Miscible Polyether/Poly(ether-acetal) Electrolyte Blends

Article abstract of DOI:10.1021/acs.macromol.0c00747

This study shows that it is possible to obtain homogeneous mixtures of two chemically distinct polymers with a lithium salt for electrolytic applications. This approach is motivated by the success of using mixtures of organic solvents in modern lithium-io

Full text of DOI:10.1021/acs.macromol.0c00747

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Article
Miscible Polyether/Poly(ether−acetal) Electrolyte Blends
Kevin W. Gao, Whitney S. Loo, Rachel L. Snyder, Brooks A. Abel, Youngwoo Choo, Andrew Lee,
Susana C. M. Teixeira, Bruce A. Garetz, Geoffrey W. Coates,* and Nitash P. Balsara*
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ABSTRACT: This study shows that it is possible to obtain
homogeneous mixtures of two chemically distinct polymers with a
lithium salt for electrolytic applications. This approach is
motivated by the success of using mixtures of organic solvents in
modern lithium-ion batteries. The properties of mixtures of a
polyether, poly(ethylene oxide) (PEO), a poly(ether−acetal),
poly(1,3,6-trioxocane) (P(2EO-MO)), and lithium bis(trifluoro-
methanesulfonyl)imide (LiTFSI) salt were studied by small-angle
neutron scattering (SANS) and electrochemical characterization in
symmetric cells. The SANS data are used to determine the
miscibility window and quantify the effect of added salt on the
thermodynamic interactions between the polymers. In the absence
of salt, PEO/P(2EO-MO) blends are homogeneous and
characterized by attractive interactions, i.e., a negative Flory−Huggins interaction parameter, χ. The addition of small amounts
of salt results in a positive effective Flory−Huggins interaction parameter, χeff, and macrophase separation. Surprisingly, miscible
blends and negative χeff parameters are obtained when the salt concentration is increased beyond a critical value. The electrochemical
properties of PEO/P(2EO-MO)/LiTFSI blends at a given salt concentration were close to those obtained in PEO/LiTFSI
electrolytes at the same salt concentration. This suggests that in the presence of PEO the electrochemical properties exhibited by
P(2EO-MO) chains are similar to those of PEO chains. This work opens the door to a new direction for creating new and improved
polymer electrolytes either by combining existing polymers and salt or by synthesizing new polymers with the specific aim of
including them in miscible polymer blend electrolytes.
empirical formulas CH2) is negligible.4,5 The reason for this
INTRODUCTION
■
is well established: mixing is usually promoted by entropic
There is considerable interest in replacing flammable organic
considerations. The entropic gain of mixing polymers with
solvents with nonvolatile polymers in rechargeable lithium
long chains, however, is orders of magnitude smaller due to the
batteries. It has long been recognized that high dielectric
connectivity of the monomers.
constant and low viscosity are necessary for rapid ion transport
The purpose of this paper is to demonstrate that it is
in liquid electrolytes. In the case of lithium-ion batteries
possible to create homogeneous mixtures of polymers with
designed to operate at room temperature, this is achieved by
different polarities to create a new type of material for use in
blending materials. Ethylene carbonate has a dielectric
lithium batteries: miscible polymer blend electrolytes.
constant of 89.8 but is a solid at room temperature (mp =
Our system of interest is a blend of a polyether,
36.4 °C) while dimethyl carbonate is a low-viscosity liquid
poly(ethylene oxide) (PEO), a poly(ether−acetal), poly-
(mp = 4.6 °C) but has a dielectric constant of 3.1.1 Neither is a
(1,3,6-trioxocane) (P(2EO-MO)), and lithium bis(trifluoro-
suitable solvent for electrolytic applications. However, a blend
methanesulfonyl)imide (LiTFSI) salt (see Figure 1). PEO has
of ethylene carbonate and dimethyl carbonate is an excellent
been thoroughly studied as a potential electrolyte for lithium
solvent for these applications and is a major component of
batteries due to its nonvolatility, electrochemical stability, and
lithium-ion battery electrolytes.
Translating the notion of liquid electrolyte mixtures to
polymer electrolyte blends is nontrivial. While most low molar
compatibility with lithium salts.6−8 The ability of PEO to
Received: March 30, 2020
Revised: June 5, 2020
mass liquids are miscible with each other (e.g., polar molecules
like ethanol are miscible in nonpolar liquids such as hexanes),
finding pairs of miscible polymers is extremely rare.2,3
Polymers with seemingly minor differences in monomer
structure are entirely immiscible. For example, the solubility
of polyethylene in polypropylene (both polymers have
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Table 1. Molar Masses and Dispersities of Homopolymers
Used in This Study
polymer
Mn (kg mol−1
)
Đ
PEO
dPEO
P(2EO-MO) sample 1
P(2EO-MO) sample 2
P(2EO-MO) sample 3
P(2EO-MO) sample 4
35.0
35.0
26.1
26.7
16.0
55.2
1.08
1.09
1.83
1.66
1.76
1.97
Table 2. Polymer Components of Blends Used in Each
Experiment
Figure 1. Chemical structure of poly(ethylene oxide) (PEO),
poly(1,3,6-trioxocane) (P(2EO-MO)), and lithium bis(trifluoro-
methanesulfonyl)imide (LiTFSI).
experiment
component 1
component 2
DSC and electrochemistry
SANS
SANS
PEO
dPEO
dPEO
P(2EO-MO) sample 1
P(2EO-MO) sample 2
P(2EO-MO) sample 3
dissolve lithium salts is due to the presence of oxygen-
containing ether linkages. The properties of P(2EO-MO)/
LiTFSI electrolytes were reported in ref 9. We expect P(2EO-
MO) to be more polar than PEO due to the increased
concentration of ether and acetal oxygens. Ternary blends with
polymer components of different polarities have been
discussed as a means for improving ion transport in a recent
theoretical paper by using a coarse-grained bead−spring
model.10
In this work, we demonstrate that PEO is miscible with
P(2EO-MO) in the neat, salt-free, state. We have also
identified a range of salt concentrations over which PEO/
P(2EO-MO)/LiTFSI blends remain miscible. We use the term
conventional polymer electrolytes to refer to binary mixtures of a
polymer and a salt such as PEO/LiTFSI or P(2EO-MO)/
LiTFSI. We use the term polymer blend electrolyte to refer to
ternary mixtures of two distinct polymers and a salt. The
thermodynamic properties of PEO/P(2EO-MO)/LiTFSI were
determined by small-angle neutron scattering (SANS) experi-
ments. The SANS results are consistent with phase behavior
inferences based on differential scanning calorimetry (DSC)
experiments. Ion transport in the polymer blend electrolytes is
compared with that obtained from conventional polymer
electrolytes (PEO/LiTFSI and P(2EO-MO)/LiTFSI) by using
both blocking and nonblocking electrodes.
stir bar. Then, BF3·OEt2 (0.130 mL, 0.02 equiv) was added
instantaneously, and the flask was sealed with a rubber septum. The
reaction gelled after 30 min such that stirring ceased, and the solution
gradually turned pink. After 1 h, the reaction was removed from the
glovebox and quenched with a 1:1 mixture of acetonitrile:water (40
mL) to give a clear, colorless solution. The crude mixture was
extracted with CH2Cl2 (30 mL × 3), dried with Na2SO4, filtered, and
rotovapped until reaching a total volume of ∼30 mL. The polymer
was then precipitated into hexanes (400 mL), redissolved in CH2Cl2
(30 mL), and precipitated again into cold isopropanol (400 mL) to
give a white solid. The polymer was dried under high vacuum
1
overnight. Typical yields ranged from 50 to 60%, and H and 13C
NMR analyses suggest that the polymerization proceeds with
excellent regioregularity. Notably, polymerization is initiated by
adventitious water in the reaction mixture. Furthermore, monomer
conversion is highly dependent on monomer concentration and
reaction temperature. Therefore, molar mass is difficult to control in
this system, and variance was expected across multiple batches.
Sample 1: Mn = 26.1 kg mol−1, Đ = 1.83. Sample 2: Mn = 16.1 kg
mol−1, Đ = 1.76. Sample 3: Mn = 26.7 kg mol−1, Đ = 1.66. Sample 4:
Mn = 55.2 kg mol−1, Đ = 1.97. Tg = −66 °C, Tm = 39 °C. Spectral data
matched that previously reported in ref 9. 1H NMR (500 MHz,
CDCl3): δ 4.74 (s, 2H), 3.69 (m, 8H) ppm. 13C NMR (125 MHz,
CDCl3): δ 95.73, 70.60, 67.02 ppm.
Polymer Blend Electrolyte Preparation and Composition.
The molar masses, Mn, and dispersities, Đ, of PEO (Polymer Source),
deuterated PEO (dPEO) (Polymer Source), and P(2EO-MO)
(synthesized as described above) used in this study are summarized
in Table 1.
Electrolytes used for SANS experiments were made up of blends of
dPEO, P(2EO-MO) (Mn = 26.7 or 16.0 kg mol−1), and LiTFSI, while
electrolytes for DSC and electrochemical experiments were made up
of blends of PEO, P(2EO-MO) (Mn = 26.1 kg mol−1), and LiTFSI
(see Table 2). Electrochemical measurements were also performed on
conventional polymer electrolytes of P(2EO-MO) (Mn = 55.2 kg
mol−1) with LiTFSI. All polymers were dried in a glovebox
antechamber under vacuum at 90 °C for at least 24 h prior to use.
LiTFSI was dried under vacuum at 120 °C for at least 72 h.
The polymer composition of the blends was 50/50 by weight. We
denote component 1 as PEO and component 2 as P(2EO-MO). The
volume fraction of each component, on a salt-free basis, is given by
MATERIALS AND METHODS
■
Synthesis of 1,3,6-Trioxocane, (2EO-MO). Diethylene glycol
(100 g, 0.942 mol), paraformaldehyde (37 g, 1.3 equiv), poly-
(phosphoric acid) (4.0 g, 0.03 equiv), and heptane (160 mL) were
combined in a 250 mL flask fitted with a Dean−Stark adapter and
condenser. The reaction was stirred at 115 °C for 12 h, and water
(∼15 mL) was collected as the bottom layer in the trap. After the
reaction mixture was cooled to room temperature, heptane was
removed via rotary evaporation to give a cloudy, viscous solution.
This oligomerized product was distilled at 150−180 °C under high
vacuum into a receiving flask cooled in a dry ice/acetone bath. The
crude mixture of diethylene glycol and 1,3,6-trioxocane was then
fractionally distilled under high vacuum at 80 °C to give clear,
colorless 1,3,6-trioxocane in 70% yield. The monomer was dried over
CaH2 for 3 days, distilled, and degassed via three freeze−pump−thaw
1
cycles. Spectral data matched that previously reported in ref 9. H
NMR (500 MHz, CDCl3): δ 4.57 (s, 2H), 3.50 (s, 8H) ppm. 13C
NMR (125 MHz, CDCl3): δ 97.91, 72.58, 70.61 ppm. HRMS
(DART-MS): m/z calculated for C5H10O3 [H]+ 119.0703; found
119.0703.
w1
ρ
+
1
ϕ1 =
w1
1
w2
ρ2
ρ
(1)
(2)
Synthesis of Poly(1,3,6-trioxocane), P(2EO-MO). In a glove-
box under a N2 atmosphere, 1,3,6-trioxocane (6.0 g, 51 mmol) and
CH2Cl2 (25.4 mL) were combined in a 100 mL flask equipped with a
and
ϕ2 = 1 − ϕ1
B
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Figure 2. (a) Representative DSC curves showing one Tg for a 50/50 blend of PEO (Mn = 35.0 kg mol−1) and P(2EO-MO) (Mn = 26.1 kg mol−1)
at r = 0.10 and two Tg values at r = 0.04. Arrows denote regions associated with the glass transition. (b) Tg as a function of salt concentration, r, for
each conventional polymer electrolyte system (solid blue triangles for PEO (Mn = 100 kg mol−1) and solid red triangles for P(2EO-MO) (Mn =
55.2 kg mol−1)) and the polymer blend electrolytes. Polymer blends possessing a single Tg at high r values (0.08 ≤ r ≤ 0.14) and blends exhibiting
two Tg values at low r values (0.02 ≤ r ≤ 0.06) are denoted by closed black squares and open black squares, respectively. The uncertainty of the Tg
measurements is assumed to be that of the instrument’s given calorimetric reproducibility and precision ( 0.05%). Data for PEO and P(2EO-MO)
were taken from ref 9.
where wi and ρi are the mass and density, respectively, of component i
in the blend. The volume fractions are approximately equal (see Table
3). The volume fraction occupied by the polymer components in the
blends containing LiTFSI is given by
Density measurements for neat P(2EO-MO) at 90 °C were taken
by measuring the mass of electrolyte within a known volume,
following procedures described previously.11 The average of three
density measurements (ρ2 = 1.32
subsequent calculations.
DSC Sample Preparation and Experiments. Samples (∼10
mg) were hermetically sealed in aluminum pans in an argon glovebox.
DSC experiments were run with two heating and cooling cycles at a
heating rate of 20 °C min−1 and a cooling rate of 5 °C min−1 using a
Thermal Advantage Q200 calorimeter at the Molecular Foundry,
Lawrence Berkeley National Lab. The temperature ranged from −80
to 120 °C. The glass transition temperature (Tg) values are obtained
from analysis of the second heating run.
SANS Sample Preparation and Experiment. Sample prepara-
tion for SANS experiments was conducted following procedures
outlined previously.12 The blends were made such that the volume
fractions of each component were ∼0.5 (see Table 3).
0.04 g cm−3) was used for
w1
w2
+
ρ
ρ
w1 1 w2 2 w
ϕ
=
polymer
salt
+
+
ρ
ρ2
ρ
(3)
1
salt
where wsalt is the mass of LiTFSI in the blend and ρsalt = 2.023 g
cm−3.11 Volume changes of mixing are ignored in our analysis.
We assume that the salt is uniformly distributed in the blend. The
salt concentration of the blends was quantified by the molar ratio of Li
atoms in the salt to O atoms in the polymers (r = [Li]/[O]),
calculated as follows:
w
salt
Msalt
SANS experiments were conducted on the NG7SANS beamline at
the National Institute of Standards and Technology Center for
Neutron Research.13 Measurements were performed with a neutron
wavelength of 6 Å and up to three sample-to-detector distances
(SDDs) of 13, 4, and 1 m. The shortest, 1 m distance, was used with a
detector offset of 25 cm to extend the scattering angle (2θ) attainable.
Overall, the three configurations allowed for access to a scattering
r =
w1
MEO
3w2
+
M2EO‐MO
(4)
where MEO is the monomer molar mass of PEO (MEO = 44.05 g
mol−1), M2EO‑MO is the monomer molar mass of P(2EO-MO)
(M2EO‑MO = 118.1 g mol−1), and Msalt is the molar mass of LiTFSI
(Msalt = 287.1 g mol−1). A factor of 3 was included as 2EO-MO
contains three oxygen atoms, while EO contains one oxygen atom per
monomer, as shown in Figure 1.
The volume fraction of PEO and the LiTFSI associated with PEO
in the polymer blend electrolytes, f, is estimated via the following
equation:
4π
wave-vector magnitude, q = sin(θ), ranging from 0.03 to 5.5 nm−1.
λ
The neutron beam size was defined by a 9.5 × 10−3 m aperture. Data
were collected at 10 °C increments between 60 and 110 °C. All
measurements were reversible and repeatable upon either heating or
cooling. Samples were equilibrated for at least 30 min at each
temperature. A 9-position Peltier cooling/heating sample changer
block was used to drive and maintain constant sample temperature.
Samples of thickness of 1 mm were used. Data were reduced by using
the software package for IGOR provided by the NIST Center for
Neutron Research.14 The total scattering intensity was corrected for
detector sensitivity, background, and empty cell contributions as well
as sample transmission and thickness.14,15
rw M
M
1
1
salt
w1 +
ρ
1
f =
rw M
3rw M
2 salt
1
salt
w1 +
w2 +
M
M
1
2
+
ρ
ρ2
(5)
1
Electrochemical Sample Preparation and Experiments.
Electrochemical sample preparation and experiments were conducted
following the procedures previously described,16 using 508 μm thick
silicone spacers and conducting the measurements at 90 °C.
Equation 5 is based on the assumption that the value of r in the PEO-
rich fluctuations is the same as that in the P(2EO-MO)-rich
fluctuations.
Electrolyte r values ranged from 0 to 0.14. All electrolyte solutions
in acetonitrile were transparent, indicating complete dispersion of all
mixture components. The electrolytes were stirred on a hot plate at 80
°C until all of the acetonitrile had evaporated and then further dried
in a glovebox antechamber under vacuum at 90 °C for 24 h to remove
any residual solvent.
RESULTS AND DISCUSSION
■
A commonly used method to determine polymer miscibility is
the measurement of the glass transition temperature, Tg, via
DSC. The existence of a single Tg is indicative of a miscible
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blend.17 Figure 2a shows DSC curves for PEO/P(2EO-MO)/
LiTFSI blends at r = 0.04 and 0.10. The r = 0.04 blend exhibits
two glass transitions (Tg1 = −46 °C, Tg2 = −38 °C) which
indicates the blend is phase separated. In contrast, the r = 0.10
blend exhibits a single glass transition (Tg = −24 °C), which
indicates that the blend is composed of a single phase. The
absence of a melting transition in the DSC data from the
higher salt blend is consistent with numerous reports in the
literature indicating that the addition of salt suppresses
crystallization of PEO.9,16,18,19 All of the thermodynamic and
electrochemical data presented in this paper were obtained
above the melting temperatures of the blends.
proportional to q−2 while I(q) is a much weaker function of
q for q < 0.4 nm−1. These features are characteristic of
scattering from a homogeneous binary polymer blend wherein
the polymer chains obey random walk statistics.21 The SANS
results regarding polymer blend miscibility are consistent with
the results obtained from DSC.
Analysis of SANS data begins with a thermodynamic model
for the polymer blend electrolytes. We start with the
thermodynamics of mixing in a two-component polymer
blend in the absence of salt. The Gibbs free energy of mixing of
a homogeneous mixture of two polymers can be described by
the Flory−Huggins theory:
Figure 2b shows the complete set of glass transition
temperatures for each polymer blend electrolyte and the
corresponding conventional polymer electrolyte taken from ref
9. In the neat blend, the Tg values of PEO and P(2EO-MO)
are too close to be distinguished by DSC. For r values between
0.02 and 0.06, the polymer blend electrolytes exhibit two Tg
values, denoted by open squares, indicating immiscibility.
However, from r = 0.08 to 0.14, the blend has a single Tg,
indicating miscibility at these higher salt concentrations. The
Tg for all systems generally increases with increasing salt
concentration. The correlation between Tg and salt loading is
attributed to the solvated ions inducing physical cross-linking
of the polymer chains.20
ϕ1 ln ϕ1
ϕ2 ln ϕ2
ΔGm
kBT
v
=
+
+ χϕ1ϕ2
N
N2
(6)
1
where ΔGm is the free energy of mixing per unit volume, kB is
the Boltzmann constant, T is the absolute temperature, ϕi is
the volume fraction of component i, Ni is the number of repeat
units in chain i, and χ is the Flory−Huggins interaction
parameter which describes the thermodynamic incompatibility
between component 1 and 2.22,23 N1, N2, and χ are based on a
reference volume, v = 0.1 nm3. A miscible blend, one that is
homogeneous down to the molecular level, requires both a
negative Gibbs free energy of mixing (ΔGm < 0) and a positive
second derivative (∂2ΔGm/∂ϕ1 > 0).17 The critical Flory−
2
The measured absolute SANS intensity, I(q), as a function
of the magnitude of the scattering vector, q, for the dPEO/
P(2EO-MO)/LiTFSI blends at 90 °C is shown in Figure 3.
Huggins interaction parameter value, χcrit, is given by the
following:
2
i
y
1 j 1
1
N2
z
j
j
j
j
z
z
z
z
χ
=
+
crit
2
N
1
(7)
k
{
Blends with χ < χcrit are predicted to be miscible, regardless of
composition.
For salt-containing mixtures, we use a simple extension of eq
6:
i
j
j
y
z
z
ϕ ln ϕ
ϕ2 ln ϕ2
ΔGm
kBT
1
1
v
= ϕ
+
+ χ ϕ ϕ
eff 1 2
j
j
j
z
z
z
polymer
N
N2
(8)
1
k
{
where ϕpolymer is the total polymer volume fraction and ϕi (i =
1 or 2) are the salt-free polymer volume fractions. The effect of
added salt is captured mainly by an effective Flory−Huggins
parameter, χeff, which depends on salt concentration. In the
limit of r → 0, ϕpolymer → 1, eq 8 reduces to eq 6, and χeff
reduces to the conventional χ parameter for polymer blends.
Following the analysis in ref 24, the absolute SANS intensity
was corrected for the contributions from scattering of the
deuterated chains as well as the contributions from the
incoherent scattering to obtain the absolute coherent SANS
intensity:
Figure 3. Measured absolute SANS intensity, I(q), vs scattering
vector, q, at 90 °C, for blends of dPEO (Mn = 35.0 kg mol−1) and
P(2EO-MO) (Mn = 26.7 kg mol−1) at varying LiTFSI salt
concentrations, r, and a dPEO/PEO sample with r = 0.10. Note
that for r = 0.02 and r = 0.06 there is an intermediate range of q that
was not recorded due to insufficient beamtime. Error bars represent
one standard deviation of the scattering data and in most cases are
smaller than the data points.
I
coh(q) = I(q) − fIdPEO/LiTFSI(q) − Iinc(q)
(9)
Also shown as a reference is a dPEO/PEO/LiTFSI blend with
volume fraction ϕ1 = 0.50 and r = 0.10 at 90 °C. Distinct
differences are apparent between the scattering profiles of
dPEO/P(2EO-MO)/LiTFSI blends with low salt concen-
trations (0.02 ≤ r ≤ 0.06) and that of the neat blend (r = 0)
and blends with high salt concentrations (r ≥ 0.08). The
blends with low salt concentration show a rapid rise in I(q) at
low q (q < 0.1 nm−1), indicative of phase separation. The neat
blend and high r-value blends have similar scattering profiles as
that of the dPEO/PEO/LiTFSI sample. In the range 0.4 < q
(nm−1) < 2, I(q) from these blends is approximately
where f is the estimated volume fraction of dPEO and LiTFSI
in our polymer blend electrolytes (f ≈ 0.5) and IdPEO/LiTFSI(q)
is the scattering from dPEO/LiTFSI mixtures taken from ref
12. Iinc(q) is the incoherent scattering background contribution
to the intensities, determined by fitting I(q) to the following
expression:
I(q) = aP(q) + b
(10)
where P(q) is a form factor given by the Debye function (see
eq 14), a is a constant scaling factor, and b is a constant
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assumed to be equal to Iinc(q).14,15,25 Figure 4 shows the
coherent SANS profiles, Icoh(q), of the miscible blends at 90
°C.
− 363) g cm−3 where T is the temperature in Kelvin.29 The
thermal expansion coefficient of P(2EO-MO) has not been
measured; it was assumed to be the same as that of PEO.
The structure factor, Sii, is given by
Sii = ϕNP(q)
(12)
i i
i
where ϕi is the volume fraction of polymer i on a salt-free basis.
coh(q) depends on three volume fractions: ϕ1, ϕ2, and
I
ϕpolymer (see eqs 11 and 12). For the blends covered in this
study, these volume fractions are listed in Table 3.
Ni is the number of repeat units in each polymer calculated
by
Mi
N =
i
ρN v
(13)
av
i
where Nav is Avogadro’s number and Mi and ρi are the polymer
molar masses (g mol−1) and densities (g cm−3) of component
i, and
Ä
É
Å
Å
Ñ
Ñ
Figure 4. SANS intensities, Icoh(q), plotted as a function of the
magnitude of the scattering vector, q, at 90 °C for the dPEO/P(2EO-
MO)/LiTFSI (P(2EO-MO) Mn = 26.7 kg mol−1) blends at the
miscible salt concentrations. Error bars represent one standard
deviation of the scattering data and in most cases are smaller than the
data points.
Åexp(−xi) − 1 + xi Ñ
Å
Å
Å
Ñ
Ñ
Ñ
P(q) = 2
i
xi2
Å
Å
Å
Ñ
Ñ
Ñ
(14)
Å
Ç
Ñ
Ö
with xi = q2Rg,i2. Both components are modeled as flexible
Gaussian chains according to
Nl 2
2
i i
Rg,i
=
The coherent scattering intensity for homogeneous PEO/
P(2EO-MO)/LiTFSI blends is calculated by using the random
phase approximation (RPA):
(15)
6
where li is the statistical segment length of each component.
The statistical segment length of PEO is l1 = 0.58 nm (based
on a 0.1 nm3 reference volume).12 The statistical segment
length of P(2EO-MO) has not been measured. In our
calculations, we assume l1 = l2 = l = 0.58α nm, where α is a
fitting parameter that accounts for differences in the statistical
segment length of PEO and P(2EO-MO) and distortions of
chains (e.g., chain stretching) in the blends.
−1
i
j
j
j
j
j
y
z
z
z
z
z
1
S11
1
S22
2
I
coh(q) = ϕ
(B − B ) v
+
− 2χeff
1
2
polymer
(11)
k
{
In our analysis, component 1 is dPEO, component 2 is P(2EO-
MO), ϕpolymer is the volume fraction of both polymer
components, dPEO and P(2EO-MO), Bi is the coherent
neutron scattering length density of component i given by Bi =
bi/νi, vi and bi are the molar monomer volumes and neutron
scattering lengths of component i, respectively, and χeff is the
effective Flory−Huggins interaction parameter between dPEO
and P(2EO-MO) both with and without salt.21,24,26−28 In the
limit q → 0, eq 11 is consistent with eq 8. The neutron
scattering lengths of dPEO and P(2EO-MO) are 4.58 × 10−12
cm and 1.32 × 10−12 cm, respectively. The molar monomer
volumes of dPEO and P(2EO-MO) were calculated in the
absence of salt (ν1 = 38.98 cm3 mol−1 and ν2 = 89.47 cm3
mol−1 at 90 °C). We assume dPEO occupies the same molar
volume as hydrogenous PEO. We thus obtain ρ1 = 1.23 g cm−3
and ρ2 = 1.32 g cm−3 at 90 °C. The temperature dependence
of monomer volumes was applied to the contrast terms, and
was determined by using the following equations: ρ1 = 1.23 −
7.31 × 10−4(T − 363) g cm−3 and ρ2 = 1.32 − 7.31 × 10−4(T
I
coh(q) values for the miscible blends were first fit to eq 11
with two adjustable parameters: α and χeff. For each blend, α
was found to be essentially invariant with temperature so α was
averaged across all temperatures and fixed. The parameter α is
greater than 1 for all blends, likely due to the increased stiffness
of P(2EO-MO) chains relative to that of the PEO chains.
These values are given in Table 3. Icoh(q) was then fit to eq 11
with only χeff as a fitting parameter. Representative RPA fits of
I
coh(q) for a dPEO/P(2EO-MO) blend with r = 0.08 are
shown in Figure 5. χeff values of −4.67 × 10−3 and 7.64 × 10−4
are obtained from the profiles at 70 °C and 90 °C, respectively.
At 110 °C, the blend is phase separated and cannot be
analyzed by RPA. Note that χeff increases with increasing
temperature.
Effective Flory−Huggins interaction parameters were
extracted by fitting Icoh(q) to RPA for all miscible blends
a
Table 3. Volume Fractions, ϕi, and α Values Used in RPA Fits of dPEO/P(2EO-MO)/LiTFSI Blends
dPEO/P(2EO-MO)/LiTFSI (dPEO Mn = 35.0 kg mol−1; P(2EO-MO) dPEO/P(2EO-MO)/LiTFSI (dPEO Mn = 35.0 kg mol−1; P(2EO-MO)
Mn = 26.7 kg mol−1
)
Mn = 16.0 kg mol−1
)
r
ϕ1
ϕ2
ϕpolymer
α
ϕ1
ϕ2
ϕpolymer
α
0
0.516
0.517
0.518
0.515
0.484
0.483
0.482
0.485
1
1.274 0.007
1.205 0.014
1.173 0.001
1.122 0.002
0.517
0.483
1
1.331 0.044
0.08
0.10
0.14
0.742
0.696
0.621
0.517
0.483
0.705
1.212 0.011
a
The errors shown correspond to one standard deviation from the temperature averaging.
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°C is larger than χcrit = 5.06 × 10−3, as expected. For r = 0.10,
we see a similarly strong dependence with temperature, and χeff
varies from −7.29 × 10−3 at 60 °C to −3.41 × 10−4 at 110 °C.
The value of A is negative and B is positive for all miscible
blends except at r = 0.14. At this concentration, A is positive
and B is negative, and there is a very weak dependence on
temperature.
Similarly, Figure 6b shows the temperature dependence of
χeff in the lower molar mass P(2EO-MO)-containing blends. At
the same salt concentration, the temperature dependences of
χeff obtained from lower and higher molar mass P(2EO-MO)
blends are similar. At r = 0, the difference in A and B values is
less than 10%, while at r = 0.10, A is within 10% while the
value of B differs by about 20% (see Table 4). The absolute
value of χeff is greater in the lower molar mass P(2EO-MO)-
containing blends than in the higher molar mass blends. χeff is
always below χcrit = 6.78 × 10−3 for these lower molar mass
blends.
Figure 5. RPA fits (solid black lines) for a dPEO/P(2EO-MO)/
LiTFSI (P(2EO-MO) Mn = 26.7 kg mol−1) blend with r = 0.08 at 70
°C (filled blue circles) and 90 °C (filled green squares). The 110 °C
measurements (open red triangles) indicate phase separation. Error
bars represent one standard deviation of the scattering data and in
most cases are smaller than the data points.
In all cases where χeff is a sensitive function of temperature,
R2 values for the linear fits are greater than 0.98 (see Table 4).
The R2 value for the r = 0.14 blend is 0.344, which is expected
as χeff is insensitive to temperature in this case.
across a range of temperatures (60 ≤ T (°C) ≤ 110) for the
high molar mass P(2EO-MO)-containing (Mn = 26.7 kg
mol−1) blends at r = 0, 0.08, 0.10, and 0.14 and the low molar
mass P(2EO-MO)-containing (Mn = 16.0 kg mol−1) blends at
r = 0 and 0.10. The temperature dependence of χeff is given by
Salt concentration is known to affect χeff in multicomponent
polymer systems.31,32 This effect has primarily been studied in
phase-separated or microphase-separated systems, e.g., poly-
styrene and PEO.33−42 In the dPEO/P(2EO-MO) (Mn = 26.7
kg mol−1) blend, the addition of salt up to r = 0.02 induces
phase separation, while sufficient salt concentrations (r ≥ 0.08)
render the mixture miscible again. The dependence of χeff on r
is shown in Figure 7 for three temperatures (70 °C, 90 °C, and
110 °C). χeff is slightly negative in the neat blend, with similar
values across the three temperatures. Addition of salt to r =
0.02 increases χeff above χcrit = 5.06 × 10−3. χ remains above
this critical value at r = 0.04 and r = 0.06. Because the samples
at 0.02 ≤ r ≤ 0.06 were immiscible at all temperatures studied,
no information about χeff is available besides a lower bound, as
indicated in Figure 7. At 90 °C and 110 °C, χeff decreases with
increasing r for r ≥ 0.08. The data in Figure 7 suggest that χeff
goes through a maximum at a value of r between 0.02 and 0.08
at 90 °C and 110 °C. At 70 °C, χeff is a nonmonotonic function
of r for r ≥ 0.08. At this temperature, χeff exhibits both a
maximum and a minimum with respect to r.
A
T
χeff
=
+ B
(16)
where A and B are empirically determined constants.3,30 For
each blend sample, χeff was linearly fit to inverse temperature
using eq 16 to extract values for A and B. These values are
summarized in Table 4.
All χeff parameters calculated in this study and their
temperature and molar mass dependence are shown in Figure
6. Solid markers represent experimental measurements, and the
solid lines are a fit to the data according to eq 16. The dashed
line denotes χcrit, which was calculated from eqs 7 and 13 for
blends comprising P(2EO-MO) of lower (16.0 kg mol−1) and
higher (26.7 kg mol−1) molar masses. Figure 6a shows the
temperature dependence of χeff in the higher molar mass
P(2EO-MO)-containing blends. In the neat state, χeff is
negative with a value of −3.07 × 10−3 at 60 °C and increases
with increasing temperature (A = −5.401), increasing to a
value of −9.67 × 10−4 at 110 °C. χeff is a more sensitive
function of temperature in the salt-containing blends where
0.08 ≤ r ≤ 0.10. For the r = 0.08 blend, χeff increases from
−4.67 × 10−3 at 70 °C to 2.77 × 10−3 at 100 °C, and phase
separation is observed experimentally at 110 °C (see Figure 5).
At 110 °C, χeff predicted by extrapolating the data below 100
We now discuss the ion transport properties of the higher
molar mass polymer blend electrolytes. For reference, we also
include ion transport properties of conventional PEO/LiTFSI
(Mn = 35.0 kg mol−1) and P(2EO-MO)/LiTFSI (Mn = 55.2 kg
mol−1) electrolytes.43 The ionic conductivity of the PEO/
P(2EO-MO)/LiTFSI blend as a function of r is shown in
Figure 8a. The conductivity increases with increasing r due to
the higher concentration of charge carrying species. To a good
Table 4. A and B Constants for dPEO/P(2EO-MO)/LiTFSI Blends at Various Salt Concentrations, r, and Their Linear Fit R2
a
Values
dPEO/P(2EO-MO)/LiTFSI (P(2EO-MO) Mn = 26.7 kg mol−1
)
dPEO/P(2EO-MO)/LiTFSI (P(2EO-MO) Mn = 16.0 kg mol−1
)
r
A
B
R2
A
B
R2
0
−5.401 0.241
−32.127 1.146
−17.682 0.305
1.383 1.350
0.0133 0.0007
0.0891 0.0032
0.0460 0.0008
−0.0072 0.0037
0.986
0.997
0.998
0.344
−5.773 0.172
0.0149 0.0005
0.994
0.08
0.10
0.14
−21.537 0.480
0.0576 0.0013
0.997
a
The errors shown represent one standard deviation of uncertainty for the fit for A and B according to eq 16.
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Figure 6. Effective Flory−Huggins interaction parameter, χeff, as a function of inverse temperature, 1/T, for the dPEO/P(2EO-MO)/LiTFSI blend
(a) with higher P(2EO-MO) molar mass (Mn = 26.7 kg mol−1) and (b) with lower P(2EO-MO) molar mass (Mn = 16.0 kg mol−1). The solid lines
are linear fits to the data according to eq 16; values for A and B are reported in Table 4. Error bars represent one standard deviation of the χeff fits
and are smaller than the symbols. Typical error bars on χ range between 5 and 20%, as previously shown in ref 24.
vice versa. The fact that the ion transport data (see Figure 8)
obtained from immiscible blends do not differ significantly
from that of miscible blends may be attributed to this effect. A
more thorough investigation into the impact of miscibility on
ion transport is warranted but is beyond the scope of this
study.
We were curious whether ion transport behavior in miscible
polymer blend electrolytes can be predicted based on the
known properties of conventional polymer electrolytes. It is
well-established that ionic conductivity in polymers depends
on the relative segmental motion of the polymer backbone,
which can be gauged by the Tg value.9,19,45,46 The Tg values of
the miscible polymer blend electrolytes (PEO/P(2EO-MO)/
LiTFSI) were consistently between the Tg values of the PEO/
LiTFSI and P(2EO-MO)/LiTFSI electrolytes (see Figure 2b).
However, conductivity measurements indicate that PEO, the
component with the lower Tg, dominates conductivity. At most
salt concentrations, this general behavior also applies to the
measured current fractions and salt diffusion coefficients (see
Figures 8b and 8c). These observations do not indicate that
only PEO chains contribute to conductivity; if this were the
case, then the conductivity of the 50/50 polymer blend
electrolytes would be half that of PEO/LiTFSI. The data in
Figures 2b, 8b, and 8c suggest that the P(2EO-MO) chains in
the miscible polymer blend electrolytes behave as if they were
PEO. It is evident that ion transport in miscible polymer blend
electrolytes differs qualitatively from that in conventional
polymer electrolytes.
We conclude this section by reviewing previous studies of
ion transport in polymer blends. It is important to distinguish
between oligomers and polymers: PEO analogues such as
tetraethylene glycol dimethyl ether (tetraglyme), a short chain
molecule comprising four ethylene oxide units, are commonly
used as solvents for electrolytic applications.47−49 The ionic
conductivity of PEO/LiTFSI mixtures is independent of chain
length when the molar mass of the PEO chains exceeds 2 kg
mol−1.50 The entanglement molar mass of PEO is also reported
to be 2 kg mol−1.51 This value (2 kg mol−1) serves as an
approximate marker to distinguish between oligomers and
polymers in the context of electrolytes. There have been a few
reports of mixtures of polymers, salts, and a third
Figure 7. Effective Flory−Huggins interaction parameter, χeff, for the
dPEO/P(2EO-MO)/LiTFSI (P(2EO-MO) Mn = 26.7 kg mol−1)
blends as a function of salt concentration, r, at three different
temperatures: 70 °C (blue circles), 90 °C (green squares), and 110
°C (red triangles). The lower limit of the error bars at 0.02 ≤ r ≤ 0.06
is the critical value for the Flory−Huggins interaction parameter, χcrit
,
at which this system phase separates. Error bars for the solid markers
represent one standard deviation of the χeff fits and are smaller than
the symbols.
approximation, the conductivity of the blend matches that of
PEO/LiTFSI at all values of r.
The salt diffusion coefficient, D, of the blend shown in
Figure 8b is similar to that of the conventional P(2EO-MO)/
LiTFSI polymer electrolyte system for r ≤ 0.02 but is nearly
equal to that of PEO/LiTFSI for higher r. The dependence of
the current fraction, ρ+, of the polymer blend on r, plotted in
Figure 8c, matches that of PEO/LiTFSI at all salt
concentrations.44
One measure of the efficacy of an electrolyte is the product
of the ionic conductivity and current fraction. This measure
gives a metric for sustaining steady currents in battery
applications at low current densities. The efficacies of all
three electrolyte systems are similar, as shown in Figure 8d.
The immiscible blends obtained in the regime 0.01 ≤ r ≤
0.06 undoubtedly contain macroscopic PEO-rich and P(2EO-
MO)-rich domains. However, we expect a considerable
concentration of P(2EO-MO) in the PEO-rich domains, and
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Figure 8. Electrochemical characterization of the PEO/P(2EO-MO)/LiTFSI blend as a function of salt concentration, r, compared with
conventional PEO/LiTFSI (Mn = 35.0 kg mol−1) and P(2EO-MO)/LiTFSI (Mn = 55.2 kg mol−1) polymer electrolyte systems. (a) Ionic
conductivity, κ, from ac impedance spectroscopy of symmetric cells with blocking electrodes. (b) Salt diffusion coefficient, D, from restricted
diffusion measurements in a lithium symmetric cell. (c) Current fractions, ρ+, calculated from the Bruce−Vincent method using a lithium
symmetric cell. (d) Efficacy, κρ+. Data were taken at 90 °C. PEO/LiTFSI data were taken from ref 43. Error bars represent the standard deviation
of three measurements.
component.52−61 Tsuchida et al. studied mixtures of PEO,
poly(methyl methacrylate) (PMMA), and lithium perchlorate
(LiClO4); however, the molar masses of examined PEO ranged
from 0.7 to 2 kg mol−1.52 While the miscibility of PEO and
PMMA is well-established in the absence of salt,62 the effect of
added salt on miscibility is not yet known. Abraham et al.
blended PEO and poly[bis((methoxyethoxy)ethoxy) phospha-
zene] (MEEP) with different lithium salts.53 The molar mass
of MEEP was not reported. Interestingly, the blends exhibited
two exothermic melting transitions: one similar to that of pure
PEO in the vicinity of 55 °C and an additional peak at 140 °C,
in spite of the fact that MEEP is amorphous. This suggests the
presence of two phases in the PEO/MEEP electrolytes. Li et al.
prepared blends of PEO, poly(2-vinylpyridine) (P2VP), and
LiClO4. While PEO and P2VP are miscible in the absence of
salt,63 the possibility of salt-induced phase separation was not
addressed. Kim et al. report both conductivity and current
fraction in mixtures of PEO, poly(oligo[oxyethylene]oxy-
sebacoyl), and LiClO4.57 This is one of the few studies on
electrochemical properties in polymer blends that go beyond
conductivity; however, miscibility of the polymers in the
presence of salt was not established. Rocco et al. studied
mixtures of PEO, poly(methyl vinyl ether−maleic acid), and
LiClO4 as well as PEO, poly(bisphenol A-co-epichlorohydrin),
poly(vinyl ethyl ether), and LiClO4 blends for use as
electrolytes.59,60 Inferences regarding miscibility were mainly
made on the basis of DSC. In contrast to all previous
studies,52−61 this paper definitively demonstrates the misci-
bility of a polymer blend electrolyte system by using a rigorous
approach based on SANS, wherein concentration fluctuations
on the nanometer length scale are quantified. Unlike previous
studies,52−61 this work compares the characteristics of the
PEO/P(2EO-MO)/LiTFSI polymer blend electrolyte system
to that of its constituent polymer electrolytes (PEO/LiTFSI
and P(2EO-MO)/LiTFSI).
CONCLUSION
■
This study demonstrates that it is possible to create
homogeneous mixtures of chemically distinct polymers and a
lithium salt for use in lithium batteries. This demonstration is
nontrivial because polymers rarely mix with each other.
Blending polymers for electrolytic applications is advantageous
because of the ease of preparation and control of physical
properties by simple changes in composition or chain lengths
of the components. This initial study, based on PEO/P(2EO-
MO)/LiTFSI, can serve as a template for future work aimed at
optimizing ion transport in polymer electrolytes in a manner
that mirrors the development of mixtures of organic solvents
used in current day lithium ion batteries. The thermodynamic
properties of PEO/P(2EO-MO)/LiTFSI blends, determined
by SANS, are surprisingly complex. This initial study is
restricted to blends with roughly equal volume fractions of
PEO and P(2EO-MO). Neat PEO/P(2EO-MO) blends
exhibit a negative Flory−Huggins interaction parameter across
the accessible temperature window. If we assume that the
phase behavior of PEO/P(2EO-MO)/LiTFSI blends can be
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approximated by Flory−Huggins theory for binary blends of
homopolymers with an effective interaction parameter that
accounts for the presence of salt, it would imply that these
blends would be miscible irrespective of blend composition
and chain lengths of the components. Adding a small amount
of LiTFSI (0.02 ≤ r ≤ 0.06) renders the PEO/P(2EO-MO)
blends immiscible; blends containing either 26.7 or 16.0 kg
mol−1 P(2EO-MO) were immiscible. Increasing the salt
concentration to r > 0.08 results in negative effective Flory−
Huggins interaction parameters across the accessible temper-
ature window, implying miscibility irrespective of blend
composition and chain lengths of the components.
Ion transport in the blends was characterized by measuring
the ionic conductivity, salt diffusion coefficient, and current
fraction. Surprisingly, the values of these parameters in blends
at a given salt concentration, r, were close to those obtained in
conventional PEO/LiTFSI electrolytes at the same value of r.
In other words, the blends that we have characterized thus far
do not exhibit superior ion transport properties. However, a
wide variety of ether- and carbonate-containing polymers have
been synthesized for electrolytic applications.64−67 This work
opens the door to a new direction for creating new and
improved polymer electrolytes either by combining existing
polymers with salt or by synthesizing new polymers with the
specific aim of including them in miscible polymer blend
electrolytes.
California 94720, United States; orcid.org/0000-0002-
9773-3571
Rachel L. Snyder − Department of Chemistry and Chemical
Biology, Cornell University, Ithaca, New York 14850, United
States; Joint Center for Energy Storage Research (JCESR),
Argonne National Laboratory, Lemont, Illinois 60439, United
States; orcid.org/0000-0002-0569-0704
Brooks A. Abel − Department of Chemistry and Chemical
Biology, Cornell University, Ithaca, New York 14850, United
States; Joint Center for Energy Storage Research (JCESR),
Argonne National Laboratory, Lemont, Illinois 60439, United
States; orcid.org/0000-0002-2288-1975
Youngwoo Choo − Materials Sciences Division, Lawrence
Berkeley National Laboratory, Berkeley, California 94720,
United States; Joint Center for Energy Storage Research
(JCESR), Argonne National Laboratory, Lemont, Illinois
60439, United States; orcid.org/0000-0003-2715-0618
Andrew Lee − Department of Chemical and Biomolecular
Engineering, NYU Tandon School of Engineering, New York
University, Brooklyn, New York 11201, United States
Susana C. M. Teixeira − NIST Center for Neutron Research,
National Institute of Standards and Technology, Gaithersburg,
Maryland 20899, United States; Department of Chemical and
Biomolecular Engineering, University of Delaware, Newark,
Delaware 19716, United States
Bruce A. Garetz − Department of Chemical and Biomolecular
Engineering, NYU Tandon School of Engineering, New York
University, Brooklyn, New York 11201, United States;
orcid.org/0000-0002-3141-7840
ASSOCIATED CONTENT
* Supporting Information
■
sı
The Supporting Information is available free of charge at
https://pubs.acs.org/doi/10.1021/acs.macromol.0c00747.
Complete contact information is available at:
https://pubs.acs.org/10.1021/acs.macromol.0c00747
Synthesis and characterization of P(2EO-MO) as well as
ac impedance spectroscopy of representative PEO/
P(2EO-MO)/LiTFSI blends (PDF)
Notes
The statements, findings, conclusions and recommendations
are those of the authors and do not necessarily reflect the view
of NIST or the U.S. Department of Commerce. Certain
commercial equipment, instruments, suppliers and software are
identified in this paper to foster understanding. Such
identification does not imply recommendation or endorsement
by the National Institute of Standards and Technology, nor
does it imply that the materials or equipment identified are
necessarily the best available for the purpose.
AUTHOR INFORMATION
Corresponding Authors
■
Nitash P. Balsara − Department of Chemical and Biomolecular
Engineering, University of California, Berkeley, Berkeley,
California 94720, United States; Materials Sciences Division,
Lawrence Berkeley National Laboratory, Berkeley, California
94720, United States; Joint Center for Energy Storage Research
(JCESR), Argonne National Laboratory, Lemont, Illinois
60439, United States; orcid.org/0000-0002-0106-5565;
Email: nbalsara@berkeley.edu
Geoffrey W. Coates − Department of Chemistry and Chemical
Biology, Cornell University, Ithaca, New York 14850, United
States; Joint Center for Energy Storage Research (JCESR),
Argonne National Laboratory, Lemont, Illinois 60439, United
States; orcid.org/0000-0002-3400-2552; Email: coates@
cornell.edu
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
■
This work was intellectually led by the Joint Center for Energy
Storage Research (JCESR), an Energy Innovation Hub funded
by the U.S. Department of Energy, Office of Science, Office of
Basic Energy Science, under Contract DE-AC02-06CH11357,
which supported synthesis work conducted by R.L.S. and
B.A.A. under the supervision of G.W.C and characterization
work conducted by K.W.G., W.S.L., and Y.C. under the
supervision of N.P.B. Characterization work conducted by A.L.
under the supervision of B.A.G. was supported by the National
Science Foundation through Award DMR-1904537. Work at
the Molecular Foundry, which is a DOE Office of Science User
Facility, was supported by Contract DE-AC02-05CH11231.
S.C.M.T. acknowledges the Center for Neutron Studies at the
University of Delaware and funding under cooperative
agreements #370NANB17H302 and #70NANB15H260 from
NIST, U.S. Department of Commerce. We acknowledge the
support of the National Institute of Standards and Technology,
Authors
Kevin W. Gao − Department of Chemical and Biomolecular
Engineering, University of California, Berkeley, Berkeley,
California 94720, United States; Materials Sciences Division,
Lawrence Berkeley National Laboratory, Berkeley, California
94720, United States; Joint Center for Energy Storage Research
(JCESR), Argonne National Laboratory, Lemont, Illinois
60439, United States; orcid.org/0000-0002-6794-1265
Whitney S. Loo − Department of Chemical and Biomolecular
Engineering, University of California, Berkeley, Berkeley,
I
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U.S. Department of Commerce, in providing the neutron
facilities used in this work. K.W.G. acknowledges funding from
a National Defense and Science Engineering Graduate
Fellowship. W.S.L. acknowledges funding from the National
Science Foundation Graduate Student Research Fellowship
DGE-1106400.
A, B
R2
κ
D
ρ+
empirical constants for fitting χ
coefficient of determination
ionic conductivity (S cm−1)
salt diffusion coefficient (cm2 s−1)
current fraction
κρ+
efficacy (S cm−1)
PMMA
LiClO4
MEEP
poly(methyl methacrylate)
lithium perchlorate
p ol y [ b i s ((m e t h o xy e t h o xy ) e t h ox y )-
phosphazene]
LIST OF SYMBOLS
■
PEO
poly(ethylene oxide)
P(2EO-MO) poly(1,3,6-trioxocane)
P2VP
poly(2-vinylpyridine)
LiTFSI
SANS
DSC
2EO-MO
Mn
lithium bis(trifluoromethanesulfonyl)imide
small-angle neutron scattering
differential scanning calorimetry
1,3,6-trioxocane
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number-average molar mass (kg mol−1)
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weight of component i (g)
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density of component i (g cm−3)
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molar ratio of lithium to oxygen atoms
monomer molar mass of PEO (g mol−1)
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volume fraction of PEO and LiTFSI associated
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number of repeat units per chain
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effective Flory−Huggins interaction parameter
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dPEO/LiTFSI(q) SANS intensity from dPEO/LiTFSI mixtures
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