J. Phys. Chem. B 2000, 104, 8017-8022
8017
Molecular Dynamics Simulation Study of LiI-Doped Diglyme and Poly(ethylene oxide) Solutions Oleg Borodin and Grant D. Smith* Departments of Materials Science and Engineering and of Chemical and Fuels Engineering, UniVersity of Utah, 122 South Central Campus DriVe, Room 304, Salt Lake City, Utah 84112 ReceiVed: March 27, 2000; In Final Form: June 2, 2000
Molecular dynamics simulations have been performed on solutions of diglyme/LiI at 363 and 450 K for compositions of ether oxygen:Li (EO:Li) ) 15:1 and 5:1 and have been compared with the results of the previous simulations of 12-repeat-unit PEO/LiI. In agreement with experiments on similar systems, the number of free ions was found to be smaller and the degree of ion aggregation greater in the diglyme/LiI solutions compared to PEO/LiI. The number of EOs coordinating each Li+ cation was found to be significantly fewer in the diglyme solutions, due to the lower solution density and short chain length, leading to the observed increase in ion aggregation. In contrast to PEO/LiI solutions, the number of free ions, ion pairs, and higher aggregates was nearly independent of temperature in the diglyme/LiI solutions for the temperature range investigated. Dynamically, the anion and cation self-diffusion coefficients were found to be greater in diglyme/ LiI when compared to PEO/LiI for EO:Li ) 15:1. However, the collective charge-diffusion coefficient and the conductivity were comparable or even lower in the diglyme/LiI solutions, reflecting the much greater extent of ion aggregation in these solutions. For EO:Li ) 5:1, both the ion self-diffusion coefficients and the conductivity were greater for the diglyme/LiI solutions. The EO-Li+ bond lifetime was shown to correlate well with the torsional autocorrelation time for complexed -O-CsC-O- dihedrals. An average lifetime of an EO-Li+ bond was estimated to be of the order 0.1 ns in diglyme/LiI solutions at 450 K, while the average diglyme molecule-Li+ bond lifetime was on the order of tens of nanoseconds, reflecting a slow rate of intermolecular cation hopping.
I. Introduction Solutions of poly(ethylene oxide) (PEO) with lithium and sodium salts have been widely studies as potential polymer electrolytes.1,2 Efforts to develop electrolytes with reduced crystallinity have included use of PEO oligomers as side groups attached to flexible backbones (e.g., methoxy-ethoxy-ethoxyphosphazene, or MEEP)3 and as low molecular weight plasticizers in gelled electrolytes.4-9 In the latter systems, it has been observed that a higher molecular weight PEO plasticizer results in lower volatility and better mechanical properties but decreased conductivity.10 Insight into the molecular-weight dependence of PEO oligomer-salt interactions and ion conduction mechanisms is, therefore, important for choosing the optimal molecular weight of either PEO plasticizer or PEO side groups in polymers, such as MEEP. The extent of ion complexation in PEO-lithium salt solutions is known to be molecular-weight-dependent.12-14 Raman spectroscopy studies of diglyme/LiCF3SO3 and 12-repeat-unit PEO/ LiCF3SO3 solutions have revealed that the number of free ions is 4-6 times lower and the number of the ion aggregates is much higher in the former. Torell et al.11 found that the number of free ions at temperatures higher than 300 K was smaller in (EO)n/LiCF3SO3 solutions for n e 4 than in solutions of 8-repeat-unit PEO/LiCF3SO3. Studies of MEEP/LiCF3SO3 solutions3 showed increasing conductivity with increasing molecular weight of the PEO oligomer side groups, reaching a plateau at six or seven EO groups per side chain. However, Raman studies on glyme/LiCF3SO3, diglyme/LiCF3SO3, and triglyme/LiCF3SO3 revealed a decrease in free ion concentration
and an increase in ion aggregation with increasing temperature,12-14 indicating that low molecular weight PEO oligomers behave more like higher molecular weight polymer electrolytes than simple liquid electrolytes, in which the fraction of free ions is observed to increase with the temperature increase. We believe that valuable insight into the influence of chain length on the behavior of PEO/salt solutions can be gained through detailed atomistic molecular dynamics (MD) simulations. To date, MD simulations of low molecular weight PEO oligomers solutions appear to be limited to the studies of NaI solutions using simplified solvent models.15,16 These studies showed an increase in ion clustering with increasing salt concentration and decreasing solvent molecular weight. No atomistic simulation studies of low molecular weight PEO oligomer solutions have been performed, nor has simulation effort been directed toward addressing the important question of the influence of PEO oligomer molecular weight on the Li+ cation environment and conductivity. Recently, we reported on the static and dynamic properties of 12-repeat-unit PEO/LiI solutions.17,18 In the present work, Li+ cation coordination, ion aggregation, and ion transport were investigated for diglyme/ LiI and compared with results for PEO/LiI. II. Simulation Methodology Simulations of PEO/LiI solutions with PEO chains of the structure H-[CH2OCH2]12-H are described in detail in our previous work.17,18 These solutions are hereafter referred to as PEO/LiI solutions. For the present study, MD simulations were performed on diglyme/LiI solutions having ether oxygen:Li (EO:
10.1021/jp0011443 CCC: $19.00 © 2000 American Chemical Society Published on Web 07/28/2000
8018 J. Phys. Chem. B, Vol. 104, No. 33, 2000
Borodin and Smith
Figure 2. Number of ether oxygen atoms participating in Li+ cation coordination as a function of distance for diglyme/LiI and PEO/LiI solutions, EO:Li ) 15:1, 363 K. Figure 1. Li-O, Li-C, and Li-I radial distribution functions in diglyme/LiI and PEO/LiI solutions, EO:Li ) 15:1 at 450 K.
Li) ratios of EO:Li ) 15:1 and EO:Li ) 5:1, as well as the pure diglyme melt at 363 and 450 K. The solutions were composed of 120 diglyme molecules with a structure H-[CH2OCH2]3-H. The solutions were created by random insertion of the lithium and iodine ions into the diglyme melt and subsequent equilibration for 2 ns at 450 K. The sampling trajectories were 2.2 ns or longer. A quantum-chemistry-based potential function described elsewhere19-20 was used. The bond lengths were constrained using the Shake algorithm.21 Simulations were performed using a velocity Verlet integrator with a 1-fs time step at a constant volume chosen so as to maintain an average pressure of 1 atm. III. Results and Discussion
Figure 3. Number of ether oxygen atoms in the Li+ cation first coordination shell in diglyme/LiI and PEO/LiI solutions at 363 K.
Li+ Cation Environment. Radial Distribution Functions. We began investigation of the chain length dependence of the Li+ cation environment by comparing Li-O, Li-Li, and Li-I radial distribution functions (RDFs) in diglyme/LiI solutions at 450 K, EO:Li ) 15:1, with those for PEO/LiI solutions, shown in Figure 1. The positions of the first and the second peaks in the RDFs are essentially the same for the diglyme/LiI and PEO/ LiI solutions, indicating a fundamental similarity in Li+ complexation. The larger magnitudes of the first and the second peaks of the Li-Li and Li-I RDFs, however, indicate morepronounced ion correlations in diglyme/LiI solutions, which is reflective of greater ion aggregation (discussed below). Qualitatively similar results were obtained at 363 K and for the EO: Li ) 5:1 solutions. Coordination of Li+ Cations by Ether Oxygens. A comparison of the number of EOs coordinating a Li+ cation as a function of distance for diglyme/LiI solutions with that for PEO/LiI solutions, EO:Li ) 15:1, is shown in Figure 2. There is, on average, one or more additional EO in the Li+ cation first coordination shell (4.0 Å) for the PEO/LiI solutions as compared to diglyme/LiI, despite the similarity in the Li-O RDFs (Figure 1). This difference is the result of the greater density of the PEO solutions (around 15%) as well as the ability of the PEO chains to contribute more than three oxygen atoms to cation coordination, as discussed below. The distribution of the number of EOs in the first coordination shell of a Li+ cation at 363 K is shown in Figure 3. While Li+
tends to be complexed by primarily five to seven EO atoms for EO:Li ) 15:1 and by three to six EO atoms for EO:Li ) 5:1 in PEO solutions, complexation by more than three EOs is rare in the diglyme solutions. More detailed analysis of the EO-Li+ cation complexation revealed that about 80% of Li+ cations are coordinated by a single diglyme molecule for EO:Li ) 15:1 and about 90% for EO:Li ) 5:1. Consequently, in diglyme/LiI solutions, a Li+ cation is most frequently complexed by three ether oxygen atoms belonging to the same diglyme molecule and occasionally by two diglyme molecules donating three and two ether oxygen atoms, respectively. In PEO/LiI solutions, however, a single PEO chain frequently contributes more than three oxygen atoms to the coordination of a Li+ cation. Because similarity in the Li+-EO structure (Figure 1) indicates similar complexation energetics in diglyme/LiI solutions as compared to PEO/LiI solutions, these results suggest that the entropy penalty for EO coordination of Li+ cations is greater in diglyme/ LiI than in PEO/LiI solutions. This finding is in accord with the suggestion of Vincent,22 who claims that polymeric solvents, in comparison with their low molecular weight analogues, undergo a much smaller loss of translational entropy upon ion solvation. Ion Clustering. The reduced ability of EO to complex Li+ cations in diglyme solutions (relative to PEO) can be expected to lead to increased cation-anion interaction and, hence, to greater ion aggregation. We monitored the number of I- anions in the first coordination sphere (4.0 Å) of Li+ cations at 363 K,
Li-Doped Diglyme and PEO Solutions
J. Phys. Chem. B, Vol. 104, No. 33, 2000 8019
Figure 6. Populations of complexed conformations in diglyme/LiI and PEO/LiI solutions at 450 K. Figure 4. Number of I- anions in the Li+ cation first coordination shell in diglyme/LiI and PEO/LiI solutions at 363 K. Also shown are experimental values for LiCF3SO3 solutions.14
Figure 5. Populations of uncomplexed conformations in diglyme/LiI and PEO/LiI solutions at 450 K.
EO:Li ) 15:1, as illustrated in Figure 4. This figure shows greater aggregation in the diglyme solutions and an increase in ion aggregation with increasing salt concentration. Greater ion aggregation in diglyme/LiI solutions compared to PEO/LiI solutions is in accord with the results from Raman spectroscopy studies on diglyme/LiCF3SO3 and PEO/LiCF3SO3, EO:Li ) 15.1 solutions14 at 363 K, as shown in Figure 4. These results are consistent with the similar phase behavior of PEO/LiI and PEO/LiCF3SO3 solutions23 and comparable donor numbers24,25 for I- and CF3SO3-. We found little difference in the ion cluster distributions in diglyme/LiI solutions between 363 and 450 K. In contrast, a strong temperature dependence of ion aggregation was observed in PEO/LiI solutions, in which a decrease in the fraction of free ions to less than 1% was found upon raising the temperature to 450 K. Conformational Properties. As was previously undertaken for PEO/LiI solutions,17 we considered separately complexed and uncomplexed -O-CsC-O- conformations. A threedihedral conformation was considered complexed if either of its EOs was within 4.0 Å of a Li+ cation and uncomplexed if otherwise. Populations of the most important uncomplexed and complexed conformations in PEO/LiI and diglyme/LiI solutions are shown in Figures 5 and 6, respectively, at 450 K. Populations of the uncomplexed conformations exhibit only weak composition dependence and are similar to those of the pure melts. Little difference is seen between diglyme and PEO conformations for either the pure melts or the uncomplexed conformations.
Populations of the complexed conformations also show only a weak composition dependence in both PEO/LiI and diglyme/ LiI solutions. This suggests that the influence of Li+ on PEO and diglyme conformations is very local. Consistent with Raman spectroscopy studies on similar systems,12 our simulations revealed that the populations of the tgt and tgg conformations increase with increasing salt concentration while the populations of ttt, tgg′, and ttg conformations decrease in both PEO/LiI and diglyme/LiI solutions. The increase in the population of tgt conformations is greater in diglyme/LiI solutions than in PEO/ LiI solutions, whereas the increase in the population of tgg conformations is more pronounced in PEO/LiI solutions. These trends can be rationalized by noting that in order for a PEO segment of six EOs to wrap around a Li+ cation it must adopt conformations containing tgg conformations.17 In diglyme/LiI solutions, geometric restrictions on wrapping the much shorter diglyme molecule around a Li+ cation are less than for the six EO segment resulting in a higher fraction of tgt conformations. This correlates well with the tgttg′ttgt/Li+ diglyme complex having the lowest energy in the gas phase.26 Ion Mobility. We began comparison of ion motion in diglyme/LiI solutions with PEO/LiI solutions by investigating ion self-diffusion coefficients (Ds), collective ion-diffusion coefficients (Dcoll), and conductivity (λ), defined as
〈R2s(t)〉 tf∞ 6t
Ds ) lim
Dcoll ) lim tf∞
1
N
∑∑
λ)
〈Ri(t)‚Rj(t)〉
N
N i)1 j)1
(1)
zizj
e2N D VkBT coll
6t
(2)
(3)
where Rs(t) is the displacement of the center-of-mass of species s during time t, N is the total numbers of Li+ cations and Ianions in the system, z is the charge of the ion given in the units of an electron charge, V is the volume of the simulation cell, T is temperature, and e is an electron charge. Diglyme, PEO, Li+ cation, and I- anion self-diffusion coefficients, together with the collective ion-diffusion coefficient and conductivity of the PEO/LiI and diglyme/LiI solutions, are given in Table 1. The Li+ cation self-diffusion coefficient of 12.5 × 10-7 cm2/s in diglyme/LiI solution at 363 K, EO:Li ) 15:1, from our simulations is comparable to the experimental
8020 J. Phys. Chem. B, Vol. 104, No. 33, 2000
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TABLE 1: Self-Diffusion Coefficients, Collective Ion-Diffusion Coefficient, and Conductivity from MD Simulations D (10-7 cm2/s) Li+
diglyme/PEO
I-
collective
{D(Li+) + D(I-)}/collective
λ (10-4 S/cm)
system
450 K
363 K
450 K
363 K
450 K
363 K
450 K
363 K
450 K
363 K
450 K
363 K
diglyme/LiI, 15:1 PEO/LiI, 15:1 diglyme/LiI, 5:1 PEO/LiI, 5:1
158 10 32.5 0.3
65 0.7 7.5 0.045
20 6.4 2.6 0.30
12.5 0.61 0.63 0.045
22 6.7 2.7 0.29
13 0.71 0.66 0.045
0.37 0.34 0.13 0.03
0.07 0.23 0.03 0.002
104 38 40 20
364 6 44 46
2.2 2.2 2.0 0.5
0.5 2.0 0.6 0.05
value of 25 × 10-7 cm2/s for tetraglyme/LiCF3SO3, EO:Li ) 1:12, at the same temperature.27 As expected, the shorter diglyme molecules diffuse faster than the 12-repeat-unit PEO molecules. Li+ cations and I- anions are also more mobile in the lower molecular weight solvent, but the increase in their mobility is less than the increase of the solvent mobility upon solvent change from PEO to diglyme. This is due to a higher fraction of relatively fast-moving uncomplexed solvent molecules in the diglyme/LiI solutions, as compared to the PEO/LiI solutions. While the rate of diffusion of the individual species is systematically larger for the diglyme solutions when compared to the PEO solutions, the collective ion-diffusion coefficients are similar or even greater for the PEO/LiI solutions at 363 K. This results in comparable or greater conductivity in the PEO solutions and is indicative of the higher degree of correlation of anion and cation motion in the diglyme solutions. The ratio of the ion self-diffusion coefficient to the collective ion diffusion, shown in Table 1, reflects dynamic-ion correlation. The influence of salt concentration, temperature, and molecular weight on the dynamic ion correlation is a combination of the influence of these effects on static ion correlations (size and distribution of ion correlations, e.g., Figure 4) as well as on “intrinsic” dynamic correlations of ion motions. For PEO/LiI, EO:Li ) 15:1, the increase in the fraction of free ions upon decreasing temperature from 450 to 363 K results in a decrease in the extent of both static and dynamic ion correlations. For diglyme/LiI, EO:Li ) 15:1 solutions, however, static ion aggregation remains essentially unchanged over the same temperature range, while the dynamic ion correlations clearly increase with a temperature decrease. This increase in intrinsic dynamic ion correlation with temperature decrease is consistent with the previous simulations that showed an increase in dynamic correlations in polymer melts upon cooling toward glass transition temperature.28 With increasing salt concentration, the probability of ion pairs decreases, while the probability of larger ion aggregates increases in both diglyme/LiI and PEO/LiI solutions. Despite the increase in static correlation, dynamic correlations are weaker at EO:Li ) 5:1 solutions when compared to EO:Li ) 15:1 solutions.29 The decrease in dynamic ion correlations with increasing salt concentration could be due to two factors: (a) diffusion of ion pairs, which does not contribute to collective diffusion, is replaced by the diffusion of fast Li+- I--Li+ aggregates with increasing salt concentration,18 or (b) large local aggregates which may resemble pure LiI with low ion correlation are formed with increasing salt concentration. Indeed, the Li+ cation transport number of pure LiI melt is close to unity, resulting in the ratio of [D(Li+) + D(I-)]/Dcollective ) 2.30 It is interesting to speculate that a further decrease in dynamic ion correlation with increasing salt concentration beyond EO:Li ) 5:1 might be seen as a result of larger pure LiI-like aggregates. If the decrease in dynamic ion correlation were to be greater than the decrease in ion mobilities, conductivity would again start to increase with increasing salt concentration, leading to “polymer in salt” electrolyte behavior.31
Figure 7. Probability distribution of EO-Li+ bond lifetimes in diglyme/LiI solutions.
Li Bond Lifetimes. EO-Li+ Bond Lifetime. The lifetime of the EO-Li+ bond is a good indicator of the strength of Li+/ diglyme and Li+/PEO interactions and provides insight into the mechanism of Li+ transport. We considered an EO-Li+ bond to exist from the moment an EO first enters the first coordination shell of a Li+ cation (4.0 Å) until the time an EO leaves it. Only those EOs that reach the position of the first peak of the Li-O radial distribution function (2.1 Å) were considered to form a stable EO-Li+ bond, and only those bonds were included in the statistics. The distributions of EO-Li+ bond lifetimes in diglyme/LiI solutions at 363 and 450 K are shown in Figure 7. Because cation mobility is known be strongly influenced by the polymer segmental motion,32 and the decay of the torsional autocorrelation function characterizing this motion was found to be described well by a stretched exponential,18 we attempted to characterize the distributions of EOLi+ bond lifetimes by a Kohlrausch-Williams-Watts (KWW) expression given as
PKWW(t) ) exp[-(t/τ)β]
(4)
The long-time behavior of the bond-lifetime distribution is not adequately described by a KWW function, shown in Figure 7. However, a modified KWW (MKWW)
PMKWW(t) ) A exp[-(t/τMKWW)β] + (1 - A) exp[-(t/τlong)] (5) represents the distributions satisfactorily. The MKWW parameters are given in Table 2. They suggest the presence of two processes. The faster process is characterized by τMKWW and is 2 orders of magnitude faster than the slower process characterized by τlong. The coefficient A being close to unity indicates the prevalence of the fast process. We associate the fast process with creation and breaking of EO-Li+ bonds, while the diglyme molecule remains bonded to the Li+ cation, in other words, without all EO of the diglyme molecule leaving the first coordination shell of the cation. We associate the second process
Li-Doped Diglyme and PEO Solutions
J. Phys. Chem. B, Vol. 104, No. 33, 2000 8021
Figure 8. Probability distribution of EO-Li+ bond lifetimes in diglyme/LiI solutions at 450 K.
Figure 9. Probability distribution of EO-Li+ bond lifetimes in diglyme/LiI and PEO/LiI solutions at 450 K.
TABLE 2: MKWW Parameters for the EO-Li+ Bond-Lifetime Distributions and Average EO-Li+ Bond Lifetime (τEO-Li+) in Diglyme/LiI Solutions temp (K)
composition
A
450 450 363 363
EO:Li ) 15:1 EO:Li ) 5:1 EO:Li ) 15:1 EO:Li ) 5:1
0.984 0.966 0.968 1
τMKWW (ns) τlong(ns) 0.089 0.112 0.209 0.505
3.04 3.45 11.7
β
τΕΟ-Li+ (ns)
0.78 0.76 0.63 0.56
0.15 0.24 0.66 0.84
with a diglyme molecule completely leaving the Li+ cation coordination shell. The characteristic time for both processes increases with increasing salt concentration or decreasing temperature. The average EO-Li+ bond lifetime (τEO-Li+), given as the time integral of the MKWW function, is also shown in Table 2 for each system. Increasing salt concentration or decreasing temperature led to longer lifetimes. The distribution of EOLi+ bond lifetimes is plotted as a function of reduced time t/τcorr,c-c in Figure 8, where τcorr,c-c is the torsional autocorrelation time18 for complexed -O-CsC-O- dihedrals. The consistent behavior of the EO-Li+ bond lifetimes vs reduced time for all solutions suggests a close relationship between the bond lifetimes and conformational dynamics. For each solution, about 50% of the EO-Li+ bonds are broken after approximately four τcorr,c-c. Note that if torsional transition time is used to define reduced time, similar scaling is not observed, suggesting that the torsional correlation time is more closely related to ion/ ether oxygen interactions in diglyme/LiI solutions. A comparison between the distribution of EO-Li+ bond lifetimes for diglyme/LiI and PEO/LiI is shown in Figure 9 at 450 K. At EO:Li ) 5:1, the distribution of EO-Li+ bond lifetimes is less dependent on the molecular weight of the solvent than it is at EO:Li ) 15:1. The probability of relatively shortlived (up to 1 ns) EO-Li+ bonds is higher in the PEO/LiI solutions than in diglyme/LiI solutions, while long-lived EOLi+ bonds are more probable in diglyme/LiI solutions. We believe that there are three important processes involved in EOLi+ bond breaking: (a) torsional transitions of the complexed dihedrals that move an EO out of the Li+ coordination shell; (b) hopping of the Li+ cation to the next EO along the chain; and (c) hopping of the Li+ cation from one chain to another (interchain cation transfer). The shorter lifetimes of EO-Li+ bonds in diglyme/LiI relative to PEO/LiI solutions for times
