A Molecular Dynamics Study - American Chemical Society

Apart from providing insights into the effect of concentration on the behavior of the EC-LiPF6 system, the present study also intends to define baseli...
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Article Cite This: J. Phys. Chem. C 2018, 122, 8173−8181

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Effect of Salt Concentration on Properties of Lithium Ion Battery Electrolytes: A Molecular Dynamics Study Bharath Ravikumar, Mahesh Mynam, and Beena Rai* TCS Research, Tata Research Development and Design Centre, 54B, Hadapsar Industrial Estate, Pune - 411013, India S Supporting Information *

ABSTRACT: Electrolyte solutions of 1 M concentration are typically used in lithium ion batteries (LIB) for optimal performance. However, recently, superconcentrated electrolytes have been proposed to be a promising alternative to 1 M solutions. Despite their improved stability features, application of the concentrated electrolytes is hindered by their poor transport properties. We probe EC-LiPF6 electrolyte system for a range of concentrations: 0.06 to 4 M using molecular dynamics simulations to study the effect of concentration on transport and structural properties. Molecular structure of the solution changes with concentration from a predominantly solvent separated ion pair (SSIP) configuration at the dilute limit to an aggregate rich configuration at high concentration. Depletion of SSIPs and formation of more aggregates at higher concentrations affect the transport properties. The present work provides insights into the relation between molecular structure and performance of the electrolyte solution and suggests ways to design novel concentrated electrolytes.

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INTRODUCTION The use of clean and renewable energy sources (e.g., solar, wind) at a higher level is a way to tackle global warming and climate change problems that the world is facing.1 Owing to their intermittent nature, effective utilization of these resources depends upon the availability of efficient energy storage systems.2,3 Lithium ion batteries (LIB), which are widely used in portable electronics, lead the list of suitable electrochemical storage systems due to their ability to offer higher energy density.4,5 In spite of being a mature and widely adopted technology in various commercial applications, cycle life (i.e., durability) and safety of the LIB are of great concern even today.6−8 One of the components of the LIB, the electrolyte plays a crucial role in the operation of the LIB. It enables the transport of ions (charge carriers) between the electrodes, while insulating them electrically. The electrolyte of the LIB, typically, is a solution of organic carbonates such as ethylene carbonate (EC), dimethyl carbonate (DMC), and lithium salts (e.g., lithium hexafluorophosphate-LiPF6 ).9,10 These carbonate solvents decompose in reaction with the active electrode materials, leading to performance and safety related issues of the LIB.11−13 It is therefore important to improve the existing electrolytes or find new materials to develop better and safer LIB. In commercial LIB, electrolytes of 1 M salt concentration are commonly used for reasons of optimal performance.14,15 Electrolytes of higher concentrations have not been explored much given their poor ionic conductivity. However, recent © 2018 American Chemical Society

experimental studies on concentrated electrolytes (e.g., 4.2 M solution of lithium bis(trisfluoromethanesulphonyl)azanide [LiTFSA] in acetonitrile) show that the concentrated solutions offer extremely good thermal and reactive stabilities.16,17 This has led to research on concentrated electrolytes as an alternative to the current electrolyte technology.18,19 Research into identification of cosolvents, additives, new solvent, and salt materials is to be pursued to make the concentrated electrolytes a viable option for advanced batteries by improving their transport properties.14,20 In the current LIB technology, EC solvent of the electrolytic solution plays a crucial role.21 It has good dielectric properties enabling better dissociation of the salt into ions.22 More importantly, the ability of the EC to form a stable passivating layer over the active surface of the electrode helped in the realization of the present generation LIB.23 However, the formation of the passivating solid−electrolyte interface (SEI) layer consumes a portion of the electrolyte during the first cycle and subsequent charge−discharge cycles of the LIB lead to the growth of the SEI layer. This along with other side reactions make the electrolyte concentrated over time degrading the long-term performance of the LIB.24 In spite of its importance, the effect of high salt concentration on the performance of the EC based electrolyte solutions is not well characterized. Study of these systems at high salt concentrations would help battery Received: March 1, 2018 Revised: March 30, 2018 Published: April 2, 2018 8173

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The Journal of Physical Chemistry C Table 1. LJ Parameters and Partial Charges26,28,29

researchers in two fronts, viz., (1) design of better electrolyte solutions (e.g., concentrated electrolytes) for advanced LIB and beyond lithium ion technologies,19 (2) understanding the performance drop of the current generation LIB with usage (i.e., charge−discharge cycles).25 In this work, as a first step to study the behavior of highly concentrated electrolytes, we simulate EC-LiPF6 electrolyte solutions for a range of concentrations up to 4 M using the classical molecular dynamics (MD) method. To the best of our knowledge, no MD simulation study has focused on the effect of LiPF6 concentration on the dynamic behavior of EC-LiPF6 solution. Apart from providing insights into the effect of concentration on the behavior of the EC-LiPF6 system, the present study also intends to define baseline values for various electrolytic properties with which the properties of mixtures (i.e., EC and cosolvents/additives) can be compared to evaluate the effect of additives or cosolvents. This comes in handy to short-list appropriate materials to enhance the performance of the EC based electrolytes.

SIMULATION DETAILS In the MD method, the electrolyte is modeled by accounting for interactions at the atomic level. We use Class II force-field model (eq 1), which is commonly used in the MD simulation of electrolytes.26 The potential function V(r) of Class II forcefield defining interactions among various atoms of the system is

∑

k b(b − b0)

bonds

+

∑

kθ(θ − θ0)

angles

+

∑

kϕ(1 + cos(nϕ − ϕ0))

dihedral

+

∑

kω(ω − ω0)

impropers

+

∑ bond − bend

+

∑ bond − bond

+

+

1 k ba((r − r0) + (r′ − r′0 ))(θ − θ0) 2 1 k bb((r − r0) + (r′ − r′0 )) 2

⎡⎛ ⎞12 ⎛ ⎞6 ⎤ σij σij 4 ϵ ∑ ij⎢⎢⎜⎜ ⎟⎟ − ⎜⎜ ⎟⎟ ⎥⎥ r ⎝ rij ⎠ ⎦ vW ⎣⎝ ij ⎠

∑ Coulomb

qiqj ϵrij

ϵ (kcal/mol)

σ (Å)

q (e)

O C Oc Cc H Li P F Li−Oc Li−P Li−O F−H F−Cc

0.17 0.066 0.210 0.105 0.030 0.10314 0.13169 0.028716 0.05551 0.014033 0.20937 0.2056 0.06546

3.0 3.5 2.96 3.75 2.5 1.4424 3.695 2.9347 2.398 3.007 2.0217 2.3951 2.9381

−0.4684 0.0330 −0.6452 1.0996 0.1041 1.0 1.07 −0.345

for EC and Li ion are taken from Soetens et al.28 and Kumar and Seminario.29 The parameters for PF6 ion are from Jorn et al.26 and Kumar and Seminario.29 These parameters are shown to predict the static properties accurately.26,29 EC-LiPF6 mixtures of concentrations ranging from 0.06 to 3.95 M are studied by simulating the systems consisting of 220 EC molecules along with a number of LiPF6 salt molecules (Ns ) in the range 1−76. Topologies of single EC and LiPF6 molecules are created using Accelrys BIOVIA Materials Studio, which are further utilized to generate the initial configuration of the system using the Packing Optimization for Molecular Dynamics Simulations (PACKMOL).30 Initial volume of the cubic box 29 × 29 × 29 Å3 is chosen such that the density of the system is closer to the reported density of EC (1.32 g/cm3) in the liquid state. Periodic boundary conditions are applied on all three sides of the cubic simulation box to represent the bulk solution. The MD simulations are conducted using an open source tool: Large Scale Atomic/Molecular Massively Parallel Simulator (LAMMPS).31 The system is simulated at temperature T = 330 K and pressure P = 1 atm so that EC remains in the liquid state.32 Nose-Hoover thermostat and barostat are applied to maintain the temperature and pressure at the prescribed state. Integration time-step of 1 fs is used. Efficient particle−particle−particle−mesh (PPPM) method is employed to compute the long-range Coulombic interactions.33 Initially, the system is allowed to evolve under constant NPT conditions (up to 15 ns) to relax the system from its initial configuration. Once it relaxes, the Nose-Hoover barostat is removed and the volume of the simulation box V is frozen to further carry out the simulation at constant NVT conditions for 15 ns. Later, the Nose-Hoover thermostat is also removed to conduct rest of the simulation in NVE ensemble. Here, N and E denote the number of atoms and the energy, respectively. For each concentration, the production phase (in NVE ensemble) is run for 30 ns. Atomic coordinates stored during the production phase are utilized to compute time-averaged results of static and dynamic properties.34

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V (r ) =

atom/pair type

(1)

where terms 1 to 4 account for the bond stretching and angle bending phenomena, dihedral torsions and nonplanar torsions (impropers), respectively. Coupled forces emerging from the bond and angle movements are modeled using terms 5 and 6. The bonded interactions (terms 1 to 6) are modeled as harmonic functions. The last two terms represent the nonbonded van der Waals (term 7) and Coulombic forces (term 8).27 For the bonded interactions, we use CFF93 force-field with parameters from Sun et al.27 A 12−6 Lennard-Jones (LJ) pair interaction model with 12 Å cutoff is used to model the van der Waals interactions. The LJ parameters and charges (Table 1)

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RESULTS AND DISCUSSION Dynamic properties of the electrolyte such as diffusivity and ionic conductivity provide the vital information about the performance of a battery. For instance, faster movement of the Li ion (Li+ ) through the solution results in higher current density of the LIB.35 Study of the trajectories of the ions under zero electric field condition within the MD simulation helps to 8174

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The Journal of Physical Chemistry C determine the diffusivity of the ions and ionic conductivity of the solution.29 We now describe the effect of salt concentration on diffusivity and conductivity. Diffusivity. The diffusivity of a particle (D) indicates the pace at which the particle is transported. The D can be computed from the mean square displacement (MSD) of the particles. In the long time limit, the MSD = ⟨[r(t) − r(0)]2⟩ varies linearly with time t, and it can be related to the D (in a three-dimensional space) using Einstein’s relation

D = lim

t →∞

MSD 6t

(2)

Here, r(t) denotes the position of a particle at time t. ⟨ ⟩ indicates ensemble average. We first compute the time average values34 of MSD for each ion from its trajectory stored (at regular intervals of 100 fs) in a production phase run of 30 ns. The averaged MSD vs t data of all the ions of a type from at least three independent simulations are further ensemble averaged. Diffusivity of a given ion is computed from the ensemble averaged MSD vs t data. In Figure 1, we plot MSD vs t of Li+ in the electrolyte of 1.04 M concentration. It becomes linear beyond 1 ns, indicating that

Figure 2. Effect of concentration on diffusivity of ions. Diffusivity of Li+ and PF6− computed for a range of salt concentrations along with the values from the literature29,39,41,42 are shown. As expected, diffusivity of both ions drops with increase in the salt concentration, and shows an exponential decay with concentration.

concentrations. The simulated diffusivities match well with the range of values reported in the literature.29,37−41 The slight differences can be attributed to various approximations involved in force-field parameters as well as the variations in simulated conditions. Figure 2 describes the effect of the salt concentration on DLi and DPF6. As expected, diffusivity of both ions decreases with increase in the salt concentration, and shows an exponential decay with concentration. We fit a linear equation for ln(D) vs C data to obtain diffusivity at the infinite dilution limit, D0, and exponential fitting parameter CD of Arrhenius relation ⎛ C ⎞ D(C) = D0 exp⎜ − ⎟ ⎝ CD ⎠

(3)

PF6−

The computed D0 values for Li and ions are 2.63 × 10−10 m2/s and 4.75 × 10−10 m2/s, respectively. A smaller value of CD for PF6− data (0.435) compared to that of the Li+ (0.472) indicates that the D of PF6− is more sensitive to increase in salt concentration. Another point to note from Figure 2 is that the difference between DLi and DPF6 is maximum at the lowest concentration. The difference decreases with increase in concentration, and becomes insignificant beyond 2 M concentration. It may indicate that both ions diffuse together at higher concentrations. Unlike in the low concentration limit, at 4 M concentration the Li+ diffuses faster compared to the counterion (Figure 2). This kind of behavior is observed in the studies dealing with concentrated electrolytes by Suo et al.43 Though the Li+ is much lighter than the PF6−, due to the presence of the bulkier solvation shell the Li+ diffuses more slowly compared to the PF6− in the low concentration limit. As the concentration increases the number of solvent molecules within the first solvation shell decreases (see Figure 6). Consequently, at higher concentrations the solvent molecules may not be encapsulating the Li+, enabling it to diffuse better compared to the heavier PF6−. This may lead to a significant rise in the transference number of Li+.43 Further studies are required to probe this in detail. Conductivity. The rate at which the electrolytic solution conducts the charge influences the charge−discharge rates of a battery and in turn its applications.44 Hence, the charge transfer rate is an important parameter in the design of novel electrolytes. As seen earlier, the estimation of the diffusivities of ions is of help to understand their mobility through the solvent. However, diffusivity alone cannot explain the effect of +

Figure 1. MSD vs t of Li+ and PF6− in solution of 1.04 M concentration. In the long time limit, MSD vs t curve shows a linear behavior. Diffusivity of an ion is obtained by fitting a linear equation (shown by lines) to the data in the linear regime. The PF6− diffuses faster than the Li+ at 1 M concentration.

the Li+ get into diffusive regime as early as 1 ns for given simulation conditions. We fit a linear equation to MSD vs t data within the time limit of 1 to 5 ns as shown. The D of Li+ (DLi ) in the solution of 1.04 M concentration (i.e., (1/6)th of the slope of MSD vs t fit) is 0.40 × 10−10 m2/s. In a similar manner, the D of the anion can be computed from the center of mass (COM) motion of the PF6 ions (PF6− ). However, for simplicity reasons it is often practiced to report D of P, which matches closely with that of COM of PF6−.36 In the present work, for anions we report D of P atoms. The diffusivity of anion (DPF6 ) in 1.04 M solution, computed using the MSD of P (Figure 1), is 0.67 × 10−10 m2/s. The formation of bulkier and stable solvation shell around the Li+ (as discussed later) is the reason for its lower mobility than that of PF6−. To estimate the system size dependency on the computed values, we conduct a simulation of 1.04 M solution in a bigger simulation box with double the number of molecules (i.e., 440 EC and 34 LiPF6 ). The D of both the ions thus obtained vary only by 2% from that obtained from Figure 1, emphasizing that the results are box size independent. Hence, we use systems containing 220 EC molecules for the rest of the study. Figure 2 shows the D of Li+ and PF6− for a range of 8175

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The Journal of Physical Chemistry C concentration on the charge transfer. Ionic conductivity (σic) quantifies the ability of the electrolytic solution to conduct the ions. The higher the ionic conductivity, the better the charge transfer rate is. From the collective mean square displacement of the ions in the solution one can compute molar conductivity (Λ) using Einstein’s relation45 Λ=

NAe 2 d lim 6nkBT t →∞ dt

As seen in Figures 2 and 3, both the diffusivity of the ions and the molar conductivity of the solution decrease with increase in concentration. An obvious reason for reduced mobility and conductivity is the increase in viscosity with salt concentration.47 Another important reason for the drop in these properties could be the formation of ion pairs and complexes that are essentially less mobile and carry less charge (per unit) compared to the free ions of dilute solution. The study of molecular structure of the solution describing the solvation of ions and dissociation of salt molecules, and analyzing the molecular clusters (i.e., salt-solvent complexes), could throw some light on how the increase in salt concentration affects the transport properties. Solvation Characteristics. One can probe the solvation of ions and dissociation of salt molecules using radial distribution function (RDF) of various entities.34 The RDF of x−y pair is defined as

∑ ∑ zizj⟨Δri·Δrj⟩ i

j

(4)

where NA is Avogadro’s number, e is an electron charge, n is the total number of ions (cations and anions), kB is Boltzmann constant, and zi is the charge on ion i. Δri = ri(t) − ri(0) is the displacement of ion i. Figure 3 shows the change in molar

gx , y(r ) =

n(r ) 4πr 2drρ

(5)

where n(r) is the number of y atoms at a radial distance r from the position of x, 4πr2dr is the volume of a shell of thickness dr at r, and ρ is the bulk number density of y atoms. Thus, RDF enables quantification of molecular configurations in a mixture of various atoms and ions like the battery electrolyte. The RDF of Li−Oc pair shows how the Li+ are solvated (i.e., surrounded by the solvent molecules). The RDF of Li−P showing how PF6− locates radially provides insights into the dissociation of salt and formation of molecular complexes. Solvation of Li Ions. In the presence of EC, the LiPF6 salt dissociates to form Li+ and PF6− and these ions are solvated by the EC molecules. The Li+ interact with the electronegative carbonyl oxygen (Oc ) strongly compared to the other atoms of EC. Hence, the RDF of Li−Oc (gLi,Oc) is commonly used to characterize the EC solvation shell around the Li+.48 For a range of salt concentrations, we plot the gLi,Oc in Figure 5. As

Figure 3. Effect of concentration on molar conductivity Λ of the solution. Similar to diffusivity of the ions, the Λ shows exponential decay with concentration. The solid line shows the linear fit of ln(Λ) vs C data.

conductivity with respect to concentration. Molar conductivity, similar to diffusivity of ions, also decreases with an increase in concentration. The linear fit of ln(Λ) vs C data shown in Figure 4 finds that the Arrhenius relation holds well for Λ vs C.

Figure 4. Effect of concentration on ionic conductivity σic. The ionic conductivity σic shows an increasing trend up to 1 M concentration, and shows a rapid decay at higher concentrations.

Figure 5. RDF of Li−Oc : gLi,Oc(r) for a range of concentrations. The peak at 1.95 Å depicts the solvent molecules in the first solvation shell, and the broader second peak about 8 Å indicates the formation of a second solvation shell at least for lower concentrations.

The ionic conductivity (σic = cΛ) plotted in Figure 4 (i.e., σic vs c) initially shows an increasing trend up to a certain concentration, beyond which it decays rapidly. The interplay between the number of available charge carriers and their ability to carry the charge defines the concentration for optimal performance. For the simulated conditions, the EC-LiPF6 system shows maximum value of σic about 1 M concentration, which is consistent with the literature.46

shown, the position of the first peak (indicating Li−Oc distance for the molecules in the first solvation shell) is at 1.95 Å, which is in good agreement with the literature.49 The appearance of a sharp peak and a deep minima in the gLi,Oc indicate that the EC forms a relatively stable solvation shell around the Li+. The radial position of the first peak rmax and its height g(rmax ) as a function of salt concentration are tabulated in Table 2. For the salt concentrations simulated in this work, the height of the first 8176

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The Journal of Physical Chemistry C Table 2. Effect of Salt Concentration on Maxima (rmax ) and Minima (rmin ) of First Peak as Well as Height of the First Peak, g(rmax ) and the Coordination Number, CN = N(rmin ) of RDF of Various Pairs pair

C (M)

rmax

g(rmax )

rmin

N(rmin )

Li−Oc

0.06 0.45 1.04 1.95 2.76 3.95 0.06 0.45 1.04 1.95 2.76 3.95 0.06 0.45 1.04 1.95 2.76 3.95 0.06 0.45 1.04 1.95 2.76 3.95

1.95 1.95 1.95 1.95 1.95 1.95 3.15 3.15 3.15 3.15 3.15 3.15 1.65 1.65 1.65 1.65 1.65 1.65 7.26 7.26 3.78 3.78 3.78 3.78

35.0 35.1 36.9 38.3 44.4 40.8 0.2 1.2 2.6 4.3 4.4 10.7 0.1 0.9 2.2 4.1 4.5 10.7 2.0 2.0 0.2 0.9 1.2 2.7

3.30 3.30 3.30 3.18 3.06 2.82 4.26 4.14 4.14 4.14 4.14 3.78 2.46 2.46 2.46 2.34 2.34 2.34 8.82 8.82 4.00 4.98 5.70 5.70

5 5 4.8 4.4 4 2.8 0.01 0.02 0.1 0.3 0.5 1.4 0.01 0.02 0.1 0.2 0.5 1.5 18.4 23.9 0.2 2.3 3.8 4.9

Li−P

Li−F

P−Oc

Figure 6. Running coordination number of Li−Oc: NLi,Oc(r) for various concentrations. The coordination number, CNLi,Oc, decreases with concentration from 5.01 (0.06 M) to 2.80 (3.95 M). The inset shows CNLi,Oc as a function of concentration. The rate of drop of CNLi,Oc increases with concentration.

suggests that the first solvation shell of Li+ containing 5 cyclic carbonates is the most stable solvation structure for 1 M concentration. The CNLi,Oc (shown in the inset of Figure 6) decreases with the increase in salt concentration. The decrease in CN with the concentration could be due to either or both of the following reasons: at higher concentrations (1) only a fractional amount of salt gets dissociated and the Li+ thus formed get solvated by EC molecules as in the dilute system, and (2) not enough EC molecules are present in the system to form a solvation shell identical to that in the dilute system (CNLi,Oc ≈ 5), leading to the formation of different EC-LiPF6 complexes at different concentrations. It is further discussed in the section on analysis of salt complexes. The rate of change of CNLi,Oc with concentration, as shown in the inset of Figure 6, increases with salt concentration. In the low concentration limit (for example, up to 1 M), the height of the second peak of the gLi,Oc decreases with increase in salt concentration, while change in the CNLi,Oc is not significant. It suggests that the additional Li+ in the solution due to increase in salt concentration from 0.06 to 1.04 M are getting coordinated by the EC molecules that are originally part of the second solvation shell at lower concentrations. Further increase in the salt concentration leads to the depletion of free EC molecules in the solution. At higher concentrations, owing to the scarcity of free EC molecules the available ones are distributed among the ions. Therefore, the change in the CNLi,Oc is significant. Solvation of PF 6 Ions. Unlike the Li + that are preferentially coordinated by carbonyl oxygens of the EC molecule, PF6− do not show strong affinity toward any of the atoms of the EC. As shown in Table 3, at low concentrations

peak, gLi,Oc(rmax ), increases with concentration up to 2.76 M, but shows a decreasing trend at higher concentrations. The second peak in the gLi,Oc appears about 8 Å. It is evident from the gLi,Oc and the gLi,Cc (see Supporting Information) that the second peak represents the second solvation shell around the Li+. Height of the second peak decreases with increase in the salt concentration. Independent of the salt concentration the gLi,Oc(r) approaches unity at higher values of r, emphasizing that the order of EC molecules with respect to the Li+ disappears in the long-range. One can determine the number of counterions or atoms of interest present in a sphere of radius R around a given ion by integrating the corresponding RDF up to R. The number of y atoms present within a sphere of radius R around the x atom, Nx,y(R) is Nx , y(R ) =

∫0

R

g x , y (r ) d r

(6)

In Figure 6, we plot the running coordination numbers of Li−Oc pair, NLi,Oc(r) for a range of concentrations. The NLi,Oc(r) is dependent on the salt concentration. The plateau in the NLi,Oc(r) about 3 Å indicates the number of Oc atoms present in the first solvation shell or the coordination number. The exact value of coordination number, CNLi,Oc, can be obtained by setting the limit of integration in eq 6 to rmin : the r corresponding to the first minimum of gLi,Oc. For 1.04 M solution the CNLi,Oc (i.e., NLi,Oc(rmin )) is 5 (see Table 2), and it falls within the range of 4−6 reported in the literature.40,49,50 It is to be noted that CNLi,Oc = 5 and the position of first peak in gLi,Oc at 1.95 Å are in good agreement with the data obtained in a polarizable forcefield simulation study.21 A recent twodimensional infrared spectroscopy study by Liang et al.51

Table 3. Interaction of various atoms of EC with PF6− at Two Different Concentrationsa C (M)

0.45

3.95

pair

rmax

g(rmax )

rmax

g(rmax )

P−Oc P−Cc P−O P−C P−H

7.26 6.06 5.34 4.14 3.54

2.0 2.5 2.1 3.8 2.7

3.78 4.50 4.62 4.26 3.66

2.7 1.8 1.6 3.1 2.1

Position of the first peak rmax , height of the first peak g(rmax ) of various RDFs. a

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The Journal of Physical Chemistry C

(SSIPthe ion pair is separated by EC solvation shell around the Li+ ). With increase in the salt concentration, the height of the first peak at r ≈ 3.15 Å increases, while the height of the broadened second peak decreases. It emphasizes that at higher concentrations only a small fraction of the LiPF6 salt exists as SSIP unlike in the dilute solution. Amplitude of the first peak in Figure 8 depicts the existence of salt in the form of contact ion pairs (CIP) and aggregates (AGG). The formation of CIP is further evident from the presence of a peak at 3.78 Å in the gP,Oc as shown in Figure 7. The peak is due to the Oc of solvent molecules that orient around Li+ of either undissociated or weakly associated LiPF6 molecules. RDF of Li−F (gLi,F) further confirms these observations. The magnitude of the first peak in gLi,F(r) at 1.65 Å depicting the ionic bond length of Li and F in LiPF6 salt molecule (Table 2) becomes more prominent with increase in concentration. In the following section we quantify various salt−solvent complexes to understand the effect of concentration on the molecular structure and the dynamic behavior of the solution. Analysis of Salt Complexes. We analyze the simulated trajectories of Li+ and P at different concentrations to study the effect of salt concentration on the formation of salt complexes in the solution. A simple procedure is used to characterize the salt complexes as follows: we first calculate the radial separation of all possible Li−P pairs and count how many P are present within the proximity of a given Li+. A cutoff distance (rc ) of 3.78 Å, which is the rmin of Li−P for 3.95 M, is used to count the number of P for all the cases presented here. Though the chosen rc is arbitrary, the analysis presented here provides insights into how the salt molecules arrange themselves in the solution at various concentrations. A Li+ is said to be in SSIP configuration (Figure 9a) if no P is present in the sphere of radius, rc = 3.78 Å around that Li+.

(e.g., 0.45 M), none of the atoms, O, C, and H, show preferential orientation toward P, the closest being H atoms showing a peak at r = 3.54 Å. On the other hand, for 3.95 M solution besides H atoms the carbonyl oxygens appear closer to P (at r = 3.78 Å). In Figure 7, we plot gP,Oc(r) for a range of concentrations. At lower concentrations only one peak at r ≈ 7 Å exists, whereas at

Figure 7. RDF of P−Oc: gP,Oc(r). Only one peak (r ≈ 7 Å) is seen at lower concentrations, whereas two peaks (r ≈ 7 Å and r = 3.78 Å) are seen at higher concentrations. Increase in height of the peak at 3.78 Å with concentration indicates that the solvent molecules approach closer to the PF6− at higher concentrations.

higher concentrations another peak about 3.78 Å is also seen in the gP,Oc. As the salt concentration increases, the amplitude of the peak at r = 3.78 Å increases indicating that the solvent molecules approach closer to the PF6−. This enhanced interaction between EC molecules and PF6− is due to the formation of contact-ion pairs and aggregates as discussed in the following section. Dissociation of Salt. RDF of Li−P pair, gLi,P, provides insights into how ions of the salt interact in the solution. In Figure 8, we plot gLi,P for a range of concentrations. At low

Figure 9. VMD52 snapshots of LiPF6 -EC complexes at different concentrations. Subfigures (a) SSIP, (b) CIP, and (c) AGG are the configurations taken from 0.45, 1.95, and 3.95 M simulations, respectively. The SSIP are in the majority at lower concentrations whereas CIP and AGG are in the majority at higher concentrations.

When only one P is found within the rc , the Li−P pair is assumed to be forming a CIP (Figure 9b). If two or more number of P are present within the rc , the Li+ is said to be a part of AGG as shown in Figure 9c. It is to be noted that the simple procedure used to identify the salt complexes may overestimate the fraction of AGG especially at higher concentrations. For the concentrations studied here, the effective volume of the spheres (of radius rc = 3.78 Å) considered around all the Li+ to identify the AGG is much smaller than the volume of the simulation box (i.e., no overlap of the spherical regions), making the proposed classification procedure appropriate. We carry out the analysis at different concentrations using the particle coordinates stored at an interval of 1 ps from a

Figure 8. RDF of Li−P: gLi,P. First peak in gLi,P at r ≈ 3.15 Å represents the salt molecules that are undissociated or weakly associated, whereas the second peak represents dissociated molecules. As the concentration increases the height of the first peak increases, while the broadened second peak decreases. It emphasizes that the dissociated fraction of the salt decreases with concentration.

concentrations, a small peak appears at 3.15 Å (i.e., the ionic bond length of Li and P in LiPF6 molecule), while a taller second peak appears at r ≈ 8 Å. It is shown earlier that at low concentrations Oc of the EC molecules interact closely with Li+ while PF6− is closer to the H atoms. The dominant peak at 8 Å shown in Figure 8 suggests that at low concentrations most of the salt exists in the form of solvent separated ion pairs 8178

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The Journal of Physical Chemistry C

salt concentration and (b) reduce the rate of fall of the ionic conductivity beyond the optimal concentration. This can be achieved by maintaining SSIP count as high as possible and reducing the drop in mobility of ions at higher concentrations. However, the cosolvents and additives should have minimal interference with the other required properties of the electrolyte. As observed, CNLi,Oc determines the number of free EC molecules and SSIP present in the solution at a given concentration. Identification of the correct salt−solvent combination that requires a minimal number of solvent molecules to form the first solvation shell (i.e., smaller CN), without compromising the ease of desolvation of Li+ , may help maintain good SSIP count at higher concentrations. The smaller CN helps achieve better reactive stability of the system by limiting the number of solvent molecules exposed to the active electrode surface.18,55,56 This in turn assists in the curtailment of solvent composition in the SEI growth ensuring safety and better cycle life of the LIB.18

production run of 10 ns. The temporal and number-averaged fraction of Li+ existing in each of the three configurations are reported in Table 4. At low concentrations (e.g., 0.45 M) most Table 4. Effect of Concentration on the Structure of Salt Complexes fraction C(M)

Ns

NSSIP

SSIP

CIP

AGG

0.06 0.45 1.04 1.95 2.76 3.95

1 7 17 34 47 76

0.99 3.2 11.3 10.9 9.4 6.5

0.986 0.840 0.667 0.320 0.201 0.086

0.014 0.151 0.274 0.362 0.379 0.241

0 0.009 0.059 0.318 0.42 0.673

of the Li+ exist as free ions, and only a small fraction (∼15%) exists in the CIP configuration. With increase in salt concentration, the fraction of the SSIP decreases while the CIP and AGG fractions increase. At 1.04 M concentration only ∼6% of the Li+ exists in the form of AGG, and this fraction increases to ∼70% at 3.95 M concentration. It is to be noted that the AGG may not be charge neutral, and hence may still contribute to the charge transfer. Analysis of formation and breakage of the AGG and mechanism of charge transfer is beyond the scope of the present work. Owing to their size the AGG are less mobile compared to the SSIP. As the concentration increases the fraction of AGG increases. The decrease in SSIP fraction and formation of more and more aggregates at higher concentrations explain the drop in diffusivities of both the ions with concentration as shown in Figure 2. As seen earlier, the Li+ diffuses more slowly compared to the PF6− due to the formation of the bulkier solvation shell. The difference in diffusivities between Li+ and PF6− is higher at low concentrations and it diminishes with the increase in concentration. Formation of the CIP and AGG at high concentrations is the reason for the reduced difference. Another factor that potentially gets affected due to the formation of the AGG is the amount of charge carried by the clusters. Limited mobility of the AGG and reduced per ion charge carrying capacity amount to lower molar conductivities at higher concentrations (Figure 3).53,54 As seen in Figure 4, the ionic conductivity shows an increasing trend up to 1.04 M concentration and falls afterward with concentration. In a similar manner the number of SSIP in solution (NSSIP = Ns × the fraction of SSIP) increases up to 1.04 M concentration and then shows a decreasing trend with concentration (Table 4). The availability of a maximum number of SSIP in the solution and better mobility of the ions compared to the concentrated solutions (>1 M) explain the observed peak in σic about 1 M concentration. Analysis of the salt complexes along with dynamic properties helps us understand how the concentration affects the diffusivity of the ions and ionic conductivity of the solution. The dynamic properties are tightly coupled with the level of dissolution and structure of the salt complexes in the solution. Optimal value of ionic conductivity is found to be attained when the solution yields a maximum number of SSIP. To reap the benefits of the concentrated electrolytes such as improved thermal and reactive stability, one needs to identify cosolvent and additive molecules and novel salt−solvent combinations that (a) shift the peak of the ionic conductivity toward higher

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CONCLUSIONS The molecular dynamics simulation study of the EC-LiPF6 system for a range of concentrations (0.06−4 M) is able to capture the effect of concentration on the static and dynamic properties of the electrolyte solution. As the concentration increases, diffusivity of both ions (Li+ and PF6− ) and the molar conductivity of the solution decreases, whereas the ionic conductivity increases with concentration to attain its peak value about 1 M concentration and then decreases. For the range of concentrations studied here, the Li+ is solvated better compared to the counterion. In the dilute solution, the Li+ are coordinated by 5 EC molecules as expected. The coordination number decreases (at an increasing rate) with an increase in the salt concentration to attain a value of 2.8 at 4 M concentration. At low concentrations, solvent separated ion pairs are dominant. As the concentration increases more of the contact ion pairs and aggregates are found in the solution. Analysis of various radial distribution functions suggests that the number of free EC molecules in the solution is depleted with an increase in salt concentration. This results in the formation of salt− solvent complexes like contact ion pairs and aggregates. Lower mobility of the aggregates due to their size and smaller amount of charge carried per ion is the reason for the decrease in the molar conductivity. The number of solvent separated ion pairs in the solution, similar to ionic conductivity, is maximum at 1 M concentration indicating that these ion pairs play a key role in the performance of the electrolyte systems. Identification of a combination of solvent, salt, and cosolvent that helps in achieving better mobility of the ions and high count of solvent separated ion pairs at higher concentration is a way to reap the benefits offered by the concentrated electrolytes. Investigations of the role played by commonly used cosolvents on the performance of concentrated electrolytes are underway.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.8b02072. MSD, RDFs, VMD snapshots (PDF) 8179

DOI: 10.1021/acs.jpcc.8b02072 J. Phys. Chem. C 2018, 122, 8173−8181

Article

The Journal of Physical Chemistry C

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Beena Rai: 0000-0002-8637-7778 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the High Performance Computing business unit at Tata Consultancy Services (TCS) for providing access to EKA supercomputer. We also thank K. Ananth Krishnan, CTO, TCS for his constant encouragement and support.

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