Ionic Conductivity of Hybrid Composite Solid Polymer Electrolytes of PEO_nLiClO₄-Cubic Li₇La₃Zr₂O₁₂ Films

Abstract

Ionic conductivity of the polyethylene oxide-LiClO₄ (PEO_nLiClO₄) solid polymer electrolyte (SPE) films with an EO:Li ratio (n) of 10, 12, 15, as well as the hybrid composite solid polymer electrolyte (CSPE) films of PEO_nLiClO₄ containing 50 wt% of cubic-Li₇La₃Zr₂O₁₂ (LLZO) sub-micron sized particles, have been studied by varying Li-salt content in the films. The complex AC dielectric permittivity and conductivity data obtained from electrical impedance measurements were fitted using a generalized power-law, including the effects of electrode polarization applied at low AC frequencies to obtain various relaxation times. In addition to increased mechanical and thermal robustness, the CSPE films show higher values of ionic conductivity, >10⁻⁴ S/cm at room temperature compared to those of SPE films with n = 12 and 15. On the contrary, the ionic conductivity of CSPE with n = 10 decreases by a factor of three compared to the corresponding SPE film due to increased polymer structural reorientation and Li-ion pairing effects. The Vogel–Tammann–Fulcher behavior of the temperature-dependent conductivity data indicates a close correlation between the ionic conductivity and polymer segmental relaxation. The PEO₁₂LiClO₄-LLZO film shows the lowest activation energy of ~0.05 eV.

1. Introduction

Li-ion conducting polymer electrolyte films have attracted much interest over the years because of their applications in all-solid-state Li-ion batteries and other energy storage/generating devices [1,2]. A solid polymer electrolyte (SPE), consisting of dissolved Li-salts in polymers, and a composite solid polymer electrolyte (CSPE) mixed with either inorganic oxide fillers or solid inorganic electrolytes are considered promising replacements for organic liquid-based electrolytes [3,4,5,6]. Research has shown that the ionic conductivity of SPE films is promoted by coupled motion of Li-ions and polymer segments in amorphous polymer regions [7,8], hence plasticizers are added to increase the fraction of amorphous regions, but adversely affect the mechanical and thermal stability of SPE films [4,5,6,9]. There have been several studies which have shown that the addition of inorganic fillers such as TiO₂, SiO₂, Al₂O₃, ZrO₂, BaTiO₃ to a plasticized host polymer electrolyte enhances the ionic conductivity while maintaining good physical properties [4,10,11,12,13]. CSPE films with high ionic conductivity (>10⁻⁴ S cm⁻¹), negligible electronic conductivity, good mechanical stability, and good electrochemical properties are desired for applications [4,5,6].

Recently, hybrid CSPE films of polyethylene oxide (PEO) complexed with LiClO₄ and filled with sub-micron to micron-sized garnet Li₇La₃Zr₂O1₂ (LLZO) particles have been intensely studied [14,15,16,17]. LLZO is an inorganic garnet-type material that occurs in both tetragonal and cubic crystalline phases, but cubic LLZO is stabilized by doping with Al [18,19,20]. The tetragonal phase of LLZO is stable, but shows a room temperature conductivity (2 × 10⁻⁶ S cm⁻¹) that is two orders of magnitude lower than that of the cubic LLZO [18]. Cubic LLZO shows good ionic conductivity (>2 × 10⁻⁴ S cm⁻¹ at 25 °C), chemical stability, and a wide electrochemical voltage window [21,22]. Zheng et al. have employed Li NMR to probe the Li-ion diffusion pathway within cubic LLZO-PEO-LiClO₄ composite electrolytes in a symmetric Li-battery cell to show that Li-ions mainly pass through LLZO ceramic particles [14]. Furthermore, a flexible PEO-Li salt-based membrane consisting of a 3D ion-conducting network of LLZO nanofibers has been shown to effectively block a dendrite formation in a symmetric Li-electrolyte-Li cell [23].

A recent study with tetragonal LLZO as a filler in PEO₁₅LiClO₄ (PEO Mw = 6 × 10⁶) showed that the addition of sub-micron sized LLZO particles increases the conductivity, reaching a maximum value of 10⁻⁵ S cm⁻¹ at 35 °C for PEO films with 52.5 wt% LLZO [15]. On the other hand, a study with cubic-LLZO micron-sized particles as a filler in PEO₂₀LiClO₄ (PEO Mw = 10⁵) showed a decrease in conductivity of the composite films with the addition of 30–50 vol% of LLZO [16]. We investigated the AC conductivity of PEO₁₅LiClO₄ (PEO Mw = 10⁶) films containing 50 wt% of cubic-LLZO particles [17]. We observed an enhancement in conductivity (1.4 × 10⁻⁴ S cm⁻¹ at 30 °C) by two orders of magnitude, compared to that of PEO₁₅LiClO₄ films. Recently, Chen et al. have reported Li-ion conductivity >10⁻⁴ S cm⁻¹ at 30 °C for the composite solid electrolyte of PEO₈ LiTFSI (PEO Mw = 6 × 10⁵) containing 10 wt% of garnet Li_6.4La₃Zr_1.4Ta_0.6O₁₂ (LLZTO) micron-sized particles [24]. Further increase in wt% of LLZTO in the composite electrolytes resulted in a decrease in Li-ion conductivity. However, their measurements on “Polymer in Ceramics” films with 80 wt% LLZTO showed that the ionic conductivity depends on the amount of LiTFSI added to the composite.

In the present work, we have investigated the effect of the Li-salt content (EO:Li ratio n = 10, 12, 15) on the AC conductivity of PEO_nLiClO₄—50 wt% cubic LLZO hybrid CSPE films as well as SPE films of PEO_nLiClO₄. We have used a comprehensive and complex dielectric function that includes ionic, segmental, and dipolar relaxation times to explain the observed dielectric permittivity and AC conductivity data rather than using simple empirical equivalent circuits which do not explain the electrode polarization at low applied AC frequencies. In addition to enhanced mechanical and thermal robustness, the CSPE films show higher values of ionic conductivity >10⁻⁴ S cm⁻¹ (30 °C) compared to those of SPE films at lower Li-ion concentration (n = 12 and 15). The analyses of temperature-dependent conductivity showed Vogel–Tammann–Fulcher (VTF) behavior, indicating a close correlation between ionic conductivity and segmental relaxation with a lower activation energy in CSPE compared to SPE. However, the ionic conductivity of CSPE decreases at a higher Li-ion concentration (n = 10), roughly by a factor of three compared to SPE. We associate this observation with structural reorientation of the PEO matrix and Li-ion aggregation effects in the presence of LLZO particles.

2. Materials and Methods

About 100 μm thickness (t) films of PEO_nLiClO₄ and PEO_nLiClO₄-LLZO with n = 10, 12 and 15 were prepared as described in detail elsewhere [17]. All films were desiccated for a day before making structural and electrochemical measurements. Infrared and Raman spectra of the films showed no solvent characteristic bands implying the absence of residual solvent in the films. Structural characterization (X-ray diffraction and scanning electron microscopy), thermal stability, and electrical impedance of the films in the 1 Hz to 300 kHz range were carried out as described in [17].

The complex permittivity,${\mathit{\epsilon }}^{*}={\mathit{\epsilon }}^{\mathbf{\prime }}-\mathit{i}{\mathit{\epsilon }}^{\mathbf{″}}$, and AC conductivity, ${\mathit{\sigma }}^{\mathbf{*}}={\mathit{\sigma }}^{\mathbf{\prime }}+\mathit{i}{\mathit{\sigma }}^{\mathbf{″}}$, were calculated using the measured real and imaginary parts of the impedance $({\mathit{Z}}^{\mathbf{*}}={\mathit{Z}}^{\mathbf{\prime }}+\mathit{i}{\mathit{Z}}^{\mathbf{″}}$) from the following relations,

$${\mathit{\epsilon }}^{\mathbf{\prime }}=\frac{\mathit{t}}{\mathit{\omega }\mathit{A}{\mathit{\epsilon }}_{\mathit{o}}} \frac{{\mathit{Z}}^{\mathbf{″}}}{{{\mathit{Z}}^{\mathbf{\prime }}}^{\mathbf{2}}+{{\mathit{Z}}^{\mathbf{″}}}^{\mathbf{2}}}$$

(1)

$${\mathit{\epsilon }}^{\mathbf{″}}=\frac{\mathit{t}}{\mathit{\omega }\mathit{A}{\mathit{\epsilon }}_{\mathit{o}}} \frac{{\mathit{Z}}^{\mathbf{\prime }}}{{{\mathit{Z}}^{\mathbf{\prime }}}^{\mathbf{2}}+{{\mathit{Z}}^{\mathbf{″}}}^{\mathbf{2}}}$$

(2)

$${\mathit{\sigma }}^{\mathbf{*}}=\mathit{i}{\mathit{\epsilon }}_{\mathit{o}}\mathit{\omega }{\mathit{\epsilon }}^{\mathbf{*}}=\mathit{i}{\mathit{\epsilon }}_{\mathit{o}}\mathit{\omega }\left({\mathit{\epsilon }}^{\mathbf{\prime }}-\mathit{i}{\mathit{\epsilon }}^{\mathbf{″}}\right)$$

(3)

where A is the area of the blocking electrode. Calculated real and imaginary parts of conductivity were fitted to the following generalized expression for the AC conductivity in ion-conducting materials [25,26].

$${\mathit{\sigma }}^{\mathbf{*}}\left(\mathit{\omega }\right)={\mathit{\sigma }}_{\mathbf{d}\mathbf{c}}-\frac{{\mathit{\sigma }}_{\mathbf{d}\mathbf{c}}-{\mathit{\sigma }}_{\mathit{o}}}{\mathbf{1}+{\left(\mathit{i}\mathit{\omega }/{\mathit{\omega }}_{\mathit{j}}\right)}^{\mathit{\alpha }}}+\mathit{i}\mathit{\omega }{\mathit{\epsilon }}_{\mathit{o}}\frac{\Delta \mathit{\epsilon }}{{\left(\mathbf{1}+{\left(\mathit{i}\mathit{\omega }/{\mathit{\omega }}_{\mathit{R}}\right)}^{\mathit{\beta }}\right)}^{\mathit{\gamma }}}$$

(4)

The above equation accounts for the electrode polarization and the relaxation processes that occur in ion-conducting polymeric materials. In Equation (4), σ_dc is the frequency-independent DC conductivity, σ_o is a pre-factor used in describing the AC conductivity in the region not affected by electrode polarization, ω_j is the frequency corresponding to the full development of electrode polarization which is also the peak frequency, f_peak,_σ″ in the σ″ vs. f plot, ω_R is the characteristic frequency of the dipole relaxation, Δε = ε_s − ε_∞ is the difference between static and high frequency limit of dielectric constant, ω is the angular frequency of the applied AC electric field, and α, β and γ are <1.

3. Results and Discussion

The XRD patterns of PEO_nLiClO₄, and PEO_nLiClO₄-LLZO films are shown in Figure 1. Two strong characteristic peaks of crystalline PEO riding on a broad background are seen in the XRD patterns, confirming the semi-crystalline nature of the polymer. Figure 1a shows the region containing the (120) and (112) peaks of PEO occurring at 2θ = 19.2° and 23.5°. PEO has a monoclinic crystalline structure with cell parameters: a = 0.796 nm, b = 1.311 nm, c = 1.930 nm, and β = 124.8° [27]. The diffraction peak profile from 2θ = 23–24° is actually a composite of (112), (032), $(\overline{1}32) ,$ $\left(\overline{2}12\right)$and $\left(\overline{2}02\right)$peaks. We can assign a small peak seen at 2θ ≈ 22.2° to the (121) peak of PEO. As the Li-ion concentration in the composite film increases, the fraction of the amorphous phase of the polymer increases leading to an increase in intensity of the broad background in the entire diffractogram from 2θ = 10° to 80° (not shown here), while PEO crystalline peaks show a relative decrease in intensity. Polymer electrolytes acquire local relaxation and segmental motion of solvent polymer chains to facilitate Li-ion motion through the amorphous phase, thus increasing the ionic conductivity. The broadening of the background peak is clearly seen in Figure 1a for SPE films without LLZO particles. The XRD patterns of CSPE films with LLZO particles are dominated by the diffraction peaks arising from crystalline cubic-LLZO. Figure 1b shows the XRD patterns of PEO_nLiClO₄-LLZO with a different Li-ion concentration. The cubic-LLZO peaks are indicated by the asterisks. It should be noted that the most intense peak of LLZO overlaps with the (120) peak of PEO, while the peak at 2θ ≈ 23.2° coincides with (112) peak of PEO. Significant changes are seen in the XRD pattern of PEO₁₀LiClO₄-LLZO (top panel of Figure 1b) where the peak at 2θ ≈ 21.8° has become somewhat intense, indicating structural reorientation of the PEO-Li matrix in the presence of LLZO particles. It is known that internal rotational degrees of freedom about C-O and C-C single bonds along the polymer backbone can adopt different periodic helical structures depending on the environment [27,28].

All the films investigated in this work were free-standing and mechanically robust, especially CSPE films with LLZO. As shown in our earlier work, the CSPE films retain their mechanical integrity at high temperatures up to 120 °C [17]. Figure 2 shows the SEM images of PEO_nLiClO₄ and PEO_nLiClO₄-LLZO films with different Li-salt content. Films with low Li-salt content (n = 15) show large, nearly spherical-shaped PEO spherulites containing crystalline PEO with a rough surface morphology. As the Li-salt content of the films increases, there is a significant change in film morphology due to the disappearance of large spherulites, indicating increased amorphous regions as confirmed by XRD results. The investigation of crystallization in a high salt PEO-salt polymer electrolyte using optical microscopy and differential scanning calorimetry has shown non-volume filling spherulites with increased amorphous regions, leading to a broad melting transition [29]. Figure 2b shows the SEM images of corresponding PEO_nLiClO₄-LLZO films. A drastic reduction in the granular size is seen in PEO₁₅LiClO₄-LLZO film compared to PEO₁₅LiClO₄. LLZO particles may act as nucleating sites for the growth of a large number of smaller PEO spherulites as seen in an earlier study with a different filler [30]. In general, the addition of LLZO particles makes PEO_nLiClO₄-LLZO film morphology smoother compared to PEO_nLiClO₄.

Figure 3 and Figure 4 show the dielectric permittivity and loss tangent (tan δ = ε″/ε′) of PEO_nLiClO₄ and PEO_nLiClO₄-LLZO films at 30 °C as a function of frequency. ε′ and ε″ show the typical frequency dependence of ion-conducting materials. The observed values of ε′ and ε″ at low frequencies are four to six orders of magnitude higher than their limiting (high frequency) values due to electrode polarization [25]. At low frequencies of the applied AC field, ions traverse long distances and accumulate on the blocking electrodes, forming an electrical double layer capacitance leading to large dielectric permittivity. As the frequency is lowered from the high-frequency region, ε′ begins to rise steeply due to the onset of electrode polarization, reaching a full development at about 100 Hz to 1 kHz for the samples. The peak in the loss tangent spectrum (Figure 4) is associated with polymer chain segmental relaxation time, τ_s, and it is calculated using the relation τ_s = 1/2π f_p, where f_p is the frequency corresponding to the peak in the loss tangent spectrum [17]. The frequency, f_j, at which the full electrode polarization occurs, is related to the ionic relaxation time and corresponds to the peak in the σ″ spectrum (Figure 5). The ionic relaxation time, τ_j, is related to f_j via τ_j = 1/2π f_j [17]. The experimental ε′ and ε″, and tan δ data shown in Figure 3 and Figure 4 are fitted using Equations (1) and (2) and the fitted data are shown as solid lines. The real and imaginary parts of conductivity data, σ′ and σ″, shown in Figure 5 are fitted using Equation (4).

Table 1. The ionic (τ_j) and segmental (τ_s) relaxation times, and other parameters obtained from fitting the complex dielectric permittivity and conductivity of PEO_nLiClO₄ and PEO_nLiClO₄-LLZO at 30 °C.

Sample	Δε	σdc (S cm−1)	τj (ms)	τs (μs)	τR (μs)	α	β	γ	τs/τj
PEO15LiClO4	15	5.8 × 10−7	1.22	38.8	0.35	0.68	0.65	1.0	0.032
PEO12LiClO4	18	6.0 × 10−5	0.15	1.38	0.32	0.82	0.60	1.0	0.009
PEO10LiClO4	20	9.5 × 10−5	0.11	1.33	0.29	0.84	0.53	1.0	0.012
PEO15LiClO4-LLZO	15	1.4 × 10−4	0.06	0.28	0.24	0.80	0.65	1.0	0.005
PEO12LiClO4-LLZO	20	2.2 × 10−4	0.05	0.12	0.04	0.88	0.70	0.65	0.002
PEO10LiClO4-LLZO	24	3.0 × 10−5	0.45	3.30	0.40	0.85	0.60	0.65	0.007

summarizes the best fit parameters Δε, σ_dc, τ_j, τ_s, τ_R α, β and γ for the PEO_nLiClO₄ and PEO_nLiClO₄-LLZO films, where τ_R = 1/ω_R is the EO-dipole relaxation time.

The ionic conductivity of PEO_nLiClO₄ film strongly depends on its Li-salt content (see Table 1). Although the number of Li-ions increases with salt content, their mobility is affected by the progressive occurrence of ion-pairing effects [31]. It is interesting to note that the ionic conductivity increases by two orders of magnitude when salt content is increased from n = 15 to n = 12, but does not change significantly upon further increase from n = 12 to n = 10. FTIR studies of PEO with LiClO₄ salt (90:10) have demonstrated the formation of ion pairs, as indicated by the presence of a shoulder peak (~635 cm⁻¹) of the main band of 623 cm⁻¹ corresponding to the free ClO₄⁻ anion [32,33]. Li-ion pairing thus limits the maximum obtainable ionic conductivity in PEO_nLiClO₄ by increasing salt content alone. As observed in numerous other CSPE containing inorganic fillers, inclusion of 50 wt% LLZO particles in PEO_nLiClO₄ not only enhances film mechanical robustness and thermal stability, but also increases ionic conductivity by more than two orders of magnitude in CSPE with n = 15, and a factor of four with n = 12. We associate this increase to smoother film morphology (see Figure 2) in CSPE due to the formation of a large number of smaller-sized PEO spherulites, thus increasing the ratio of amorphous to crystalline PEO [30,34]. On the other hand, the ionic conductivity CSPE with n = 10 decreases by a factor of three compared to corresponding SPE film due to increased polymer structural reorientation (see top panel of Figure 1b). It is also interesting to note that PEO₁₀LiClO₄-LLZO seems to contain slightly larger spherulites compared to PEO₁₂LiClO₄-LLZO (see Figure 2b). This could be due to increased ion-pairing effects which are known to occur at high salt concentrations [31,32].

The presence of a single peak in the spectrum of tan δ (Figure 4a, b) confirms the Li-ion-dipolar coupled cooperative segmental motion of PEO macromolecules in these electrolytes [35]. In Figure 4a, the peak shifts to a higher frequency in both PEO₁₀LiClO₄ and PEO₁₂LiClO₄ films compared to PEO₁₅LiClO₄. As the Li-salt increases in PEO_nLiClO₄, τ_s and τ_j values are reduced significantly, reaching limiting values around n = 10. As explained earlier, further increase in salt content (n = 10) resulted in the slowing of both ion and polymer segmental motions due to ion-pairing effects. However, CSPE films of PEO_nLiClO₄-LLZO with n = 15 and 12 show even further reduction in τ_s by a factor two, and τ_j by a factor of four. The ionic and segmental relaxation times listed in Table 1 clearly show an intimate coupling between ionic conductivity and segmental motion. The ratio τ_s/τ_j, called the decoupling ratio, of less than one is indicative of a strong coupling [36,37,38]. The decoupling ratios for all the composite films studied in this work are in the range of 0.002 to 0.032 (Table 1) implying a strong coupling between ionic conductivity and segmental motion, i.e., the ionic motion is facilitated by the polymer segmental motion. The observed value of ionic conductivity of 2.2 × 10⁻⁴ S cm⁻¹ in PEO₁₂LiClO₄-LLZO is the highest among all the composite films studied in this work. This is higher than the conductivity reported for PEO₁₅LiClO₄-tetragonal-LLZO [15] and PEO₁₅LiClO₄-cubic-LLZO [16].

To investigate the nature of the ion-conduction process in these composite films, we have studied the temperature dependence of ionic conductivity. The shifting of peak frequency to higher values of tan δ with increasing temperature is an indication of a thermally activated conduction process, and the temperature dependence of conductivity does not follow Arrhenius law [31]. Many polymer electrolytes exhibit Non-Arrhenius temperature dependence of conductivity due to the coupling of ionic motion and polymer segmental dynamics. Such temperature dependence of conductivity is often described by an empirical equation [39,40,41,42]. We have analyzed the measured temperature dependence of conductivity data using the VTF equation [17],

$$\sigma =A{e}^{-E_a/k_B\left(T-T_o\right)}$$

(5)

where A is a constant related to the number of charge carriers. E_a is the activation energy barrier for Li-ion motion, and T_o is the ideal glass transition temperature. In general, the observed value of glass transition temperature T_g > T_o is where the polymer becomes macroscopically rubbery rather than glassy. The excess thermal energy, k_B (T − T_g), provides the mobility to the polymer chain segments.

Figure 6 shows the conductivity versus reciprocal of temperature for PEO_nLiClO₄ and PEO_nLLZO-LiClO₄ films. The solid lines in Figure 6 represent the fitted data using Equation (5), and the excellent fits obtained indicate the temperature dependence of conductivity, and is described by the VTF equation implying a coupled motion of Li-ions with the polymer segmental motion.

Table 2. Activation energy and T_o of PEO_nLiClO₄ and PEO_nLiClO₄-LLZO obtained fitting the temperature-dependent ionic conductivity with VTF model.

Sample	Ea (eV)	To (K)
PEO15LiClO4	0.32	175
PEO12LiClO4	0.09	192
PEO10LiClO4	0.09	197
PEO15LiClO4-LLZO	0.07	185
PEO12LiClO4-LLZO	0.05	198
PEO10LiClO4-LLZO	0.09	185

shows the activation energy and the T_o for PEO_nLiClO₄ and PEO_nLLZO-LiClO₄ films using the VTF equation. In ceramic-free films, the activation energy of PEO₁₅LiClO₄ is 0.32 eV and decreases by more than a factor of three with increasing the Li-salt content. For CSPE films of PEO_nLiClO₄-LLZO with n = 12 and 15, the activation energy decreases nearly by a factor of five. T_o values of 50 K–80 K below the glass transition temperature (Tg ≈ 245 K) are in agreement with the values observed for other PEO-based electrolytes [39,40,41,42].

4. Conclusions

We have studied the effect of Li-salt content on the ionic conductivity of SPE films of PEO_nLiClO₄ and CSPE films of PEO_nLiClO₄-LLZO containing 50 wt% sub-micron sized cubic Li₇La₃Zr₂O₁₂ (LLZO) particles, with n = 10, 12, and 15. Ionic and polymer relaxation times obtained from the fitting of the complex permittivity and conductivity data to a generalized power-law indicate a strong coupling between ionic conductivity and segmental motion, and the ionic motion is facilitated by the polymer segmental motion. In ceramic-free PEO_nLiClO₄ films, the ionic conductivity increases by two orders of magnitude when Li-salt content is increased (n = 15 to n = 12) and does not change significantly upon further increase of Li-salt content (n = 12 to n = 10). On the other hand, the addition of 50 wt% LLZO particles not only enhances film mechanical robustness and thermal stability, but also increases ionic conductivity by more than two orders of magnitude in CSPE films with n = 15 due to the formation of a large number of smaller sized PEO spherulites. The PEO_nLiClO₄-LLZO CSPE film with n = 12 appears to yield the optimum ionic conductivity of 2.2 × 10⁻⁴ S cm⁻¹ at 30 °C, and further increase in Li-loading resulted in a decrease in conductivity due to the polymer recrystallization and ion-pairing effects. The temperature-dependent ionic conductivity follows the Vogel–Tammann–Fulcher behavior, suggesting a thermally activated conduction process, and the activation energy decreases from 0.35 eV in PEO₁₅LiClO₄ SPE film to 0.05 eV in PEO₁₂LiClO₄-LLZO CSPE film. With further adjustments in Li-salt content and LLZO concentration, it may be possible to improve the ionic conductivity to achieve a higher value desired for applications.