Quantitative Mapping of Molecular Substituents to Macroscopic Properties Enables Predictive Design of Oligoethylene Glycol-Based Lithium Electrolytes.

Molecular details often dictate the macroscopic properties of materials, yet due to their vastly different length scales, relationships between molecular structure and bulk properties can be difficult to predict a priori, requiring Edisonian optimizations and preventing rational design. Here, we introduce an easy-to-execute strategy based on linear free energy relationships (LFERs) that enables quantitative correlation and prediction of how molecular modifications, i.e., substituents, impact the ensemble properties of materials. First, we developed substituent parameters based on inexpensive, DFT-computed energetics of elementary pairwise interactions between a given substituent and other constant components of the material. These substituent parameters were then used as inputs to regression analyses of experimentally measured bulk properties, generating a predictive statistical model. We applied this approach to a widely studied class of electrolyte materials: oligo-ethylene glycol (OEG)-LiTFSI mixtures; the resulting model enables elucidation of fundamental physical principles that govern the properties of these electrolytes and also enables prediction of the properties of novel, improved OEG-LiTFSI-based electrolytes. The framework presented here for using context-specific substituent parameters will potentially enhance the throughput of screening new molecular designs for next-generation energy storage devices and other materials-oriented contexts where classical substituent parameters (e.g., Hammett parameters) may not be available or effective.

Introduction

Quantitative parameters for understanding molecular substituent effects[1,2] have broad applications across chemistry[3] (examples include catalysis,[4] organic semiconductors,[5] and molecular recognition[6]). Through systematic examination of the impacts of substituents on the thermodynamics or kinetics of a process of interest, it becomes possible to unveil mechanistic details that can guide the design of improved processes. In materials-based systems, however, quantitatively predicting how molecular modifications will translate across length scales to yield macroscopic property changes is especially challenging.[7,8] For example, in the field of organic lithium conducting electrolytes, where ion transport is controlled by a dynamic ensemble of all microscopic structures formed between the electrolyte solvent, a dissolved lithium salt, and other possible additives, novel electrolyte components are often designed using chemical intuition and Edisonian (i.e., trial and error) optimization. Although this approach has led to significant advances, it cannot provide a priori quantitative predictions of the properties of novel electrolytes.[9−14] A quantitative model for understanding the impacts of molecular substituents on bulk lithium electrolyte properties will significantly advance the development of next-generation energy storage devices that require molecularly optimized electrolytes with high ionic conductivities[15] at room temperature, e.g., on par with current liquid carbonate electrolytes (∼10 mS cm–1 at 298 K) or solid-state ceramics (e.g., a sulfide-based superionic conductor with ionic conductivity of 25 mS cm–1 at 298 K),[16] yet with improved safety and processability profiles.[17] Moreover, the approach to developing such a quantitative model could be broadly applied to other complex materials systems where molecular features drive macroscopic function.

Seeking an electrolyte system to serve as the basis for building such a model, we chose the broadly used and widely studied class of electrolytes based on the oligoethylene glycol (OEG) structural unit, e.g., glymes and poly(ethylene oxide) (PEO), and the salt LiTFSI (Figure a). Optimized OEG-based electrolytes display good lithium ion conductivities (e.g., 1.6 mS cm–1 at 303 K for tetraglyme[18] and up to 0.45 mS cm–1 at 298 K for an OEG-based polymer electrolyte[19]) and promising electrochemical and mechanical stabilities. Moreover, extensive efforts toward improving the properties of OEG-based electrolytes via introducing substituents/comonomers to OEG/PEO materials,[20,21] incorporating OEG/PEO into block copolymers,[22,23] manipulating OEG/PEO architecture,[24,25] screening various salt anions,[12,26] using small-molecule additives,[27,28] and/or employing polymer blends[29] have been reported. Nevertheless, despite this rich precedent, limitations of existing experimental and computational methods have precluded the development of a quantitative, easy-to-implement model for predicting the properties of new OEG-based electrolytes. Experimentally, it is difficult to individually interrogate each aspect of Li+ solvation and transport and to deconvolute the complex causes of experimental observations.[30] Computationally, although advanced tools can be used to elucidate specific substituent effects in OEG-based systems, these approaches each have significant drawbacks.[31−36] For example, while molecular dynamics (MD) simulations have revealed that the spacing between lithium solvation sites in PEO is critical to ionic conductivity,[34,37] such simulations rely on classical hand-tuned force fields that need expensive parametrization for new substituents and are typically limited to semiquantitative agreement. These issues make it difficult to extend MD-based findings to a range of substituents and to predict the properties of new substituents de novo.[38] Moreover, MD simulations are limited by the computational cost of simulating the desired time- and length-scales that govern lithium conduction within polymers,[39,40] making screening of a large compositional space difficult. Though electronic structure methods like density function theory (DFT) are typically more amenable to extrapolation and more accurate than classic force fields,[41,42] they are much slower than MD (∼105 times)[43] at the same scale and are typically limited to screening the properties of isolated molecules or small clusters. Meanwhile, purely statistical approaches such as machine learning (ML) have proven helpful for learning complex correlations between bulk properties and descriptors (either based on structures[44] or properties[45,46]), but these methods typically require large data sets and have poor transferability, especially when not backed by physics-based invariants.[47] Lastly, methods based on linear free energy relationships (LFERs) have been widely used to elucidate mechanisms of chemical reactions and catalytic transformations.[1,2,48−50] For example, multidimensional regression analysis built upon LFERs has provided insights into the complex thermodynamic and kinetic effects in determining the selectivity of catalytic reactions.[48] Nevertheless, such approaches require access to relevant descriptors (e.g., Hammett parameters or other calculated substituent parameters) that are unique to each substituent; such descriptors and methods have not, to our knowledge, been developed in the context of lithium electrolyte materials.

Figure 1

Experimental design principles and workflow for probing the role of substituents in oligo-ethylene glycol (OEG) LiTFSI-based electrolytes. (a) Substituents (R) introduce new noncovalent interactions to OEG. (b) The pairwise interaction energies (ΔEi–) of each substituent with Li+, TFSI–, DME, and itself (self-association) in the gas phase were obtained using DFT calculations. These calculated substituent parameters were then correlated to (c) experimental measurements through (d) a regression model, which then allows (e) prediction of the experimental properties of new compounds and elucidates design principles.

Here, we introduce a strategy based on multidimensional LFERs that provides quantitative correlations between molecular substituents and bulk properties in OEG-based electrolytes (Figure ). This approach does not require an existing set of substituent parameters or modeling the exact dynamic ensemble of all microscopic species in such systems. Instead, it leverages simple DFT calculations to obtain pairwise interaction energies that serve as unique descriptors for substituents in OEG-based electrolytes (Figure b). Simple statistical models (Figure d, regression analysis) based on the Arrhenius (main text) and Vogel–Tammann–Fulcher (VTF, Section S4 in the SI) equations are then used to correlate these descriptors (substituent parameters) with experimentally observed variables obtained for a small library of synthesized OEG-based electrolytes. The regression generated a quantitative model that provides mechanistic insights into the role of substituents in these electrolytes as well as the ability to predict the properties of new OEG-based electrolytes (Figure e). The latter was verified by the synthesis and characterization of three OEG-based electrolytes that were predicted and observed to have comparably high, medium, and low conductivity. To the best of our knowledge, this work comprises the first example of using elementary energy-to-ensemble property mapping in the context of organic materials, providing unique insights into a broadly important class of electrolytes for next-generation energy storage applications.

Model System Design

General Approach and Model System Design

To begin, we designed and obtained 11 OEGs with different substituents introduced to 6–7 ethylene glycol (EG) units (Figure a, see Sections S2 and S6 in the SI for synthetic procedures and molecular characterization data). The parent octaglyme was included to provide a library of 12 experimental compounds with substituents that span a range of chemical characteristics including hydrogen bond donors (e.g., triazole, urea, thiourea, thiourethane, hydroxyl group) and acceptors (e.g., triazole, carbonate, urea, thiourea, thiourethane, hydroxyl group), Lewis acids (e.g., (glycolato)diboron, benzenediboronic ester) and bases (e.g., carbonate, triazole, thioether, hydroxyl), and nonpolar aromatics (e.g., xylenes). The structures of substituents used for DFT calculations are defined as the smallest fragment separated by ether oxygen atoms from the OEG chain and terminated by methyl groups (Figure b). A general, unambiguous procedure for selecting the substituent structure, which can be applied to newly designed OEG derivatives, can be found in the SI (Section S1).

Figure 2

(a) Library of OEG derivatives that contain varied substituents (R) studied in this work. (b) R groups used for pairwise DFT calculations (see Section S1 for general rules for selecting the structure of the R group for a given oligomer). (c) Temperature-dependent molal ionic conductivities and (d) inverse viscosities of OEG–LiTFSI electrolytes (LiTFSI, Li/O = 1/12). The molality of LiTFSI in each sample (1.1−2.1 mol kg–1) was determined by the number of moles of LiTFSI divided by the mass of the oligomer. The parent octaglyme electrolyte is shown in red; all other substituents are color-coded as shown in part b.

Four substituent (R)-derived binary complexes and their pairwise interaction energies in the gas phase (R–Li+,[51]R–TFSI, R–EG, and R–R) are used to represent the additional intermolecular interactions induced by the substituents in the bulk phase (Figure a,b); these interactions will ultimately perturb the electrolyte properties relative to the parent electrolyte based on octaglyme (we used a first-order approximation assuming that these 4 interaction energies can capture the underpinning physical factors affecting ion diffusion; other potential substituent effects, such as inductive effects introduced to the OEG chain by substituents, are expected to be comparatively small and thus are not explicitly included in our regression model). The key goal of this work is to build a model that allows us to explain and predict these perturbations, which, due to competing outcomes associated with each interaction, would be very difficult using chemical intuition alone. For example, one could reasonably hypothesize that increasing R–Li+ and R–TFSI interaction strengths could promote salt dissociation and therefore increase ionic conductivity; one could also reasonably hypothesize, however, that increasing these interactions would increase viscosity and therefore decrease ionic conductivity.

In order to quantify the strengths of these four pairwise interactions, DFT calculations of the substituent fragments (Figure b) and an isolated dimethoxyethane (DME), the latter representing octaglyme, are used (Figure b), providing a set of substituent parameters that can be mapped onto the experimentally measured properties of these electrolytes. Then, the experimentally measured conductivity and viscosity of each electrolyte (Figure c) were correlated to these DFT-obtained parameters through regression analysis to generate a predictive model (Figure d).

Results and Discussion

Temperature-Dependent Ionic Conductivity and Viscosity Measurements

The temperature-dependent molal ionic conductivity (normalized by molal concentration in mol kg–1) and viscosity of each of the 12 OEG-based oligomers blended with LiTFSI at a Li/O ratio of 1/12 are provided in Figure c,d, respectively (see Figure S1 for examples of raw electrochemical impedance spectroscopy and Figure S2 for absolute ionic conductivity data). We selected a constant Li/O ratio (1/12, commonly used for OEG-based electrolytes) to better isolate the differences between these substituents. Only ether oxygen atoms were counted for the Li/O ratio, and the resulting molality of the 12 electrolyte mixtures ranges from 1.1−2.1 mol kg–1. The results clearly show that the changes of molecular substituents significantly impact these ensemble properties, with variations in conductivity and viscosity that span ∼3 orders of magnitude. The range of the molal conductivities of the 12 OEG–LiTFSI-based electrolytes at 353 K (0.0005–0.004 S cm–1/mol kg–1) is consistent with the reported molar conductivity[52] of glyme–LiTFSI mixtures (0.5–3 S cm2 mol–1 = 0.0005–0.003 S cm–1/mol L–1, 353 K, the density of OEG–salt mixtures is usually ∼1 kg L–1).[52,53] In addition, molal conductivity and viscosity are inversely correlated (see Figure S3 for the correlations between conductivity and molar viscosity, also known as Walden analysis), in agreement with data collected for glyme-based electrolytes as well.[52,54,55] Finally, introducing substituents was generally observed to lower molal ionic conductivity and increase viscosity compared to the parent octaglyme-based electrolyte.

The temperature-dependent conductivity and viscosity data were analyzed using the Arrhenius equation (ln Ym = ln A – Ea/kT, T as temperature in Kelvin, k as the Boltzmann constant), from which activation energy, Ea, and pre-exponential factor, A, were extracted (Tables S1 and S2) for each electrolyte, with excellent fit (Figures S4 and S5). The fitted Ea of the octaglyme-based electrolyte (conductivity, 0.29 ± 0.02 eV; and viscosity, 0.29 ± 0.02 eV) is close to the reported values for related OEG-based electrolytes (e.g., Ea of the conductivity of 2 M LiTFSI in tetraglyme was reported to be 0.34 eV).[53] Interestingly, Ea for the octaglyme electrolyte is the lowest among the 12 oligomers, and the introduction of substituents leads to considerable increases in Ea (the highest Ea is 0.65 eV for conductivity and 0.66 eV for viscosity, both for benzenediboronic ester). The increase in Ea across different oligomers is mirrored by the growth in A (Figure S6), an effect known as the enthalpy–entropy compensation.[56,57]

As the molal conductivity and viscosity (Figure c,d) exhibit some temperature-dependent deviation from the Arrhenius model, we also analyzed the data using the VTF equation[58] (ln A – Ea/k(T – T0), where T0 = Tg – 50 K and Tg is glass transition temperature),[58] yielding a similar goodness-of-fit (Figures S4 and S5 and Tables S3 and S4) as the Arrhenius equation-based analysis. Unlike the Arrhenius model which yields Ea values spanning a wide range (0.30–0.65 eV), the values of Ea and A obtained from the VTF model are quite close to each other (e.g., Ea for conductivity ranges from 0.10 to 0.13 eV, Figure S7 and Tables S1–S4), presumably due to the inclusion of experimentally determined Tg (T0 = Tg – 50 K) values in the VTF fitting equation. The Tg values for these oligomers span a wide range of temperatures (40 K, Section S7 and Table S5) and were found to correlate well to molal conductivity, viscosity, and the Arrhenius Ea (Figures S8 and S9). As a result, the fitted Ea based on the VTF equation is less informative in reflecting the difference between the modified oligomers, which to a large degree is due to Tg. Thus, in the following sections, where we try to connect substituent parameters to characteristic physical properties of these OEG electrolytes, we selected the Arrhenius equation to build our regression model upon and to obtain the free energy relationship. In addition, the Arrhenius model has other advantages including simplicity (fewer fitting parameters), not requiring an experimentally measured Tg (or predicted Tg in the cases of new compounds), and ease of comparison with previous reports[52,54] on glyme-based electrolytes.

To understand the underpinning cause of the vastly different conductivities of these OEG–LiTFSI-based electrolytes, we used Raman spectroscopy to confirm a similarly high degree of LiTFSI dissociation for each electrolyte. The vibration band in the range 720–760 cm–1 (corresponding to the S–N symmetric stretching vibration coupled with the CF3 bending of TFSI–) has been shown to enable quantification of the relative population of free and coordinated TFSI–.[59,60] We first verified our capability of conducting the same analysis by obtaining the trend for salt dissociation in various glyme–LiTFSI-based electrolytes (monoglyme < triglyme < tetraglyme, Figure S10), in agreement with the literature.[52,54] Subsequently, Raman spectra in the same range (720–760 cm–1) were collected on 6 selected OEG–LiTFSI electrolytes (Figure S11), revealing high degrees of salt dissociation comparable with octaglyme–LiTFSI for all cases (<20% monodentate LiTFSI contact ion pair). These results suggest that the difference observed in ionic conductivity of these electrolytes (Figure c) cannot be reasonably explained by changes in free ion concentrations.

Based on the fact that the molal conductivities of these electrolytes inversely correlate to viscosities (Figure c,d and Figure S3), and previous works show that the reciprocal of viscosity is approximately equated to ionic mobility,[61,62] the primary reason for the conductivity of these OEG–LiTFSI electrolytes to vary is the change of ionic mobility. Increasing intermolecular interactions between polymer chains have been shown to decrease ion mobility,[63] motivating our approach of connecting pairwise interaction energies to the conduction properties of OEG–LiTFSI electrolytes.

DFT Calculations of Substituent-Based Pairwise Interaction Energies

The interaction energies of binary complexes between each substituent and Li+, TFSI–, DME, and itself (Figure b), which represent supramolecular interactions (e.g., electrostatic, hydrogen bond, van der Waals) in the electrolyte, were computed using DFT (Figure and Table S6). We chose the DFT functional (BP86-D3/def2-SVP) to minimize computational cost while maintaining good accuracy for noncovalent interactions, particularly through empirical dispersion corrections.[64,65] We additionally computed the interaction energies at a more expensive ω-B97/xD/def2-TZVP level of theory. The higher level of theory with long-range correlated DFT functional is well benchmarked and highly accurate for noncovalent interactions.[66] For comparison, the results obtained from the higher level of theory (Tables S8 and S9) showed similar trends and slightly different values compared to the lower level of theory selected for this work (Tables S6 and S7).

Figure 3

Pairwise noncovalent interaction energies induced by the substituents (BP86-D3/def2-SVP) normalized to the maximum values within the series (e.g., ΔELi– is normalized by dividing each energy value by the maximum ΔELi– value within the series). Top, Li+ interaction, ΔELi–; bottom, DME interaction, ΔEDME–; left, TFSI– interaction, ΔETFSI–; right, substituent−substituent interaction, ΔE. Each panel a–l corresponds to 1 of the 12 substituents, with the chemical structure noted on the plot.

These interaction energies (Figure and Table S6) were used subsequently in the regression fitting of temperature-dependent conductivity and viscosity data. For each calculation, randomly generated initial geometries for a binary complex between the substituent model and its counterparts (Li+, TFSI–, DME, or itself) were optimized in the gas phase (see Section S1 in the SI for the general methods and Section S8 for the optimized geometries). Interaction energies (ΔELi–, ΔETFSI–, ΔEDME–, and ΔE) in the gas phase were then obtained based on the single point energies of the optimized geometry relative to the individual unimolecular species; the values for each electrolyte are provided as 4-dimensional representations in Figure .

Our calculations show that, among the 4 interactions, R–Li+ is the strongest for all substituents. Its value ranges from −4.3 to −2.5 eV (−420 to −250 kJ mol–1), with the ratio between maximum and minimum ∼2. (Glycolato)diboron, carbonate, urea, and thioether display the strongest Li+ binding (greater than −3.5 eV = −350 kJ mol–1) among the 12 substituents. Thiourethane, triazole, thiourea, o-xylene, and benzenediboronic ester substituents have intermediate Li+ binding (−3 to −3.5 eV or −300 to −350 kJ mol–1), and DME, p-xylene, and hydroxyl groups have the weakest Li+ binding (−2.5 to −3 eV or −250 to −300 kJ mol–1), as shown in Figure and Figure S12. The other three interactions are weaker than R–Li+, following the order of R–TFSI– > R–R > R–DME. The strength of the R–TFSI– interaction ranges from −130 to −70 kJ mol–1, with the max/min ratio also ∼2. Stronger R–TFSI– interactions were seen among the substituents with hydrogen bond donors such as triazole, urea, thiourea, and thiourethane (−1 to −1.3 eV or −100 to −130 kJ mol–1Figure S12), while groups such as DME display weaker R–TFSI– interactions (Figure S12). On the contrary, the strengths of the R–R and R–DME interactions for the 12 electrolytes both vary in a relatively greater range with max/min ∼4 (ΔE ranges from −1 to −0.27 eV or −100 to −26 kJ mol–1, and ΔE ranges from −0.7 to −0.2 eV or −70 to −20 kJ mol–1, Figure S12). It is notable that substituents with hydrogen bond donors/acceptors (urea, thiourea, thiourethane), π-systems (benzenediboronic ester), and strong dipoles (urea, thiourea, thiourethane, and triazole) display strong self-association (R–R) and R–DME interactions.

As these 4 interaction energies are expected to establish a multidimensional description of chemical modifications of the OEG electrolytes, we checked for correlations between them (Figure S12) as well as for potential correlations with other commonly used substituent parameters (i.e., meta and para Hammett constants and dipole moments, Table S10 and Figures S13–S15). The strengths of the R–Li+ interaction do not appear to correlate to other interactions. The R–R interaction shows a linear correlation with R–DME (r2 = 0.82), presumably on account of similar underpinning binding motifs (e.g., hydrogen bond, dipole–dipole). The R–R interaction also displays a weaker linear correlation (r2 = 0.49) with R-TFSI–. Lastly, plots of these calculated binding energies against meta and para Hammett constants[67] and dipole moments revealed no trends (Figures S13a, S14a, and S15a), suggesting that our calculations captured features of these substituents that are not represented by these existing substituent parameters.

Establishing a Quantitative Model from Experimental Data and Calculated Energetics

With our experimental results (Figure c,d) and calculated substituent parameters (Figure ) in hand, we set out to build a quantitative model relating these two data sets through regression analysis. We note that the experimental conductivity and viscosity data do not show satisfactory trends with any one of the 4 DFT-calculated substituent parameters discussed above (Figures S16 and S17), meta (Figure S13b) and para (Figure S14b) Hammett constants, or the dipole moments of each substituent (Figure S15b). Thus, as has been observed in other contexts such as catalysis,[48,49] the experimental conductivity and viscosity data cannot be captured using a single substituent parameter.

Given that the Arrhenius expression can model our experimental conductivity and viscosity data well (see above), we correlated the substituent-dependent DFT interaction energies (Figure ) to the activation energy and the pre-exponential factor in the Arrhenius equation:where the intercept parameters A0 and Ea0 represent the OEG components of the oligomers, establishing a baseline value of the pre-exponential factor and the activation energy, respectively, and b is a constant reflecting enthalpy–entropy compensation.[57] The term a1ΔELi– + a2ΔETFSI– + a3ΔEDME– + a4ΔE comprises a linear combination of substituent-dependent DFT interaction energies (Figure ), which accounts for substituent-induced perturbations to the oligomers. The values of a reflect the importance of the corresponding substituent parameters. We note that higher-order polynomial terms, including cross-terms between these interaction energies, may add capacity to the model but, given the size of the data set, would result in overfitting. The regression analysis of the experimental conductivities (Figure a) and viscosities (Figure b) yielded good fitting results (r2 ≥ 0.98) and provided two unique sets of fitted constants (A0, Ea0, b, and a, where i = 1, 2, 3, and 4) for conductivity and viscosity. To verify the regression model, we examined the values of the fitted parameters. The value of b (conductivity, 27.3; viscosity, 25.8) is close to the actual enthalpy–entropy compensation factors of these electrolyte–salt mixtures determined by individual fitting of the temperature-dependent data (conductivity, 27.6; viscosity, 27.6; Figure S6). The values of Ea0 (conductivity, 0.24 eV; viscosity, 0.24 eV) are close to unmodified glymes (e.g., Ea of octaglyme conductivity, 0.29 ± 0.02 eV; viscosity, 0.29 ± 0.02 eV; Tables S2 and S3) with 0.05 eV difference. The “predicted” activation energy of each oligomer as determined by the regression (Ea0 + ∑a ΔE) also matches well with the actual activation energy obtained from fitting individual temperature-dependent data (Figure S18).

Figure 4

Experimental (a) molal conductivity and (b) viscosity (inversed) for all oligomers at various temperatures plotted against fitted values using the model (eq ) with values in Table . For modeled conductivity, ln Y = ln 11.9 + 27.3 (0.013ΔELi– + 0.079ΔETFSI– + 0.20ΔEDME– – 0.63ΔE) – (0.24 + 0.013ΔELi– + 0.079ΔETFSI– + 0.20ΔEDME– – 0.63ΔEdimer–)/kT, goodness-of-fitting r2 = 0.98. For modeled inversed viscosity, ln Y = ln 2.37 × 104 + 25.8 (0.015ΔELi– + 0.092ΔETFSI– + 0.22ΔEDME– – 0.67ΔE) – (0.24 + 0.015ΔELi– + 0.092ΔETFSI– + 0.22ΔEDME– – 0.67ΔE)/kT, goodness-of-fitting, r2 = 0.99.

Table 1

Summary of Fitting Resultsa

	r2	RMSE	A0	Ea0 (eV)	b	a1; Li+	a2; TFSI–	a3; DME	a4; dimer
conductivity	0.98	0.31	11.9	0.24	27.3	0.013	0.079	0.20	–0.63
viscosity	0.99	0.31	2.37 × 104	0.24	25.8	0.015	0.092	0.22	–0.67

ln Y = ln A0 + b(a1ΔELi– + a2ΔETFSI– + a3ΔEDME– + a4ΔE) – (Ea0 + a1ΔELi– + a2ΔETFSI– + a3ΔEDME– + a4ΔEdimer–)/kT, where Y is either conductivity or viscosity determined by experiments, ΔE is substituent parameter, and A0, b, and ai are fitted parameters.

We note that the activation energy in the Arrhenius equation does not correspond to a single molecular process, but rather a combination of thermal activation and changes in free volume,[68,69] suggesting that there is no simple correlation between the fitted Ea and any of the DFT-calculated pairwise interaction energies individually.

Testing of the Model by Predicting the Properties of New OEG–LiTFSI-Based Electrolytes

To test the ability of our model to predict the properties of new OEG–LiTFSI electrolytes, we manually generated a library of 32 new substituents, calculated their substituent parameters, and predicted the conductivity and viscosity of the corresponding electrolytes using the regression model with the fitted parameters (Table S7). Guided by perceived ease-of-synthesis, we selected and synthesized three new OEG derivatives (Figure a) from the 32 predictions. The 3 new compounds are based on propylene (Figure b), diisopropylsilyl (Figure c), and sulfone (Figure d) substituents, which were predicted to yield electrolytes with high, medium, and low molal conductivity, respectively. Notably, the propylene-substituted electrolyte (Figure b), in addition to 4 of the other manually generated electrolytes, was predicted to have greater conductivity (0.86 mS cm–1/mol kg–1 at 298 K, predicted value) than the parent octaglyme electrolyte (0.54 mS cm–1/mol kg–1 at 298 K, experimental value), suggesting that subtle, difficult-to-predict substituent modifications (e.g., the addition of a single methylene group) can be exploited to improve upon the properties of classical OEG-based electrolytes.

Figure 5

(a) Molecular structures and (b–d) the substituent parameters (BP86-D3/def2-SVP, normalized to the maximum values within the series) of the 3 newly designed OEG–LiTFSI electrolytes (propylene, diisopropylsilyl, and sulfone). Top, bottom, left, and right are R–Li+, R–DME, R–TFSI–, and R–R interactions, respectively. Experimental (e) molal conductivity and (f) viscosity of the 3 newly designed electrolytes as a function of the predicted values (in comparison with data used in the fitting in gray). Temperature-dependent (g) molal conductivity and (h) viscosity of the electrolytes (LiTFSI, Li/O = 1/12). Dots indicate experimental results, and open circles indicate predicted values. The 12 training electrolytes are in gray, and the 3 new electrolytes are in colors.

Our model does indeed enable prediction of viscosity and conductivity for these novel OEG–LiTFSI-based electrolytes, as shown in Figure e–h. The propylene-, diisopropylsilyl-, and sulfone-substituted electrolytes displayed the predicted high to medium to low conductivity and inverse viscosity trend, respectively. In addition, the experimentally measured molal conductivities and viscosities of the 3 new electrolytes at 298 K, for example (propylene, 0.62 mS/mol kg–1 and 0.59 P; diisopropylsilyl, 0.24 mS/mol kg–1 and 2.0 P; sulfone, 0.086 mS/mol kg–1 and 10.9 P), closely match the predicted values at the same temperature (propylene, 0.86 mS/mol kg–1 and 0.62 P; diisopropylsilyl, 0.37 mS/mol kg–1 and 1.60 P; sulfone, 0.052 mS/mol kg–1 and 16.8 P), indicating excellent accuracy of the prediction. These results show that our model, which is based on mapping pairwise interaction energies as substituent parameters to ensemble properties, can identify new materials with enhanced properties compared to the training set.

We note that our model also predicted that fluorinated OEG-derivatives would display improved properties (Figure S19). During the course of preparing this manuscript, Bao and co-workers reported similar fluorinated OEGs.[70] Although their system is slightly different from ours (e.g., salt used and the length of the OEGs), their data generally agree with our prediction that fluorinated substituents can result in highly conductive OEG electrolytes (Figure S19).

Supporting the Physical Basis for Our DFT-Calculated Substituent Parameters Using Molecular Dynamics (MD) Simulations

As discussed above, our model allows for the prediction of novel OEG–LiTFSI electrolyte properties from simple DFT-calculated pairwise interaction energies. While successful, we sought to determine if these energies realistically reflect bulk solvation energies and solvation structures. Thus, we conducted MD simulations for three of the OEG-based (thiourea, propylene, and sulfone) LiTFSI electrolytes in the bulk phase (see Section S5 in the SI for more details). In general, the solvation structures and time-averaged interaction energies of the 3 electrolytes extracted from classical MD matched well with the elementary DFT calculations (Figures and 7).

Figure 6

Pairwise interaction energy involving thiourea, propylene, and sulfone substituents obtained from different methods. Gray, DFT-calculated interaction energies of the ground state complexes reported in Figures and 5; cyan, the same pairwise interaction energies between molecular fragments, obtained from MD simulations; yellow, time-averaged interaction energies in condensed phases extracted from MD simulations. Both MD and DFT values are normalized using the maximum values within the series.

Figure 7

Examples of solvation structures involving R–Li+, R–TFSI–, R–R, and R–EO interactions extracted from MD simulations and DFT optimized geometries of the same interactions using (a) thiourea-, (b) sulfone-, and (c) propylene-based electrolytes. MD simulations were conducted using the entire OEG molecule in the condensed phase. DFT calculations were based on substituents (vide supra) in the gas phase.

First, the geometry optimizations of the four complexes (R–Li, R–TFSI–, R–DME, and R–R) were repeated using classical interatomic potentials instead of DFT. The resulting pairwise interaction energies (ΔEMDmin) are the MD calculated versions of the substituent parameters discussed above, allowing us to validate the classical interatomic potentials and to provide a solid basis of comparison between gas phase (DFT) and condensed phase calculations (MD). Next, condensed phase simulations of electrolytes were conducted and provided time-averaged interaction energies, ⟨EMD(t)⟩, for R–Li, R–TFSI, R–DME, and R–R. Comparing these three interaction energies reveals that while their absolute values differ, they show very similar trends across the 3 electrolytes studied (Figure ). For example, the ⟨EMD(t)⟩ values (Figure , yellow bars) are close to the ΔE (DFT-calculated energies) values, suggesting that the DFT-calculated substituent parameters reflect the strength of the actual intermolecular interactions in the condensed phase to some degree.

In addition, the condensed phase simulations allowed us to manually extract solvation structures involving the substituents. We note that, for structures involving R–TFSI, R–DME, and R–R interactions, on account of their shallower potential energy surfaces (all of these interactions are much weaker than EO-Li+ interactions), the configurational degrees of freedom are high. As a result, the structures shown in Figure are representatives of many other possible configurations. However, common features shared by the structures obtained from condensed phase simulations and DFT calculations can still be observed. First, we note that, for the solvation structures extracted from MD for all three OEG derivatives, Li+ is solvated by the entire OEG derivative, with the formation of 3–4 pairs of close contacts between the ether oxygen atoms (Figure , all R–Li structures). This finding agrees with previously reported Li+ coordination environments (solvated by 4–5 ether oxygen atoms) in glyme-based electrolytes.[54,71,72] In addition, the R groups assist the Li+ coordination in a synergistic fashion (Figure ). While the DFT structures do not have 4 ether oxygens available due to the fragmented substituents, such Li–ether oxygen close contact and substituent participation are still present in all the DFT optimized complexes as well. We also observed the presence of hydrogen bonds between the CH2 groups adjacent to oxygen atoms and TFSI– in both the MD and DFT structure, consistent with previous work.[73] For thiourea, strong NH hydrogen bonding with TFSI– and with oxygen atoms (Figure a) was observed in both MD and DFT structures. Thus, while the MD and DFT structures are not exactly the same, their common features suggest that the gas phase calculations on molecular fragments are able to match some of the characteristic solvation structures observed in the simulated condensed phase.

R–R Self-Association Governs Conductivity and Viscosity

With the MD simulations supporting the physical basis for our DFT-calculated substituent parameters, we now analyze the fitted regression model to obtain design principles for the OEG–LiTFSI-based electrolytes. The absolute value of a indicates the magnitude of the impact of the corresponding interaction energy on conductivity and viscosity with greater absolute value meaning more significant impact. The sign of ai indicates the direction of the impact with positive a indicating that increasing the corresponding pairwise interaction energy will lead to higher conductivity and lower viscosity while negative a indicates the opposite. As shown in Table , a4 for both conductivity and viscosity have negative signs, and their absolute values (a4 = −0.63 and −0.67 for conductivity and viscosity, respectively) are much larger than those of a1, a2, and a3 (a1 = 0.013 and 0.015, a2 = 0.079 and 0.092, and a3 = 0.20 and 0.22 for conductivity and viscosity, respectively), indicating that the R–R self-association might be the dominant factor impacting the large changes in the conductivity and viscosity of these electrolytes (Figures S16d and S17d).

To examine the role of R–R self-association in further detail and to determine if it applies to a broader set of electrolytes beyond those studied above, a parallel coordinate analysis (conductivity, Figure ; viscosity, Figure S20) was conducted using the prediction model. 1000 virtual substituents were generated using a Monte Carlo approach. Each virtual substituent has 4 randomly generated substituent parameters (interaction energies) within the range established by the previous DFT-calculated substituent parameters. While these virtual substituents do not necessarily have corresponding chemical structures, they sample the whole space of all possible combinations of the substituent parameters. Thus, predicting the molal conductivity and viscosity of these virtual substituents allows us to understand general features of the regression model.

Figure 8

(a) Parallel coordinate analysis of the prediction model. Each line represents a virtual substituent that has 4 substituent parameters as indicated by its intercepts with the 4 axes. Each substituent parameter is normalized to the maximum value within the series. These virtual substituents (numeric combinations of 4 substituent parameters) are generated using a Monte Carlo approach. The color of each line represents the predicted molal conductivity using our model (eq ) at 303 K. (b) Predicted molal conductivity as functions of each substituent parameter.

The predicted properties were color-coded onto the lines where a single line represents a unique set of substituent parameters (Figure a, more saturated color corresponds to higher conductivity and lower viscosity). The results showed that electrolytes with high conductivity and low viscosity (more saturated lines) mostly cluster at the region of low self-association energy, suggesting that the self-association (ΔE) has the most significant impact on the properties. Consistently, the single interaction energy ΔE showed the highest correlation (Figures S16d and S17d) with experimental conductivity (at 298 K, r2 = 0.86; at 363 K, r2 = 0.81) and viscosity (at 298 K, r2 = 0.85; at 363 K, r2 = 0.88) data. The coordinates were also separated (Figure b and Figure S20b) to demonstrate the significance of each substituent parameter. It is interesting to note that the strength of the R–R interaction is weaker than R–Li+ and R–TFSI– in general; however, it can still have a more significant impact on conductivity and viscosity than the other interactions.

Finally, we note that, while dipole moment alone does not explain the observed change in properties, dipole moments of polar substituents (dipole moment >1.5 D) correlate well with ΔE and experimental conductivity (Figure S21). Thus, as a first approximation, nonpolar substituents are more promising than highly polar substituents when optimizing the conductivity of OEG electrolytes.

Proposed Mechanism for the Role of Substituents in OEG–LiTFSI Electrolytes

Combining all experimental and theoretical results, here we formulate a mechanism showing how substituents impact the properties of OEG–LiTFSI electrolytes. First, our results show the following: LiTFSI is highly dissociated in all of the studied electrolytes (Raman spectroscopy, Figure S11). The main origin of the vastly different conductivity is the change of ion mobility (Raman spectroscopy and Walden analysis, Figures S11 and S3). Li+ is primarily solvated by EO segments with R groups participating in a cooperative manner (MD, Figure ). DFT-calculated substituent parameters can reflect condensed phase solvation (Figure ). The R–R self-interaction (ΔE substituent parameter) dominates the ionic conductivities and viscosities in the regression model (Figure ). Thus, the major impact of substituents on the resulting conductivity of OEG–LiTFSI electrolytes is the additional intermolecular interactions (as probed by ΔE) between the electrolyte molecules reducing the mobility of the solvated Li+ ions (OEG-Li+ complexes as the charge carriers, Figure ). For example, stronger self-association interactions between the substituents can induce higher energetic barriers for the Li+ cation to diffuse with the oligomer molecule solvating it and/or to hop between molecules (Figure ), manifested as higher viscosity as well as higher fitted activation energy, Ea (viscosity vs ΔE, Figure S17; Ea vs ΔE, Figure S22).

Figure 9

Proposed mechanistic view (a) weak and (b) strong self-association interactions between substituents can result in high and low ionic conductivity, respectively.

Finally, we note that the molecular weights of the oligomers studied here fall between common solvents such as glymes and entangled polymer electrolytes (Figure S23). Thus, for electrolytes based on polymers with molecular weights in the entanglement regime, the conduction mechanism (i.e., chain segmental motion) is different from the oligomers used in this study.[15] There has been a report, however, showing that interchain interactions in such polymer electrolytes can negatively impact Li+ conductivity,[63] which mirrors our findings in the oligomer regime and suggests that there are intrinsic similarities between the liquid-like OEG–LiTFSI electrolytes and entangled polymer electrolytes above their Tg. We envision that, for polymer electrolytes with high molecular weights, although their entanglement prevents Li+ from diffusing with individual macromolecules, interchain self-association interactions[74] can still create energy barriers that increase Tg, enhance crystallinity, and decrease segmental motion dynamics that support Li+ conduction when above Tg. Thus, it may be possible to utilize our method to study the impact of substituents on polymer electrolytes beyond entanglement. In addition, we also envision that the approach demonstrated here can be replicated (with some modifications) to quantitatively study and predict the properties of OEG electrolytes at various salt concentrations and with multiple substituents.

Safety Statement

No unexpected or unusually high safety hazards were encountered.

Conclusions

We reported a new method of quantitatively evaluating the impact of substituents on the properties of OEG–LiTFSI-based electrolytes. The method is complementary to the commonly used MD, DFT, and purely statistical approaches to understanding the impacts of molecular modifications to electrolytes and is less limited by the difficulties of obtaining a complete dynamic ensemble of the complex electrolyte–salt mixtures. Our framework is based on mapping the complex ensemble properties (e.g., conductivity and viscosity) to a set of custom-built substituent parameters easily obtained from DFT-calculated pairwise interaction energies. Using this method, we predicted the properties of newly designed OEG-electrolytes and experimentally verified 3 of these predictions with one of them having slightly enhanced conductivity compared to the parent octaglyme. In addition, our model revealed physical insights and design principles for OEG–LiTFSI-based electrolytes. We found that the self-association interaction is the most significant factor to consider when introducing substituents to OEG–LiTFSI-based electrolytes as this interaction can greatly impact the mobility of charge carriers within the electrolytes. While the method demonstrated here uses OEG–LiTFSI-based electrolytes as the model system, we envision that it can be applied in a wide range of similar systems where substituent modifications are introduced to a primary structure, and where pairwise noncovalent interaction energies can be used as substituent parameters to describe these modifications.