Introduction

Solid polymer electrolytes (SPEs) with ion conductivity, forming by dissolving metal-ion salts in solid ion-coordinating polymers, such as poly(ethylene oxide) (PEO), have received great attention from both academic and industrial scales in recent decades for realizing all-solid-state rechargeable lithium battery^[1-3]. To achieve high conductivity, people normally pursue an amorphous system without any crystal form for over 30 years, since it was widely believed that ionic conductivity occurred predominantly in the amorphous phase above the glass transition temperature (T_g), driven by the local random Brownian motion of segment chains in the amorphous polymer^[4]. However, Bruce et al.^[5] recently demonstrated that crystalline polymer electrolytes exhibit even higher ionic conductivity than their amorphous counterparts and they believed that the transport mechanism of the crystalline polymer electrolytes should be different from that of the "liquid-like" amorphous polymer electrolytes. The knowledge of crystalline polymer electrolytes structure was vital for exploring the ion transport mechanism, thus many excellent works had been carried and solved the crystal structure of crystalline polymer electrolytes^[6-15]. These studies demonstrated that the organization and order of the crystal structure can improve the conductivity of crystalline polymer electrolytes. However, the ion transport mechanism is still puzzling, for example, the conductivity of LiAsF₆/PEO₆-1k [here 1k denotes the molecular weight (M_w) of PEO is 1 000 g/mol] with the ether-oxygen-to-lithium ratio of EO:Li=6:1 is one order higher than that of LiAsF₆/PEO₆-2k, while the crystallinities of two samples are almost identical and their crystal structures are the same^[16]. Therefore, their works motivated further researches on the ion-transportation mechanism of crystalline polymer electrolytes, especially the research on the microscopic level.

In this paper, by using solid-state nuclear magnetic resonance (SSNMR) spectroscopy on LiAsF₆/PEO₆ complexes, we demonstrate that the spin-lattice relaxation time (T₁) and the linewidth are not good indicators to characterize the higher conductivity, while correlation rate ${k_{\rm SAE}}$ from spin alignment echo (SAE) experiments is a better indicator to characterize the higher conductivity.

1 Experimental 1.1 Sample preparation

LiAsF₆ (Sigma Aldrich LLC., 99.8%) was dried at 50 ℃ for 24 h under dynamic vacuum. Methoxy-end-capped PEO-1k and PEO-2k (Sigma Aldrich LLC., 99.8%) were dried at 30 ℃ for 4 days under dynamic vacuum before use, and methoxy-end-capped PEO-6k and PEO-10k (Sigma Aldrich LLC., 99.8%) were dried at 40 ℃ for 24 h under dynamic vacuum before use. Anhydrous acetonitrile (HPLC/ACS, 99.9%) used as received was utilized as the common solvent for all samples.

The mixture of PEO-nk (n=1, 2, 6, 10) and LiAsF₆ with the ether-oxygen-to-lithium ratio of EO:Li=6:1 were added to anhydrous acetonitrile by mechanical stirring about 24 h, respectively. The solutions were poured into a small wild-mouth bottle respectively, and then the solvent was allowed to evaporate gradually in dry air at room temperature. The obtained white powders were dried overnight in the drying oven, and then annealed at 45 ℃ under dynamic vacuum for two weeks. The yielded samples were referred to as α-LiAsF₆/PEO₆-nk (n=1, 2, 6, 10). Their preparation could be also found in Ref. [16]. All manipulations were carried out under a Nitrogen-filled dry glove box.

1.2 SSNMR experiments

All SSNMR experiments were performed on a Bruker AvanceⅢ spectrometer with a ¹H frequency of 600.13 MHz. Commercial Bruker triple-resonance 4 mm magic-angle spinning (MAS) probes and 4 mm zirconia rotor, which permit spinning frequencies up to 12 kHz±2 Hz, were used for all experiments. The samples were packed into the rotors under a N₂-filled glove box. The length of ⁷Li π/2 pulse was 2 μs, and the ⁷Li signal was transferred from ¹H by cross-polarization (CP). All the ⁷Li shifts were calibrated with respect to 1 mol/L LiCl solution (δ_Li 0). All the NMR spectra were processed with Bruker Topspin 2.0 software.

2 Results and discussion 2.1 Spectral characteristics and conductivities of α-LiAsF₆/PEO₆ complexes

A series of α-LiAsF₆/PEO₆-nk (n=1, 2, 6, 10) complexes were chosen for this study. Their structures are reported to be similar, and composed of pairs of PEO chains that individually fold to form a half cylinder, which in turn interlocked, forming tunnels within which the Li⁺ locate, coordinated by 3 ether oxygen from 1 chain and 2 oxygen from the other chain. The anions do not coordinate to the cations and are located outside the chains^[17].

The ionic conductivity of α-LiAsF₆/PEO₆ complexes series with respect to temperature could be found in Ref. [16]. The behaviors are evident, that is, the conductivity rises rapidly by roughly 2.5 orders of magnitude with the PEO M_w values decreasing from 10k to 1k.

⁷Li CP/MAS results for α-LiAsF₆/PEO₆-nk (n=1, 2, 6, 10) at room temperature are shown in Fig. 1. It is found that with the decrease of the M_w value, the peak width of ⁷Li spectra evidently increases.

2.2 ⁷Li SAE spectra

SAE spectra is a powerful technique for detecting Li⁺ motion in crystalline and even amorphous materials^[18-23]. Because of the very long T₁ and very low natural abundance (7.4%) of ⁶Li nuclei, ⁶Li SAE correlation functions are difficult to access. Thus ⁷Li SAE correlation spectra were employed here to probe the Li⁺ motion. The dipolar interactions between the different Li sites are very small (~80 Hz) since the smallest Li-Li distance is 0.54 nm and 0.65 nm according to the reported crystal structure of α-LiAsF₆/PEO₆-1k.

Three pulse sequence introduced by Jeener-Broekaert^[24], 90˚-t_p-45˚-t_m-45˚, is used with the recycle delay more than 5T₁. For fixed evolution time ${t_p} = 10 \mu s$ and mixing time $({t_{\rm m}})$ ranging from 10^-4 s to 10 s, echoes can be read out at $t = {t_p}$, where t is the acquisition time, then an ensemble averaged two-time correlation function ${S_2}({t_m})$ can be obtained as^[23]

$ {S_2}({t_m}) = \frac{9}{{20}} < {\rm sin}[{\omega _Q}({t_m} = 0){t_p}]{\rm sin}[{\omega _Q}({t_m}){t_p}] > $

(1)

Here ${\omega _Q}$ is orientation-dependent quadrupole frequency which is determined by the quadrupole coupling constant ${C_Q}$ as well as the asymmetry parameter of the interaction ${\eta _Q}$, while < > denotes the powder average. The correlation function ${S_2}({t_m})$ of the Li⁺ motion (Fig. 2) can be well described by a Kohlrausch-Williams-Watts (KWW) function:

$ {S_2}({t_m}) = {\rm exp}\left[ { - {{(\frac{{{t_m}}}{{{\tau _{\rm SAE}}}})}^{{\beta _{{\rm SAE}}}}}} \right] $

(2)

Here ${\tau _{\rm SAE}}$ is the so-called correlation time, and it is inverse proportional to the rate ${k_{\rm SAE}}$. ${\beta _{\rm SAE}}$ is a stretching exponent factor for this stretched exponential with $0 < {\beta _{\rm SAE}} < 1$. The fitting results of all the four systems are listed in Table 1 and the fitting curves are shown in Fig. 2. Usually the hopping rate of Li⁺ (${k_{\rm hop}}$) is considered to be in the same level of ${k_{\rm SAE}}$. It's interesting to note that with the decrease in M_w value of PEO, the ${k_{\rm SAE}}$ remarkably increases, which is consistent with the phenomenon of the conductivity. This phenomenon happens due to the fact that with low PEO M_w, the crystal structure is more ordered, which possibly form a better tunnel for Li migration. Furthermore, the decrease of the term ${\beta _{\rm SAE}}$ with the increase in M_w of PEO suggests that the movement of lithium ions become more anisotropic when the PEO M_w increases. As long as the M_w of PEO increases to 10k, the crystal structure needs to deform to accommodate the chain folding, which possibly destroys the Li⁺ hopping tunnel, leading to more anisotropic Li⁺ movement.

It is interesting to observe that with the increase in M_w of PEO, T₁ values of ⁷Li and ¹H increase significantly. This suggested that the spin-lattice relaxation time is not the dominant indicator to characterize the higher conductivity. Furthermore, with the increase in M_w of PEO, the ⁷Li linewidth slightly decrease, compared with ${k_{\rm SAE}}$. Therefore, we could infer that the ⁷Li linewidth is also not a good indicator. Above all, our results suggested that correlation rate ${k_{\rm SAE}}$ is a better indicator to characterize the higher conductivity.

In conclusion, the mechanism for Li⁺ hopping for PEO with different M_w values is suggested. For PEO-1k and PEO-2k samples, PEO segments are crystallized in an extended-chain phase structure [Fig. 3(a)], and two polymer chains could form a continuous tunnel for the Li⁺ movement, which leads to higher conductivity. However, for the complexes with M_w of PEO larger than 6 k, the polymer chains form lamellae with folding-chain structures, as shown in Fig. 3(b). At the folding point, the Li-ion could not move along the tunnel, therefore the Li⁺ percolation pathway was destroyed, which leads to lower conductivity^[14].

3 Conclusion

By using SSNMR spectroscopy on LiAsF₆/PEO₆ complexes, we demonstrate that the spin-lattice relaxation time and the linewidth are not good indicators to characterize the higher conductivity, while correlation rate ${k_{\rm SAE}}$ from SAE experiments is a better indicator to characterize the higher conductivity. Furthermore, we demonstrate that the chain folding would lead to lower correlation rate ${k_{\rm SAE}}$ and also lead to lower conductivity. So we believe that in order to get higher conductivity, we should prepare the samples with higher correlation rate ${k_{\rm SAE}}$. It's plausible to anticipate that the doping in α-LiAsF₆/PEO₆-1k system, which is in order to increase the conductivity, should not introduce the chain folding in the PEO chains and not destroy the crystal structure.