2.1. Description of Polymers Investigated by Solid-State NMR
Comb-like copolymers with soft and hard blocks, i.e., with low and high Tg
s, display phase segregation when prepared as films [12
]. This behaviour is key to promote good ionic conductivity and to prevent dendrite growth [20
]. Comb-like copolymers are based on a poly(styrene) (PS) backbone obtained by anionic polymerization. PS backbone is used as a reinforcement block for preventing dendrite growth during cell operation, phenyl groups are very rigid structures. The backbone is a hard block with a reported Young Modulus of 3 GPa [8
]. Grafting poly(ethylene glycol) methyl ether methacrylate (PEGMA) with a Mn
= 500 was done by atom-transfer radical polymerization (ATRP). Poly(ethylene glycol) is known to be a very good polymer for Li+
transportation, moreover short chains have a highest conductivity due by the lack of crystallinity. PEGMA is polymerized by soft radical polymerization while ethylene oxide is polymerized by a less safe process only. This monomer enables the formation of highly branched structures as a polymer graft. Both techniques allow narrow poly(dispersity), which facilitates the structure-properties relationship, and therefore better control of the desired properties. Scheme 1
shows the structure of the polymers investigated in this article.
In order to make a comprehensive comparison between the structures, different ratios of soft/hard blocks were selected. Table 1
reports the different characteristics of the polymers that are reported in ref. [12
]. The PEGMA/PS ratio is important because it has been directly related to the electrochemical performance of the cells [12
]. Polymer 3 was not used as SPE because the high molecular weight of the PEGMA block made it impossible to dissolve in a reasonable amount of solvent. All the polymers were doped with bis(trifluoromethane)sulfonimide lithium salt (LiTFISI) to promote ionic conductivity. Consequently, the study of this polymer by solid-state NMR is an interesting tool for elucidating the lithium motion. The rigidity of the structure is assessed by solid-state 13
C NMR, and an improved understanding of the polymer micro-structure is obtained, as reported in the case of cross-linked polymers [21
]. The purpose of this study is to develop a relationship between the lithium mobility and the electrochemical results.
2.2. Characterization of Copolymers by 13C Solid-State NMR
C NMR is invaluable for the characterization of polymers [22
]. Qualitative information is obtained for the dynamics in heterogeneous systems. The signal is obtained using different polarization schemes, which preferentially excite rigid or dynamic molecular segments. In this work, cross-polarization is used to excite the rigid regions, while a simple 90° pulse excites the rigid and mobile segments. Experimental details are reported in Appendix A
. Figure 1
shows the results for three different polymers with differing PEGMA to PS ratios.
The cross-polarization spectra (left column in Figure 1
) are dominated by the PS main chain (peaks at 150 and 125 ppm) while the direct-pulse with low-power decoupling spectra (right column in Figure 1
) are dominated by the poly(ethylene glycol) chains at 70 ppm. A fraction of PEGMA between 25–75 ppm is observed on the cross-polarization spectra, which indicates that the PEGMA chains display considerable rigidity. More specifically, the PEGMA backbones (25–50 ppm) appear to be less mobile than the pendant groups (70 ppm), which have lower intensity. However, it should be noted that the pendant groups are still rigid enough to show up in the cross-polarization spectra. This partial rigidity of pendant groups possibly results from their coordination with lithium salts. Furthermore, the 13
C NMR results show that the phase segregation reported by Daigle et al. [12
] is not complete and that a model consisting of two perfectly separated blocks has to be refined. As the PS fraction is reduced, the efficiency of the cross-polarization decreases. Finally, an observation of the relative intensities between cross-polarization spectra gives an immediate diagnostic of the relative rigidity of a given copolymer series. For example, based on the relative spectral intensities shown in Figure 1
, sample 3 appears to have a stronger rigid phase component compared to samples 1 and 2. We believe that some fluid parts of sample 3 have to be considered as rigid because the lithium ions strongly coordinated the PEGMA chains for forming “ionomer” as demonstrated in previous publication [12
]; those parts are “frozen” and the ratio reported in Table 1
is based on GPC analysis.
The same methodology is used to determine changes in internal dynamics with temperature. Figure 2
shows the evolution of 13
C spectra for sample 3 with temperature.
The effect of temperature of the PEGMA phase is unambiguous: as temperature decreased, the mobility of the PEGMA chains is reduced as expected. The very low signal on the pendant chains on the DP spectrum, and the appearance of the carbonyl peak at 175 ppm on the CP spectrum, reflects the strong stiffening of the chains at 246 K. This effect is directly correlated to the poor ionic conductivity at low temperatures, especially near the glass transition point (225 K). The glass transition of poly(styrene) is ca. 373 K, and the signal at 30 ppm is characteristic of the poly(styrene) backbone, indicating that PS is already rigid at the highest temperatures studied in this work. The poly(styrene) phase was not observed in the DP spectra because the temperatures were too far from the glass transition. No major changes in the PEGMA segments are observed between 299 K and 340 K since they are not affected by the melting of chains.
2.3. Lithium Diffusion in the Membranes by 7Li Solid-State NMR
C spectra provide information on the polymer rigidity, and 7
Li NMR is useful to monitor the mobility of Li+
ions, which are qualitatively correlated to the conductivity of the material. Due to the very high mobility of lithium in our samples, 7
Li spectra consist of a single sharp peak with full-widths at half height as low as 12 Hz, which reach a maximum at low temperatures of 120 Hz (Figure 3
). This is almost two orders of magnitude lower than the linewidths reported for polyurethane-poly(dimethylsiloxane) copolymers [17
]. The highest ionic conductivity reported in Table 1
is 2.54 × 10−4
at 60 °C, which is higher (about 3 times) than those reported earlier [17
], so we can evaluate qualitatively the ionic conductivity of a polymer by this method. Interestingly, 1
H decoupling appears to have no effect on the 7
Li linewidth in our samples: thus, the mobility of lithium ions is sufficient to completely eliminate 1
Li dipolar couplings.
While 7Li linewidths are influenced by motions with correlation times shorter than μs, faster motions with correlation times in the nanoseconds will contribute to longitudinal relaxation (T1) of the NMR signal. Thus, T1 characterizes fast motion that facilitates lithium diffusion.
Sample 2 in Figure 4
has the fastest lithium motion (shorter T1
relaxation times), which is not in agreement with the ionic conductivity reported in Table 1
. Also, it appears that temperature had less influence on the lithium mobility in this polymer. Mobility in samples 1 and 3 dropped around 263 K, which is related to the crystallization of poly(ethylene glycol) pendant chains in graft copolymers. Figure 2
shows that low temperatures have a great effect on solidification of the polymer chains (PEGMA). The close correlation between the mobility of lithium ions and the motions of PEGMA pendant chains suggests a strong association between the lithium ions and PEGMA groups.
Sample 3 shows the lowest lithium mobility (see Figure 4
), despite the highest ratio of PEGMA. We explain this behavior as resulting from the strangling of the polymeric chains due to the high molecular weight (1,000,000 g mol−1
), which hinders the motion of lithium [12
Lin et al. [17
] calculated the activation energy (Ea
) of lithium diffusion from the slope of the curve at low temperatures by the Arrhenius relationship. This information is relevant for sample 3 because it is impossible to obtain using AC impedance measurements because this polymer cannot be prepared as a thin film. Table 2
reports the results using the two methods. A qualitative correlation is observed with an approximate difference of a factor of 2 between the two methods, the same factor was also reported in reference [17
]. The relaxation time depends on the size of the mobile segments of the polymer electrolyte; one should note that there would be a range of sizes of the mobile polymeric segments and the relaxation time would be some sort of average value. Thus it would be a rough and approximate measure. The activation energy and conductivity as determined by the impedance measurements would be more significant in comparing the conductivity mechanisms of different polymers. Moreover, AC impedance allowed the measurements of long-scale motion while the solid-state NMR 7
Li measurements are related with local motion of Li+
, so that can contribute also for the difference of values measured for conductivity and by consequence Ea
. Nevertheless, the NMR measurements indicate that the activation energy of polymers 2 and 3 is similar. It also important to note that the result obtained for sample 1 by solid-state NMR is within the same magnitude of the normal thermal fluctuation (4 kT = 9.6 kJ), thus the value is probably none applicable in this case.