Insights into the Pseudocapacitive Behavior of Sulfurized Polymer Electrodes for Li–S Batteries

Abstract Practical applications of sulfurized polymer (SP) materials in Li–S batteries (LSBs) are often written off due to their low S content (≈35 wt%). Unlike conventional S8/C composite cathodes, SP materials are shown to function as pseudocapacitors with an active carbon backbone using a comprehensive array of tools including in situ Raman and electrochemical impedance spectroscopy. Critical metric analysis of LSBs containing SP materials with an active carbon skeleton shows that SP cathodes with 35 wt% S are suitable for 350 Wh kg−1 target at the cell level if S loading >5 mg cm−2, electrolyte‐to‐sulfur ratio <2 µL mg−1, and negative‐to‐positive ratio <5 can be achieved. Although 3D current collectors can enable such high loadings, they often add excess mass decreasing the total capacity. An “active” carbon nanotube bucky sandwich current collector developed here offsets its excess weight by contributing to the electric double layer capacity. SP cathodes (35 wt% S) with ≈5.5 mg cm−2 of S loading (≈15.8 mg cm−2 of SP loading) yield a sulfur‐level gravimetric capacity ≈1360 mAh gs −1 (≈690 mAh gs −1), electrode level capacity 200 mAh gelectrode −1 (100 mAh gelectrode −1), and areal capacity ≈7.8 mAh cm−2 (≈4.0 mAh cm−2) at 0.1C (1C) rate for ≈100 cycles at E/S ratio = 7 µL mg−1.

: A comparison of the Raman spectra of activated carbon and SP-1 in 1200-1700 cm -1 shows similarity in their carbon bonding environment.     Figure S10: (a) shows electrochemical impedance spectra (EIS) obtained during first cycle at various discharge voltages for S 8 /C coated on Al/C (S loading: ~1 mg/cm 2 ) at a discharge rate of 0.1C. (b) shows EIS spectra obtained at 1 st , 5 th , 10 th , 25 th , 50 th and 100 th cycles S 8 /C coated on Al/C at a discharge rate of 2.5C.
As shown in Fig. S10a, we found that S 8 /C electrodes initially showed double layer capacitance up to 2.6 V. We attribute this to ~30 wt. % SuperP conducting C that was added to make S 8 /C electrode electrically conducting. Upon the initiation of lithium sulfide formation below 2.6 V, the capacitive feature disappears and broad circular features corresponding to the formation of various higher and lower Li polysulfides are observed. At 1.8 V, Li 2 S formation occurs with almost no capacitive features. The evolution of EIS spectra for S 8 /C samples over 100 cycles is shown in Fig. S10b.

Double-layer and ion-diffusion processes in EIS:
In case of ideal electric double layer formation, there is no charge transfer or depletion of redox active species concentration near the electrode. Considering the capacitance to be constant, the charge is proportional to the potential (V). (1).
From the above equation, the rate of change of charge (i.e., current) is seen to be proportional to the rate of change of potential. (2).
Upon performing a Fourier transform on equation 2, we can see that Thus, the Nyquist plot for an ideal double layer has no real component. If a sine wave potential is applied, the resulting current is a cosine, and a phase shift of (corresponding to a vertical line in the Nyquist plot) is observed. Although C dl is ideally independent of frequency, the experimentally measured phase shift depends on frequency due to additional circuit elements in series and in parallel arising from surface roughness, chemical heterogeneity, nonuniform charge adsorption etc. Thus, lines with high slope in the Nyquist plot are related to C dl .

Separator (Anode side) Li foil Pouch Cell after 20 cycles (a) (b) (c)
On the other hand, if a redox process is present, some redox species (e.g., Li + ions) are consumed leading to the concentration gradient near the electrode surface. If the charge consumed in the redox process is (a fraction of the concentration of redox species present near the electrode surface) for a given change in potential (∆V), we may express the diffusion capacitance as (5).
Suppose that concentration of depleted ions is given by within a distance d from the electrode surface, we may express (6).
Considering D to be the diffusion coefficient of ions, it may be seen that d (average region of ion depletion) is dependent on frequency as √ (7).
Therefore, we find that √ is dependent upon frequency. We can re-write this as ⁄ (8).
Given that √ , the diffusion current is This corresponds to a real resistance for charge flow √ ⁄ (10).
We can express the total impedance as ⁄ ⁄ (11).
As it can be seen, and both have the same frequency dependence, which leads to a phase shift which has lower slope than double layer formation.