General Trend of Negative Li Effective Charge in Ionic Liquid

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General Trend of Negative Li Effective Charge in Ionic Liquid Electrolytes Nicola Molinari, Jonathan Pradana Mailoa, and Boris Kozinsky J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.9b00798 • Publication Date (Web): 18 Apr 2019 Downloaded from http://pubs.acs.org on April 18, 2019

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The Journal of Physical Chemistry Letters

General Trend of Negative Li Effective Charge in Ionic Liquid Electrolytes Nicola Molinari,∗,† Jonathan P Mailoa,‡ and Boris Kozinsky∗,†,‡ †John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA ‡Robert Bosch LLC, Research and Technology Center, Cambridge, MA 02142, USA E-mail: [email protected]; [email protected]

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Abstract We show that strong cation-anion interactions in a wide range of lithium-salt/ionic liquid mixtures result in a negative lithium transference number, using molecular dynamics simulations and rigorous concentrated solution theory. This behavior fundamentally deviates from the one obtained using self-diffusion coefficient analysis, and explains well recent experimental electrophoretic NMR measurements, which account for ion correlations.

We extend these findings to several ionic liquid compositions.

We investigate the degree of spatial ionic coordination employing single-linkage cluster analysis, unveiling asymmetrical anion-cation clusters. We formulate a way to compute the effective lithium charge, and show that lithium-containing clusters carry a negative charge in a remarkably wide range of compositions and concentrations. This finding has significant implications for the overall performance of battery cells based on ionic liquid electrolytes. It also provides a rigorous prediction recipe and design protocol for optimizing transport properties in next-generation highly correlated electrolytes.

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Ionic liquids (IL) have recently experienced a surge of interest justified by their vast applicability as, for instance, catalysts,1–3 tailored solvents,4,5 and electrolytes in solar cells and batteries. 6–10 Specifically for Li+-ion and Na+ batteries, room temperature ILs exhibit properties such as low volatility, low flammability, and higher chemical and thermal stability as compared to standard organic solvents, which make them attractive for technological applications as electrolytes.6,11–14 As the transport properties of the electrolyte largely determine the charge/discharge rate capabilities of the battery, ionic conductivity in Li+-salt/IL mixtures has been the target of extensive investigations. 13,15,16 In particular, what should be maximized is not the total ionic conductivity, κ, but its portion carried by the cation of interest, κLi, which is measured + by the product of the total conductivity and the transference number tLi , the latter indicat-

ing the cation’s fractional contribution to κ.17–19 Experimentally, t+Liis commonly inferred from the self-diffusion coefficients, determined by pulsed-field-gradient-NMR,

20–23

thus ne-

glecting effects due to correlated ion migration. Only recently, electrophoretic NMR-based (eNMR24,25) analysis of the ion mobilities was adopted by Zhang et al.26 and Gouverneur et al.27,28 to determine transference numbers in IL without any assumption on ion aggregation. The measurement of electrophoretic mobilities, which account for the correlation in ion migration, unveiled surprising transport anomalies such as negative transference number. 28 As molecular dynamics (MD) can be leveraged to obtain atomistic-level insights into the coordination, mobility, and aggregation between different species that are nearly inaccessible by experimental studies, computer simulations provide a powerful framework to gain fundamental understanding and complement the experimental observations. Additionally it should be noted that it is rather difficult to reliably measure transference numbers experimentally,29 and MD simulations provide a key complementary investigation tool. To the best of our knowledge, the computational community unanimously followed the recipe to calculate t+Lifrom the self-diffusivities, therefore ignoring important intra- and inter-species correlation present in this class of systems. In a previous work, we extensively characterized

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the limitation of the dilute-limit approach to compute transport properties and predicted a negative transference number for a promising Na+-ion electrolyte system.30 In this manuscript we study the transport properties of several Li+-salt/ionic liquid mixtures by combining molecular dynamics with fully-correlated multi-species concentrated solution theory, and we report following findings. First, we computationally confirm the measured negative tLi+ ,28 and extend this surprising result to different chemistries and systems, suggesting this as a universal trend in Li+-salt/IL mixtures. Second, we characterize the atomistic nature of the anion-cation clusters, and highlight how negatively-charged ion clusters, resulting from an anion-cation number imbalance, are a necessary but not sufficient condition for a negative tLi+ . Finally, to investigate this point further we formulate a way to calculate the Li+ “effective charge”, which agrees well with experimental measurements using state-of-the-art eNMR analysis.

To create a low-density non-overlapping initial structure, we place Li+, [Emim]+ (Figure 1a), and an anion (either [BF4] – , [PF6] – , [TFO] – , [TFSI] – , [HCOO] – , [MS] – , or [BNZ] – , Figure 1(b-h)) randomly on the vertices of a three-dimensional cubic grid.30,31 For all seven Li+–

N + N (a) [Emim]+

O F 3C

S N O

F

F

F B8 F

F P8

F

FF

(b) [BF4]–

O 8

S O

(e) [TFSI]–

H

F3C

F

S

O

O8

(d) [TFO]–

(c) [PF6]–

O

O CF3

O

F

H3C

C O8

O

S O O

(f) [HCOO]–

(g) [MS]–

O 8

C (h) [BNZ]–

O8

Figure 1: Molecular structure of the ionic liquid cation [Emim]+, and the anions [BF4] – , [PF6] – , [TFO] – , [TFSI] – , [HCOO] – , [MS] – , and [BNZ] – . [Emim]+– anion systems we study the range of Li+-anion molar fractions ranging from 0.0 to 1.0, with 0.1 increments. The number of Li+, [Emim]+, and anion molecules for each system 4


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and salt molar fraction is reported in the Supplementary Information, Section 1. For every salt molar fraction we generate four independent structures, which we then use to compute uncertainties as standard deviations among such ensembles. All molecular dynamics (MD) simulations have periodic boundary conditions and are performed using the LAMMPS code. 32 We adopt the All-Atom Optimized Potentials for Liquid Simulation (OPLS-AA) force-field to model the atomic interactions. 33,34 Following the established practice in the ionic liquid literature, in this work the point charges assigned to every atomic species are rescaled, to 80 % of the original value, with the aim to mimic the average charge screening due to polarisation, and charge transfer effects. 35–37 The cost-effective charge-rescaling is widely adopted in favor of polarizable models, such as self-consistent inducible dipoles 38 or Drude oscillators,39 since their positive gains are counterbalanced by a significant increase in computational cost and difficulty in parameterization. Both choices of the OPLS-AA parameters and 80 % charge rescaling are motivated by the extensive studies recently performed by Acevedo et al.35,40,41 The authors methodically compared a range of properties of ionic liquid systems (density, heat of vaporization, viscosity, surface tension, self-diffusivity) computed using their OPLS IL parameters, with atomic charges rescaled by 80 %, to experimental and ab-initio data and, in summary, excellent agreement was reported. We use a timestep of δt = 1.0 fs and a velocity-Verlet algorithm to evolve the equation of motions, while a Nosé-Hoover barostat (1000 δt coupling) and thermostat (100 δt coupling) enforce pressure and temperature, respectively.42–44 The equilibration routine, used to overcome local energy barriers in search of lower energy minima, follows the structure generation and comprises a set of energy minimizations, compression/decompression, and annealing stages, broadly based on previous works30,45,46 (full details in the Supplementary Information, Section 3). To compute the transport properties, every structure is evolved for 60 ns in a constant number of particles, volume, and temperature ensemble. The volume is equal to that of the last stage of the equilibration routine, while the temperature is maintained constant at

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358 K. Throughout the simulations the position of the center of mass of all three species in a given structure is recorded every 10 kδt = 10 ps for post-processing. Subsequently, the data is analyzed using the Wheeler-Newman approach, 47 which yields transport properties that accounts for the intra- and inter-species correlation. The adoption of fully correlated transport theory is a vital step to uncover transport anomalies such as a negative transference number, otherwise impossible to be found with the commonly-adopted dilute solution theory approach. 30 Whilst an extensive discussion on the Wheeler-Newman method is presented in a companion paper (along with examples of correlation function versus time and matrix elements of the mass-transport matrix30), we remind the reader the key results and formalism in Section 6 of the Supplementary Information. Our choice of the reference position is the center of mass of the entire system, as there is no single species that could be treated as a “solvent”.

The systems are methodically characterized by computing the density at different temperature values ranging from 278 K to 358 K at steps of 10 K. Density values from the literature are mainly found for xLi[ANION] = 0.0,48–52 while the paucity of experimental data prevents us from more extensive comparisons at higher molar fractions. Fortunately, the specific forcefield parameters utilized in this work have been thoroughly tested by Acevedo et al.,35,40 giving us the confidence necessary to proceed with our investigation. For the sake of brevity, all density results and technical details are reported in the Supplementary Information, Section 4. Additionally, in Section 5 of the Supplementary Information we provide the radial distribution functions (RDF) between Li+ and all the atoms constituting the anion, as well as with only the coordinating species. We also compare the location of the first RDF peak with results from the literature,

53–58

where available. For both density and RDF we find

good agreement with previous literature. The transference number tLi+ indicates the cation’s relative contribution to the total conductivity, and, therefore, it is of central importance for technological applications. Figure 2

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reports t+Li, as computed using multi-component concentrated solution theory.30,47 Strikingly, 1.0

0.8

0.6

0.93

0.95

0.96

0.98

0.87

0.94

0.95

0.79

0.75

0.75

0.64

0.84

0.76

0.42

0.56

0.41

0.37

0.31

0.52

0.40

0.16

0.33

0.13

0.10

0.08

0.07

-0.12 -0.09

0.01

0.09

-0.14 -0.01 -0.17 -0.14 -0.10

0.8

0.6

0.4 -0.12 -0.02 -0.20 -0.03 -0.35 -0.21 -0.13

0.4 -0.14 -0.06 -0.14 -0.04 -0.29 -0.22 -0.13

0.2

Li transference number

1.0

xLi[ANION]-

-0.13 -0.06 -0.09 -0.02 -0.21 -0.14 -0.11

0.2 -0.10 -0.05 -0.05 -0.01 -0.15 -0.10 -0.04

0.0

-0.05 -0.03 -0.05 -0.01 -0.04 -0.05 -0.03

0.00

0.00

0.00

0.00

0.00

0.00

0.00

[PF6]-

[TFO]-

[TFSI]-

[HCOO]-

[MS]-

[BNZ]-

-0.2 0.0

[BF4]-

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


Figure 2: t+Li for all systems and all xLi[ANION]. a negative t+Licharacterizes all chemistries investigated in this work. The observed trend is the same across all seven systems investigated. 1. At xLi[ANION] = 0.0 t+Liis trivially 0.00 as there are no Li+ in the system. + is negative, ranging from −0.01 to 2. At xLi[ANION] lower than approximately 0.5/0.6 tLi

−0.30. + 3. At xLi[ANION] greater than 0.6 tLi becomes positive, reaching values close to unity for

xLi[ANION] = 1.0, corresponding to the limit of a pure salt system, and resembling a singleion solid-state electrolyte.30 While not reported here for the sake of brevity, the ensemble uncertainties of the computed transference numbers are generally small, indicating a weak dependence of Li t+ on the ini7



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tial structure. This gives us confidence that the chosen number of independently-generated structures is sufficient, and the results statistically robust. To the best of our knowledge, Gouverneur et al. are the first authors to measure experimentally a negative t+Liin Li+-salt/ionic liquid mixtures using eNMR. 28 In this work we study, among others, the two systems investigated in Ref.28 (Li+-[Emim]+-[BF4] – and Li+-[Emim]+-[TFSI] – ), and compare the findings in Table 1 . The trend of decreasing t+Lifor + Table 1: Comparison of tLi as computed in this work and using eNMR28 for two Li+-salt/ionic liquid mixtures. The two molar concentrations investigated experimentally do not match the molar fractions from this work, therefore the computed result are interpolated from the two closest xLi[ANION], see Section 2 of the Supplementary Information.

System Li+-[Emim]+-[BF4] – Li+-[Emim]+-[TFSI] –

Concentration /mol L−1 0.25 0.50 0.25 0.50

texp Li

tLi

−0.020(4) −0.041(5) −0.027(5) −0.037(4)

−0.019(4) −0.039(4) −0.009(5) −0.012(5)

increasing molar fraction is well reproduced by our calculations. Additionally, we find outstanding agreement for [BF4] – , while a larger discrepancy is observed for [TFSI] – . Ultimately, the charge/discharge rates and efficiency of the whole battery are controlled by the trade-off between t+ and ionic conductivity: a t+ close to unity with a low conductivLi

Li

ity is as technologically impractical as the opposite combination. Consequently the product between the total conductivity and t+Li, which indicates the fraction of conductivity due to Li+, κLi = κ · t+Li, is often regarded as a good practical indicator for electrolyte optimization. Figure 3(a-c) show κLi (and κ for reference) for Li+-[Emim]+-[PF6] – , Li+-[Emim]+-[TFO] – , and Li+-[Emim]+-[TFSI] – , respectively (and comparison with the available literature59–63). Consistently with previous experimental28,64 and computational30 IL literature, the total conductivity (κ, blue curve, right y axis) decreases with increasing xLi[ANION], its maximum value is achieved when the system is a pure IL solution.

As tLi+ becomes negative at the

smallest concentration of Li+ in the system, the κLi is also non-negligibly negative as κ is

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Figure 3: Li+ conductivity (red curves, left y axis, comparison from 59–63) and total conductivity (blue curves, right y axis) for three example systems. + at its highest at small xLi[ANION]. Conversely, at xLi[ANION] showing a positive tLi , κ is at its

lowest, therefore resulting in a small κLi. This once more highlights the importance of treating these systems with fully-correlated solution theory. To the best of our knowledge, previous computational studies of t+Li for such ternary systems neglected to adopt fully-correlated multi-component solution theory, therefore predicting incorrect behaviors for a vast class of mixtures, as we show in this work. For instance, in these systems uncorrelated analysis shows a steadily increasing t+Li with xLi[ANION] (Supplementary Information, Section 8), therefore it predicts a fictitious optimal molar fraction that maximizes κLi. This inaccuracy can be found in several experimental studies employing ideal solution-based approaches, 64,65 such as the Bruce-Vincent analysis, 66,67 and only recently a few groups are highlighting its flaws for transference number predictions. 28 In this work we find a general trend of negative transference numbers in a wide range of Li+-salt/ionic liquid mixtures, effectively casting doubts on the potential of these systems as next generation electrolytes for energy storage. The molecular resolution of our simulations allows us to directly investigate the instantaneous coordination environment (also referred to as clusters) population. It is worth highlighting that this analysis is purely structural, and no time dependence is analyzed at this stage. We group Li+ cations and anions into clusters by looking at their spatial correla9



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tion during the simulation, i.e., where anions and cations are located nearby. At every snapshot, clusters are identified following a variant of the single-linkage clustering algorithm previously used for such analysis:30,46 Li+ atoms and anions are iteratively grouped based on the threshold distance corresponding to the location of the first minimum of the Li+‘coordinating species’ RDF. At every snapshot and for all structures in the ensemble at a given xLi[ANION] (four for every chemistry and molar fraction), we record the composition and number of appearances of every cluster. The final reported cluster frequency is the ratio between the number of appearances of the specific cluster and the total number of appearances of all clusters. Figure 4 presents the cluster analysis for Li+-[Emim]+-[BF4] – , a1,2,3, and Li+-[Emim]+[PF6] – , b1,2,3., where different indices indicate different xLi[ANION]. In particular, from the

Figure 4: Cluster analysis for Li+-[Emim]+-[BF4] – , a1,2,3, and Li+-[Emim]+-[PF6] – , b1,2,3. left, the first two columns correspond to mixtures possessing a negative t+ , while t+ is posiLi

10


Li

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tive for the third column. The cluster population is partitioned in either small clusters (left inset) or clusters nearly including all Li+(right inset), and essentially nothing in between. The percentage at the bottom of every inset shows the overall fraction of clusters in that specific inset, therefore providing an indication on the structural organization of the mixture. Finally, the oblique black lines show where neutral clusters would lie. First we observe that all clusters lie above the oblique black line, in other words, anion molecules systematically outnumber Li+ in clusters, confirming the asymmetrical clusters hypothesis. Second, the cluster distributions are substantially different going from + xLi[ANION] = 0.4 to xLi[ANION] = 0.6, while concurrently tLi changes from negative to pos-

itive. At lower xLi[ANION] small clusters dominate in the systems, and they can contribute negatively to t+Li. Conversely, the large-clusters extreme corresponds to a percolating salt region, in which Li+ is more mobile than the anion, essentially corresponding to a single-ion diffusion scenario. 30 Thus, the more dominant is this configuration, the higher isLit+ . Third, we want to emphasize that asymmetrical coordination is a necessary but not sufficient con+ dition to obtain a negative tLi . The instantaneous picture given by the cluster analysis

provides an upper bound to the maximum absolute “effective charge”, qE, carried by lithium (and its coordination cage). In other words, over time, the Li+ atom at the center of a given cluster can move together with any number ranging from all to none of the surrounding coordinating anions. In the extreme limit, where the coordination remains constant over time, corresponding to a permanent cluster, Li+ carries a qE equal to 1 − N , where N is the number of anion molecules constituting its cluster. On the other hand, if the anion is completely immobile over time, qE would be close to unity. We find the concept of cation effective charge, qE, quite revealing as it provides an average picture, both over time and Li+ atoms, of the charge carried by the cation of interest. As discussed above, qE is bounded to be greater than 1 − N , where N is the number of anion molecules constituting a Li+ -anion cluster. Experimentally, the ratio between the measurements of self-diffusion coefficient (via NMR) and electrophoretic mobility (via eNMR) allows

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an estimation of qE.28,68,69 Here we propose a method to computationally estimate qE. Starting from the Nernst-Einstein relation, Eq. 1, and multiplying both sides by e qLi nLi, where nLi = NLi/V

is the Li+ number density, we obtain the conductivity due to Li+, κLi,

Eq. 2. µ = Li

eqLi D

Li

KB T 2 2 nLi e e qLi nLi µLi = qLi DLi = κUC Li KB T + qE = Sign tLi

KBT κUC Li t+ e2nLiDLi e2nLiDLi

(1) (2) (3)

In Ref.28 the authors substitute µLi = µeNMR Li , use an effective lithium charge, qE, instead of the nominal charge qLi = +1, and solve for qE. Equivalently, we can split the Li+ conUC ductivity as κUC · t+ ,Liwhere the UC superscript indicates quantities computed with Li = κ

the uncorrelated Nernst-Einstein formalism. As the transference number is the fractional conductivity carried by Li+, it is expected to be invariant on the method used to compute it, provided the approach properly takes into account the physical correlation present in the + system. Therefore here we use tLi computed with fully-correlated multi-component theory,

and solve for qE, obtaining Eq. 3. Figure 5 shows the effective Li+ charge for Li+-[Emim]+-[BF4] – , (a), Li+-[Emim]+-[PF6] – , (b), Li+-[Emim]+-[TFO] – , (c), and Li+-[Emim]+-[TFSI] – , (d). At relatively low xLi[ANION] qE is negative as one would expect from the sign of tLi+ , and its value is between 1 − N and 0 as previously discussed. The value of qE can help to further rationalize the t+Lifindings. The [TFO] – anion, which has the lowest t+Liamong the four examples presented here, also exhibits the lowest qE in the concentration range where Li t+ is at its lowest, suggesting that the [TFO] – coordination around a given Li+ is more persistent than, for instance, [TFSI] – that + has a higher tLi and qE. Conversely, at xLi[ANION] close to unity the value qE ≈ +1 is ap-

proached, reconfirming the single-ion solid-state limit for large molar fractions caused by the formation of large percolating clusters. We highlight that the approximation of con12


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Figure 5: Li+ effective charge for four of the systems investigated in this study. Black squares are experimental values from. 28 stant nLi is valid when the intra-species Li+ correlation is negligible, and we find this to be the case. More details in Section 7 of the Supplementary Information. Additionally, future work focuses on accounting for dynamical heterogeneities arising from differences in lithium dynamics, similarly to a cluster-level analysis of the conductivity recently proposed, 70 but incorporating cluster lifetime as well as cluster-cluster interactions.

In summary, in this work we investigated the transport properties of several Li+-salt/ionic liquid mixtures via atomistic modeling and MD simulations, reaching two main conclusions. First, the widely overlooked anion-cation correlation results in a negative transference number. This confirms recent experimental results on a subset of these mixtures, and extends it to different chemistries, effectively suggesting a general trend in negative transference number for Li+-salt/ionic liquid mixtures in a surprisingly wide range of Li+ ion concentrations. A negative t+Liresults in a negative Li+ contribution to the total conductivity, emphasizing the need to carefully consider the technological impact of correlation in ionic liquids on the overall battery performance. Second, we investigate and characterize the anion-cation 13



clusters and find that negatively-charged ion coordination is a necessary but not sufficient condition for a negative tLi+ . The reason is that the negative cluster has to move at least for some amount of time together with Li+. To investigate this point further, we formulate a way to compute the Li+ “effective charge”, which agrees well with experimental measurements using state-of-the-art Electrophoretic NMR analysis. We hypothesize that rational design of next-generation ionic liquid electrolytes should involve strategies to decouple Li+ motion from that of the anion, and this is a subject of an ongoing investigation.

Supporting Information Available Supporting Information: Specific number of atoms/molecules at every xLi[ANION], Molar fraction to molarity relations, details of the equilibration procedure, densities as a function of temperature, RDFs, correlated transport remarks, intra-species correlation, uncorrelated t+ Li.

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General Trend of Negative Li Effective Charge in Ionic Liquid

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