Characterization of polymer electrolytes by dielectric response using electrochemical impedance spectroscopy

Chin Han Chan; Hans-Werner Kammer

doi:10.1515/pac-2017-0911

Article Publicly Available

Characterization of polymer electrolytes by dielectric response using electrochemical impedance spectroscopy

Chin Han Chan and Hans-Werner Kammer

Published/Copyright: February 8, 2018

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From the journal Pure and Applied Chemistry Volume 90 Issue 6

Abstract

Authors present a phenomenological view on dielectric relaxation in polymer electrolytes, which is monitored by electrochemical impedance spectroscopy. Molecular interaction of polymer chains with salt molecules (or dipole-dipole interaction between segments and salt molecules) leads to dipolar molecular entities. Frequency-dependant impedance spectra are the key quantities of the interest for determination of electric properties of materials and their interfaces with conducting electrodes. Salt concentration serves as parameter. Bulk and interfacial properties of the samples are discussed in terms of impedance (Z^*) and modulus (M^*) spectra. We focus on two different classes of systems, i.e. high molar mass of poly(ethylene oxide) (PEO)+lithium perchlorate (LiClO₄) (i.e. the inorganic salt) and epoxidized natural rubber (ENR-25) with 25 mol% of epoxide content+LiClO₄. Impedance spectra with salt content as parameter tell us that we have interaction between dipolar entities leading to dispersion of relaxation times. However, as scaling relations show, dispersion of relaxation times does not depend on salt content in the PEO system. The relaxation peak for the imaginary part of electric modulus (M″) provides information on long-range motion of dipoles. Summarizing the results from imaginary part of impedance spectrum (Z″), tan δ (imaginary/real of permittivities) and M″ for the two systems under the discussion, PEO behaves like a mixture of chains with dipoles. There are interactions between the dipoles, but they are relaxing individually. Therefore, we see PEO-salt system as a polymer electrolyte where only a tiny fraction of added salt molecules becomes electrically active in promoting conductance. However, ENR-25-salt system behaves just as a macroscopic dipole and it can not display electrode polarization or electric relaxation because there is no mobility of individual dipoles. Hence, ENR-25-salt does not form a polymer electrolyte in the classic sense.

Keywords: dielectric response; electrochemical impedance spectroscopy; epoxidized natural rubber; POLYCHAR-25; poly(ethylene oxide); polymer electrolytes

Introduction

Solid polymer electrolytes (SPEs) are usually mixtures of organic polymer and inorganic salt [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12] and they are seen as ionic conductors in analogy to aqueous salt solutions. The molecular mechanism of conduction of polymer electrolytes is not well understood or the understanding from a molecular point of view requires further exploration. This is so because the nature of charge carriers is not very well known. Thus, we may have molecular interaction of polymer chains by salt molecules leading to polar molecular entities, which are capable of dipole-dipole interaction between polymer segments and salt molecules [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], in some systems even moving H-bonds along polymer chains [29], [30], [31], [32], [33], [34], [35]. These polar molecular entities are immobilized and gain mobility only by the aid of chain relaxations [31], [32]. It is challenging to delineate this complex situation from a molecular point of view and estimate reliable values of charge carrier mobility. Therefore, we will see it from phenomenological point of view as development of polarization, alignment and relaxation of dipoles and describe it in electrochemical terms [23], [27], [28], [36], [37]. Thus, we have simply dipoles, in most cases interacting with each other, and theses dipoles are more or less oriented and moving under action of the external field. The experimental fact of electrode polarization, frequently seen as a nuisance in use of polymer electrolytes, plays an important role in our understanding of conductivity. It turns out that only a tiny fraction of added salt molecules becomes electrically active in promoting conductance [22].

Since 1980s, the studies of poly(ethylene oxide) (PEO) polymer host with additon of lithium (Li) salt retain extensive research interest as solid polymer electrolytes (SPEs) for highly efficient batteries for solid state devices [27], [38], [39], [40], [41], [42], [43], [44], [45], [46], [47], [48]. The first system in this study is high molar mass PEO with semicrystalline morphology added with Li salt. It is not only in-homogeneous from point of view of morphology but it is also in-homogeneous with respect to electric conductivity. It is generally accepted that conductance occurs only in amorphous regions of semicrystalline PEO [24], [48], [49], [50], [51], [52], [53], [54], [55], [56]. Double layers are formed not only at electrode-electrolyte interface in impedance spectroscopy but also in the inhomogeneous system at borders of amorphous-crystalline regions. We see in-homogeneity causes the fact that (electric) conductivity is primarily ruled by dielectric relaxation (of dipoles) at room temperature; only at high temperature (above the melting temperature of PEO), electric relaxation (flow) becomes important.

Another system under the discussion consists of epoxidized natural rubber with 25 mol% of epoxide content (ENR-25) added with lithium perchlorate (LiCO₄). ENR-25 is an amorphous system [28], [37], [52], [57], [58], [59], [60]. Addition of Li-salt leads here to formation of a macroscopic dipole [22], [27], [28], [37], [57]. The sample acts as capacity exhibiting very low dielectric constant even at high salt content and does not form an interfacial capacitance electrode-electrolyte.

Electrochemical impedance spectroscopy (EIS) was adopted to elucidate the dielectric relaxation in SPEs. Frequency-dependant impedance spectra are the key quantities of the interest for determination of electric properties of the SPEs and their interfaces with conducting electrodes. Two different classes of systems, i.e. high molar mass PEO added with LiClO₄ and ENR-25 with addition of LiClO₄ were the focus of this work. From the phenomenological response of imaginary part of impedance spectrum (Z″), tan δ (imaginary/real of permittivities) and the imaginary part of electric modulus (M″), we observe PEO behaves like a mixture of chains with dipoles. There are interactions between the dipoles, but they are relaxing individually. Therefore, we see PEO-salt system as a polymer electrolyte where only a tiny fraction of added salt molecules becomes electrically active in promoting conductance. However, ENR-25-salt system behaves just as a macroscopic dipole and it can not display electrode polarization or electric relaxation because there is no mobility of individual dipoles. Hence, ENR-25-salt does not form a polymer electrolyte in the classic sense. The presentation of this work emphasizes on how to discuss this difficult matter in simpler manner. This work is a summary of our previous contribution to polymer electrolytes [6], [7], [22], [24], [27], [28], [37], [48], [52], [53], [55], [56], [57], [58], [61], [62], [63], [64], [65], [66] with the emphasis on Refs. [22], [23], [27], [28], [37].

Basics

For SPEs, conductance originates from reorientation of dipolar entities. In impedance spectroscopy, the sample forms usually a parallel plate capacitor with area A and thickness ϑ. The complex capacitance (C^*) is given by

(1)C∗=ε∗Co=εoε∗Aϑ

Complex permittivity (ε^*) is closely related to complex impedance (Z^*), which we see as the key quantity of impedance spectroscopy. In dynamic formulation, it is given in the linear range by

(2)Z∗=1C˙∗

with C˙∗ being derivative of capacitance with respect to time and Co=εoAϑ geometric capacitance of vacuo; ε_o=8.854.10⁻¹² F m⁻¹ or [A·s(V·m)⁻¹] as permittivity of vacuo. For periodic changes in electric field, electrochemical AC data might be presented in the following interrelated formulations and discussed accordingly

Impedance Z∗=Z′+iZ″=1iωCoε∗

Permittivity ε∗=ε′−iε″

(3)Electric modulus M∗=M′+iM″=1ε∗

M′=CoωZ″ M″=CoωZ′

tan δ=ε″ε′=M″M′=Z′Z″

where, X′ and X″ denote real and imaginary parts of quantity X, ω and f represent angular frequency and frequency, respectively (ω=2πf). All of them are closely related to complex conductivity:

σ∗=iωεoε∗ M∗=iωCoZ∗

(4)σ′=ϑAZ′|Z|2 σ″=ϑAZ″|Z|2

σDC∝ε″ω

We recognize that besides impedance Z^*, permittivity ε^* is a central quantity as shown in Eq. (1). It follows according to Eq. (1): C′∝ε″ and C″∝ε″. Hence, ε′ gives the stored energy and ε″ gives the dissipated energy for conductivity. We note here, impedance is the key quantity of impedance spectroscopy. Interpretation of impedance and electric modulus reads:

Z′ represents Ohmic resistance
Z″ can be seen as non-Ohmic resistance (e.g. capacity resistance as the consequence of sample acts as capacitor in EIS). It displays characteristic frequencies especially for dipole (or dielectric) relaxation resulting from local motions of charged entities
M″ (due to its proportionality to Z′) gives “electric” relaxation of flowing charged entities (dipoles) that is it is coined by non-local motion. Resonance occurs when externally imposed frequency agrees with dipole relaxation frequency.
σ′ is coined by flow of charges (dissipation of charges)
σ″ reflects storage of charges

Therefore, permittivity related to dielectric behavior of materials and the interpretation of permittivity reads:

The real part of permittivity ε′ [or dielectric constant when ε′(f→∞); f denotes frequency] indicates the ability of the material (in this case, polymer is referred) to store energy reversibly from the applied electric field.
The imaginary part of permittivity ε″ represents dielectric loss. Polarization (here alignment of dipoles) of a polymer electrolyte varies under an applied oscillating electric field. Some of the energy is dissipated due to dipole migration (or the flow of charged entities), conduction, or conversion into thermal energy (via molecular vibration).

Impedance spectroscopy is a powerful method for determination of electric properties of materials and their interfaces with conducting electrodes. Most of the polymer electrolytes comprise inhomogeneities, especially grain boundaries or electrode-electrolyte interfaces, which have different physical properties as compared to bulk. These regions are well separately observed in impedance and modulus spectra.

Materials

Sample preparation and experimental procedures using electrochemical impedance spectroscopy are published elsewhere [22], [23], [27], [67]. Data were taken from these. Therefore, we exclude experimental details in this publication. Here, we list only the polymers and frequency range and measurement temperature of EIS (Table 1). In the following, we discuss impedance spectra of the systems given in Table 1.

Table 1:

Characteristics of polymer electrolytes.

Polymer	M_w (g mol⁻¹)	Salt content Y_S^a	Frequency range (Hz)	T^b (K)	T_g (°C)	T_m (°C)
PEO	300 K	0.005–0.12	50–1 MHz	298	−60	65
ENR-25	300 K	0.01–0.30	50–1 MHz	298	−42	–

^aY_S, mass salt/mass polymer; salt: LiClO₄.
^bMeasurement temperature of EIS.
M_w denotes mass average molar mass estimated using gel permeation chromatography.
T_g and T_m are glass transition temperature and melting temperature estimated using differential scanning calorimetry.

Results and discussion

Impedance spectrum

We note here, real part of impedance (Z′) reflects Ohmic resistance of the sample whereas imaginary part (Z″) accounts for non-Ohmic resistance. The maximum in Z″ at ω_max, displayed under action of an oscillating electric field, gives the main relaxation, which originates from orientation of dipoles, and is born by interplay of samples’ resistance and capacitance. With increasing salt content added to PEO, the orientation of dipoles becomes more complicated, therefore ω_max increases (c.f. Fig. 1). In simplest case, Z″ displays just a (dielectric) relaxation peak at frequency ω_max characterized by one relaxation time constant, τ=(ω_max)⁻¹, where this relaxation is called Debye relaxation. Under these conditions, it approaches zero for frequencies ω<ω_max and decreases monotonically in the opposite frequency range. However, the situation changes when the systems studied become inhomogeneous with respect to conductivity. Domains with relatively good conductivity are interspersed with poorly conducting areas. Accumulated charges form in interfacial region of the electrode-electrolyte; i.e. a double layer with extremely high resistance at low frequencies. Development of double-layer (or onset of electrode polarization) is visible as minimum of Z″ as a function of f with ω_min<ω_max. It affects relaxation; we observe dispersion of relaxation times that is we do not have any more ideal Debye relaxation. Besides, ω_cross is the crossing of Z′=Z″; and ω_max≈ω_cross is recorded in Fig. 1. It means, systems are close to Debye relaxation.

Fig. 1:

Impedance versus frequency for PEO for the indicated Y_S at room temperature; solid markers – real part, open markers – imaginary part.

We note for the spectra given in Fig. 1:

(5)In low-frequency range: ωmin≤ω≤ωmax and Z′≈const and Z″<Z′

Besides, three frequencies were observed, where

(6)ωmin<ωmax<ωcross

increase in ω_min and ω_max is depicted with added salt content (at T=const).
the maximal relaxation peak for Z″ (Z″max) describes Debye relaxation (i.e. under ideal conditions where no interactions between dipoles, only one relaxation time τ and ω_max=ω_cross). It results from reorientation of dipoles. Interaction between dipoles leads to dispersion of relaxation times which is indicated by ω_max<ω_cross.
Z′=const (abbreviated as Z_o) for ω→0. Z_o slightly depends on f especially at higher salt content. This is caused by greater deviation from Debye relaxation at higher salt content. Lower Z_o for higher electrode polarization is noted.
Z′ increases at ω=const (in the range ω→0) with decreasing Y_S.
both Z′ and Z″ increase in the limit ω→0 (for ω<ω_min) due to electrode polarization (formation of double-layer or onset of electrode polarization). This leads to dispersion of relaxation times.

The characteristic differences of the impedance spectra of ENR-25+salt systems (c.f. Fig. 2) as compared to PEO+salt systems (see Fig. 1) are:-

Fig. 2:

Impedance versus frequency for ENR-25 for Y_S=0.15 and 0.25 at room temperature; solid markers – real part, open markers – imaginary part.

Only one broad (dielectric) relaxation peak for Z″ at ω_max at quite high salt content (Y_S>0.2). The low frequency peak for Z″ at ω_min shifts to very low frequency and is not accessible under the experimental condition.
At Y_S>0.2, ω→0, Z′=const and Z″→0. Hence, no further relaxation in the ENR-25 systems is seen.
Instead of ω_max≈ω_cross (for PEO systems), one recognizes ω_max<ω_cross for ENR-25 systems. This implies there is no ideal (dipolar) Debye relaxation (characterized by one relaxation time), we have always dispersion of relaxation times. Here, we see ω_max as average over the dispersion of relaxation times or the mean value.
Merging of Z′, belonging to different salt content, appears at much higher frequency as for PEO.
No accumulation of dipoles in the interfacial region of the electrode-electrolyte is seen because ω_min is not observed or ω_min is very close to zero frequency. Consequently no electrode polarization.

As a consequence, ENR-25 at Y_S>0.2 behaves like a macroscopic dipole or mobility of microscopic dipoles is restricted to localized motions.

PEO systems are polymers comprising dipoles of sufficient mobility (or drift) under the action of oscillating electric field. Relaxations in this system mean reorganization of dipoles in statistical distribution (not aligned). This reorganization is coined by some cooperative motions of the entities. However, this is not observed in ENR-25 systems because the dipoles are immobilized.

Permittivity spectra

Permittivity ε^* reflects dielectric response of the systems under discussion after Eq. (1). The focus on this section is the power-law dependence of imaginary part of permittivity on frequency in low-frequency range (ω_min≤ω≤ω_max). This is important, since we have σ′∝ωε″. We start the discussion with PEO systems.

Figure 3 shows in the low-frequency region (in the range between the “squares”), we have ε″∝ω⁻ⁿ and ω_crossε=ω_cross^Z. Hence, when exponent n is close to unity (or n=1, i.e. only one relaxation time constant), quantity σ′ approaches σ_DC and becomes nearly independent of frequency (σ′=const for ω→0).

Fig. 3:

Permittivity versus frequency for PEO at room temperature for Y_S=0.01 and 0.1; squares mark ω_min and ω_max of Z″ (in low frequency region); solid markers – ε′, open markers – ε″.

Again, the double-logarithmic plots in Fig. 3 tells us on linear decrease in ε″ in the range ω_min … ω_max, that is the following power law exists

(7)ε″∝ 1ωn with n<1

The regression curves after Eq. (7) for the double-logarithmic plots in Fig. 3 yield:-

n=0.94 for YS=0.01

n=0.92 for YS=0.1

Thus, we observe dispersion of relaxation times (i.e. n<1), but we are still close to Debye relaxation (with n=1). Concomitantly, one observes a slight frequency dependence of σ′ instead of σ′=const for ω→0 (c.f. Fig. 10).

Now, we turn to ENR-25 systems. The regression curves after Eq. (7) for the double-logarithmic plots in Fig. 4 yield n=0.89 for Y_S=0.25. Exponent points towards dispersion of relaxation times.

Fig. 4:

Permittivity versus frequency for ENR-25 at room temperature for Y_S=0.15 and 0.25; square represents ω_max of Z″; solid markers – ε′, open markers – ε″.

Comparison of ε″ for PEO and ENR-25 systems studied in Fig. 5 enhances the discussion before. For frequencies ω<ω_max, we recognize an increase in ε″ after Eq. (7) (for ENR-25 n=0.89). It means, we observe for both systems that dispersion of relaxation times in the range of ω_min…ω_max (where ω_min is very small for ENR-25). Moreover, it turns out ε″_ENR-25≈ε″_PEO in the limit ω→0, hence, it leads to σ_DC,ENR-25≈σ_DC,PEO (~10⁻⁶ S cm⁻¹) for the two systems. Thus, the conductance process in the range ω_min…ω_max preferably depends on salt concentration and less dependence on the polymer. We also find strict dependence of ε″ after Eq. (7) in the low frequency range for ENR-25 whereas PEO displays a more complicated dependence for frequencies ω<ω_min due to electrode polarization, but, nevertheless we have in acceptable approximation ε″_ENR-25≈ε″_PEO.

Fig. 5:

Comparison of ε″ for SPEs. Open markers – PEO+Y_S=0.1; solid markers – ENR-25+Y_S=0.25 and squares indicate ω_min and ω_max.

The tangent loss spectra

The ratio of mobile and stored dipoles, expressed by ratio ε″/ε′ [this ratio is defined as tangent loss (tan δ) in Eq. (3)], should be maximum (ωmaxδ) near characteristic frequency ω_min of Z″ (ωminZ″) due to piling up of charges near interfacial region (ωminZ″≈ωmaxδ) as depicted in Fig. 6 for PEO systems. One observes electrode polarization. Tan δ spectra of PEO systems display nice relaxation peaks at ωmaxδ and ωmaxδ<≈ωminZ″.

$Fig. 6: Tan δ versus frequency for PEO systems at different YS as indicated; the open squares mark ωmaxδ<≈ωminZ″.$\omega _{{\rm{max}}}^\delta \mathop < \limits_ \approx \omega _{{\rm{min}}}^{Z''}.$$

Fig. 6:

Tan δ versus frequency for PEO systems at different Y_S as indicated; the open squares mark ωmaxδ<≈ωminZ″.

For Debye approximation, one would have equality of the two frequencies (ωminZ″=ωmaxδ). Thus, dispersion of the relaxation times causes lowering of frequency ωmaxδ as compared to characteristic frequency ωminZ″. With increasing salt content, tan δ appears at higher level and shifts to higher frequency ωmaxδ. However, the difference of the two frequencies (ωminZ″−ωmaxδ) decreases with ascending salt content. Thus, we have increasing strength of relaxation and also increasing number of relaxing dipoles in PEO systems with ascending salt content (as the area below the peak shows). When one compares ε^* and tan δ, one clearly recognizes dipolar relaxation in the electrode-polarization process (as strong coupling of dipole motion along polymer chains and segmental relaxation of polymer) displayed here by tan δ but no relaxation peak in ε″. Hence, we have to see electrode-polarization relaxation as coined by localized dipolar motion restricted by surrounding polymer chains.

For tan δ spectra of ENR-25 systems, we do not observe ωmaxδ because there is no electrode-polarization relaxation as already illustrated in Fig. 2. We observe monotonic decrease in tan δ that is no dipolar relaxation emanates. This is in consistency to the Z″ spectra of ENR-25 systems which do not show characteristic frequency ωminZ″.

Electric modulus

General versions of modulus and impedance are given in Eq. (3). Electric modulus after Eq. (3) might be given as dynamic quantity, M″∝Z˙′ with Z˙′ being time derivative of Z′. After a few manipulations, we get the symmetric version pointing towards the center of the problem:

(8)M″∝ωZ′

(9)Z″R∝ωε′

We are looking for comparison of them in low-frequency range (ω_min≤ω≤ω_max). The key point is neither Z′ nor ε′ display an extreme value, but ωZ′ and ωε′ do. Eqs. (8) and (9) read in full

M″=CoωZ′

Z″=Co|Z|2ωε′

Hence, we may also write in low-frequency region (i.e. ω_min≤ω≤ω_max)

M″=ωτ with CoR=τ

Z″R=ε′ωτ

Thus, for ideal Debye relaxation, we have

(M″)max=(Z″R)max

since ω_maxτ=1. Hence, we observe collapse of the two functions in one master curve. Non-Ohm resistances determine Z″(ω) whereas M″(ω) is proportional to real part of impedance. Consequently, the first one reflects localized dipolar motion whereas the second one is an expression of non-localized or long-range electric motion.

Equation (8) manifests, imaginary part of modulus points towards electric relaxation or non-local transport of charged entities in the low-frequency range (ω_min≤ω≤ω_max). It indicates long-range motion of dipoles coupled to segmental motions of chains in the low-frequency range. In that sense, it is a complement to imaginary part of impedance, Eq. (9), which reflects dielectric relaxation bound to short-range irregular motion of charges.

PEO systems exhibit dielectric relaxation peaks in spectra Z″(ω) and M″(ω) as Figs. 1 and 8 demonstrate. Quantity M″∝ωZ′ exhibits a maximum at frequency ωmaxM″ reflecting the transition from long-range motion for frequencies ω<ωmaxM″ to local irregular motion in the range of high frequencies because charged entities cannot follow any more externally imposed rapid changes of electric field (c.f. Fig. 8). Frequency ωmaxM″ shifts to lower values for PEO systems at room temperature. This is consistent with variation of Z′ [or of (σ_DC)⁻¹] shown in Fig. 1.

Fig. 7:

Tan δ versus frequency for ENR-25 SPEs at different Y_S as indicated.

$Fig. 8: M″ versus frequency for PEO systems at indicated YS; squares give ωmaxZ″.$\omega _{{\rm{max}}}^{Z''}.$$

Fig. 8:

M″ versus frequency for PEO systems at indicated Y_S; squares give ωmaxZ″.

(10)ωmaxZ″<ωcrossZ′/Z″<ωmaxM″

Inequality of Eq. (10) reflects dispersion of relaxation times. Coincidence of the three characteristic frequencies provides information on the process ruling charge transport in the system. If ωmaxZ″=ωcrossZ′/Z″=ωmaxM″ is obeyed, condensation of the two scaled functions Z′/Z″max and M″/M″max appears as natural consequence. Hence under this condition, we have dominance of electric relaxation or long-range motion of charged entities for frequencies ω<ωmaxZ″ and short-range motions become dominant only for ω>ωmaxM″. Generally, for conduction based on long-range motion, a relaxation peak appears in spectrum M″(ω) (c.f. Fig. 8), but, no peak occurs in the corresponding ε″(ω)-spectrum (see Fig. 4). However, a peak representing the dielectric relaxation process occurs in Z″(ω) (c.f. Fig. 1).

Comparison of scaled spectra allows for distinguishing localized relaxations and long-range electric relaxation (flow) since functions Z″(ω) and M″(ω) give information about relevant motions of charge carriers in the system according to Eqs. (7) and (8). This is explicitly demonstrated in Fig. 9 for PEO system at Y_S=0.1. This system is coined by mismatch of the two scaled functions. Addition of salt to PEO leads to reduced influence of crystallinity of PEO on the expense of long-range motion or dominance of dielectric relaxation. Charge transport is governed by short-range incessant random motions. In other words, it indicates conductivity is dominated by localized motion of dipolar structures in the PEO systems. Long-range motions are of minor influence. Generally, ωmaxM″−ωmaxZ″ announces dispersion of relaxation times and development of localized motion. In short, Debye relaxation is accompanied by long-range motion of dipolar entities.

$Fig. 9: Scaled representation X′/X″max$X'/{X''_{\max }}$ for PEO system at YS=0.1 at 298 K.$

Fig. 9:

Scaled representation X′/X″max for PEO system at Y_S=0.1 at 298 K.

Conductivity spectra

Conductivity σ is related to dynamic permittivity in the linear range

(11)σ∗=εoε˙∗

For periodic changes, Eq. (11) turns into Eq. (4). Real and imaginary parts of conductivity are related to permittivity as in Eq. (12)

(12)σ′∝ωε″ σ″∝ωε′

We note here again, Eq. (7) with exponent n<1, but close to unity. Imaginary part of permittivity is related to dissipation of energy by conduction. After Eqs. (12) and (7), we expect σ′≈const in the low-frequency limit. This is illustrated in Fig. 10 for complex conductivity of PEO system at Y_S=0.1 in the range ω_min…ω_max.

Fig. 10:

Complex conductivity versus frequency for PEO system at Y_S=0.1; squares symbolize ω_min and ω_max.

Real part of conductivity represents dissipation of energy due to dipole or flow of charge carrier (i.e. flow of energy), whereas imaginary part reflects stored energy in the sample out from the electric field. Charge transport contributes only weakly to conductivity. In range of ω_max<ω_cross, conductivity is preferably ruled by dielectric response of the system. Taking into account Eq. (7), it follows in range of ω_max<ω_cross

(13)σ′∝ω1−n

Thus, power-law of Eq. (7) provides information on conductivity. In case n<1, as found for PEO systems, one observes slight increase in conductivity σ′ in the range between characteristic frequencies, ω_min and ω_max, indicating slight deviation from Debye relaxation. Extrapolation to frequencies beyond ω_min yields σ′(ω→0)=σ_DC (the so-called DC conductivity) (c.f. Fig. 10). For frequencies ω<ω_min, electrode polarization appears, conductivity decreases (i.e. σ′ decreases whereas σ″ increases).

Imaginary part σ″ is related to stored energy from the electric field after Eq. (12). Therefore, it loses energy during electrode polarization and conductance process. Comparison with Fig. 3 tells us that ε′≈const at high frequencies. As a consequence, we observe for both PEO and ENR-25 systems as Figs. 10 and 11 reveal

Fig. 11:

Complex conductivity versus frequency for ENR-25 system at Y_S=0.25; square marks ω_max.

(14)σ′∝ωn∗ for high frequencies

We note here, exponent n^* Eq. (14) (for high frequency range) is not equivalent to exponent of n in Eq. (13) (in range of ω_max<ω_cross).

ENR-25 system at Y_S=0.25 displays only one characteristic relaxation peak ω_max (see Fig. 11). The low frequency peak ω_min shifts to very low frequency and was not experimentally accessible. Thus, we observe σ′≈const and σ″→0 for ω→0 since there is no storage of charges in the interfacial region.

Conductivity of ENR-25 systems (with the higher salt content) exhibits approximately the same conductivity σ′ in the low frequency range as PEO systems. But, real part of conductivity of ENR-25 system decreases below ω_max and eventually turns into constancy due to negligible electrode polarization. Thus, we observe conductivity in the low-frequency range at same order of magnitude for PEO and ENR systems, which is independent of polymer and depends only on salt content. The ENR-25 systems at low salt content are insulator. In contrast to PEO systems, it exhibits conductivity only at high salt content.

Conclusion

Summarizing all the results from impedance spectra (e.g. dynamic quantities or reduced representations versus fequency etc) for the systems under discussion, we state different relaxation responses for the PEO and ENR-25 systems. For PEO+salt systems, dipoles are developing (even without electric field) under the action of osicilating electric field, they are able to make different motions or there are different modes of motion. Most of dipoles are partly immobilized, imprisoned in cages formed by molecular potential walls. They can carry out only localized motions because they are unable to be at rest (due to quantum mechanics). This mode is especially existent at high frequencies. At low frequencies a few of them (having the correct position) can carry out non-localized motions, for example hopping along the chain molecules. In short, PEO sytems have dominant dielectric relaxation, localized motion, and to minor extent electric flow (long-range motion) in the low-frequency regime. There are interactions between dipoles, but they are relaxing individually. Hence, we observe, σ^*, ε^* and M^* versus frequency show that both dielectric relaxation and charge transport are contributing to conductivity. Hence, we regard PEO sytems as a polymer electrolyte.

On the other hand, ENR-25 systems at high salt content show only one dielectric relaxation peak, no relaxation related to electrode polarization (which is visible in tan δ) and no relaxation of dipoles after long-range motion (which is visible in M″). Hence, ENR-25 systems comprise of macroscopic dipoles (due to immobile dipolar entities). These macroscopic dipoles are illustrated as relaxation in Z″ spectra. These systems are unable to generate myriads of molecular dipoles. Thus, in strictest sense, this (ENR-25+salt) system is not polymer electrolyte at room temperature.

We show in this work that EIS is a useful and easy method to elucidate the different dielectric responses for polymer electrolytes in simpler manner.

Article note:

A collection of invited papers based on presentations at the 25^th POLYCHAR 2017 World Forum on Advanced Materials Kuala Lumpur, Malaysia, October 9–13, 2017.

Acknowledgement

The authors gratefully acknowledge Assoc. Prof. Dr. Lai Har Sim, and Amirah Hashifudin for the complex impedance data for PEO, which were used in this paper. This work is supported by Geran Inisiatif Penyeliaan [600-IRMI/MyRA 5/3/GIP (061/2017)], Funder Id: 10.13039/501100004625 and LESTARI grant [600-IRMI/MyRA 5/3/LESTARI (072/2017)] by Universiti Teknologi MARA, Malaysia.

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Published Online: 2018-2-8

Published in Print: 2018-6-27

©2018 IUPAC & De Gruyter. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. For more information, please visit: http://creativecommons.org/licenses/by-nc-nd/4.0/

Articles in the same Issue

https://doi.org/10.1515/pac-2017-0911

Keywords for this article

dielectric response; electrochemical impedance spectroscopy; epoxidized natural rubber; POLYCHAR-25; poly(ethylene oxide); polymer electrolytes