Salt-in-water and water-in-salt electrolytes: the effects of the asymmetry in cation and anion valence on their properties

Abstract

We investigated the structural, dynamic, energetic, and electrostatic properties of electrolytes based on the ion pairs LiCl and Li₂SO₄. Atomistic molecular dynamics simulations were used to simulate these aqueous electrolytic solutions at two different concentrations 2 M (normal) and 21 M (superconcentrated, WiSE). The effects of the valence asymmetry of the Li₂SO₄ electrolyte were also discussed for both salt concentrations. Our results differ in the physical aspect of pure electrolytes, showing the drastic effect of high concentration, in particular on the viscosity, which is dramatically increased in WiSE. This is a consequence of their reduced ionic mobility and has a direct effect on ionic conductivity. Also, our results for graphene-based supercapacitors, as indicated by some experimental work, do not indicate any better performance of WiSEs over normal electrolytes. In fact, the differences in the total capacitance, due to the concentration of ions, presented by both electrolytes are negligible. The valence asymmetry can be clearly observed in some properties but for most of them its effects could not be quantified or isolated.

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Introduction

Electrochemical energy storage devices, such as batteries and supercapacitors, are considered as one of the best options for storing energy produced from renewable resources.^1–3 For both batteries and supercapacitors a key factor for their functioning and effectiveness is the good performance of their electrolyte solutions.^1,4,5 The search for more efficient electrolytes heavily involves aqueous electrolytes due to their cost and safety since such electrolytes are non-flammable and produced only with water and cheap salts (such as nitrates and sulfates) which reduces drastically the cost of electrolytes.⁵ Furthermore, aqueous electrolytes have high ionic conductivity, which typically exceeds by up to two orders of magnitude that of electrolytes based on organic solvents, which allows for a higher power capability.⁵ Despite these important features and desirable characteristics, aqueous electrolytes have limited energy density performance due to their low electrochemical window. This window is about 1.2 V, and when reached, it starts the process of decomposition of water into H₂ and O₂, ruining the entire functioning of the device.⁵

Intense research has been carried out on improving the performance of aqueous electrolytes to mitigate the limitation related to their electrochemical window. This has been done using many different approaches, but one, in particular, has attracted a lot of attention recently. In 2015 Suo and colleagues published an important paper investigating the properties and performance of “water-in-salt” electrolytes (WiSE).⁶ The notable feature of this type of electrolyte is that the hydration structure of salt is very different from that found in normal aqueous (salt-in-water) electrolytes. In WiSE the salt is not only coordinated by water molecules, but also by counterions (anions) dispersed in the solution. These electrolytes have increased electrochemical stability compared to normal aqueous electrolytes. This advantage is because the electrolyte forms a passivating layer on the electrode surface, further suppressing H₂ evolution. With this, the electrochemical window of the aqueous electrodes can be increased to almost 3 V.⁶ Following this pioneering work, several studies on the energetic and structural properties of these promising electrolytes have been reported showing remarkable results when applied as electrolytes to lithium batteries and supercapacitors.^7–11

In addition to the improvement that highly concentrated electrolytes can bring, there is still an aspect that can play a significant role in the performance of electrolytes, but it has still been little investigated: the valence asymmetry of the electrolyte. This asymmetry is present when the valence of the cations and anions is not the same. For example, the aqueous LiCl electrolyte has symmetry (1 : 1), in this case, both the cation and anion have a valence of modulus 1, on the other hand, the aqueous Li₂SO₄ electrolyte is asymmetric (1 : 2) since the anion has a valence whose modulus is double that of the cation. Therefore, this last electrolyte is said to have valence asymmetry. In general, this asymmetry will be observed whenever the ratio between the velocity of the ions differs from (z : z). This subject was recently investigated by Gupta and Stone, who studied the effect of valence asymmetry in the scope of mean field theory.¹² They argue that the magnitude of the valence is what determines the mutual force exerted by the ions when cations and anions have different valences. In this case, the magnitudes of the forces experienced by the cations and anions are uneven, which leads to an asymmetry in the properties of the electrical double layer (EDL), which can have significant implications for the development of more efficient electrolytes. For example, they found that this asymmetry has an expressive effect on the diffuse charge dynamics, thus having direct consequences on the determination of the charge density and capacitance of devices for storing electrochemical energy.¹²

This work has a dual purpose. The first is the investigation at the atomistic level of differences in the properties of LiCl and Li₂SO₄ aqueous electrolytes at normal (2 M) and superconcentrated (21 M, WiSE) concentrations. This will be done both by investigating the structural and dynamic properties of pure electrolytes as well as by studying the electrostatic properties of graphene electrolytic cells, for which we will determine their electrostatic potential profile and total capacitance. A second objective was to verify if our models are able to quantify the effects of the asymmetry of the valence asymmetry of the Li₂SO₄ electrolyte in relation to the symmetrical valence electrolyte LiCl. In this last point, any difference we can attribute to valence asymmetry will be important. Since we employ more realistic models through atomistic molecular dynamics simulations, which explicitly consider important effects such as specific interactions and hydration forces, our results can corroborate the predictions of mean field theory.¹²

Computational simulations

We investigated the properties of electrolytes using two different simulation series. In the first, we studied the structural, energetic, and dynamic properties of pure electrolytes. In the second series, we employed the investigated solutions in graphene electrolytic cells to evaluate their properties as electrolytes for supercapacitors. In both series, the electrolytes investigated were LiCl and Li₂SO₄ normal (salt-in-water, 2 M) and superconcentrated (water-in-salt, WiSE, 21 M) aqueous solutions. For all solutions 4.0 nm cubic starting boxes were generated. The molecular representations of the simulation boxes are given in Fig. 1 and the composition of each simulation is shown in Table 1. In this table, we highlight the valence asymmetry (2 : 1) for the case of sulfate solutions, for which we have two cations for each anion in the solution.

Fig. 1 Molecular representations of the investigated systems. (a and b) normal LiCl and Li₂SO₄ electrolytes, respectively. (c and d) Superconcentrated (WiSE) LiCl and Li₂SO₄ electrolytes, respectively. Cyan, pink, blue and yellow represent the water molecules, lithium cations, chloride anions and sulfate, respectively. Hydrogen atoms are omitted for the sake of clarity.

Table 1 Composition of the investigated normal (2 M) and water-in-salt (21 M) electrolytes. For Li₂SO₄ two times more cations are needed than anions, which defines the valence asymmetry of this electrolyte

Electrolytes	Ion pairs	Li cations	Cl/SO4 anions	Water molecules
LiCl (2 M)	72	72	72	2000
Li2SO4 (2 M)	60	120	60	1800
LiCl (21 M)	454	454	454	1200
Li2SO4 (21 M)	378	756	378	1000

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For the supercapacitors, the simulation cells were generated by a two-step procedure: first, the electrolyte was placed between two rigid 3.4 nm × 3.2 nm graphene electrodes, and the cells were relaxed only in the z-direction such that a new length z was obtained. Then, a new cell was generated using the relaxed distance z, but now with a 30 nm-vacuum slab inserted outside the two electrodes. With this procedure we ensured that all cells had the adequate size in order to hold the ideal number of atoms and still maintain the bulk density in the center of the electrolytic cells. The molecular representations of the supercapacitor simulation cells are provided in Fig. 2 and the details of the composition of each simulation are shown in Table 2.

Fig. 2 Molecular representations of the normal (top) and water-in-salt (bottom) electrolyte based uncharged supercapacitor. Cyan, pink, blue and yellow represent the water molecules, lithium cations, chloride anion and sulfate anion, respectively. Graphene layers are shown in gray spheres.

Table 2 Composition of the investigated supercapacitors

Supercapacitors	Li cations	Cl/SO4 anions	water molecules	Box (x, y, z) nm^3
LiCl (2 M)	144	144	4000	(3.4, 3.1, 11.5)
Li2SO4 (2 M)	224	112	3100	(3.4, 3.1, 11.0)
LiCl (21 M)	946	946	2500	(3.4, 3.1, 11.2)
Li2SO4 (21 M)	1514	757	2000	(3.4, 3.1, 11.5)

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For all molecular systems, we employ potential models based on the OPLS-AA force field to describe intermolecular interactions.¹³ The water molecule was treated using the SPC model.¹⁴ These models have been successfully applied in the description of the dynamical properties of pure ionic liquids and aqueous electrolytes and also in the modeling of the electric double layer in graphene supercapacitors.^8,15,16 Atomic partial charges and Lennard-Jones parameters of the ions were taken directly from the OPLS, with the exception of the SO₄²⁻ anion, which was taken from the parameterization from Jungwirth and co-workers.¹⁷ The electronic continuum correction (ECC) was applied to all ions. Standard force fields using full charges to describe divalent ions do not accurately capture ion pairing in aqueous solutions and overestimate the strength of ion–ion interactions with respect to ion–water interactions.^17,18

In ECC force fields, polarization electronics is taken into account and the charges of all ions are scaled by the inverse square root of the electronics of the dielectric constant of water and reducing the radius of each ion to achieve the required ion–water distances.¹⁷ This correction has been shown to improve significantly the ion pairing properties and structure of multivalent ions in electrolytic solutions compared to standard approaches.^17–20 The details of the force field parameters are summarized in Table 3.

Table 3 Force field parameters of ions used in simulations of Li₂SO₄ and LiCl aqueous solutions

	σ (Å)	ε (kJ mol^−1)	Charge ECC
Li^+	1.80	0.07647	+0.75
Cl^−	4.417	0.4928	−0.75
S	3.550	1.046	+1.50
O (of sulfate)	3.150	0.8368	−0.75

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The equilibration process of the electrolyte solutions was performed in an isothermal–isobaric ensemble (NPT) with T = 300 K and p = 1 atm for 10 ns. With this run, we accumulate enough configurations to the statistics of the structural and energetic analyses. Then, from the NPT equilibrated configurations, we performed new runs using the canonical ensemble (NVT) for 100 ns under normal conditions. This NVT improved sampling was used to determine the dynamic properties of the electrolytes, such as the diffusion coefficient, viscosity, and ionic conductivity.

This is done by dynamically distributing the electrode charge using the constant potential method implemented by Laird and co-workers for the study of electrified interfaces.^21,22 Both methods are equivalent to low potential differences (typically <2 V). As we are interested in smaller potentials here, we will employ the first model taking advantage of its large advantage concerning computational cost. In this way, each supercapacitor was simulated at seven different surface charge densities from σ = 0 (discharged supercapacitor) to σ = ±4.8 μC cm⁻² evenly incremented by 0.8 μC cm⁻². We applied the same procedure in recent work on graphene-based supercapacitors.²³

For all NPT simulations, the Parrinello–Rahman barostat²⁴ was used to maintain the constant pressure with a time constant of 2 ps and a compressibility constant of 4.5 × 10⁻⁵ bar⁻¹. In the case of supercapacitors, the pressure control was done using semiisotropic coupling in a way in which only z length could vary. To ensure a constant temperature in the Nosé–Hoover thermostat²⁵ a time constant of 2 ps was used. The Lennard-Jones interaction was computed by the classical shifted force technique while the long-range electrostatic correction was estimated by the Particle–Mesh–Ewald method (PME)²⁶ which was applied beyond a cutoff radius of 0.9 nm. Periodic boundaries were employed in all directions. The integration time-step was 2.0 fs and the coordinates and thermodynamic properties were stored every 0.1 ps. All simulation cells were generated using the PACKMOL code²⁷ and all molecular dynamics simulations were performed using the GROMACS 2020 molecular dynamics package.²⁸

Results and discussion

To characterize the electrolytes and compare their structural properties, mainly about valence asymmetry, we determined a series of properties presented in Table 4. The characteristic differences are evident when comparing normal electrolytes and water-in-salt. WiSE have a higher mass density than the normal electrolyte, in particular for the Li₂SO₄ solution whose mass density is 56% higher in WiSE concentration than in normal concentration. Although no experimental results were found for Li₂SO₄ solutions, our results are compatible with other similar electrolytes, such as LiCl solutions for which the density at 3.5 M was 1076.3 kg m⁻³, while at a higher concentration, of 15.2 M, the value has been increased to 1286.2 kg m⁻³.^29,30

Table 4 Normal and WiSE system properties: mass density (ρ), cohesive energy (E_c), average number of hydrogen bonds (#HB), diffusion coefficient (D), viscosity (η) and ionic conductivity (σ). The cohesive energy was obtained by the ratio between the internal energy of vaporization and liquid molar volume: E_c = ΔU_vap/V_m. The standard deviation for D, η and σ was assessed by dividing the trajectory into smaller blocks. 10 ns-blocks were used for diffusion coefficients and viscosity while blocks of 30 ns were performed for ionic conductivity. The final value was obtained as the mean overall block and its corresponding standard deviation

	Normal (2 M)		WiSE (21 M)
Property	LiCl	Li2SO4	LiCl	Li2SO4
ρ (kg m^−3)	996.8 ± 6.0	1119.2 ± 6.6	1191.2 ± 6.0	1751.1 ± 4.6
E c (kJ mol^−1 nm^−3)	1598 ± 5	2416 ± 6	4265 ± 5	9356 ± 38
# HB's	3388 ± 22	3135 ± 23	1456 ± 20	1269 ± 20
D water (10^−7 cm^2 s^−1)	362.3 ± 1.4	230.6 ± 1.7	89.7 ± 0.6	25.2 ± 0.5
D cation (10^−7 cm^2 s^−1)	164.3 ± 5.5	80.3 ± 1.5	55.5 ± 0.7	11.3 ± 0.3
D anion (10^−7 cm^2 s^−1)	270.4 ± 9.1	63.9 ± 0.8	57.5 ± 0.5	8.4 ± 0.1
η (cP)	1.0 ± 0.2	1.8 ± 0.5	23.0 ± 0.5	84.2 ± 0.9
σ (S m^−1)	12.1 ± 2.4	5.5 ± 0.6	8.82 ± 1.4	1.0 ± 0.1

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The cohesive energy quantifies the total intermolecular interaction of a solution and is an indicator of its thermodynamics stability. This is the effect of the intense network of electrostatic interactions, and the result of a much larger number of ionic pairs present in the solution. In another view, this energy is also larger for the sulfate-based solution than for chloride one, by circa 2.0 times. This can be rationalized in terms of the formation of hydrogen bonds since the SO₄²⁻ anions can form hydrogen bonds with water molecules, and besides that, this is a divalent anion, which intensifies, even more, the electrostatics among ions directly affecting the cohesive energy. Both effects lead to the increase of the internal energy of vaporization of the electrolyte and consequently its cohesive energy.⁸

Table 4 also presents the average number of hydrogen bonds (HB) present in each system. The hydrogen bonds are defined based on a simple geometric criterion, where two tagged molecules are considered to be bonded if the value of the donor–acceptor distance (r) is less than the r_HB value and the hydrogen–donor–acceptor angle (α) is less than the α_HB value. In the GROMAC software we used the gmx hbond routine to compute and analyze all the hydrogen bonds present in the systems.²⁸ We use the default values of r_HB = 0.35 nm and α_HB = 30° to calculate water–water and water–sulfate hydrogen bonds,³¹ and their generalization to water–chloride hydrogen bonds, r_HB = 0.41 nm and α_HB = 30°, based on radial distribution functions.³² As can be seen, the value of this property is higher for normal electrolytes than for WiSE. This is expected since WiSE has much fewer water molecules, which are responsible for most of the hydrogen bonds in the electrolytes.^7,8 The higher concentration of ions leads to an increase in electrostatic interactions, which dominates the intrinsic energy of WiSE. The reduction in the HB from the normal electrolyte to WiSE is ∼2.4 times for both salts.

The transport properties of an electrolyte are important indicators for determining its performance. The diffusion coefficient, viscosity, and ionic conductivity were calculated for all solutions and are presented in Table 4. For diffusion coefficients and viscosities, blocks of 10 ns were used, while for ionic conductivity, blocks of 30 ns were needed. A first analysis concerns the ionic mobility assessed by the diffusion coefficient, D, which was obtained by the linear adjustment of the mean quadratic displacement of r_i and it was possible to calculate the D using the Einstein relation:³³

This mean square displacement was calculated by the routine gmx msd.²⁸ For the diffusion analyses in this paper, the time between the reference points for the MSD calculation was 10 ps and the diffusion constant was calculated by least squares fitting of the MSD straight line portion, from 1 ns to 2 ns, for each block of 10 ns analyzed.

Table 4 presents the ionic diffusion coefficient for all molecular species (water, Li⁺, Cl⁻ and SO₄²⁻) at both concentrations. Regarding the electrolyte composition, our results indicate greater mobility of all species in Cl-based electrolyte than in SO₄ one, spanning from 1.6 times for water molecules in normal electrolyte up to ∼7 times for SO₄²⁻ anions in WiSE. Considering the concentrations, the mobility of the components is drastically reduced in the superconcentrated electrolytes, as expected. Note that this decrease is more accentuated in Li₂SO₄ electrolytes, by up to ∼9 times as we can see D_water (from 231 to 25 × 10⁻⁷ cm⁻² s⁻¹). For LiCl electrolytes, this reduction is only 4 times (from 362 to 90 × 10⁻⁷ cm⁻² s⁻¹). We also note that in LiCl electrolytes, the anion presents higher mobility than the cation Li⁺ but the opposite is observed for Li₂SO₄ electrolytes. This is due not only to the size of SO₄²⁻, which is greater than that of Li⁺, but also due to its valence which is two times higher. Although in these results it is impossible to decouple the effects of these two factors (size and valence), certainly valence plays a crucial role in determining the diffusion coefficient and valence asymmetry can justifies the relative reduction of anion diffusion at high concentrations.

The reduction in the mobility of ions and water directly affects the other dynamic properties of electrolytes, such as viscosity and ionic conductivity. In this work, viscosity, η, was obtained from the Green–Kubo formula by integrating the autocorrelation function of elements outside the diagonal of the pressure tensor, P_αβ(t):³⁴

For the estimation of shear viscosities, we employed an analysis scheme similar to the one proposed in ref. 35. From Table 4, we can observe that SO₄-based electrolytes are about 2–4 times more viscous than Cl-based ones, which is consistent with the fact that the SO₄ anion is divalent, and forms hydrogen bonds with water, both characteristics, directly associated with increased viscosity. Again, although we cannot specify the contribution of each effect, we can at least partially attribute the higher viscosity of the Li₂SO₄ electrolyte to the higher valence and size of its anion. When we compare the same electrolyte at different concentrations, normal and WiSE, we see that the shear viscosity increases by more than one order of magnitude; this increase being ∼23 times for the Cl-based electrolyte (going from 1 to 23 cP) and ∼47 times for the SO₄ based electrolyte (going from 1.8 to 84 cP). This large increase in WiSE viscosity compared to the normal electrolyte is naturally due to the very high concentration of ions in the electrolyte, which in turn is directly related to the high cohesive energy of these superconcentrated solutions.^7,8 Again, no experimental data for the viscosity of the Li₂SO₄ electrolytes were found. However, for a LiCl solution at a concentration of 1.9 M was the viscosity was found to be 1.2 cP, while for a concentration of 15.5 M the viscosity was 16.8 cP.³⁶ Although these values cannot be directly comparable, we see that both follow the trend of a strong increase in viscosity as the concentration increases. At this point it is interesting to note that the trends for diffusivity and viscosity are in good agreement with the behavior expected by the Stokes–Einstein equation, which states that viscosity is inversely proportional to the diffusion coefficient.

The ionic conductivity, σ, measures the tendency of a solution to conduct ions. This involves ionic movement from one location to another through the electrolyte. The Einstein–Helfand method was employed to determine the ionic conductivity by using the linear slope of the mean displacement of the collective translational dipole moments, M_j:³⁷

where , r_i being the coordinate of the center of mass of the ion i. Table 4 shows that ionic conductivity follows the inverse trend of viscosity, which decreases as the viscosity increases. For both concentrations, 2 M and 21 M, the LiCl solution proved to be a better ionic conductor than Li₂SO₄, and overall, the highest conductivity was found for the LiCl solution at normal concentration, 12.1 S m⁻¹. This value is about 2.2 times higher than the corresponding SO₄²⁻ anion-based solution. For the WiSE concentration, the LiCl solution is almost 9 times more conductive than Li₂SO₄, which has the lowest ionic conductivity among all solutions, 1.0. The comparison between the concentrations shows that in all cases, the superconcentrated electrolytes have lower ionic conductivity, up to 5.5 times, as is the case with the Li₂SO₄ solution, which reduces from 5.5 in 2 M to 1.0 in 21 M.

The interactions between ions and molecules are responsible for the structural properties of solutions. Such properties are investigated here in terms of radial distribution functions of the center of mass (RDF), the corresponding coordination number, calculated by the running integral of each RDF, and the spatial density functions (SDF). Fig. 3 presents selected RDFs for both normal (blue curve) and WiSE (red curve) concentrations. From Fig. 3, we can also compare the structuring of water molecules in normal and WiS electrolytes as well as in pure water (black line). As expected, water molecules are more structured in pure water than in mixtures; the black peak, corresponding to the RDF of pure water, is higher and narrower than the peaks observed for normal and WiS electrolytes. At 2 M, the RDF distribution of water is very similar to that of pure water for both salts, however with increasing LiCl or Li₂SO₄ concentration, the heights of the first peak in the RDFs decrease and become wider, while the weak peak at about 4.5 Å decreases with increasing salt concentration.

Fig. 3 Radial distribution functions for the center-of-mass for LiCl (top) and Li₂SO₄ (bottom) electrolytes. Normal concentrations are presented in the blue line and water-in-salt concentrations in the red line. The black line in water–water plots refers to bulk (pure) water.

In pure water, each water molecule is on average solvated by ∼5.5 water molecules, this value is close to that obtained for LiCl and Li₂SO₄ solutions at 2 M concentration (see Table 5). Upon increasing the salt concentration to 21 M, the water–water coordination number (CN) decreases to 4.0 in the LiCl solution and to 4.3 for the Li₂SO₄ solution. This behavior has been previously observed in computational simulations of LiTFSI electrolytes at high concentrations.⁷

Table 5 Coordination number of cation–water, anion–water and cation–anion pairs. The analysis was carried out for the first coordination sphere

Pair	Normal (2 M)		WiSE (21 M)
	LiCl	Li2SO4	LiCl	Li2SO4
Water–water	5.4	5.9	4.0	4.3
Cation–water	3.9	3.5	2.4	1.4
Anion–water	6.9	14.4	5.7	12.2
Cation–anion	0.1	0.5	1.5	2.6

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For all solutions, the pair correlation functions of Li–water present their first peak at 0.25 nm with a narrow shape, indicating a well-defined orientation of the water molecules in the first hydration shell (see Fig. 3b and f). Lithium ions are highly coordinated with about 3.5–4.0 in 2 M aqueous water solutions of LiCl. This result is consistent with the observation that the lithium ion is solvated by four water molecules.^38,39 However, it is important to emphasize the reduction in the height of the first peaks of the RDF (Li–water) with the increase in concentration. In fact, lithium solvation is severely reduced in WiSE by up to 2.5 times (from 3.5 water molecules in 2 M Li₂SO₄ solution to 1.4 in 21 Li₂SO₄ solution), which is a direct consequence of the reduction of water amount in superconcentrated electrolytes.

The asymmetry in cation and anion valence clearly manifests itself in the analysis of the RDF of anion–water pairs. The corresponding first peaks (see the middle panels in Fig. 3) of the anion–water RDFs are farther away (0.4–0.5 nm), lower but broader than the corresponding Li–water pairs. As the valence of the SO₄²⁻ anion is twice the valence of the Cl⁻ anion, we observed a strong impact on the structuring of the electrolytes and, as we can see in Table 5, the number of water molecules coordinated with the SO₄²⁻ anion is twice as high as that coordinates the anion Cl⁻. This valence asymmetry is also manifested in RDF's cation–anion, whose first coordination sphere ends at an intermediate distance of ∼0.30 nm and have narrow and intense peaks. For these distributions, we see from Table 5 that the SO₄²⁻ anion coordinates a much larger number of cations than the Cl⁻ anion.

Several aspects of aqueous electrolyte solutions are directly related to ions modifying the local structure of water. Highly charged ions cause strong electrostatic ordering of nearby water molecules and reduce their H bonds. For example, in a recent study, Mukherjee and Saha showed that the presence of divalent ions, such as SO₄²⁻, has a much greater impact on the local structure of the aqueous solution than a monovalent ion such as Cl⁻.⁴⁰ Both reduce the translational and rotational entropy of the surrounding water molecules, but SO₄²⁻ does it to a much greater extent. Effects of this nature justify the detailed investigation of the effects of valence asymmetry for the properties of electrolytes, those that affect their performance as electrolytes for batteries and supercapacitors.

The analysis of the structure of electrolytes through the analysis of RDFs can be complemented by determining the spatial distribution functions, SDFs.⁴¹ The SDF is a three-dimensional distribution of probabilities of finding the molecules/ions of the system in a particular configuration and provide us with additional insights into the local structure and its relationship with the properties of these systems. In this work our interest is in determining the distribution of a given ion around a water molecule, as well as the distribution of water molecules around SO₄²⁻ anion. It is worth mentioning that the distributions around the anion Cl⁻ and the cation Li⁺ were not calculated since for these systems, which have only symmetrical spherical interactions, the pair distribution function will not contain angular dependence, and the SDF will simply be a spherical shell.

Two first blocks of Fig. 4 present the SDF around SO₄²⁻ anions; the first being the water distribution (in dark green) and the second the Li⁺ distribution (in red) around the anion. These SDFs make clear the structural impact of concentration on the coordination of the SO₄²⁻ anion, showing that the distributions of water molecules and Li⁺ cations show opposite trends. This is because in 2 M there are more water molecules and fewer Li⁺ cations, so SDF is more intense for water than for Li⁺. The situation is reversed for the 21 M concentration, where the amount of Li⁺ cation is much greater, reflecting a greater intensity of its SDF. It is interesting to note that the water and Li⁺ distributions overlap out of phase, i.e., where the water SDF has the maximum intensity the cation one has minimum intensity and vice versa. The last three blocks of Fig. 4 show the ion SDFs around the water molecule. Here we can see that in all three cases the SDF is more spatially distributed for the 2 M concentration and more compact for 21 M. We also see that the anion and cation distributions tend to overlap, which indicates a strong cation–anion correlation in the water coordination structure.

Fig. 4 Spatial density functions for water around ions and ions around water in normal and WiSEs.

To investigate the performance of electrolytes we created graphene electrolytic cells from which we determined the structural properties of the electrical double layer formed at the electrode–electrolyte interface as well as its electrostatic properties. The formation of an EDL is an important physical process of purely electrostatic origin and, in principle, reversible, being the main electrochemical energy storage pathway of a supercapacitor.

Analysis of the structure and composition of the EDL can be done in terms of the mass density profile of water and ions in the vicinity of the device's electrodes. In Fig. 5, the mass density profiles are presented, both normalized in relation to the bulk density. This normalization is convenient because, in addition to standardizing the graphs, it facilitates the analysis of the relative heights between the profile peaks. The analysis is performed for the supercapacitor charged with a 4.8 μC cm⁻² charge, but it does not change qualitatively for the other charges used. We see that for all profiles the layering arrangement of the electrolyte extends over an ∼1 nm range from the electrode surface (as can be seen by the ion SDF, top of Fig. 5), except for WiSE Li₂SO₄, for which density fluctuations can be observed beyond this distance. This behavior is characteristic for aqueous electrolytes in contact with graphene electrodes.^42,43 We also see the high density of lithium ions in the EDL (blue curve) close to the negative electrode, with very intense peaks in all cases, except again from WiSE Li₂SO₄, for which the SO₄²⁻ anion strongly interacts with the negative electrode. These peaks for cations are always accompanied by smaller peaks corresponding to anions and water, which are also adsorbed, in smaller numbers, from the surface of the negative electrode. On the other hand, the EDL on the positive electrode surface is composed of a higher density of anions and water, especially at normal concentrations. In all cases the anions project into direct contact with the positive electrode, which can be seen by the black curved tail, closest to its surface. The behavior of the EDL and its composition in the results we present here are consistent with the EDL structures for aqueous electrodes that have been found previously.^42,43

Fig. 5 At the top, the SDF of the ions on the surface of the graphene highlighting the formed electric double layer close to the electrodes. At bottom, the number density profiles for the LiCl-based supercapacitor (set of panels at top) and Li₂SO₄-based supercapacitor (set of panels at bottom). Blue, red and black lines represent anion, cation and water distributions, respectively. Gray vertical bars represent the graphene electrode positions. For all plots we consider the charged supercapacitor with 4.8 μC cm⁻².

The effects of valence asymmetry could not be observed in the mass density profiles. As the peaks related to Cl⁻ and SO₄²⁻ anions depend on their shape and size, it is not possible to isolate this effect, since the geometry of the anions is very different. Even so, although the peaks related to anions are very similar, it is possible that the asymmetry effect is being masked by some other simultaneous effect. This could only be observed in a model system, where all anions had equal parameters, differing only in their valence.

The electrostatic potential profile was determined in this work by integrating the one-dimensional Poisson equation along the length z of the box, according to the expression:

where ρ_z(z′) is the charge density of each ionic species.⁴⁴ From the obtained potential profile it is possible to determine the total potential drop across the device using the difference ΔΔΦ = ΔΦ^charg − ΔΦ^uncharg where ΔΦ = Φ⁺ − Φ⁻ for both charge and uncharged electrode situations (Φ⁺ and Φ⁻ are the potentials on the positive and negative electrodes).

The electrostatic potential profiles obtained for all electrolytes are shown in Fig. 6 for the discharged (black curve) and charged (with a density of 4.8 mC cm⁻², red curve) supercapacitors. As is typical for aqueous electrolytes, these profiles show fluctuations on the surface of the electrodes that attenuate to within ∼1.0 nm for electrolytes at normal concentration and go beyond 1.5 nm for WiSEs.

Fig. 6 Electrostatic potential profile (V) as a function of the distance (nm) for all electrolytes investigated here. The potentials near the electrodes are in an enlarged scale to favor a comparison of the profiles. Black and red curve represent the profile for the uncharged and charged (4.8 μC cm⁻²) supercapacitors.

There is no evidence that charge asymmetry had any influence on liquids at normal concentrations; note that the corresponding curves for LiCl and Li₂SO₄ electrolytes are very similar. On the other hand, the same comparison for the WiSE liquid shows a fluctuation that persists for a much longer distance, for the Li₂SO₄ electrolyte. Here, it is possible that the effect of charge asymmetry has some relevant role since there is a much larger number of divalent anions in the electrolyte and, consequently, a greater influence of these on the electrostatic potential profiles. In any case, there is no observable effect on the absolute value of the downside potential.

The potential drop along the supercapacitors shows a direct relationship with the charge density: the higher the charge, the greater the potential. The values found for the potential drops were associated with the two respective charge densities to obtain the σ × Δϕ curves presented in Fig. 7. In these plots all values for drop potential were corrected with potential zero charge.⁴⁴ The linear adjustments in the positive and negative potential portions allowed us to obtain the capacitances of negative (C⁻) and positive (C⁺) electrodes. These capacitances taken in a series combination resulted in the total EDL capacitance (C^total) of the supercapacitor, as shown in Table 6.

Fig. 7 Surface charge density (μC cm⁻²) as a function of the potential drop in the electrode (V). Each graph presents two linear adjustments, one for the negative electrode and the other for the positive electrode. The slope of this adjustment gives us the electrode capacitance.

Table 6 Values of electrode capacitance and total capacitance (in μF cm⁻²) obtained from the slope of the adjusted line for the simulated curves σ × Δϕ

Supercapacitors	C ^−	C ^+	C ^total
LiCl (2 M)	5.75	4.53	2.53
LiCl (21 M)	5.44	4.71	2.52
Li2SO4 (2 M)	6.55	5.51	3.00
Li2SO4 (21 M)	6.01	5.86	2.97

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The negative and positive electrode capacitances showed asymmetry related to the composition of the double layer, indicated by the difference between the values C⁻ and C⁺, which ranged from 2.5% for the WiSE Li₂SO₄ supercapacitor to 21% for the LiCl supercapacitor at normal concentration. This asymmetry in electrode capacitances, which has already been observed in previous work, originates from the asymmetry in the ions and their different interaction with the electrodes.¹⁵ The results for the double-layer total capacitance suggest that Li₂SO₄ supercapacitors (∼3.0 μF cm⁻²) can have up to 20% more yield than LiCl supercapacitors (∼2.5 μF cm⁻²), regardless of the concentration. For the capacitances the valence asymmetry, if any, was masked by other concurrent effects. More detailed and specific work will be needed to reveal the contribution of these effects.

Conclusions

Atomistic molecular dynamics simulations were employed to investigate the properties of electrolytes based on LiCl and Li₂SO₄ ion pairs at two different concentrations 2 M (normal) and 21 M (superconcentrated, WiSE). For this, a series of simulations was carried out in order to determine the structural, dynamic, and energetic properties of the pure electrolytes. The second series of simulations was conducted to investigate the performance of the solutions as electrolytes in supercapacitors. In this case, we determine their electrostatic properties, such as the electrostatic potential profile and the electrical double layer capacitance. The effects of valence asymmetry of the Li₂SO₄ electrolyte were discussed for all analyses performed.

The structural, dynamic, and energetic properties characterized the physical aspect of pure electrolytes, showing the drastic effect of high concentration. For example, the viscosity of LiCl and Li₂SO₄ aqueous electrolytes is about ∼23 and ∼47 times higher for water-in-salt electrolytes than for normal concentrations. This is a consequence of their reduced ionic mobility and has a direct effect on ionic conductivity. In this work we made reasonable inferences about the valence asymmetry effect but, a definitive conclusion can be obtained only from results using standardized models (where all other parameters are equal), with identical LJ particles. This protocol is the only way to reveal the quantitative aspect of the valence effects. This work is being prepared and we would submit it for review shortly.

Our results do not reveal the advantages of WiSEs compared to normal electrolytes, as indicated by some experimental work.^45–47 In fact, the differences in the total capacitance, due to the concentration of ions, presented by both electrolytes are negligible. Similar discrepancies between simulated and experimental results have been observed before in other computational work involving normal electrolytes and superconcentrated electrolytes.^8,48 and is probably due to some effect that occurs at the electrode/electrolyte interface and is not being captured by classical simulations. As is well known, classical simulations do not take into account any important effects such as oxidation reactions that occur in pseudocapacitive systems and that drastically influence the final value of capacitance.

Finally, the valence asymmetry can be unmistakably observed in some properties. However, in most of them, when present, the effects of this asymmetry could not be quantified or isolated, indicating that specific calculations, in model systems, will need to be performed so that it is possible to unequivocally assess the real magnitude of these effects.

Conflicts of interest

There are no conflicts to declare.

Author contributions

A. M., D. A. C. S.: investigation, formal analysis and visualization of data, writing – original and review draft. E. E. F.: investigation, conceptualisation, methodology, supervision, writing – original and review draft.

Acknowledgements

The authors gratefully acknowledge support from FAPESP (São Paulo Research Foundation) and Shell, Grant Number 2017/11631-2, the strategic importance of the support given by ANP (Brazil's National Oil, Natural Gas and Biofuels Agency) through the R&D levy regulation and CNPq (National Council for Scientific and Technological Development).

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