Does Ion Aggregation Impact Polymer Dynamics and Conductivity in

Article pubs.acs.org/Macromolecules

Does Ion Aggregation Impact Polymer Dynamics and Conductivity in PEO-Based Single Ion Conductors? Kokonad Sinha and Janna Maranas* Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States S Supporting Information *

ABSTRACT: We describe quasi-elastic neutron scattering measurements of polymer backbone dynamics in PEO-based single ion conductors with varying morphologies. These morphologies include aggregates, multiplets and ion pairs, where the dominant ion state varies with cation identity: Li+ samples are mostly aggregates, Cs+ samples are mostly ion pairs, and Na+ samples contain a range of ion states. The conductivities of these samples are roughly equivalent, suggesting that ion state does not have a large impact on conductivity. Because conductivity is connected to polymer dynamics, we use quasi-elastic neutron scattering to assess polymer dynamics in all three samples. In all three ionomers, the motion of the PEO spacer is slower near the ionic comonomer [anchor atoms] than it is in the spacer midpoint [bridge atoms], leading to two fractions in the measured dynamics. Anchor atom dynamics depend on cation content but not on the different morphologies associated with cation identity. We thus conclude that for this system of ionomers, polymer dynamics and ion transport are independent of morphology.

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with ether oxygen (EO) atoms,9−12 although exceptions have been observed in crystalline polymers.13−15 One disadvantage of SPEs is that the fraction of conductivity from the cation (transference number) can be as low as 20− 30%,16 implying a large contribution from the anion. This poses a practical problem for lithium ion batteries, because anion accumulation at the electrode can result in reverse polarization, greatly increasing cell resistance and degrading performance.17,18 One way to address this issue is to choose a heavy anion with low mobility. Another is to covalently bond the anion to the polymer backbone,19−36 forming a single ion conductor. Because the anion is part of the polymer backbone, single ion conductors have transference numbers of unity.27,37−50 Single ion conductors are a class of ionomers in which the free ion is soluble in the host polymer. In contrast to ionomers with clear phase separation, single ion conductors can have limited aggregation [single ions or ion pairs], intermediate aggregation [clusters of ∼3−10 ions or multiplets], or larger aggregates.51−53 All states can exist within the same single ion conductor, and the extent of microphase separation can increase as the temperature increases.54−60 In the single ion conductor we study, the anion is sulfonate (SO3−) covalently bonded to the PEO backbone as shown in Figure 1a. The ionomer is prepared with varying repeat units in the PEO spacer [N = 9, 13 or 25], degree of sulfonation [Y, %], and cation identity [Na+, Li+ or Cs+]. The ion content (molar ratio of cations to ether oxygen atoms) is a function of both

INTRODUCTION Lithium ion batteries are common in portable electronics such as cell phones because they have high energy density and are

Figure 1. [A] Chemical structure of PEOx-Y%Na, where x = 400, 600, 1100 g/mol corresponding to N = 9, 13, 25 repeat units, respectively. [B] Schematic illustrating the location of bridge and anchor atoms.

rechargeable. The emergence of these batteries in electric and hybrid vehicles emphasizes the utility of further improvements: the cell phone battery may not benefit significantly from a further reduction in size but the vehicle battery will. One possibility is the lithium metal anode, which is incompatible with a liquid electrolyte due to formation of dendrite on recharging. As a result, solid polymer electrolytes (SPEs) are a frequently studied alternative.1−8 SPEs contain a polymer host such as poly(ethylene oxide) (PEO); the ether oxygen atoms on the backbone help solvate the cation. It is commonly believed that ionic conduction takes place when the cation moves through the amorphous polymer host by coordinating © 2014 American Chemical Society

Received: September 9, 2013 Revised: March 24, 2014 Published: April 7, 2014 2718

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will have smaller surface areas compared to their smaller counterparts. Here we report on the variation of anchor and bridge atom fraction and dynamics as a function of the differing aggregation states in the (Li, Na, Cs) series. This includes two temperatures at which the aggregation states vary, and one measurement where all systems are aggregated. We discuss the role of anchor atom mobility on conductivity, and the possibility of conductivity modes via aggregates.

spacer length and degree of sulfonation. The work described in this paper is part of a collaborative effort to study this series of ionomers using a variety of probes such as NMR,61,62 dielectric relaxation spectroscopy (DRS),19−21,35,63 molecular dynamics (MD) simulations,64−66 FTIR,67 ab initio calculations,68 X-ray scattering, 42,69,70 and quasi elastic neutron scattering (QENS).71,72 We combine these measurement techniques to understand the interplay of dynamics, morphology, and ionic transport and to identify the key elements that contribute to high conductivity in single ion conductors. Because ion motion is related to motion of the polymer, in prior studies we investigated the dynamics of the PEO backbone as a function of ion content (PEO600-Y%Na where Y ranges from 0 to 100%),71 and spacer length (PEOx-100%Na where x = 400/600/1100 g/mol)72 using quasi-elastic neutron scattering [QENS]. QENS is an effective method to isolate polymer dynamics in SPEs because the motion of hydrogen in the polymer dominates the QENS signal, and is frequently applied.10,12,13,71−73 In the current manuscript, we study the influence of cation identity (Li, Na, Cs) on polymer dynamics, thus completing the series. For the systems shown in Figure 1, the scattering is dominated by the incoherent scattering of hydrogen atoms on the PEO spacer. Because the anion is covalently bonded to the polymer backbone, the mobility of the spacer is reduced relative to pure PEO. The dynamics of the PEO spacer depend on the presence and size of the ionic aggregates, spacer flexibility, chain length, cation-polymer binding energy, and cation−anion binding energy. In the series (Li, Na, Cs), cation-polymer binding energy and cation−anion binding energy vary: smaller cations bind more strongly to both the polymer and the anion. Because it is the competition between cation−anion and cation−PEO binding that determines the degree of solvation, it is not clear which will dominate among this series. It is also not clear what role the flexibility of the PEO spacer plays in solvation: shorter spacers may be more restricted and less able to form conformations that favor solvation. Increased aggregation has been observed for smaller cations with stronger binding energies in other single ion conductors.74,75 Two recent papers examined the aggregation of the PEOx100%Y ionomers.59,60 The Li cation is the smallest, and in PEOx-100%Li, aggregates are present at all temperatures. The Na cation is 22% larger than Li, and the PEOx-100%Na series does not have clear evidence for aggregation below 350 K. Instead, SAXS data suggest mostly multiplets (3−10 ion clusters), consistent with a weaker cation−anion association. The Cs cation is 75% larger than Li, and the PEOx-100%Cs series is primarily ion pairs, again with aggregation appearing around 350 K. Interestingly, this series of aggregation states, aggregates (Li), multiplets (Na), and pairs (Cs), do not have significantly different conductivities.21 This may be because conduction occurs primarily through the solvated cations [single ions], but FTIR on the Na series suggests that no single ions are present.67 Our investigation of the PEOx-100%Na series demonstrates a link between the motion of atoms neighboring the isophthalate group [anchor atoms] and conductivity. Motion of the faster midspacer [bridge] atoms is not connected to conductivity, consistent with the FTIR results mentioned above. Because the anchor atoms border the isophthalate group, and thus the anion and ion aggregates, both the fraction of anchor atoms and their mobility is likely to vary with aggregation state. In particular, systems with larger aggregates

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EXPERIMENTAL DETAILS Sample Synthesis. The ionomers were synthesized using poly(ethylene glycol) (PEG) oligomer diols and dimethyl 5-

Table 1. Properties of Samplesa sample PEO400-100% Li PEO400-100% Na* PEO400-100% Cs PEO600-100% Li* PEO600-100% Na* PEO600-100% Cs PEO1100100%Li PEO1100100%Na* PEO1100100%Cs a

cation:EO ratio

ion content (mole fraction)

Tg (K)

molecular weight (g/mol)

1:9

0.111

285

3300

1:9

0.111

295

3300

1:9

0.111

294

3300

1:13

0.077

258

4600

1:13

0.077

267

4600

1:13

0.077

270

4600

1:25

0.04

236

4500

1:25

0.04

236

4500

1:25

0.04

238

4500

Asterisks indicate samples measured on all three spectrometers.

Table 2. Incoherent Scattering Contribution from Spacer in PEOx-100%M sample

Li

Na

Cs

PEO400-100%M PEO600-100%M PEO1100-100%M

84.75 87.26 90.14

84.71 87.23 90.12

84.69 87.22 90.12

Table 3. Spatial and Temporal Ranges for Instruments Used in This Work instrument

spatial range, Å

time range

resolution, μeV

DCS BASIS HFBS

3−11 4−11 4−11

1−50 ps 37 to 750 ps 250 ps to 2.5 ns

56 3.5 0.85

sulfoisophthalate sodium salt in a two-step melt transesterification process. The details of the preparation are established in previous publications.21 We used 1H NMR to verify the molecular weight of the PEO spacers (400, 600, and 1100 g/mol in this study). The ionomers were purified by exhaustive diafiltration in deionized water to remove monomers, polymerization catalyst, and any ionic impurities. To create the series (M = Li/Na/Cs) in PEOx-100%M, the sodium cation was exchanged to lithium or cesium by aqueous diafiltration with an excess of LiCl or CsCl salts, then exhaustively dialyzed to remove salt impurities. The concentrated ionomer solution was freeze-dried and vacuum-dried at 120 °C to constant mass.19,21 We consider all spacer lengths (x 2719

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backbone. Because the incoherent cross section of hydrogen is an order of magnitude larger the incoherent or coherent scattering of other atoms in our samples (C, H, O, S and Li/ Na/Cs), we expect the signal to be dominated by the incoherent scattering of hydrogen on the PEO repeats. Although some hydrogen is present in the isophthate group, this is a small fraction of the total hydrogen. Table 2 demonstrates this by presenting the incoherent scattering of atoms on the PEO spacer compared to incoherent and coherent scattering all other atoms. As this ranges from 84 to 91%, we assume the QENS signal is dominated by the selfmotion of hydrogen on the PEO spacer. To cover a large dynamic range, we conducted QENS measurements on three different instruments: the disk chopper spectrometer (DCS)76 and the high flux backscattering spectrometer (HFBS)77 at the NIST Center for Neutron Research, Gaithersburg, MD, and the Backscattering Spectrometer (BASIS)78 at the Spallation Neutron Source (SNS), Oak Ridge National Laboratories, Oak Ridge, TN. Characteristics of these instruments are given in Table 3. The DCS is a direct geometry time-of-flight spectrometer, and the HFBS and BASIS use backscattering (HFBS) and near-backscattering (BASIS) geometry, which increases resolution by minimizing the wavelength spread of the scattered beam. The long time limit of each spectrometer is directly connected to instrument resolution. On DCS, this is depends on the incident wavelength (4.8 Å) and the resolution setting on the choppers (medium). These choices dictate the accessible spatial range, and also the short time limit through the kinematic limitation relating changes of energy and wave vector. The spatial scale and long time limit of BASIS is also connected to the incident wavelength (6.4 Å). Kinematic restraints are not an issue for BASIS or HFBS, and the short time limit of these instruments are dictated by the energy spread in incident neutrons: ± 17 μeV for HFBS and ±110 μeV for BASIS. The spatial ranges accessed by HFBS and BASIS are comparable to those of DCS, such that the resulting data provides q-resolved dynamic information from 1 ps to 2.5 ns. All of the three instruments require an annular geometry for the sample, which we prepare as a uniformly thin polymer film between two aluminum foils. The film thickness is selected to allow 10% of the neutrons to be scattered; this gives good signal intensity with low probability of multiple scattering. All sample data is measured against a resolution function R(Q,ω), which we obtain with a vanadium standard that is immobile in the conditions of the measurement. For most samples, we measured at 298, 323, and 348 K allowing 1 h for thermal equilibration at each temperature. PEO400−100%Na and PEO400−100%Cs were not measured on BASIS at 298 because their dynamics are slower than the BASIS window. The intensity of scattered neutrons is a function of momentum transfer (Q) and frequency (ω). We reduce raw data from the DCS and HFBS using NCNR’s in-house developed software data acquisition and visualization environment (DAVE) and raw data from the BASIS instrument using software developed at the SNS. Both software correct for detector efficiencies using the resolution data, and subtract the empty can and background from the raw data to give I(Q,ω). The total intensity I(Q,ω) is a convoluted integral of the resolution function R(Q,ω) and sample dynamics S(Q,ω), and thus the sample scattering in the frequency domain is obtained by deconvolution with the resolution function.

Figure 2. Illustration of frequency domain (A) and inverse Fourier transformed time domain (B). Sample: PEOx-100%Cs [x = 400, 600, 1100]. Temperature: 348 K. Spatial scale: Q = 1 Å−1.

Figure 3. Self-intermediate scattering function from DCS (triangles), BASIS (circles), and HFBS (squares). Sample: PEO600−100%Na. Temperature: 348 K. Spatial scale: 1 Å−1.

= 400/600/1100 g/mol); the samples are summarized in Table 1. Because all samples are fully ionized, we refer to the PEOx100%M samples in the format x-M (e.g., 600-Li stands for PEO600−100%Li). Neutron Scattering. We use quasi elastic neutron scattering (QENS) to quantify polymer dynamics by monitoring the energy change of scattered neutrons. The scattering signal depends on the respective scattering cross sections (a quantitative measure of the probability of scattering) of the constituent atoms. Each atom can scatter coherently or incoherently; coherent scattering probes motion relative to other atoms, whereas incoherent scattering probes motion of single atoms. The signal we are interested in is the incoherent scattering from the PEO repeats on the polymer 2720

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Figure 4. Fit parameters obtained from DCS, BASIS and HFBS [open symbols] compared to those obtained fro m BASIS alone [connected filled symbols]. [A] bridge and anchor relaxation times for PEOx-100%Na (T = 348 K); [B] bridge and anchor relaxation times for PEO600−100%Li.

I(Q , ω) = S(Q , ω) ⊗ R(Q , ω)

β(Q )⎤ ⎡ ⎛ t ⎞ ⎥ S(Q , t ) = exp⎢ −⎜ ⎟ ⎢⎣ ⎝ τ(Q ) ⎠ ⎥⎦

(1)

The frequency domain data obtained from BASIS for PEOx100%Cs (where x = 400, 600, 1100) at 348 K are shown in Figure 2a. The PEO1100−100%Cs data deviates most from the elastic resolution (green data), implying that it has the fastest dynamics. This is expected as PEO1100−100%Cs has the lowest ion content, and therefore the highest mobility, consistent with PEO-based SPEs in the amorphous phase10,79,80 and observations in our previous work.71,72 Because our study involves the merging and comparison of data from other QENS instruments,71,72 and to allow for the possibility of using analytical fits with a stretched exponential, we perform an inverse Fourier transformation of the frequency (energy) domain data to the time domain. In the time domain, the total scattering is a product of the sample scattering and the resolution I ( Q , t ) = S ( Q , t )R (Q , t )

(3)

where τ is a characteristic time, and the stretching exponential β represents the width of the relaxation time distribution. Data Treatment. In previous work on Na ionomers, we identified two segmental relaxations and assigned them to atoms near the isophthalate group [anchor atoms] and atoms in the middle of the PEO spacer [bridge atoms].71,72 The overall dynamics is a weighted sum of these two processes S(Q , t ) = XANCHOR S(Q , t )ANCHOR + (1 − XANCHOR )S (Q , t )BRIDGE

(4)

where each S(Q,t)i is fit using eq 3 and XANCHOR is the fraction of hydrogen atoms that contribute to the anchor atom relaxation. Although most data sets required two processes, we observed two limiting cases where a single process is observed: high temperature, low ion content and high Q, in which only the fast KBRIDGE is observed (XANCHOR → 0), and low temperature, high ion content, and low Q, in which only the slow KANCHOR is observed (XANCHOR → 1). The fitting process described above was performed with data from DCS and HFBS. This includes PEO400−100%Na, PEO600−100%Na, and PEO1100−100%Na. The PEO600− 100%Li sample was measured on these instruments, but is reported for the first time here. All samples in the current study were measured on BASIS. In Figure 3, we investigate consistency between the three instruments, using the PEO600−100%Na sample as an example. The original positions of the S(Q,t) data on the y-axis for the three instruments (filled data points) do not fall in a continuous curve because they access different energy windows and thus

(2)

and sample scattering is isolated by division rather than deconvolution. The resulting self-intermediate scattering function is plotted in the time domain in Figure 2b. Widening of the quasi-elastic line in Figure 2a appears as a faster decay in the time domain, and the same trend [longer spacer lengths are faster] is observed. To describe the data in concise form, we fit the S(Q,t) decay curves to obtain a characteristic relaxation time. For this purpose we recognize that the dynamics of polymers and other soft materials often exhibit a distribution of relaxation times, rather than Debye or single relaxation. Thus, we chose the stretched exponential or Kohlrausch−William−Watts (KWW) expression81 2721

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Figure 5. The influence of ion aggregation on relaxation times and anchor atom fractions. (A) PEO400−100%M; (B) PEO600−100%M; (C) PEO1100−100%M. M = Li (black), Na (green), and Cs (red). The spatial scale is Q = 1.55 Å−1. Sample aggregates are shaded with a striped diagonal pattern. Measurements are not available for PEO400−100%Li or PEO400−100%M (M = Na/Cs) at 298 K. Samples with XANCHOR = 1 do not have bridge relaxation times.

Supporting Information, requires assuming that the Q dependence of bridge atom relaxation time is independent of ion content. For the Li and Na samples we have measured on all three instruments, this is the case. We examine the validity of this procedure by comparing τBRIDGE and τANCHOR obtained from BASIS alone to those obtained using all three instruments. As shown in Figure 4, the times extracted using BASIS alone and those extracted using the full decay are remarkably consistent. We are thus confident to apply the same methodology to the remaining samples in Table 1, which have only BASIS data. The reader is cautioned that this procedure is only applicable to these samples and is not general in nature.

the fraction of anchor atoms is larger for instruments that access longer time scales. When we allow XANCHOR to be instrument specific, fit parameters from all three instruments are consistent. Once the fit parameters are known, we can shift the data to lie on a single curve as if it were measured on a single instrument accessing the entire energy window (see Figure 3). The shifted data (unfilled symbols) is for visualization purposes only, and is independent of the fit parameters. In samples where DCS and HFBS data is not available, it is challenging to resolve the dynamics from bridge and anchor relaxations because the BASIS data alone can be described with a single process. The one process fits to the BASIS data return low values of the stretching parameter [∼0.35], from which it is clear that the data contain two processes that cannot be adequately resolved. To address the possibility of two underlying processes for samples that have only BASIS data, we have devised a procedure in which the two-process fit is mathematically connected to the one process fit of BASIS, allowing us to assign characteristic times for the two processes and the anchor atom fraction. The procedure, presented in the

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RESULTS AND DISCUSSION

The goal of this study is to observe the effect of aggregation on PEO backbone dynamics. As discussed previously, morphology varies with ion identity in the PEOx-100%M system. The Li ionomers form distinct aggregates, the Cs ionomers pair significantly, and a range of ion states are present in the Na 2722

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Table 4. Fraction of Bridge Atoms (XBRIDGE) and Anchor Region Ion Content for PEOx-100%M Systems at 298, 323, and 348 Ka temp, K

sample

ether oxygens in PEO spacer

ion content

XBRIDGE

cation:EO ratio bridge|anchor

anchor region ion content

298

600-Li 600-Na 600-Cs 1100-Li 1100-Na 1100-Cs 400-Na 400-Cs 600-Li 600-Na 600-Cs 1100-Li 1100-Na 1100-Cs 400-Na 400-Cs 600-Li 600-Na 600-Cs 1100-Li 1100-Na 1100-Cs

13

0.077

25

0.04

9

0.111

13

0.077

25

0.04

9

0.11

13

0.077

25

0.04

0.06 0.07 0.05 0.32 0.25 0.31 0.01 0.03 0.28 0.26 0.22 0.53 0.50 0.55 0.18 0.24 0.45 0.45 0.45 0.61 0.63 0.65

100:1|12:1 100:1|12:1 100:1|12:1 100:1|18:1 100:1|20:1 100:1|19:1 100:1|8:1 100:1|8:1 100:1|10:1 100:1|10:1 100:1|11:1 100:1|14:1 100:1|14:1 100:1|13:1 100:1|8:1 100:1|7:1 100:1|8:1 100:1|8:1 100:1|8:1 100:1|12:1 100:1|11:1 100:1|11:1

0.082 0.082 0.083 0.054 0.050 0.053 0.124 0.124 0.104 0.101 0.096 0.074 0.070 0.077 0.133 0.143 0.133 0.131 0.131 0.086 0.092 0.095

323

348

a

Cation:EO ratios are rounded to the nearest whole number.

Figure 6. Schematics of anchor atoms around [A] aggregates, [B] multiplets, and [C] ion pairs.

ionomers.59,60 The impact of this variation on polymer dynamics is not immediately obvious, and depends on the level of cation association with ether oxygens as well as anions. For example, if cations that interact with anions do not also associate with anchor region ether oxygens, the anchor region dynamics should be fastest for pairs. If this is not the case, anchor region dynamics may be slower because of increased EO-cation association. The cation−EO interaction strength and the number of oxygen coordinations preferred by Cs, Na, and Li will also play a role In Figure 5, we present relaxation times and anchor atom fraction for all samples. Surprisingly, all dynamic parameters are independent of aggregation. We have previously observed that bridge atom relaxation times are independent of ion content above 1:100,71,72 [mole fraction is smaller but X in 1:X is smaller] suggesting that the bridge region becomes saturated with ions and further increases in ion content are accommodated by the anchor region. The invariance of bridge atom dynamics with morphology suggests that greater aggregation does not displace ions to the bridge regions. This is consistent with FTIR evidence that no single ions are present in the Na ionomers.67 It is quite unusual that anchor atom relaxation times and the anchor atom fraction are also independent of morphology, as covalent bonding constrains anchor atoms in close proximity to anions. Either the number

and interaction strength of EO-cation associations are identical, or offsetting effects are present. We first estimate the ion content of the anchor atom region. To do so, we utilize a prior observation71 that bridge ion relaxation times are invariant above overall ion contents of 0.01, leading to the conclusion that bridge atoms have an ion content of 1:100. This observation was made for Na ionomers, for which we performed a comprehensive study of ion content on dynamics. We assume this assumption is also valid for Li and Cs ionomers, as the available data on ion content [400, 600, and 1100 molecular weight spacers for Cs at 323 and 348 K; 600, and 1100 molecular weight spacers for Li at all temperatures] suggests that it still holds. We use this assumption in combination with the fractions of bridge and anchor atoms to determine the anchor region ion contents based on a method previously reported.72 We summarize the results in Table 4. Although it depends on given spacer length (which changes overall ion content) and temperature (which changes the fraction of bridge atoms), the anchor region ion content is invariant to cation identity. We can use the dynamic data, in combination with observations from small angle scattering,59,60 to develop a working schematic of the morphologies of ion pairs, multiplets, and larger aggregates. From scattering, we know that the aggregates are not spherical, that aggregates dominate the Li 2723

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pairs, multiplets and a six-cation aggregate, based on linear morphology are presented in Figure 6. In the linear morphology, the fractions of anchor atoms are roughly equal because all cations are exposed to the surrounding polymer rather than sequestered between anions. One exception to the linear shape is the quadruple ion [B], in which the linear and square forms are equally exposed. This is confirmed from simulations, in which both shapes are observed.82 The schematics in Figure 6, allow for the possibility of increased EO coordination for end cations. This coordination must involve primarily the same spacer [no change in crosslinking with aggregate size] and not recruit significantly more EO [no change in anchor atom relaxation time with aggregate size]. The cation radii increases in the order Li < Na < Cs, causing the binding energies (to both anion and EO) to decrease in the order Li > Na > Cs. As a result, the preferred EO (or Os, we define Os as an oxygen in the SO3 group) coordination is smallest for Li [4−5 EO or Os] and largest for Cs. Because there are three Os on the anion, it is likely that the cations in ion strings associate with two Os from one anion neighbor, and one Os from the anion on the opposite side. This provides three associations per cation, leaving 1−2 from EOs that border the string. Larger cations like Cs prefer the increased number of EO coordinations possible with pairs, and may provide the driving force behind the pair dominated morphology of the Cs ionomer. Thus, the more plentiful but weaker Cs-EO interactions balance the less plentiful but stronger Li−EO interactions. It is useful to understand what allows aggregates to be conductive. We have recently reported a mechanism in which string-like aggregates assist conductivity by promoting charge transport in excess of ion transport.66 The mechanism is similar in spirit to the Grotthus mechanism for proton transport,83,84 and occurs when a cation joins a string followed by another cation leaving from the opposite end. The simulation for which this was observed [PEO600−100%Na] has significantly higher single ion content [35%] than is suggested for the corresponding experimental system, and does not require two relaxations to describe calculated self-intermediate scattering functions, although atom mobility does vary along the spacer as suggested by bridge and anchor regions. Our observations of bridge and anchor atom movement are consistent with this mechanism, in particular the observation that the fraction of bridge atoms is invariant to cation identity. However, the conductivity remains controlled by anchor relaxation time, [Figure 7] presumably because ions leaving through an aggregate-assisted mechanism must still penetrate the anchor region prior to joining another aggregate. If this is the case, complete decoupling of ion and polymer motion could occur if string-like aggregates become percolating. In the samples we investigate here, the highest level of aggregation [regardless of cation identity] occurs at the highest temperature [348 K]. We note that at this temperature, the long relaxation times cause a smaller drop in conductivity than similar anchor relaxation times in 298 and 323 K. At a EO:cation ratio of 14:1, the highest ion contents in this investigation are less than the more common PEO/salt electrolytes. We have not studied samples with higher ion content because the sharp drop in conductivity suggested this would not be useful. The results presented here suggest that higher ion contents may improve, rather than hinder, conductivity.

Figure 7. Conductivity12,13 vs anchor atom relaxation time (Q = 1 Å−1) for PEO600-Y%Na [connected blue cross], PEOx-Li [black], PEOx-Na [green] and PEOx-Cs [red] for spacer lengths 400 [circles], 600 [squares], and 1100 [triangles] at (a) 298, (b) 323, and (c) 348 K.

system at all temperatures, pairs dominate the Cs ionomer at all temperatures, and a range of aggregation states are present in the Na ionomer with a shift toward larger ionomers above 350 K. Both FTIR67 and dielectric relaxation27 data suggest that few, if any single ions are present, consistent with the low bridge ion content [1%] deduced from QENS. From the present data, we know that the anchor fractions of pair dominated [Cs], aggregate dominated [Li], and a range of aggregate types [Na] are similar. Physically, this means that the fraction of the PEO spacer associated with pairs or aggregates does not vary with aggregate size. Because we observe little variation anchor relaxation times with cation identity, the dynamics of the anchor region hydrogen atoms are also insensitive to aggregate size. This suggests that the extent and strength of polymer−cation−polymer interactions do not vary with aggregate size, unless they cancel one another. Molecular dynamics simulations64−66 suggest that ion aggregates are string like, which is consistent with all the present data. Schematics of 2724

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CONCLUDING REMARKS This paper is the third and final paper describing the polymer dynamics in PEO-based ionomers, where the anion is attached to the solvating PEO spacer via an isophthalate group. These contributions, 7 1 , 7 2 and others on the same systems27−29,69,70,85,86,64−68 suggest that their conduction differs from the majority of the SPE literature. Despite the negligible fraction of cations solvated by the PEO spacer and the predominance of aggregated ions, the conductivity equals that of PEO/salt SPEs when transformed to cation conductivity via the transference number. These aggregates may be highly conductive, but separated by the sluggish anchor regions of the PEO spacer. New design criteria for SPEs may be to promote high aspect ratio aggregates while keeping ion content high enough that they form percolated networks. Such a system, if achieved, would decouple ion dynamics from polymer dynamics and enable tuning of each to deliver highly conductive polymer membranes with the mechanical strength required to prevent dendrite formation.

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ASSOCIATED CONTENT

S Supporting Information *

Details of how the corresponding data was resolved to the constituent bridge and anchor atom relaxations, for samples that have been measured only on BASIS.This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*(J.M.) E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the Department of Energy, Office of Basic Energy Sciences, under Grant No. DEFG02-07ER46409. The authors gratefully acknowledge Shichen Dou, Dan King, and Greg Tudryn for ionomer synthesis and dialysis. We also thank Scott Milner, Michael Janik, Ralph Colby, Jim Runt, Karen Winey, and Karl Mueller for helpful discussions. This work utilized facilities supported in part by the National Science Foundation under Agreement No. DMR-0454672. We acknowledge the support of the National Institute of Standards and Technology, U.S. Department of Commerce, in providing the neutron research facilities used in this work.

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