Solvent Blends of Ethylene Carbonate and Ethyl Methyl Carbonate

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Dielectric Constants for Quantum Chemistry and Li-ion Batteries: Solvent Blends of Ethylene Carbonate and Ethyl Methyl Carbonate David Scott Hall, Julian Self, and Jeff R. Dahn J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b06022 • Publication Date (Web): 09 Sep 2015 Downloaded from http://pubs.acs.org on September 15, 2015

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The Journal of Physical Chemistry

Dielectric Constants for Quantum Chemistry and Li-Ion Batteries: Solvent Blends of Ethylene Carbonate and Ethyl Methyl Carbonate David S. Hall, Julian Self, J. R. Dahn† Department of Physics and Atmospheric Science, Dalhousie University, Halifax NS, Canada, B3H4R2 †

email: [email protected]

1. Abstract This work reports measurements of the dielectric constants of ethylene carbonate (EC)/ethyl methyl carbonate (EMC) blends between 25 – 60°C. Dielectric constants were measured using a cylindrical capacitance cell and a frequency response analyser. EC and EMC form non-ideal mixtures that cannot be described by a simple linear mixing model. A quadratic mixing rule was instead adopted and the mixing parameter is reported for 25 – 60°C. The results of this article may be used to calculate the dielectric constant of any EC/EMC mixture over this temperature range with ≤ 4 % estimated error. By modeling the ionic dissociation of lithium hexafluorophosphate (LiPF6) in various solvents, the significance of the dielectric constant on quantum chemistry simulations of chemical processes is explored. The effect of the dielectric constant accuracy on electrochemical processes was similarly evaluated by calculating the solvation energy of neutral and singly oxidized vinylene carbonate in various solvents. It is demonstrated that the exact value of the dielectric constant can significantly affect calculation accuracy when ε < 40, which is the case for the most commonly used EC/EMC blends.

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Keywords: Dielectric constant, static permittivity, relative permittivity, lithium-ion batteries, Liion batteries, computational chemistry, quantum chemistry, density functional theory


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2. Introduction Quantum chemistry (QC), as a complement to experimental results, is a promising way to uncover and explore processes in complex chemical systems. In Li-ion battery (LIB) research, QC simulations have been used to investigate physical and chemical properties of solvents,1–7 electrolyte salts,2,3,8–12 and electrolyte additives.1–3,13–16 The accuracy of calculated values is well known to depend heavily on the methods, especially whether an appropriate level of theory or a sufficiently large basis set has been used.17 For liquid-state and solution species, including the solvents, salts, and additives mentioned above, a good solvation model is also essential to obtain reliable results. Solvent properties are known to affect chemical equilibrium constants, the rates and mechanisms of reactions, and the molecular structures of dissolved species.18,19 Moreover, these differences are often not trivial; kinetic studies have demonstrated that the nature of a solvent can alter the rate of chemical reactions by many orders of magnitude.20 Perhaps the simplest and most robust solvation model is the polarizable continuum model (PCM), which comes standard with commercial QC software.21 The PCM relies primarily on representing liquid solvents by their dielectric constants (static permittivity, ε). The molecular system under study is placed within a cavity with the properties of vacuum (ε = 1) and the surrounding space has the properties of the desired solvent. The currently recommended implementation of this model within Gaussian09 uses the integral equation formalism variant and a universal force field to define the cavity (IEFPCM-UFF).22 Despite its simplicity, this method does an excellent job of modeling the effects of solvation effects on geometries and energies, provided an accurate dielectric constant is known.21,23



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There are more complex solvation models that may improve the accuracy of calculated solvation energies, especially for ionic species, such as the SMD (a universal Solvation Model based on solute electron Density),24,25 ONIOM (“our own n-layered integrated molecular orbital+molecular mechanics”),26,27 COSMO (conductor-like screening model),28–30 or hybrid cluster/continuum modeling, the explicit representation of a few solvent molecules around the solute (i.e. a solvation cluster) surrounded by a PCM. These models nonetheless represent the bulk solvent as a polarizable continuum. Thus, the accuracies of these models are all limited by how well the input dielectric constant represents the bulk solvent. Commercial LIBs typically use solvent blends.31 These usually consist of a cyclic organic carbonate (high ε, high viscosity) and a linear organic carbonate (low ε, low viscosity) to balance electrolyte dissociation and ionic mobility in the solvent. Table 1 summarizes the available dielectric constant data for several common solvent components. Dielectric constants have also been reported for several PC-containing blends. For example, equimolar PC/EMC and PC/DME mixtures have ε = 27.8 or 35.8, respectively, at 25 °C.32 Ding et al. provide equations, from fitted data, that allow the value of ε to be calculated for binary mixtures of PC with DEC or EC in any proportion for -40 °C ≤ T ≤ 60 °C.33 Binary mixtures of EC with various non-carbonate solvents have also been studied.34 However, these represent only a few of the solvent blends in use, and without exact values of ε, approximations have had to be made for QC calculations. Many researchers have used the dielectric constants of various solvents, such as diethyl ether (ε = 4.24),3 tetrahydrofuran (ε = 7.43),1 acetone (ε = 20.5),3 1,2-ethanediol (ε = 40.2)10 or water (ε = 78.4)3, whereas others have used numeric values, such as ε = 5.6735 and ε = 60.0.16 Without reliable dielectric data, it is very difficult to assess the accuracy of QC results. Clearly, accurately


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measured solvent properties will improve the reliability of computational studies of LIB chemistry.



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Table 1

Literature dielectric constants (ε) for common solvent blend components in LIBs.

Solvent

Temperature (°C) 20 25

Linear Carbonates Diethyl carbonate (DEC)

Dimethoxyethane (DME) Dimethyl ethylene carbonate (DMEC) Ethyl methyl carbonate (EMC) Cyclic Carbonates Butylene carbonate (BC) Ethylene carbonate (EC)

40

50

60

70

92.8 33

90.5 40 89.78 36 89.6 38 89.1 34 88.6 33 61.7 33

85.1 34 84.7 33

81.0 34 81.0 33

77.3 34

59.5 33

57.4 33

57 39 2.985 36

2.9 37 2.4 32

57.5 40 N/Ab

56.1 40 95.3c 34

Propylene carbonate (PC)

66.6 40 66.14 36 66.3 33

Glycerin carbonate (GC)

111.5 40

65.5 40 64.9 37 64.9 32 64.6 34 109.7 40

63.9 33

24 °C.

b c

30

2.82a 36 2.82 37 2.82 38 3.08 36 3.12 37 3.12 38 7.2 32

Dimethyl carbonate (DMC)

a

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The melting point of EC is 34-37 °C

Calculated by extrapolation from higher temperature

The vast majority of electrolyte additive work in this laboratory has used Li-ion pouch cells containing the control electrolyte 1M LiPF6 EC/EMC 3:7 (w:w) in which the additives are incorporated. In order to use quantum chemistry to understand aspects of the additive work, it is essential to have accurate dielectric constants. In this work, the dielectric constant of EC/EMC solvent blends was measured over the range 25 – 60°C. EC/EMC blends are widely used in both research and commercial cells so these results will be of considerable and immediate value. This


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article also assesses the impact of the solvation model on calculated results for both the chemical and electrochemical processes that occur in a cell. 3. Experimental Methods Dielectric constant (static permittivity) measurements A cylindrical cell for the dielectric constant measurements of gases or liquids was constructed based on the design of Jacobs and Greer.41 The cell, shown in Figure 1b, consists of a can, which serves as the outer electrode, and a lid (Figure 1d), which is electrically insulated from the can by a Teflon O-ring (shown in Figure 1c). The lid is directly connected to a hollow inner cylinder (Figure 1d). The inner electrode is electrically insulated from the rest of the inner cylinder by Teflon O-rings and a Teflon sleeve. The gap between the inside of the can (cylindrical central hole in Figure 1c) and the outside of the inner electrode is ~0.5 mm. A wire within the inner cylinder connects the inner electrode to a banana socket (shown at the top of Figure 1d) at the centre of the lid. A blind hole drilled directly into the exterior side of the can (shown in Figure 1b) fits a second banana plug.



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The capacitance cell was wired in parallel with a resistor that ranged from 1 – 100 kΩ, placed in a temperature control box and connected to a BioLogic VMP3 multistat with impedance plug-in module (specified range: 10 µHz – 1 MHz), as shown in Figure 2. The frequency response analyzer (FRA) was controlled using EC-Lab software (v10.34, Bio-Logic – Science Instruments). The impedance was measured over the range 600 kHz – 600 Hz using a 100 mV sine wave amplitude. The data was fitted to a simple RC circuit using EIS Spectrum Analyzer software (v1.0).42 A representative dataset, collected for acetone, is presented as a Nyquist plot in Figure 3. The resistance was varied to obtain as much of the semi-circle as possible, within the operating frequencies of the FRA.

Computational methods All calculations were performed using the Gaussian software package (G09.d01).22 Density functional theory (DFT) geometry optimizations and energy calculations used the B3LYP/6-311++G(2df,2pd) method.43–47 Owing to its excellent performance in a variety of energy calculations, the B3LYP functional is the most widely used functional.48 The simple calculations on small molecules in this work are not expected to be significantly affected by the limitations of B3LYP, which include hydrogen bonding, transition states, and long-range van der Waals interactions.48–52 Indeed, it has been shown that calculated solvation energies are not significantly affected by the choice of functional.53 Solvation effects were modeled using the IEFPCM-UFF model. Thermal contributions to the Gibbs free energy were calculated at room temperature (25°C).


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4. Results and Discussion The theoretical capacitance of the cell may be estimated by considering an infinite cylindrical capacitor, where the inner electrode diameter is a and the outer electrode diameter is b. The capacitance of a length L may then be expressed as a function of the dielectric constant of the medium between the electrodes, ε, where ε0 is the permittivity of free space (1).54 =×

20

ln

(1)

The dimensions of our cell are a = 25.45 ± 0.03 mm, b = 26.31 ± 0.03 mm, and L = 37.34 ± 0.05 mm, which predicts a linear calibration graph with slope 0.056 ± 0.002 nF. This estimate was compared with experimental data, measured at 25.0°C, from a series of standards with known dielectric constants: argon gas (ε = 1.43), chloroform (ε = 4.71), dichloromethane (ε = 8.93), acetone (ε = 20.5), ethanol (ε = 24.9), dimethyl sulfoxide (ε = 46.8), and water (ε = 78.4).22,36 The linear regression of the calibration data gave a slope of 0.057 nF. The calculated and experimental slopes agree within the measurement uncertainty of the capacitance cell dimensions. A slight disagreement may be expected because the cylindrical electrodes are not exactly smooth, parallel, or concentric, because of end effects not considered in the derivation of equation (1) and because of possible contributions from the wires, cables and circuit geometry. However, the results of Das and Chakrabarty suggest that end effects in this geometry should cause the capacitance to deviate by not more than a few percent.55 Moreover, the calibration data shows a negative deviation from linearity at high dielectric constants. Therefore, a quadratic calibration curve constructed from the standards and the fit, shown in Figure 4, has excellent agreement with experimentally measured data (R2 = 0.9998), which indicates that the cell precision is good. At room temperature, the absolute deviation of the standards was |∆ε| < 0.06, 9 ACS Paragon Plus Environment


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the mean difference was -0.01, and the mean absolute difference was 0.02. These indicate that the accuracy of the calibrated capacitance cell should also be quite good. Although equation (1) predicts a linear relationship between C and ε, the calibration curve in Figure 4 was used to determine ε from the measured values of C. The quadratic fit was constrained to pass through the origin. The validity of the calibration at different temperatures (25 ≤ T ≤ 60°C) was then tested with acetone and dichloromethane (Figure 5). The measurement uncertainty is greater than for measurements at 25 °C. Nevertheless, the experimentally measured dielectric constant for both solvents was a good match (|∆ε| ≤ 0.35, mean absolute difference = 0.20) to published values, indicating that the calibration curve may be used over this temperature range. As such, the dielectric constants for pure EMC and for two representative EC/EMC blends were measured at different temperatures (Figure 5). Although clear temperature-dependent trends are visible for the EC/EMC blends, the temperature-dependence of the dielectric constant of pure EMC may have been less than the uncertainty of the measurements themselves (|∆ε| ≤ 0.35 across the temperatures used in this work). Therefore, the dielectric constant of pure EMC at 25.0°C, εEMC = 3.5, may be approximately used over the temperature range 25°C ≤ T ≤ 60°C. This result is in good general agreement, in terms of an absolute error, with the published values for EMC at room temperature (cf. 3.0,36 2.9,37 2.432). It is noted that the measurement error of the capacitance cell used in this work is very small at 25 °C (|∆ε| < 0.06), whereas the cited works do not discuss their experimental uncertainty. The CRC Handbook of Chemistry and Physics is a commonly used resource for physical values. In its massive compilation of dielectric constants of solvents, the temperature dependence is fit to a linear or quadratic equation (2):36 10 ACS Paragon Plus Environment

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() = + + 2

(2)

Following this convention, the experimental values in Figure 5 were fitted and the parameters are reported in Table 2. The data was sufficiently linear that a quadratic term was not used (cT2) in the regressions, to avoid overfitting the data. These parameters were then used to calculate dielectric constants for 1:1 and 3:7 EC/EMC blends at regular temperature intervals (Table 3). These values may be used as the input parameter for the PCM model in QC research. The temperature dependence parameters were also calculated from the dielectric constant data for EC reported by Seward and Vieira and by Ding (R2 = 0.9990).33,34 The dielectric constant data for EC was already available from multiple sources and is shown below to match our solvent blend data very well. Moreover, EC is challenging to work with on account of its high melting point (34-37 °C). Therefore, further measurements of pure EC were not performed as a part of this study.

Table 2

Fitted temperature-dependence parameters for calculating the dielectric constant (ε) of EC/EMC solvent blends and pure EC over the range 25 – 60 °C using equation (2). To avoid overfitting the data, the quadratic term (cT2) was not used for our solvent blend data.

a b c a

3:7 40.30 -0.07320

1:1 82.61 -0.1645

ECa 293.7 -0.9002 7.858 × 10-4

Calculated from published data.33,34

Table 3

Dielectric constants (ε) for EC/EMC binary mixtures (by mass ratio) and pure EC at representative temperatures, calculated using equation (2) and the parameters in Table 11 ACS Paragon Plus Environment


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2. The accuracy of the measurements in this work is estimated to be ∆ε ± 0.06 at 25 °C and ∆ε ± 0.6 at all other temperatures. T (°C) 25 30 35 40 45 50 55 60 a

Ε 3:7 18.5 18.1 17.7 17.4 17.0 16.6 16.3 15.9

1:1 33.6 32.8 31.9 31.1 30.3 29.5 28.6 27.8

ECa 95.2 93.0 90.9 88.9 86.8 84.9 82.9 81.0

Calculated from published data.33,34

It is also possible to calculate the dielectric constant of a blend of n solvents, i, based on the properties of the pure components. For ideal solutions, the dielectric constant of the mixture, εm, depends on the dielectric constants of the individual solvents, εi, and the molar volumes, νi, as well as the molar fractions, xi. The molar volumes may be calculated from the pure substance molar masses, Mi, and densities, ρi (3).39 =

(3)

The dielectric constant of the mixture is then assumed to be a linear combination of the dielectric constants of the pure components as given by equation (4). =

∑ ∑

(4)

The ideal mixture approximation generally works well when the components have similar chemical structures. This approach is therefore expected to provide good estimates for blends that consist wholly of cyclic carbonates or linear carbonates.


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Using equation (4), the dielectric constants of EC/EMC mixtures were calculated at 25°C (Figure 6). EC is a solid at this temperature, so the density used in equation (3) may not accurately represent the molar volume of EC in solution. Moreover, the dielectric constant for EC at this temperature, taken from Table 1, is extrapolated from higher temperature values. Nevertheless, this approach produces the curve in Figure 6, which is compared with our experimental values for 1:1 and 3:7 EC/EMC blends. The theoretical curve overestimates the dielectric constant of the solvent blends by 28 % and 39 %, respectively. Therefore, blends of EC and EMC may not properly be treated as an ideal solution. Deviations between calculated and observed values are quite common when using simple linear models. Therefore, the quadratic mixing rule proposed by Wang and Anderko was adopted.56 This requires the additional calculation of the component polarizations, p, as given by equation (5). =

( − 1)(2 + 1) 9

(5)

The mixture polarization, pm, is then calculated, which introduces an empirical binary mixing parameter, kij, as given by equations (6) and (7): = ()" =

∑ ∑" " ()"

(6)

∑

1 ( + " " )(1 + #" ) 2

(7)

The dielectric constant of the mixture may then be calculated by entering the mixture polarization into equation (5) and solving the quadratic equation for ε. This method may also be applied to ternary blends if all the binary mixing parameters are known.56 Using the measured dielectric constants at 25 °C for 1:1 and 3:7 blends of EC and EMC, the EC/EMC mixing



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parameter was determined to be kij = -0.492. The mixing parameter increases slightly over the range 25°C ≤ T ≤ 60°C, as listed in Table 4, although this may be an artifact of using room temperature density values, rather than the true density at each temperature. Using the results in this work, one may now calculate the dielectric constant for EC/EMC solvent blends of any composition over this temperature range, as shown in Figure 7. The error between the data points from Table 3 and the calculated values in Figure 7 is 1 – 4 % for the 1:1 solutions and 0 – 1 % for the 3:7 mixtures, here the error is greatest at 60°C for both mixtures.

Table 4

Mixing parameters (kij) for calculating the dielectric constant of EC/EMC solvent blends using the dielectric constants of EC listed in Table 3 and the approximation that εEMC ≈ 3.5 over 25 – 60 °C.

T (°C) 25 30 35 40 45 50 55 60

kij -0.492 -0.495 -0.502 -0.504 -0.509 -0.517 -0.524 -0.532

This work has hinged upon the hypothesis that the dielectric constant will have a significant effect on calculated values, e.g., reaction energies, in QC-LIB research. Conversely, the null hypothesis, which deserves equal consideration, is that the effects of this parameter’s exact value are negligible. For example, Wang et al. found that there is little difference in the calculated standard oxidation potentials over the range 40 ≤ ε ≤ 80.16 Already, it has been shown


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that EC/EMC solvent blends with ≤ 50 % EC content by weight are below this range. Therefore, QC calculations were performed to gauge solvation model effects at lower solvent polarity. First, the dissociation of electrolyte salts in different solvents was considered. Chemical dissociation is highly important in batteries, since only dissociated ions can contribute to ionic conductivity. Lithium hexafluorophosphate (LiPF6) was chosen as a representative salt.31,57 The free energy of dissociation (∆Gdiss) in various solvents, as defined by their dielectric constants, is shown in Figure 8. ∆Gdiss is defined as the free energy change for the dissociation reaction of the dissolved but associated salt, LiPF6, to form free ions in solution, Li+ and PF6–. For ε ≥ 40, the exact value of the dielectric constant parameter has little effect on the calculated reaction energy (± 4.7 kJ mol-1). This is consistent with the results of Wang et al.16 However, below this range (i.e., ε < 40) the dissociation energy has greater dependency on this parameter and the calculated free energy of reaction becomes positive at ε < 15. This result is consistent with the general agreement that linear carbonates, which typically have ε < 5, will not fully dissociate lithium salts.31 LiPF6 is useful because of its high solubility in nonpolar solvents. However, this salt does not fully dissociate in solution.32,58,59 Rather, the dissolved salt forms ion pairs, which do not contribute to the solution conductivity. The calculations presented in the present work consider the simple dissociation of these dissolved ion pairs. The assumption is made that the salt is soluble at standard activity (i.e., ~1 mol kg-1). The effects of solvation shells, which are specific to each solvent and exceed the simplistic PCM, and solution ionic strength were ignored. Nevertheless, the general trend is expected to accurately represent the dissociation of LiPF6 dissociation in solvents of different polarity. Moreover, the dissociation of representative for calculations of other chemical processes in solution.


LiPF6 is


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The result shown in Figure 8 indicates that LiPF6 dissociation is greater in more polar solvents, which predicts that conductivity is also greater because of the larger concentration of charge carriers. This agrees with the results of Ding et al., who reported that the conductivity of isomolal LiPF6 solutions in EC/EMC increases with EC content.60 Given the solution viscosity is greater at higher EC content,31 the result may not be attributed to changes in the ionic mobilities. Rather, this supports our prediction that the ionic dissociation increases with solvent polarity. This general trend for the ionic dissociation of LiPF6 has also been experimentally observed for propylene carbonate (ε ~ 65), γ-butyrolactone (ε ~ 39) and selected blends of PC/DME (ε ~ 35) and PC/EMC (ε ~ 27).32,36,58 More generally, the result in Figure 8 demonstrates that using an incorrect dielectric constant can significantly affect the calculation accuracy, to the point that reaction spontaneity may be predicted incorrectly. Given that all of the EC/EMC solvent blends in this work have ε < 40, this demonstrates the importance of accurate solvation modeling in QCLIB research. Second, the potential effects of the dielectric parameter on calculations of an electrochemical process were considered. For this, the contribution of the solvation energy on the standard potential of vinylene carbonate (VC) oxidation, a widely popular electrolyte additive,31,61–64 was determined. The calculation of standard electrode potentials for the oxidation and reduction of molecules has previously been discussed elsewhere.3,16 The term ‘standard electrode potential’ is used here, rather than ‘oxidation potential’ or ‘reduction potential’ to more accurately describe these calculations. This method predicts the potential where there is an equilibrium between the reduced and oxidized species, at standard state. That is, the free energy of reaction at standard state, ∆G0, is set to exactly zero. This equilibrium condition is stressed because without an overpotential, neither net oxidation nor reduction will occur. Figure 9 shows


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the calculated solvation energy of neutral VC and the singly oxidized [VC]+ cation in various solvents, as defined by their dielectric constant. Again, there is little effect on calculated results in the range 40 ≤ ε ≤ 80 (± 0.03 eV). However, the effect of solution properties on solvation energy is important in less polar solutions. For example, if the standard potential of VC oxidation is calculated using ε = 30 when ε = 15 is more appropriate, then the solvation term will contribute a final error of 0.09 V. In another example, if the solvent is modeled as water (ε = 78.4) but is closer to ε = 10, then this error is ~0.23 V. Finally, if no solvation model is used but the solvent properties are ε = 10, then the calculated oxidation potential will be ~2.3 V too high. For comparison, the error associated with SMD, IEFPCM, and other PCM models for neutral species is on the order of ~1 kcal mol-1 (~ 0.05 eV) or less.28,53 It is also well-known that the dielectric constant used in the PCM can affect the stable geometry properties, including bond lengths and angles.65 Therefore, an unknown dielectric constant can significantly detract from calculation accuracy using implicit solvation modeling in LIB research. The solvation modeling of ionic species poses additional challenges, where the calculation error can be an order of magnitude greater than for neutral molecules.53 For this reason, other solvation models are often used, including COSMO, ONIOM, and hybrid cluster/continuum methods. In the simplest hybrid model, the solute is within a primary solvation shell and then surrounded by the PCM. Although static cluster modeling does a poor job of representing the dynamic nature of liquid-phase solvents, it can nevertheless provide insight into solute-solvent interactions that the PCM alone cannot.66,67 However, these methods still require that the properties of the bulk solvent are known. In particular, the polarizable continuum is always described by its dielectric constant. Therefore, the stable geometry (including solvent packing, solute-solvent distances, etc.) will be affected by whether this parameter is known.65



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Likewise, energy calculations will also be affected. For example, von Wald Cresce et al. studied [LiECn]+ and [LiPCn]+complexes using a hybrid solvation cluster/PCM model (ε = 1, 20, 78) and the LC-ωPBE functional or the G4MP2 level of theory.68 These methods are more appropriate for calculations involving solute-solvent clusters because of the tendency of B3LYP to overestimate cation-solvent binding energies. The calculated reduction potential varies by 2.06 eV over the range 1 ≤ ε ≤ 20. As shown in Figure 7 and summarized in Table 3, the commonly used 3:7 EC/EMC solvent blend is ε < 20 for T ≥ 25 °C. Clearly, knowledge of the solvent dielectric constant is prerequisite for accurate solvation modeling. It is therefore hoped that the solution properties reported in this work will lay the groundwork for more accurate calculations of solvation energies and standard electrode potentials in EC/EMC binary mixtures. Therefore, it is concluded that the exact value of the dielectric constant can significantly affect QC calculations for both chemical and electrochemical processes in LIBs. 5. Conclusions Dielectric constants are needed for accurate QC calculations for LIBs, yet reliable values are not reported for most solvent blends. In this work, the necessary parameters to accurately model pure EMC, 3:7 EC/EMC, and 1:1 EC/EMC over the temperature range 25°C ≤ T ≤ 60°C are reported. The experimentally measured values at room temperature did not match theoretical dielectric constants of EC/EMC blends, as calculated from linear combinations of molar volumes and the pure component properties. Instead, the quadratic mixing rule proposed by Wang and Anderko56 was adopted and the mixing parameter was found over the whole temperature range. Using this mixing rule and the parameters reported in this work, the dielectric constant of any EC/EMC solvent blend may be calculated for 25°C ≤ T ≤ 60°C. Compared with the measured


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values reported here, the calculated values have ≤ 4 % error for 1:1 mixtures and ≤ 1 % error for 3:7 mixtures. Finally, the published statement that the exact value of the dielectric constant has a relatively small effect on QC calculations for polar solvents (40 ≤ ε ≤ 80) is in agreement with results found here.16 However, the accuracy of QC calculations can be greatly compromised in less polar solvents (ε < 40). This includes models of both chemical and electrochemical processes. For example, solvent properties can affect the predicted spontaneity of salt dissociation or introduce large errors in calculated standard electrode potentials for the oxidation or reduction of molecules. It is therefore hoped that the results of this work will be adopted to improve the accuracy of QC calculations of the chemical modeling in LIBs. 6. Acknowledgements This work was conducted with the financial support of 3M Canada. Computational facilities were provided by ACENET (Atlantic Computational Excellence Network) and funded by the Canada Foundation for Innovation (CFI), the Atlantic Canada Opportunities Agency (ACOA) and the provinces of Newfoundland and Labrador, Nova Scotia, and New Brunswick. The authors acknowledge the contributions of Simon Trussler for constructing and collaborating in the design of the capacitance cell.



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7. References (1)

Bhatt, M. D.; O’Dwyer, C. The Role of Carbonate and Sulfite Additives in Propylene Carbonate-Based Electrolytes on the Formation of SEI Layers at Graphitic Li-Ion Battery Anodes. J. Electrochem. Soc. 2014, 161 (9), A1415–A1421.

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Bhatt, M. D.; O’Dwyer, C. Recent Progress in Theoretical and Computational Investigations of Li-Ion Battery Materials and Electrolytes. Phys. Chem. Chem. Phys. 2015, 17 (7), 4799–4844.

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Borodin, O.; Behl, W.; Jow, T. R. Oxidative Stability and Initial Decomposition Reactions of Carbonate, Sulfone, and Alkyl Phosphate-Based Electrolytes. J. Phys. Chem. C 2013, 117 (17), 8661–8682.

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Tavassol, H.; Buthker, J. W.; Ferguson, G. A.; Curtiss, L. A.; Gewirth, A. A. Solvent Oligomerization during SEI Formation on Model Systems for Li-Ion Battery Anodes. J. Electrochem. Soc. 2012, 159 (6), A730–A738.

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Vollmer, J. M.; Curtiss, L. A.; Vissers, D. R.; Amine, K. Reduction Mechanisms of Ethylene, Propylene, and Vinylethylene Carbonates A Quantum Chemical Study. J. Electrochem. Soc. 2004, 151 (1), A178–A183.

(6)

Xing, L.; Borodin, O. Oxidation Induced Decomposition of Ethylene Carbonate from DFT Calculations - Importance of Explicitly Treating Surrounding Solvent. Phys. Chem. Chem. Phys. 2012, 14 (37), 12838–12843.

(7)

Xing, L.; Li, W.; Wang, C.; Gu, F.; Xu, M.; Tan, C.; Yi, J. Theoretical Investigations on Oxidative Stability of Solvents and Oxidative Decomposition Mechanism of Ethylene Carbonate for Lithium Ion Battery Use. J. Phys. Chem. B 2009, 113 (52), 16596–16602.


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(8)

Carboni, M.; Spezia, R.; Brutti, S. Perfluoroalkyl-Fluorophosphate Anions for High Voltage Electrolytes in Lithium Cells: DFT Study. J. Phys. Chem. C 2014, 118 (42), 24221–24230.

(9)

Lau, K. C.; Lu, J.; Low, J.; Peng, D.; Wu, H.; Albishri, H. M.; Al-Hady, D. A.; Curtiss, L. A.; Amine, K. Investigation of the Decomposition Mechanism of Lithium Bis(oxalate)borate (LiBOB) Salt in the Electrolyte of an Aprotic Li–O2 Battery. Energy Technol. 2014, 2 (4), 348–354.

(10) Li, S.; Li, X.; Zhang, H.; Mao, L.; Cui, X. Oxidative Stability and Reduction Decomposition Mechanism Studies on a Novel Salt: Lithium Difluoro(sulfato)borate. RSC Adv. 2015, 5 (23), 18000–18007. (11) Li, Z.; Borodin, O.; Smith, G. D.; Bedrov, D. Effect of Organic Solvents on Li+ Ion Solvation and Transport in Ionic Liquid Electrolytes: A Molecular Dynamics Simulation Study. J. Phys. Chem. B 2015, 119 (7), 3085–3096. (12) Tachikawa, H. Mechanism of Dissolution of a Lithium Salt in an Electrolytic Solvent in a Lithium Ion Secondary Battery: A Direct Ab Initio Molecular Dynamics (AIMD) Study. ChemPhysChem 2014, 15 (8), 1604–1610. (13) Martínez-de la Hoz, J. M.; Balbuena, P. B. Reduction Mechanisms of Additives on Si Anodes of Li-Ion Batteries. Phys. Chem. Chem. Phys. 2014, 16 (32), 17091–17098. (14) Wang, R. L.; Dahn, J. R. Computational Estimates of Stability of Redox Shuttle Additives for Li-Ion Cells. J. Electrochem. Soc. 2006, 153 (10), A1922–A1928. (15) Wang, R. L.; Moshurchak, L. M.; Lamanna, W. M.; Bulinski, M.; Dahn, J. R. A Combined Computational/Experimental Study on Tertbutyl- and Methoxy-Substituted



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Benzene Derivatives as Redox Shuttles for Lithium-Ion Cells. J. Electrochem. Soc. 2008, 155 (1), A66–A73. (16) Wang, R. L.; Buhrmester, C.; Dahn, J. R. Calculations of Oxidation Potentials of Redox Shuttle Additives for Li-Ion Cells. J. Electrochem. Soc. 2006, 153 (2), A445–A449. (17) Thomas, J. R.; DeLeeuw, B. J.; Vacek, G.; Crawford, T. D.; Yamaguchi, Y.; Iii, H. F. S. The Balance between Theoretical Method and Basis Set Quality: A Systematic Study of Equilibrium Geometries, Dipole Moments, Harmonic Vibrational Frequencies, and Infrared Intensities. J. Chem. Phys. 1993, 99 (1), 403–416. (18) Dilling, W. L. The Effect of Solvent on the Electronic Transitions of Benzophenone and Its O- and P-Hydroxy Derivatives. J. Org. Chem. 1966, 31 (4), 1045–1050. (19) Solvents and Solvent Effects in Organic Chemistry, 4th ed.; Reichardt, C., Welton, T., Eds.; Wiley-VCH Verlag GmbH & Co. KGaA: Weinheim, Germany, 2011. (20) Alexander, R.; Ko, E. C. F.; Parker, A. J.; Broxton, T. J. Solvation of Ions. XIV. ProticDipolar Aprotic Solvent Effects on Rates of Bimolecular Reactions. Solvent Activity Coefficients of Reactants and Transition States at 25°. J. Am. Chem. Soc. 1968, 90 (19), 5049–5069. (21) Tomasi, J.; Mennucci, B.; Cammi, R. Quantum Mechanical Continuum Solvation Models. Chem. Rev. 2005, 105 (8), 2999–3094. (22) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. Gaussian 09; Gaussian, Inc.: Wallingford, CT, USA, 2009.


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(23) Tomasi, J.; Mennucci, B.; Cancès, E. The IEF Version of the PCM Solvation Method: An Overview of a New Method Addressed to Study Molecular Solutes at the QM Ab Initio Level. J. Mol. Struct. THEOCHEM 1999, 464 (1–3), 211–226. (24) Marenich, A. V.; Cramer, C. J.; Truhlar, D. G. Performance of SM6, SM8, and SMD on the SAMPL1 Test Set for the Prediction of Small-Molecule Solvation Free Energies†. J. Phys. Chem. B 2009, 113 (14), 4538–4543. (25) Marenich, A. V.; Cramer, C. J.; Truhlar, D. G. Universal Solvation Model Based on Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric Constant and Atomic Surface Tensions. J. Phys. Chem. B 2009, 113 (18), 6378– 6396. (26) Mo, S. J.; Vreven, T.; Mennucci, B.; Morokuma, K.; Tomasi, J. Theoretical Study of the SN2 Reaction of Cl−(H2O)+CH3Cl Using Our Own N-Layered Integrated Molecular Orbital and Molecular Mechanics Polarizable Continuum Model Method (ONIOM, PCM). Theor. Chem. Acc. 2004, 111 (2-6), 154–161. (27) Vreven, T.; Mennucci, B.; Silva, C. O. da; Morokuma, K.; Tomasi, J. The ONIOM-PCM Method: Combining the Hybrid Molecular Orbital Method and the Polarizable Continuum Model for Solvation. Application to the Geometry and Properties of a Merocyanine in Solution. J. Chem. Phys. 2001, 115 (1), 62–72. (28) Klamt, A.; Mennucci, B.; Tomasi, J.; Barone, V.; Curutchet, C.; Orozco, M.; Luque, F. J. On the Performance of Continuum Solvation Methods. A Comment on “Universal Approaches to Solvation Modeling.” Acc. Chem. Res. 2009, 42 (4), 489–492. (29) Klamt, A. The COSMO and COSMO-RS Solvation Models. Wiley Interdiscip. Rev. Comput. Mol. Sci. 2011, 1 (5), 699–709.



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(47) McLean, A. D.; Chandler, G. S. Contracted Gaussian Basis Sets for Molecular Calculations. I. Second Row Atoms, Z=11–18. J. Chem. Phys. 1980, 72 (10), 5639–5648. (48) Wodrich, M. D.; Corminboeuf, C.; Schreiner, P. R.; Fokin, A. A.; Schleyer, P. von R. How Accurate Are DFT Treatments of Organic Energies? Org. Lett. 2007, 9 (10), 1851– 1854. (49) Lynch, B. J.; Truhlar, D. G. How Well Can Hybrid Density Functional Methods Predict Transition State Geometries and Barrier Heights? J. Phys. Chem. A 2001, 105 (13), 2936– 2941. (50) Lynch, B. J.; Fast, P. L.; Harris, M.; Truhlar, D. G. Adiabatic Connection for Kinetics. J. Phys. Chem. A 2000, 104 (21), 4811–4815. (51) Tsuzuki, S.; Lüthi, H. P. Interaction Energies of van Der Waals and Hydrogen Bonded Systems Calculated Using Density Functional Theory: Assessing the PW91 Model. J. Chem. Phys. 2001, 114 (9), 3949–3957. (52) Zhao, Y.; Tishchenko, O.; Truhlar, D. G. How Well Can Density Functional Methods Describe Hydrogen Bonds to Π Acceptors? J. Phys. Chem. B 2005, 109 (41), 19046– 19051. (53) Rayne, S.; Forest, K. Accuracy of Computational Solvation Free Energies for Neutral and Ionic Compounds: Dependence on Level of Theory and Solvent Model. Nat. Preced. 2010. (54) Griffiths, D. J. Introduction to Electrodynamics, 3rd ed..; Prentice Hall: Upper Saddle River, NJ, 1999. (55) Das, B. N.; Chakrabarty, S. B. Capacitance and Charge Distribution of Two Cylindrical Conductors of Finite Length. Sci. Meas. Technol. IEE Proc. - 1997, 144 (6), 280–286.


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(56) Wang, P.; Anderko, A. Computation of Dielectric Constants of Solvent Mixtures and Electrolyte Solutions. Fluid Phase Equilibria 2001, 186 (1–2), 103–122. (57) Dahbi, M.; Ghamouss, F.; Tran-Van, F.; Lemordant, D.; Anouti, M. Comparative Study of EC/DMC LiTFSI and LiPF6 Electrolytes for Electrochemical Storage. J. Power Sources 2011, 196 (22), 9743–9750. (58) Ue, M. Mobility and Ionic Association of Lithium and Quaternary Ammonium Salts in Propylene Carbonate and γ‐Butyrolactone. J. Electrochem. Soc. 1994, 141 (12), 3336– 3342. (59) Xu, K. Nonaqueous Liquid Electrolytes for Lithium-Based Rechargeable Batteries. Chem. Rev. 2004, 104 (10), 4303–4418. (60) Ding, M. S.; Xu, K.; Zhang, S. S.; Amine, K.; Henriksen, G. L.; Jow, T. R. Change of Conductivity with Salt Content, Solvent Composition, and Temperature for Electrolytes of LiPF6 in Ethylene Carbonate-Ethyl Methyl Carbonate. J. Electrochem. Soc. 2001, 148 (10), A1196–A1204. (61) El Ouatani, L.; Dedryvère, R.; Siret, C.; Biensan, P.; Gonbeau, D. Effect of Vinylene Carbonate Additive in Li-Ion Batteries: Comparison of LiCoO2 ⁄ C , LiFePO4 ⁄ C , and LiCoO2 ⁄ Li4Ti5O12 Systems. J. Electrochem. Soc. 2009, 156 (6), A468–A477. (62) El Ouatani, L.; Dedryvère, R.; Siret, C.; Biensan, P.; Reynaud, S.; Iratçabal, P.; Gonbeau, D. The Effect of Vinylene Carbonate Additive on Surface Film Formation on Both Electrodes in Li-Ion Batteries. J. Electrochem. Soc. 2009, 156 (2), A103–A113. (63) Zhang, B.; Metzger, M.; Solchenbach, S.; Payne, M.; Meini, S.; Gasteiger, H. A.; Garsuch, A.; Lucht, B. L. Role of 1,3-Propane Sultone and Vinylene Carbonate in Solid Electrolyte Interface Formation and Gas Generation. J. Phys. Chem. C 2015.



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(64) Zhang, S. S. A Review on Electrolyte Additives for Lithium-Ion Batteries. J. Power Sources 2006, 162 (2), 1379–1394. (65) Cramer, C. J. Essentials of Computational Chemistry: Theories and Models, 2nd ed.; John Wiley & Sons: West Sussex, England, 2004. (66) Borodin, O.; Smith, G. D. Quantum Chemistry and Molecular Dynamics Simulation Study of Dimethyl Carbonate: Ethylene Carbonate Electrolytes Doped with LiPF6. J. Phys. Chem. B 2009, 113 (6), 1763–1776. (67) Scheers, J.; Niedzicki, L.; Żukowska, G. Z.; Johansson, P.; Wieczorek, W.; Jacobsson, P. Ion–ion and Ion–solvent Interactions in Lithium Imidazolide Electrolytes Studied by Raman Spectroscopy and DFT Models. Phys. Chem. Chem. Phys. 2011, 13 (23), 11136– 11147. (68) Von Wald Cresce, A.; Borodin, O.; Xu, K. Correlating Li+ Solvation Sheath Structure with Interphasial Chemistry on Graphite. J. Phys. Chem. C 2012, 116 (50), 26111–26117.

Figure 1 (a) Scale diagram of the capacitance cell for liquids and gases used in this work. (b) The fully assembled cell. (c) Top view of the can. (d) Side view of the lid and inner electrode.

Figure 2 Diagram showing the capacitance cell wired in parallel with a resistor, which ranged from 1 – 100 kΩ, and connected to a frequency response analyzer (FRA). The apparatus was placed in a temperature control box (∆T = ± 0.1 °C).


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Figure 3 Sample Nyquist plot showing the measured impedance at 25.0°C of the capacitance cell, filled with acetone, wired in parallel with a 1 kΩ resistor.

Figure 4 Quadratic calibration curve showing the relationship between the measured capacitance and the dielectric constant (ε) of the filled cell at 25.0°C. The curve was constrained to pass through the origin. R2 = 0.9998.

Figure 5 Temperature-dependence of the dielectric constant (ε) of EC/EMC solvent blends. The data (points) were fit using linear regressions (solid lines). Acetone and dichloromethane were used to confirm the accuracy of the capacitance cell. The measured data (points) are found to be a good match (|∆ε| ≤ 0.35, mean absolute difference = 0.20) with the literature dielectric constants (dashed lines).36

Figure 6 The dielectric constants of EC/EMC ideal mixtures at 25.0 °C were calculated using a linear approximation (solid red line) and the quadratic mixing rule proposed by Wang and Anderko56 when kij = -0.49 (dashed blue line). The experimental values for 3:7 and 1:1 blends are shown for comparison (solid black circles).

Figure 7 The dielectric constants of EC/EMC mixtures calculated at 5 °C temperature intervals over the range 25 – 60 °C using the quadratic mixing parameters in Table 4 (solid red lines). Data points from Table 3 are shown for comparison.



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Figure 8 The calculated free energy of LiPF6 dissociation in various solvents, as defined by their dielectric constants, at 25.0 °C.

Figure 9 The calculated free energy of solvation for neutral vinylene carbonate (VC) and the singly oxidized [VC]+ cation in various solvents, as defined by their dielectric constants, at 25.0 °C.


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(a) Scale diagram of the capacitance cell for liquids and gases used in this work. (b) The fully assembled cell. (c) Top view of the can. (d) Side view of the lid and inner electrode. 131x59mm (300 x 300 DPI)

ACS Paragon Plus Environment


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Diagram showing the capacitance cell wired in parallel with a resistor, which ranged from 1 – 100 kΩ, and connected to a frequency response analyzer (FRA). The apparatus was placed in a temperature control box (∆T = ± 0.1 °C). 49x44mm (300 x 300 DPI)


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Sample Nyquist plot showing the measured impedance at 25.0°C of the capacitance cell, filled with acetone, wired in parallel with a 1 kΩ resistor. 174x89mm (300 x 300 DPI)



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Quadratic calibration curve showing the relationship between the measured capacitance and the dielectric constant (ε) of the filled cell at 25.0°C. The curve was constrained to pass through the origin. R2 = 0.9998. 163x91mm (300 x 300 DPI)


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Temperature-dependence of the dielectric constant (ε) of EC/EMC solvent blends. The data (points) were fit using linear regressions (solid lines). Acetone and dichloromethane were used to confirm the accuracy of the capacitance cell. The measured data (points) are found to be a good match (|∆ε| ≤ 0.35, mean absolute difference = 0.20) with the literature dielectric constants (dashed lines).31 167x111mm (300 x 300 DPI)



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The dielectric constants of EC/EMC ideal mixtures at 25.0 °C were calculated using a linear approximation (solid red line) and the quadratic mixing rule proposed by Wang and Anderko45 when kij = -0.49 (dashed blue line). The experimental values for 3:7 and 1:1 blends are shown for comparison (solid black circles). 168x90mm (300 x 300 DPI)


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The dielectric constants of EC/EMC mixtures calculated at 5 °C temperature intervals over the range 25 – 60 °C using the quadratic mixing parameters in Table 4 (solid red lines). Data points from Table 3 are shown for comparison. 168x101mm (300 x 300 DPI)



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The calculated free energy of LiPF6 dissociation in various solvents, as defined by their dielectric constants, at 25.0 °C. 170x87mm (300 x 300 DPI)


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The calculated free energy of solvation for neutral vinylene carbonate (VC) and the singly oxidized [VC]+ cation in various solvents, as defined by their dielectric constants, at 25.0 °C. 166x92mm (300 x 300 DPI)



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Figure for table of contents only. 88x38mm (300 x 300 DPI)


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Solvent Blends of Ethylene Carbonate and Ethyl Methyl Carbonate

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