ConductivityâRelaxation Relations in Nanocomposite Polymer

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Conductivity – Relaxation Relations in Nanocomposite Polymer Electrolytes Containing Ionic Liquid Mansoureh Shojaatalhosseini, Khalid Elamin, and Jan Swenson J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b03985 • Publication Date (Web): 19 Sep 2017 Downloaded from http://pubs.acs.org on September 24, 2017

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The Journal of Physical Chemistry

Conductivity – Relaxation Relations in Nanocomposite Polymer Electrolytes Containing Ionic Liquid +

+#

Mansoureh Shojaatalhosseini , Khalid Elamin

+*

and Jan Swenson

+ Department of Physics, Chalmers University of Technology, SE-412 96 Göteborg, Sweden # Department of Chemistry and Chemical Engineering, Chalmers University of Technology, SE-412 96 Göteborg, Sweden

*Corresponding author: [email protected]

ABSTRACT In this study we have used nonocomposite polymer electrolytes, consisting of poly(ethylene oxide) (PEO), δ-Al2O3 nanoparticles and lithium bis(trifluoromethanesolfonyl)imide (LiTFSI) salt (with 4 wt% δ-Al2O3 and PEO:Li ratios of 16:1 and 8:1), and added different amounts of the ionic liquid 1-butyl-3-methylimidazolium bis(trifluoromethanesolfonyl)imide (BMITFSI). The aim was to elucidate whether the ionic liquid is able to dissociate the Li-ions from the ether oxygens and thereby decouple the ionic conductivity from the segmental polymer dynamics. The results from DSC and dielectric spectroscopy show that the ionic liquid speeds up both the segmental polymer dynamics and the motion of the Li+ ions. However, a close comparison between the structural (α) relaxation process, given by the segmental polymer dynamics, and the ionic conductivity shows that the motion of the Li+ ions decouples from the segmental polymer dynamics at higher concentrations of the ionic liquid (≥ 20 wt%) and instead becomes more related to the viscosity of the ionic liquid. This decoupling increases with decreasing temperature. In addition to the structural α-relaxation, two more local relaxation processes, denoted β and γ, are observed. The β-relaxation becomes slightly faster at the highest concentration of the ionic liquid (at least for the lower salt concentration), whereas the γrelaxation is unaffected by the ionic liquid, over the whole concentration range 0-40 wt%.

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1. INTRODUCTION Lithium ion batteries have received much attention as rechargeable batteries due to their high energy and power density. Conventional lithium ion batteries are generally using a liquid as electrolyte. These liquid electrolytes have a sufficiently high ionic conductivity (typically around 10-3 S/cm at room temperature), but suffer from poor mechanical stability, which makes it difficult to reach the safety conditions required for Li-ion batteries. A common approach to obtain electrolytes with good mechanical and safety properties is to use polymer based electrolytes, which can be solid at the working temperature of the battery. However, such solid polymer electrolytes have also their drawbacks due to the fact that they are generally exhibiting too low ionic conductivities at room temperature to be suitable for batteries and other electrochemical devices.1-4

The most common polymer electrolytes are based on poly(ethylene oxide) (PEO), and one reason for the relatively low conductivities of PEO based electrolytes is that PEO is semicrystalline, since the ionic conductivity is considerably reduced in the crystalline regions of the polymer electrolyte.5,6 Instead, it has been established that the ionic conductivity of PEO based solid electrolytes is closely coupled to the large-scale segmental polymer motions, i.e. the structural (α) relaxation.7-9 Hence, the conductivity of PEO based electrolytes can be enhanced by reducing the crystallinity, and thereby enhancing the polymer chain dynamics, on average. To achieve this, one common approach is to add inorganic nanoparticles, so called nano-fillers, into the polymer electrolyte, forming nanocomposite polymer electrolytes.10-14 The properties of this new class of solid polymer electrolytes are very much dependent on the size, concentration, chemical nature of the surface groups of the fillers, and the filler-chain interactions. These fillers also tend to affect the ion-pairing and ion-clustering in polymer electrolytes. Furthermore, in addition to reducing the crystallinity, the nano-fillers improve the


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macroscopic mechanical properties and safety issues by making the electrolyte more solid at a given temperature.10,15 However, despite that the nano-fillers make the electrolyte more solidlike on a macroscopic length-scale, recent studies16-18 of PEO based nanocomposite polymer electrolytes have shown that the segmental polymer dynamics of the amorphous parts of the polymer speed up, provided that the interaction between the polymer chains and the nanoparticles is non-attractive, as in the case of the here used δ-Al2O3 particles. This explains why the ionic conductivity is enhanced by two orders of magnitude when non-attractive δAl2O3 particles are introduced to the polymer electrolyte.16,17,19 Thus, the addition of δ-Al2O3 nano-fillers is able to increase both the mechanical stability and the ionic conductivity of the solid polymer electrolyte, but nevertheless the ionic conductivity is still too low for most applications.

One of the more recent and most promising approaches to increase the ionic conductivity of polymer based electrolytes is to add room temperature ionic liquids.20-22 The high ionic conductivity, good thermal and electrochemical stability, non-flammability and negligible vapor pressure of ionic liquids make them to a useful component in advanced electrochemical devices, such as batteries, fuel cells, supercapacitors, solar cells, etc. Thus, the incorporation of ionic liquids into polymer based electrolytes may improve the thermal properties, the electrochemical stability and enhance the ionic conductivity.20,21,23 However, the addition of an ionic liquid is not always increasing the ionic conductivity. If the interaction between the mobile Li+ ions and the anions of the ionic liquid is strong, the conductivity goes down. Hence, it is crucial that the interaction between the Li+ ions and the anions of the ionic liquid does not become too strong. Previous studies have indicated that it is beneficial for the conductivity if the Li-salt and the ionic liquid have the same anion.20,21 This approach seems to decouple the Li+ ions from the anions, and increase the room temperature conductivity to nearly 10-3



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S/cm,20,21 i.e. close to a value desirable for most applications. However, the drawback of adding an ionic liquid to a polymer electrolyte is that the mechanical properties are negatively affected. In this study we are partly overcoming this problem by the addition of the δ-Al2O3 nano-fillers, which, as mentioned above, improves both the mechanical properties as well as the ionic conductivity of ordinary polymer electrolytes. Here we show that this approach is promising by finding that a reasonable conductivity can be reached already at relatively low concentrations of the ionic liquid, where the electrolyte is still macroscopically solid at room temperature. We are also able to show how the conduction mechanism changes with increasing concentration of the ionic liquid.

2. EXPERIMENTAL SECTION The polymer electrolyte samples were prepared by first blending an appropriate amount of fumed δ-Al2O3 nano-particles (of size 20 nm and purchased from Degussa) in acetonitrile. This solution was stirred in an ultrasonic bath for 4-5 hours to obtain a homogenous solution. Thereafter, the polymer (PEO of molecular weight 6 million g/mol, from Polysciences Inc.) was added to the solution in small quantities during magnetic stirring to avoid agglomeration. After the desired amount of the polymer had been added, the solution was stirred for an additional day by the magnetic stirring, before the ionic liquid (BMITFSI, from Aldrich) was added to the solution, in case the sample contained the ionic liquid. Finally, the Li-salt (LiTFSI, from Aldrich) was added to the solution and stirred for a few more hours, before the solution was poured on a PTFE petri dish and vacuum dried at 323 K for 24 hours to fully remove the acetonitrile solvent as well as moisture. The removal of acetonitrile was furthermore verified by thermogravimetric analysis (TGA), performed on TG 209 F1 Iris from Netsch. The drying of the samples resulted in free-standing thin polymer electrolyte films with a thickness of about 100-150 µm. All polymer samples contained 4 g δ-Al2O3 nano-particles per 100 g polymer, and


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two different salt concentrations were prepared with O:Li (ether oxygens per Li+ ion) ratios of 16:1 and 8:1, respectively. For both salt concentrations, samples with 0, 10, 20, 30 and 40 wt% BMITFSI were prepared (these weight fractions of BMITFSI were added to 100 wt% of PEOLiTFSI). For comparison, a sample of pure BMITFSI was also measured.

The surface morphology of the polymer electrolyte films was studied by using a Zeiss Ultra 55 Scanning Electron Microscopy (SEM). For this work the cross-section SEM images were taken with a secondary electron detector using a 1 kV accelerating voltage.

For determinations of glass transition and crystallization temperatures, DSC measurements were carried out on a piece of each sample, encapsulated in a hermatic aluminium pan, using a TA instrument Q1000 DSC. The samples were first cooled to 123 K with a cooling rate of 30 K/min and thereafter heated to 423 K with a heating rate of 10 K/min, under nitrogen atmosphere. This procedure was repeated three times. The Tg value was defined as the midpoint in the step of Cp during the heating in the second cycle.

Dielectric measurements were performed with a Novocontrol GmBH broadband dielectric spectrometer, equipped with a Quatro Cryosystem temperature control unit. The polymer electrolyte films were placed between two gold plated electrodes and dielectric measurements were performed in the frequency and temperature ranges 10–2 – 107 Hz and 135 K – 365 K, respectively. The temperature was increased in steps of 5 K and at each temperature an equilibration time of 10 min was used.



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3. RESULTS AND DISCUSSION 3.1 SEM measurements Figure 1 (a–f) reveals the morphology of PEO-Al2O3, PEO-LiTFSI-16:1, PEO-LiTFSI-16:1 20 wt% IL, PEO-LiTFSI-16:1 40 wt% IL, PEO-LiTFSI-8:1 10 wt% IL and PEO-LiTFSI-8:1 30 wt% IL. The cross-section SEM picture shown in Fig. 1 (a) reveal that the polymer film of PEO-Al2O3 has a rough surface morphology with a large number of crystalline domains. By blending the low concentration of salt (16:1) to PEO-Al2O3, crystalline spherulitic domains are formed as shown in Fig. 1 (b). By adding the ionic liquid (BMITFSI) to PEO-LiTFSI-16:1 the crystalline spherulitic domains decrease, and thereby the smoothness of the surface morphology increases, as shown in Fig. 1 (c and d) for PEO-LiTFSI-16:1 20 wt% IL and PEO-LiTFSI-16:1 40 wt% IL, respectively. The findings are very similar to what previously have been observed for PEO based solid electrolytes containing LiTFSI and BMIMTFSI,24 and indicate that the addition of the ionic liquid increases the amorphous phase and reduces the size of the crystalline spherulitic domains. The reduction of crystalline spherulitic domains is even more pronounced for the higher salt concentration (8:1), where it can be seen in Fig. 1 (e and f) that the surface morphology is very smooth (i.e. no evident morphological features are clearly seen) due to fully amorphous samples.


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(a)

(b)

(c)

(d)

(e

(f

Fig.1 SEM micrographs of PEO-Al2O3 (a), PEO-LiTFSI-16:1 (b), PEOLiTFSI-16:1 20 wt% IL (c) and PEO-LiTFSI-16:1 40 wt% IL (d).

3.2 DSC measurements In Fig. 2(a) the variation of Tg is shown for all the measured samples. The sample without any Li-salt and ionic liquid (PEO with 4 wt% δ-Al2O3) exhibits a Tg at 215 K, which is close to previously reported values for pure PEO17. By adding the Li-salt, an increase of Tg to about 235 K is observed due to the interaction between the ether oxygens of the PEO chains and the Li ions of the salt. This interaction gives rise to a crosslinking between polymer segments, which



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decreases the flexibility of the polymer chains and makes them stiffer. By blending the ionic liquid with the polymer-salt-filler samples, Tg decreases to about 220 K for both salt concentrations at a concentration of 20 wt% ionic liquid, see Table 1. This decrease of Tg can be explained by a plasticizing effect of the ionic liquid. The relatively small molecules of the ionic liquid reduce the packing of the polymer chain segments and facilitate their dynamics, leading to a lower Tg. However, the addition of higher concentrations of the ionic liquid (30 and 40 wt%) does not reduce Tg further. Thus, it appears as a full effect of the ionic liquid for speeding up the segmental motions of the polymer chains is already obtained at 20 wt% of the ionic liquid, at least at temperatures around Tg.

Figure 2(b) shows that all polymer samples, except the samples with the high concentration of Li-salt (8:1) which also contain the ionic liquid, exhibit an endothermic melting peak in the temperature range 310-340 K during heating. For most of the samples also cold crystallization (i.e. crystallization during heating) is observed as an exothermic peak at 260-280 K. From the figure it is also evident that the crystallinity decreases with increasing concentrations of both the Li-salt and the ionic liquid, in consistency with the results obtained from the SEM measurements, discussed above. However, the pure ionic liquid crystallizes also, as evident from the substantial melting peak at 270 K. Thus, crystallization of both the polymer and the ionic liquid can be avoided by making a suitable mix of these two main components of the electrolyte. Since crystallinity is detrimental for the ionic conductivity, a reduced crystallinity should be beneficial for the conductivity.


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Fig. 2. DSC heating scans for the investigated samples, given in panel (a). (a) shows the low temperature range of each scan, where the calorimetric Tg can be observed as a small negative (endothermic) step in the heat low. These Tg values are given in Table 1. In (b) the high temperature range of each scan is shown, where cooled crystallization is observed as a positive (exothermic) peak and melting as a negative (endothermic) peak. The curves are vertically shifted for clarity.

Table 1. Different values obtained from the dielectric and calorimetric investigations of the samples. See the main text for further explanations. Sample PEO-LiTFSI-16:1-0 % IL

Conductivity σ (S cm-1) @ 300 K 9.6x10-6

Averag.Conct. Factor K 4.4x10-10

Fragility D 10

Tg (DSC) K Tg (BDS) @ 100 s K 236 232

-11

11

227

225

-10

12

220

222

-11

8.1x10

9

220

222

3.3x10

-6

2.2x10

-5

PEO-LiTFSI-16:1-30 % IL

4.6x10

-5


1.0x10-4

1.1x10-10

9

221

222

1.1x10

-5

-10

35

232

227

3.3x10

-5

-10

35

230

224

1.3x10

-4

-10

39

221

220

1.6x10

-4

-10

38

225

220


1.3x10

-4

-11

8.9x10

37

220

218

PEO-Alumium Oxide

-

-

-

215

214

15

185

182

PEO-LiTFSI-16:1-10 % IL PEO-LiTFSI-16:1-20 % IL

PEO-LiTFSI-8:1-0 % IL PEO-LiTFSI-8:1-10 % IL PEO-LiTFSI-8:1-20 % IL PEO-LiTFSI-8:1-30 % IL

BMITFSI

4.2x10

-3

3.3x10 1.1x10

2.7x10 1.3x10

2.8x10 1.4x10

-11

4.8x10



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3.3 Dielectric relaxation processes Fig. 3 shows the frequency dependence of the imaginary part of the permittivity (ε″) for PEOLiTFSI (16:1) containing 4 wt% δ-Al2O3 and 10 wt% BMITFSI, at some selected temperatures. As typically for PEO-based electrolytes, three relaxation processes, commonly denoted α, β and γ, can be observed.25-28 The α-relaxation is, as mentioned above, due to segmental polymer dynamics, whereas the β-relaxation is commonly attributed to more local segmental motions of polymer chains in the vicinity of crystalline regions. However, the strength of the β-relaxation increases with increasing salt concentration and it is clearly observed even when the sample is fully amorphous, as in the present case of all the samples of the highest salt concentration containing the ionic liquid. This implies that it must have a more general origin. The dissociated Li+ ions tend to coordinate to the ether oxygens of the polymer and this “anchorage” of Li+ ions gives rise to polymer segments “confined” between two neighbouring Li+ ions coordinating to the polymer chain. The most probable origin of the β-relaxation is therefore that it arises from the local segmental motions of such ‘‘confined’’ polymer segments.29,30


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Fig. 3. Frequency dependence of the imaginary part of the permittivity for PEO-LiTFSI (16:1) containing 4 wt% δ-Al2O3 and 10 wt% BMITFSI, at some selected temperatures. Three relaxation process and a low frequency dispersion, mainly due to d.c. conductivity, can be observed over the measured temperature range, although all processes are generally not shown simultaneously at a given temperature.

The γ-relaxation is the fastest observable relaxation process in Fig. 3, and it has been assigned to a local intra-molecular twisting motion of ethylene (-CH2-CH2-) parts or to local motions of the chain ends of the polymer.28,31 However, also in this case the assignment is further complicated by the fact that the pure ionic liquid exhibits a relaxation process on a similar time scale and activation energy (see below). To obtain more accurate values of the relaxation times and their temperature dependences ε″ was fitted by these three relaxation processes and a low frequency dispersion due to a contribution from ionic conductivity, as shown in Fig. 4. Therefore, ε″ was described by a sum of a conductivity term, a Havriliak–Negami function32



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for the α-process and Cole-Cole functions33 for the β and γ processes:

ε ′′(ω ) =

∆ε β ∆εγ ∆εα σ dc + + + b a εoω (1+ (iωτ α )a ) 1+ (iωτ β ) 1+ (iωτ γ )a

(1)

where ω=2πf is the angular frequency, σdc is the d.c. conductivity and εo is the vacuum permittivity. The relaxation times and the dielectric strengths for the α, β and γ-processes are represented as τα, τβ, τγ and ∆εα, ∆εβ, ∆εγ respectively. The shape parameter a determines the symmetric broadening of the relaxation processes, whereas parameter b controls the asymmetric broadening of the Havriliak–Negami function.

Fig. 4. Frequency dependence of the imaginary part of the permittivity for PEO-LiTFSI (16:1) containing 4 wt% δ-Al2O3 and 10 wt% BMITFSI, at T=235 K. The solid line is the total fit to the experimental data, using Eq. 1. The dashed lines show the four contributions used to describe the experimental data; a conductivity term, a Havriliak– Negami function for the α-relaxation and Cole-Cole functions for the β- and γ-relaxations.


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Temperature dependences of the so obtained relaxation times are shown in Fig. 5. In Fig. 5(a) the temperature dependences of all three relaxation processes are shown for the same sample as shown in Figs. 3 and 4, whereas in Fig. 5(b-d) the relaxation times of the α, β, and γ process, respectively, are compared between the studied samples. The temperature dependence of the αrelaxation time is clearly non-Arrhenius, in contrast to the β and γ processes, and therefore best described by the Vogel-Fulcher-Tammann (VFT) equation.34-37

 DTo  τ α = τ o exp    T − To 

(2)

where, τo is the relaxation time extrapolated to infinite temperature and T0 is the temperature where τα extrapolates to infinity. The parameter D determines the deviation from Arrhenius temperature dependence, and is therefore related to the fragility of the supercooled polymer system (where a small D-value means a fragile system and a large D-value a “strong” system).38 From the curve fitting of the temperature dependence of the α-relaxation this Dparameter has been determined for the investigated samples and presented in Table 1. It can be seen that D increases with increasing salt concentration, but is, within the experimental errors, independent of the concentration of the ionic liquid. The former finding can be explained by the cross-linking of polymer segments caused by bridging Li+ ions, giving a stronger network forming character of the polymer system.

From the temperature dependence of the α-relaxation it is also possible to determine a so-called dielectric (or dynamic) glass transition temperature, as the temperature where the α-relaxation time reaches 100 s. These dielectric Tg-values are shown in the last column of Table 1, and can be compared with the corresponding calorimetric Tg. As can be seen, a good agreement is generally observed (an even better agreement had been obtained if the onset of the calorimetric Tg had been chosen instead of its midpoint). The finding that Tg is not changing at high



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concentrations of the ionic liquid (i.e. in the concentration range 20-40 wt%) implies that τα is not changing at Tg in this concentration range. At higher temperatures a slight speeding up of τα is observed also in this concentration range of the ionic liquid for the lower salt concentration. This implies that for the lower salt concentration the more large-scale segmental polymer dynamics is somewhat more affected by the ionic liquid at high temperatures than at low temperatures close to Tg.

Fig. 5(c) shows that the β-relaxation slows down considerably when the lithium salt is introduced. If the assignment of the β-relaxation made above is correct this is not a surprising result. In fact, the main origin of the relaxation process is not even likely to be the same since polymer segments can obviously not be “confined” between two neighbouring Li+ ions coordinating to the polymer chain without any Li+ ions in the polymer system. The figure shows also that the ionic liquid has a minor effect on the dynamics of these “confined” polymer segments. Only for the lowest salt concentration and the highest concentration of the ionic liquid the β-relaxation is somewhat faster at higher temperatures.

In contrast, the γ-relaxation is not affected by the salt or the ionic liquid, as shown in Fig. 5(d). This observation supports the interpretation that it is due to very local motions of PEO segments. Interestingly, the pure ionic liquid exhibits a β-relaxation which is basically identical to this γ-relaxation of the polymer. This coincidence makes it even less likely that the time scale of the observed relaxation process should change with the concentration of the ionic liquid.


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Fig. 5. Dielectric relaxation times as obtained from the curve fitting procedure described above and shown in Fig. 5. (a) shows the temperature dependences of the α-, β- and γrelaxation times of PEO-LiTFSI (16:1) containing 4 wt% δ-Al2O3 and 10 wt% BMITFSI. In (b-d) the relaxation times of α, β and γ, respectively, are compared for all the samples. In (b) the temperature dependences of τα have been fitted by the VFT equation (Eq. 2). The inset in (b) shows the temperature dependences of τα for BMITFSI. In (b) the data points for the samples of the highest salt concentration and the ionic liquid concentrations 20, 30, and 40 wt% are basically overlapping, in (c) the data points of all samples, except PEO-Al2O3 and PEO-LITFSI (16:1) with 40 wt% BMITFSI, are overlapping and in (d) all samples, except pure BMITFSI, have overlapping data points.



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3.4 Ionic conductivity Figure 6 shows the real part of the frequency dependent conductivity at different temperatures for the sample with the salt concentration 16:1 and 40 wt% ionic liquid. Three characteristic frequency ranges can be observed. At the lowest frequencies (and most clearly observed at high temperatures) the conductivity decreases with decreasing frequency due to polarization effects, and at the highest frequencies and lowest temperatures the conductivity increases with increasing frequency due to an a.c. conductivity contribution added to the frequency independent d.c. conductivity, σdc, present between these two frequency ranges. At intermediate frequencies and temperatures the contributions from polarization effects and a.c. conductivity are minor and therefore the frequency dependence is weak in this range and the ionic conductivity is basically equal to the true d.c. conductivity. This plateau region shifts to higher frequencies with increasing temperature due to that the onset frequency of both polarization effects and a.c. conductivity increases with increasing temperature. In Fig. 6 the value of σdc has been taken as the inflection point of each conductivity spectrum.


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Fig. 6. Frequency dependence of the real part of the ionic conductivity of PEO-LiTFSI (16:1) containing 4 wt% δ-Al2O3 and 40 wt% BMITFSI at some selected temperatures. The crosses mark the frequencies where the real part of the conductivity, σ'(fc) = 2σdc.

From these estimations of the d.c. conductivity at different temperatures we have plotted in Fig. 7 the temperature dependence of σdc for the measured samples. In Table 1 we also give σdc at room temperature (300 K) for the different samples. Fig. 7 shows that the ionic conductivity increases both with increasing salt concentration and increasing concentration of the ionic liquid. However, at room temperature the conductivity increases only up to 20 wt% ionic liquid in the case of the higher salt concentration. This saturation of σdc above 20 wt% ionic liquid suggests that the Li-salt interferes detrimentally with the conduction process in the pure ionic liquid, since σdc of the pure ionic liquid is substantially higher, as seen in Fig. 7. From the nonArrhenius temperature dependences shown in Fig. 7 it is also clear that the conduction process is of a similar cooperative character as the structural α-relaxation. In fact, it is highly interesting to determine whether the ionic conductivity remains coupled to the segmental polymer dynamics also after the ionic liquid has been added or if the ionic liquid changes the 17 Environment ACS Paragon Plus


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conduction mechanism. We have used two approaches to elucidate this. Firstly, we have estimated how the concentration of mobile ions changes with the concentration of the ionic liquid and, secondly, we have investigated whether the motion of the mobile Li+ ions becomes decoupled from the segmental polymer dynamics, i.e. the structural α-relaxation, after the ionic liquid has been added.

Fig. 7. Temperature dependence of the ionic d.c. conductivity for the measured samples.

Let us start with the estimation of the concentration of mobile ions. At the higher frequencies, i.e. in the a.c. conductivity regime, the real part of the conductivity, σ'(f), can be expressed in terms of σdc and a characteristic frequency, fc, using the Almond-West relation,39 σ'(f) = σdc[1+(f/fc)n]

(3)


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where f is the frequency and n is the power-law exponent, with 0≤n≤1. The characteristic frequency, fc, marks the onset of a.c. conductivity, and it can be defined as the frequency where the real part of the conductivity σ'(fc) = 2σdc. Previous studies have shown that the onset frequency fc to a good approximation represents the hopping frequency, fH, associated with the Nernst-Einstein relation, i.e. fc~fH.40-42 Thus, we are able to determine the ion hopping frequency fH by fitting the Almond-West relation to the real part of the complex conductivity σ'(f), as shown in Fig. 6. It is not possible to determine fH at room temperature for all samples since it increases dramatically with increasing concentration of the ionic liquid, as also shown in Fig. 6, and therefore its value becomes higher than the measured frequency range in the samples with a high concentration of the ionic liquid. Nevertheless, this rapid increase of fH with increasing concentration of the ionic liquid is interesting to note.

By estimating fH it is also possible to determine the concentration of mobile Li+ ions by using the Nernst-Einstein relation,

σ dc = enc µ =

nc e 2γλ 2 H RωH k BT

(4)

where nc is the concentration of mobile charge carriers, µ is their mobility, e is the electronic charge, γ is a geometrical factor for ion hopping, λ is the hopping distance, kB is the Boltzmann constant, and HR is the Haven’s ratio. Unfortunately, it is not possible to determine all quantities given in Eq. 4, but the equation can be simplified to:

σ dc = KT −1ωH

(5)

where K is the mobile concentration factor that depends upon the concentration of mobile ions and ωH=2πfH.43



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Using this simplified equation, it is possible to determine the mobile concentration factor, K, for all our ion conducting samples, at least at lower temperatures where fH can be determined. The results show that the concentration factor is temperature independent, within experimental errors, and therefore we present values in Table 1, which have been averaged over 5 temperatures. Perhaps somewhat surprising the calculated values of K show that it tends to decrease with increasing concentration of the ionic liquids. Since it seems unlikely that the concentration of mobile Li+ ions should decrease with increasing concentration of the ionic liquid, this finding is most likely a result of that the hopping distance λ (as given in Eq. 4) decreases with increasing concentration of the ionic liquid. However, this decrease in hopping distance is more than fully compensated by an increase of the hopping frequency fH, resulting in increased, or at least preserved, σdc with increasing concentration of the ionic liquid. The changes of K and fH seem to be gradual and continuous over the whole concentration range of the ionic liquid, and therefore suggest that also the ion conduction mechanism changes gradually over the studied concentration range.

To determine whether the motion of the mobile Li+ ions becomes decoupled from the segmental polymer dynamics, i.e. the structural α-relaxation, in the presence of the ionic liquid we have plotted the temperature dependences of both τα and 1/σdc for the samples of the lower salt concentration in Fig. 8 If the motion of the mobile Li+ ions would be coupled to the segmental polymer dynamics for all these samples it would be possible to get the data points of

τα and 1/σdc to overlap for each sample, provided that they overlap for the sample without any ionic liquid. In Fig. 8 the scales of τα and 1/σdc have been chosen so there is an almost perfect overlap of their temperature dependences for the sample containing no ionic liquid. This supports previous findings that the ionic conductivity of a polymer electrolyte, without any added ionic liquid or other type of solvent, is directly coupled to the structural α-relaxation.7-


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9,16,17

Since the data points of τα and 1/σdc almost coincide also for the sample with 10 wt%

ionic liquid, it is clear that this coupling is basically maintained also for this sample. However, for the samples with ≥ 20 wt% ionic liquid it is evident in Fig. 8 that the data points of τα and 1/σdc do not coincide, showing that the ionic conductivity decouples from the structural αrelaxation. This implies that the conductivity increases more rapidly than the α-relaxation speeds up with increasing concentration of the ionic liquid. Fig. 8 shows that the decoupling increases both with increasing concentration of the ionic liquid and with decreasing temperature. Thus, also this second approach to elucidate whether the conduction mechanism changes with the concentration of the ionic liquid shows that there is a rather continuous change of the mechanism over the whole concentration range, at least above 10 wt% of the ionic liquid.

Fig. 8. Temperature dependences of both the structural α-relaxation time (solid symbols) and the ionic d.c. conductivity (corresponding open symbols) for the samples of the lower



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salt concentration, 16:1, as shown in the figure. See the main text for the implication of the figure.

4. CONCLUSIONS In this study the ionic liquid BMITFSI has been added to a nonocomposite polymer electrolyte of PEO, δ-Al2O3 nanoparticles and the lithium salt LiTFSI. By this approach it is possible to reach a room temperature conductivity above 10-4 S/cm, while good mechanical properties of the nanocomposite are maintained. Thus, the solid electrolyte system appears to be reasonably promising for battery applications, although the main focus of this study was to understand how the ion conduction mechanism is altered by the ionic liquid. By comparing the concentration and temperature dependences of the ionic conductivity and the structural α-relaxation for the lower salt concentration we are able to conclude that the two dynamical properties are coupled in the whole temperature range down to Tg for concentrations up to 10 wt% ionic liquid. However, already at 20 wt% of the ionic liquid the ionic conductivity decouples from the αrelaxation time, and this decoupling increases with decreasing temperature and increasing concentration of the ionic liquid. This implies that even if the α-relaxation speeds up (particularly at higher temperatures) when the concentration of the ionic liquid increases above 10 wt%, the ionic conductivity increases even more. Hence, the motions of the Li+ ions are no longer directly related to the segmental polymer dynamics, but depend also on the amount and viscosity of the ionic liquid. Also the mobile ion concentration factor and the hopping frequency change gradually with increasing concentration of the ionic liquid, which further supports that there is a continuous change of the ion conduction mechanism with increasing concentration of the ionic liquid. This information is valuable for understanding how future solid electrolytes should be designed in order to reach a simultaneous optimization of the ionic conductivity and the mechanical stability.


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ACKNOWLEDGEMENTS The authors wish to acknowledge Anders Kvist for his help with the SEM measurements and the Swedish Energy Agency and the Swedish Research Council for financial support.

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ConductivityâRelaxation Relations in Nanocomposite Polymer

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