Molecular Mobility in Mixed “Water-in-Salt” Solutions of LiOAc and KOAc According to NMR Data

Diffusion coefficients of ions and water have been measured in two- and three-component concentrated (“water-in-salt”) aqueous solutions of KOAc and LiOAc, which were proposed as new electrolytes for water-based Li-ion batteries. It was demonstrated that the diffusion coefficient for acetate anion is greater than for lithium cation one in the KOAc-containing solutions and the difference grows under increasing concentration of potassium acetate. Water diffusion is also faster comparing with lithium cation and acetate anion in all solutions studied. Temperature dependences of spin–lattice relaxation rates (1/T1) of 1H, 7Li, and 39K nuclei have been measured for both ions and water. The dependences do not reach their maxima for most samples, and only for acetate anion in sample IV (31.9 mol KOAc–8.0 mol LiOAc–H2O) it turned out to be possible the reliable calculation of the rotational correlation time τc. Comparison of the translational (via D) and rotational (via τc) mobility of the acetate anion near the eutectic point showed that the Stokes–Einstein relation is valid for this solution only in a small high-temperature part of the studied range, but not for the lower temperatures.


Introduction
Electrolyte solutions are a key component of energy storage devices, including Li-ion batteries (LIBs).Currently, the electrolyte of a device usually consists of a lithium salt solution in a non-aqueous organic solvent such as acetonitrile, ethylene carbonate, or an appropriate ionic liquid (see Ref. [1,2] and references within).Pure water was not considered as a good solvent due to the narrow electrochemical window (1.23 V).However, during the last decade the "water-in-salt" (WIS) systems were proposed as new electrolytes for water-based LIBs.First, L. Suo with coauthors [3] showed that the use of a highly concentrated "water-insalt" solution of lithium bis(trifluoromethane sulfonyl)imide (LiTFSI) made it possible to extend the electrochemical window of water-based electrolytes up to ≈ 3 V and this may become a promising direction in the search for new electrolytes for water-based LIBs.Though the authors of the work [3] implemented the wider window in the system with strong hydrogen bond F¯-H 2 O, one could expect that this salt solution is not a unique example of that kind.Indeed, further investigations of highly concentrated WIS systems have led to the discovery of a number of electrolytes with extended electrochemical windows, that may be promising for the creation of aqueous lithium-ion batteries whose capacity and cycle life will be comparable to commercial non-aqueous ones.As a result, nowadays WIS aqueous electrolyte investigations are in strong progress (see, for example, [4][5][6][7] and references within).Among these works, the electrochemical properties of highly concentrated aqueous systems of alkali metal acetates such as LiOAc-KOAc-H 2 O and LiOAc-CsOAc-H 2 O attracted the attention of researchers [8][9][10].In particular, LiOAc-KOAc-H 2 O triple systems were thoroughly tested and it was shown that the mutual concentration of salts in the mixture had a significant effect on the character of ion mobility, and consequently on the electrical conductivity of such systems [8].The authors demonstrated that the eutectic ratio occurred at the LiOAc molar fraction of 0.2 (32 m KOAc + 8 m LiOAc aqueous solution), i.e. the maximum solubility of salts is achieved with only ≈ 1.4 water molecules per cation (both K + and Li + ).For comparison, 27 m KOAc aqueous solution (close to the saturated solution at room temperature) corresponds to ≈ 2.1 water molecules per K + cation.
The purpose of this work was to study molecular mobility and local structure in the LiOAc-KOAc-H 2 O system using NMR methods on 1 H, 7 Li, and 39 K nuclei by measuring the diffusion coefficients and relaxation rates for Li + ( 7 Li) and K + ( 39 K) cations, OAc¯ anion ( 1 H) and water ( 1 H).The collection of the prepared samples, which are planned in our experiments, correspond to the scheme of the samples studied in [8].Here we present the results of the investigation of the samples, which composition are close (i) to saturated solutions of LiOAc or KOAc (I and II in Table 1), and (ii) to the eutectic point (samples III and IV in Table 1).
Molecular Mobility in Mixed "Water-in-Salt" Solutions of… 2 Experimental

Sample Preparation and Composition
The samples were prepared at the Institute of Chemistry of Saint Petersburg State University.For the preparation of all samples, the pure lithium acetate dihydrate LiOAc•2H 2 O (99%, «Lenreactive») and dry potassium acetate (KOAc) were used.Potassium acetate was synthesized by reacting potassium carbonate and acetic acid (60%).The product was recrystallized from distilled water, and its purity was controlled by X-ray phase analysis and FTIR.The composition of the samples is given in Table 1.To control the sample's composition, a total concentration of the acetate anion was measured by comparing the integral intensities of the water and acetate anion lines in the 1 H spectrum.For all samples, a good coincidence of the NMR results with the preparation ones was obtained.

NMR Measurements
NMR measurements were carried out using Bruker Avance III 500 MHz Spectrometer at 500 MHz for 1 H nuclei, 194.33 MHz for 7 Li, and 23.33 MHz for 39 K. To measure the diffusion coefficients (D) the rf pulse sequences for Stimulated Echo and pulse magnetic gradients were used.The inversion recovery pulse sequence "π-t-π/2" was used for the spin-lattice relaxation time (T 1 ) measurements (with 16 different values of t for each experiment).The methods used for measuring relaxation times and diffusion coefficients make it possible to obtain results with an accuracy of about 3%.NMR measurements were made in Centre for Magnetic Resonance of Research Park of St. Petersburg State University.

Diffusion
We have measured the temperature dependences of the diffusion coefficients of the acetate anions and water using 1 H NMR and of the Li + cations using 7 Li NMR.Selected data are shown in Figs. 1 and 2, and other dependencies show a similar behavior.As it is evident from Fig. 1, the diffusion coefficients are practically identical for the Li + cation and CH 3 COO¯ anion in the concentrated aqueous solution of lithium acetate.It means that the diffusion of these ions is strictly correlated throughout the studied temperature range, i.e. it could be supposed that the system consists of a variety of fluctuating "clusters" which include a number of counter ions.The microstructure of the "clusters" is not yet clear but one can conclude that counter ions cannot be simply in the form of LiOAc molecules (contact ion pair) because in that case, the conductivity of the system must be very low that does not correspond to the experiment.It is noteworthy that the diffusion of water hydrogens is much faster than the diffusion of ions that indicates a significant role of hydrogen exchange in the translational movement of hydrogen atoms in the solution under study.The effect of this process on translational mobility in pure water is much less noticeable due to the high mobility of H 2 O molecules as a whole.
On another hand, in mixed solutions the diffusion coefficients of the lithium cation and the acetate anion diverge (see an example in Fig. 2).Apparently, this means that the microstructure of the "clusters" changes with the Li/K ratio in the electrolyte.Unfortunately, it is impossible to measure the diffusion coefficient of the potassium cation using NMR diffusometry due to the very short relaxation time T 1 for 39 K nuclei (see item "Relaxation").Thus, the question of the correlation between the movement of potassium cations and ions of other varieties remains open.In the entire temperature range, the diffusion coefficient of water is greater than that of both the lithium cation and acetate anion despite the extremely small amount of water (only ≈ 1.4 water molecules per cation of both types), that can also be explained only by the existence of an exchange of hydrogen atoms (or protons) between water molecules.
In the first approximation, the temperature dependences of the diffusion coefficients can be approximated by straight lines (see an example in Fig. 1) and, based on them, the "effective" (averaged) activation energies (E a ) of translational motion Molecular Mobility in Mixed "Water-in-Salt" Solutions of… can be calculated.In Table 2 we summarized the activation energies for the ions and water molecules for all samples, and the results allow one to make some conclusions.First, for the anion and Li + cation activation energies are close for all samples, and it means that the cation and anion movement are correlated in all compositions studied (recall that concentrated solutions are being studied).Second, the activation energies for water diffusion are somewhat lower comparing with the ions.It is possible that this is, in particular, the result of the proton exchange contribution.

Relaxation
We have measured the temperature dependences of spin-lattice relaxation times (T 1 ) for the samples studied using NMR of 1 H (H 2 O and CH 3 COO¯), 7 Li (Li + ), and 39 K (K + ) nuclei.The examples of the temperature dependences of the relaxation rates (1/T 1 ) for samples II and IV are presented in Figs. 3 and 4. The relaxation rates of the 39 K nuclei are much higher compared with the 1 H ones due to strong quadrupole mechanism relaxation.In most cases, the temperature dependencies of the relaxation rates 1/T 1 for the samples studied demonstrate a monotonic growth under temperature decreasing, and only some CH 3 COO¯ lines show a kind of 1/T 1 maxima, that allowed the reliable direct calculation of reorientation correlation times (τ c ) on the basis of the approaches of Solomon [11] or, for the simplest cases, of Bloembergen Fig. 3 The temperature dependences of 1 H relaxation rates (1/T 1 ) for water and CH 3 -group of the acetate anion (CH 3 COO¯) in sample IV et al. [12].As examples, we demonstrate the 1 H data for sample IV (Fig. 3) and the τ c temperature dependence for the acetate-anion (Fig. 5).At first glance, the τ c dependence looks like Arrhenius one, and it is possible to estimate the averaged activation energy in the whole temperature range.As a result, we obtained about 20 kJ/mol and it is much less than 34 kJ/mol, calculated from diffusion data (see Table 2).The situation is typical for many liquids when the translational mobility decreases faster with a decrease in temperature than the reorientation mobility.This is especially typical for the molecular group CH 3 -of polyatomic ions or molecules.

Comparison of Translation and Reorientation Dynamics
Using the τ c and D values for the CH 3 -group of the acetate anion for sample IV one can test translation and rotation (reorientation) mobility of the anion in more details.As can be seen from Fig. 6, the product of τ c and D looks like a constant at high temperatures, but it decreases at low temperatures.It means that translational and rotational movements of the anion are coupled at high temperature, however, this correlation begins to break when the temperature drops.A similar behavior was observed for a number of ionic liquids (see [13] and references within).
Fig. 4 The temperature dependence of the 1/T 1 relaxation rate of 39 K nuclei in sample II, 27 m KOAc aqueous solution Fig. 5 The temperature dependence of τ c calculated for CH 3 -group of the acetate anion (CH 3 COO¯) using data of Fig. 3 1 3 Molecular Mobility in Mixed "Water-in-Salt" Solutions of…

Conclusion
Temperature dependences of spin-lattice relaxation times (T 1 ) of different nuclei and diffusion coefficients (D) were measured for the cations, CH 3 COO¯ anion, and water in two-and three-component concentrated KOAc and LiOAc aqueous solutions.The diffusion data demonstrate that in the KOAc-containing solutions the diffusion coefficients of acetate anion are higher than of lithium cation ones, and the difference grows under increasing concentration of the potassium acetate.The water diffusion is faster comparing with lithium cation and acetate anion in all samples studied.The activation energy (E a ) of translational motion for the anion and Li + cation occur close in all samples which reflects the correlation in the movement of these two ions.Lower activation energies for water diffusion are, possibly, the result of the proton exchange contribution.The temperature dependences of relaxation rates (1/T 1 ) did not reach their maxima for most samples.As a result, it was not possible to perform the reliable direct calculation of reorientation correlation times (τ c ).Nevertheless, it turned out to be possible for sample IV (31.9 mol KOAc-8.0 mol LiOAc-H 2 O), and we were able to compare the translational (via D) and rotational (via τ c ) mobility of the acetate anion near the eutectic point.The comparison shows that the Stokes-Einstein relation is valid for this solution only in a small (high-temperature) part of the studied range, but not for the lower temperatures.It means that translational and rotational movements of the anion are coupled at high temperature, however, this correlation begins to break when the temperature drops.

Table 2
The activation energies (E a ) calculated from the diffusion data