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Electrochimica Acta 57 (2011) 228– 236

Contents lists available at ScienceDirect

Electrochimica Acta

j ourna l ho me pag e: www.elsev ier .com/ locate /e lec tac ta

ranched polyethylene/poly(ethylene oxide) as a host matrix for Li-ion batterylectrolytes: A molecular dynamics study

aniel Brandell a,∗, Priit Priimägib, Heiki Kasemägib, Alvo Aabloob

Department of Materials Chemistry, Uppsala University, The Ångström Laboratory, Box 538, 75211 Uppsala, SwedenIMS Lab, Institute of Technology, University of Tartu, Nooruse 1, 50411 Tartu, Estonia

r t i c l e i n f o

rticle history:eceived 29 November 2010eceived in revised form 4 March 2011ccepted 4 March 2011

a b s t r a c t

This article discusses the structural and dynamic properties of a model polymer electrolyte systemsuitable for Li-ion batteries, investigated by Molecular Dynamics simulations at 293 K. It consists of anon-polar polyethylene backbone, onto which polar oligomeric polyethylene oxide side-chains of length4–15 EO units are attached. LiPF6 salt is dissolved into the matrix to a concentration corresponding to a

vailable online 12 March 2011

eywords:olymer electrolyteolecular dynamics

ide-chainsi diffusion

Li:EO ratio of 1:12. It is found that the system display significantly higher mobility values that linear PEOusing the same concentration, which is attributed to the high side-chain dynamics and the polar/non-polar topology of the system. An optimum side-chain length of 10 EO units is found for many properties,such as the dissolution of salt, although the Li+ ion diffusion was found to be the highest for side-chainlengths of 15 EO units: 1.54 × 10−13 m2 s−1.

© 2011 Elsevier Ltd. All rights reserved.

. Introduction

The last two decades have seen a growing interest for solidolymer electrolytes (SPEs), primarily because of their use inolid-state lithium batteries, but also for electrochromic devices,ctuators, sensors, solar cells, etc. SPEs are formed by dissolving

salt into a polymer matrix, conventionally poly(ethylene oxide)PEO), –(CH2–CH2–O)n–. However, the ion conductivity in PEO isonsidered to be too low for using Li-containing SPEs in commercialattery applications [1,2].

After the discovery that the ion transport generally occurredn the amorphous regions of PEO [3], several strategies have beenaken to improve the ion conductivity by increasing the amorphousontent of the SPE. A number of approaches have been used: addingrganic plasticizers [4,5], using lithium salts with large anions [6,7],r modifying the polymer network, for example by adding side-hains [8–11].

Although significant improvement of the conductivity can bechieved, it is still usually not considered to be enough. How-ver, a more profound knowledge about the structure-dynamicroperties of the SPEs can result in discovering the fundamen-

al transport mechanisms, which might be advantageous in theevelopment of new SPE materials. One particularly useful method-logy for studying these processes in SPEs is Molecular Dynamic

∗ Corresponding author. Tel.: +46 18 4713747; fax: +46 18 513548.E-mail address: Daniel.Brandell@mkem.uu.se (D. Brandell).

013-4686/$ – see front matter © 2011 Elsevier Ltd. All rights reserved.oi:10.1016/j.electacta.2011.03.022

(MD) simulations. In previous studies, we have explored the influ-ence of side-chains in PEO-based SPEs [12–14]. Karo and Brandell[14] performed a systematic investigation of a branched PEOxLiPF6(x = 10 or 30) system at 293 K, were the side-chain length andseparation was varied from 3 to 50 EO units, and could find ten-dencies of optimal side-chain configurations depending on saltcontent: the ionic transport was significantly higher for manybut short side-chains at higher concentration, while side-chainlengths of 7–9 EO units promoted conductivity at lower concen-tration.

In the MD simulations reported here, we continue to analyze thebranched SPEs. We have investigated a system with polar ethyleneoxide side-chains on a non-polar polyethylene (PE) backbone. Thisdual polarity of the SPE system can promote a nano-scale separa-tion and ordering of the macromolecular constituents, which forother polymeric systems – such as the perfluorosulfonic acid fuelcell membranes [15] – provide structures which have shown tostrongly promote ionic transport [16]. Ordered phases of SPEs havealso recently attracted significant interest since the discovery thatthey can promote conductivity under certain conditions [17–19].

The PE/PEO system has been investigated for different side-chain lengths with LiPF6 salt, at a Li:EO ratio 1:12 at 293 K,which can be treated as a model system for SPEs with an abil-ity for structural self-organization. A linear PEO SPE with the

same salt concentration has also been simulated as reference.It should be noted that this constitutes a model system; noexperimental studies of an electrolyte homologue have beenpublished. On the other hand, electrolytes of block copolymers

himica Acta 57 (2011) 228– 236 229

ps

2

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Table 1Equilibrium densities of the simulated systems.

Side-chain length Density (kg m−3)

4 EO units 8856 EO units 10218 EO units 109810 EO units 1143

FLr

D. Brandell et al. / Electroc

oly(ethylene)–poly(ethylene oxide) have been investigated [20],howing promising conductivity values.

. Methodology

In an MD simulation, the model consists of interacting atomsithin a simulations box. Newton’s equations of motions are solved

epeatedly for all atoms, thus generating a short “movie” sequencef the material which can be analyzed statistically. The resultepends explicitly on the description of the forces between the

nteracting atoms; the so called Force Field.The force field here has previously been used in [12–14], and

ontains the intra- and intermolecular potential interactions in PEOaken from Neyertz, Thomas and co-workers [21–23], and LiPF6nteractions taken from Borodin et al. [24]. The side-chain linkage-oint torsional potential was developed in [12]. The polyethyleneorce field was taken from Menvitch et al. [25] and Saiz et al. [26].

Using the MCGEN software [27], which implements a Monte-arlo approach, six different branched PE/PEO systems wereenerated with Li+ and PF6

− ions, all at a Li:EO ration 1:12, and

sing one single oligomer of a PE backbone. The side-chain lengthsere either 4, 6, 8, 10, 12 or 15 EO units long, ethoxy-group end-

apped and attached to the backbone with an O–C linkage. Theide-chain attachment points were separated by 5 CH2-units along

ig. 1. The final snapshots of the MD boxes for side-chain lengths of 4 EO units (a), 10 EOi+ ions are represented with yellow spheres and PF6

− ions are blue. Hydrogens are omitteferred to the web version of this article.)

12 EO units 120615 EO units 1248

the backbone. The number of side-chains varied between 51 and148 in order to keep the Li:EO ratio constant for the different sim-ulated systems. A reference system of linear PEO12LiPF6 was alsosimulated as reference.

All different polymeric systems were generated in cubic60 A × 60 A × 60 A MD boxes, including a substantial part of freevolume for relaxation, and simulated using the DL POLY software[28] with periodic boundary conditions. They were first relaxedfor first 2 ns in the NVT ensemble and 20 ns in the NPT ensem-ble at 293 K with tethered salt ion positions. The ions were then

released, and the system further equilibrated for 2 ns in the NVTensemble, after which it showed equilibrium properties in termsof energy and pressure. The final simulations were run for 20 nsin the NPT ensemble, at normal pressure and temperature (1 bar

units (b) and 15 EO units (c). The PE backbone is grey, the PEO side-chains are red,ed. (For interpretation of the references to colour in this figure legend, the reader is

230 D. Brandell et al. / Electrochimica Acta 57 (2011) 228– 236

the n

atei

3

3

tt1tm

Fig. 2. The degree of paired or clustered cations and anions (a) and

nd 293 K) using a time-step of 1 fs and collecting data every ps ofhe final 10 ns. The box sizes were around 40 A × 40 A × 40 A afterquilibration, reaching normal densities with increasing density forncreasing ethylene oxide content (see Table 1).

. Result and discussion

.1. Structure

A qualitative inspection of the MD boxes gives an overview ofhe topology and the self-organization of the systems. Fig. 1 shows

he final snapshots of the simulation boxes of the systems with 4,0 and 15 EO units side-chain length, respectively. It is clear fromhese pictures that the ions dissolve in the polar parts of the poly-

er matrix, which is expected due to the favorable interactions

umber of coordinating anions (b) for different side-chain lengths.

between the ions and the ether oxygens. It is also visible that dif-ferent parts of the hydrophobic backbone tend to bind to each other,forming somewhat of a separate phase. In other parts of the back-bone, the non-polar polyethylene chain tends to form helices, thusshielding it from unwanted interactions with the hydrophobic side-chains. This nano-scale separation tend to be more pronounced asthe side-chains grow longer, perhaps due to the increased degreeof covalent bonding between the different EO units. On the otherhand, the time-scale for the MD simulations does not allow thisphase-separation to run to any large degree of completeness.

Fig. 2a displays the degree of ion pairing in the system. It is clear

that the amount of completely dissolved cations is highest for thehighest side-chain length, while the systems with shortest side-chains (4 or 6 EO units) have a much higher degree of ion pairingand clustering (>50%). The reason for this might well be that the

D. Brandell et al. / Electrochimica Acta 57 (2011) 228– 236 231

F ighbous two d

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ctaaist

ig. 3. Typical structures found in the polymer electrolyte with distances to the neide-chain length of 8 EO units (a), a Li+ ion acting as a physical cross-link between

hort side-chains are closer to the backbone, and therefore have lessossibilities of entanglement and forming a uniform PEO matrix.hort side-chains can for example not complex a Li+ cation solelyithout ether oxygens from neighbouring side-chains.

It is more difficult to see any obvious trends for the cation–anionoordination numbers in Fig. 2b, although there is a slight tendencyo lower numbers for longer side-chain lengths, not least for 10nd 12 EO side-chain lengths. Highly complexed cations are rare in

ll systems, and the most frequently occurring cluster is ion pair-ng. This is also in agreement with experimental studies [29]. Theystem with longest side-chain is somewhat in contrast to this pic-ure, with a low degree of pairing but with significant clustering.

ring atoms around Li highlighted: A 2 Li+–2 PF6− cluster found in the system with

ifferent side-chains of 15 EO units length (b).

A closer inspection of the simulation boxes show that the ion clus-ters usually consists of 2 Li+ ions and 2–3 PF6

− anions (a typicalexample is shown in Fig. 3a), with the largest cluster found for thesystem with 4 EO side-chain length. That the number of anions gen-erally is slightly larger in than the number of cations also explainthe difference in amount of paired ions seen for some systems inFig. 2a.

The EO complexation of Li+ is shown in more detail in Fig. 4,

where it is illustrated to which of the side-chains in the matrixthe Li+ ions are coordinated to. It is clear that the amount ofLi+ ions complexed by the same side-chain steadily increases upto side-chain lengths of 10 EO units, where after it drops. At the

232 D. Brandell et al. / Electrochimica Acta 57 (2011) 228– 236

nation

ssswictfllga

Fig. 4. Li coordi

ame time, the amount of Li+ ions coordinated to neighbouringide-chains falls from a high ratio for short side-chains, when theide-chain increases. This confirms the picture discussed above,ith short side-chains being unable to complex the cations, which

nstead has to be coordinated to anions and to neighbouring side-hains or side-chains from elsewhere on the backbone. Whenhe side-chain grows longer, a more uniform PEO matrix can beormed, where the number of EO units at intermediate side-chain

engths is enough to complex the cations. At even higher side-chainengths, above 10 EO units, the PEO matrix becomes entan-led, and the coordination to different side-chains are increasinggain, with increasing possibilities for the cations to form phys-

Fig. 5. Summary of the average

to side-chains.

ical cross-links between the side-chains (see Fig. 3b). These twotrends – the increased possibilities for Li+ complexion and theincreased entanglement as the side-chains grows longer – togetherexplains the observed similarities between the 8 and 15 EO unitssystems.

The entire cation coordination sphere is summed up in Fig. 5,where the coordination numbers of Li+ to EOs and PF6

− anionsare plotted for different side-chain lengths, for distance <3 A (Li–O)

and <4.5 A (Li–P), respectively. The total coordination number of Liin the system is 6–7, which can be considered high although notunrealistic, and is also a result of the distance criteria. This is alsoclear from the Li–F and Li–O radial distribution functions, plotted

Li coordination sphere.

D. Brandell et al. / Electrochimica Acta 57 (2011) 228– 236 233

b) rad

iinhasP

bsEnc1a

Fig. 6. Li–F (a) and Li–O (

n Fig. 6. As expected, the EO coordination increases with decreas-ng PF6

− coordination, and vice versa, while the total coordinationumber is increasing with increasing EO coordination due to stericindrance and electrostatic repulsion upon anion coordination. Aslso stated above, the cation–anion coordination number decreasesomewhat with increasing side-chain length, since a more uniformEO matrix can better dissolve the salt.

It is interesting to note that the ether oxygen coordination num-er in Fig. 5 exactly follows the trend of the Li+ coordination to theame side-chain, displayed in Fig. 4. There is thus a tendency for theO coordination number to increase when the cations are coordi-

ated to sequential EOs on the same side-chains. The ether oxygenoordination number is therefore highest at side-chain lengths of0 EO units, which seem to be an optimum length for wrappinground the cations. Although 10 EO units are more than what is

ial distribution functions.

necessary for complexation of Li+ (6–7 EO), the unfavorable inter-actions between the backbone and the cations might result in the“extra” optimum side-chain length.

When the side-chains become longer, they have a tendency tocurl up around the cations and become entangled with each other.This is shown in Fig. 7, which display the time-average radius valueof the radius of gyration (Rg) of the side-chains in the box; a lowervalue corresponding to a smaller all-over size. Naturally, longerside-chains result in a larger radius of gyration, since they con-sist of more EO units. However, the increase in Rg with side-chainlength is not particularly strong (less than a factor of two for an

increase from 4 to 15 EO units), and there is clearly an increasinggap between the maximum value of the individual side-chains –which corresponds to a more linear side-chain conformation – andthe mean values. When the side-chain length increases beyond 10

234 D. Brandell et al. / Electrochimica Acta 57 (2011) 228– 236

yratio

Ea1tictR

3

utTli

csooLoscb

TD

Fig. 7. Maximum and mean values of the radius of g

O units, it can be seen that Rg increases somewhat faster, and thusdopts a slightly more linear conformation. This is again due to that0 EO is the side-chain length which is necessary for maximizinghe wrapping around the cations; while extra EO units stretch outnto the polymer matrix. At the longest side-chain length, the side-hains become increasingly entangled, resulting in that they looseheir side-chain character and a corresponding stabilization of theg values.

.2. Dynamics

The dynamics of the different atomic species is from an MD sim-lation normally evaluated from the mean-square-displacement ofhe particles, which is proportionally to the diffusion coefficients.he diffusion coefficients are listed for all different side-chainengths and the linear PEO reference system in Table 2, and alsollustrated in Fig. 8.

It is striking how much higher the calculated diffusion coeffi-ients of both ether oxygens, Li+ and PF6

− ions are in the branchedystem than in the linear PEO matrix – the difference are in therder of one magnitude for the ionic species. The values, which aref the same order of magnitude as measured experimentally foriPF6–PEO systems [30], are somewhat lower as compared to previ-

usly studies branched PEO systems [14], but which also generallyhowed higher mobility as compared to linear PEO12LiPF6. Theonductivity increase is also analogous to experimentally studiedlock-copolymer systems of PE/PEO [20]. However, the differences

able 2iffusion coefficients and transport numbers in the simulated systems.

Side-chain length Li P

D (m2 s−1) t+ D (m2 s−1) t−

4 EO units 8.4 × 10−14 0.41 1.2 × 10−13 0.596 EO units 9.5 × 10−14 0.53 8.3 × 10−14 0.478 EO units 6.8 × 10−14 0.48 7.5 × 10−14 0.5210 EO units 1.2 × 10−13 0.36 2.2 × 10−13 0.6312 EO units 1.1 × 10−13 0.29 2.6 × 10−13 0.7115 EO units 1.5 × 10−13 0.58 1.1 × 10−13 0.42Linear PEO 1.4 × 10−14 0.21 5.2 × 10−14 0.78

n of the side-chains for different side-chain lengths.

with the linear system are larger for the PE/PEO systems than forbranched PEO, and display more consistently higher mobility. Thismight be an effect of the hydrophobic backbone part, which mightinduce a higher side-chain mobility due to the polar/non-polarrepulsion and also due to local structural arrangements which pro-motes mobility.

The ether oxygens are the most mobile species, which is alsoconsistent with previous MD simulations [12–14]. As expected,the side-chain atoms are also much more mobile than the back-bone atoms, due to the slower segmental movements of largermolecules. The ionic mobility is lower than the EO mobility dueto the strong electrostatic interactions and the high degree of ionpairing. Normally, anion mobility is generally higher than cationmobility in PEO-based electrolytes [29], which is evident for mostof the simulated systems (see Table 2; where t− > 0.5). However,the rather large positive transport numbers might indicate that thesystems are still in the sub-diffusive domain [31].

The mobility values are correlated in the sense that some sys-tems display generally higher mobility for all their species thanothers – their polymer configuration seem to promote mobility.This is expected, since there is a high degree of interaction betweenthe different polar species in the systems. However, this correla-tion is not very strong. For example, the highest Li+, PF6

− and etheroxygen mobility can be found in three different systems (15, 12and 10 EO units side-chain length, respectively). Nevertheless, itis clear that longer side-chain lengths generally promotes mobility– a dramatic increase can be seen for side-chain lengths of 10 EOunits and above. It is more difficult to explain, though, the very highEO mobility for 10 EO units side-chain length does not have a sig-nificantly higher Li-mobility associated with it, since the degree ofLi–EO complexation is highest for this system (see Fig. 5). It gives apicture of complexed side-chain atoms twisting around more stableLi+ ions.

In order to achieve a better picture of the ionic transport inthe systems, the individual dynamic events have been studied ingreater detail. The Li+ ions move with a jumping or hopping mech-

anism through the matrix. Fig. 9 displays the amounts of differenttypes of interactions between the Li+ ions and the side-chains. Theanions are also involved in dynamic events with the cations, but toa lesser degree.

D. Brandell et al. / Electrochimica Acta 57 (2011) 228– 236 235

Fig. 8. Calculated diffusion coefficients for different atomic species in the PE/PEO branched and in linear PEO LiPF6 electrolyte systems.

F ains in

aomtntchiv

sl

ig. 9. The amount of different types of dynamic interaction between Li and side-chot represent any general trend.

It is clear that the general level of dynamic events is not large;lthough the sampling time is as long as 10 ns, less than a quarterf the Li ions are involved in different transport processes. Further-ore, the dynamic events are dominated by short time jumps of

he cations, in and out of the direct coordination sphere. This isot difficult to understand, considering the rather low simulationemperature. The incoming and leaving EOs into or out from theoordination sphere rather corresponds to mobility in the polymerost matrix than any real ionic transport. Instead, the Li ions chang-

ng coordination sphere (denoted “Oeth interchange”) are the more

ital for the conductivity behaviour of the material.

It can be seen from Fig. 9 that the number of dynamic events areignificantly lower for two of the systems: the 6 and 8 EO side-chainengths. This is also consistent with their lower diffusion coefficient

n the simulated systems. Note that the line is only there to guide the eye, and does

seen in Fig. 8. That the 4 EO side-chain length system displays a highnumber of dynamic events (Fig. 9) but low overall mobility (Fig. 8)can be explained by the very low degree of Li+ jumps in the system.

4. Conclusions

This article has presented results from MD simulations of a seriesof polymer electrolytes consisting of a non-polar polyethylenebackbone with covalently bonded polar hydrophilic side-chains fora LiPF6 concentration equal to a Li:EO ratio of 1:12. The length of

the side-chain has been systematically varied. The systems displaysignificantly higher mobility than linear PEO of the same concen-tration, which can be attributed to the self-organization of theparts of the system which exhibit different polarities. However,

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36 D. Brandell et al. / Electroc

imulations run at longer time-scales are necessary in order tonvestigate this phase-separation in more detail.

It has also been found that there are clear differences in theystem when the side-chain length is 10 EO units or longer. Thiside-chain length make it possible for the side-chain to completelyrap around the cations, leading to a higher degree of ion dis-

ociation and better mobility properties, and there is thus clearndications of an optimal side-chain length. It is however difficulto draw more general conclusions from this study, since the system

ight still – although the simulation times are substantial – be inhe sub-diffusive regime and there is an obvious lack of experimen-al data to compare with. Further work should include experimentaltudies and simulations at higher temperatures. It could also bepeculated that covalently binding the anions to the side-chainsould alter the conductivity properties of the system, not least in

erms of higher transport numbers for lithium.

cknowledgements

This work has been carried out in the HPC Centre at the Univer-ity of Tartu and has been financed by Estonian Science Foundationrant #6763 and the EU-FP7 project SUPERLION. We would also

ike to thank Professor Michel Armand, Université de Picardie Juleserne, for fruitful discussions.

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