Additive effect of fluoroethylene and difluoroethylene carbonates for the solid electrolyte interphase film formation in sodium-ion batteries: a quantum chemical study

Abstract

Sodium (Na)-ion batteries (NIBs) are attracting noticeable interest in recent years as post lithium (Li)-ion batteries (LIBs) due to the “unlimited” abundance of sodium in the Earth's crust. To improve the performance of secondary batteries, solid electrolyte interface (SEI) film-forming additives in electrolyte solutions are widely used in general and fluoroethylene carbonate (FEC) additive is known to increase the NIB performance, while difluoroethylene carbonate (DFEC) is inefficient in spite of it being a similar molecule substituted by only one fluorine atom. Such fine behavior of electrolyte additives in the NIBs is not thoroughly understood, i.e., the FEC–DFEC mystery. In this article, to understand the chemical roles of these additives atomistically, we have investigated the reduction decomposition mechanism of three complexes, i.e., Na⁺ coordinated propylene carbonate (Na⁺–PC), Na⁺–FEC and Na⁺–DFEC using sophisticated computational methods. The activation energy barriers of Na⁺–PC, Na⁺–FEC and Na⁺–DFEC are found in the gas phase as 11.696, 7.050, and 15.125 kcal mol⁻¹ respectively, while, in solution phase (PC as solvent of dielectric constant 64.4), those barriers become 9.993, 6.594 and 14.012 kcal mol⁻¹ respectively. Because the lower activation barrier of FEC facilitates the faster decomposition than those of PC and DFEC, it is clearly expected that the faster decomposition of FEC than that of PC must be one of the important factors necessary to improve the SEI film formation. However, DFEC reductive decomposition is slower than those of PC and FEC due to its higher activation energy barrier. Another important factor is that the DFEC decomposition does not yield NaF, whereas FEC does on its decomposition. This could also be a key reason why FEC is a better additive than DFEC.

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1. Introduction

Rechargeable lithium (Li)-ion batteries (LIBs) have become successful and sophisticated energy storage devices as secondary batteries since the last two decades. The operating principle of the LIB is currently considered as the key technology for electric vehicle propulsion, while, in parallel, its efficiency and safe performance is starting to be evaluated for stationary applications.¹ However, the implementation of a Li-based technology for mass storage faces an important challenge linked to Li availability. Since the Li element in LIB is a rare metal, its cost has increased with the growth in demand. There is a concern that Li resources cannot cope over the next decades with the foreseen staggering energy storage demands. In anticipation of such a scenario, new sustainable chemistries must be developed, and the most appealing alternative is to use sodium (Na)-ion batteries (NIBs) as a replacement for LIBs, because the Na element is very abundant on Earth.^2,3 In addition, there are several reasons to use sodium instead of lithium; such as the intercalation chemistry of sodium is similar to that of lithium and it is an element easy to recycle. Besides them, the structures, components, systems and charge storage mechanisms of NIBs are similar to those of LIBs, except that Li-ions are replaced with Na-ions. While the energy density of NIBs will always fall short that of LIBs, it is certainly an option for the large-scale applications owing to the lower cost.⁴

In the secondary batteries, the decomposition of liquid electrolyte molecules during the initial charging processes results in the formation of solid electrolyte interphase (SEI) film on the anode surface. Since the SEI film highly determines crucial properties of the battery such as cycle performance, stability and safety, the study of microscopic formation processes and structures of the SEI film became one of the key areas of research in the performance and development of NIBs. Although the progress in the Na intercalation chemistry is analogous to that in the Li one,⁵ the study of Na-based systems sometime falls into oblivion due to the rapid advent and success of the Li-ion technology. However, for sustainability reasons, the Na-based technology has recently recaptured the scientific community's attention.^6–8 In spite of a large number of efforts directed to the search for new electrode materials for NIBs, the studies dealing with the electrolytes are scarce. However, the available studies on the electrolytes demonstrated that the SEI film formed on the carbonaceous electrodes is different between in the Na-based and in Li-based electrolytes even on using the same electrolytes.^6,9

Thus, by designing better electrolyte for NIBs, it is possible to enhance the energy/power density and the cycle life of NIBs. However, there has been very few experimental studies on designing electrolytes devoted in the area of NIB research. In an early study on the electrolyte solvents by Alcàntara et al.,¹⁰ it was revealed that the tetrahydrofuran (THF)-solvent and a mixture of ethylene carbonate (EC)/THF improve the cycle performance compared to the EC/dimethyl carbonate (DMC) and 1,2-dimethoxyethane (DME) electrolytes. In another study on electrolyte solvents with NaClO₄, it was shown that the propylene carbonate (PC) and the EC/diethyl carbonate (DEC) electrolyte mixed solution exhibits high reversible capacity, while the EC/DMC and EC/ethyl methyl carbonate (EMC) electrolyte solution mixtures exhibit insufficient performance.⁶ Palacin and co-workers also tested various electrolyte solutions by changing the Na salts, solvents and solvent mixtures using three electrode cells. As a result, it was proved that the best cyclic performance is shown in case of NaClO₄ dissolved in the cyclic carbonates such as EC and PC.¹¹ Recent study proved that the primary radical dissociation products of EC and PC electrolyte readily form secondary and tertiary radicals by the sequential addition of electrons. These radicals favors the formation of polymeric products.¹² The aforementioned experimental observations showed that the distinct behavior of electrolytes can influence the SEI film formation on their decomposition during the initial cycles. Thus, there is a need to understand the mechanistic details of electrolytes to design better electrolytes for NIBs.

In addition to electrolytes, another key material to improve the performance of NIBs is electrolyte additives. The film-forming additives into electrolyte solutions are widely used to improve the performance of LIBs.^13–16 For example, vinylene carbonate (VC), fluoroethylene carbonate (FEC), ethylene sulfite (ES) and trans difluoroethylene carbonate (DFEC) are well-known electrolyte additives for LIBs.^14–19 In a recent study, it was revealed that the FEC is also an efficient electrolyte additive to improve the reversible capacity of NIBs. However, other additives such as VC, ES and DFEC showed the insufficient performance.¹⁹ Previous studies clarified that PC electrolyte and additives such as FEC and DFEC decomposed by electro-reduction during the SEI film formation in NIB.^2,19 The above studies prove that the film forming additives have a significant role on the performance of NIBs, as the reductive decomposition products of additives effectively contribute to the SEI film formation.

To reveal the reductive decomposition mechanism, checking the feasibility of reaction steps and eventually finding the kinetically and thermodynamically favorable mechanisms for electrolyte decomposition, computational studies are necessary. In this regard, various computational studies are devoted to understand the reductive decomposition mechanism of electrolytes in LIBs such as the two-electron reduction pathway of EC (or PC) producing Li₂CO₃ and ethylene (or propylene) gas and one-electron reduction pathway, producing the lithium alkyl bicarbonate and ethylene (or propylene) gas as major products.^20,21 In a recent study, the co-existence of one- and two-electron reductive decomposition pathways of EC (or PC) was proposed.²² A possible two-step reduction mechanism of EC including a two-electron process followed by a one-electron process was also proposed.²³

However, previous experimental studies revealed a conflicting behavior on the performance of various additives in NIBs. It is interesting that the fluorine-substituted ethylene derivatives such as FEC and DFEC show conflicting behavior in NIBs,¹⁹ because these derivatives differ only in the number of fluorine atoms. Precisely, the FEC additive improved the NIBs performance, while DFEC shows no beneficial effect. The previous experimental studies could not explain the reasons behind the conflicting behavior of these fluorine-substituted additives why such a small difference in the number of substituted fluorine atoms could result in two different electrochemical extremes. To reveal this FEC–DFEC mystery, it is essential to know the effect of fluorine atom on the reductive decomposition of FEC and DFEC during the SEI film formation. To the best of our knowledge, there is no study which deals with the reductive decomposition of electrolytes in NIBs. Thus, in this article, we have studied theoretically the reductive decomposition mechanism of Na⁺–PC, Na⁺–FEC and Na⁺–DFEC complexes, for the first time, by carrying out the sophisticated density functional theory (DFT) calculations.

2. Theoretical methodology

According to the previous studies on the reduction energy profiles of various electrolytes in LIBs,^24–29 all geometry optimizations of the intermediates (INs) and transition states (TSs) were performed using the density functional theory (DFT) method at B3LYP/6-311++G(d,p) calculation level. The present theoretical method has been applied because it predicts the reaction energies very well in comparison to ab initio methods for reductive ring-opening of electrolytes in LIB with favorable balance between accuracy and computational efficiency.^29,30 To confirm INs and TSs, the vibrational frequency analysis calculations were performed with the same method and basis set as those for the geometry optimizations. The Gibbs free energies, hereafter “free energy”, were calculated at 298.15 K. To obtain the solvation free energies, we performed single point calculations within the universal solvation model SMD,^31,32 by using the DFT-B3LYP/6-311++G(d,p) level of theory on the gas phase B3LYP/6-311++G(d,p) optimized geometries. In this study, the PC electrolyte was represented by a dielectric continuum with a “dielectric constant” (ε) 64.4. Then, the solution phase refers hereafter to the PC solution phase throughout this article. Free energies of reactant species in solution G^(s)₂₉₈ were obtained by adding the SMD free energies of solvation to the gas phase free energies of the reactant species. It should be noted that, to the best of our knowledge, there is no report for the solvation free energy of an electron in the electrolyte system that we will discuss in the present study. Thus, we adopted the free energy of an electron in water. Such approach was also used in the previous studies.^25,29 The Gaussian 09 package was used for all calculations in the present study.³³

3. Results and discussion

We initially discuss about the reduction potentials and frontier molecular orbital energies of electrolyte molecules, and it is followed by the detailed discussion of one- and two-electron reduction mechanisms of PC, FEC and DFEC complexes.

3.1. Reduction potentials of PC, FEC and DFEC: additives are reduced prior to solvent PC electrolyte

To predict the reduction potentials (E⁰) of reactant species, we have used a thermodynamic cycle as shown in Scheme 1.^34,35,47 In this cycle, ΔG_sol(S) and ΔG_sol(S⁻) are the solvation free energies of a molecule S and its anion S⁻, respectively, and ΔG^red_gas is the redox free energy difference in gas phase. The solvation free energy difference ΔG^red_sol of the reduction reaction is calculated as follows,

ΔG^red_sol = ΔG_sol(S⁻) + ΔG^red_gas − ΔG_sol(S). (1)

Scheme 1 The thermodynamic cycle used for the calculation of reduction potentials.

The reduction potential E⁰ of the molecule can be related to ΔG_sol as follows,

where F is Faraday's constant and 1.73 is the numerical value of absolute reduction potential at 298.15 K related to the Na/Na⁺ reference electrode in volts. The absolute reduction potentials of Na/Na⁺ and Li/Li⁺ were calculated by combining the standard electrode potentials of Li/Li⁺ 3.05 V (ref. 36) and Na/Na⁺ 2.71 V (ref. 37) with the standard hydrogen electrode potential 4.44 V.³⁶ The above procedure results in the absolute reduction potentials as 1.39 V and 1.73 V for Li/Li⁺ and Na/Na⁺ electrodes respectively. It is worth noting, however, that in some previous studies, the absolute reduction potential for Li/Li⁺ was considered as 1.46 V to obtain the reduction potential of PC.^25,29

Table 1 depicts the calculated reduction potentials and frontier molecular orbital energies of PC, FEC and DFEC with reference to the Na/Na⁺ reference electrode. To validate the present calculation results, we have calculated the PC reduction potential with reference to the Li/Li⁺ reference electrode (1.39 V). In the present study, the PC reduction potential with respect to Li/Li⁺ reference electrode is 1.31 V. This value reproduces well the experimental value from 1.00 to 1.60 V in LIBs.³⁸ This reveals that the computational procedure used for the estimation of reduction potentials in the present study is good enough to reproduce the experimental reduction potentials. Among the calculated reduction potentials (see Table 1) of single electrolyte molecules with reference to the Na/Na⁺ electrode, it was found that PC molecule has the lower reduction potential (0.97 V) than in the FEC and DFEC molecules, while FEC molecule does the highest reduction potential (1.37 V) in the three.

Table 1 Calculated reduction potentials of PC, FEC and DFEC (E⁰ in V) and the frontier molecular orbital energies (in eV) for PC, FEC and DFEC (E⁰ of Na⁺-complexes of Na⁺–PC, Na⁺–FEC and Na⁺–DFEC are given in parentheses)

Compounds	E^0	Frontier molecular orbital energy
		HOMO	LUMO
PC	0.97 (1.66)	−8.364	−0.599
FEC	1.37 (1.83)	−8.974	−0.641
DFEC	1.35 (1.89)	−9.467	−0.659

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On the other hand, we have also estimated the reduction potentials of Na⁺-coordinated electrolyte molecules, i.e., Na⁺–PC, Na⁺–FEC and Na⁺–DFEC (Table 1). As a result, the Na⁺–DFEC complex showed higher reduction potential (1.89 V) than Na⁺–FEC, followed by Na⁺–PC. These results suggest that the additives such as FEC and DFEC molecules can be earlier reduced on the anode surface than PC molecules during the charging process. Moreover, the low-lying LUMOs of FEC and DFEC also imply their readiness to be reduced prior to PC. The decomposition mechanism of PC electrolyte molecules with these additives will be discussed clearly in the following sections.

3.2. Reduction mechanism of PC: two-electron reduction of PC forms Na₂CO₃ and propene

Scheme 2 represents the possible reductive decomposition pathways of Na⁺–coordinated PC complex. To elucidate the mechanism of bond breaking in the Na⁺–PC complex during the electrochemical reduction process, those bond orders of a Na⁺–PC complex (PC–IN1) and a Na⁺–PC⁻ (PC–IN2) after obtaining an electron were calculated using the natural population analysis (Table 2). All the bond orders decreased in the Na⁺–PC⁻ complex (PC–IN2), showing the elongation of its bonds after obtaining an electron. In addition, it is evident from the smaller bond order of the C₍₄₎–O₍₃₎ bond, that this bond is weaker than the other bonds in PC–IN1 and PC–IN2 complexes.

Scheme 2 Schematic representation of two-electron reduction mechanism of Na⁺–PC.

Table 2 Calculated bond orders of Na⁺–PC and Na⁺–PC˙ complexes after obtaining an electron using the natural population analysis

Bonds	Bond order
	Na^+–PC (PC–IN1)	Na^+–PC˙ (PC–IN2)
C(4)–C(5)	1.987	0.994
C(4)–O(3)	1.978	0.991
C(5)–O(1)	1.982	0.992
C(2)–O(1)	1.993	0.995
C(2)–O(3)	1.992	0.995

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On the basis of the bond order analysis and the previously proposed reaction mechanism of PC in LIBs,^39–41 we have considered similarly the dissociation of C₍₄₎–O₍₃₎ bond of Na⁺–PC complex to form an open anion radical (PC–IN4). In further reaction, PC–IN4 can dissociate by two possible pathways as described in Scheme 2 by the cleavage of C₍₅₎–O₍₁₎ bond which results in Na₂CO₃ and propylene gas as final products (Route P1). This pathway is similar to the previously proposed decomposition mechanism of Li⁺-coordinated Li⁺–EC and Li⁺–PC complexes.^{20,22,36–41} On the other hand, PC–IN4 can also dissociate by the cleavage of C₍₂₎–O₍₁₎ bond (Route P2) which proceeds through a transition state (PC-TS7) to form CO₂ and 2-methyloxirane as final products.

In comparison with the two possible reaction pathways of PC–IN1 energetically in gas phase (see Fig. S1 in ESI†), it was understood that Route P2 proceeds via a high activation energy barrier (51.909 kcal mol⁻¹), while Route P1 has no reaction barrier. Thus, from above discussion, it can be said that Route P1 is the favorable reaction pathway in gas phase. In Route P1, the reaction proceeds by two-electron reduction mechanism where two electrons were sequentially added to the Na⁺–PC complex. Similar treatment such as sequential addition of two electrons was attributed for the two-electron reduction mechanism of Na⁺–FEC and Na⁺–DFEC also in the present study. The reduction energy profile of Route P1 was illustrated in Fig. 1. In this mechanism, PC–IN1 is directly reduced to form a stable product (PC–IN2). Further, this intermediate forms an open anion radical due to the cleavage of C₍₄₎–O₍₃₎ bond, through a transition state (PC-TS3) with an activation barrier of 11.696 kcal mol⁻¹ in gas phase (Table 3). On the contrary, in the solution phase, the PC–IN1 is more easily reduced to form a more stable product relative to PC–IN2 than that in gas phase. Further, this reaction proceeds through a small energy barrier (9.993 kcal mol⁻¹) and forms an open anion radical (PC–IN4). This radical further reduced to form the terminated product (PC–IN5) by accepting the second electron. Upon optimizing PC–IN5 after the addition of Na⁺ ion, the final products Na₂CO₃ and propylene gas are directly formed through a barrierless reaction. It is consistent with the previous report that similar barrierless reactions were proposed for the Li⁺-coordinated EC and PC electrolyte reduction mechanism.^25,41

Fig. 1 Potential energy profile (ΔE in kcal mol⁻¹) in gas phase at the B3LYP/6-311++G(d,p) level of theory and the corresponding solvation Gibbs free energies (ΔG_sol in kcal mol⁻¹, underlined) at the SMD-B3LYP/6-311++G(d,p)//B3LYP/6-311++G(d,p) level of theory for the possible reductive decomposition process of Na⁺–propylene carbonate (Na⁺–PC) (Route P1).

Table 3 Calculated activation barrier energies (in kcal mol⁻¹) of the Na⁺–PC, Na⁺–FEC and Na⁺–DFEC complexes in gas phase and PC solution phase

Reaction	Activation barrier energy
	Gas phase	PC solution phase
Na^+–PC
PC–IN2 → PC–IN4	11.696	9.993
Na^+–FEC
FEC–IN2 → FEC–IN4	7.050	6.594
FEC–IN4 → FEC–IN6	6.530	5.802
FEC–IN7 → FEC–IN9	6.271	4.783
FEC–IN2 → FEC–IN11	11.868	10.139
FEC–IN12 → FEC–IN14	81.848	80.888
Na^+–DFEC
DFEC–IN2 → DFEC–IN4	15.125	14.012
DFEC–IN5 → DFEC–IN7	1.581	0.839
DFEC–IN2 → DFEC–IN10	22.683	21.829
DFEC–IN10 → DFEC–IN12	8.929	8.451
DFEC–IN13 → DFEC–IN15	5.949	4.841
DFEC–IN13 → DFEC–IN17	10.785	8.884

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In the solution phase, this process was estimated to proceed through a small energy barrier unlike in the gas phase. Then, the final products (PC–IN6) were formed from PC–IN5 through barrierless reaction. However, in the solution phase, the addition of the second electron brought about the less stable reduced product which, upon adding Na⁺ ion to the reduced product, instantly led to the stable final products (PC–IN6). Finally, it is concluded that the overall reaction of PC decomposition mainly passes through a transition state (PC-TS3) to form an open anion structure by the cleavage of C–O bond of PC–IN2 and is exoergic in both gas phase and the solution phase.

3.3. Reduction mechanism of FEC: FEC decomposes through one-electron reduction

We have investigated the possible one- and two-electron decomposition mechanisms of Na⁺–FEC complex, which is known to be a promising additive for improving the SEI films on the graphite surfaces in NIBs.¹⁹ The possible decomposition pathways of FEC are shown in Scheme 3. In this scheme, by accepting one electron, the FEC molecule is initially reduced to form FEC–IN2, which can further dissociate mainly in four different pathways, i.e., Route F1 to Route F5.

Scheme 3 Schematic representation of possible one- and two-electron reduction mechanisms of Na⁺–FEC.

Both Route F1 and Route F2 are similar to the previously proposed FEC decomposition mechanism in LIBs.⁴² In Route F1, the dissociation of C₍₂₎–O₍₃₎ bond leading to the ring cleavage forms an open anion radical (FEC–IN4). This is a multi-step reaction, which leads to removal of F⁻ anion followed by the release of CO₂ and an organic radical. The overall reaction proceeds through one-electron reduction mechanism. The final products (FEC–IN9) can be further reduced, and should become a part of the SEI film. Indeed, CO₂ reduction may yield an oxalate (C₂O₄²⁻), as reported in some studies.^43,44 The CHOCH₂˙ in FEC–IN9 is an active free radical, which reacts with other reaction species, forming polymer products.⁴² In Route F1, a NaF complex is formed by F⁻ anion reacting with Na⁺ cation.

On the other hand, FEC–IN2 can also dissociate through the C₍₅₎–O₍₁₎ bond cleavage so as to form an open anion radical FEC–IN11, similar to PC and EC products (e.g. PC–IN4 in Scheme 2) in LIBs,.^20–23 This mechanism (Route F2), follows two-electron reduction and forms Na₂CO₃ and fluoro alkene as final products, i.e., FEC–IN15. FEC–IN2 has also a chance to proceed to the dissociation of C₍₄₎–O₍₃₎ bond in Route F4 (Scheme 3), which forms an open anion radical FEC–IN19, showing further reduction leading to FEC–IN20. Another reaction pathway (Route F5) involves the elimination of hydrogen fluoride (HF) from FEC to form vinylene carbonate (VC), i.e., FEC–IN22.

To elucidate the adequacy of reaction pathways represented in Scheme 3, we have investigated their potential energy profiles in the gas phase and they are depicted in Fig. S2.† This results clearly indicate that the initial formation of FEC–IN4 via FEC-TS3 transition state is the most favorable reaction pathway (Route F1) with a lower activation energy barrier than those in the other reaction pathways. Along with Route F1, Route F2 is the next lower activation barrier reaction and is a similar pathway proposed for the FEC decomposition in LIBs.⁴² On the basis of these findings in gas phase, we further discussed Route F1 and Route F2 in detail in both gas and the solution phase.

3.3.1. FEC reaction: Route F1. In the FEC reaction, Route F1 proceeds through one-electron reduction as shown in Scheme 3, and its reduction potential energy profiles were depicted in Fig. 2. In this mechanism, the FEC molecule was directly reduced to form a reductive reaction product (FEC–IN2). As discussed in the Subsection 3.1., based on the reduction potential, it is clear that FEC is more easily reduced on the anode surface than PC. In gas phase, the reduced product further decomposes to form an open anion radical (FEC–IN4) by the cleavage of C₍₂₎–O₍₃₎ bond through a transition state (FEC-TS3) with an energy barrier of 7.050 kcal mol⁻¹ (Table 3). In the solution phase, this reaction occurs through a lower energy barrier (6.594 kcal mol⁻¹) compared to in gas phase. In the next process, FEC–IN6 is formed by breaking the C₍₄₎–F₍₇₎ bond of FEC–IN4. This reaction proceeds through a transition state FEC-TS5 with 6.530 kcal mol⁻¹ of an activation energy (Table 3). Such F⁻ anion can react with Na⁺ ion so as to form a NaF complex, which is similar to the LiF formation in LIBs.^22,23

Fig. 2 Potential energy profiles (ΔE in kcal mol⁻¹) at the B3LYP/6-311++G(d,p) level of theory and Gibbs free energy (ΔG_sol in kcal mol⁻¹, underlined) at the SMD-B3LYP/6-311++G(d,p)//B3LYP/6-311++G(d,p) level of theory for possible reductive decomposition process of Na⁺–fluoroethylene carbonate (Na⁺–FEC).

In solution, FEC–IN6 was formed via the activation barrier of 5.802 kcal mol⁻¹, which is slightly lower than that in gas phase. In both gas and the solution phases, FEC–IN4 is the stable intermediate than the others. In the following processes, we removed the NaF complex from the product, and reoptimized the geometry to FEC–IN7 to initiate the C₍₅₎–O₍₁₎ bond dissociation in a separate intermediate. In the next process, FEC–IN7 decomposed into CO₂ and CHOCH₂˙ radical by breaking the C₍₅₎–O₍₁₎ bond through FEC-TS8 transition state to the final product (FEC–IN9). This activation energy is 6.271 kcal mol⁻¹ in gas phase, while it became lower in the solution phase (4.783 kcal mol⁻¹) refer Table 3 for activation energies. Apart from this, FEC–IN7 forms CO by the cleavage of C₍₂₎–O₍₁₎ bond (Route F3) via FEC-TS16 transition state with 18.978 kcal mol⁻¹ activation energy in gas phase (Fig. S2†). The formation of CO proceeds by higher activation energy than the formation of CO₂. Thus, in gas phase, the formation of CO₂ is more favorable than that of CO in Route F3. Overall, the electrolyte solvent (PC in the present article) significantly affected the reductive decomposition processes, where all reaction products were less stable in the solution phase in comparison to those in gas phase. On the other hand, smaller activation energies in the solution phase indicate that the decomposition of FEC easily occurs in the solution phase compared to in gas phase.

3.3.2. FEC reaction: Route F2. Scheme 3 illustrates the two-electron reduction mechanism of FEC as shown in Route F2. The reduction reaction energy profile is depicted in Fig. 2. By accepting an electron, the FEC molecule formed a reduced product (FEC–IN2). FEC–IN2 is further reduced by breaking the C₍₅₎–O₍₁₎ bond, similar in the way of PC and EC electrolyte decomposition.^21–23 This process leads to the ring opening and the formation of an open anion radical complex (FEC–IN11) through the transition state (FEC-TS10) with an activation energy of 11.868 kcal mol⁻¹ (Table 3). In the next process, further reduction of FEC–IN11 occurred by accepting the second electron, leading to the reduced reaction product (FEC–IN12). This FEC–IN12 is more stable than other intermediates in the present reaction pathway. This intermediate should have longer life time because the further reaction is not favorable due to its high activation energy (81.848 kcal mol⁻¹). Thus, FEC–IN12 complex may undergo the further reaction with another FEC–IN12 molecules or with other reaction products, which yields the formation of dimerization and polymerization products during the SEI film formation. This clearly indicates that the addition of further electron drastically stabilizes the open anion radical.

The decomposition of FEC–IN12 leads to stable final products in the following processes. However, because the C₍₄₎–O₍₃₎ bond cleavage in FEC–IN12 brought about the formation of FEC–IN14 complex through FEC-TS13 with a quite high activation energy of 81.848 kcal mol⁻¹ (Table 3), this succession of processes is not a feasible reaction pathway, meaning that such reaction may occur scarcely. In the solution phase, this reaction proceeds via lower reaction barrier of open anion radical formation than in the gas phase by 1.729 kcal mol⁻¹. The formation of FEC–IN14 via FEC-TS13 also proceeded via the smaller activation energy than that in gas phase by 0.688 kcal mol⁻¹. Similarly, in the solution phase also FEC–IN12 is the most stable intermediate.

Overall, in FEC reductive decomposition pathways, the one-electron reduction (Route F1) is more favorable with lower activation barrier than two-electron reduction of FEC. After the one-electron reduction of FEC–IN1, a C₍₂₎–O₍₃₎ bond of FEC–IN2 can easily undergo homolytic fission with lower activation energy (7.050 kcal mol⁻¹) than that of C₍₅₎–O₍₁₎ bond fission (11.868 kcal mol⁻¹) in gas phase. In one-electron reduction, all the activation barriers appeared below 7 kcal mol⁻¹ energy (Table 3), while the activation barriers increased in the two-electron reduction. Hence, it is clear from the present results that a FEC molecule can easily decompose through the one-electron mechanism and the two-electron mechanism is less favorable.

3.4. Reduction mechanism of DFEC: two-electron reduction is favorable in DFEC decomposition

Herein, we have investigated the possible one- and two-electron reduction decomposition pathways of DFEC as depicted in Scheme 4. To the best of our knowledge, there are no reports on the systematic study of DFEC reduction mechanism either in LIBs or in NIBs. Initially, a DFEC molecule is reduced by accepting one electron to form DFEC–IN2. Further, this reduced product can dissociate through two possible pathways. One is dissociation of C₍₄₎–O₍₃₎ bond, while another one is C₍₂₎–O₍₃₎ bond cleavage. In each pathway, the five-membered ring cleavage occurs so as to form an open radical anion.

Scheme 4 Schematic representation of possible one- and two-electron reduction mechanism of Na⁺–DFEC.

In Route D1, an open anion radical accepts an additional electron and forms DFEC–IN5. Then, DFEC–IN5 dissociates into DFEC–IN7 by the cleavage of C₍₅₎–O₍₁₎ bond. Finally, the addition of Na⁺ ion to DFEC–IN7 leads to final products such as Na₂CO₃ and difluoro alkene. On the other hand, in Route D2, DFEC–IN12 is formed by the cleavage of C₍₄₎–F₍₇₎ bond of a radical anion (DFEC–IN10). The F⁻ anion formed in the above step can react with Na⁺ ion in the electrolyte solution and forms the NaF complex. In the next process, DFEC–IN13 dissociates through two possible reaction pathways such as cleavage of C₍₅₎–O₍₁₎ and C₍₂₎–O₍₁₎ bonds. In the former reaction pathway (Route D2), the cleavage of C₍₅₎–O₍₁₎ bond forms CO₂ and CHFCHO˙ radical as final products. In the latter pathway (Route D3) the C₍₂₎–O₍₁₎ bond cleavage forms DFEC–IN17 complex. This complex is reduced by accepting the second electron to form DFEC–IN18. Finally, the addition of Na⁺ to DFEC–IN18 results into glyoxal and NaF as final products.

In Route D2 and Route D3, the NaF complex is one of the final products, however, such NaF complex formation is not observed in Route D1. The final products formed in Route D1 such as Na₂CO₃ and difluoroalkene, as well as the final products formed in Route D3 such as CO and glyoxal are stable products. However, the final products of Route D2 such as CO₂ and CHFCHO˙ are reactive, which may participate in further reactions.

3.4.1. DFEC reaction: Route D1. Fig. 3 depicts the reduction energy profile of Route D1 and this reaction pathway proceeds through the two-electron reduction mechanism. By accepting an electron, DFEC molecule forms a reduced product (DFEC–IN2). Then, DFEC–IN4 was formed by dissociating the C₍₄₎–O₍₃₎ bond of DFEC–IN2 via DFEC-TS3 transition state with 15.125 kcal mol⁻¹ (Table 3) of activation energy barrier in gas phase. In the next step, DFEC–IN4 accepts an electron to form an anionic product (DFEC–IN5). Then, DFEC–IN7 is obtained by the C₍₅₎–O₍₁₎ bond dissociation through DFEC-TS6 transition state with a quite small activation barrier of 1.581 kcal mol⁻¹. Finally, the addition of Na⁺ ion to DFEC–IN7 results in Na₂CO₃ and difluoroalkenes as final products (DFEC–IN8). In the solution phase, reactions of Route D1 proceed with smaller reaction barrier than those in the gas phase. For example, the ring-opening reaction from DFEC–IN2 to DFEC–IN4 proceeds through the activation barrier of 14.012 kcal mol⁻¹ in the solution phase (Table 3), which is smaller than the activation barrier in gas phase (15.125 kcal mol⁻¹). Upon the second electron reduction, DFEC–IN4 gave a less stable DFEC–IN5 in electrolyte solution. The C₍₅₎–O₍₁₎ bond dissociation in solution phase occurs with smaller activation energy barrier than that in gas phase. Overall, this reaction follows by small activation barriers in the solution phase.

Fig. 3 Potential energy (ΔE in kcal mol⁻¹) at B3LYP/6-311++G(d,p) level of theory and Gibbs free energy (ΔG_sol in kcal mol⁻¹, underlined) at SMD-B3LYP/6-311++G(d,p)//B3LYP/6-311++G(d,p) level of theory for possible reductive decomposition process of Na⁺–difluoroethylene carbonate (Na⁺–DFEC).

3.4.2. DFEC reaction: Route D2. The DFEC reaction Route D2 was shown in Scheme 4 and its reduction energy profile was depicted in Fig. 3. As depicted in Route D2, the reductive product DFEC–IN2 decomposed by opening the five-membered ring, to form an open anion radical (DFEC–IN10) through homolytic fission of C₍₂₎–O₍₃₎ bond via DFEC-TS9 transition state with the activation energy barrier of 22.683 kcal mol⁻¹ (Table 3). In the next process, F⁻ anion dissociates from DFEC–IN10 to form DFEC–IN12 through DFEC-TS11 transition state with the activation barrier of 8.929 kcal mol⁻¹ (Table 3). In the solution phase, DFEC–IN12 is formed via 8.451 kcal mol⁻¹ reaction barrier, which is slightly lower than that in gas phase. Further in this reaction, we removed the NaF from DFEC–IN12 to obtain DFEC–IN13 upon the reoptimization. The reactive open radical DFEC–IN13 yielded CO₂ and CHFCHO˙ radical by dissociating C₍₅₎–O₍₁₎ bond via DFEC-TS14. This reaction proceeds with small activation energy barrier (4.841 kcal mol⁻¹) in the solution phase than in the gas phase (5.949 kcal mol⁻¹). The lower reaction barriers in Route D2 indicate that the faster decomposition of Na⁺–DFEC in the PC electrolyte solvent. DFEC–IN13 can dissociate through either of the two reaction pathways one is the C₍₅₎–O₍₁₎ bond dissociation which forms CO₂ and CHFCHO˙ radical as final products and the other proceeds through the homolytic C₍₂₎–O₍₁₎ bond fission, that forms CO and glyoxal as final products (Scheme 4). The latter mechanism is discussed in the following section.

3.4.3. DFEC reaction: Route D3. Scheme 4 illustrates another DFEC two-electron reduction mechanism (Route D3), where the DFEC molecule decomposes into CO and glyoxal as final products (DFEC–IN19). The reduction energy profile was depicted in Fig. 3. As described in the previous section, DFEC–IN13 can also dissociate through C₍₂₎–O₍₁₎ bond. The dissociation of C₍₂₎–O₍₁₎ bond leads to CO and radical anion (DFEC–IN17) via the transition state DFEC-TS16 with the activation energy barrier of 10.785 kcal mol⁻¹ (Table 3). This radical DFEC–IN17 was further reduced by accepting one electron and formed a stable anion DFEC–IN18. DFEC–IN18 is the most stable intermediate than other reaction products in this reaction pathway (Route D3). The addition of Na⁺ ions to DFEC–IN18 formed glyoxal and NaF as final products by the dissociation of C₍₅₎–F₍₈₎ bond. The final step of this reaction is a barrierless reaction, where we could not find any transition state.

Overall, in the DFEC reductive decomposition pathways, Route D1 is favorable with a lower activation energy barrier (15.125 kcal mol⁻¹) of C₍₄₎–O₍₃₎ bond dissociation, while, Route D2 and D3, are not with a relatively high reaction energy barrier (22.683 kcal mol⁻¹).

3.5. FEC improves the SEI film formation, while DFEC shows trivial effect

As discussed in Section 3.1., both FEC and DFEC additives showed the higher reduction potentials than solvent PC. This means that these additives can be reduced prior to the PC molecules to dominate the SEI film formation by their breakdown products. However, the higher reduction potentials of these additives should not be an important reason for the inferiority of DFEC additive since they show the similar qualitative tendency. Thus, the differences in the energetics and the reaction products between these additives could be more essential to evaluate their role in the formation of effective SEI film in NIBs.

The decomposition reactions of these additives proceeded in the multistep reaction pathways. In the FEC-added PC electrolyte system, the FEC molecules decompose to form CO₂, CHOCH₂˙ radical and NaF products through one-electron reduction mechanism. This results support the findings in recent work of FEC decomposition in LIBs by Leung et al.⁴² On the other hand, in the DFEC-added PC electrolyte system, the DFEC molecules decompose via the two-electron reduction mechanism to form Na₂CO₃ and difluoroalkene products. The significant difference in the decomposition products of FEC and DFEC is the formation of NaF complex in FEC decomposition, whereas NaF complex is absent in the DFEC decomposition. Recent studies on LIBs suggest that LiF complexes play the role of glue in the organic SEI film components during the SEI film formation.⁴⁵ The F atoms of LiF complex form strong bindings with the Li atoms of multiple organic SEI film components and connect them.⁴⁵ In accordance with the above results, NaF can also act as a glue between the organic SEI film components, which form an effective SEI film in the FEC additive electrolyte system. Thus, the formation of NaF complex is likely to be related to the effectiveness of FEC in comparison to DFEC.

In the FEC-added system, the solvent PC molecules also decompose simultaneously with the FEC decomposition. In fact, the kinetically favorable FEC decomposition should be faster than PC electrolyte decomposition. Hence, the FEC-decomposed products have a chance to show a significant effect on the SEI film formation. On the other hand, in the DFEC-added system, the solvent PC molecules mainly decompose more due to their lower energy barrier and higher concentration than DFEC. Precisely, it is plausible that very less DFEC molecules can decompose until the SEI film can be formed to prevent the solvent PC molecules from their reduction on the anode surface. Therefore, in the DFEC-added electrolyte, the inactive DFEC molecules should play a role to produce large cavities during the SEI film formation. In conclusion, it can be said that the addition of DFEC has no significant impact on the performance of NIBs due to its lower reactivity than the PC electrolyte and the absence of NaF complex formation on its decomposition.

4. Concluding remarks

In gas phase, the FEC decomposition mechanism was found more favorable in one-electron reduction of Na⁺–FEC than in two-electron reduction owing to the former lower activation energy of C₍₂₎–O₍₃₎ bond homolytic fission (7.050 kcal mol⁻¹) than the latter of C₍₅₎–O₍₁₎ bond fission (11.868 kcal mol⁻¹). On the other hand, in the DFEC decomposition mechanism, the C₍₄₎–O₍₃₎ bond dissociation is more favorable owing to its lower activation energy barrier 15.125 kcal mol⁻¹ than the C₍₂₎–O₍₃₎ bond dissociation, which showed activation energy 22.683 kcal mol⁻¹. However, the C₍₄₎–O₍₃₎ bond dissociation of PC occurred with lower activation energy 11.696 kcal mol⁻¹ than the DFEC decomposition, which has also a higher activation barrier (15.125 kcal mol⁻¹) than the FEC one (7.050 kcal mol⁻¹).

In the solution phase, the reduction reactions of FEC, DFEC and PC become slightly faster than those in gas phase because of the decrease of activation energy less than 2 kcal mol⁻¹ in all complexes. Based on the these energetic results and products formed after decomposition, it can be concluded that, the FEC addition to the PC electrolyte should improve the performance of NIBs by enhancing the SEI film formation due to its favorable reduction decomposition with the lower activation energy barrier and the production of NaF complex, which should make the SEI film stable by gluing the organic SEI film components.⁴⁵ On the other hand, the addition of DFEC must show rather trivial effect on the performance of NIBs because of its less favorable decomposition, along with the absence of NaF complex. Thus, in the DFEC-added electrolyte system, the presence of inactive DFEC molecules should result in large cavities during the SEI film formation and reduce the stability of SEI film.

In addition, the FEC molecule yields F⁻, CHOCH₂˙ radical and CO₂ as final products, while DFEC molecule decomposes to form Na₂CO₃ and C₂H₂F₂ as the final products. In this case, the efficient association of FEC reaction products must be essential to form an effective and compact SEI film. To deeper understanding of FEC and DFEC additive effect in NIBs, the structural study on the molecular assembly of the reaction products during the SEI film formation is necessary. To deal with such molecular assembly of reaction products leading to the SEI film, we have recently proposed a new atomistic reaction simulation method, the hybrid Monte Carlo (MC)/molecular dynamics (MD) reaction method (or Red Moon method).⁴⁶ In fact, the hybrid MC/MD reaction method has been successfully applied not only to an interfacial polycondensation⁴⁷ but also to both LIBs⁴⁸ and NIBs⁴⁹ and provided theoretically the spatial structures of SEI films that cannot be easily observed in conventional experimental investigations.^48,49 Hence in the next study, we will investigate the SEI film formation in the DFEC-added PC electrolyte systems on the anode surface by considering the important findings in the DFEC reduction reactions clarified here.

Conflict of interest

The authors declare no competing financial interest.

Acknowledgements

This work was supported by the Core Research for Evolutional Science and Technology (CREST) of the Japan Science Technology Agency (JST); by a Grant-in-Aid for Science Research from the Ministry of Education, Culture, Sport, Science and Technology (MEXT) in Japan; and also by the MEXT programs “Elements Strategy Initiative for Catalysts and Batteries (ESICB)” and the FLAGSHIP2020 within the priority study5 (Development of new fundamental technologies for high-efficiency energy creation, conversion/storage and use).

References

1. R. Berthelot, D. Carlier and C. Delmas, Nat. Mater., 2011, 10, 74.
2. N. Yabuuchi, K. Kubota, M. Dahbi and S. Komaba, Chem. Rev., 2014, 114, 11636.
3. M. D. Slater, D. Kim, E. Lee and C. S. Johnson, Adv. Funct. Mater., 2013, 23, 947.
4. B. Dunn, H. Kamath and J.-M. Tarascon, Science, 2011, 334, 6058.
5. K. M. Abraham, Solid State Ionics, 1982, 7, 199.
6. S. Komaba, W. Murata, T. Ishikawa, N. Yabuuchi, T. Ozeki, T. Nakayama, A. Ogata, K. Gotoh and K. Fujiwara, Adv. Funct. Mater., 2011, 21, 3859.
7. V. Palomares, P. Serras, I. Villaluenga, K. B. Hueso, J. Carretero-Gonzalez and T. Rojo, Energy Environ. Sci., 2012, 5, 5884.
8. S. W. Kim, D.-H. Seo, X. Ma, G. Ceder and K. Kang, Adv. Energy Mater., 2012, 2, 710.
9. X. Xia, M. N. Obrovac and J. R. Dahn, Electrochem. Solid-State Lett., 2011, 14, A130.
10. R. Alcántara, P. Lavela, G. F. Ortiz and J. L. Tirado, Electrochem. Solid-State Lett., 2005, 8, A222.
11. A. Ponrouch, E. Marchante, M. Courty, J.-M. Tarascon and M. R. Palacín, Energy Environ. Sci., 2012, 5, 8572.
12. I. A. Shkrob, Y. Zhu, T. W. Marin and D. Abraham, J. Phys. Chem. C, 2013, 117, 19255.
13. S.-K. Jeong, M. Inaba, R. Mogi, Y. Iriyama, T. Abe and Z. Ogumi, Langmuir, 2001, 17, 8281.
14. R. Mogi, M. Inaba, S.-K. Jeong, Y. Iriyama, T. Abe and Z. Ogumi, J. Electrochem. Soc., 2002, 149, A1578.
15. H. Nakai, T. Kubota, A. Kita and A. Kawashima, J. Electrochem. Soc., 2011, 158, A798.
16. O. Borodin, W. Behl and T. R. Jow, J. Phys. Chem. C, 2013, 117, 8661.
17. M. Kobayashi, T. Inoguchi, T. Iida, T. Tanioka, H. Kumase and Y. Fukai, J. Fluorine Chem., 2003, 120, 105.
18. G. H. Wrodnigg, J. O. Besenhard and M. J. Winter, J. Electrochem. Soc., 1999, 146, 470.
19. S. Komaba, T. Ishikawa, N. Yabuuchi, W. Murata, A. Ito and Y. Ohsawa, ACS Appl. Mater. Interfaces, 2011, 3, 4165.
20. A. N. Dey and B. P. Sullivan, J. Electrochem. Soc., 1970, 117, 222.
21. D. Aurbach, Y. Eineli, O. Chusid, Y. Carmeli, M. Babai and H. Yamin, J. Electrochem. Soc., 1994, 141, 603.
22. Z. X. Shu, R. S. McMillan and J. J. Murray, J. Electrochem. Soc., 1993, 140, 922.
23. A. Naji, J. Ghanbaja, B. Humbert, P. Willmann and D. Billaud, J. Power Sources, 1996, 63, 33.
24. L. Xing, C. Wang, W. Li, M. Xu, X. Meng and S. Zhao, J. Phys. Chem. B, 2009, 113, 5181.
25. J. M. Vollmer, L. A. Curtiss, D. R. Vissers and K. Aminec, J. Electrochem. Soc., 2004, 151, A178.
26. K. Tasaki, J. Phys. Chem. B, 2005, 109, 2920.
27. M. Xu, L. Hao, Y. Liu, W. Li, L. Xing and B. Li, J. Phys. Chem. C, 2011, 115, 6085.
28. B. Li, M. Xu, T. Li, W. Li and S. Hu, Electrochem. Commun., 2012, 17, 92.
29. E. G. Leggesse and J.-C. Jiang, J. Phys. Chem. A, 2012, 116, 11025.
30. Y.-K. Han and S. U. Lee, Theor. Chem. Acc., 2004, 112, 106.
31. A. V. Marenich, C. J. Cramer and D. G. Truhlar, J. Phys. Chem. B, 2009, 113, 6378.
32. K. Leung, Chem. Phys. Lett., 2013, 568, 1.
33. M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery Jr, J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, Ö. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski and D. J. Fox, Gaussian 09, Revision D.01, Gaussian, Inc., Wallingford CT, 2009.
34. L. E. Roy, E. Jakubikova, M. G. Guthrie and E. R. Batista, J. Phys. Chem. A, 2009, 113, 6745.
35. O. Borodin, M. Olguin, C. E. Spear, K. W. Leiter and J. Knap, Nanotechnology, 2015, 26, 354003.
36. S. Trasatti, Pure Appl. Chem., 1986, 58, 955.
37. Y. Marcus, Pure Appl. Chem., 1985, 57, 1129.
38. X. Zhang, R. Kostecki, T. J. Richardson, J. K. Pugh and P. N. Ross Jr, J. Electrochem. Soc., 2001, 148, A1341.
39. Y. Bu, Y. Liu and C. Deng, J. Mol. Struct.: THEOCHEM, 1998, 422, 219.
40. D. Aurbach, Y. Gofer, M. Ben-Zion and P. Aped, J. Electroanal. Chem., 1992, 339, 451.
41. Y. Wang, S. Nakamura, M. Ue and P. B. Balbuena, J. Am. Chem. Soc., 2001, 123, 11708.
42. K. Leung, S. B. Rempe, M. E. Foster, Y. Ma, J. M. Martinez del la Hoz, N. Sai and P. B. Balbuena, J. Electrochem. Soc., 2014, 161, A213.
43. V. Etacheri, O. Haik, Y. Goffer, G. A. Roberts, I. C. Stefan, R. Fasching and D. Aurbach, Langmuir, 2012, 28, 965.
44. R. Elazari, G. Salitra, G. Gershinsky, A. Garsuch, A. Panchenko and D. Aurbach, J. Electrochem. Soc., 2012, 159, A1440.
45. Y. Okuno, K. Ushirogata, K. Sodeyama and Y. Tateyama, Phys. Chem. Chem. Phys., 2016, 18, 8643.
46. M. Nagaoka, Y. Suzuki, T. Okamoto and N. Takenaka, Phys. Chem. Chem. Phys., 2014, 118, 10874.
47. Y. Suzuki, Y. Koyano and M. Nagaoka, J. Phys. Chem. C, 2015, 119, 6776.
48. N. Takenaka, Y. Suzuki, H. Sakai and M. Nagaoka, J. Phys. Chem. C, 2014, 118, 10874.
49. N. Takenaka, Y. Suzuki, H. Sakai, U. Purushotham and M. Nagaoka, J. Phys. Chem. C, 2015, 119, 18046.

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Footnote

† Electronic supplementary information (ESI) available: Potential energy profiles of Na⁺–PC, Na⁺–FEC in gas phase. Optimized geometries with respective bond lengths of intermediates, products and transition states formed in the Na⁺–PC, Na⁺–FEC and Na⁺–DFEC complexes reductive decomposition mechanism. See DOI: 10.1039/c6ra09560g

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