental

relaxation as mentioned earlier This also implies that the polymer

segmental relaxation and ionic motion are well coupled with each

other

Furthermore, Kim et al.[78]and Uma et al.[79]have explained

the curvature feature of dc conductivity versus inverse

tempera-ture They have conﬁrmed that the VTF behavior can still be

retained, in which the ion transport is correlated with the polymer

segmental motion However, in Ref.[80], the coupling between

cation transport and segmental motion of the polymer has been

demonstrated by the curvature of dc ionic conductivity versus

1000/T As earlier mentioned, the free volume model can be used to

understand the correlation between ion transport and segmental

mobility The extensive and intensive survey of literature revealed

that most of researchers have applied the free volume model to

interpret the abrupt increase in the dc conductivity at high

tem-peratures (Arrhenius or VTF behavior) This agrees with the

explanation that the polymer will expand and produce free volume

as the temperature increases Therefore, through the produced free

volume, the polymer segments, ions or solvated molecules can

easily move Consequently, increased values are expected in ion and

segmental mobility, which will assist the ion transport[81] The

question is, despite the existence of polymer segmental motion,

why does still the Arrhenius conductivity linearly behave at higher

temperatures? This can be explained by the fact that, at higher

temperature, the increase in conductivity can be attributed to the vibrational dynamics of the polymer backbone and side chains The increase of vibrational amplitude can bring the coordination sites closer together and enable the ions to hop from their occupied site

to an adjacent empty site, using less energy[8] In other words, the polymer segmental motion is decoupled completely from the ionic motion, i.e., the polymer segmental motion just brings the coor-dination sites closer together and hence ions can be easily hopped from one site to another The pattern of dc conductivity versus 1000/T as a result becomes linear as occurred for ionic crystals From the above discussion, it is understood that the linear and curvature behaviors of dc conductivity can be ascribed to the coupling and decoupling mechanisms between the ionic and polymer segmental motions, respectively

It is understood from the above discussions on Arrhenius and VTF models that the increase of ion conductivity can be attributed

to the hopping rate and segmental mobility increments, respec-tively In addition to these models upon ion transport and con-ductivity behavior, ion dissociation energy and dielectric constant also have a great inﬂuence on the conductivity behavior of a polymer electrolyte It has been reported that the dielectric relax-ation study in ion conducting polymer electrolytes provides infor-mation with regard to the characteristics of ionic and molecular interactions[82] Recently, many researchers have considered the dielectric analysis in their studies to understand and explain the Fig 7 Temperature dependence of dc conductivity of (a) pure PEO, (b) (PEO þ NaClO 3 ) (90:10), (c) (PEO þ NaClO 3 ) (80:20), and (d) (PEO þ NaClO 3 ) (70:30) [72]

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conductivity behavior of solid and nanocomposite polymer

elec-trolytes[4,12,83e86] Ion transport study is the subject of

investi-gation by many researchers and various articles have been

published previously on different polymer

electrolytes/nano-composites and most of them interpreted the conduction

mecha-nism based on VTF and Arrhenius models without deep insights

[87e96] The focus of researchers on SPEs and nanocomposites is

related to that fact that SPEs are light weight,ﬂexible and they are

important for power storage technologies such as super-capacitors

and lithium-ion batteries[89,91e96] Petrowsky and Frech in their

recent works[97,98]have hypothesized that the dc conductivity is

not only temperature-dependent, but is also a function of the

dielectric constant in organic liquid electrolytes They have also

explained the curvature feature of dc conductivity due to the

de-pendency of pre-exponential factor,so, on the dielectric constant,

sðT;ε 0 Þ¼sοðε 0 ðTÞÞexp

Ea kBT

4.3 Role of dielectric constant on ion conduction mechanism

The concentration of ionic species in polymer electrolyte

de-pends on the dielectric constant of the host polymer and the lattice

energy of the salt In other words, the higher the dielectric constant

of the host polymer and/or the lower the lattice energy of the added

salt, the higher the charge carrier concentration[99,100] The dc

ionic conductivity,s, of an electrolyte can be given as[100]:

s¼X

i

where ni is the charge carriers concentration, q is the electron

charge andmiis the ions mobility, where i refers to the type of the

ions[4] It is clear from Eq.(10)that the ionic conductivity (s) can

be increased by increasing either the charge carrier concentration

(n) or the ionic species mobility in the system It has also been

reported that the carrier density, n, relies mainly on both

dissociation energy (U) and dielectric permittivity (ε0) of the host

material as given below[101,102]:

where kB and T refer to the Boltzmann constant and absolute temperature, respectively However, due to the presence of direct link between dielectric permittivity (ε0) and charge carriers, the

increase of dielectric constant could be interpreted as a fractional increase in charge concentrations in the electrolyte This is due to the fact that dielectric constant is related to the ratio of the material capacitance (C) to the capacitance of the empty cell (Co) (ε׳ ¼ C/Co) while the capacitance is also related to the amount of stored charge (C¼ Q/V), where Q is the total charge and V is applied voltage As it

is stated in Eq.(10), conductivity (s) depends on the amount of charge carrier concentration (n) and the mobility of the ionic spe-cies in the system[103] However, from Eq (11), charge carrier concentration (n) can be increased by increasing the dielectric constant Therefore, the conductivity increases with the increase of dielectric constant based on Eqs.(10 and 11) The above equations indicate the fact that the dielectric analysis is an informative approach to study the conductivity behavior of polymer electro-lytes [4] Thus, from the models presented in previous sections regarding the ion transport and the correlation between dc con-ductivity and dielectric constant ε0, it is understood that ion

transport in polymer electrolytes is a complicated subject[104] The incomplete understanding of the cation transport mechanism

in polymer electrolytes is believed to be one of the main obstacles

in fulﬁlling a high conducting polymer electrolyte at room tem-perature[105,106] Ramesh et al.[107]have used dielectric con-stant to study the conductivity behavior of non-plasticized and plasticized PVC-PMMA-LiCF3SO3polymer electrolyte, in which the increase of the dielectric constant of the plasticized system is attributed to the increase of charge carrier density

In Ref [108], the effect of ethylene carbonate (EC) on the dielectric properties of PVA:LiBr:H2SO4 polymer electrolyte was studied It was shown that the increment of storage charge was Fig 8 Temperature dependence of ionic conductivity for PVAc:PVdF:LiClO 4 polymer electrolytes containing various blend ratios [77]

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