Synthesis and modeling of polysiloxane-based salt-in-polymer electrolytes with various additives

Article abstract of DOI:10.1021/jp907832q

The effect of both nanoparticles and low molecular weight borate esters on the ionic conductivity of crosslinked polysiloxanes was systematically investigated by means of measuring conductivity spectra in the impedance regime at temperatures between -30 a

Full text of DOI:10.1021/jp907832q

J. Phys. Chem. B 2009, 113, 15473–15484
15473
Synthesis and Modeling of Polysiloxane-Based Salt-in-Polymer Electrolytes with Various
Additives
Y. Karatas,*,†,§,⊥ Radha D. Banhatti,‡,| N. Kaskhedikar,†,|,⊥ M. Burjanadze,†,| K. Funke,‡,| and
Hans-D. Wiemho¨fer†,|
Institute of Inorganic and Analytical Chemistry, UniVersity of Mu¨nster, Germany, Institute of Physical
Chemistry, UniVersity of Mu¨nster, Germany, Department of Chemistry, Ahi EVran UniVersity, Turkey,
Sonderforschungsbereich 458, UniVersity of Mu¨nster, Germany, and International Graduate School of
Chemistry (GSC-MS), Germany
ReceiVed: August 13, 2009; ReVised Manuscript ReceiVed: September 30, 2009
The effect of both nanoparticles and low molecular weight borate esters on the ionic conductivity of cross-
linked polysiloxanes was systematically investigated by means of measuring conductivity spectra in the
impedance regime at temperatures between -30 and 90 °C. Salt-in-polymer electrolytes were prepared by
dissolving lithium triflate (LiSO3CF3) in comblike polysiloxanes bearing one methyl and one oligoether side
group per silicon. An amount of 10 mol % of the oligoether side groups exhibited a terminal allytrimethox-
ysilane serving as a cross-linker moiety (T0.1OPS). Thus prepared polymer electrolyte membranes were
completely amorphous and mechanically stable with an optimum conductivity value of 5.7 × 10-5 S · cm-1
at 15 wt % of lithium triflate (LiSO3CF3) at room temperature (T0.1OPS + 15 wt % LiSO3CF3). Further
investigations concerned the influence of additives, i.e., nanosized ceramic fillers (R-Al2O3 and SiO2, up to
10 wt %) as well as two low molecular weight borate esters (tris(2-(2-methoxyethoxy)ethyl) borate (B2) and
tris(2-(2-(2-methoxyethoxy)ethoxy)ethyl) borate (B3)) with maximum concentrations of 40 wt % as referred
to polysiloxane T0.1OPS. The addition of borate esters resulted in a considerable increase of the conductivity,
while still maintaining the mechanical stability. Optimum conductivities of 3.7 × 10-5 and 1.6 × 10-4 S·cm-1
were measured for B2 and B3, respectively, at room temperature. A fit of the temperature-dependent DC
conductivity by the empirical Vogel-Tammann-Fulcher (VTF) equation showed that there was an increased
number density of mobile charge carriers in the case of borate esters as additives. However, the shape of the
conductivity spectra in the dispersive regime changed considerably in going from nanoparticles as additives
to borate esters. A careful and consistent modeling of the conductivity spectra and of the temperature dependence
of the DC conductivity was done within the framework of the MIGRATION concept. The result was that the
addition of borate esters to the polymer host most probably increased both number density of mobile charge
carriers as well as their mobility.
Introduction
loxane) with oligoether side chains via hydrosilylation in the
presence of a platinum catalyst3,4 is apparently the most
The first types of ion conducting polymer to be considered
for battery applications were those formed by blending high
molecular weight poly(ethylene oxide) (PEO) with a lithium
salt as originally reported by Wright et al. in 1973.1 This system,
however, suffered from low conductivity (∼10-8 S·cm-1) at
room temperature due to its semicrystalline nature. Recognizing
the fact that ionic transport takes place in particular in the
amorphous region of the matrix, numerous branched or grafted
copolymer structures have been designed with poly(ethylene
oxide) either as copolymer units or side chains with completely
amorphous structure.2
promising method for the synthesis of comblike functionalized
polysiloxanes. Modification of the polysiloxanes is rather easy
by introducing different substituents in parallel or subsequently.
Apart from many other polysiloxane-based systems, numerous
comblike polysiloxanes have been synthesized during the last
few decades via hydrosilylation and investigated as possible
candidates for polymer electrolytes.5-17 The room-temperature
conductivities observed in many of such “salt-in-polysiloxane”
electrolytes ranged between 10-5 and 10-4 S·cm-1 6-11
How-
.
ever, the low Tg is accompanied by a viscous, almost liquid
behavior. Cross-linked polysiloxane membranes circumvent this
problem and show good mechanical properties. Their conduc-
tivities, however, were distinctly lower.12-17
Comblike polysiloxanes are one of the best polymers satisfy-
ing the structural requirements as polymer electrolytes owing
to their extremely low glass transition temperatures and high
chain flexibility. The functionalization of poly(methylhydrosi-
Therefore, in this contribution, we investigate routes to
improve the conductivity of cross-linked salt-in-polysiloxane
networks by additives and analyze the influence on the ion
transport mechanism by high frequency impedance spectros-
copy. One approach, well-known from studies on PEO-based
polymer electrolytes, is the use of inorganic nanoparticle fillers
such as TiO2, Al2O3, and SiO2, and another approach is the
dissolution of low molecular weight solvents which can act as
* Corresponding author. Department of Chemistry, Ahi Evran University,
Asik Pasa Campus, 40200 Kirsehir, Turkey. E-mail: ykaratas@ahievran.edu.tr.
Fax: +90 386 211 45 25.
† Institute of Inorganic and Analytical Chemistry, University of Mu¨nster.
‡ Institute of Physical Chemistry, University of Mu¨nster.
§ Department of Chemistry, Ahi Evran University.
| Sonderforschungsbereich 458, University of Mu¨nster.
⊥ International Graduate School of Chemistry (GSC-MS).
10.1021/jp907832q CCC: $40.75  2009 American Chemical Society
Published on Web 10/21/2009

15474 J. Phys. Chem. B, Vol. 113, No. 47, 2009
Karatas et al.
plasticizers or can enhance ion dissociation due to selective
interaction with ions.
polymer electrolytes is the first example in its class. Its detailed
investigation would help to compare filler effects on the most
commonly employed polymer electrolytes based on polyethylene
oxide, polyphosphazene, and polysiloxane. The present study
deals mostly with the effect exerted by inorganic fillers and
borate esters on the mechanical and electrical properties of the
polymer electrolyte host, which is based on cross-linked
polysiloxane. Moreover, the study includes the modeling of the
temperature dependence of the DC conductivities by the
empirical VTF equation and the MIGRATION concept.
The first report on adding ceramic powder for improving the
mechanical properties of PEO-based polymer electrolytes dates
back to the beginning of the eighties.18 Up to now, great efforts
have been devoted to such composite polymer electrolytes to
enhance the ionic conductivities.19-29 Although a direct relation
with increasing filler content was generally mentioned, the
optimum concentration of this component varied over a wide
range. For poly(ethylene oxide)-based polymer electrolyte
composites, for example, a conductivity enhancement was
obtained at around 10 wt % by many authors.21-26 There is a
common agreement that the conductivity is enhanced as
polyether crystallinity is reduced; however, Wieczorek et al.19,20
reported a change in conductivity due to acid-base-type
interactions involving polyether oxygens and filler acid or base
centers.
Experimental Section
Materials. All reactions were carried out under an atmosphere
of dry nitrogen gas and using standard vacuum-line Schlenk
techniques. Tetrahydrofuran (THF, 99.9%, Riedel-de Hae¨n) and
toluene (99.7%, Scharlau) were distilled from sodium ben-
zophenone ketyl prior to use. Poly(methylhydrosiloxane) (PMHS,
Mn ) 1700-3200, Aldrich), 2-(2-methoxyethoxy)ethanol, and
2-(2-(2-methoxyethoxy)ethoxy)ethanol were stored over acti-
vated molecular sieves (type 4A) and used without further
purification. SiO2 (7 nm, Aldrich) and γ-Al2O3 (40 nm, Aldrich)
were dried under vacuum at 250 °C for 24 h and stored in a
glovebox. Dibutyltin dilaurate (DBTL, >97%, Merck), boric acid
(>99%, Riedel-de Hae¨n), and lithium triflate (purum, Fluka)
were used as received.
Equipment. All NMR spectra were measured using a Bruker
AC 200 and a Varian Mercury 400 Plus spectrometer. The
spectra were recorded using CDCl3 as the solvent and tetram-
ethylsilane (TMS) as the internal reference. Most assignments
were based on a series of 2D NMR experiments.
The molecular weights and molecular weight distributions
(PDI) of the polymer precursors were determined by a gel
permeation chromatograph, equipped with two PSS-SDV linear
XL columns (8 × 300 mm, 5 µ) from Polymer Standards Service
(PSS, Mainz), an RI-detector (agilent), and a η-1001 viscosim-
eter (WGE Dr. Bures). The column was calibrated with
polystyrene (ReadyCal standard, PSS, Mainz). The flow rate
was 1 mL/min of tetrahydrofuran with a 0.1 wt % solution of
tetra-n-butylammonium bromide.
Differential scanning calorimetry (DSC) was used to obtain
the glass transition temperatures (Tg) and other primary transi-
tions of the polymers. The DSC thermograms were recorded
using a Netzsch DSC 204 at a heating rate of 10 K/min between
-150 °C and +150 °C under an atmosphere of dry nitrogen.
FT-IR spectra of the polymers and polymer electrolytes were
measured in a Bruker IFS 113v IR or a Schimadzu IRPrestige-
21 spectrometer.
The ionic conductivities of the polymer electrolyte samples
were determined by impedance spectroscopy. The membranes
were sandwiched between two ion blocking stainless steel
platinum foil electrodes (1 cm2 surface area each). All measure-
ments were carried out under an atmosphere of dry nitrogen.
The measurements were performed using Novocontrol Alpha
High Resolution Dielectric Analyzer integrated with Quatro
Cryosystem in a frequency range from 3 × 106 to 10-2 Hz. A
predominant ohmic contribution to the impedance was found
at intermediate frequencies, which is attributed to the bulk
polymer, hence used to calculate the total conductivity.
Synthesis. Tris(2-(2-methoxyethoxy)ethyl) borate (B2) was
synthesized similar to the method described by Giercyzk et al.43
Amounts of 30.9 g (0.5 mol) of boric acid, 192.3 g (1.6 mol)
of 2-(2-methoxyethoxy)ethanol, and 100 mL of toluene were
placed into a 500 mL round-bottom flask attached to a
Dean-Stark apparatus with a reflux condenser. The solution
Most of the investigations on composite polymer electrolytes
have been focused on PEO and related polyethers. Only a few
examples are available for the role of fillers in polymer
electrolytes with an inorganic backbone. Polyphosphazenes27-29
are among the most prominent of them. For polysiloxane-based
electrolytes, up to now, there are no systematic studies about
the influence of ceramic fillers to our knowledge. Nanosized
Al2O3 particles were reported to increase the conductivity in
amino functionalized polyphosphazenes.29 On the other hand,
the addition of filler particles to completely amorphous poly-
phosphazene resulted in a decrease or only a negligible change
in the conductivity, even with an optimum filler content of 2.5
wt %.27,28 These results open up the questions whether (i) the
effect of filler particles is strongly dependent on the morpho-
logical properties of the system under study or (ii) surface groups
of the ceramic particles play also an active role in the ion
conduction mechanism.
Another approach to improve the ionic conductivity of a
polymer electrolyte is to add small amounts of low molecular
weight nonprotic organic solvents such as ethylene carbonate,
propylene carbonate, dialkyl carbonate, or their mixtures, which
serve as plasticizers. Such solvents with high dielectric constants
enhance the dissociation and also the solubility of the salt and
hence increase the ionic conductivity. However, they impart
problems in the applications as they are volatile and flammable.
Borate esters have been therefore attracting a growing interest
as a new type of additives, as they can lead to higher
conductivities by trapping the anions due to their Lewis acidic
nature, in spite of a very low solvent dielectric constant.
Moreover, they have high flash points.30,31 Many borate esters
have been recently synthesized and studied both as additives30-36
and as solvents37-42 in salt-in-polymer electrolytes. It is therefore
of interest to analyze their influence on conduction of polysi-
loxane-based electrolytes.
A central part of the present study involves the preparation
of mechanically stable polysiloxane-based salt-in-polymer elec-
trolytes, a systematic study of their conductivity spectra from
impedance spectroscopy, and a careful analysis in terms of
recent models and achievements concerning ion transport
mechanisms. This also helps to investigate the influence of the
included additives on the temperature dependence of the DC
conductivity of the salt-in-polymer electrolyte (T0.1OPS + 15
wt % LiSO3CF3). Another issue of the detailed analysis of
conductivity spectra is that it enables us to study changes in
the dispersive behavior of its conductivity resulting from
inclusion of these additives. To our knowledge, the effect of
ceramic fillers on the conductivity of polysiloxane-based

Polysiloxane-Based Salt-in-Polymer Electrolytes
J. Phys. Chem. B, Vol. 113, No. 47, 2009 15475
SCHEME 1: Synthesis of Tris(oxaalkyl)borates B2 (n )
2) and B3 (n ) 3)
SCHEME 2: Synthesis of Polymer Precursor
Figure 1. Representative FT-IR spectra of T0.1OPS and corresponding
polymer electrolyte with 20 wt % LiSO3CF3. Dotted line corresponds
to 904 cm-1
.
nanoparticle case the prepared solutions were kept in an
ultrasonic bath for 15 min before continuing with the next steps.
was refluxed until no more water was isolated (24 h). After
removing the solvent, the oily product was distilled under
reduced pressure (181 °C, 1.4 mmHg) to yield colorless B2,
153.5 g (83%). 1H NMR (CDCl3): δ ) 3.88 (dd, 6H), 3.57 (dd,
6H), 3.53 (dd, 6H), 3.47 (dd, 6H), 3.31 (s, 9H). 13C NMR
(CDCl3): δ ) 71.8, 71.5, 70.3, 62.6, 58.9. 11B NMR (CDCl3):
18.0.
Tris(2-(2-(2-methoxyethoxy)ethoxy)ethyl) borate (B3) was
synthesized as B2 (Scheme 1). The following reagents and
quantities are used: boric acid (15.5 g, 0.25 mol), 2-(2-(2-
methoxyethoxy)ethoxy)ethanol (131.4 g, 0.8 mol), toluene (100
mL). The product was isolated under high vacuum (222 °C, 5
× 10-2 mmHg) to yield B3, 112 g (90%). 1H NMR (CDCl3): δ
) 3.88 (dd, 6H), 3.65-3.57 (m, 18H), 3.54 (dd, 6H), 3.50 (dd,
6H), 3.33 (s, 9H). 13C NMR (CDCl3): δ ) 71.5, 71.2, 70.3,
70.1, 70.0, 62.3, 58.5. 11B NMR (CDCl3): 18.1.
Result and Discussion
T0.1OPS-Based Polymer Electrolytes. The cross-linking and
the interaction of lithium salt with the polymer electrolytes
complexed with varying amounts of LiSO3CF3 were investigated
by FT-IR. Representative FT-IR spectra of pure T0.1OPS and
of the corresponding polymer electrolyte with 20 wt % salt are
given in Figure 1.
The characteristic stretching signal of -Si-O-CH3 at 904
cm-1, indicated in the figure as a dotted line on the spectrum,
was monitored to judge the cross-linking efficiency of the
precursor polymer. The signal almost entirely vanished in the
presence of DBTL as a catalyst, indicating that these groups
were extensively involved in the sol-gel cross-linking of the
precursor.
The precursor polymer can be easily identified with the
characteristic doublet of the polysiloxanes containing more than
eight silicon atoms seen close to 1100 and 1020 cm-1. The
strong and very characteristic symmetric deformation of Si-CH3
appears at 1261 cm-1. The only band characteristic of C-O-C
groups is seen at around 1237 cm-1 as a shoulder due to the
shielding of a quite strong Si-O-Si band at the same region.
Hence, the monitoring of the coordination effect of the cations,
resulting in frequency shift of the C-O-C signal to the lower
frequencies with increasing salt concentration, is rather difficult.
Nevertheless, the broadening and slight shifting of the signal
at around 1100 cm-1 to the lower frequencies could be attributed
to the cation-oligoether interaction in a coarse approach. In
addition, the similar changes of the SO2 deformation band at
640 cm-1 with increasing salt content are consistent with the
interpretation of free ion and higher aggregates.46 Unfortunately,
the other characteristic stretchings of the triflate anion used to
investigate many salt-in-polymer systems, for example, sym-
metric SO3 vibration at around 1030 cm-1, were useless for this
case since they are partially or fully overlapped with the polymer
frequencies.
Thermal properties of the polymer were investigated using
DSC. As shown in Figure 2, a small crystallization peak was
observed for the precursor polymer, which melted subsequently
at around -36 °C. This crystallization behavior, as commonly
observed for polymers having relatively long side chain,
disappeared completely even after the addition of 5 wt % lithium
salt. The polymers and corresponding polymer electrolytes were
stable up to at least 150 °C with no primary transitions belonging
to the polymer. The Tg value of the precursor polymer (-83.5
°C) shifted gradually to the higher values as the amount of salt
Platinum-catalyzed functionalization of poly(methylhydrosi-
loxane) via hydrosilylation was used to prepare the precursor
polymer. The details of the synthesis can be found in our
preceding study.17 There, the polymer electrolyte with 10 mol
% cross-linker (T0.1OPS) was found to be optimum in terms of
mechanical properties and conductivities (Scheme 2). Therefore,
this polymer precursor was chosen as the model polymer to
investigate the effect of nanoparticles and the borate esters.
Preparation of Polysiloxane-Based Polymer Electrolytes.
The cross-linking of T0.1OPS was performed using dibutyltin
dilaurate (DBTL) for better cross-linking efficiency and dimen-
sional stability of the prepared membranes.44,45 The ratio of
catalyst to the number of trimethoxysilane moiety was kept as
0.25 for all cases. In a typical cross-linking, 0.7 g (2.34 × 10-4
mol of -Si(OMe3)3) of the precursor polymer was dissolved in
2 mL of THF, and a required amount of lithium salt from a
stock solution (0.2 g/mL) was added and thoroughly mixed for
1 h before the addition of 35 µL (0.59 × 10-4 mol) of DBTL
as catalyst. The resulting solution was mixed further for half
an hour and poured into polypropylene molds with a diameter
of 5.5 cm, and the solvent was removed to dryness under
vacuum at least for 3 h. Finally, the curing of the sample was
completed in an oven at 40 °C in 2 days, and the sample was
then dried for another day under vacuum. Homogeneous and
transparent films with average thickness of 130 µm were
obtained in this way. These films were insoluble in all solvents;
only swollen in THF.
Composite polymer electrolytes with nanoparticles and borate
esters were prepared analogously. These components were only
mixed at the beginning with polymer solution, and in the

15476 J. Phys. Chem. B, Vol. 113, No. 47, 2009
Karatas et al.
electrolytes were in the range from 3.4 × 10-8 to 6.7 × 10-9
S·cm-1 at -30 °C and from 2.0 × 10-5 to 5.3 × 10-5 S·cm-1
at 90 °C. As seen in Figure 3, the conductivity increased with
increasing salt content and peaked at an optimum concentration
of about 15 wt % of the salt. A similar behavior was found in
other salt-in-polymer electrolytes. The acceleration of the drop
in the ionic conductivity at lower temperatures can be attributed
to the higher viscosity of the system gained by the salt content,
which relates inversely to the mobility of the ions as given by
the Stocks-Einstein relation47 and also to the formation of ion
pairs and higher aggregates.48 At low salt content, the mobility
of the ions is relatively unaffected by concentration. At higher
concentrations, the conductivity drops due to the reduced ion
mobility, which is caused by an increase in inter- and intramo-
lecular coordinations of the polymer host to the salt creating
transient (ionic) cross-links. In addition, above a critical
concentration, ion pairs and higher aggregates, which are less
mobile, are predicted to form and, therefore, influence the
conductivity.2
Figure 2. DSC thermogram of T0.1OPS for varying amounts (x) of
lithium triflate cross-linked by DBTL.
TABLE 1: Glass Transition Temperature of T0.1OPS and
Its Polymer Electrolytes, Ratios of Side Chain O:Li for the
Corresponding wt % of Lithium Triflate (LiSO3CF3), and
Fitting Parameters of VTF Equation to the
Temperature-Dependent Conductivities
salt
(wt %)
ratio
(O:Li)
Tg
[K]
T0
[K]
σ0 × 103
B
[K]
kBB
[eV]
In terms of stability, structural homogeneity, and conductivity,
the optimum properties among T0.1OPS-based polymer elec-
trolytes were reached at 15 wt % lithium triflate concentration.
The conductivity was on the limit of 10-5 S·cm-1. In the
following, the effects of nanoparticles and low molecular weight
additives are investigated in an attempt to further enhance the
conductivity without sacrificing the mechanical properties. For
simplicity, T0.1OPS-LiSCF15 will be used for T0.1OPS + 15 wt
% LiSO3CF3.
Polymer Electrolytes with Nanoparticles. The glass transi-
tion temperatures (Tg) of both Al2O3 and SiO2 composite
polymer electrolytes, as obtained from DSC measurements, are
listed in Table 2. The composites were stable within the
temperature range studied, i.e., at least up to 150 °C. The Tg
value of T0.1OPS-LiSCF15 was found to be -64.7 °C as seen
in Table 1. Neither Al2O3 nor SiO2 addition caused a perceivable
change indicating that the coordination between Li+ ions and
polysiloxane was not significantly affected by the third component.
Figures 4(a) and (b) are Arrhenius plots of the ionic
conductivities of T0.1OPS-LiSCF15 composite polymer elec-
trolytes containing Al2O3 and SiO2 particles, respectively. The
conductivity for particle free polymer electrolyte is also given
for comparison.
As seen in Figure 4(a), no significant increase in the
conductivity was attained as compared to the particle free
polymer electrolyte. The overall decrease in the conductivity
cannot be attributed to the restricted segmental motion of the
polymer host since the glass transition temperatures of the
polymer host remained almost constant as discussed above.
Rather, the lengthening of the conduction pathway due to the
phase separation between polymer host and alumina particles
seemed to be responsible for this behavior. An increase in the
concentration of alumina in the host causes a dilution of the
polymer matrix as well as lengthening of the conduction
pathway. Moreover, the surface properties of the particles have
crucial effects on the electrical properties, since it may form
acid-base-type interaction with polymer chains and salt in the
matrix, as explained by Wieczorek for poly(ethylene oxide)-
based polymer electrolytes.19,20 The initial increase among the
alumina-containing composites could be therefore due to the
interaction of alumina with the salt to promote ion dissociation
thus the number of free ions leading to an increase in
conductivity to some extent.25 On the other hand, the conductiv-
ity started decreasing again when 8 wt % alumina concentration
was reached. This trend could be explained by a great increase
[S·cm-1
]
0
5
10
12.5
15
20
-
189.6
194.6
201.4
204.7
208.5
215.4
-
-
-
52
26
21
17
13
190
181
178
184
185
0.3
1.5
2.8
3.8
4.8
450
664
770
721
824
0.039
0.057
0.066
0.062
0.071
in the polymer electrolyte increased (Figure 2, and Table 1).
This progressive rise can be attributed to the decrease in the
segmental mobility of the side chain. This behavior is usually
interpreted as a result of the effects of an increase in intra- and
intermolecular coordinations between coordinating sites on the
same or different polymer chains caused by the ions acting as
transient cross-links. Moreover, the very small transition detected
around 0 °C was ascribed to the catalyst.
Impedance measurements were performed in the temperature
range from -30 to 90 °C. The as-obtained polymer electrolytes
were free-standing membranes and easy to handle. A salt-free
membrane was prepared to determine the effect of DBTL, if
any, on the ionic conductivity. The measured conductivity was
in semiconducting level, and the contribution to the poorest
polymer electrolyte system investigated in this study was less
than 1% overall. The ionic conductivities were measured for
up to 20 wt % lithium triflate salt content. The temperature
dependence of the ionic conductivity is shown in Figure 3.
The concentration of the lithium salt was varied systematically
to find the optimum doping concentration for the polymer
electrolyte system. The conductivities of the as-prepared polymer
Figure 3. Arrhenius plot of the DC conductivity of T0.1OPS for
different amounts (x) of lithium triflate.

Polysiloxane-Based Salt-in-Polymer Electrolytes
J. Phys. Chem. B, Vol. 113, No. 47, 2009 15477
TABLE 2: Glass Transition Temperatures (Tg) and Fitting Parameters of the VTF Equation to the Temperature-Dependent
Conductivities of T0.1OPS + 15 wt % LiSO3CF3 Polymer Electrolyte Mixed with Al2O3, SiO2, B2, and B3
Al2O3 (wt %) Tg [K] T0 [K] σ0 × 103 [S·cm-1
]
B [K] kBB [eV] SiO2 (wt %) Tg [K] T0 [K] σ0 × 103 [S·cm-1
] B [K] kBB [eV]
2
208.5
206.6
207.5
208.4
207.4
185
187
185
185
185
1.8
1.9
1.6
3.3
3.4
685
677
695
692
696
0.059
0.058
0.060
0.060
0.060
2
4
6
8
10
207.5
208.2
208.4
208.3
207.1
185
183
185
185
184
2.2
3.8
1.9
1.8
3.3
686
725
692
690
702
0.059
0.062
0.060
0.060
0.060
4
6
8
10
B2 (wt %) Tg [K] T0 [K] σ0 × 103 [S·cm-1
]
B [K] kBB [eV] B3 (wt %) Tg [K] T0 [K] σ0 × 103 [S·cm-1
]
B [K] kBB [eV]
10
20
30
40
207.2
207.1
206.8
204.9
186
186
187
187
9.8
13.2
18.7
15.1
667
682
682
666
0.058
0.059
0.059
0.057
10
20
30
40
199.5
198.9
195.9
196.1
188
188
187
186
8.3
10.3
16.8
21.2
540
542
560
567
0.047
0.047
0.048
0.049
in the interaction between ions and the surface of the fillers in
addition to the adsorption like process taking place at the surface
as reported by Liu, which is accompanied by an increase in
lithium transference number.49 Such a similar behavior was also
reported in the sense of transference number for nanoparticle
embedded polyphosphazenes.29 In any case, the effect of alumina
on the conductivity of particle free polymer electrolyte was not
pronounced as is usually the case for PEO-based polymer
electrolytes.
The effect of SiO2 was also not much different from Al2O3
as seen in Figure 4(b). The maximum conductivity was observed
for 4 wt % silica content, which then tailed away similarly.
This maximum observed at lower silica particle concentration
as compared to alumina particles can be explained by the
relatively high surface area of finer silica particles. The reasoning
for alumina incorporated composite polymer electrolytes is also
valid for the samples with silica particles.
Polymer Electrolytes with Borate Esters. Borate esters are
interesting compounds since they can be used as a plasticizer
as well as a Lewis acid that can trap the anions and lead to an
increase in lithium transference number.2,50,51 Therefore the effect
of tris(2-(2-methoxyethoxy)ethyl) borate (B2) and tris(2-(2-(2-
methoxyethoxy)ethoxy)ethyl) borate (B3) on electrical properties
of the T0.1OPS-LiSCF15 polymer electrolytes was studied. The
polymer electrolytes were loaded to the upper limit (40 wt %
for both), where the membranes could still be peeled out of the
polypropylene molds.
The thermal properties of the polymer electrolytes were
scanned in the temperature range from -100 °C up to 150 °C.
They were completely amorphous with pretty low Tg values as
listed in Table 2. The Tg value of borate ester free electrolyte
(-64.7 °C) decreased gradually to -68.3 and -77.1 °C with
the addition of B2 and B3, respectively. These results showed
that B3 was more efficient as plasticizer and therefore would
in principle contribute more to the conductivity value as it
reduced the viscosity of the system more.
Arrhenius plots of the temperature dependence of ionic
conductivity of T0.1OPS-LiSCF15-based polymer electrolytes
doped with B2 and B3 each were given in Figures 5(a) and (b),
respectively. The conductivity for borate ester free polymer
electrolyte is also plotted for comparison.
The ionic transport in a gel electrolyte can be achieved by
the sum of the fast diffusive motion of the low molecular weight
components and the slow diffusive motion of the polymer
segments in the matrix according to Svanberg.52,53 The temper-
ature dependence of the faster diffusive process of the two was
Arrhenius type, while the segmental motion deviated from
Arrhenius behavior. As depicted in Figures 5(a) and (b), the
temperature dependence of conductivity values of polymer
electrolytes plasticized by both borate esters was higher than
the borate ester free electrolyte, and the conductivity plots were
all non-Arrhenius. It implies that the ionic conductivity was
mainly dominated by transport due to segmental motion of the
polymer chains, although the positive effect of borates was
obvious. The decreased viscosity by the addition of borates
seemed to be the one reason for the increase in ionic conductiv-
ity. The improvement with B3 was more significant than B2
reaching above 10-4 S·cm-1 and in harmony with the Tg values
obtained for the electrolytes (see Table 2). Moreover, ab initio
calculations on B2 and pentaglyme, which has the same number
of oxygen atoms, indicated that borate ester interacted especially
with the anion part of the Mg(ClO4)2 salt much more efficiently
than oligoether derivatives.39 This Lewis acid-base-type inter-
action is not too strong to interact with lithium triflate to deplete
them near the polysiloxane.37 Because of the higher permittivity
of borate esters, therefore, stronger interactions with salt as
Figure 4. Arrhenius plots of ionic conductivities of T0.1OPS-LiSCF15 composite polymer electrolytes containing varying amounts (x) of nanoparticles
of (a) Al2O3 and (b) SiO2. LiSCF15 in the figure corresponds to 15 wt % LiSO3CF3. Filled symbols correspond to particle free electrolyte for
comparison.

15478 J. Phys. Chem. B, Vol. 113, No. 47, 2009
Karatas et al.
Figure 5. Arrhenius plot of T0.1OPS-LiSCF15 composite polymer electrolytes with varying amounts (x) of (a) B2 and (b) B3. LiSCF15 in the
figure corresponds to 15 wt % LiSO3CF3. Filled symbols correspond to borate ester free electrolyte for comparison.
compared to ethylene oxide units may be expected increasing
the concentration of the carrier ion, hence the conductivity.
The conductivity of B2-based electrolytes increased up to 30
wt % of the borate ester and remained then almost constant.
This concentration corresponds to approximately 1:1 ratio of
borate ester to lithium triflate and can be thought of as the
optimum point when a stoichiometric interaction of electron-
deficient boron center with the salt is considered. The increasing
trend among B3-containing electrolytes was followed ceaselessly
until 40 wt % of the borate ester. The preparation was not carried
out at 50 wt %, corresponding to a 1:1 ratio of B3 to lithium
triflate, because it resulted in mechanically unstable membranes.
Thus, no judgment could be done concerning the higher
concentrations. But overall, it can be concluded that both borate
esters yielded to a great increase in ionic conductivity as
compared to nanoparticles.
Fitting and Modeling of the Temperature-Dependent Ionic
Conductivities. VTF Modeling. The temperature-dependent
ionic conductivities of the polymer electrolytes showed notice-
able deviations from the Arrhenius law as seen in Figures 3-5.
This suggests that the oligoether side chains are instrumental
for the transport of the ions. As for many other amorphous
polymer electrolytes, the curves could be fitted by an empirical
Vogel-Tammann-Fulcher (VTF) equation
The inverse relation between salt concentration and conductivity
at sufficiently low temperatures can therefore be well described
by this empirical equation. On the other hand, the temperature
increase gives rise to the number of free ions as described by
the term σ0 (refer to Table 1 for the numerical values) that works
against the effect of T0. Therefore, the conductivity curves as
also seen in Figure 3 converge usually at a certain temperature
and then start diverging under the influence of σ0 dominating
the conductivity value at higher temperatures.
The temperature dependence of the ionic conductivities after
the addition of nanoparticles (Figure 4) and low molecular
weight borate esters (Figure 5) is also fitted by an empirical
VTF equation, and the parameters are listed in Table 2. The
general expectation for the difference T0 - Tg was nicely
followed in fitting results. The T0 values are all approximately
20 °C lower than the Tg values determined by DSC and remained
unchanged. The pseudoactivation energy containing the term,
B, was not affected by the addition of particles indicating that
there was no considerable change in the ion conduction
mechanism according to the VTF equation.
The prefactor, σ0, which relates to the number of mobile
charge carriers, remained unchanged in the case of alumina and
silica particles, but an increasing trend was observed for borate
esters. It increased linearly up to 30 wt % of B2 and then
decreased. The similar correlation for B3 was also valid. The
harmony between the experimental data and the fittings by the
VTF equation should not be overlooked. In addition, lower
values of pseudoactivation energies (kBB) of B3 containing
polymer electrolytes than that of B2 could be interpreted as
easiness of corresponding ion transport thus higher conductivity
as experimentally found.
The empirical VTF equation (eq 1) is often employed to fit
the non-Arrhenius behavior of the temperature dependence
of the conductivity in fragile amorphous materials. Although
attempts have been taken to relate the VTF equation to
macroscopic models, like free volume and configurational
entropy models for ion transport,2 no straightforward interpreta-
tion of the constants B and T0 could be concluded. Moreover,
these macroscopic models describe the motion of the polymer
host to reproduce the conductivity caused by the mobile ions.
Consistent Modeling of the Conductivity Spectra. Recently,
Funke et al.54-58 developed an equation which links the short-
time ion dynamics to the long-time dynamics, namely, the DC
conductivity. This has been done by modeling the frequency-
dependent spectra based on the MIGRATION concept, where
the acronym stands for MIsmatch Generated Relaxation for the
Accommodation and Transport of IONs. We discuss this in brief
here, but details can be found elsewhere in the literature.59-62
σ ) σ0 exp[-B/(T - T0)]
(1)
where T0 is the ideal glass transition temperature; B includes
the pseudoactivation energy (Ea ) kBB); and σ0 is a weakly
temperature-dependent prefactor. Table 1 summarizes the VTF
parameters obtained from the fits of the conductivity plots as
presented in Figure 3.
The prefactor, σ0, might be related to the number of mobile
charge carriers in the system.2 As the lithium concentration
increases, σ0 should also increase. A linear correlation of σ0
with lithium salt concentration exists for the (T0.1OPS +
LiSO3CF3) system as seen in Table 1. The term B can be thought
of as the energy barrier for the rotational motion of polymer
segments,2 and the value of that is predicted to increase
monotonously as the concentration of the lithium salt rises as
is also the case for this system. This is commonly attributed to
the stiffening of polymer segments due to the increased amount
of ionic cross-links formed in the matrix. Moreover, T0 values
as usually observed lie 20-50 °C below the Tg values as seen
in Table 1. At lower temperatures, the conductivity value
according to the VTF equation is greatly affected by the value
of T0, which is closely related to the glass transition temperature.

Polysiloxane-Based Salt-in-Polymer Electrolytes
J. Phys. Chem. B, Vol. 113, No. 47, 2009 15479
The MIGRATION concept has been employed for a wide
class of materials to model their conductivity spectra. This is a
hopping model of ion conduction for structurally disordered
materials such as fast ion conductors, alkali ion glasses, molten
salts, and salt-in-polymer electrolytes, where the ion dynamics
must be considered a strongly correlated process. Any hop of
an ion when viewed at very short times (experimentally at high
frequencies, say in the submillimeter wave regime) is always
successful, and the corresponding conductivity is denoted as
high-frequency conductivity, σHF. After this hop, several cor-
related forward-backward hops of the ion may ensue. Eventu-
ally only a fraction of all such hops will prove successful,
leading to the observed DC conductivity. The correlated
forward-backward hops result in a dispersion of the conductiv-
ity, i.e., in the observed conductivity spectra.
If the sites of the ions are rather well-defined and if the
network is nearly immobile, as in the case of crystalline fast
ion conductors and glasses, then both the measured σDC(T) and
the inferred σHF(T) (which in most cases is swamped over by
the low-frequency flank of the vibrational component) are
Arrhenius activated. However, in molten salts and salt-in-
polymer electrolytes, where the ion sites are not predefined and
where the network is not immobile, the HF conductivity is
Arrhenius activated, while the DC conductivity is not.
In general, one can write
polymer host. Indeed, recent MD simulations on poly(ethylene
oxide) with LiBF4 imply that long-range transport of ions in
the polymer happens as the mobile ions are transferred from
one polymer chain to the other by the segmental motion of the
polymer.63
From eqs 2 and 3, it is evident that the modeling of the
temperature dependence of the non-Arrhenius conductivity is
thus linked to finding an expression for W∞(T) based on the
dispersive features of the model spectra.55,56 In general, the
onset- and the end-frequencies of the conductivity dispersion,
νO and νE, show different temperature dependences. In particular,
using the basic relation between the jump rate and the coefficient
of self-diffusion as well as the Nernst-Einstein relation, we
find that νO ∝ TσDC(T). Here, ωO ) 2πνO is the rate of successful
hops. Similarly, the elementary hopping rate, Γ0, is proportional
to TσHF(T). From the model,59-62 it is found that νE ) (Γ0/2π)BK,
and the temperature dependence of this is more complex. In
the case of molten salts, where the ion sites are not predefined,
it has been found that the backward hop of an ion is not
thermally activated. This “roll-back mechanism” has been
discussed extensively elsewhere.57,64 We assumed a similar
scenario for salt-in-polymer electrolytes.55,56 In contrast to
systems with Arrhenius DC conductivity, where B(T) ∝ 1/T,
this would imply B(T) ∝ (ωΕ/Γ0)1/K for systems with non-
Arrhenius DC conductivity. Using the definition, W∞(T) ) e-B(T)
,
we get W∞(T) ) exp[-γ exp((E*/K)/kBT)], where γ is a
proportionality constant. This expression along with that given
by eq 3 when inserted in eq 2 yields
σDC(T) ) σHF(T) · W∞(T)
(2)
where W∞(T) is the fraction of successful hops for a given
temperature. Since σHF(T) is Arrhenius activated, it can be
written as
E*
kBT
E*/K
kBT
TσDC(T) ) R exp -
- γ exp
(4)
(
)
]
[
The three parameters, R, E*, and γ, can be determined by fitting
the DC conductivity data. It is to be noted that unlike the VTF
equation this fit does not have a singularity at any temperature.
Moreover, one of the parameters, namely, E*, has an obvious
physical meaning.
R
T
E*
kBT
σHF(T) ) exp -
(3)
[
]
Here R is a pre-exponential factor, and E* is the activation
energy required for an elementary displacive step.
In the following, we present a detailed and systematic
modeling of the conductivity spectra in the impedance regime,
for the following systems: (a) T0.1OPS-LiSCF15 polymer
electrolyte without any additives, as well as with additives: (b)
10 wt % Al2O3, (c) 10 wt % SiO2, (d) 40 wt % B2, and (e) 40
wt % B3. In the left panels of the Figures 6(a-e), the real part
of the frequency-dependent conductivity is plotted for different
temperatures as log10(Tσ′(ν)) vs log10(ν). In the right panels of
Figures 6(a-e), the imaginary part of the frequency-dependent
permittivity is plotted for different temperatures as log10(ε′′(ν))
vs log10(ν). Note that ε′′(ν) ) σ′(ν)/2πνε0 where ε0 is the
permittivity of free space. The experimental data are plotted as
symbols. The MIGRATION concept model curves are plotted
as solid lines. Since the dispersion spans only a few decades,
the correct shape of the model curves is best ascertained from
the complex part of the permittivity data. Hence both kinds of
plot are presented.
It is seen from conductivity spectra of each system that the
onset points of the conductivity dispersion of each isotherm,
indicated as νOmig, are found to fall on a straight line with a
slope of about one. This implies that these spectra can be scaled
to yield master curves, on shifting each isotherm along this line.
The time-temperature superposition principle59-62 is thus
obeyed and implies that the mechanism of ion conduction does
not change with temperature. It simply gets faster or slower as
the temperature is increased or decreased, respectively. The
value of the parameter K, 2.1, is found to reproduce the
From eq 2, we can write W∞(T) ) e-B(T), where B is a
parameter of the model indicating the magnitude of conductivity
dispersion in a log-log plot.
On the frequency axis, the dispersion is characterized by an
onset-frequency, νO, and an end-frequency, νE. The shape around
the onset region is unique for various kinds of structurally
disordered ion conductors and is described by the model
parameter K. It is found that the parameter K takes on a value
from 1 in molten electrolytes to about 2 in glassy electrolytes,
depending on whether the onset of the dispersion is abrupt or
gradual, respectively. More specifically, the conductivity spectra
of the widely studied fragile supercooled melt 0.6 Ca(NO3)2 ·0.4
KNO3 above a critical temperature (TT > Tg) can be fit with K
) 1.2, signifying that nearest neighbor relaxations happen
instantaneously and facilitate ion transport.54 NaPF6 dissolved
in cross-linked poly(ethylene oxide)-poly(propylene oxide)
random copolymer (PEO:PPO) constitutes the first example of
a salt-in-polymer electrolyte whose conductivity spectra have
been modeled in terms of the MIGRATION concept.55,56 The
value of the parameter K, which is 2 in this case, is similar to
the one required for many glassy ion conductors.59 In alkali ion
glasses, the value of K ) 2 is seen to result from the long-
range Coulomb interactions between the mobile cations, while
the network remains immobile. In a salt-in-polymer electrolyte,
however, the value of K ) 2 could very well reflect the coupling
of the motion of the mobile ion to the segmental motion of the

15480 J. Phys. Chem. B, Vol. 113, No. 47, 2009
Karatas et al.
Figure 6. Log-log representations of the real part of the frequency-dependent conductivities of (a) T0.1OPS-LiSCF15 polymer electrolyte,
and additives (b) 10 wt % Al2O3, (c) 10 wt % SiO2, (d) 40 wt % B2, and (e) 40 wt % B3 taken in the impedance regime are given in the
left panels. In each of these systems, the onset frequencies of the conductivity dispersion, νO, are marked as filled circles and found to satisfy
the time-temperature superposition principle. Log-log representations of the dielectric loss spectra of the same polymer electrolyte system
with the corresponding additives are presented in the right panels. The figures show the experimental data as symbols and the model curves
as solid lines (the values of the parameter K used for each system are given). See text for details.

Polysiloxane-Based Salt-in-Polymer Electrolytes
J. Phys. Chem. B, Vol. 113, No. 47, 2009 15481
Figure 7. Arrhenius-type plots of ln(TσDC) (filled squares) vs 1000 K/T of (a) T0.1OPS-LiSCF15 polymer electrolyte and corresponding composite
systems with (b) 10 wt % Al2O3, (c) 10 wt % SiO2, (d) 40 wt % B2, and (e) 40 wt % B3. Solid lines are fits using eq 4. The fit parameters E*, R,
and γ are listed in the table. VTF fits are given as dashed lines for comparison. The plots also include ln(TσHF) as open squares as calculated from
eq 3 using the given fit parameters (see text for details).
experimental spectra of Figures 6(a-c). For the borate esters
as additives, Figures 6(d) and (e), the values of K are 1.8 and
1.6, respectively. This change in the value of the parameter K
could reflect the previously mentioned fact that the addition of
the borate esters enhances the concentration of carrier ions. We
will look closely into this aspect a little later.
Using the values of the parameter K as obtained from
modeling the conductivity spectra, we are now in a position to
use eq 4 for fitting the temperature dependence of the DC
conductivity. The DC conductivities of the five compositions
studied in Figures 6(a-e) are plotted in Figures 7(a-e) as
ln(TσDC(T)) vs 1000 K/T. The solid curves are fits from eq 4.
The parameters obtained by the fitting are listed in the table of
Figure 7. For comparison, the empirical VTF fits are also plotted
in this representation as dashed lines. Using the values of E*
and R in eq 3, σHF is calculated and is also plotted in Figures
7(a-e).
0.05-0.06 eV, while σ0 shows a marked increase as one goes
from nanoparticles to borate esters as additives.
The E* values obtained from the MIGRATION concept for
the investigated polysiloxane-based polymer electrolyte are
about 0.21-0.26 eV. These values are rather similar to the value
of E* of about 0.25 eV found for NaPF6 dissolved in PEO:
PPO random copolymer.56 This large activation energy for an
elementary displacive step for salt-in-polymer electrolytes can
be understood if one regards the elementary displacive step to
involve a coupling of the segmental motion of the polymer host
with that of the mobile ion. In the work of Pas et al.,55,56 it was
inferred that the coupling between segmental motion and ionic
transport may well also be reflected by a value of about 2 for
the parameter K, which is needed for modeling the experimental
conductivity spectra. This is also the trend observed here.
For a discussion of the effect of nanoparticle fillers versus
borate esters as additives, see Figures 8(a) and (b). Here we
present the impedance spectra of samples containing 10 wt %
Al2O3 and with 40 wt % B2, taken at three temperatures, along
with the complete conductivity spectra as calculated from the
model. The agreement between the spectra and the data is fairly
good except for the σDC value at the lowest temperature. More
Considering the parameters T0, σ0, and kBB from Table 2 of
the VTF fits for the specific compositions presented in Figures
7(a-e), it is in the first place evident that both Tg and T0 remain
practically constant. Second, the value of the pseudoactivation
energy [kBB] also changes only marginally, being about

15482 J. Phys. Chem. B, Vol. 113, No. 47, 2009
Karatas et al.
Figure 8. Log-log representation of conductivity spectra of T0.1OPS-LiSCF15 polymer electrolyte with (a) 10 wt % Al2O3 and (b) 40 wt % B2
as open symbols for temperatures from 243 to 263 K with model curves as solid lines. The νOmig (filled circles) and Γ0/2π (filled squares) are also
given for each temperature.
Figure 9. Log-log representation of experimental and model conductivity spectra of T0.1OPS-LiSCF15 and corresponding systems with additives
at (a) 243 K and (b) 253 K. The conductivities shown are normalized by σDC. The parameters are listed in Table 3.
mig
TABLE 3: Model Parameter K Found by Reproducing the Shape of the Experimental Spectra and νO Obtained by Shifting
the Model Curve onto the Experimental Spectraa
additives (wt %)
K
log10[(σDCT)/S cm-1 K]
log10(υmOig/Hz)
log10[(Γ0/2π)/Hz]
B
log10[(σHFT)/S cm-1 K]
T ) 243 K
T ) 253 K
-
2.1
2.1
2.1
1.8
1.6
2.1
2.1
2.1
1.8
1.6
-5.23
-5.16
-5.14
-4.50
-3.52
-4.55
-4.49
-4.49
-3.79
-2.94
3.79
3.82
3.92
4.60
5.46
4.56
4.55
4.64
5.36
6.08
6.856
6.865
6.929
7.617
8.143
7.157
7.136
7.200
7.867
8.350
5.22
5.17
5.09
5.11
4.34
4.14
4.12
4.06
3.94
3.39
-2.96
-2.91
-2.93
-2.29
-1.64
-2.75
-2.70
-2.72
-2.08
-1.47
Al2O3 (10)
SiO2 (10)
B2 (40)
B3 (40)
-
Al2O3 (10)
SiO2 (10)
B2 (40)
B3 (40)
a The other parameters are obtained as fits of eqs 3 and 4 to the temperature-dependent DC conductivity. See text and Figures 6 and 7 for
details.
importantly, it is seen that Γ0/2π, where Γ0 is the elementary
measured at higher frequencies. However, they would not
contribute to DC conductivity. Such features have been seen
and analyzed in the complete conductivity spectra of NaPF6 and
MgClO4 dissolved in PEO:PPO random copolymer.55,56 In these
systems, the conducting species are bulky anions, and the
relatively small cations are loosely bound to the polymer host
and show a localized and caged motion as a Nearly Constant
Loss (NCL-type) component.65-68
hopping rate, is found to lie in the impedance regime. For glassy
electrolytes, the value of the elementary hopping rate is normally
found at higher frequencies. This is also in contrast to the salt-
in-polymer electrolyte systems with both NaPF6 and MgClO4
dissolved in PEO:PPO random copolymer.55,56 In glassy elec-
trolytes, as well as in the anion conducting salt-in-polymer
electrolytes, the higher value of the elementary hopping rate,
Γ0, is indicative of the hopping of the mobile ion being rather
independent of its network. However, in the current systems
under study, the low values of Γ0 can be taken as a clear
indication that the Li+ ion dynamics are slow and collective
and coupled to the polymer backbone.
The complete conductivity spectra as calculated from the
model, see Figures 8(a) and (b), correspond only to those hops
that eventually become successful and contribute to DC
conductivity. Purely localized motion of dipolar and nonpolar
types, such as the coupled motion of the polymer side chains
with that of the bulky anions or rotational diffusion of the bulky
anions, respectively, could be seen in conductivity spectra when
We can now return to look closely into the features of the
conductivity spectra as revealed by the model and try to decode
the information from the model parameters. To this effect, scaled
conductivities, σ(ν)/σDC, are plotted versus frequency for
temperatures T ) 243 K and T ) 253 K (see the log-log plots
of Figures 9(a) and (b)). The figures contain both experimental
and model spectra. The model parameters corresponding to these
figures are given in Table 3. In the figures, three parameters
show distinct trends as one goes from nanoparticle fillers to
borate esters: (i) the onset frequency, νO, increases by about

Polysiloxane-Based Salt-in-Polymer Electrolytes
J. Phys. Chem. B, Vol. 113, No. 47, 2009 15483
1.5 decades; (ii) the value of K decreases from 2.1 to 1.6; (iii)
the magnitude of the dispersion decreases by about half a
decade.
insight regarding the collective ion dynamics at higher frequen-
cies. Conductivity measurements at higher frequencies would
provide additional information on the short-time dynamics of
the ions.
The reduced value of the parameter K is usually attributed
to an increased carrier density.59 However, the first feature shows
that the effect of addition of borate esters to the salt-in-polymer
electrolytes results in an early onset (on the time scale) of DC
conduction. This implies that the effect of the borate esters as
additives not only enhances the carrier concentration but also
facilitates conduction. This is in agreement with the absolute
values of the DC conductivities (see Table 3). Evidently, for
borate esters, the DC conductivity sets in rapidly and earlier,
resulting in an enhanced value of σDC compared to the salt-in-
polymer electrolyte system without any additive or with other
additives.
From Table 3, one can infer that the decrease of the magnitude
of conductivity dispersion, B, defined as B ) γ exp[(E*/K)/
(kBT)] (see text above eq 4), is largely due to the decrease of γ
in the case of the borate esters. It has been discussed in relation
to fluidity and conductivity in CKN58 that the parameter γ
reflects a temperature-independent geometric factor. In short,
both the elementary displacive step and the correlated hops of
ions are favorably influenced by the addition of borate esters.
This insight into the ion dynamics has been made possible by
a systematic study and consistent modeling of the ion dynamics
in these systems. On the other hand, the VTF fits, though
excellent, can provide very little insight into the ion dynamics.
Acknowledgment. We are grateful to the Deutsche Fors-
chungsgemeinschaft for the financial support of this work within
SFB 458. Y. Karatas and N. Kaskhedikar would like to thank
the International Graduate School of Chemistry at the University
of Muenster for their doctoral fellowships.
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polymer host has more decisive effect on the electrical properties
of the composite polymer electrolytes than acid-base-type
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