Electrochemical Properties for Ionic Liquid/Polymer Electrolyte Systems

NAM KU PARK, YOUNG CHAN BAE

Division of Chemical Engineering and Molecular Thermodynamics Laboratory, Hanyang University, Seoul 133-791, Korea

Received 24 July 2009; revised 9 October 2009; accepted 14 October 2009
DOI: 10.1002/polb.21891
Published online in Wiley InterScience (www.interscience.wiley.com).

ABSTRACT:

The ionic liquid (1-ethyl-3-methylimidazolium hexa-

fluorouphophate) ([emim][PF

6

]) with different molecular weights

of poly(ethylene oxide) (PEO) (MW

¼ 4600; 10,000; 14,000;

20,000; 35,000, and 100,000) has been characterized at various
temperatures and compositions using phase behaviors and ionic
conductivity. A molecular thermodynamic model based on a
combination of the previous theory (BH model) by Chang et al.,
a nonrandomness theory (NR model), and the Pitzer-Debye-
Hu¨ckel theory modified by Guggenheim (PDH model) consid-
ered not only short-range specific interactions between the poly-
mer and a cation of the ionic liquid (IL), but also long-range
electrostatic forces between anions and cations within the IL. We
have derived a new melting point depression theory based on
this BH-NR-PDH model. We also established an ionic conductiv-
ity model, based on the Nernst-Einstein equation, in which the
diffusion coefficient is derived from the BH-NR-PDH model. The
proposed model takes into account that the mobility of cations

in the IL and the motions of the polymer host by expressing the
effective chemical potential as the sum of the chemical poten-
tials of the polymer and the IL. To describe the segmental

motion of the cation and polymer chain, the effective coordi-
nated unit parameter is introduced. The derived coordinated
unit parameter for each state is used to determine the ionic con-
ductivities of the given systems. Quantitative results from the
proposed model are in good agreement with experimental data.
The results indicate that the molecular weight of the polymer
and the surrounding temperature play important roles in deter-
mining eutectic points and ionic conductivities of the given sys-
tems.

V

C

2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym

Phys 48: 212

–219, 2010

KEYWORDS:

conducting

polymer;

ionic

conductivity;

ionic

liquids; melting point; melting point depression; phase behav-
ior; Pitzer-Debye-Hu¨ckel model; poly(ethylene glycol)

INTRODUCTION

Ionic liquids (ILs) are novel and functional

solvents with unique properties, such as negligible volatility,
thermal stability, and relatively high polarity.

1

–3

Given the

wide range of possible cation and anion combinations, a
large variety of very useful application-related ionic liquids
are able to be created through the easy modification of spe-
cific functional groups within the ionic components.

4

–7

The

alkyl imidazolim based ionic liquids have been investigated
as possible electrolytes for their application as batteries and
capacitors.

8,9

Polymer-based electrolyte materials have been reported as
promising materials for use in these applications due to their
unique properties, such as high ionic conductivity, the ability
to provide good electrode/electrolyte contact, and physical
flexibility.

10,11

Use of solid polymer electrolyte systems avoids

problems associated with liquid electrolytes, such as leakage
and gas formation during solvent decomposition. Also, a sys-
tem with only thin-film electrodes and electrolytes can be
made very compact, lightweight, and highly reliable.

In this study, we developed a new melting point depression
theory based on a thermodynamic model with three contri-
butions: mixing of the polymer and the IL, a nonrandomness
effect, and a long-range electrostatic interaction. The first

two contributions are manifestations of the Chang et al.
theory

12,13

and the nonrandom

14

model, respectively. The

last is based on the Pitzer Debye-Hu¨ckel expression.

15,16

This

electrostatic interaction occurs because of the dissociation of
electrolytes in solution and the resulting change in the long-
range Columbic forces between ions, which introduces
changes in their observable behavior. The IL was dissociated
completely and the consequential increase in the ion

–ion

interactions was corrected by assuming the IL to be a parti-
cle. Comparisons of theoretical melting point predictions
with experimental data were made for various PEG and IL
systems; the model systems were used to predict eutectic
points for various compositions and different ranges of
temperature.

We used the diffusion coefficient, for which the driving force
is based on a chemical potential gradient. To account for the
effects of both the IL and polymer concurrently, the sum of
each chemical potential was differentiated with concentra-
tion. Each chemical potential was calculated from the phase
diagram of the given system using Flory’s melting point
depression theory

15

combined with our BH-NR-PDH model.

Combining

the

derived

diffusion

coefficient

equation

with the Nernst-Einstein relationship yielded the final

Correspondence to: Y. C. Bae (E-mail: [e-mail])
Journal of Polymer Science: Part B: Polymer Physics, Vol. 48, 212

–219 (2010)

V

C

2009 Wiley Periodicals, Inc.

212

INTERSCIENCE.WILEY.COM/JOURNAL/JPOLB

conductivity equation. Comparison of the proposed theory
with experimental data was performed for various PEG and
IL systems, including the cations and anions of the IL.

EXPERIMENTAL

Sample Preparation
PEO (MW

¼ 4600; 10,000; 14,000; 20,000; 35,000) and

PEG (MW

¼ 100,000) were obtained from Aldrich Chemical

Co. and were used without further purification. 1-ethyl-3-
methylimidazolium hexafluorophosphate [emim] [PF

6

] was

also supplied by Aldrich Chemical Co. and was used as-
received. Weighed amounts of PEO and IL were dissolved in
a minimum amount of distilled deionized (DDI) water
(

<99.9%) and then stirred overnight to form homogeneous

solutions. Films were made by casting the solutions onto
glass plates and drying for 24 h at room temperature. Then
they were transferred to a vacuum oven and dried at 50

C

for 24 h. The films were used only after crystallization was
completed.

Thermo-Optical Analysis
Melting point measurements of PEO/IL systems were carried
out by thermo-optical analysis (TOA). This technique utilizes
a heating

–cooling stage, a photodiode (Mettler FP80), and a

microprocessor (Mettler FP90). The scan rate was 1.0

C/

min. An IBM PC was used for data acquisition.

Differential Scanning Calorimetry
A Perkin

–Elmer DSC-7 was used to measure the heats of

fusion and melting temperatures of pure polymer and IL at a
heating rate of 10

C/min from 10

C to 120

C. The heats

of fusion of the various PEOs (MW

¼ 4600; 10,000; 14,000;

20,000; 35,000) and PEG (MW

¼ 100,000) were 99.43 J/g,

123.5 J/g, 131.6 J/g, 133.9 J/g, 135.9 J/g, and 233.8 J/g,
respectively. The heat of fusion of the IL was 71.72 J/g.

Ionic Conductivity Measurement
Ionic conductivity was determined by AC impedance at a fre-
quency range of 1 MHz to 0.1 Hz (10 mV signal amplitude)
using an impedance analyzer (Gamry reference 600). Appro-
priate amounts of PEO and IL were dissolved in distilled
deionized (DDI) water (

<99.9%). The solutions were well

stirred and cast onto a stainless steel plate and left at room
temperature for solvent evaporation. The resulting film was
dried in a vacuum oven at 50

C for at least 24 h. The pre-

pared polymer electrolyte film was sandwiched between two
stainless steel (SS) electrodes for conductivity measure-
ments. The ionic conductivity (r) was calculated from im-
pedance data, using the relation r

¼ L/RA, where L and A

are the thickness and area of the polymer electrolyte, respec-
tively, and R is the bulk resistance, as derived from the AC
impedance spectrum. Linear sweep voltammetry was per-
formed on SS working electrodes at 40, 50, 60, and 70

C,

with counter and reference electrodes of IL, at a scanning
rate of 1.0 mV/s.

MODEL DESCRIPTION

Various types of interactions are taken into account when
describing the activity of SPE/salt systems. In this study, the

excess Helmholtz free energy is calculated as the sum of three
contributions:

DA ¼ DA

BH

þ DA

NR

þ DA

PDH

(1)

The terms on the right-hand side of eq 1 represent the con-
tribution of the mixing of the polymer and salt based on the
Chang et al. model (BH),

12,13

the nonrandom contribution

based on the expression proposed by Panayiotou et al.
(NR),

14

and the long-range interaction contribution caused

by the Coulombic electrostatic forces that mainly describe
the direct effects of charge interactions (PDH).

The melting point depression theory by Flory

15

is the basis

for the activities required for evaluating electrochemical
properties of the given systems Three electrochemical prop-
erties (OCV, D

s

, j) are related to the activity of the given sys-

tem and three pair-wise interaction parameters D

ij

through

expressions developed by Newman.

16

BH-NR Model
In this work, we develop a new thermodynamic framework
to describe the nonrandom distribution of salt in the SPE
system. The chemical potential of each component is calcu-
lated as a sum of two contributions. Helmholtz’s free energy
of mixing for the binary polymer solution is defined as
follows:

DA ¼ DA

BH

þ DA

NR

(2)

To consider a salt effect for the free energy of mixing, we
assume that the salt is a particle. Chemical potentials for
each component are given as follows:

Dl

1

¼ @D

mix

A

@N

1



T;N

2

¼ lnð1  /

2

Þ þ /

2

1

 r

1

r

2



þ z

2

q

1

ln

h

1

/

1

þ q

1

ðh

2

 /

2

Þ þ q

2

r

1

/

2

r

2

/

1

ð/

1

 h

1

Þ





ð3Þ

Dl

2

¼ @D

mix

A

@N

2



T;N

1

¼ ln /

2

þ ð1  /

2

Þ 1  r

2

r

1



þ z

2

q

2

ln

h

2

/

2

þ q

2

ðh

1

 /

2

Þ þ q

1

r

2

/

1

r

1

/

2

ð/

2

 h

2

Þ





ð4Þ

where,

Y ¼

1
2

B

1
~T



A

a

1

ð2/

2

 1Þ



 ln 1  a

1

ð2/

2

 1Þ

1

 a

0

ð2/

2

 1Þ

fexpð1=~TÞ  1g





ð5Þ

We use the local composition expression by Panayiotou et al.
to describe the nonrandom contribution:

Dl

i

kT



NR

¼ zq

i

2

ln

C

ii

(6)

where the surface factor zq

i

is calculated from

ARTICLE

IONIC LIQUID/POLYMER ELECTROLYTE SYSTEMS, KU PARK AND BAE

213

zq

i

¼ r

i

ðz  2Þ þ 2

(7)

For the binary solution, the nonrandomness factor between
ij pairs in eq 7, C

ij

, is given by

14

C

12

¼

2

1

þ 1  4h

1

h

2

ð1  G

12

Þ

½



1

=2

(8)

where h

i

is the overall surface area fraction of component i

defined as h

i

: N

i

zq

i

/Nzq and the energy factor G

12

is

defined by

G

ij

 exp aDd~e

ð

Þ

(9)

ðDd~e ¼ d~e

11

þ d

~e

22

 2d

~e

12

Þ

where N

i

and N represent the number of components i and

the total number of molecules, respectively. The parameter a
is introduced to represent the degree of nonrandomness.
The additional correlation to define the nonrandomness fac-
tor is given by

C

ii

¼

1



P

j6¼i

h

j

C

ij

h

i

(10)

where

C

ij

(i = j) is considered to be an independent variable.

Substitution of eq 10 into eq 6 corresponds to Guggenheim’s
molecular treatment.

17

Long-Range Electrostatic Contribution
A long-range electrostatic contribution is represented by the
Pitzer-Debye-Hu¨ckel equation.

18

Its expression for the excess

Gibbs free energy, normalized to the mole fraction of a unit
for the solvent and zero mole fractions for electrolytes, is
given as follows:

G

ex



;PDH

¼ 

X

k

x

k

!

4A

x

I

x

q





ln 1

þ q



I

1

=2

x





(11)

where A

x

is the usual Debye-Hu¨ckel parameter and I

x

is the

ionic strength. Equations for each are as follows:

A

x

¼

1
3

2pN

A

q

s

m

s



1

=2

e

2

e

0

e

s

kT



3

=2

; I

x

¼

1
2

X

z

2
i

x

i

(12)

where x

i

and z

i

are the mole fraction and the charge number

of the i

th

component, respectively. The closest approach pa-

rameter, q



, is defined by

q



¼ r

0

2

 10

6

e

2

N

A

q

s

m

s

e

0

e

s

kT



1

=2

¼ B

x

T

1

=2

(13)

where r

o

is the hard core radius, e is the electron charge, N

A

is Avogadro’s number, e

o

is the permittivity of vacuum, e

s

is

the relative permittivity of the solvent, m

s

is the solvent mo-

lecular weight, and q

s

is the solvent density. The expression

for the activity coefficient of a solvent is

ln c

el
2

¼

2A

x

I

3

=2

x

1

þ q



I

1

=2

x

(14)

and for an ion i, derived from eq 11

ln c

;PDH
i

¼ z

2
i

A

x

2

q



ln

ð1 þ q



I

1

=2

x

Þ þ I

1

=2

x

ð1  2I

x

=z

2
i

Þ

1

þ q



I

1

=2

x

"

#

ð15Þ

Equation 15 reduces to eq 14 for z

i

¼ 0. The resulting equa-

tion for c

i

of a specific ionic component i of charge z

i

has

one adjustable model parameter, q



. Pitzer’s recommendation

for multi-component systems where q



varies with the mole

fraction is either to take a fixed average value for q



or to

treat it as a fitting parameter.

19

From the definition, the mean activity (a

v

6

) and the activity

coefficient of component i (a

i

) are

a

v

6

¼ a

v

þ

þ

a

v





;

a

i

¼ c

i

x

i

(16)

The chemical potential of the long-range contribution is then
calculated by

l

6

¼ l

0

6

þ vRT lnðc

6

xÞ

(17)

where v

i

is the stoichiometric coefficient and v is defined as

v ¼ v

þ

þ v



.

The Melting Point Depression Theory
In a semicrystalline system, the condition of equilibrium
between a crystalline polymer and the polymer unit in solu-
tion may be described as follows

15

:

l

c

u

 l

0
u

¼ l

u

 l

0
u

(18)

where l

c

u

, l

u

, and l

0
u

are the chemical potentials of the crys-

talline polymer segment unit, the liquid (amorphous) poly-
mer segment unit, and the standard state, respectively. Now
the formal difference of appearing on the left-hand side is
expected as follows:

l

c

u

 l

0
u

¼ DH

u

ð1  T=T

0

m

Þ

(19)

where

DH

u

is the heat of fusion per segment unit, and T

m

and T

0
m

are the melting point temperatures of the species in

a mixture and a pure phase, respectively. Equation 19 can be
restated as follows:

l

u

 l

0
u

¼ V

u

V

1

r

1

r

2

@DA

@N

2



T;V;N

1

(20)

where V

1

and V

u

are the molar volumes of the salt and of

the repeating unit, respectively. By substituting eqs 19 and
20 into eq 18 and replacing T by T

m,2

, the equilibrium melt-

ing temperature of the mixture is given by

1

T

m

;2



1

T

0

m

;2

¼  k

DH

u

V

u

V

1

r

1

r

2

l

2

 l

0
2

kT

m

;2



(21)

JOURNAL OF POLYMER SCIENCE: PART B:

POLYMER PHYSICS

DOI 10.1002/POLB

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INTERSCIENCE.WILEY.COM/JOURNAL/JPOLB

The subscripts 1, 2, and u refer to the salt, the polymer, and
the polymer segment unit, respectively. Similarly, we obtain
for the salt (Component 1)

1

T

m

;1



1

T

0

m

;1

¼  k

DH

1

l

1

 l

0
1

kT

m

;1



(22)

Substituting eqs 3, 6, and 14 into eq 21 gives the equilib-
rium melting temperature of Component 2 as

1

T

m

;2



1

T

0

m

;2

¼  k

DH

u

V

u

V

1

r

1

r

2

ln /

2

þ ð1  /

2

Þ 1  r

2

r

1



þ z

2

q

2

ln

h

2

/

2

þ q

2

ðh

1

 /

2

Þ þ q

1

r

2

/

1

r

1

/

2

ð/

2

 h

2

Þ





þ zq

2

2

ln

C

22

þ v lnðc

el
2

xÞ



ð23Þ

and substituting eqs 2, 6, and 15 into eq 22 gives

1

T

m

;1



1

T

0

m

;1

¼  k

DH

1

ln

ð1  /

2

Þ þ /

2

1

 r

1

r

2



þ z

2

q

1

ln

h

1

/

1

þ q

1

ðh

2

 /

2

Þ þ q

2

r

1

/

2

r

2

/

1

ð/

1

 h

1

Þ





þ zq

1

2

ln

C

11

þ vRT lnðc

6

xÞ



ð24Þ

From eqs 23 and 24, we can predict the phase diagrams of
binary polymer/IL systems.

The Ionic Conductivity Theory
For binary diffusion in gases or liquids, the generalized
Fick’s equation for heat and mass is as follows

20

:

J



A

¼ cD

AB

x

A

r ln a

A

þ

1

cRT

½ð/

A

 x

A

Þr

p



qx

A

x

B

ðg

A

 g

B

Þ þ k

T

r ln T

ð25Þ

This equation indicates that the thermodynamics of irreversi-
ble processes dictates using the activity gradient as the driving
force for concentration diffusion. This requires a diffusion
coefficient which is different from Fick’s first law. When the
pressure-, thermal-, and forced-diffusion terms are dropped,
eq 25 for binary electrolytes is simplified to

J



s

¼ D



C

s

r ln a

s

(26)

where D



, C

s

, and a

s

are the self-diffusion coefficient, the

concentration, and the activity of the salt, respectively. Using
the fact that the activity is a function of concentration, this
equation may be rewritten as

J



s

¼ D



C

s

d ln a

s

dC

s



rC

s

(27)

Equation 27 and the original Fick’s equation, J



s

¼ D

s

!C

s

,

can be compared using the measured diffusion coefficient D

s

(based on a concentration driving force)

21

D

s

¼ D



d ln a

s

d ln c

s



(28)

where D



characterizes the component mobility in the ab-

sence of any system interactions.

22

This again may be rewrit-

ten using the fact that the activity is related to the chemical
potential by ln a ¼

Dl
RT

as follows:

D

s

¼ D



C

s

d

Dl

s

RT

 

dC

s

(29)

To express the transfer effect of cations in the conductivity
model, the chemical potential in eq 29 is replaced by the
sum of chemical potentials of ionic liquids and diverse poly-
mer units, which are given by

D

s

¼ D



C

s

d

Dl

eff

RT





dC

s

;

Dl

eff

RT

¼ D

l

s

RT

þ k

eff

Dl

u

RT

(30)

where k

eff

is the effective transfer unit of IL. A mathematical

form of k

0

e

xC

s

is adopted for k

eff

based on the exponentially

decreasing coordinating units, where k

0

and x are adjustable

model parameters, respectively. These parameters are medi-
tated between ion pairs and specific interaction between
nonshared electrons on oxygen ion. These factors are
assumed and related with chemical effects on the binary sys-
tems and between anions and cations.

Thus, using the Nernst-Einstein relationship for a multi-com-
ponent system yields the conductivity equation for the sys-
tem of ILs/polymer electrolytes with the form:

r

¼ F

2

RT

X

i

z

2
i

v

i

D

i

C

i

(31)

where F is the Faraday constant. As we assume that the
phase for the given condition is a binary system of ionic
liquids and polymers, the moving object is a cation. If the
charge effect of each ion remains for the ion interactions,
this assumption transforms eq 31 into the simple form

r

¼ F

2

C

s

RT

D

s

X

i

z

2
i

(32)

TABLE 1

Physical Properties of PEO, PEG, and Ionic Liquid

MW
(g/mol)

T

0

m

(K)

DH
(J/g)

Density
(g/cm)

V

u

(cm

3

/mol)

PEO

4,600

339.15

99.43

1.21

36.6

10,000

339.15

123.5

1.21

36.6

14,000

339.15

131.6

1.21

36.6

20,000

339.15

133.9

1.21

36.6

35,000

339.15

135.9

1.21

36.6

PEG

100,000

340.15

150.6

1.07

36.6

[Emim]
[PF

6

]

256.13

334.05

69.73

1.514

78.5

ARTICLE

IONIC LIQUID/POLYMER ELECTROLYTE SYSTEMS, KU PARK AND BAE

215

Substituting eq 30 into eq 32 gives the final ionic conductiv-
ity equation for ionic liquids/polymer systems

r

¼ F

2

C

s

RT

D



C

s

d

Dl

s

RT

þ k

0

e

xC

s

Dl

u

RT





dC

s

X

i

z

2
i

(33)

where the chemical potentials are given by



l

s

RT

¼ ln 1  /

2

ð

Þ þ /

2

1

 r

1

r

2



þ z

2

q

1

ln

h

1

/

1

þ q

1

h

2

 /

2

ð

Þ þ q

2

r

1

/

2

r

2

/

1

/

1

 h

1

ð

Þ





þ zq

1

2

ln

C

11

þ vRT ln r

s

x

ð

Þ ð34Þ

and

l

u

RT

¼ V

u

V

1

 r

1

r

2

 ðln /

2

þ ð1  /

2

Þ 1  r

2

r

1



þ z

2

q

2

ln

h

2

/

2

þ q

2

h

1

 /

2

ð

Þ þ q

1

r

2

/

1

r

1

/

2

/

2

 h

2

ð

Þ





þ zq

2

2

ln

C

22

þ v lnðr

el

2

xÞÞ ð35Þ

Table 1 gives physical properties of various PEO/IL systems
and the model parameters are listed in Table 2. The estimated
eutectic point at the intersection of the two curves is wt % of
ionic liquid

 0.5. Model parameters are determined and

listed in Table 3. In this case, the co-ordinated unit parameter,
k

eff

, is nearly a unity that means the PEG/IL system has nearly

one-to-one bonding between the cations and polymer unit
such as nonshared electrons on oxygen ion.

RESULTS AND DISCUSSION

Figure 1 shows how to determine two different T

m

’s using

TOA for the generation of a PEO/IL system. The melting
point 1 is approximately the same for all generated poly-
mer/IL mixtures. The melting point 2 is attributed to the
transition from the intracrystalline amorphous polymer and
crystalline

complex

to

the

intercrystalline

amorphous

polymer.

Figures 2

–7 represent the phase behaviors of the poly (ethyl-

ene glycol) (MW

¼ 4600; 10,000; 14,000; 20,000; 35,000;

100,000)/IL systems. The open squares and circles represent

TABLE 2

Chemical Potential Parameters for PEG/IL and PEO/IL

Systems

e/

k (K)

de

12

/

k (K)

B

x

(K

1/2

)

PEG/[emim][PF

6

]

103.199

260.195

1,002.37

PEO/[emim][PF

6

]

126.317

266.834

1,420.32

TABLE 3

Diffusion and Co-Ordinated Unit Parameters for PEG/

IL and PEO/IL Systems

Temperature
(K)

D



(cm

2

/s)

k

0

(

)

x
(cm

3

/mol)

PEG(MW:

4600)/
[emim]
[PF

6

]

313.15

3.1452

 10

6

0.0171

174.451

323.15

6.5373

 10

5

0.0848

140.550

333.15

7.1262

 10

5

0.0734

131.547

343.15

9.4912

 10

5

0.0502

128.651

PEO(MW:

100,000)/
[emim]

[PF

6

]

313.15

3.4225

 10

5

0.0465

170.932

323.15

8.7336

 10

5

0.866

158.256

333.15

9.6917

 10

5

0.454

157.295

343.15

1.2731

 10

4

0.195

150.861

FIGURE 1

A typical TOA result for determining the melting

point temperature of a polymer/IL system.

FIGURE 2

The phase diagram for the poly (ethylene glycol)

(MW

¼ 4600)/1-ethyl-3-methylimidazolium hexafluorophos-

phate system. The open squares and circles represent experi-
mental data of PEG/IL system obtained using the TOA
technique.

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the experimental data, while the solid line has been calcu-
lated with the proposed model. From the experimental data,
several phases are observed: the liquid phase (L) located at
a low wt % of salt (wt %) at high temperatures, the mixed
phase of PEO and IL at a low wt % of salt at low tempera-
tures, the mixed phase of liquid PEO and crystalline complex
at a high wt % of salt and high wt % of IL at high tempera-
tures, and the mixed phase of PEO and crystalline complex
at a high wt % of IL at low temperatures. As shown in
Figures 2

–7, there are slight deviations between the theoreti-

cal predictions and the experimental data in the region of
high IL concentrations. This may be due to the specific inter-
actions between the group of long chains with the polymer
and IL that are not considered in this model. The eutectic
point is present at a level of near equal compositions.

We let the number of the salt segment, r

1

, be unity and cal-

culated the number of polymer units, r

2

, using specific vol-

umes V

1

and V

2

for solvent and polymer, respectively:

r

2

¼ M

2

V

2

M

1

V

1

(36)

where M

1

and M

2

are molecular masses for salt and polymer,

respectively. g and z are set to be 0.3 and 6, respectively, as
suggested by Hu et al.

23

For the present work, we let the

nonrandomness parameter, a, be 0.03, which is a characteris-
tic value for PEO/IL systems.

Figures 8 and 9 show the ionic conductivities of PEO/IL sys-
tems at 313.15 K and 343.15 K. Open circles represent the

FIGURE 3

The phase diagram for the poly(ethylene glycol)

(MW

¼ 10,000)/1-ethyl-3-methylimidazolium hexafluorophosphate

system. The open squares and circles represent experimental data
of PEG/IL system obtained using the TOA technique.

FIGURE 4

The phase diagram for the poly(ethylene glycol)

(MW

¼ 14,000)/1-ethyl-3-methylimidazolium hexafluorophos-

phate system. The open squares and circles represent experi-
mental data of PEG/IL system obtained using the TOA
technique.

FIGURE 5

The phase diagram for the poly(ethylene glycol)

(MW

¼ 20,000)/1-ethyl-3-methylimidazolium hexafluorophos-

phate system. The open squares and circles represent experimen-
tal data of PEG/IL system obtained using the TOA technique.

FIGURE 6

The phase diagram for the poly (ethylene glycol)

(MW

¼ 35,000)/1-ethyl-3-methylimidazolium hexafluorophos-

phate system. The open squares and circles represent experi-
mental data of PEG/IL system obtained using the TOA
technique.

ARTICLE

IONIC LIQUID/POLYMER ELECTROLYTE SYSTEMS, KU PARK AND BAE

217

experimental data and the lines are calculated by the pro-
posed model. To investigate the effect of the molecular
weight of the polymer on the ionic conductivity for the given
systems, we considered two common features of the poly-
mer, the specific interaction parameter and the melting tem-
perature. PEG with long polymer chain groups has higher
interaction energy and slightly higher melting temperature
than those with short chain groups. The relationship
between ionic conductivity and the molecular weight of the
polymer does not have a significant effect. Figure 8 shown
the specific trend for the high ionic conductivity of PEO (MW
¼ 100,000) comparing to other polymers because longer
polymer chains were less effect to cations of IL. A huge
group of polymer chains had many holes to move into the
given system. However, the high viscosity and poor solubility

of PEO was difficult to be applied to make a polymer
electrolyte.

Figures 10 and 11 compare the ionic conductivities between
the PEG (MW

¼ 4600)/IL and PEO (MW ¼ 100,000)/IL sys-

tems at different temperatures. Optimized ionic conductiv-
ities of 2.665

 10

5

S/cm at 40

C and 2.64

 10

2

S/cm

at 70

C were obtained for [emim] [PF

6

]/PEG at an IL vol-

ume fraction of 0.5. This result indicates that the trend of
ionic conductivity is related to that of the phase behavior. At
343.15 K, the ionic conductivities of the two systems were
higher than that of the systems at 313.15 K. This result can
be ascribed to the presence of amorphous and crystalline
regions at that temperature. This explains the results of the
ionic liquid/PEG phase diagram, with the low ionic conduc-
tivity at low temperatures falling below the amorphous
region; it is not possible for the cation of the ionic liquids to
be active in the mixture. As a result, the trend of ionic con-
ductivity shows that all polymer/IL systems had more effec-
tive conductivity in the amorphous regions.

FIGURE 7

The phase diagram for the poly (ethylene oxide)

(MW

¼ 100,000)/1-ethyl-3-methylimidazolium hexafluorophos-

phate system. The open squares and circles represent experi-
mental data of PEG/IL system obtained using the TOA
technique.

FIGURE 8

Ionic conductivity of PEG/IL systems at 313.75 K. All

the symbols represent experimental data from our work and
the lines are calculated using the proposed model.

FIGURE 9

Ionic conductivity of PEG/IL systems at 343.75 K. All

the symbols represent experimental data from our work and
the lines are calculated using the proposed model.

FIGURE 10

Ionic conductivity of PEG (MW

¼ 4,600)/IL systems.

All the symbols represent experimental data from our work
and the lines are calculated using the proposed model.

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DOI 10.1002/POLB

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CONCLUSION

A polymer-based binary system is subject to the laws of clas-
sical thermodynamics and can be described by phase behav-
iors. As a result of thermal analysis, the phase diagrams
were constructed and the liquid curves between a crystalline
phase and amorphous phase were calculated using a lattice
theory based on Flory’s melting point depression concept.
The degree of melting point depression depends on the
intermolecular forces associated with the molecular weights
of PEG, the compositions, and the thermal histories. The pro-
posed model considers both IL-polymer interactions (Chang
et al’s BH theory) and ion-ion interactions (Pitzer-Debye-
Hu¨ckel expression theory) and describes very well the phase
behaviors of polymer/IL systems.

The trend of ionic conductivity for the polymer/IL systems
shows that the amorphous regions of the given systems
were more affected by ionic conductivity than were the crys-
talline regions. We also determined in the ionic conductivity
model that the concentration dependence of the diffusion
coefficient was expressed by differentiating chemical poten-
tial with concentration to relate the phase behavior of the
given system to the diffusion and ionic conductivity. The cal-
culated values using the proposed model agree well with the
experimental data for the PEG/IL systems.

This work was supported by the Korea Science and Engineering
Foundation (KOSEF) grant funded from the Ministry of Educa-
tion, Science and Technology (MEST) of Korea for the Center for
Next Generation Dye-sensitized Solar Cells (No. 2009-0063373).

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FIGURE 11

Ionic conductivity of PEO (MW

¼ 100,000)/IL sys-

tems. All the symbols represent experimental data from our
work and the lines are calculated using the proposed model.

ARTICLE

IONIC LIQUID/POLYMER ELECTROLYTE SYSTEMS, KU PARK AND BAE

219