Predicting Ion Association in Sodium Electrolytes - ACS Publications

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Predicting Ion Association in Sodium Electrolytes: A Transferrable Model for Investigating Glymes Ke Li, Susith R. Galle Kankanamge, Thomas K. Weldeghiorghis, Ryan Jorn, Daniel G Kuroda, and Revati Kumar J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b09995 • Publication Date (Web): 22 Nov 2017 Downloaded from http://pubs.acs.org on November 28, 2017

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The Journal of Physical Chemistry

Predicting Ion Association in Sodium Electrolytes: A Transferrable Model for Investigating Glymes Li Ke,‡ Susith R Galle Kankanamge,‡ Thomas K Weldeghiorghis,‡ Ryan Jorn,† Daniel G. Kuroda,‡ and Revati Kumar*‡ † Department of Chemistry, Villanova University, Villanova, Pennsylvania 19085, United States ‡ Department of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70803, United States *Address correspondence to [email protected]

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ABSTRACT:

Given the prior success in developing lithium batteries for similar purposes,

many of the same types of solvent molecules and salt pairings have been investigated as electrolytes in sodium-ion and sodium-oxygen systems. Of these candidates, ether-containing electrolytes have emerged as a promising material as a result of their electrochemical stability and utility in tuning the pertinent electrochemistry. The ability for ethers to chelate metal ions provides a unique feature to ion solvation structure, however its role in changing the association of ions in solution has not been fully explored. By using computational simulations validated by FTIR and NMR spectroscopy, detailed descriptions of the changes to solvation structure as a result of chelation and concentration were investigated for a series of ethers (monoglyme to tetraglyme). From these simulations it can clearly be seen that with increasing chelation, ion association is diminished in a nonlinear fashion. For a monoglyme solvent, sodiums are entirely coordinated by triflates in solution, even at low concentrations. In contrast, tetraglymes retain a significant solvent separation of sodium cations from triflate anions even at high concentrations. The former implies that the utility of monoglyme and diglyme solvents for sodium-air batteries in specific is likely linked to their favoring ion association while the poor performance of tetraglyme is a result of its excessive binding to sodium. Finally, triglyme was shown to produce anomalous behavior as a result of a mismatch between sodium coordination and steric interactions.


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INTRODUCTION The challenges associated with long-term fossil fuel consumption for transportation are multitudinous, ranging from environmental to economic.1-2 In an effort to convert from fossil fuel dependence to a renewable paradigm, lithium energy storage technology has been introduced to the automotive market.3 Continued success in transitioning to all electric vehicles depends on the development of batteries with greater energy and power densities matched with sustainable charge/discharge capacity. In order to capitalize on the knowledge base obtained from decades of studying lithium batteries, one can move down Group 1 of the periodic table and consider the benefits of swapping sodium for lithium.4 The greatest advantage of sodium over lithium is economic in the sense that sodium has a much higher natural abundance than lithium. Hence, the fuel for a sodium storage system will be much cheaper in the long term than its lithium counterpart.5 In addition to lower cost, sodium electrochemistry is similar enough to lithium to suggest that analogous intercalation electrodes can be developed for sodium-ion batteries as well as oxygen cathodes for metal-air systems.6 An improved understanding of the basic operation of both sodium-ion and sodium-air devices has raised several fundamental challenges to making the technologies more competitive.4, 7-8

In regards to the electrolyte, greater insight is needed into the charge transport behavior of the

electrolyte, the nature of the electrolyte/electrode interface, the types of chemical side reactions taking place during charge/discharge, and the factors influencing electrochemical stability.9 By connecting the choice of solvent and metal salt with electrolyte performance, one can gain greater predictive capability to rationally guide electrolyte design. In the case of lithium-ion batteries, optimizing viscosity and electrochemical stability has almost universally favored a mixture of cyclic and linear carbonates with a dissolved lithium salt.10 Borrowing from these



efforts, sodium salts dissolved in mixtures of ethylene carbonate (EC), propylene carbonate (PC), ethyl methyl carbonate (EMC), dimethyl carbonate(DMC), and diethyl carbonate (DEC) have been optimized for better battery performance.11-14 It was found that mixtures of cyclic and linear carbonates provided optimal charge transport properties, i.e. low viscosity and high bulk conductivity, while the passivating layers formed on the electrodes from mixtures of EC and PC protected the electrolyte from rapid degradation.15 The latter observation is in keeping with findings for lithium-ion systems in which carbonate solvents have been preferred for their ability to passivate anode surfaces and stabilize the electrolyte interface for charge transport.16 The price for this passivation is the removal of metal ions from charge cycling and hence diminished capacity to store charge. In the case of sodium electrolytes, the reaction of the carbonates with the electrodes may be more problematic as a result of the solubility of the resulting sodium carbonate.17 If the reaction product does not stick to the electrode surface, then continual dissolution leaves the reactive surface exposed to the electrolyte and promotes further capacity loss over time.18 Furthermore, for sodium-air systems it has been noted that carbonates are not conducive to the formation of the desired sodium superoxide, resulting in the formation of sodium carbonates in competition with the desired product.19 Ethers present an intriguing alternative to carbonates and have recently seen greater emphasis in both sodium-ion and sodium-air systems. To date, the most popular ether solvents are the glyme series which consist of a varying number of ethylene glycol [–OCH2CH2O–] subunits starting from monoglyme (CH3OCH2CH2OCH3).9 The first solvation shell for metal cations dissolved in glymes consists of ether oxygens with around 6 total coordinating each sodium,20-21 and between 5 to 6 binding each sodium in concentrated crystal solvate structures.22 Coordination numbers in the ethers tend to be higher than those for corresponding carbonate


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solvents,11, 23-24 and agrees with a stronger binding to the ether. The stronger coordination is attributed to a chelating effect, especially for longer glyme molecules capable of wrapping around the sodium ion, and results from donation of electron density from the lone pairs on the oxygens to the metal cation.25 Significant electron donation is evidenced by the increased oxidative stability of the ether molecules at high salt concentration.26 The binding of the metal ions also has significant impact on the performance of sodium energy storage devices built with glyme electrolytes via the formation of ternary graphite intercalation complexes.27-29 In addition to producing tremendous gains of capacity retention during charge/discharge from forming intercalation complexes,30 the use of glyme electrolytes may also improve the kinetics of discharge in comparison to carbonate solvents.31 Ether electrolytes have proven beneficial for facilitating oxide formation in both sodium and lithium-air devices as a result of a subtle interplay between superoxide anion solvation and product precipitation.8 The nature of the sodium superoxide deposits formed during discharge has been rationalized by a simple model describing a competition between a surface mediated multi-electron process and a solution-based mechanism.21 The role of the electrolyte in favoring one mechanism over the other can be attributed to the selection of solvent,32 while the role of the metal salt seems to differ between lithium and sodium systems.33-34 In both cases, the selection of a solvent capable of donating electron density to the metal cation allows for greater stability of the cation and superoxide anion as a pair in solution.32, 35 Greater solubility favors the solutionbased mechanism over the surface-based reaction that produces the peroxide in both lithium and sodium systems.8 For lithium, the role of the metal salt can also favor the solution-based process by strong ion association blocking the lithium ions from reacting directly with the superoxide anions.33 A recent study for sodium suggests that the phenomena is not reproduced with sodium



salts, leaving the selection of solvent as the key parameter for tuning discharge capacity.34 While ethers lack a high donor number, Lutz et al. have shown that their chelating ability plays a large role in the successful production of sodium superoxide.21 Furthermore, Lutz et al. provided one of the most detailed investigations of the impact of chelation by varying the lengths of the glymes used in the electrolyte and studying the resulting discharge product. They found that for short glymes, where chelation is minimal, the solution-based process is favored and produces large cubes of the superoxide. However, when longer glyme molecules are used, the chelation is too strong to the sodium cation and actually works against the formation of the sodium superoxide by preventing saturation of the double layer.21 While the long-term prospects of ether electrolytes for metal-air systems remains clouded by questions of stability,36 clearly a better understanding of the chelation and ion association in glymes is critical to their use in sodium energy storage technology. In light of the importance of the chelating ability of glymes to both sodium-ion and sodium-air electrochemistry, it is paramount to understand the metal solvation structure as a function of counter anion binding and glyme length. Computational modeling in particular is well suited to studying solvation trends and has seen increasing connection with spectroscopy to elucidate electrolyte properties.11,

20, 37

In spite of its recent relevance, it seems that few

computational studies have been conducted to detail the trends in ion association for sodium salts in glyme solutions. Regarding the role of ion association, Jónsson and Johansson performed ab initio calculations with solvation models to emphasize the general importance of anion structure and charge delocalization on ion association.38 Inclusion of explicit solvation was considered by Dhumal et al. in a series of gas phase ab initio DFT studies of the coordination structure of sodium salts by glymes of varying chain length.39-42 By accounting for the chelation effect, they


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validated the notion that cation-anion binding weakens as the glyme length increases. This work was extended recently by Tsuzuki et al. with a detailed study of the electrostatic interactions between a TFSA counter anion, sodium cations, and glymes within MP2.25 Condensed phase calculations accounting for both enthalpic and entropic contributions to solvation have focused mostly on carbonate mixtures.11,

23

To our knowledge only a handful of reports have been

provided of simulations of sodium in fully atomistic glyme electrolytes,20-21 though several have appeared for lithium systems.43-45 Given the significance to sodium energy storage, the goal of this work is to further explore the role of chelation and concentration on ion association in glyme electrolytes. In a previous study, a new force field was developed and validated for describing ion interactions with diglyme, specifically sodium triflate.20 In that case, the influence of salt concentration on ion association was considered and reinforced the experimental observation that increased ion pairing occurred with greater salt content. Having demonstrated the utility of this approach, the goal of the present work is twofold: to validate the transferability of the model to glymes of varying length and to explore the impact of concentration in tandem with chelation. METHODOLOGY a. Experimental Sodium

trifluoromethanesulfonate

(CF3SO3Na,

>98%),

diglyme

((CH3)2[CH2CH2O]2O, >99%) and tetraglyme ((CH3)2[CH2CH2O]4O, >99%) were obtained from Acros Organics. Monoglyme, ((CH3)2[CH2CH2O]O, >99%) was obtained from MilliporeSigma and triglyme ((CH3)2[CH2CH2O]3O, >99%) was obtained from Alfa Aesar. All the chemicals were used without further purification. Solutions having 1.0M and 1.5M concentrations were prepared by simply mixing the components stored in a N2 filled glovebox. Fourier Transform



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Infrared (FTIR) experiments were conducted using a Bruker Tensor 27 spectrometer with 0.5 cm-1 resolution in absorption mode. The samples were prepared using a transmission cell (Harrick Scientific) consisting of a pair of 2 mm calcium fluoride windows without a spacer. Each FTIR spectrum was recorded as an average of 40 individual scans and the measurements were done at 25 °C. Pulse field gradient (PFG) diffusion experiments were performed on a 400 MHz Bruker AV spectrometer with a wide bore magnet using a Diff60 diffusion probe and Great 1/60 gradient amplifier. The diffusion probe has a gradient sensitivity of 600 mT/Am (60G/Acm). Diffusion data were collected at 25°C, and the sample temperature was controlled using a Bruker BVT 3000 digital variable temperature controller. The probe gradient coil temperature was controlled using a Neslab Merlin M33 (Thermo Scientific) recirculating chiller. Diffusion experiments were focused on the 1H of the glyme molecules locate at d= 3.6-4. Note that all of the different peaks produced a diffusion coefficient within 3%. Diffusion experiments consist of pulse gradient stimulated echo (diffSTE) sequences that used the same sequences as described in Ref.

46

. In brief, the diffusion data were collected with constant

gradient pulse duration (d) and diffusion time (D). A 2 ms homospoil gradient pulse was used to remove unwanted signal. For all three samples, a gradient pulse duration of 1 ms and diffusion times between 20-80 ms were used. The maximum gradient strength (g) used was between 120 and 160 G/cm for all samples. The gradient strength (g) was varied between the maximum value and 5% of the maximum value linearly in 32 increments. Each experiment was performed twice in which 16 scans per step were averaged. The diffusion constant (D), was determined by fitting experimental data to the Stejskal-Tanner-equation,47 ! !"

= 𝑒 %&

' ( ' ) ' (∆%, )0 .

(1)


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where S is signal attenuated by gradient pulses, S0 is the reference signal (with no gradient attenuation), g is the gyromagnetic ratio of the observed nucleus (1H), and the other variables are from the pulse sequence. b. Classical Molecular Dynamics Simulations The force-field used is based on the previously developed model for a diglyme electrolyte containing the metal salt sodium triflate.20 In the prior study, the diglyme molecules were modeled using the PCFF force-field and the interaction of the solvent with the sodium and the ion-ion interactions were parameterized using the variational force-matching algorithm on data from ab initio MD simulations.48 In this work, the force field for each of the different glymes is obtained from the PCFF model, while the ion-solvent and the ion-ion interactions are the same as those used in the previous study.20 The initial structures of monoglyme, diglyme, triglyme, tetraglyme, and sodium triflate were built using the Avogadro software (See Figure 1).49 Four cubic simulation boxes were constructed with side length ~40 Å for monoglyme, ~38 Å for diglyme, ~ 41 Å for triglyme, ~45 Å for tetraglyme, and were populated using a random packing algorithm in Packmol.50 For monoglyme, each simulation box contained 360 monoglyme molecules with a varying number of sodium triflate pairs to account for the correct concentration: 19 for 0.5 M, 38 for 1.0 M, 57 for 1.5 M, 76 for 2.0 M. For diglyme, each simulation box contained 230 diglyme molecules with the following number of sodium triflate pairs: 17 for 0.5 M, 34 for 1.0 M, 51 for 1.5 M, 68 for 2.0 M. For triglyme, the simulation box contained 213 triglyme molecules with: 19 sodium triflate pairs for 0.5 M, 39 for 1.0 M, 58 for 1.5 M, 78 for 2.0 M. For tetraglyme, the simulation box contained 213 tetraglyme molecules with: 29 sodium triflates for 0.5 M, 58 for 1.0 M, 87 for 1.5 M, 116 for 2.0 M. After random packing, each box was equilibrated in the NVT ensemble for 1 ns at a temperature of 300 K, followed by 3ns



simulation in the NPT (temperature of 300 K and pressure of 1 atm) ensemble via the NoseHoover thermostat and barostat. Finally, 10 ns production runs were carried out in the NVE ensemble. All of the above simulations were carried out within the LAMMPS software package51 under periodic boundary conditions with a 1 fs time step using Ewald, specifically PPPM, to account for long-range electrostatics. RESULTS AND DISCUSSION a. Force field validation The validation of the force field was carried out by comparing two different properties of the system: ion association by the degree of ion-pairing and diffusion constants of glyme molecules. The ion-paring is a useful metric because it validates the short range interaction (local structure) of the simulation, while the diffusion constant takes into account long range interactions. In the case of ion-paring the computational results were compared with FTIR experiments. The FTIR study of ion pairs between sodium and triflate ions focused on the SO3 symmetric stretching of the triflate (1005cm-1 - 1055 cm-1) because it has been previously shown to be sensitive to the composition of the sulfonate solvation shell.20 Figure 2 a shows the SO3 symmetric stretch of sodium triflate in each glyme. The spectra shown in Figures 2 b and 2 c provide four major peaks in the region of interest for monoglyme and diglyme, while only three bands can be observed for triglyme and tetraglyme. The peaks at ~1033 cm-1, ~1038 cm-1 and ~1045 cm-1 have been previously assigned by Wahler et al.20 as well as by other studies52-54 to free ion, contact ion pair, and aggregate, respectively. While the ion-pair refers to triflate ion interacting with one sodium, the aggregate reflects those triflate ions interacting with more than one sodium ion. The fourth peak located between 1015 cm-1 and 1025 cm-1 is a solvent band. Modeling of the IR spectra with a Voight profile for each


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of the assigned peaks allows us to obtain the area of each species (Ai) from which the fraction of free triflate ions is derived as: 𝑋2344 = 𝐴2344 𝐴 6789: .20 The fraction of free ions obtained from the FTIR experiments can be compared with the results of the molecular dynamics simulations as presented in the next section and summarized in Table 1. At 1.0 M salt solution, the monoglyme clearly shows a negligible amount of free ion in both experiment and simulations while triglyme has the highest free ion probability. Overall, there is very good agreement between experiments and theory in both solvent and concentration dependence since the simulations capture the trends for free ion probability. Surprisingly, even though the force-field itself was developed specifically for sodium triflate in diglyme, the results validate the use of the force field for this family of glyme molecules and sodium triflate. In addition to probing solvation structure, the average diffusion coefficients of the glyme molecules at 1.0 M sodium triflate concentration were obtained from spin echo NMR experiments and compared with results from the simulations. Table 1 compares the values of the diffusion coefficient from experiments and simulations and once again shows excellent agreement. In particular, the simulation captures the solvent dependence of the diffusion coefficient even when the system has only two solvent molecules per sodium triflate pair, as in the case of 1M sodium triflate in tetraglyme. In summary, the results show that the force field correctly captures not only the local and overall structure of the glymes solutions, as seen in the fraction of free molecules, but also longer range dynamics as evidenced by the diffusion constant. Based on these findings, the same methodology is used in the next section to study the effect of concentration and glyme structure on the chelation and ion association in various glymes. b. Solvation structure



The local structure surrounding the sodium ions in the different electrolytes is obtained from the radial distribution function (RDF) for the sodium ion (Na) and atoms of either the solvent (O of glymes) or the anion (S, O, and C of triflate) as a function of increasing glyme chain length (see Figure 3). Figure 3 displays the radial distribution function of the local structure around the sodium ion for 1M solutions along with the integrated coordination number 𝑛 𝑟 =

3 4𝜋𝑟 ? 𝜌𝑔(𝑟)𝑑𝑟, C

where 𝜌 is the density. In this case, the first minimum in the radial

distribution function defines the first solvation shell and the value of n at this point is the average coordination number. Figure 3 shows that the first solvation shell is well defined within the first 3 Å of the cation and is comprised almost exclusively of ether and sulfonate oxygens. The first peak in the RDF for the carbon atom of the anion (~4.6 Å) is at larger distances than the corresponding feature for the sulfur atom (~3.6 Å), in agreement with previous results showing that it is the sulfur oxygens (Os) that mainly coordinate the cation and not the -CF3 group. The peak in the sodium–glyme oxygen RDF clearly shows a shift to smaller values as one increases the glyme length, with monoglyme oxygens being the farthest away on average and tetraglyme having the closest binding oxygens. Tighter binding of the cation with increasing chain length is in keeping with a greater chelation effect and agrees with previous studies.21, 25 The impact of chelation on ion association is hinted at by the changes in the RDF’s, but is more clearly evident in the reported coordination numbers. One definitely sees a slight shift in the location of the first maxima for the sodium–triflate oxygen and the sodium–sulfur RDF’s in going from monoglyme to diglyme, which supports the idea of weaker anion binding as a result of stronger chelation. The trend in RDF structure does not continue for the longer glymes, however, with the first peak moving back to slightly shorter distances for triglyme and tetraglyme. While peak locations are not indicative of radical changes to potential solvation structures, the average coordination


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clearly indicates the preference for contact ion pairs changing substantially as a result of chelation. As seen in Figure 3, the number of triflate anions coordinating to sodium decreases from around 2 in the monoglyme solution (aggregate structures of multiple ions) to a little less than 1 for diglyme (contact ion pairs) before dropping to 0.5 for triglyme and tetraglyme (solvent separated ions present). The radial distribution functions for solutions with different salt concentrations exhibit the same general behavior as those reported previously (Figures S1-S4 in supporting information).20 The corresponding average oxygen coordination numbers of the first solvation shell around the sodium ion as a function of concentration are tabulated in Table 2. The overall average coordination of approximately 6 to 7 oxygen atoms (from either the solvent or the anion) remains consistent irrespective of glyme size or salt concentration and is in agreement with previous crystal structures of glyme-Na+ solvates.22 The nearly even match between the triflate oxygen coordination number and that of the sulfur indicates that the majority of the triflate ions interact with the sodium ion through one of its oxygen atoms. Hence bidentate structures, where two O atoms of the triflate coordinate to the same sodium ion, are not significant at the concentrations considered. While the total oxygen coordination number does not vary greatly with concentration, the relative contribution from oxygen atoms of the anion or the glyme is greatly influenced by the electrolyte composition. From Table 2, it is apparent that the composition of the cation’s first solvation shell is directly influenced by the salt concentration and structure of the solvent. As expected, increasing the salt concentration increases the number of anions in the average solvation structure with a corresponding decrease in the participation of glyme oxygens. The trend in average coordination is supported by characterization of the relative populations of



solvation structures reported in Table 3.

In each case, the move towards higher average

coordination is accompanied by a shift in the probability distribution towards higher anion content structures. However, the change in number of anions in the first solvation shell as a function of the glyme chain length is non monotonic. From mono-, to di-, to triglyme, the glyme participation in the Na+ solvation shell increases, but decreases from tri- to tetraglyme. Examining the distribution of solvation structures, one can see that in the case of triglyme only the solvent separated ion pair (no coordinating anions) and the aggregate structure (2 coordinating aions) are allowed. The altered behavior of triglyme is connected to the mismatch between the number of chelating oxygens from a single triglyme molecule and the overall desired coordination number for sodium, as shown below. More importantly, this subtle change is also seen in Table 1 from the FTIR data and provides further validation of the model employed. The differences in triglyme chelation have been attributed to changes in the intercalation properties of sodium-ion batteries, providing further evidence of the important link between ion solvation and battery performance and further confidence in the validity of our approach.27 The non-monotonic effect with glyme chain length highlights an important observation that the chelation capacity of the glyme on the sodium ion does not necessarily define the solvation structure of Na+ and steric as well as entropic effects remain critical to capturing the appropriate structure. The behavior of solvation with salt concentration shows a clear trend in which the counter anion increases its participation in the Na+ solvation shell as more salt is added to the solution. Analysis of the Na+ coordination reveals that the ion-pair formation in monoglyme is unusually different as compared to other glymes, even at low concentration. Even at 0.5 M, the electrolyte contains substantial populations with one or more triflates in contact with the cation.


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In contrast, the other glymes always present a population of free ions in solution, which decreases with increasing salt concentration. Interestingly, neither the population of free ions nor ion pairs show a gradual increase with chain length as seen for the oxygen coordination number of Na+. In this case, the triglyme shows an anomalously high fraction of uncoordinated sodium ions, even at a high salt concentration of 2 M, which agrees with the previous discussion of the unexpected change in oxygen coordination number for triglyme. Moreover, Na+ in diglyme shows the largest fraction of single ion-pairing at all concentrations as compared to other glymes. The main solvation environments seen from simulations for the different glymes are shown in Figure 4. In the case of monoglyme, two dominant structures are observed at low concentration: one in which the sodium ion is coordinated by three monoglyme molecules and one triflate anion, and another where the sodium ion coordinated by two monoglyme molecules and two triflate anions. As the concentration is increased, aggregation starts to take place and configurations consisting of multiple triflate anions become more significant. For the case of diglyme, two structures (see Table 3 and Figure 4) are typically seen at all the studied concentrations. The dominant structure has sodium ion coordinated with two diglyme molecules and one triflate anion, while the second has the sodium ion coordinated to two diglyme molecules with the anion separated from the first solvation shell. With increasing salt concentration, the percentage of the second structure goes down, and the percentage of first one increases.

Interestingly, the portion of aggregate structures in diglyme with two anions

coordinated remains less than the three anion population, although admittedly the populations of both remain small. The behavior of the larger aggregates in diglyme hints at the phenomena seen in the case of triglyme as discussed subsequently.

The representative structures for

triglyme at low concentration have sodium ion coordinated either to two triglyme molecules or to



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one triglyme and two triflate anions. With increasing salt concentration, the percentage of structures in which sodium ion has triflate ions in its solvation shell significantly increases to a point in which the two structures appear with the similar probabilities above 1.0 M. It is clear from these images that the contact ion pair structure is hindered by the inability to provide a high enough coordination number to sodium with a single triflate and a single triglyme. Finally, the solvation of the sodium ion in tetraglyme presents all of the solvation environments with one, two, and three triflate ions even at low concentrations (see Figure 4). The dominant Na+ solvation environment at low concentrations has the sodium ion coordinated to two tetraglyme molecules, but with increasing salt concentration structures in which the sodium ion coordinates with one tetraglyme molecule and more than one triflate anion become more important. There is also a small but non-negligible percentage in which sodium coordinates with only a single tetraglyme. The rise of these configurations provides evidence that as the glyme length increases, the system begins to more closely mirror the behavior seen in long oligomers used to represent PEO55 and provides an important bridge for future work.

Interestingly for tetraglyme, an

increase in the salt concentration does not directly increase the population of the Na+ coordinated with multiple triflate ions, but instead the concentration of the sodium ions coordinated with one triflate ion increases at expenses of those Na+ that do not have a triflate in its solvation shell (Table 3). The simulations show that Na+ ions in glymes present a coordination number between 6 and 7 oxygens. Thus all the structures that do not meet this requirement either are not observed or do not have a significant population. This is the case of diglyme when two triflates are present and of triglyme with one triflate ion. This observation can be rationalized based on the following argument. The mono- and diglyme molecules are of shorter chain length and hence the sodium


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ion can accommodate multiple glyme molecules and one triflate in the solvation shell to fulfill the overall coordination of six to seven O atoms. In the case of triglyme, two triglymes can easily coordinate to the sodium ion and fulfill its coordination without requiring a triflate anion. However, one triglyme does not have the necessary number of oxygen atoms to coordinate to the sodium ion with just one triflate anion. Hence, a minimum of two triflate ions is needed when only one triglyme is coordinating the sodium ion. A similar argument can be used to explain the lack of solvation structures having two diglymes and two triflate ions. Interestingly, the solvation of Na+ in tetraglyme shows structures having a single tetraglyme molecule chelating the sodium ion, which does have the same number of O atoms coordinating the sodium ion as the case of one triflate with one triglyme. However, the tetraglyme forms a tight solvation shell around the sodium ion and hence a compact environment. The hypothetical triglyme case with one triflate and one triglyme would be a comparatively open structure thereby allowing another molecule to be part of the solvation environment. This other molecule would have to be a triflate since another triglyme molecule would be too large to fit in the solvation shell and interaction with a single O of triglyme will trigger the chelating effect due to the cooperativity of the chelating effect. c. Diffusion of molecular components The diffusion constants were calculated from simulations from the slope of the root mean square deviation of the center of mass of the glyme molecules, triflate ions, and sodium at different salt concentrations (see Figures S5-S7 in supporting information). The self-diffusion coefficient for the glymes show the expected behavior where diffusion decreases with increasing salt concentration (Figure 5 and Table 4) due to their strong interaction with sodium ions. In agreement with the size of the molecules, monoglyme shows the highest values of self-diffusion,



while increasing the glyme chain length, or its effective volume, decreases the diffusion constant. This is not surprising given that the viscosity increases with glyme chain length as well as with salt concentration and that the number of free glyme molecules also decrease with the glyme chain length even for the same salt concentration. As previously mentioned, the diffusion constant of the glymes at 1.0 M salt concentration present good agreement between experiment and simulation (Table 1). From a fundamental perspective, it is surprising that the force-field does quite well in getting the trends and relative ratios of the diffusion constants in the glyme series correct, despite the fact that the force-field was developed for the diglyme based electrolyte. This observation reinforces the idea that the force-field captures the essential structural and dynamical features of the system and is transferable over the glyme series. The self-diffusion coefficients of the ionic components (see Figure 6 and Table 4) present the same trend as the glyme molecules, namely that the ions in solutions of the smaller glymes have larger diffusion coefficients. However, the overall magnitude of the self-diffusion coefficient is approximately three times lower than the glyme molecules themselves. The result shows that the motion of the ionic components is dominated by the size of the glyme molecules since the number of free molecules and the magnitude of the diffusion coefficient (as shown by the Stokes-Einstein relation) increase with decreasing size of the glyme molecule. In addition, the self-diffusion coefficient shows that positive and negative ions share similar magnitudes in agreement with the large degree of ion pairing observed in these systems. Moreover, the average diffusion coefficient for ions in glymes with 3 or 4 units is larger for the anion because of a better chelation of the cation which increases not only the number of “free” triflate ions, but also the “effective” ionic radius of the cation. CONCLUSION


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The impact of chelation and salt concentration on the sodium solvation environment in glyme electrolytes was explored using a combination of FTIR spectroscopy, NMR, and atomistic simulations. The solvation shell is seen, from simulations, to change non-monotonically as a function of glyme chain length, especially with respect to ion pairing effects. For example, triglyme is an outlier in this respect with a large fraction of non-contact pair ions in solution even at high salt concentrations. Diglyme has the largest fraction of ion-pairing, but with just one counterion in the solvation shell of the sodium. Monoglyme, on the other hand, has contact ion pairs even at dilute concentrations and indeed the fraction of non-contact ion pairs is negligible. Monoglyme, triglyme and tetraglyme, unlike diglyme, show structures with more than one counter ion in the first solvation shell around the cation. These results imply that monoglyme and diglyme present a good compromise in terms of allowing for ion association that could lead to stabilization of the sodium/superoxide pair dissolved at the cathode interface. A secondary aspect of this work was to test whether the force-field developed for a sample monomer would give a reasonable decription of the various glyme based electrolytes. The results for the fraction of free ions from simulation are consistent with FTIR spectroscopy, validating the force-field for the glyme based electrolytes. In addition, the simulation results with respect to glyme diffusion constant at 1.0 M are in keeping with the experimental trends, providing further validation of the force-field. ASSOCIATED CONTENT Supporting Information This Supporting Information is available free of charge on the ACS Publications website at DOI: Radial distribution functions, for different concentrations and glyme chain length, along with the integrated coordination number for the sodium ion with the trfilate O atom, triflate S atom and



the glyme O atoms are plotted as well as the root mean square deviation of the glyme center of mass, the sodium ion, and the center of mass of the triflate ion as a function of time. The following files are available free of charge. Figures S1 to S7 (PDF)

AUTHOR INFORMATION Corresponding Author * E-mail: [email protected]. Tel: (+1) 225-578-0907 ORCID Daniel G. Kuroda: 0000-0002-4752-7024 Revati Kumar: 0000-0002-3272-8720 Ryan Jorn: 0000-0002-0192-9298

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT The current work was supported in part by start-up funds provided to DGK and RK by the Department of Chemistry and computer time allotted by the high performance center at LSU and the Louisiana Optical Network Initiative.

REFERENCES


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Figure 1.The glyme series with increasing chain length from monoglyme to tetraglyme are shown, followed by the triflate anion. Red corresponds to O atoms, blue to C atoms, yellow to S, pink to F atoms, and white to H atoms.



Figure 2. a) Sketch of the symmetric stretch of SO3-. b)Normalized solvent subtracted FTIR spectra of sodium triflate in different glymes, black: monoglyme, red: diglyme, blue: triglyme and green: tetraglyme, 1.0M and (c) 1.5M.


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Table 1. Comparison between experiments and simulations of the solvent dependence of the free ion probability and diffusion constant of the glyme molecules. Diff. Coef. (x10-10 m2s-1)

Fraction of free ions Solvent

1.0 M Simulation

Diglyme

1.0 M Exp. 0.020 ±0.005 0.29 ±0.02

Triglyme Tetraglyme

Monoglyme

1.5 M Simulation

1.0 M Exp.

1.0 M Simulation

0

24.0

33

0.2

1.5 M Exp. 0.010 ±0.002 0.25 ±0.02

0.1

7.6

4

0.52 ±0.02

0.7

0.49 ±0.02

0.5

2.9

1

0.46 ±0.01

0.6

0.44 ±0.01

0.4

1.6

0.3

0



Figure 3. Radial distribution functions (solid lines) and coordination numbers (dashed lines) for (a) Na-O ( all oxygens from glymes), (b) Na-S (sulfur from triflate), (c) Na-Os (sulfonate oxygen) and (d) Na-C(carbon from triflate) from classical MD simulation at 1.0 M. Green, blue, red, and black lines represent monoglyme, diglyme, triglyme, and tetraglyme, respectively.


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Table 2. Coordination Number for sodium (Na) ion at different salt concentrations as a function of glyme chain length. Og stands for glyme oxygen atoms and Os for triflate oxygen atoms. Solvent

Monoglyme

Diglyme

Triglyme

Tetraglyme

Conc. (M)

Na-Og

Na-Os

Na-S

0.5

4.4

1.9

1.9

1.0

4.1

2.1

2.1

1.5

4.0

2.1

2.1

2.0

3.5

2.5

2.4

0.5

6.0

0.8

0.8

1.0

6.0

0.9

0.9

1.5

5.9

1.0

1.0

2.0

5.3

1.4

1.4

0.5

7.4

0.3

0.3

1.0

6.8

0.6

0.6

1.5

6.6

0.7

0.7

2.0

6.1

1.1

1.0

0.5

6.4

0.5

0.5

1.0

6.3

0.6

0.5

1.5

5.7

0.8

0.8

2.0

5.5

1.1

1.1



Table 3. Distribution of the number of triflate ions (anions) in the first solvation shell of sodium as a function of glyme chain length and salt concentration. Solvent Monoglyme Diglyme Triglyme Tetraglyme Monoglyme Diglyme Triglyme Tetraglyme Monoglyme Diglyme Triglyme Tetraglyme Monoglyme Diglyme Triglyme Tetraglyme

Populations (%) 0 1 2 ≥3 0.5 M 0 48 41 11 20 80 0 0 85 0 15 0 67 23 7 3 1.0 M 0 36 49 15 15 85 0 0 69 0 31 0 56 33 10 1 1.5 M 0 42 39 19 11 84 1 4 52 0 45 3 36 54 6 4 2.0 M 0 42 39 19 11 84 1 4 52 0 40 8 32 44 18 6


Page 30 of 35

Triglyme

Diglyme

N/A

N/A

N/A

Tetraglyme

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Monoglyme

Page 31 of 35

Figure 4. Sample solvation structures for sodium ion in the different glyme solutions. Sodium ion (purple) coordinated by glymes and the triflate anion (for color scheme see Figure 1).



Figure 5. Self-diffusion as a function of salt concentration for glyme molecules, monoglyme (green), diglyme (blue), triglyme (red), tetraglyme(black).


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Figure 6. (a) Self-diffusion as a function of salt concentration for sodium (left panel) and triflate (right panel) in monoglyme (green), diglyme (blue), triglyme (red), tetraglyme(black).



Page 34 of 35

Table 4: Self diffusion constant of the two ions as well as the glyme solvent as a function of salt concentration. Units in Å2/ns. Solvent Monoglyme

Diglyme

Triglyme

Tetraglyme

Species

0.5 M

1.0 M

1.5 M

2.0 M

Na

131

77

34

21

Triflate

132

80

34

22

Glyme

472

331

214

170

Na

34

15

8

4

Triflate

38

18

10

4

Glyme

88

40

23

12

Na

7

4

2

1

Triflate

10

5

3

1

Glyme

17

10

6

2

Na

3

1

1

1

Triflate

4

2

1

1

Glyme

5

3

1.5

1


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