Estimating and Comparing the Electrical Properties of a Homologous

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Estimating and Comparing the Electrical Properties of a Homologous Series of Polyethylene Carbonate and Polyester Copolymer Electrolytes Lee P. McMaster Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b02846 • Publication Date (Web): 02 Oct 2017 Downloaded from http://pubs.acs.org on October 3, 2017

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Industrial & Engineering Chemistry Research

Estimating and Comparing the Electrical Properties of a Homologous Series of Polyethylene Carbonate and Polyester Copolymer Electrolytes Lee P. McMaster* 215 S. Ocean Grande Drive, #201, Ponte Vedra, FL 32082 Abstract

A pseudo chemical equilibrium model has been used to estimate and compare the glass transition temperatures and ionic conductivities of solid polymer electrolytes (SPE’s) made with amorphous aliphatic ether-containing polyethylene carbonate and polyester copolymers. Model parameters were estimated using experimental data from prior studies for three polyethylene carbonate and three polyester copolymer SPE’s and then extended to other SPE’s within each homologous series. The estimated properties are compared and generally agree with available published experimental data over a range of copolymer compositions with LiFSI and LiTFSI. Simple models using available data for the lithium ion transference number of the polyethylene carbonate copolymer SPE’s were also developed. Results from the models are used to estimate and compare the balance of electrical properties for this range SPE’s with polyethylene oxide with LiTFSI at low salt concentrations and with polyethylene carbonate with LiFSI at high salt concentrations over a range of temperatures.

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Introduction Solid polymer electrolytes (SPE) based on polyethylene oxide (PEO) have been extensively investigated over the past two decades in an attempt to capture advantages in safety and design flexibility compared with liquid based electrolytes. Although systems using PEO-based SPE’s have attractive low glass transition temperatures, PEO crystallization below 60⁰C reduces ionic conductivity significantly without structural modification to retain an amorphous SPE. In addition, amorphous systems using PEO at low salt concentrations suffer from low lithium ion transference numbers (tLi+) generally below 0.25 under typical use conditions. These deficiencies have led to a sustained academic research effort to understand the underlying transport mechanisms which control electrolyte performance and to develop new materials which capitalize on these understandings. The goal of this paper is to utilize results from this research to suggest some practical engineering-based methods for correlating, estimating and comparing the performance of homologs within classes of these newer SPE’s. The Tominaga group1,2,3 has pioneered one approach, the use of amorphous polyethylene carbonate (PEC) at high salt concentrations, generally referred to as a “polymer in salt” system. Although many different polymer hosts can be utilized in this way, PEC is particularly effective in spite of its relatively high glass transition temperature (Tg = 20⁰C compared with a Tg = 65⁰C for PEO). PEC is made directly from inexpensive raw materials, CO2 and ethylene oxide, and is miscible with fluoro and perfluoroalkyl disulfonyl imide based lithium salts such as bis(fluorosulfonylimide) (LiFSI), bis(trifluoromethylsulfonylimide) (LiTFSI) and bis(perfluoroethylsulfonylimide) (LiBETI) over broad composition and temperature ranges.


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Furthermore, the fundamental mechanism of lithium ion conduction at high salt concentrations in PEC is thought to be facilitated by salt anion aggregates which lead to relatively weak complexes of lithium ions with carbonyl oxygens in PEC4,2,3 in contrast to PEO where very strong iondipole interactions lead to a crosslinked-like structure involving lithium ions and ether oxygens over broad range of salt concentration. Figure 1 compares the estimates of Tg and ionic conductivity at 60⁰C of a PEC (containing 4.8 mole % EO) and of PEO vs. LiFSI weight fraction. Although one paper noted a small increase in Tg for PEC at low salt concentrations4, others have observed a monotonic decrease of Tg with increasing salt concentration, displaying no apparent effect of lithium ion-carbonyl oxygen complexes on Tg. The Tg’s of the pure salts cannot be measured experimentally because they are crystalline, but their “intrinsic” Tg’s can be inferred by extrapolation to a 1.0 salt weight fraction. Experimental results from the Tominaga group show that the measured Tg’s of PEC’s with LiFSI containing small amounts of EO in the backbone are quite sensitive to EO levels between 1 and 5 mole % EO (Supporting Information). The experimental data used in this study are from Tominaga, Nanthana and Tohyama1 for a PEC containing 4.8 mole % EO with LiTFSI and from Tominaga and Yamazaki2 for the same PEC composition with LiFSI. The Tg’s of both SPE’s can be fitted with the Fox equation;

= + ,

(1)

using their experimentally measured Tg for this PEC of 290 K (17⁰C) with a Tg =205 K (68⁰C) for LiTFSI (R2 = 0.966) and a Tg = 211 K (-62⁰C) for LiFSI (R2 = 0.9996). In this equation, wi represents component weight fraction and pure component glass transition

temperature.


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On the other hand, the Tg of PEO initially increases with salt concentration due to the strong lithium ion-ether oxygen dipole interactions before reaching a maximum (Tg,max) and subsequently decreasing as the concentration of lithium ion-ether oxygen complexes decreases and plasticizing effect of the FSI- anion increases.

Figure 1

Estimates of Tg and Ionic Conductivity (Log (σ (S/cm)) at 60⁰C) for

Polyethylene Carbonate (4.8 mole % EO) and Polyethylene Oxide with LiFSI The vertical dashed lines in Figure 1 segment the lithium salt concentration into three zones to aid in interpreting changes in ionic conductivity. At very low salt concentrations (left of dashed vertical red line), both the PEC and PEO SPE’s are starved for lithium ions so that the full benefit of polymer and lithium ion coordination cannot be achieved; i. e., there are simply too few lithium ions available to take full advantage of the coordination potential of the available carbonyl oxygens of the PEC or the ether oxygens of the PEO. In this zone, ionic conductivity


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increases with salt concentration, even though for the PEO SPE, Tg is also increasing. However, above a critical salt concentration to the right of the red dashed line and to the left of the black dashed line, the crosslinking impact of the strong lithium ion-ether oxygen complexes leads to a reduction in ionic conductivity (starting at Log (σmax)) for the PEO SPE. The ionic conductivity of the PEC SPE, in contrast to the PEO SPE, continues to increase in this low salt zone, consistent with its monotonically decreasing Tg. At sufficiently high salt concentrations, the ionic conductivities of both systems increase as the impact of the lithium ion-ether oxygen complexes subsides for the PEO SPE’s and the plasticizing impact of the FSI- anion dominates for both polymers. This zone is shown as the high salt concentration zone in Figure 1. At very high salt concentrations, the ionic conductivities of both SPE’s converge toward an implied “intrinsic” conductivity of the pure salt. However, the pure salts are crystalline solids below 100⁰C; so, these intrinsic conductivities represent upper limits which cannot be reached. For PEC, these SPE’s are reported to remain single phase up to at least 0.80 LiTFSI or LiFSI weight fraction1,2. Of these three sulfonyl imide salts with PEC, the LiTFSI SPE yields the highest ionic conductivity at low salt concentrations (20 weight percent) whereas the PEC/LiFSI SPE yields the highest ionic conductivity at high salt concentrations (80 weight percent) (Supporting Information). Furthermore, the lithium ion transference numbers for PEC based SPE’s are relatively high (tLi+> 0.5) for both LiTFSI and LiFSI at higher salt concentrations. Although longer chain polyalkylene carbonates possess lower glass transition temperatures than PEC, the work of Sun and co-workers5 with polytrimethylene carbonate with LiTFSI shows, compared with PEC with LiTFSI, this polyalkylene carbonate has a slightly lower ionic conductivity at a low salt concentration of about 0.20 LiTFSI weight fraction. At much higher


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salt concentrations between 0.5-0.6 LiTFSI weight fractions, glass transition temperatures begin to increase, perhaps indicating a loss of complete salt miscibility. Ionic conductivities begin to decrease with salt concentration at roughly 0.25 LiTFSI weight fraction, and at 0.6 LiTFSI weight fraction, conductivity at 60⁰C is lower than that of PEC with LiTFSI by more than factor of 100X (Supporting Information). However, ionic conductivities at very high LiTFSI concentrations were not investigated. Nor have use of LiFSI or incorporation of aliphatic ether groups into these polymers been reported. Recently, Pesko and coworkers6 have presented ionic conductivity results for LiTFSI-based SPE’s with two types of amorphous aliphatic polyester copolymers containing ether oxygens. Interestingly, they found, contrary to the PEC SPE’s, that the ionic conductivity of a polyester (polypropylene glutarate) SPE which contains only carboxyl groups (excluding end groups) behaves qualitatively like PEO rather than PEC, with an initial increase in ionic conductivity with increasing LiTFSI concentration followed by a leveling off and small decrease beyond the lithium ion starved zone. Furthermore, the computational and experimental results of an earlier study by Webb, Jung, Pesko and co-workers7 at very low salt concentrations show, in contrast with aliphatic polycarbonates, that the carbonyl oxygens of these polyesters behave similar to the ether oxygens of PEO in forming strong complexes with lithium ions. Furthermore, Webb and coworkers found the alkoxyl oxygens of the polyesters are excluded from the primary solvation shell of the lithium ions and do not participate in the range bonding motifs revealed by molecular dynamic modeling. The Tominaga group also investigated a range of polyethylene carbonate-based copolymer SPE’s prepared by copolymerizing CO2 with glycidyl ethers8,9,10. Their work covers a broad range of lithium salt concentrations (LiFSI), including the high salt concentration zone where


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PEC excels as an SPE. The results from the work of these two groups provide the data to develop models which allow estimation and comparison of the Tg’s and ionic conductivities of a homologous series of aliphatic ether containing polyethylene carbonate and of similarly structured polyester copolymer SPE’s with LiFSI and LiTFSI. Using Tg to Estimate the Ionic Conductivity of Polyethylene Carbonate and Polyester Copolymer SPE’s Figure 1 shows that there is a unique relationship between ionic conductivity and Tg for PEC with LiFSI since the former increases continuously with salt concentration whereas the latter decreases continuously. This is not true for PEO, 100% polyesters or aliphatic ether containing side chain polyethylene carbonates and polyesters where there may be two or three compositions which have the same Tg with potentially different conductivities. Focusing on the composition range beyond the lithium ion starved zone, Figure 2 illustrates conceptually two potential types of dependence of ionic conductivity on Tg. The dashed lines in this figure illustrate a system such as PEO with LiTFSI where the ionic conductivity at any Tg is higher at low salt concentrations than it is at high salt concentrations. As the salt concentration increases starting at the point where the system is no longer lithium ion starved (red dashed vertical line in Figure 1), the short dashed line in Figure 2 illustrates a decreasing ionic conductivity as Tg increases until reaching a minimum at Tg,max (black vertical dashed line in Figure 1). On further increases in salt concentration (long dashed line), Tg decreases while ionic conductivity increases until the salt saturation concentration limit is reached. The solid line illustrates the unique situation where there is symmetry between high and low salt concentrations such that the two dashed lines of ionic conductivity vs. Tg collapse into a singular dependence similar to that of PEC.


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Figure 2

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Conceptual Illustration of the Dependence of Ionic Conductivity on the Tg of

the SPE. Arrows reflect Direction of Increasing Lithium Salt Concentration. Morioka, Ota and Tominaga10 have measured the Tg and ionic conductivity of amorphous polyethylene carbonates with side chain aliphatic ether groups as a function of LiFSI concentration. Using their terminology (Chart 1), PEtGEC corresponds to EO/CO=1, PME1C to EO/CO=2 and PME2C to EO/CO=3 ether oxygens (EO) per carbonyl oxygen (CO) in the main chain.


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Chart 1

Structures of Aliphatic Ether Side Chain Polyethylene Carbonates, using the

same Designations and Adapted with Permission from Morioka, Ota and Tominaga10. Copyright 2016 Elsevier.

They found that the Tg’s of these SPE’s increase initially with LiFSI concentration following a relationship similar to PEO, before falling with further increases. The explanation for this behavior, as with PEO, is that the strong complexation of lithium ions with ether oxygens dominates at low LiFSI concentrations whereas the plasticizing effect of the FSI- anion dominates at high LiFSI concentrations. Their conductivity data at 60⁰C, along with the conductivity results for PEC (4.8% EO) with LiFSI2, are plotted as Log (σ) vs. Tg in Figure 3. Excluding the two enclosed data points, these side chain copolymers follow a linear, symmetrical relationship as illustrated by the solid line in Figure 2; i.e. Log σ = +

(2)


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and are constants with dimensions consistent with the variables shown and unique to the range of SPE’s for which they were correlated. The two enclosed data points for PEtGEC deviate from that symmetrical behavior at higher Tg but return to the correlation at lower Tg, both for low and high salt concentrations. The cause of this deviation from the correlation for the two enclosed data points (PEtGEC at a molar ratio of Li/(EO+CO) of 0.2 and 0.3) is uncertain but may be related to the higher methylene/methyl group per ether oxygen ratio of this copolymer. This copolymer also exhibits a surprisingly high fraction of weakly interacting carbonyl groups at lower Li/(EO+CO) molar ratios10. In any case, these two data points, which only impact low conductivity systems, were excluded from the dashed line correlation shown in Figure 3. The use of these linear correlations also closely follows predicted ionic conductivity values at 60⁰C from the Vogel-Tammann-Fulcher (VTF) equation for available individual temperature scans at different LiFSI concentrations for both the side chain copolymers and for PEC (Supporting Information). Note also that the ionic conductivities of PEC and the side chain copolymers converge to identical ionic conductivities at Tg = -62⁰C, the intrinsic Tg of LiFSI from the use of the Fox equation for this PEC and LiFSI. This ionic conductivity (1.7 X 10-3 S/cm at 60⁰C) at Tg = -62⁰C corresponds to the “intrinsic” conductivity of LiFSI.


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Figure 3

Logarithm of Ionic Conductivity at 60⁰C vs. Glass Transition Temperature

for PEC (4.8 mole % EO) and Polyethylene Carbonates with Aliphatic Ether Side Chain Groups with LiFSI. Data for PEC from Tominaga and Yamazaki2 and for Polyethylene Carbonates with Side Chain Groups from Morioka, Ota and Tominaga10. A similar approach was applied to the polyester copolymer data of Pesko and coworkers6. Using their terminology, Pesko evaluated the polyesters in Chart 2 with LiTFSI over a broad range of temperatures with LiTFSI concentrations in a range from near zero to about 30 weight %.


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Chart 2

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Polyester Chemical Structures using the same Designations and Adapted

with Permission from Pesko, Jung, Hasan, Webb, Coates, Miller III & Balsara6. Copyright 2016 Elsevier.

The majority of their data were measured in the lithium ion starved zone; however, their results do include ionic conductivities at the transition between this zone and the low salt concentration zone (see Figure 1). Their data do not extend into the high salt concentration zone. In this paper, it is assumed that all of these polyester SPE’s remain single phase and homogeneous in both the low and high salt concentration zones. Using their experimental VTF equation parameters at the terminus of the lithium ion starved zone, their data are shown in Figure 4 along with data for PEC (4.8% EO) with LiTFSI at 60⁰C. The PEC data imply an intrinsic ionic conductivity at 60⁰C of 1.0 X 10-4 S/cm, roughly 17X lower than that of PEC with LiFSI. With the exception of PEO and Polyester 2b, the data for the other polyesters follow a linear relationship of Log (σ) vs. Tg. For this study, the assumption has been made that Log (σ) vs. Tg correlations for the individual SPE’s in the low salt concentration zone (see Figure 2) follow the same linear relationship that the homologous series of polyesters follows at the terminus between the lithium ion starved zone and the low salt concentration zone. However, these data do not converge to


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the intrinsic Tg of LiTFSI. Rather the slope of this low salt concentration relationship is nearly the same as that of PEC with LiTFSI. This observation implies that Log (σ) for polyester SPE’s are nonsymmetrical about Tg,max (black dashed lines in Figure 4 follow the same trend as the dashed lines of Figure 2). Assuming the polymer-salt mixtures remain homogeneous and a linear relationship also exists between Log (σ) vs. Tg at high salt concentrations, the ionic conductivity should converge to the intrinsic conductivity of LiTFSI at its intrinsic Tg = -68⁰C. An example of this type of relationship is shown for Polyester 1a (long dashed line) in Figure 4. The ionic conductivities of the PEO and Polyester 2b SPE’s are displaced upward by ∆ Log (σ (S/cm) @ 60⁰C) ≈ 0.5 compared with the other polyester SPE’s. These higher conductivities are consistent with the results of Pesko6, although they also found similar behavior using their methodology for Polyester 1b whereas the ionic conductivity of this SPE aligns with the other polyesters using the methodology of this study. Their experimental error bands for the ionic conductivity of Polyester 2b are much greater than those of the other polyesters, with the lower end only slightly above the linear correlation for the other polyesters shown in Figure 4. Furthermore, Webb and coworkers’ molecular dynamic simulations7 did not find any unusual behavior for this polyester compared with the others. So, it is possible that its ionic conductivity may also follow the same linear correlation as the other polyesters. But, in this study, the mean value of the ionic conductivity reported by Pesko for Polyester 2b has been retained.


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Figure 4

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Logarithm of Ionic Conductivity for PEO, the Polyesters and PEC with

LiTFSI at T = 60⁰C. Short Dashed Lines Correspond to Data at the Terminus of the Lithium Ion Starved Zone (Log (σmax)). Long Dashed Line for Polyester 1a Extends to Intrinsic Conductivity of PEC at Tg = -68⁰C. PEO and Polyester Data from Pesko, Jung, Hasan, Webb, Coates, Miller III & Balsara6 and PEC Data from Tominaga, Nanthana and Tohyama1. The coefficients and squared correlation coefficient of the assumed linear relationship for these SPE’s are shown in Table 1. It should be noted that the LiTFSI-based SPE’s with PEC and the polyesters have lower sensitivities of changes in Log (σ) with changes in Tg (coefficient ) than the LiFSI SPE’s with PEC and the side chain polyethylene carbonates.


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Table 1

Estimated Parameters for Equation 2 using Data from Tominaga and

Yamazaki2, from Morioka, Ota and Tominaga10, from Tominaga, Nanthana and Tohyama1 and from Pesko, Webb, Jung, Hasan, Webb, Coates, Miller III, and Balsara6.

For the polyesters, it is assumed that their ionic conductivities at high salt concentrations beyond the peak Tg (See Figure 1) are lower at any Tg than the corresponding conductivity at the same Tg at low salt concentration. Following the nonsymmetrical Log (σ) dependence on Tg shown in Figure 2 and assuming a linear relationship between Log (σ) and Tg in the high salt concentration zone above the salt concentration at Tg,max; Log σ = + ! ,

(3)

These coefficients can be computed from the values of , and ,"#$ for the polyester SPE’s in the low salt concentration zone, and from , %& and '()* %& . Here the subscript “int”, refers to the intrinsic properties of the lithium salt (LiTFSI) deduced from extrapolation of the Fox equation for the Tg correlation of PEC-LiTFSI to 100% salt concentration and the use of Equation 2 with the and for PEC with LiTFSI from Table 1. =

+, -./0 12 12 ,345 ,./0 1,345

(4)


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! = '()* %& − , %&

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(5)

Pseudo Chemical Equilibrium Model for Estimating the Tg of the SPE’s Utilization of these relationships between Log (σ) and Tg requires estimation of the SPE Tg as a function of changes in the type of lithium salt, salt concentration and changes in the chemical structure of the polymer in the SPE. Based on the analyses and explanations of Morioka10 and of Webb7, a pseudo chemical equilibrium model is proposed which assumes that 1/Tg of the copolymer electrolyte follows the Fox equation for the plasticizing effect of FSI- or TFSI- anions balanced by components proportional to the concentration of lithium ion complexes with ether oxygens and with carbonyl oxygens in the polymers, raising the Tg;

=

+

− 78'9 : ;?'9 : are constants, 8'9 : ; (13)

In order to match the PEO SPE σmax, this constant is set at 5.32X10-4 (K-1) for the LiFSI-based copolymer SPE’s and at 3.82X10-4 (K-1) for the LiTFSI-based copolymer SPE’s. These values were used for the side chain copolymers in Chart 1, except for lowest EO content polyethylene carbonate (PEtGEC) where > = 0 and 78'9 : ;

Estimating and Comparing the Electrical Properties of a Homologous

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