Determination of inelastic mean free path for solid polymer electrolytes: PTMC:LiBOB and PCL:LiBOB Open Access

To improve safety and energy density of state-of-the-art lithium-ion batteries, solid polymer electrolytes (SPEs) have been developed as an alternative to conventional liquid electrolytes. SPEs eliminate the hazard of using flammable solvents and offer advantages for flexible battery systems.^1–3 However, similar to liquid electrolytes, SPEs are limited by their electrochemical stability, leading to inevitable degradation. Consequently, degradation and solid electrolyte interphase (SEI) formation at the electrolyte/electrode interface pose critical challenges for high-energy-density applications.

Polyethylene oxide (PEO), the most extensively studied polymer, exhibits low Li transference number and limited electrochemical stability at high voltages.⁴ To address these limitations, various polymer materials and lithium salts have been investigated as alternative candidates.⁵ 

Poly(trimethylene carbonate) (PTMC) and poly(⁠ $ε$-caprolactone) (PCL) have shown higher oxidation potentials (4.5–5 V vs Li⁺/Li) compared to PEO.^6,7 These polymers are also less hydrophilic than PEO, reducing the risk of water contamination. Their potential as host materials in SPEs and their degradation behavior when in contact with lithium have been previously studied.^8–10 In this study, we investigate PTMC and PCL together with a salt: lithium bis(oxalate)borate (LiBOB), which has received considerable attention as it promotes ionic conductivity when combined with some polymers (e.g., PEO) in SPEs.¹¹ 

X-ray photoelectron spectroscopy (PES) is used in both fundamental and applied research across materials science, electrochemistry, and catalysis as a surface analysis technique. Conventional laboratory-based PES systems typically operate with soft x rays (⁠ $<2$ keV), while hard x-ray photoelectron spectroscopy (HAXPES) uses hard x rays (⁠ $>2$ keV), increasing electron kinetic energy and thereby extending the probing depth.^12,13 In lithium-ion battery studies, the high surface and chemical sensitivity of PES has made it an important technique for investigating surface structures and reactions at interfaces. HAXPES further enhances this capability by providing a probing depth suitable for investigating buried layers such as the SEI.^14,15

The probability of observing a photoelectron from within a solid depends on atomic photoionization cross section and the probability of electrons scattering on the way to the surface. Only electrons from a finite depth can thus contribute to the signal—this makes PES surface-sensitive. The depth limitation is determined by the effective attenuation length (EAL) of the electron. Here, the EAL is dominated by inelastic scattering at high kinetic energy.¹⁶ The inelastic mean free path (IMFP) depends on the kinetic energy of the emitted electron and properties of the measured material, such as density, molecular weight, bandgap energy, and number of valence electrons.^17,18

PES, together with electrochemical and material characterization techniques, has been applied to study different types of SPEs and their degradation.^10,19,20 However, the IMFP for SPEs is generally unknown, thus adding relatively large uncertainties when characterizing the depth distribution of different species in the interface region. The information depth of SPE studies, determined by the IMFP, is usually obtained by simply using the known IMFP from other materials or predictive models. With a more accurate IMFP value, PES analysis can provide thickness information and depth profiles for chemical characterization on a more precise scale. Here, we compare measured IMFPs using the overlayer method as outlined below, with numbers obtained from the universal curve and the TPP-2M formula.^18,21

In this work, the overlayer method is applied in reverse to determine the EAL of the photoelectrons in the film with a known thickness. The elastic scattering effects are negligible if the kinetic energy of the photoelectrons is high enough (⁠ $>2$ keV). In the present case, the EAL is identical to the IMFP.¹⁶ It is, therefore, possible to estimate the IMFP of the photoelectrons when probing the overlayer with a high photon energy x-ray source.

Surface roughness affects spectral intensity measured by photoelectron spectroscopy, as the local surface normal deviates from the average surface normal.^25,26 Atomic force microscopy (AFM) allows us to investigate the impact of surface roughness on the estimated IMFPs obtained.

Using the overlayer method, the IMFP of two polymers, PTMC and PCL, together with two polymer electrolytes containing 25 wt. % LiBOB: PTMC:LiBOB, and PCL:LiBOB, are determined using an in-house HAXPES (Ga K $α$⁠, $hν=9.25$ keV), manufactured by Scienta Omicron.²⁷ The chemical structures of the polymers and LiBOB are shown in Fig. 1. All the polymer and SPE films were spin-coated on Au substrates.

In the HAXPES experiments, the angle between the Ga K $α$ source emission axis and the analyzer axis is fixed at 90°. The electron emission angle—defined as the angle between the analyzer axis and the surface normal—was varied by tilting the sample to obtain different surface sensitivities.²⁸ In our experiments, 2° corresponds to a grazing incidence condition and 22° gives a more surface-sensitive condition. Figure 4 shows an illustration of the experimental geometry.

The reference samples: bare Au, infinitely-thick PTMC, PCL, PTMC:LiBOB, and PCL:LiBOB films, were measured under the same photon energy (9.25 keV) and pass energy (500 eV) as the examined samples. The reference films were prepared sufficiently thick to make sure that the photoelectrons detected by the spectrometer were emitted only from the films during the HAXPES measurements. The examined samples include thin PTMC, PCL, PTMC:LiBOB, and PCL:LiBOB films on Au substrates, with two thicknesses of film for each type.

The C 1s and O 1s spectra of reference samples are shown in Fig. 2. The PTMC- or PCL-related features are marked as green and the signals from the LiBOB salt are presented as a dashed line. Detailed descriptions of the spectra can be found in the supplementary material. The relative intensity of alkane/hydrocarbon (C-C/C-H) compared to other C 1s features reflects the expected chemical composition of PTMC or PCL, suggesting negligible hydrocarbon contamination, i.e., the bulk composition of the reference samples is nearly identical to the surface composition.

In the O 1s spectra of the reference samples, the intensity ratios between the polymer and LiBOB features are used to fit the examined samples. The O 1s and Au 4p_3/2 core-levels are selected to investigate the contributions from the overlayer (polymer or SPE film) relative to those of the Au substrate. Since the electrons emitted from these core-levels have similar kinetic energies, the differences in the energy dependence of inelastic scattering behavior can then be considered negligible. Also, the transmission function for the spectrometer is then the same. Signals from the two core-levels were measured in the same data acquisition process to eliminate variances in instrumental settings.

Figures 3(a)–3(d) shows the O 1s and Au 4p_3/2 spectra of the examined samples with the Tougaard background subtraction, measured at electron emission angles of 2° and 22°. A broad spectral feature at approximately 546 eV originates from the Au substrate. As the angle increases to 22°, the relative intensity of the Au 4p_3/2 peak to O 1s peaks decreases.

To calculate the IMFP using Eq. (1), the area ratio of the O 1s peaks in the overlayer reference films and the Au 4p_3/2 peak area in the Au substrate reference sample were used as the ratio of sensitivity factors, $SO/SS$⁠. The Au 4p_3/2 peak area and the sum of the O 1s peak areas obtained from the thin samples were used as $IS$ and $IO$⁠. The thickness d for each sample was measured by a surface profiler with a resolution of 6 Å. Figure 4 shows the calculated IMFPs of the polymers and SPEs, and Table I lists the average IMFP values and average deviation. Detailed values can be found in Table S1. In general, the estimated IMFPs for the PTMC:LiBOB are larger than those for the PTMC. Similarly, the PCL:LiBOB exhibits a larger IMFP than the pure PCL.

The single scattering albedo depends on the transport and inelastic mean free paths, not generally known. We use the empirical equation [Eq. (9) in László³⁴] to estimate $ω$ at 8718 eV—the mean kinetic energy of electron emitted from O 1s (overlayer). $β$ values at 9 keV are taken from Trzhaskovskaya and Yarzhemsky.³⁵ Based on these values, $βeff(2°)$ is calculated to be 1.888, 1.892, and 1.454 for PTMC, PCL, and Au, respectively.³⁶ The variations in $βeff$ between 2° and 22° are less than 0.2‰ for the polymers and 2‰ for Au. These small variations are negligible and therefore do not contribute to the observed intensity ratio changes.

It is known that surface roughness affects spectral intensity measured by photoelectron spectroscopy.^25,26 For a surface that is not flat, there are local variations in surface normal on the sample. Thus, electrons collected by the analyzer are actually electrons emanating from a distribution of emission angles. Also, surface roughness introduces shadowing effects on emitted electrons. Certain emitted electrons are shadowed by the rough features on the surface on their way to the analyzer. This effect is more pronounced at larger emission angles. These two effects lead to systematic uncertainties in the IMFP determined by the overlayer method.

To investigate the surface roughness of the spin-coated polymer and SPE films, AFM measurements were conducted following the HAXPES measurements. Figures 5(a)–5(d) show the AFM images and corresponding line profiles for the 12 nm PTMC, 23.4 nm PTMC:LiBOB, 9 nm PCL, and 21.5 nm PCL:LiBOB films, with a measurement area of 20  $×$ 20  $μm2$⁠. Additional AFM images and line profiles of the samples with different thicknesses are provided in Fig. S1. Figure 5(e) shows the root mean square (RMS) roughness values of all polymer and SPE films, which were calculated from the line profiles.

Spherical bumps in nano-scale can be observed in the 12 nm PTMC film. The height of these bumps ranges mainly between 2 and 5 nm, as indicated by the line profile, which gives a lower root mean square roughness value compared to other samples. These nano-structures are absent in the thicker PTMC film and the PTMC:LiBOB films.

In the PCL-based films, domains in different orientations are observed, with crystal-like branches growing within these domains.³⁷ This lamellar structure aligns with the semi-crystalline property of PCL at room temperature.³⁸ The PCL:LiBOB films exhibit thicker branches with less density compared to the PCL films. This indicates a reduced crystallinity of the polymer matrix in the PCL:LiBOB films, which can be attributed to the addition of LiBOB in the polymer matrix. Nano-scale pits are present in both the 9 and 11 nm PCL, with a depth of roughly 5 nm. In the AFM images of the PCL:LiBOB films, there are irregular nano-particles distributed across the surface. As shown in Fig. 5(e), the PCL-based films, especially the PCL:LiBOB films, exhibit slightly higher roughness than the PTMC-based films.

In both the PTMC and PCL cases, the estimated IMFP of SPE is greater than that of the pure polymer. According to the predictive equation first proposed by Tanuma et al., the IMFP of electrons increases as the density of the material decreases.^17,18 In the case of PCL:LiBOB, the crystallinity of the polymer matrix is reduced by dissolving LiBOB in it. As the amorphous region increases in the polymer matrix and the polymer chains become more loosely packed, this could result in a lower density than the pure polymer. This reduction in density explains the observed trend of increased IMFP in SPEs compared to pure polymers.

The surface morphologies of the PCL-based films exhibit higher roughness compared to the PTMC-based films. In the PCL-based films, the domains and branches in different orientations result in higher RMS roughness values. Also, the irregular nano-particles observed in the PCL:LiBOB film, which could be precipitated or undissolved LiBOB crystals, further contribute to high surface roughness in PCL:LiBOB films. In contrast, the PTMC:LiBOB films are more homogeneous without LiBOB crystals remaining or forming.

According to the study on the measured IMFP by Powell et al., the mean deviation of IMFPs measured by elastic-peak electron spectroscopy to a function fitted to all such IMFPs was 12.3%.³⁹ This gives an indication of the uncertainties in estimating IMFP with the elastic-peak electron spectroscopy technique. In our work, the average deviation of the estimated IMFPs ranges from 0.55% to 25.74%. If the samples were perfectly flat, no difference between emission angles in the estimated IMFP would be expected. In our case, surface roughness influences the uncertainty of the estimated IMFP. The shadowing effect (predicted to be more prominent at higher emission angles^25,26) in our experiments is minimized when the films' surface normal is nearly parallel to the analyzer axis. However, variations in local electron emission angles still play a role in systematic uncertainties.

To benchmark the obtained IMFP values, we compare them with calculated IMFPs at a photoelectron kinetic energy of 8718 eV. According to the universal curve, the IMFP of electron at 8718 eV is 8.12 nm, calculated using the coefficient for organic compounds in the equation, $λ=0.087E1/2$⁠.²¹ It is well known that the universal curve does not hold universally as the IMFP is material dependent. In our case, the predicted IMFP obtained by the universal curve underestimates the IMFP by more than 50%. The TPP-2M formula proposed by Tanuma et al. requires parameters including the number of valence electrons, bulk density, atomic mass, and bandgap energy to calculate the IMFP at a given energy (using QUASES software⁴⁰).¹⁸ However, properties like density are sample-dependent, and the bandgap is unavailable for some polymers and most SPEs, making it impossible to estimate their IMFPs using this formula. For PTMC and PCL, the calculated IMFP at 8718 eV is 17.62 and 17.85 nm, respectively, with a bulk density of 1.31  $g/cm3$ for PTMC and 1.1  $g/cm3$ for PCL. The bandgap energy of PCL is 4.712 eV. As no reported value is available for PTMC, the same bandgap energy is assumed for PTMC.^41–43 These calculated IMFPs for the polymers deviate less than 5% from the IMFPs determined at 2° here.

In summary, we have investigated spin-coated PTMC, PTMC: LiBOB, PCL, and PCL: LiBOB films with HAXPES (Ga K $α$⁠) to determine the IMFPs using the overlayer method for these films. Overall, the IMFPs of the SPEs are greater than those of the pure polymers. This increase in IMFP is attributed to the reduction in crystallinity of the polymer matrix caused by the addition of LiBOB, which leads to a decrease in overall density. The effects of surface roughness on the estimated IMFP using the overlayer method are underlined and should be considered when doing quantitative thickness analysis. Accurate IMFP values are essential for reliable depth profile analysis and thickness estimation. Combining HAXPES and AFM allows determination of IMFPs and how surface roughness impacts the uncertainty in the process, not only for these specific materials but also for a broader range of systems. The method used in this work can be combined with calculation studies to better understand the limitations of this method and current IMFP models.