Investigating the Physical State of Polymer Electrolyte: Influence of Temperature and LiTFSI Concentration on the Phase of the Different States of the Polymer Electrolyte PEO-LiTFSI

A critical analysis of the physical state {solid or liquid state} of the PEO-LiTFSI system was investigated in this study. The findings show one crystallite type in PEO and four in LiTFSI. The physical state of the binary mixture PEO-LiTFSI is predominate by the semi-crystalline properties of pure PEO when we is lower than 33 wt%, and the crystallization of the mixture is only induced by PEO. Nevertheless, LiTFSI reduces the degree of crystallinity of PEO due to its solvation by a part of PEO crystallites. Besides, as the solubility limit of LiTFSI in PEO is achieved, salt crystallites appear within the resulting electrolyte. These crystallites in the high we domain were identified as LiTFSI crystallites complexed with PEO. However, rising temperature promotes their dissolution. The functional groups implicated in the crystallization of PEO-LiTFSI have been highlighted using the IR technique. Besides, the experimental result shows that the glass transition temperature (Tg) and the melting point (Tm) of the binary mixture exhibit a non-linear trend with we and Mw. A simple mathematical treatment is proposed to predict glass transition temperature as a function of we and Mw. Our model considers the additive effect of lithium salt on the Tg variation.


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2][3] Accumulators are generally composed of at least two electrodes separated by an electrolyte.Therefore, understanding the electrochemical and mechanical properties of electrodes and electrolytes helps define and control or even improve the performance of batteries.Furthermore, the rate of lithiation and delithiation of electrodes depends on the ability of the electrolyte to conduct the ions.Thus, the choice of electrolyte seems very important and involves a profound investigation of this crucial element of the batteries.Low molecular weight liquid electrolytes are the most used for manufacturing conventional Li-ions batteries [4][5][6][7][8][9][10][11][12][13][14][15] because they have interesting ionic conductivity; for example, EC/DEC (1:1 vol.) solution containing 1 M of LiPF 6 salt exhibits 0.95 S.m −1 at 25 °C.However, liquid electrolytes suffer from two significant drawbacks: i) they are indeed subject to the formation of a solid electrolyte interface (SEI) exhibiting some passivating behavior 16 ; ii) Besides, during the recharge, the appearance of dendrites could occur with short circuits and subsequent safety problems. 17,180][21][22][23][24][25] The ceramicbased electrolytes have: i) high ionic conductivity (∼ 1 S m −1 at room temperature) 20 and ii) high electrochemical stability (compared to the stability of other solid polymer electrolytes or even to a monomer or oligomer liquid electrolytes).Conversely, ceramicbased electrolytes could sometimes exhibit low chemical stability and poor mechanical properties, 19,[26][27][28][29][30] compromising their relevance.][33][34] Various methodologies were involved in overcoming these drawbacks in improving the properties of these electrolytes (ionic conduction, mechanical properties, etc), such as blending, 27,30 crosslinking, plasticizing, 33,[35][36][37] or quenching. 38ue to the great flexibility of its chains and its quasi-null vapor pressure, 18,30,34,[39][40][41][42][43][44] the PEO-based electrolyte, or electrolyte with poly (ethylene oxide) (PEO) as a solvent, looks to be a good choice among the existing solid polymer electrolytes.In the current investigation, the physical state of the PEO-LiTFSI polymer electrolyte -a mixture of poly (ethylene oxide, or PEO) and lithium salt bis(trifluoromethane sulfonyl imide, or LiTFSI-was studied.According to Yixuan Guo et al., the advantage of inorganic solutes is their great electrochemical stability. 16The electrochemical behavior of PEO-LiTFSI has been studied by linear sweep voltammetry by several authors, and the results show that PEO-LiTFSI electrolytes are stable until 3.6 V. 45,46 The achieved study is limited to DSC and IR analyses, expecting to determine the existence of different phases in the PEO-LiTFSI electrolytes solid state at various temperatures and concentrations of LiTFSI in PEO.The presence of crystalline phases in the electrolyte as a function of the lithium salt concentration translates to a loss in conductivity, and it is essential to determine their existence to propose the appropriate electrolyte composition offering the homogeneous transport pathway.8][49][50][51][52] Toe et al. have demonstrated that the solvation state can affect ionic conductivity.They prove that according to the domain of concentration, the ion motion behaviors can be completely different.Indeed, the conduction by solvation of lithium ions in PEO at 90 °C is possible until 37.6 wt% of LiTFSI in PEO; from 37.6 wt%, the accumulation of LiTFSI adducts impedes the conduction. 47ven while polymers have strong mechanical characteristics at temperatures below 100 °C, they are complicated materials whose temperature-dependent mechanical characteristics are still poorly understood.Additionally, it is believed that these features are directly related to their global conformation structure at the chain scale, or the flexibility of the polymer chains, as well as to the functional groups that are attached to the ends of the chains and their molecular weight.In conclusion, there is a close connection between the solvation state and the mechanical properties of the polymer electrolytes.The electrolytes resulting from mixing the semi-crystalline polymer PEO with the lithium salt LiTFSI could exhibit amorphous or/and crystalline phases (Fig. 1) as a function of the distribution of the species.Using a semicrystalline polymer (Fig. 1) will increase the probability of having crystalline phases in the resulting PEO-LiTFSI electrolyte.The resulting electrolyte could thus be partially ordered or fully disordered, and its performance depends on its physical state, which depends on the operating temperature and the solute concentration.
The crystalline phase of the semi-crystalline electrolyte melts at a specific temperature related to its melting enthalpy.Furthermore, the organization of the macromolecules into the electrolyte (e.g., its state) can be evaluated by the changes in enthalpy.Therefore, an analogy between the physical state of the polymer electrolyte and the temperature dependency on enthalpy shown in Fig. 2 is suggested.
As a result, three areas were observed, and different states (structures i and j) were presented for each.
In Fig. 2, for temperatures lower than the crystallization temperature (T c ), the polymer electrolyte, in solid state and assumed to have a dense structure, exhibiting an enthalpy noted H i .Increasing the temperature to the melting point temperature (T m ) causes the enthalpy to increase from H i to H j and allows the melting of the crystalline phase.The difference ΔH = H j − H i corresponds to the latent heat of fusion of the solid electrolyte.As a result, the compact structure of the electrolyte for T < T c disappears, and the chains start to move freely by the segmental relaxation principle.For temperatures higher than T m , the enthalpy increases slowly.Consequently, the electrolyte is in a liquid state and is less dense, giving a wholly dispersed structure or amorphous rubbery phase.
The measurement of the enthalpy as a function of the temperature of a given "multiphase system" could enable: (a) to get some information on the microstructure of the electrolyte and on the evolution of its physical state and (b) to evaluate the relative percentage of each crystallite by determining the enthalpy of the observed changes on each crystallite (i) and then by using the Euler Eq. 1.
Where: ΔH i and i χ are respectively the melting enthalpy and the mass fraction of the crystallites (i) in the electrolyte presenting  m i and m being respectively the mass of the microcrystals (i) and the total mass of the electrolyte); ΔH is the melting enthalpy of the electrolyte.
5][56] The segmental motions or relaxation of the polymer chains and the mobility of ions are closely dependent on the physical state of the electrolyte.Understanding and controlling the physical state of PEO-LiTFSI is essential for optimizing the ion transport characteristics in this electrolyte.Therefore, it is essential to evaluate the physical state of the polymer electrolyte as a function of temperature and composition and to evidence the solvation state of the LiTFSI by the oxygen atom of PEO.
This work aims to rigorously introduce the physical state of the PEO-LiTFSI system and the resulting phases in correlation with the concentration and the operating temperature.The primary goal is to identify a region in which the microstructure of the polymer electrolyte seems homogeneous.Indeed, a homogeneous phase is important to assume continuous media for numerical modeling of the electrochemical properties of these systems.

Experimental
Preparation of the electrolyte.-Highmolecular weight polymer PEO (M w = 200 kg/mol), lithium salt LiTFSI, and anhydrous acetonitrile (ACN) were purchased from FISHER SCIENTIFIC SAS and stored in a glovebox under argon at low moisture (1-3 ppm H 2 O and O 2 ).Special care was taken to avoid water and oxygen contamination because they can deteriorate the chemical, electrochemical, and photochemical stability of the polymer electrolyte. 40,44,57][60] Firstly, the solubility of the PEO in ACN was determined at 60 °C.PEO powder was added step-by-step in ACN liquid solvent under magnetic stirring: it was found that 7 wt% of the PEO can be dissolved into ACN (∼93 wt%) after ∼5 hours of stirring; the obtained binary solution is limpid.Therefore, for the experiments performed in the present study (all carried out in glovebox), the desired amount of the powder of LiTFSI is added into the above binary solution.The obtained ternary solution is maintained under stirring for 15 hours before casting it in a glass petri dish for a preliminary drying (7 hours) at room temperature.Then, the obtained polymer electrolyte film is dried at 80 °C for 24 hours (expecting to remove the residues of ACN), and then the electrolyte cools until room temperature.
The samples for DSC were prepared under the glovebox as follows: a slice of 5 to 12 mg of the PEO200K-LiTFSI polymer electrolyte was inserted in an aluminum pan and sealed with a hermetic aluminum lid.Note that, as reported by N. A. Stolwijk et al., the mass of the electrolyte sample does not significantly impact the measurement by DSC. 31 DSC measurement.-TheDSC analysis involves heating or cooling the sample and monitoring the resulting heat flow.Then the following methodology was used: (i) the electrolyte sample is pre-cooled to −70 °C and held at this temperature for 5 minutes, expecting to freeze its structural state by blocking the local segmental motion of polymer chains.(ii) the sample was quenched from −70 °C to 170 °C or 250 °C with a temperature scan rate of 20 °C min −1 .Note that all the experiments were done under a nitrogen atmosphere and repeated at least three times with different samples at the same concentration to validate the reproducibility of the methodology.The experiments were done with TA INSTRUMENTS DSC Q2000.
Infrared measurement.-Theinfrared (IR) technique involves analyzing the absorption of light by molecules when subjected to energy.We have prepared samples for the IR technique in an argonfilled glovebox.The sample included pure PEO, LiTFSI, and mixtures of PEO-LiTFSI at the salt weight fraction 9, 33, and 70 wt% were analyzed by IR techniques.We placed the sample on circular glasses inside a sealed and temperature-controlled cell (Linkam THMS600) to conduct the analysis.The thermo-regulated cell was then positioned on the support of the IR spectrometer.As incident light passes through the sample, the atoms vibrate, absorbing some light.The absorption spectra are utilized to characterize the structure of the samples.Note that The IR technique was made using a ThermoScientific Mid-infrared Miscrocope IN 10 MX with an MCT detector.The spectral resolution was 8 cm −1 , and 64 scans were performed by measurement.

Results and Discussions
DSC results.-Theoreticallyexpected thermogram,.-Duringthe DSC analysis, the heat flow absorbed or produced by the electrolyte is monitored as a function of the applied temperature ramp, and the obtaining graph is called a DSC thermogram.The ECS Advances, 2023 2 040509 thermogram gives access to the glass transition temperature, the crystallization temperature, or the melting point of the polymer electrolyte when the electrolyte presents a multiphase microstructure.Figure 3 indicates the theoretical thermograms obtained for a semi-crystalline (a) and an amorphous polymer electrolyte (b).The thermogram shows leaps in the heat flux corresponding to the physical changes seen, allowing for determining the temperatures of the observed changes in the physical state and the fluctuation of the related energy.][62][63][64][65][66][67][68] The first variation (jump) observed corresponds to the glass transition ({T ⩽ T g }, Domain A, Figs.3a and 3b).This is a secondorder thermodynamic transition in which the solid semi-crystalline polymer electrolyte initially in a glassy phase (poor mechanical properties due to the strong limitation of the local conformations of its molecules; no segmental relaxation of the PEO chains are possible) transforms into a softer rubber phase, in which segmental motions are possible.Increasing the temperature can cause different physical changes in the solid "soft" electrolyte as a function of its crystallinity.The thermogram may detect any temperature-induced transition phase, such as the melting of crystallites when the solid electrolyte exhibits microstructure heterogeneities (i.e., simultaneously both crystallines and amorphous phases, See Fig. 1).On the other hand, an amorphous solid polymer electrolyte has no defined melting point and does not give a signal, i.e., any endothermic or exothermic peaks, during the heating process by DSC techniques.The amorphous electrolyte in a solid state is generally considered a liquid with infinite viscosity, decreasing as the temperature increases.By the way, only the crystalline phase can be detected by DSC, leading to an endothermic or exothermic peak on the thermogram associated with the melt of crystallites.
In the domain B, Fig. 3a for {T g < T = T m }, the polymer electrolyte does not exhibit any signal, translating thermal stability of crystallites; whatever its state (semi-crystalline rubbery phase, i.e., the juxtaposition of crystalline and amorphous phases), no physical changes occur.Consequently, there are not any crystallites that can melt in the corresponding temperature domain.
Domain C, Fig. 3a for a temperature around T m , the thermogram exhibits a peak attributed to the melting of the crystallite fraction in the semi-crystalline electrolyte.The crystallites melt, giving an amorphous polymer like a viscous liquid.The endothermic peak area lets us determine the energy required to melt crystallite fraction.Domain D, Fig. 3a: No peak observed in the thermogram for temperatures higher than the melting point temperature {T > T m } because the obtained molten polymer electrolyte is fully amorphous.Domain D, Fig. 3b, the polymer is in an amorphous phase.This phase could be in both solid and liquid state.Due to the absence of domains B and C, it is not possible to use the DSC technique to deduce the melting point of the solid state of the amorphous phase.
The physical state of PEO-LiTFSI is evaluated regarding the LiTFSI concentration and the operating temperature.
Impact of the temperature scan rate on the thermogram.-Beforeconcluding the validity of the DSC technique for the thermal characterization of PEO-LiTFSI, the effect of the temperature scan rate on the thermogram shape will be examined.
W. Gorecki et al., using the polymer electrolyte PEO900K-LiTFSI, i.e., PEO-LiTFSI (with M w = 900 kg mol −1 ) heated from −73 to 127 °C, have shown that the temperature scan rate didn't affect the DSC thermogram shape. 56he effects of the temperature scan rate of the DSC technique on the methodology used were investigated by applying 5 °C min −1 , 10 °C min −1 , and 20 °C min −1 .Figure 4 presents the results of PEO200K-LiTFSI (M w = 200 kg mol −1 and a LiTFSI mass percentage w e = 50 wt%), using the proposed methodology (curve of Heat flow as a function of temperature).It will be possible to determine how the molecular weight of PEO affects the scan rate by using a different molecular weight than that used by W. Gorecki and coworkers.The outstanding information shown by the curve "Heat flow as a function of temperature" is the small peak near the T g (∼−20 °C); it could translate as an artifact of the temperature ramp used.For temperatures higher than the glass transition temperature, the obtained curves do not exhibit any change meaning that the used mixture is amorphous.
However, the temperature scan rate (5 °C min −1 , 10 °C min −1 , and 20 °C min −1 ) does not significantly impact the shape of the thermogram.Consequently, the determined glass transition temperature and the melting point of the polymer electrolyte will both be unaffected overall.Thanks to our results, we show that as PEO900K-LiTFSI, the PEO200K-LiTFSI electrolytes are not impacted by the scan rate temperature, which means they present similar behavior with the scan rate.In light of this, we can say that the temperature scan rate of the approach employed does not affect the physical state of the high molecular weight polymer electrolyte.We can conclude that the proposed methodology used for DSC analysis is suitable for the thermal characterization of PEO-LiTFSI.To shorten the time required for the methodology, we decided to use a temperature scan rate for the tests of 20 °C min −1 .
Thermograms of the mixture PEO200K-LiTFSI: Thermogram reproducibility after various cycles of temperature ramp used.-Aspreviously indicated, the mixture PEO200K-LiTFSI was prepared using an M w = 200 kg/mol PEO and LiTFSI salt.Then, successive  thermograms (cycle 1 to cycle 5) were performed with the same sample of electrolyte and at the same temperature ramp conditions.At the end of each thermogram, the sample is re-cooled at room temperature and maintained at this temperature for 15 minutes before starting a new thermogram.The results of all the samples analyzed show that the first-cycle thermogram is not superimposable on subsequent cycles.Beyond the difference in heat flow, cycle 1 of the electrolytes at w e = 33 wt%, in particular, revealed principally two melting points.The results are presented in Fig. 5.
In Fig. 5, all the thermograms show a first zone, i.e., for a temperature variation from −70 °C to −40 °C, attributed to the glass transition temperature of the mixture (i.e., PEO200K-LiTFSI) located at −43 °C.The first thermogram (performed with the fresh electrolyte, blue curve/cycle 1, in Fig. 5) exhibits two endothermic peaks (i.e., two melting points) at ∼32 and ∼42 °C, meaning at least two different types of micro-crystallites in the solid electrolyte (before melting).The four successive thermograms plotted, quasiidentical, are different from the first thermogram.They show only one endothermic peak at ∼32 °C.This means only one crystallite type remains in the mixture after the first cycle (melting and cooling).The first cycle seems to uniformize the solid.It exhibits only one for the following cycles.In addition to the endothermic peak, the subsequent cycles show an exothermic peak at ∼6 °C.After the first thermogram, the measured heat flow of the peak of the thermograms cycles 2 to 5 of Fig. 5 slightly increases with the number of cycles (6 to 13%, in comparison to cycle 2), meaning that the physical state of the solid electrolyte obtained at the end of each cycle, is not affected by the method, only a slight change of the electrolyte crystallinity can be evidenced.
Chen et al. performed the thermogravimetric analysis (TGA) thermogram on the binary mixture (PEO-LiTFSI). 55The results showed no mass loss at the temperature range of interest, thus confirming the chemical stability of the mixture against the temperature.
The glass transition temperature and melting point of the electrolyte did not change, so we infer the conservation of its physical state.Furthermore, it was found that the heat flow only increases slightly with the number of cycles after the first cycle.Therefore, the PEO-based polymer electrolyte is thermally stable in the appropriate temperature range, as shown by the fact that the physical state of the electrolyte is unaffected by reasonable numbers of thermal cycles utilizing the same analysis approach (i.e., the same temperature ramp at each cycle).
This finding demonstrates that within the selected temperature range T ∈ [−70, 200 °C], the cooling process, rather than altering the physical state of the electrolyte, can affect the microstructure by limiting its crystalline phases due to the PEO chains relaxation process.As a result, we can conclude that the PEO200K-LiTFSI polymer electrolyte does not undergo an irreversible change in its physical state when working at temperatures below 200 °C.
Thermograms of the pure compounds LiTFSI and PEO.-The pure PEO and LiTFSI were analyzed by DSC to evidence eventual physical state changes and determine their corresponding melting point(s).The obtained thermograms showed good reproducibility regarding the position of peaks meaning that both PEO and LiTFSI were not degraded by the temperature ramp used.The DSC thermogram of the pure PEO shows two zones where the heat flow changes: i) the first, located at −57 °C, is attributed to its glass transition temperature; ii) the second signal is an endothermic peak located at + 66 °C.It represents the melting of the crystallites of the PEO with ΔH = 165 J g −1 .The enthalpy variation (ΔH) is the surface area of the endothermic peak.The polymer electrolyte is semi-crystalline and presents amorphous and crystalline phases in its solid physical state.Due to the dense nature of the crystallites, the amorphous phase of the semi-crystalline electrolyte will reach the liquid state before the crystalline phase.The thermogram in Fig. 6 a shows that the pure PEO has only one kind of crystallographic structure in its solid state due to the presence of only one peak in its thermogram.
Figure 6b is the thermogram of pure LiTFSI, which is inorganic crystalline lithium salt.More complex, the thermogram of the LiTFSI exhibits several signals; the thermogram is also reproducible, thus confirming the LiTFSI thermal stability.Four peaks were observed respectively at temperatures indicated in Table I.The DSC analysis shows that its solid state presents four types of crystallographic structures.The explanation for the trend of the thermogram of LiTFSI is linked to the polymorphism aspect of its crystallites.DSC technique does not make it possible to deduce the crystallographic structure of the crystallites presented by the peaks.
LiTFSI is in a liquid state above 234 °C, 7,37 so peak 4 corresponds to the transition from a solid to a liquid state and could be attributed to the melting of the last crystallites of the salt.Peaks 1, 2, and 3 are other crystallographic structures in the LiTFSI.0][71][72][73] For example, in the thermal characterization of the pure LiTFSI by cooling methodology, M. Marczewski et al. have found peaks 3 and 4 and interpreted peak 3 as a solid-solid transition. 7Besides, D. Fauteux et al. observed the peaks of structures 2, 3, and 4; they associated peak 3 with the melting point and peak 4 with the boiling point. 64However, this interpretation of peaks 3 and 4 is incorrect because LiTFSI melts at 234 °C.Peak 1 as peaks 2 and 3 of pure LiTFSI are solid-solid transitions.Therefore, we can conclude that the solid state of the LiTFSI crystallites adopts various crystallographic structural arrangements as a function of the operating temperature.Then, it is necessary to determine their solubility and thermal stability in the PEO.
Notice that transition peak 3 involves a higher enthalpy value than the others.According to Paulechka et al., the crystallites at  ECS Advances, 2023 2 040509 peaks 2 and 3 are the most stable. 73These results prove that LiTFSI and PEO may present crystalline phases in the resulting electrolyte.
Both pure LiTFSI and PEO melting heat flows will be used as reference points when analyzing the binary mixture's heat flow.
Impact of the weight fraction of lithium salt on the physical state of the electrolyte.-Next,the dependence of the physical state and the phases within the solid state of the mixture PEO-LiTFSI against the weight fraction of LiTFSI and the temperature was investigated through the DSC technique.Mixtures of PEO-LiTFSI were prepared by varying the salt weight fraction as previously described.At least two cycles were performed in each sample, and the results were reported in Fig. 7.
The melting enthalpies and the corresponding melting point of crystallites were evaluated using the data of the DSC thermograms, and the results are reported in Table II.Note that the data of melting point and enthalpy of sample 100 wt%, i.e., the pure LiTFSI, is reported in Table I.
The melting enthalpy of the polymer electrolyte changes with the lithium salt concentration, meaning that the lithium salt interreacts with the semi-crystalline polymer and changes its microstructure.This implies that the interactional forces between PEO and LiTFSI are stronger than those between the PEO chains (i.e., solvation of lithium-ion by PEO).
The thermograms in Figs.7a-7c exhibit a variety of endothermic peaks that are linked to the melting of crystalline phases.
(I) The curves of Fig. 7a exhibit an endothermic peak located at temperatures variable with the salt weight fraction (w e ) (see Table II); these temperatures are very close to the one measured for the melting of the crystallites of pure PEO.Besides, the mass melting enthalpy decreases as the salt weight fraction increases.In contrast, no peak of the pure LiTFSI crystallites was found in the binary mixture.In this concentration domain, the solvation of LiTFSI by the PEO enables the total dissociation of LiTFSI.Thus, a fraction of PEO crystallites disappears because of the lithium solvation.
Using the Fourier-transform infrared spectroscopy (FTIR) method, S. J. Wen et al. show that in the dilute region, the complexation of the PEO with the LiTFSI did not occur. 39ccording to Jean-Marc Haudin, the decrease of the melting enthalpy could be explained, on the one hand, by the decrease in the size of the crystallites and, on the other hand, by the increase of the segmental motion of a polymer. 74We conclude that in this domain, only crystallites of PEO exist in the electrolyte.These crystallites are surrounded by a solid state of the solvated phase of LiTFSI with PEO chains.(II) In Fig. 7b, the thermogram of PEO-LiTFSI at 33.33 wt% (magenta curve) shows two peaks.Indeed, at this ECS Advances, 2023 2 040509 concentration, the PEO-LiTFSI presents an exothermic peak at 6 °C and an endothermal peak at 32 °C.The endothermic peak corresponds to the melting of crystallites.We have no explanation for the exothermic peak.In Fig. 7b, the darkorchid and deep-sky-blue curves, for the salt fractions in the range from 37 wt% to 50 wt%, the electrolyte appears amorphous due to the lack of endothermic peaks (meaning no melting point, so no crystallites at microscopic scale).The whole PEO is involved in the solvation of the lithium salt, and there is no free crystallized PEO in the mixture.(III) In the curves of Fig. 7c, for w e higher than 50 wt%, new endothermic peaks appear; The melting temperature gap is larger than the one obtained previously, and the melting enthalpy is close to that of the LiTFSI.The presence of peaks means that part of the electrolyte becomes semi-crystalline again, and their melting enthalpies are in the same magnitude as peaks 2 and 3 of the pure LiTFSI (Reported in Tables I and  II).Note that larger endothermic peaks mean the crystallite fusion starts at a "low" temperature (∼66 °C), even if the peak temperature reaches higher values (∼90 °C).J. Olmedo-Martinez et al. have reported that the increase in w e induces the decrease of the mechanical properties of the polymer 75 because the LiTFSI acts as a plasticizer. 76Therefore, the melting temperature of the crystallites of the electrolyte should continuously decrease if the lithium salt is completely dissociated, which is not true experimentally at high w e .The melting point of the PEO is lower compared to that of the LiTFSI.Thus, we suspect the presence of small and heterogeneous sizes of LiTFSI crystallites complexed with PEO, related to the lack of PEO for its total dissociation by solvation.These LiTFSI crystallites are coated with PEO chains due to the strong interactions of LiTFSI with PEO.Also, from 66.50 °C onwards, the binary mixture could present two states, i.e., complexed LiTFSI solid state immersed in an amorphous state of PEO.However, increasing the temperature increases the solubility of LiTFSI in the PEO and thus dissociates the segregated phases of LiTFSI in the PEO.The complexation hypotheses, i.e., LiTFSI complexed with PEO, are put forward by certain authors. 37,58,76sides, the DSC thermograms enable the determination of the glass transition temperature using the half-height point of heat capacity change and the melting point by heat flow integration method.Therefore, the phase diagram of the binary mixture is deduced by the determination of the melting point as a function of w e to illustrate the physical state of the binary mixture PEO-LiTFSI according to the operating temperature.
Glass transition temperature.The glass transition temperature T g of the PEO200K-LiTFSI polymer electrolytes was determined from the thermograms.The results are presented in Fig. 8 (curve i) and compared to the values reported in the bibliography. 31,37The glass transition temperature (T g ) of electrolyte PEO200K-LiTFSI increases from −57 to −37 °C as w e increase from 0 to 23 wt%, but when w e is above 23 wt%, it remains practically constant.The behaviour up to 25 wt% was also mentioned by N. A. Stolwijk et al., using PEO8000K-LiTFSI (curve ii). 31Conversely, Lascaud et al. used a lower molecular weight PEO (i.e., 4 kg mol −1 ) and claimed that the T g of PEO4K-LiTFSI electrolyte continuously increases from −72 to 35 °C as w e increases. 37otably, electrolytes with low molecular weight polymer exhibit more pronounced changes in the glass transition temperature than those with high molecular weight polymer.The slight variation of the T g of high M w polymer electrolyte with w e could mean that the LiTFSI effect is lower on long chains of PEO; The interactions of LiTFSI do not significantly alter the overall mechanical behavior of high molecular weight PEO compared to the lower one.
James E. Mark proposed an empirical {Eq.2} linking the glass transition temperature of the pure polymer (T g 0 ) and its molecular weight (M w ). 65 Where: -K 0 is a constant depending on the properties of the polymer -M w is the molecular weight of the polymer -T g 0 ∞ is the glass transition temperature of the infinite molecular weight polymer.
The T g 0 of PEO with 8000 kg mol −1 obtained by Stolwijk et al. 31 appears to be similar to the one obtained in the present work for a PEO with 200 kg/mol.Therefore, we can conclude that around a certain value, the molecular weight of the polymer (M w ) does not affect its glass transition temperature.This could mean that both  We propose to express the effect of the salt weight fraction on T g by the sum of an exponential term and a polynomial function in the form of Eq. 3 to obtain a predictive empirical law that enables estimation of the glass transition temperature T g as a function of both the polymer molecular weight (M w ) and the salt weight fraction (w e ), i.e., the glass transition temperature T g = f (w e; M w ).The model assumes that the effects of the solute on the solvent are additive.The theoretical evolutions of the T g = f (w e ) for the three different PEO molecular weights were represented in Fig. 8 (continuous lines (i), (ii), and (iii)), and the agreement appears satisfactory.Degree of crystallinity.The glass transition temperature and the crystalline phase of the polymer electrolyte affect ionic transport.In addition to the glass transition temperature, it appears attractive to determine the degree of crystallinity of the binary mixture PEO-LiTFSI solid state.Besides, the mass enthalpy in melting the crystallites in the binary mixture relates to its degree of crystallinity.Determining the degree of crystallinity allows for deducing the fraction of the amorphous area in the mixture, which is the amount of conductive area of the electrolyte.This section expects to evaluate the fraction of certain crystallites in the PEO-LiTFSI electrolytes through the corresponding enthalpy variation.The degree of crystallinity could be defined as the weight fraction of the crystalline phase in the electrolyte.PEO and complexed crystallites in the electrolyte (LiTFSI_PEO) require energy to melt.In light of the various phases of crystallites, it is possible to establish the Euler law from Eq. 1 for a PEO-LiTFSI electrolyte {Eq.5}.
Where H m Δ is the melting enthalpy of the electrolyte; is the melting enthalpy of pure crystalline PEO, 31 and PEO χ is the degree of the crystalline phase of the PEO in the electrolyte; H m LiTFSI_PEO Δ is the melting enthalpy of the pure complexed crystallites (LiTFSI_PEO) and LiTFSI_PEO χ its fraction in the electrolyte.Note that the relative degree of crystallinity of the PEO versus the amount of PEO in the mixture could be obtained using the expression Thanks to the thermograms in Fig. 7, two crystallization zones of the polymer electrolyte were deduced.Indeed, only the PEO is in the crystalline phase when w e are lower than 33 wt%.On the other hand, in the domain of high weight fraction of LiTFSI, i.e., w e higher than 50 wt%, the PEO is amorphous, and only the LiTFSI crystallites complexed with PEO exist in the electrolyte.Therefore, the enthalpy needed to melt the crystallites in the polymer electrolyte is given by Eq. 5 according to the enthalpy of different crystallite types.Thus, the degree of crystallinity of the polymer electrolyte is deduced as a function of the weight fraction of lithium salt using Eq.6 when we have only crystallites of PEO (i.e., w e ⩽ 33 wt%, and Eq. 7 for the crystallites of LiTFSI in the highly concentrated domain where PEO is fully amorphous (i.e., w e ⩾ 50 wt%).
In the range of high w e , evaluating the degree of crystallinity of the electrolyte requires the precise identification of the crystallites and their enthalpy of fusion.Note that the melting enthalpy of crystallites in the mixture is reported in Table II.Regarding their melting point, the crystallites in the higher domain were attributed to the crystallite giving peaks 2, 3, and 4 of the pure LiTFSI.Their degree of crystallinity in the resulting binary mixture was deduced using the enthalpy value given in Table I (for H m LiTFSI PEO _ ) and Table II (for H m Δ ).The results are shown in Table III.Note that, as well as w e increases until 33 wt%, the degree of crystallinity of the binary mixture decreases.
According to our result, lithium salt has various effects on the electrolyte: (i) in moderate amounts, it helps to reduce the degree of crystallinity of the PEO until the PEO becomes amorphous (ii) finally, when the amount of LiTFSI is too high in the polymer solvent, a part of LiTFSI interacts with the PEO without either solvation or dissociation, thus promoting the binary system's re-crystallization. 47Nevertheless, increasing the operating temperature enhances the ability of the PEO to dissolve the segregated phase of LiTFSI.
Phase diagram of the mixture PEO-LiTFSI.The phase diagram of the binary mixture PEO-LiTFSI was constructed by deducing its melting point and glass transition temperature from the obtained thermogram at different salt weight fractions, as shown in Fig. 9.The different phases in the solid state were carefully studied.The dependence of the melting point of PEO-LiTFSI with the salt weight fraction is correlated with the ability of LiTFSI to interact with PEO.Indeed, when w e is lower than 33 wt%, the melting point of the PEO crystallites decreases from 66 °C to 33 °C.This decrease in the melting point of PEO-LiTFSI is linked to the solvation of LiTFSI by a part of the semi-crystalline PEO, which induces the reduction in the size of the spherulites of the PEO.The binary mixture is solid for temperatures below its melting point.Under glass transition temperature {solid state (I) on Fig. 9}, the phase of the solid state is semi-crystalline vitreous.For the temperature ranges from T g to T m , we get the solid-state (II), and this solid-state of PEO-LiTFSI is in the semi-crystalline rubbery phase.Above T m , the crystallites in the solid state (II) melt, and the mixture is in an amorphous phase.
For w e ∈ [33, 50 wt% [, the PEO-LiTFSI system appears amorphous as no melting point of crystallites was observed using DSC technique.This domain was introduced by S. Lascaud  the gap of the crystallinity. 37The absence of melting point in this domain was also obtained by D. Fauteux et al. 64 Indeed, the binary mixture PEO-LiTFSI in this domain seems homogeneous at the microscopic scale because any crystallite melt is detectable by the DSC technique.The solid-state (I) is in the amorphous vitreous phase, and the solid state (II) is in the amorphous rubbery phase.Besides, for w e higher than 50 wt%, we denote the increase of the melting point of the electrolyte induced by the formation of LiTFSI crystallites complexed with PEO in the electrolyte.In addition, around 70 wt% of LiTFSI, the resulting electrolyte presents at least two melting points.The first is a solid-solid transition, i.e., phase transition without a change of physical state.The last one is attributed to the solid-liquid transition.
The deduced phase diagram and its comparison with the one found in the bibliography 37,64 enable us to conclude that high molecular weight polymer electrolytes (PEO-LiTFSI) present the same physical state and, consequently, a similar microstructure.Besides, IR analyses were performed.IR characterizations expect to collect information on the structural function of the electrolyte groups able to generate crystalline phases.
Infrared results.-Thefundamental idea behind the infrared method is to apply an infrared (IR) beam to the sample and measure the intensity of the light absorbed by the vibration of the atoms.Each molecule has a level of energetic vibration because electronic transitions between vibrational levels are correlated to particular wavenumber. 77Depending on the nature of the bonds in the molecule, atom oscillations can be harmonious or disharmonic.In this way, knowing the vibrational frequencies gives access to the molecular structure.The quantized energy levels related to the corresponding vibrational frequencies of the molecule are its possible vibrational states.1][82][83] Note that the harmonic oscillator frequencies are given by Hooke's law. 84or more comprehension of the physical state of the polymer electrolyte and the different phases, we have analyzed the PEO, LiTFSI, and the mixture PEO-LiTFSI by the IR technique.Figure 10 shows the vibration nodes of the functional groups in PEO and LiTFSI at various temperatures.Indeed, the bonds in molecules vibrate under an active energetic solicitation.Depending on the chemical nature of the bond and the properties of atoms involved in the molecules, the stiffness of the chemical bonds can be strong or weak, and the resulting frequencies allow the identification of the atomic organization. 77Figure 10 shows that the IR spectra of pure PEO and LiTFSI and the mixture PEO-LiTFSI present various peaks and bands.
(i) In Fig. 10a, at the wavenumber 3394 cm −1 , the PEO exhibits an intense IR peak corresponding to the stretching vibrations of the hydroxyl group present in the polymer chains.6][87] The peak intensities for wavenumbers from 1000 to 700 cm −1 and those from 1500 to 1300 cm −1 almost decrease at temperatures above 60 °C.Furthermore, the shape of the peaks becomes asymmetric and broader after 60 °C.This is because the solid state's stiffness is higher than the liquid state.According to the DSC results, the fusion of crystallites in the pure PEO starts at 60 °C; thus, we can conclude that the chemical functions C-O-C and -CH 2 O induce the crystallization of the semi-crystalline polymer.In addition, Irina et al. have previously shown that the functional group CH 2 vibrations are also characteristic of crystalline PEO. 87ii) In Fig. 10b, the functional groups in LiTFSI, especially the anions TFSI -, vibrate at different wavenumbers.The functional groups in the anions TFSI -are found from 2700 to 700 cm −1 . 77,86,88,89Remarks that adding the LiTFSI in PEO changes the intensity and the shape of the peaks of C-O-C, confirming oxygen atoms' implication in LiTFSI solvation.For wavenumbers between 2100 and 1400 cm −1 , the pure LiTFSI IR peak intensities are mainly impacted by the temperature transition from 20 to 50 °C.Indeed, for operating temperatures above 50 °C, the crystallites of peak 2 of LiTFSI found from DSC results are melted.Therefore, comparing the infrared peaks at 20 °C with those above 50 °C, the chemical functions at wavenumbers between 2100 and 1400 cm −1 , i.e., -CF 3 and SO 2 -N, could be at the origin of DSC's peak 2 crystallites.(iii) Figure 10c shows that the wavenumbers of all peaks in the spectrum of the mixture PEO-LiTFSI at weight fraction 9 wt% remain conserved with rising temperature.Furthermore, the PEO's peaks obtained through infrared analysis are conserved, which confirms the thermal stability of the mixture PEO-LiTFSI at w e = 9 wt% and the complete solvation of LiTFSI by PEO.than 2000 cm −1 , IR peaks of both PEO and LiTFSI were observed in the mixture.The DSC results show that the LiTFSI is completely solvated in the PEO at 33 wt%; consequently, functional groups of LiTFSI at wavenumber from 4000 to 2000 induce the crystallization of the LiTFSI in the PEO (i.e., S-CF 3 , -CF 3 , and SO 2 -N).(v) As for the binary mixture of Fig. 10e, i.e., mixture at 70 wt% of LiTFSI, we notice a slight variation in the intensities of IR peaks.Moreover, the wavenumbers of the IR peaks are similar to those found in pure LiTFSI with certain peaks of PEO.This leads us to conclude that LiTFSI induces the crystallization of PEO-LiTFSI in this domain.Additionally, we observe a drop in the chemical function's strength at wavenumbers between 2100 and 1400 cm −1 in the mixture of PEO and LiTFSI at w e = 70 wt% due to the complete solvation of the crystallites of these functional groups (see Fig. 10b for the concerning functional groups).
Figure 10 highlights the non-dependence of the internal vibration wavenumbers on temperature.It is evident that a rise in temperature changes the distance between the chains of the polymers and, consequently, changes the intensity and the shape of the lattice vibrational frequencies.The spectrum of molten polymer shows a characteristic band of amorphous material.It is proved that LiTFSI is solvated by oxygen atoms of PEO. 47,54We understand why the LiTFSI contributes to the de-crystallization of PEO.

Conclusion
The physical state, including the corresponding physical phase of the polymer electrolyte, is an essential factor influencing the performance of the resulting batteries.This study showed that: (i) The glass transition temperature depends mainly on the molecular weight of the polymer solvent.However, increasing the salt weight fraction in the mixture can increase the T g .(ii) The melting point of PEO-LiTFSI depends mainly on the salt weight fraction.Through DSC thermograms, we defined the different physical states and deduced the degree of crystallinity of the solid state of the PEO-LiTFSI system according to the working temperature and the salt weight fraction.Pure PEO presents one crystallite type, while pure LiTFSI has four types.However, LiTFSI can decrease or increase the degree of crystallinity of the resulting electrolyte depending on its weight fraction.When w e ⩽ 33 wt%, crystallites observed were attributed to free PEO not or partially involved in the solvation of the lithium salt.In contrast, when w e is higher than 50 wt%, the crystallites are reformed and could be associated with the small and heterogeneous sizes of LiTFSI adducts LiTFSI with PEO.The liquid state of the binary combination requires more research.More studies on the chemical properties of the binary mixture at a high weight fraction of lithium salt may provide information on the possible chemical bond formation and the stability of the complexes.The theoretical and experimental investigation we do centers on the determination of the physical state.Although the DSC analysis portion provides a method for studying PEO-LiTFSI, it is clear that more electrochemical analyses are required to confirm the material's usefulness as an electrolyte in solid-state batteries.

Appendix
Demonstration of the formula used for evaluating the degree of crystallinity According to the Euler law, the total enthalpy variation of an electrolyte is given by the sum of the enthalpy variation of each phase transition of each crystallite (i.e., solid to liquid), as introduced by the Eq.A•1.
Where: ΔH i and i χ are, respectively, the melting enthalpy and the mass fraction of the crystallite (i) in the electrolyte presenting number (k) crystallites, and H ∆ is the melting enthalpy of the electrolyte.Supposing that the electrolyte contains simultaneously crystallites of PEO and that of LiTFSI complexed PEO chains, Eq.A•1 becomes Eq.A•2 Where m c_PEO and m c_LiTFSI_PEO are the mass of crystallites of PEO and that of LiTFSI complexed PEO chains, respectively.m PEO and m are the mass of the PEO and electrolyte respectively.Eq.A•2 can be rewritten by Eq.A•3.

0
the properties of the polymer (kg.mol −1 .°C)m c_PEO Mass of PEO crystallites (kg) m c_LiTFSI_PEO Mass of complexed LiTFSI coated in PEO crystallites (kg) m Mass of the electrolyte (kg) M w Molecular weight of PEO (kg/mol) R Gas constant (J/(K*mol)) T g Glass transition temperature of the pure PEO (°C) T g 0 ∞ Glass transition temperature of pure PEO at infinite M w (°C) T g Glass transition temperature of the polymer electrolyte (

Figure 1 .
Figure 1.Schematic representation at PEO chains scale of a semicrystalline electrolyte.

Figure 2 .
Figure 2. Schematic representation of the temperature dependence: (i) on the enthalpy of the solid electrolyte, and (ii) on an evolution of the crystalline "chains state."

Figure 3 .
Figure 3. Theoretical DSC thermogram obtained during the heating process of (a) semi-crystalline polymer electrolyte and (b) amorphous polymer electrolyte.

Figure 4 .
Figure 4. DSC thermograms of the PEO200K-LiTFSI electrolyte at various temperature scan rates with w e = 50 wt%.

Figure 8 .∞ 0 ∞∞
Figure 8. Glass transition temperature dependence on the weight fraction of lithium salt for various molecular weights of PEO.Blue diamonds: present study 200 kg mol −1 ; red stars: Stolwijk et al. 8000 k g mol −131 ; black triangles: Lascaud et al. 37 ; Continuous line (i), (ii), and (iii) proposed predictive model of T g .

∞
is the modified value of T g 0 by adding the salt in the PEO -K el is the modified value of K 0 by squared w e α is a physical constant The parameters T , g el ∞ and K el represent how much the K 0 and T g 0 ∞ of the glass transition temperature of PEO are modified by the LiTFSI.Physically, the parameter α is the equilibrium weight fraction at which the impact of salt on the infinite glass transition is equilibrated.The parameter T g el ∞ present dimension of temperature (°C) and the parameter K el dimension of temperature multiplied by the dimension of molecular weight (kg.mol −1 .°C).The parameters (T , g el ∞ α, and K el ) introduced into the empirical law are deduced using MATLAB software and the least squared methodology to obtain the smallest value of the root mean squared error.

(
See appendix for more details on the equation).
of crystallinity of the PEO versus the amount of PEO ( PEO χ′ ), and the term m m c_PEO_LiTFSI that of complexed LiTFSI ( LiTFSI_PEO χ).Finally, we obtain the Eq.A•4.

Table I .
Table of characteristic melting enthalpy variation of the lithium salt LiTFSI.

Table II .
Melting point and enthalpy of the binary mixture PEO-LiTFSI as a function of the salt weight fraction w e .

Table III .
et al. as ECS Advances, 2023 2 040509 Degree of crystallinity (χ) of the PEO-LiTFSI polymer electrolyte as a function of the weight fraction of lithium salt (w e ).