Theoretical study of the reductive decomposition of 1,3-propane sultone: SEI forming additive in lithium-ion batteries†

Ermias Girma Leggesse and Jyh-Chiang Jiang *
Department of Chemical Engineering, National Taiwan University of Science and Technology, Taipei 106, Taiwan, R.O.C. E-mail: jcjiang@mail.ntust.edu.tw; Fax: 886 2 2737 6644; Tel: 886 2 2737 6653

First published on 4th April 2012

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1. Introduction

Lithium-ion batteries are used in various portable electric devices such as cell phones and laptops since they offer several advantages over other types of rechargeable batteries, including high energy density, lightweight design, and longer lifespan.^1–4 They are also a promising source of energy for hybrid electric vehicles (HEVs) and plug-in hybrid electric vehicles (PHEVs), along with other applications.⁵ As a result of this they are being considered as a leading contender for a clean and sustainable energy source.

Among the wide spectrum of polar solvents used in lithium ion batteries, cyclic diesters of carbonic acid have attracted a lot of research attention especially after their role in the formation of a protective film on the graphite electrode was recognized.⁶ This film, which was first named a “solid electrolyte interphase” (SEI) by Peled,⁷ lies between the electrode and the electrolyte solution, and it is conductive to lithium ions but nonconductive to electrons. As the SEI layer highly determines some of the critical properties of the lithium ion battery such as safety, cyclability and power capability, the study of its formation process and morphology has become one of the key areas of research in the performance development of lithium ion batteries. Amidst the cyclic diesters of carbonic acids, propylene carbonate (PC) is the most popular solvent since it exhibits remarkable properties because of its ability to dissolve and dissociate lithium salts leading to electrolytes having high ionic conductivity over a wide temperature range.^8,9 However, PC can easily decompose on graphite and co-insert with Li-ion into the graphite electrode which results in the destruction of the graphite electrode and reduces its reversible capacity.^10–16 Since the intercalation of lithium ions into graphite occurs at low potentials (below 0.25 V vs. Li/Li⁺), the relative solvents and salts are partially reduced to form SEI on the surface of graphite electrode, which is associated with irreversible capacity loss.^17–19 Many methods have been reported to suppress the intercalation of the solvent into graphite. One method is by using proper electrolyte additives, which would help to generate an efficient SEI layer.

In recent years, sulfur based additives have been reported to facilitate the formation of SEI when present in small amount together with PC or a mixture of PC and other solvents.^20–27 Organic sulfites such as 1,3-propane sultone (PS) have been found to be a good solid electrolyte interphase film-forming additive for lithium ion batteries containing PC as a solvent.^28–30 However, there are very few reported studies about the mechanism by which these additives promote the formation of a stable SEI layer on the anode material. In this paper, density functional theory calculations have been carried out to carefully analyze the role of 1,3-propane sultone (PS) as a SEI forming additive, starting with the electroreductive decomposition of PS in the gas phase, and then taking into account the solvent effect with the supermolecular models (PS)Li⁺(PC)_n (n = 0,1).

2. Computational details

All the theoretical investigations have been carried out using density functional theory (DFT) with the B3LYP method^31–34 using 6-311++G(d,p) basis set as presented in the Gaussian 09 package.³⁵ A spin-unrestricted scheme was used for the odd number electron systems to allow for any possible bond cleavage during geometry optimization. To confirm the transition states and make zero point energy (ZPE) corrections, frequency analyses are done with the same basis set as for the geometry optimization. Intrinsic reaction coordinate (IRC) calculations were also performed to confirm whether the reaction path of respective chemical reaction correctly connects the stationary points under consideration. Unless otherwise stated, the relative energies indicate those with ZPE correction, and Gibbs free energies and enthalpies are calculated at 298.15 K. The spin contamination was considered by comparison of the expectation value of the <S²> operator. Before annihilation <S²> was generally between 0.75 and 0.77 for the doublet states, which is close to the doublet state S² value of 0.75,³⁶ confirming that the spin contamination would have an insignificant effect on the result. Natural bond orbital (NBO)³⁷ analysis with the same basis set was performed with the NBO program included in the Gaussian program package. The potential energy and Gibbs free energy profile diagrams for the reductive decomposition mechanisms are constructed by using the energies relative to the isolated reactant in the first step of the corresponding reduction processes and by setting the energy of the electron to be zero. The implicit solvent effect was accounted for by using the implicit solvation model with density (SMD) method³⁸ as implemented in Gaussian 09 where the dielectric constant of PC, 64.9, was chosen in relation to the conditions implemented in the experiments. The SMD model is based on the integral–equation–formalism polarizable continuum model (IEF-PCM) protocol for bulk electrostatics that involves an integration of the nonhomogeneous Poisson equation and on a cavity dispersion–solvent–structure protocol for the nonelectrostatic contribution to the free energy of solvation.³⁸ The bonding characteristics between lithium and the solvent molecules were investigated by using Bader's atoms in molecules (AIM) theory.³⁹ In the present work, we used the electron density function ρ(r) and its Laplacian ∇²ρ(r) to elucidate the structural results and bonding properties at the bond critical points.

In order to assist our thermodynamic considerations for the electroreductive decomposition pathways, transition state theory⁴⁰ was employed to estimate the reaction rate constants for the ring opening steps. Assuming that all molecules that cross the barrier proceed to become products, the rate constant k at 298.15 K was calculated by using the following equation:

	(1)

where, k_B is the Boltzmann constant, Q(T) and Q(T)^≠ are partition functions for the reactant and TS, respectively, and E^≠ is the zero-point barrier for the reaction. Rotational, translational, vibrational and electronic contributions to the partition functions are obtained after geometry optimizations.

3. Results and discussion

3.1. Reductive dissociation of PS in vacuum and bulk solvent

The calculated frontier molecular orbital energies and vertical electron affinities (EA_v) of PS and PC in vacuum and bulk solvent are listed in Table 1. Vertical electron affinity is defined as the energy difference between the neutral molecule and its negative ion at their initial geometry.⁴¹ The LUMO energy of PS (−0.17 eV) is lower than that of PC (−0.02 eV), indicating the readiness of PS to be reduced on the anode surface prior to PC. Moreover, the vertical electron affinity of PS in solution is significantly higher than PC (3.27 vs.1.72 eV, respectively) implying the superior ability of PS to gain the first electron in solvent than PC. The negative gas phase EA_v value for PS and PC implies that the neutral species is more stable than the anion.

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The potential energy and Gibbs free energy profile of reductive dissociation of isolated PS in vacuum is shown in Fig. 1, and relative energies and Gibbs free energies are listed in Table 2. In the gas phase reductive decomposition, initially, PS (1) can be reduced to the radical anion 2 followed by ring opening reactions. Two kinds of heterolytic ring opening reactions could take place starting from the radical anion 2; S–O cleavage via transition state 3 or S–C cleavage via transition state 7. However the energy barriers for the two paths are considerably different, where the S–C cleavage has a higher energy barrier than S–O (3.75 vs.1.61 kcal mol⁻¹). Similarly, the effective energy barriers for the ring cleavage steps (1→4 and 1→8) are 8.73 and 6.56 kcal mol⁻¹ respectively. As a result, the path which proceeds through the transition state 3 to generate 4 seems the most probable path for gas phase reductive decomposition of PS. Moreover, as seen from Table 2 and Fig. 1, this path continues through the cleavage of S–O to give a final product which is lower in energy by 0.59 kcal mol⁻¹ than the alternative path.

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However, based on our calculation, the positive change in Gibbs free energy (+4.46 kcal mol⁻¹) for the addition of an electron to give the radical anion (1→2) indicates the process is likely to proceed in the reverse direction spontaneously. Moreover, the negative gas phase EA_v value for PS also shows that the neutral species is more stable than the anion. Hence, similar to what has been reported for propylene carbonate and ethylene carbonate,^42,43 in the gas phase, the PS reductive decomposition is thermodynamically unfavourable. However, it is possible that PS can undergo one- as well as two-electron reduction processes in the bulk solvent. The origin of this difference can be explained by examining the frontier molecular orbitals of PS and its reduced form both in solution and gas phase.

Fig. 2 highlights the difference between gas and solution phase electronic structures. It represents the lowest unoccupied molecular orbital (LUMO) of PS and singly occupied molecular orbital (SOMO) of PS⁻ in the gas phase and in solution. The difference arises as a result of the implicit solvation effect implemented by the continuum polarizable solvation models. The model represents the electric polarization of the dielectric medium surrounding the solute (in this case PS) by a discrete number of point charges in which the molecular orbitals of the solute are affected by the charge distribution of the solute molecule in the dielectric continuum.⁴⁴ As can be seen from Fig. 2, the LUMO of PS is almost identical to the SOMO of PS⁻ in the gas phase as a result of the filling up of the LUMO by the incoming electron. In the gas phase reduction, since the incoming electron resides outside the molecule no significant bond stretching is observed (1→2). However, the LUMO of PS in the solution phase lies entirely inside the molecule thus the incoming electron occupies the S–O antibonding orbitals which facilitate the stretching of the bond leading to its scission (see Fig. S1† for optimized geometries).

The potential energy and Gibbs free energy profiles of reductive dissociation of PS in solution are shown in Fig. 3, and the relative energies and Gibbs free energies are listed in Table 3. The reduction of PS in solvent is possible owing to the stabilization of the reduction intermediate (12) by the implicit solvent effect which is evident from the negative free energy and the associated vertical electron affinity (−76.44 and −75.45 kcal mol⁻¹, respectively). The radical anion intermediate 12 then proceeds to give the final gaseous products via transition state 13, which is has a relatively small energy barrier of 15.81 kcal mol⁻¹. The located transition state has been confirmed by IRC calculations and the vibrational modes of its eigenvectors. As seen from the NBO calculation, the spin density shows the unpaired electron is shifted from the oxygen atom of 12 to the sulphur atom of the final product.

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3.2. The effect of salt in the reductive decomposition of PS

The stripping of the solvation sheath of Li⁺, which involves partial dissolution and anion formation on the electrode, is reported to be the major energy consuming step in lithium ion batteries.^45–47 Based on this phenomenon, Park et al.⁴⁸ demonstrated that the low Li⁺-ion binding affinity is an important characteristics of SEI forming additives. The calculated Li⁺ binding energy for PS in the bulk solvent is 11.86 kcal mol⁻¹, which is quite enough to propose the existence of the salt effect in the system. The relatively longer O–Li⁺ distance in Li⁺(PS) as compared to Li⁺(PC) (2.00 vs.1.84 Å respectively) (see Fig. S2†) as well as the lower Li⁺ binding energy with PS (11.86 kcal mol⁻¹ for PS and 16.18 kcal mol⁻¹ for PC at SMD-B3LYP/6-311++G(d,p)) shows the weaker solvation ability of PS to Li⁺. This observation is also supported by the AIM calculations for Li⁺(PS) and Li⁺(PC) in which ρ(r) and its Laplacian ∇²ρ(r) at the bond critical point (bcp) between lithium and oxygen for Li⁺(PC) [ρ(r) = 0.036, ∇²ρ(r) = 0.296] are higher than Li⁺(PS) [ρ(r) = 0.025, ∇²ρ(r) = 0.172].

The potential energy and Gibbs free energy profiles of reductive dissociation of Li⁺(PS) in solution are shown in Fig. 4, and relative energies and Gibbs free energies are presented in Table 4. Since Li⁺ has higher electron affinity than the PS molecule, the electron is transferred to Li⁺ of 16 which is supported by a population analysis on the spin density in which the unpaired electron is mainly located on the Lithium atom with a coefficient of about 0.93. The heterolytic ring opening reaction could happen to 16, which proceeds through a transition state 17 with a ring opening barrier of 3.61 kcal mol⁻¹ to give a relatively stable primary radical 18. The formation of this primary radical is accompanied by the release of more energy, −89.24 kcal mol⁻¹ relative to 15. A population density analysis on the spin density shows that the unpaired electron is totally shifted to the terminal carbon atom (C3) of the primary radical 18 with a coefficient of about 0.99. The transition state 17 connecting 16 with 18 is confirmed by IRC calculations and by identification of an imaginary frequency corresponding to relevant vibrational modes.

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The termination reactions of the radical 18, which is formed from the initial reduction of Li⁺(PS), are investigated comprehensively and presented in Fig. 5. The radical could go through termination reactions either by reacting with other species which are involved in the initial reduction process or self-dimerization. There is also possibility of further reduction of the radical by gaining an electron from the polarized electrode. As shown in Fig. 5, further reduction of 18 generates 19 which is a very reactive carbanion. The resulting carbanion may decompose to give LiSO₃⁻ and propylene gas (21) through a transition state 20 with an energy barrier of 22.39 kcal mol⁻¹.

The ion pairing reaction that involves 21 and Li⁺(PS) is barrierless reaction which produces an inorganic product, lithium sulfite 22 (ΔG = −149.19 kcal mol⁻¹). The ion pairing reaction between 18 and Li⁺(PS) is also a barrierless reaction generating C–Li carbide product 25 which has a significantly higher ΔG compared to the generation of 22 (−21.06 vs. −149.19 kcal mol⁻¹). Another termination reaction of 18 is homocoupling or dimerization reaction to give 24. It can be assumed that whenever two such radicals come in close proximity they will collide and react to generate a dimer. Nevertheless, for an effective combination we need to have a high concentration of the radicals which is difficult to achieve since the radicals involved in the reaction have short life times as a result of reactions with other molecules. However, the difference in ΔG between the dimerization reaction and the reduction of 18 is not significant (−64.18 vs. −64.52 kcal mol⁻¹) showing the possibility for the formation of the dimer. This observation might be associated with a phenomenon called “cage effect”^49,50 in which radicals generated in solution are held in close proximity and will have a high probability of undergoing a dimerization reaction. Even though the concentration of the radicals is low, a solvent shell or “cage” surrounds the two radical increasing the collusion between the two before breaking through the “cage”.

Besides these termination paths, an interesting termination possibility of 8 to generate a carbide product similar to 25, proceeds through electron pairing between 18 and intermediate 16 from the initial reduction of Li⁺(PS). It has been reported that the formation of the Li carbide species in the reductive decomposition of EC and PC^18,42 proceeds via a two-electron reduction mechanism similar to the generation of 23. The extra stability of 23 over 25, as seen from the ΔG value (−43.54 vs. −21.06 kcal mol⁻¹), can be ascribed to the fact that the added electrons in the case of 23 are distributed on the two separate species (18 and 16), rather than being added to only 18, and form a carbanion.

All of the above proposed good passivating species (Li₂SO₃, (CH–CH₂–CH₂–OSO₂Li)₂ and lithium carbides) are compact and polar. Their passivating properties can be attributed to the possibility of good adhesion to the surface of a negative electrode as a result of their inherent ionic structure and polarity. In addition to the conceivable presence of electrostatic interactions between the negatively charged electrode surface and lithium ions of these species, the presence of a lithium rich compact polycrystalline layer of inorganic species such as Li₂SO₃ could also facilitate Li ion diffusion though the protective film. It is believed that Li intercalation into the negative electrode (graphite) is composed of several successive processes including the migration of Li ions through the protective film followed by insertion into the carbon supported by charge transfer at the film–electrode interface and finally, solid state diffusion of lithium into the graphite.^47,51–53 We can speculate that as a result of the possible presence of interstitial sites in this lithium rich solid ionic compounds the diffusion of lithium ions though the protective film will be facilitated.⁵⁴

3.3. Reductive decomposition of (PC)–Li⁺(PS)

Assuming there will be a qualitative difference between the first solvation effects and those originating from the bulk, we chose to follow a “hybrid model”⁵⁵ which includes the first solvation shell explicitly and treats the rest of the system with the implicit solvation model using SMD calculation. The weaker solvation ability of PS to Li⁺ is shown by the relatively longer O–Li⁺ distance in (PC)–Li⁺(PS) (2.01/2.14 vs. 1.83 Å for PS and PC respectively) (see Fig. S3†). This observation is also supported by the AIM calculations for (PC)–Li⁺(PS) in which ρ(r) = 0.024 and its Laplacian ∇²ρ(r) = 0.157 at the bond critical point (bcp) between lithium and the carbonyl oxygen of PS and ρ(r) = 0.017 , ∇²ρ(r) = 0.109 at the bond critical point (bcp) between lithium and ethereal oxygen of PS while ρ(r) = 0.036 , ∇²ρ(r) = 0.283 at the bond critical point (bcp) between lithium and carbonyl oxygen of PC in (PC)–Li⁺(PS). Moreover, the calculated values for both ρ(r) and ∇²ρ(r) are positive, supporting the identification of the O–Li⁺ interaction as having a charge-shift character.^56,57

The potential energy and Gibbs free energy profile of reductive dissociation of (PC)–Li⁺(PS) in solution is shown in Fig. 6, and relative energies and Gibbs free energies are presented in Table 5. Compared to the isolated PS molecule, (PC)–Li⁺(PS) can easily accept an electron from the polarized electrode and is reduced as denoted by its high positive vertical electron affinity (88.51 kcal mol⁻¹). Since the LUMO of (PC)–Li⁺(PS) lies entirely on PS, upon addition of an electron, the O–S (ethereal oxygen) antibonding orbitals are occupied and bond stretching is facilitated ultimately leading to barrierless ring opening of the PS moiety. This finding is consistent with the NBO charge distribution which shows that the additional electron is mainly located on the oxygen atom of the reduced species 27 with a coefficient of 0.58 as shown in Table 5. The initial reduction intermediate (16) of Li⁺(PS) is higher in energy when compared to the reduction intermediate of (PC)–Li⁺(PS) (27), −38.80 vs. −88.51 kcal mol⁻¹. Hence, the extra stability of 27 can be attributed to the presence of extra coordinated PC molecules.

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As a result of the inner-sphere electron transfer process, the radical intermediate 27 proceeds via a transition state 28 to give a primary radical intermediate (29) in which the unpaired electron is totally shifted from the ethereal oxygen to the terminal carbon (C3) with a coefficient of 0.99. Some possible termination path for the primary radical 29 is also shown in Fig. 7. A barrierless homocoupling or dimerization reaction of 29 to form (PC–Li(O₂S)O(CH₂)₃)₂, 34, is the most favorable reaction, as seen from its lowest Gibbs free energy of reaction (ΔG = −62.57). Due to the probable existence of reduced interactions between the lone pair of the less nucleophilic oxygen atom of 29 with the radical center, the primary radical could undergo another barrierless dimerization where the nucleophilic radical attacks the more electron-rich oxygen atom of another radical bringing about PC–Li(O₂S)O(CH₂)₃O(SO₂)Li–PC, 35, and propylene gas. Another possible way is the combination of 29 with the initial reduction intermediate 27 through electron pairing which generates a solvated organic salt containing an ether functionality PC–LiOS(O)(CH₂)₃O(CH₂)₃OS(O)OLi–PC, 36, via a relatively favorable path compared to the generation of 35 (−58.27 vs. −56.78 kcal mol⁻¹). There is also the possibility of further reduction of the radical by gaining an electron from the polarized electrode to generate PC–LiSO₃⁻ (32) which could react with (PC)–Li⁺(PS) to produce Li₂SO₃ solvated by one PS and two PC. The Gibbs free energy for the reactions which generate propylene gas is less negative compared to the favorable path which indicates that gas evolution in PC based solution is suppressed by the presence of PS. It should be noted that the production of gasses (e.g. propylene) is reported elsewhere^58,59 as the failure mechanism of PC for lithium ion batteries employing graphite as the anode material.

A comparison of the potential energy profile for reductive decomposition of PS, Li⁺(PS) and (PC)–Li⁺(PS) is shown in Fig. 8. As can be seen from the figure, Li⁺(PS) is the most easy to decompose, passing through a relatively lower C–S bond cleavage energy barrier (2.89 kcal mol⁻¹), to yield a primary radical with the lowest relative energy (−89.24 kcal mol⁻¹). The rate constants for the reactions 16→17 (TS) → 18, 12→13 (TS)→14 and 27→28 (TS)→29 were calculated using (eqn 1) and was found to be 1.81 × 10¹⁰ s⁻¹, 1.86 × 10² s⁻¹ and 2.87 × 10⁻¹ s⁻¹ respectively (see Table S1† for vibrational, electronic, translational, rotational and calculated molecular partition functions) confirming the ring opening step in Li⁺(PS) decomposition takes place at a much faster rate compared to a similar step in free PS and (PC)–Li⁺(PS). On the basis of the above discussed kinetic and thermodynamic aspects, the reactivity towards electroreductive decomposition of the three models can be ordered as follows: Li⁺(PS) > PS > (PC)–Li⁺(PS). Moreover, it should be noted that in addition to the favorable termination products from the reductive decomposition of Li⁺(PS), there is also a possibility that the termination products of the primary radical from the reduction of (PC)–Li⁺(PS) could participate in the formation of SEI.

Based on the above discussion, the protective film forming behaviour of PS can be clarified by considering a relatively higher reduction potential of PS in PC based electrolyte. Even though the interaction of the reduction products of PS with the surface of the electrode needs further work, because of the lower lithium ion interaction with 26 and 15 as shown by AIM calculation relative to PC, it is unlikely that PS co-intercalates into the negative electrode with lithium ions. Generally speaking, the presence of PS in PC based electrolytes of lithium ion batteries will probably hinder the solvent reduction as a result of its preferential reduction to yield more stable reductive decomposition intermediates.

4. Conclusion

Density functional theory calculations have been carried out for PS and (PS)Li⁺(PC)_n (n = 0,1) to investigate the role of PS as SEI forming electrolyte additive of lithium ion battery. Once the anode is polarized to low potentials in PC based electrolytes, PS is reduced prior to PC to give a stable reduction intermediate in which the electron is transferred to Li⁺. This stable intermediate may undergo a decomposition reaction via heterolytic ring opening to give a relatively stable primary radical. The products from the termination reactions of the primary radical (Li₂SO₃, (CH–CH₂–CH₂–OSO₂Li)₂, and Li–C carbides) and (PC–Li(O₂S)O(CH₂)₃)₂ from the reduction of (PC)–Li⁺(PS) would build up an effective SEI film. Even though further experimental work needs to be done in analyzing the products formed as a result of PS reduction, its higher reduction potential and weak binding to Li⁺ could help to illustrate the role PS plays as an electrolyte additive. Thus, the PS reduction products could help to promote the formation of an effective SEI film before the reduction of PC; and as a consequence, prevents excessive reduction of the solvents used in the system.

Acknowledgements

This work was supported by the National Science Council of Taiwan (NSC-100-3113-E-011-002). We are also grateful to the National Center of High-Performance Computing for computer time and facilities.

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Footnote

† Electronic Supplementary Information (ESI) available: The optimized geometries for the reductive decomposition processes of PS, Li+(PS) and (PC)-Li+(PS). Vibrational, electronic, translational, rotational and calculated molecular partition functions for selected molecules. See DOI: 10.1039/c2ra20200j/

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