Ion correlations in quaternary ionic liquids electrolytes

Lithium-ion batteries are currently the most popular and widely used energy storage devices, almost omnipresent within modern society in portable devices, electrical vehicles, energy storage stations, and so on. The demand for more efficient, more durable, and more sustainable batteries is rapidly growing. The electrolyte is a key element to improve the performance of lithium-ion batteries. In this work, we focus on quaternary ionic liquid electrolyte (ILE), which uses a four-component ionic liquid as the solvent. Quaternary ILE has found wide applications in energy storage systems, but the ion transport in the electrolyte has not been fully characterized to provide the best strategy for performance optimisation. In this work, we systematically analyse the ion transport in the quaternary ILE and uncover how the correlations between various ions affect the conductivity of the electrolyte. We have found that lithium ions are transported in charge clusters, leading to a negative effective transference number of lithium ions. Furthermore, we identify the stable cluster conformations in ILE by cluster analysis and quantum chemical computing. This work highlights the necessity of considering ion correlations in multi-component electrolyte systems.


Introduction
Ionic liquid electrolytes (ILEs) [1][2][3][4] are a type of molten salt that can serve as an alternative to traditional electrolytes in lithium-ion batteries.These salts have gained popularity in recent years due to their potential to enhance battery performance and safety [5][6][7].One key benefit of ILEs is their high conductivity and stability, which enables the use of lithium metal as an anode, leading to higher energy density [8,9].ILEs also have low volatility and flammability, contributing to improved battery safety.Additionally, their wide operating temperature range makes them suitable for a range of applications, such as electric vehicles, consumer electronics, and energy storage systems [10].
The three essential transport properties of ILEs that influence their performance in batteries are the ion diffusion coefficient (D), the ion conductivity (σ), and the cation transfer number (t + Li ) [11][12][13].These properties measure the effectiveness of ILEs as an electrolyte in batteries.Experimentally, the collective salt diffusion coefficient can be determined using the confined diffusion method and the individual ion diffusion coefficient can be obtained using the pulsed field gradient nuclear magnetic resonance (PFG-NMR) [14,15].The ionic conductivity is typically measured through alternating current impedance spectroscopy with a small applied voltage (∼10 mV) [16][17][18].The transport number is usually established through a steady-state current method, which is limited to dilute electrolytes due to its reliance on ideal solution behaviour [19,20].The conductivity and ion transference number are crucial for evaluating the performance of ion transport and are essential for improving the electrolyte's performance [21][22][23][24][25]. Therefore, a significant amount of research and development focuses on enhancing ion conductivity and ion transference numbers.However, in practical battery operations involving liquid electrolytes, especially ILEs, both the lithium ions and the anions contribute to the charge transport, so it is insufficient to solely increase lithium-ion transmission.A comprehensive understanding of the transport behaviour of different ions in the solution, the correlation between ions, and the underlying electrolyte transport mechanism and model is necessary to effectively optimise the performance of the electrolyte.
In recent years, there has been a growing trend among researchers to utilize simulation methods to investigate the ion related behaviour of electrolyte ions [26][27][28].For example, Otero-Mato et al investigated the conductivity of ionic-liquid/alcohol mixtures and found the effect of ion correlations is most relevant at concentrations close to the conductivity maximum [27].Meanwhile, Popov et al systematically studied the transport behaviours of LiTFSI and LiFSI in highly concentrated aqueous and acetonitrile solutions.Based on their analysis, they found that a change in the solvent concentration can suppress the anion-cation contribution to conductivity and increase the Li + transference number [29].Similarly, the effect of concentration and temperature on the ion transport in diglyme-based sodium ion electrolyte were reported by Ardhra et al [30].They showed that the ionic correlations have to be considered to correctly predict the experimentally observed trends in ion conductivity.However, only binary or ternary ILEs have been considered in the abovementioned studies.The behaviour of ion transport in typical quaternary ILEs has yet to be elucidated.
In this work, we employ molecular dynamics (MD) simulations to investigate the transport characteristics (ion diffusion coefficient, ionic conductivity, ion transfer number) of LiTFSI-[Bmim][PF 6 ], a common quaternary ILEs used in energy storage devices.We consider a wide range of concentrations of lithium salts from 0.5-3 mol l −1 , typical of the concentration used in applications.Since methods for computing the transport characteristics for multi-component ILEs have not been well established, we calculate and compare the transport characteristics with and without considerations for ion correlations.Through the comparisons, we uncover the transport mechanism of Li + in the quaternary ILE and elucidate how the microscopic interactions between ions and the solvent molecules influence the macroscopic transport properties.We demonstrate the important effects of ion correlations on the conductivity of quaternary ILEs.This work explores the electrolyte transport properties of ILEs at the molecular level and provides a basis for optimizing electrolyte composition for batteries.

Simulation model and computational details
In this work all-atom MD simulations were produced for the lithium salt LiTFSI with five different concentrations from 0.5 mol l −1 to 3 mol l −1 , 50 ion pairs Li + -TFSI − were placed in a periodic boundary box containing different numbers of [Bmim][PF 6 ] (figure 1).The initial configurations of the simulated models were constructed by using the Packmol package [31].All the MD simulations were carried out in the Lammps software [32].Details of the simulation procedure are given as follows: each simulation system is relaxed in the canonical (NVT) ensemble for the first 5 ns and then in the isothermal-isobaric (NPT) ensemble for the next 10 ns.Production simulation is carried out for 20 ns in the NPT ensemble and for 60 ns in the NVT ensemble to achieve the configurational equilibria.The Verlet algorithm with a time step of 1.0 fs is employed to integrate Newton's equations of motion.The van der Waals interaction is treated with the Lennard-Jones potential.The partial charges of these ILs were obtained by following the restrained electrostatic potential procedure [33].During the simulation, the trajectories are recorded at every 0.1 ps for further post-analysis.The optimized all-atom force field based on the Amber force field which scaled down the atomic partial charges by a charge scaling factor of 0.8 was used to describe all ions ([Bmim] + , [PF 6 ] − , TFSI − and Li + ) [34][35][36].Meanwhile, in order to demonstrate the accuracy of charge scaling in this work, the difference in density and viscosity of the two force fields when the charge is 1 and 0.8 were compared, which are discussed in detail in the supplementary information.In order to avoid randomness in molecular simulation, we simulated the same process pair five times for the same system, and the simulation details are shown below.

Diffusion coefficient
We first analyse the self-diffusion coefficient (D) in the quaternary ILE.The self-diffusion coefficient is typically calculated by fitting the slope of the mean square displacement (MSD) as a function of time over long periods.However, the simulation time scale is often not sufficiently long to achieve consistent results,  and the values of D vary greatly depending on the fitting interval.To obtain the most accurate ion diffusion coefficients, we first introduce a metric, β, for assessing the appropriateness of the time interval, with its value given by [37] Generally, if β < 1, the ion is not in the diffusive regime due to the sluggish dynamics.Thus, we choose time intervals long enough such that β = 1 and evaluate the MSD over these intervals.To achieve this, we take 10 ns of the equilibrated trajectories after 50 ns of equilibration.The MSD for ions in this interval is presented for the lithium ions in figure 2(A) (and for all other ions in the supplementary information).The corresponding self-diffusion coefficients of ions are plotted in figure 2(B).The simulation results revealed that regardless of the lithium salt concentration, the trend of the self-diffusion coefficient follows , which is consistent with our previous work [38].This is surprising, as Li + has the lowest mobility in ionic liquids despite its smallest volume.This hints at the strong correlations between Li + and other ions, as suggested by Liu and Maginn that Li + has the smallest diffusivity because it interacts strongly with the anions in the ionic liquid [39].We also observe that all ions have the largest self-diffusion coefficient when the Li + concentration is at 2 mol l −1 ; therefore, 2 mol l −1 is the optimal lithium salt concentration for LiTFSI-[Bmim][PF 6 ].

Ionic conductivity
Of the three transport properties, ionic conductivity (σ) is considered the most crucial metric indicating the performance of the electrolyte.In the case of ILEs, most studies calculate the ion conductivity from the self-diffusion coefficient using the Nernst-Einstein Equation.However, it is important to note that ionic conductivity is a measure of net charge flow and can be impacted differently by associated ion motion.Therefore, it is necessary to consider the effects of ion-ion correlation.As highlighted in the recent work by Arthur and Jeffrey [40] Such effects can be accounted for using the Green-Kubo framework on ionic movements [41].Applying the Green-Kubo formalism, the ion conductivity can be calculated using the following expression: where N is the number of ions in the electrolyte, V is the volume, k b is the Boltzmann's constant, T is the temperature, q x (x = i, j) indicates the charge of the xth ion, and R x (t) (x = i, j) is the position of the xth the ion at a given time t.The angular bracket <…> denotes an ensemble average and the sum Σ runs over all the ions in the electrolyte.Equation ( 2) reduces to the Nernst-Einstein relation when ionic correlations are ignored.
In table 1, we tabulated the total conductivity without the considering the ion correlations (using the Nernst-Einstein Equation) and with ion correlations (using the Green-Kubo formalism).At high concentrations of lithium ions, there is significant deviation between the two values of conductivities, suggesting strong ion correlation present in this regime.Based on equation ( 2), the ion conductivity consists of three types of contributions: first, from the ion diffusivities of each species through the terms with i = j in the summation; second, from the correlations between ions of the same species (terms with i ̸ = j with i, j being the same species); third, from the correlations between ions of different species (terms with i ̸ = j with i, j being different species).We denote the three types of contributions by the self-diffusivity terms σ s ion (including ), the intra-species ion correlation terms σ d ion (including ), and the inter-species ion correlation terms ), respectively.The different contributions towards the total conductivity σ tot are schematically illustrated in figure 3(A), where the diagonal triangles represent the self-diffusivity terms, the diagonal squares represent the intra-species ion correlation terms, and the off-diagonal squares represent the inter-species ion correlation terms.The total conductivity can then be expressed as [25] where The self-diffusivity term σ s ion of different ion types are shown in figure 3(B).Regardless of lithium ion concentration, they are all sorted according to the following order: . This indicates that the mobility of cations and anions in ionic liquids are both greater than that of lithium salts without considering ionic correlation.As mentioned in section 3.1, this trend is unexpected, as the Li + is the least mobile despite its small volume.This implies that Li + tend to associate with other ions, resulting in fewer free Li + that can move rapidly.Additionally, we note that σ s and its individual-species contributions all increase with lithium-ion concentration, but the increase is the most rapid at around 2 mol l −1 .Even though the σ s continues to increase beyond 2 mol l −1 , the rate of increase in conductivity slows down dramatically.The ability to conduct electric current in ionic liquid is nonlinear with the concentration of lithium salt.Therefore, one might only achieve marginal gain in conductivity by increasing lithium-ion concentration if the lithium-ion concentration is beyond this concentration.Thus, exploring the suitable conditions for the concentration of lithium salt is crucial important to improving electrolyte performance.Similar conclusions were also reported in our previous research [38,42].The surprising trend in the self-diffusivity term prompts us to look further into the possible correlation between the ions.We first performed a detailed analysis of the intra-species ion correlation σ d ion for the four ion species as shown in figure 3(C).Unlike σ s ion , we found that σ d ion for some species can be negative, indicating a negative contribution to the total conductivity.Similar observations were also made by McDaniel and Son [25] in organic electrolytes composed of binary mixtures of 1-butyl-3-methylimidazolium tetrafluoroborate [Bmim][BF 4 ] and 1,2-dichloroethane, acetone, acetonitrile, and water solvents.Such negative values in ion conductivity suggest that ions of the species are moving in the opposite directions on average, resulting in reduced conductivity.For the species present in the system, we find [PF 6 ] − contributing positively to conductivity, TFSI − contributing negatively, and [Bmim] + contribution changes from positive to negative as the concentration increases.The intra-species ion correlation for Li + is insignificant compared to other species, indicating minimal correlations among Li + ions in the system and rather independent movement for each Li + .
On the other hand, the inter-species ion correlation σ d ion1, ion2 suggest strong correlations between ions of opposite charges, as shown in figure 3 always yields negative values regardless of the concentration, indicating strong correlation between Li + and [PF 6 ] − in ILE.Therefore, we hypothesize that Li + and [PF 6 ] − form ion pairs/clusters in the ILE, which in turn affects the total conductivity.Therefore, it is advisable to minimize the inter-species ion correlations to achieve optimal conductivity, and the optimal concentration range for this to occur is at around 2 mol l −1 .
To further illustrate the impact of the three types of conductivity (σ s ion , σ d ion , σ d ion1,ion2 ) on the overall conductivity of the electrolyte, we plot the three contributions in figure 3(E) separately.It could be found that the sum of the conductivity σ s ion and σ d ion is positive at all concentrations, indicating that these two types of conductivities contribute positively to the total conductivity.However, the total sum of σ d ion1,ion2 changes in an irregular manner.This is due to the fact that the calculation of σ d ion1,ion2 depends on the ratio of different ions.When the number of Li + is significantly less than that of ILs, there is a large statistical uncertainty.However, it is clear that the inter-species correlation contribution σ d ion1,ion2 to the total conductivity becomes negative as the concentration of lithium salt increases.Therefore, there should be an optimal maximum lithium concentration for when we design Li-based ILEs.

Transference number
The last essential transport property of ILEs is the transference number of lithium ion (t + Li ), which is the fraction of total electric current carried by the lithium ion.The transference number can be measured using the PFG-NMR technique, but the measurements are often inaccurate.The PFG-NMR assumes that the ions are completely dissociated and move independently, and computes the transference number through the Nernst-Einstein equation through However, based on the discussions in section 3.2, we note that the conductivities cannot be calculated using only the self-diffusivity terms of the ions.Therefore, a more accurate way calculating the transference number, taking the effects of ion correlation into account, would be [43] where σ is calculated based on the Green-Kubo formalism defined in equation ( 2).The quantity t eff Li is defined as the effective transference number of lithium ions.
In table 1, we observe that t NE Li increases with the increased lithium salt concentration for all ILE systems in this work.However, t NE Li (equation ( 4)) is only considered correct in very dilute solutions (the concentration of lithium salt less than 0.01 M).In fact, the typical concentration of lithium salt used in batteries are usually greater than 1 M, and there is significant interaction between ions in electrolytes.Meanwhile, many studies have shown that when lithium salt dissolved in a solvent, not all ions decompose into solvated Li + and [X] − ions and some remain as neutral [Li][X] ion pairs.
With ion correlation considered in the computation of transference number, there are, surprisingly, negative values of t eff Li at high and low concentrations of lithium salt.Such negative values cannot appear if all lithium ions are dissociated and suggest the presence of lithium-ion clusters in the system.Additionally, the negative effective transference number means that the contribution of lithium ions to the conductivity is negative, and the anions have to play a bigger role in carrying the currents.This observation is in agreement with results reported by Gouverneur et al [43] and Molinari et al [44], which showed that the strong cation-anion interaction resulted in a negative lithium transfer number in the ILE systems.Gouverneur et al also suggested the negatively charged ion clusters caused by the imbalance of the number of negative cations is a necessary condition for negative t eff  Li , but not a sufficient condition [43].

Cluster analysis
The investigation into ion correlations in section 3.2 and the negative transference numbers in section 3.3 suggest that Li + ions are strongly correlated with other ions during the transport.In figure 3(D), we observe In which β is an auxiliary function if i and j are in the same cluster at time t 0, otherwise .
The definition of a cluster requires a chosen geometric criterion.In this work, we select the first peak value of the radial distribution function of two molecules i and j ) to be a simple distance criterion for being connected within an aggregate.A cluster consists of molecules that are each connected to at least one molecule within the aggregate.And N gives the number of possible clusters within the given distance, T is the time, t represents the initial time, and τ gives the increasing time.⟨. ..⟩ represents the ensemble average of the clusters between Li + and [PF 6 ] − throughout the trajectory.As figure 4(B), take 1.5 mol l −1 LiTFSI/[Bmim][PF 6 ] as example, the lifetimes of the three types of cluster satisfies the following order: (Li[PF 6 ] 2 ) − > Li[PF 6 ] > (Li 2 [PF 6 ]) + .The cluster of (Li 2 [PF 6 ]) + decays the slowest, indicating that this type of cluster has the longest lifetime.We then integrated the autocorrelation functions to obtain the average lifetimes for clusters.The obtained lifetime of the clusters are tabulated in figure 4(C).At low concentrations, (Li 2 [PF 6 ]) + has the longest lifetime, but the cluster confined the movement of multiple Li + ions, affecting the conductivity.At high concentrations, the ion pair Li[PF 6 ] has the longest lifetime, and the neutral pair does not contribute to conductivity as well.The lifetimes of (Li 2 [PF 6 ]) + and Li[PF 6 ] crossover when the Li concentration is at approximately 2 mol l −1 , and that is the concentration optimal for the ILE's conductivity.

Conclusion
In this work, we investigated the effect of lithium concentration on the lithium ion transfer mechanism in quaternary ionic liquids electrolytes LiTFSI-[Bmim][PF 6 ].To the best of our knowledge, this is the first systematic investigation of ion correlations for ionic liquids involving four components.We illustrated the presence of the strong ion correlations and the prevalence of Li-ion clusters in the system.As a result, the conductivity changes non-monotonically with Li ion concentration and there is even negative transference number of Li ions at concentrations.By calculating major transport properties of the electrolyte including diffusion coefficients, conductivity and transference number of Li + , we determine that the optimal Li + concentration in the ILEs is around 2 mol l −1 for such quaternary ILE.This work elucidates the ion transfer mechanisms in ILEs, presents valuable perspectives on improving conductivity models, and provides an optimal Li concentration to guide the design of ILEs.

Table 1 .
Total conductivity and transference number of Li +.
(D).In particular, at high Li concentrations (beyond 2 mol l −1 ), the σ dLi,PF6 shows large negative values.As Li and PF6 are oppositely charged, the large negative values of σ dLi,PF6indicate that the two ions are moving in the same direction.Similarly, at low Li + concentrations, which means high concentrations of [Bmim] + , σ d Bmim,PF6 is strongly negative, indicating that the oppositely-charged [Bmim] + and [PF 6 ] − move in the same direction.When ions of opposite charges move in the same direction, they contributed minimally to the conductivity.Additionally, it is evident that σ d