Electrochemical Stability of Functionalized Cyclic Phosphonium (CylP+nA−) Ionic Liquid Based Battery Electrolytes

Gopi Krishna Phani Dathar; Shanthi Pandian; Srinivasa G. Raju; Da-Hye Park; Hyo-Rang Kang; Krishnan S. Hariharan

doi:10.1149/2.1131606jes

Realizing high capacity Li-ion batteries and advanced Li batteries requires deploying electrodes with higher energy densities. Moving from graphite to Li metal anode multiplies the energy density of anodes by a factor of approximately 10, however, transition from graphite to Li metal anode is limited by electrode corrosion, Li plating and dendritic growth resulting from electrochemical instability of traditionally used organic electrolytes. Though a lot of research has been carried out over the past two decades in the direction of design and development of stable electrolytes and protective coatings for Li metal anodes, to limit electrode corrosion and structural degradation caused by electrolyte breakdown at the electrode/electrolyte interface, it still remains as one of the important and emerging research areas in electrochemical energy storage.^1,2

The important features to look out for while selecting an electrolyte for batteries are the chemical and electrochemical stability (at electrode/electrolyte interfaces), thermal stability and good ionic conductivity. Room Temperature Ionic Liquids (RTILs) are organic salts composed of weakly bound cation/anionic species³ which have been reported as potential alternatives to currently preferred liquid electrolytes.⁴ RTILs feature wide electrochemical windows, low vapor pressures and good thermal stability and due to their intrinsic properties, RTILs have been used in both chemical and electrochemical applications such as catalysis,^5,6 organic synthesis,^7,8 batteries, fuel cells and organic solar cells.^2,9 Utilizing wider electrochemical windows and thermal stability of RTILs, it is considered possible to design stable electrolytes and realize batteries with high energy density and enhanced safety.^4,10 Hence ILs with the cations based on imidazolium, piperidinium, pyrrolidinium and tetraalkyl − phosphonium, and a few functionalized derivatives of the above cations, along with commonly used anions, were researched as potential alternatives to currently used organic electrolytes.^4,11–22 However, compared to the enormous chemical space spanned by the combinations of cations plus their functionalized derivatives and anions that can form ILs, the amount of exploration done so far is minimal.^23,24 There remains a lot of opportunity available in exploring the rich chemical landscape of ILs, and the potential to discover a better electrolyte for the next generation electrochemical energy storage devices exists.

In this paper, we present a systematic investigation of electrochemical stability of barely researched cyclic phosphonium (or phospholanium) cation CylP⁺_n(n = 5 or 6) based ionic liquids. CylP⁺_n (n = 5 and 6) are phosphorous analogs of pyrrolidinium and piperidinium cations (shown in Fig. 1). Despite being conceptualized and patented few years ago,²⁵ and studied using first principles calculations in few publications,^26,27 CylP⁺_nA⁻ ILs were not routinely synthesized and characterized,^28,29 and detailed electrochemical experiments to qualify CylP⁺₅ based ILs as battery electrolytes are yet to be performed. In this paper, we study the electrochemical stability of functionalized CylP⁺_n (n = 5) ions to explore the chemical space spanned by functional modifications and to identify the relavant chemical structures that are potential alternatives to currently used organic electrolytes.

**Figure 1.** Phosphorous analogs of Pyrrolidinium, piperidinium ILs and commonly used anions.

In phosphonium cation IL family, functionalized acyclic tetraalkyl phosphonium cations (analogs of tetraalkylammonium ILs) were studied extensively and concluded in the literature as better candidates for electrolytes with higher reduction stability and lower viscosity compared to the nitrogen analogs.^30–38 The general consensus from the first principles calculations on acyclic phosphonium cations is that the phosphonium ILs have wider electrochemical stability windows (EW) and hence higher cathodic limits relative to nitrogen analogs.^26,27,39 The better reduction stability of phosphonium cations is ascribed to the empty d-orbitals in phosphorous that result in stronger binding of functionalities, and hence increased resistance to reduction.²⁷

In previous studies, the reduction stability of phospholanium cations was calculated from 1e⁻ reduction calculations resulting in annihilation of cation and subsequent dissociation of functionalities. Though it seems to be the dominant pathway, more than one pathway is probable for 1e⁻ reduction when certain functionalities (such as ethers, aminophenyl) are used to functionalize base phospholanium cations. In this paper, we explore more than one reaction pathway for 1e⁻ reduction (and subsequent electron transfers) to get insights into the electrochemical stability of CylP⁺_n cations and the functional substitutents. We show that the inherent reduction/ oxidation stability of the functional groups (and the substituents on the functional group) is also important in determining the overall electrochemical stability of cations.

Here we report the calculations of model R − CylP⁺₅ − R' ions – variants with alkane −, amine −, ether − and cyclic alkene − functional group substitution at the two free terminals (R and R') of the CylP⁺₅ ions (shown in Figure 2). The choice of functional groups include some moieties with electron-withdrawing character and the others with electron-donating character since the substituent constants have significant effect on the reduction stability of CylP⁺₅ ions. Electron donating/electron withdrawing character of the functional group affects the reduction stability of the cations where the propensity to acquire an electron decreases when functionalized by electron-donating groups (EDGs) and increases when functionalized by electron-withdrawing groups (EWGs).³⁹ It is intuitive and we also find in our calculations that electron-donating groups (EDGs) like alkyls, cyclic alkenes and amines increase the reduction stability compared to ether substituents (EWGs). However, substituent constants alone cannot explain the electrochemical stability of R − CylP⁺₅ − R' ions; solvation energies and enthalpy of lithiation that determine the inherent redox stability of substituents also play a significant role. We discuss the contribution of the above factors in determining the electrochemical stability of R − CylP⁺₅ − R' ions in this paper.

**Figure 2.** List of functionalities: linear *alkyls*, cyclic *alkenes*, *ethers* and *amines*.

Methodology

We have constructed a model of R − CylP⁺₅ − R' ion with two methyl groups (as the starting point) and generated a combinatorial library with a new set of cations by symmetric (R = R') and asymmetric substitution (R = CH₃; R ≠ R') of 23 functionalities categorzied into four sets: linear alkanes, cyclic alkenes, ethers and amines. We use DFT to calculate redox free energies and electrochemical stabilities of functionalized R − CylP⁺₅ − R' ions. Theory and computational approach to calculate EWs and electrochemical stability against Li⁺/Li are presented here. The model reactions (schemes A–C) for 1e⁻ reduction to determine the electrochemical stability are also presented.

Quantum chemistry based methods such as Density Functional theory (DFT) are very well suited to predict electrochemical stabilities of electrolytes and lithium salts and identify candidate materials.^39–45 In the past, quantum chemistry calculations have been extensively used by multiple research groups to provide invaluable insights into electrolyte decomposition pathways that determine the inherent redox stability of electrolytes in the bulk and at the electrode/electrolyte interfaces.^46–53 High-throughput computational methodology employing DFT was also reported to screen the combinatorial libraries of probable candidate materials for electrolytes based on the relative energy level alignment (HOMO/LUMO) at the electrode/electrolyte interfaces.^54,55

Electrochemical windows

EW is a good descriptor to predict electrochemical stability of IL electrolytes. It is typically calculated as the difference between their oxidation and reduction potentials (anodic (V_AL) and cathodic (V_CL) limits).^26,56 When ILs are deployed as electrolytes in Li-ion batteries, V_AL and V_CL are compared against the redox potential of Li electrode ,⁵⁷ and it can be concluded that electrolytes are electrochemically stable when its cathodic limit is lower compared to standard Li electrode potential and anodic limit is higher compared to a given cathode. The reduction stability of an ionic liquid electrolyte when interfaced with Li electrode is a function of electron affinity of the cation (or anion), stability of corresponding dissociated species and the solvation energy of the free radicals.^26,27 Similarly, the oxidation stability is a function of ionization potential of the anion (or cation) and the solvation energies of oxidized species. The electrochemical stability window is then calculated as the difference between the minimum of oxidation and reduction potentials of cations and anions.

The cathodic/anodic limits are set by either cations or anions that are determined by the minimum of redox potentials of both species. The ΔSCF procedure⁵⁶ reported in the literature to calculate reduction potential overestimates the EW as the dissociation since solvation of radicals post reduction are not taken into account.^26,27 Solvation energy of the functionalities depend on their corresponding radical-solvent interactions that affect the electrochemical stability of the cations. Hence, in this paper, the cathodic limit is calculated from the reduction free energies of cation plus the solvation energies of the dissociated radicals as shown in Figure 3 and described in Reaction schematics section. The anodic limit of an anion is calculated from the oxidation potentials as the difference in free energies of the ion and the oxidized species (without dissociation). The dissociation of anions that can proceed through multiple channels is not considered here. Hence, the anodic limit of ILs calculated in this paper correspond to the upper limit of anodic stability of a given IL pair.

**Figure 3.** Schematics of 1e⁻ and 2e⁻ reduction reactions. Scheme A - Reduction-dissociation of cation followed by lithiation of solvated radicals; Scheme B and Scheme C – dissociation and lithiation of functional group followed by lithaition/reduction of phospholanium cation. R/R' in schemes B and C correspond to *ethers* and *amino* *phenyl* functionalities respectively. − OX in scheme B corresponds to organic groups, − *oxymethyl*, − *oxyethene*, − *oxybenzene*, − *oxyterbutyl* and − *oxy*1, 4 *dioxane*. Y in scheme C corresponds to organic groups NH₂ and − OC₆H₅ (*diphenyl* *ether*).

Reaction schematics

The electrolyte decomposition at the Li interface can thus be summarized into four steps: (i) electron transfer from electrode to electrolyte, (ii) dissociation post reduction, (iii) solvation of radicals and (iv) lithiation of solvated radicals. The reaction free energies of the above four steps will determine the electrochemical stability of CylP⁺_n ions at the Li electrode interface. Reduction potentials of the cations in the combinatorial library are thus calculated from the free energies of decomposition reactions (shown in Figure 3). The first and second electron reduction reactions were represented in Scheme A where the first electron transfer from Li electrode to cation results in (R − CylP⁺₅) − R' bond dissociation and solvated neutral cyclic phosphonium and free radicals; subsequent electron transfer results in lithiation of the free radicals. For ether − and aminophenyl − functionalized cations, we explored other possibilities of decomposition, schemes B and C, where the lithiation of functional group precedes the reduction of phospholanium cation. The overall reduction stability is then determined from the minimum of reduction potentials from all the calculations. Oxidation potentials of cations (and anions) are calculated from the free energies of initial and corresponding oxidized species without dissociation.

Reaction free energies and redox potentials

For a given cation/anion, the 1e⁻ reduction/oxidation reactions of cations are represented by R⁺ + e⁻ → P and R⁺ → R^{2 +} + e⁻, respectively, where R⁺ upon acquiring an electron is reduced to products, P, and upon losing an electron results in oxidized species R^{2 +}. Oxidation of anions is represented by A⁻ → A + e⁻ where A⁻ upon losing an electron results in neutral species A. The free energies of reduction and oxidation processes, ΔG°_Red and ΔG°_Ox, are calculated based on the thermodynamic cycles shown in Figure 4.

**Figure 4.** Thermodynamic chemical cycles for evaluating free energies of R − *CylP*⁺₅ − R'A⁻ redox reactions.

In the reduction cycle, R⁺ and P correspond to the reactants and products, ΔG°_Rxn is the difference between free energies of products and reactants in gas phase, ΔG°_s(P) and ΔG°_s(R⁺) are the solvation energies of products and reactants. In oxidation cycles, R⁺/R^{2 +} and A⁻/A correspond to initial and oxidized states respectively. EA_(A) and IP are the electron affinity of the anion and ionization potential of the cation respectively. The cathodic and anodic limits with reference to Li electrode are then calculated as⁵⁸

where 4.44 V and −3.05 V correspond to the SHE value in absolute potential scale at room temperature and the Li standard electrode potential Vs SHE for aqueous solutions, respectively.⁵⁹ It is then concluded that the cation is electrochemically stable to reduction upto the cathodic limit against Li⁺/Li.

The free energies of lithiation resulting from subsequent electron transfers are calculated as

where G_{Li − R} is the free energies of lithiated radical, and μ_Li is the chemical potential of lithium in Li electrode, respectively. μ_Li is calculated as the sum of the energy of Li atom in solution and the enthalpy of sublimation of lithium (Δ_fH°_gas(Li) = 1.65 eV).⁶⁰ The free energies of lithiation for reactions shown in schemes B and C are also calculated using similar equation as above.

Computational methodology

Geometry optimization calculations in vacuo and in solution using a continuum solvation model were performed using a meta-GGA functional, M06-L, and triple-ζ basis, 6-311+G(2d,p) as implemented in Gaussian09 quantum chemistry package.⁶¹ Meta-GGA functionals in combination with double-ζ and triple-ζ basis sets were reported to result in lowest mean absolute deviation in interaction energies of 236 different ion-pair strcutures containing both protic and aprotic ionic liquids.⁶² In conjunction with M06-L, we have used SMD (universal solvation model)⁶³ for implicit solvation calculations which is based on quantum mechanical charge density of a solute molecule interacting with a dielectric continuum. The solvation free energy comprises bulk electrostatic contribution calculated using self consistent reaction field approach in integral-equation-formalism polarizable continuum model (IEF-PCM) and cavity-dispersion-solvent-structure term arising from short-range interactions between the solute and solvent molecules. The dielectric constant of ε = 10.186 ( ∼ ε_RTIL) is used in all the calculations. Models of solvated ILs are important since stabilization of reduced/oxidized ions by the solvent molecules must be taken into account and typically performed in vacuo (gas phase) calculations lack proper description of molecule-solvent interactions. Since it is computationally expensive to use fully solvated IL models, solvent approximation in the form of a solute-molecule interacting with a dielectric continuum with a certain ε value (that matches with bulk ILs) is often employed to correct energies calculated in vacuo.⁴⁵ All the energies reported in this paper correspond to energies including solvation and free energy contributions to the total energy were calculated from vibrational frequencies and statistical mechanics corrections.

Results

Calculated free energy profiles of one and two e⁻ reduction reactions for representative models are shown in Figures 5a–5d. Calculated free energies of one and two e⁻ reduction reactions for all symmetrically and asymmetrically substituted R − CylP⁺₅ − R' ions are listed in Supp. Info, Tables S1 and S2. Li electrode reference is also shown in the figure, ΔG°_ref = −1.4 eV. The reaction products with energies below the Li reference are unstable at the interface and the difference in the absolute values of ΔG°_Red and ΔG°_ref corresponds to the reduction stability of cations at the Li interface.

**Figure 5.** Free energy profiles of one and two e⁻ reduction reactions of representative models. R/R' = CH₃, NH₂ and *phenyl* (a) *dimethyl* *ether* (b) *para* − *aminophenyl* (c) and *diphenyl* *ether* (d).

The general trends observed from the calculated data are (i) reductive decomposition of all the variants in the combinatorial library follow scheme A shown in Figure 3 and (ii) ΔG°_Red for first electron transfer from Li electrode to cation is downhill in all the cases indicating instability at the Li interface and (iii) asymmetric substitution of functionalities (Vs symmetric substitution) did not improve the reductive stability of phospholanium cations. The first electron transfer is thus the rate determining step in all the cases. We further highlight the relative energetics of reductive decomposition in this section that reveal interesting trends in the reduction stabilities upon varying the substituent functional groups. In this study, energy barriers for decomposition of reduced phospholanium ions, and concomitant first and second electron transfers are not explicitly modeled. Hence the effect of stability of lithiated products (resulting from second electron transfer) on the thermodynamic barrier for first electron transfer is not evident from our calculations.