Phase Separation and Water Channel Formation in Sulfonated Block Copolyimide

Abstract

We compared experimental and simulated data to investigate the phase separation and water channel formation of proton exchange membranes (PEMs) for fuel cell. Sulfonated block copolyimides (SPIs) were adopted as model polymers for experiments and simulations, and Nafion was used as a reference. Nafion and SPIs were observed to have different microscopic structures such as constituent atoms, backbone rigidity, and the locations of sulfonic acid groups, all of which significantly affect phenomenological properties at the macroscopic level such as density, water uptake, and proton conductivity. In particular, SPIs show much weaker microphase separation than Nafion, mainly due to the lower mobility of sulfonic acid groups and the existence of acceptable sites for hydrogen bonding even in hydrophobic segments, which impedes water channel formation for proton transport. As a result, the phase separation behavior and the resulting water channel formation are the major factors affecting macroscopic properties of PEMs such as water uptake and proton transport.

Full text

Phase Separation and Water Channel Formation in Sulfonated Block Copolyimide
Chi Hoon Park,†Chang Hyun Lee,†Joon-Yong Sohn,†,§ Ho Bum Park,†,‡ Michael D. Guiver,‡,⊥
and Young Moo Lee*,†,‡
School of Chemical Engineering, Hanyang UniVersity, Seoul 133-791, Korea, WCU Department of Energy
Engineering, Hanyang UniVersity, Seoul 133-791, Korea, AdVanced Radiation Technology Institute, Korea
Atomic Energy Research Institute, Jeongeup-si, Jeollabuk-do 580-185, Korea, and Institute for Chemical
Process & EnVironmental Technology, National Research Council, Ottawa, Ontario K1A 0R6, Canada
ReceiVed: June 21, 2010; ReVised Manuscript ReceiVed: August 11, 2010
We compared experimental and simulated data to investigate the phase separation and water channel formation
of proton exchange membranes (PEMs) for fuel cell. Sulfonated block copolyimides (SPIs) were adopted as
model polymers for experiments and simulations, and Nafion was used as a reference. Nafion and SPIs were
observed to have different microscopic structures such as constituent atoms, backbone rigidity, and the locations
of sulfonic acid groups, all of which significantly affect phenomenological properties at the macroscopic
level such as density, water uptake, and proton conductivity. In particular, SPIs show much weaker microphase
separation than Nafion, mainly due to the lower mobility of sulfonic acid groups and the existence of acceptable
sites for hydrogen bonding even in hydrophobic segments, which impedes water channel formation for proton
transport. As a result, the phase separation behavior and the resulting water channel formation are the major
factors affecting macroscopic properties of PEMs such as water uptake and proton transport.
1. Introduction
Recent efforts to combat global warming include scientific
and technical attempts to develop power sources that minimize
the production of greenhouse gases such as carbon dioxide and
methane that characterize the combustion of conventional fuels.
One of the most promising candidates is the proton exchange
membrane fuel cell (PEMFC), which exhibits high energy
efficiency and low pollutant emissions, particularly when used
for mobile and stationary applications.1,2
Proton exchange membranes (PEMs) play key roles in
PEMFCs as polymer electrolytes to selectively transport protons.
Nafion (DuPont, NC, U.S.A.) is a representative PEM, consist-
ing of perfluorinated backbones and side chains ending in
sulfonic acid groups. Although developed in the 1960s, Nafion
is still widely used due to its excellent chemical stability and
proton conductivity. However, the cost of Nafion remains high
because the polymerization process of perfluorinated polymer
is complex and must be carried out under harsh conditions such
as high temperature and high pressure.3-5Moreover, the
mechanical stability and proton conductivity of Nafion can
decrease when it is heated over 80 °C, owing to its low glass-
transition temperature.4,5
To overcome these problems, sulfonated hydrocarbon PEMs
have been investigated as alternatives.5-8In general, the costs
of hydrocarbon PEMs are lower than those of Nafion because
hydrocarbon PEMs can be polymerized under mild conditions
using cheap monomers. In addition, they maintain mechanical
stability and proton conductivity over a wide temperature range
due to their high thermal stability resulting from high glass-
transition temperatures.4,5 Despite these advantages, hydrocarbon
PEMs exhibit lower proton conductivities than Nafion consider-
ing their higher ion exchange capacities (IECs). Accordingly,
IECs must be increased to obtain desirable levels of proton
conductivity, but increase of IECs results in excessive water
uptake and swelling ratio in hydrocarbon PEMs.9
The most widely accepted explanation for the differences in
macroscopic properties between Nafion and hydrocarbon PEMs
such as water uptake and proton conductivity is that they exhibit
different water channel formation properties. Water channel
formation affects pathways for proton transport under hydrated
conditions (microphase separation). Nafion forms wider, more
separated, less branched water channels than hydrocarbon PEMs
due to stronger phase separation.9,10 Accordingly, much research
has been devoted to understanding the structures of PEMs and
their relationships to macroscopic properties.11,12 However, the
previous reports exhibit a limitation to show the exact structure
on a microscopic level despite their persuasive conclusions based
on the experimental data.
Molecular simulations have gained attention as one of the
powerful tools to elucidate the complex structures of PEMs.
As molecular simulation can give various information about
polymer morphology and structure-property relationships on
atomistic and molecular levels, many papers dealing with
surfactants,13,14 biomaterials,15 gas separation membranes,16-18
and related topics have been published. For PEMs, extensive
studies have been carried out to investigate their peculiar
structures and proton transport behavior.19,20 Paddison used ab
initio strategy to study proton dissociation of the sulfonic acid
group in triflic acid and p-toluene sulfonic acid, simulating
Nafion and PEEKK models, respectively.21 Later, he and Elliott
performed ab initio calculations to investigate proton dissociation
of the short side chain of a perfluorosulfonic acid membrane
such as Nafion and the resulting proton transfer with solvent
molecules.22 Vishnyakov and Neimark used molecular dynamics
(MD) simulation of the Nafion oligomer with water and/or
methanol to study their solvation of sulfonic acid groups.23-25
* To whom correspondence should be addressed. Tel: +82-2-2220-0525.
E-mail: ymlee@hanyang.ac.kr.
†School of Chemical Engineering, Hanyang University.
§Korea Atomic Energy Research Institute.
‡WCU Department of Energy Engineering, Hanyang University.
⊥National Research Council.
J. Phys. Chem. B 2010, 114, 12036–1204512036
10.1021/jp105708m 2010 American Chemical Society
Published on Web 08/24/2010

Voth’s group studied proton transport in water and Nafion based
on the multistate empirical valence bond (MS-EVB) model to
describe more exactly the Grotthuss hopping mechanism.26-29
Spohr investigated the effect on proton transport of charge
delocalization in sulfonic acid groups using the modified EVB
model by Kornyshev group.30,31 However, most reports on PEMs
have focused on Nafion. Therefore, structural information on
phase separation behaviors of hydrocarbon PEMs obtained using
molecular simulation is rare.32
In the present study, sulfonated block copolyimides (SPIs)
were chosen as representative hydrocarbon PEMs33-39 to explore
the relationship among microscopic phase-separated structures,
water channel formation, and macroscopic physical properties.
We prepared SPIs with different compositions of hydrophilic
and hydrophobic segments and characterized their densities,
proton conductivities, and water uptakes. On the basis of the
experimental data, molecular simulations were then performed,
and the experimental and simulated data were compared. Nafion
was used as a reference sample to compare phase separation
properties and the resulting water channel formation. These
comparisons of experimental and simulated data for PEMs
provide valuable information on the design of hydrocarbon
PEMs with the properties desired for a variety of applications.
2. Experimental Procedures
2.1. Materials. 1,4,5,8-Naphthalenetetracarboxylic dianhy-
dride (NTDA), triethylamine (Et3N), benzoic acid, and m-cresol
were purchased from Aldrich Chemical Co. (WI, U.S.A.) and
used as received. 4,4′-Diaminodiphenyl ether (ODA) and 3,5-
diaminobenzoic acid (DBA) were purchased from Tokyo
Chemical Industry (TCI, Tokyo, Japan). 4,4′-Diaminodiphenyl
ether-2,2′-disulfonic acid (SODA) was synthesized via direct
sulfonation of ODA.40 DBA and SODA were sublimated
overnight at 80 °C in a vacuum oven before use.
2.2. Synthesis of Sulfonated Block Copolyimides. Table 1
shows the molecular compositions of the SPIs used in this paper.
The hydrophilic segment contents ranged from 0.2 to 0.8 mol
fraction. SPI-2 refers to SPIs with mole fractions of hydrophilic
and hydrophobic segments of 0.2 and 0.8, respectively. The
synthetic route of SPI-2 is described in the next paragraph.33,41
For the formation of hydrophilic segments, 0.288 g (0.8
mmol) of SODA and 0.291 g (2.88 mmol) of Et3N were
completely dissolved into 4.2 g of m-cresol in a 250 mL three-
neck flask under nitrogen atmosphere. Then, 0.322 g (1.2 mmol)
of NTDA and 0.208 g (1.704 mmol) of benzoic acid were added
and stirred vigorously at room temperature for 2 h. For the
formation of hydrophobic segments, 2.422 g (3.2 mmol) of
ODA, 0.680 g (6.72 mmol) of Et3N, and 9.8 g of m-cresol were
added into the above solution containing hydrophilic segments.
After completely dissolving the ingredients into solution, the
rest of the NTDA portion (0.751 g; 2.8 mmol) was introduced
together with 0.486 g (3.976 mmol) of benzoic acid with
consideration of their stoichiometry.
Then, the mixture was heated at 80 °C for 4 h and at 180 °C
for 20 h. After casting onto a glass plate, the copolyimide
solution was dried in an oven under vacuum conditions at 80
°C for 1 h and 150 °C for 10 h, successively. The cast films
were soaked in 1 M MeOH aqueous solution at room temper-
ature for1htoremove residual solvent. For the acidification
of copolyimides in the triethylammonium salt form, the
membranes were immersed in 1 M HCl aqueous solution at
room temperature for 10 h and washed with deionized water to
remove residual acid.
2.3. Characterization. Conventional titration methods (ASTM
2187) were used to measure ion exchange capacity (IEC). Dry
membrane films (4 cm ×4 cm) were weighed and then
immersed in a 0.01 N NaCl aqueous solution for 24 h. After
protons were completely released from the sulfonic acid groups
of the copolyimide membranes, the solution was titrated with a
0.01 N NaOH aqueous solution. The IEC values (meq g-1) were
calculated using the volume of the NaOH aqueous solution
added in the acidic solution and the weight of each film.
Density was measured by buoyancy methods using a top-
loading electronic Mettler Toledo Balance (Greifensee, Swit-
zerland) with a density kit. The membrane samples were
TABLE 1: Model Construction Parameters
sample molar ratio composition
location of
sulfonic
acid group
backbone
structure name
hydrophilic
moieties
hydrophobic
moieties molecule
molecular
weight
number of
molecules
ratio
mass
ratio
volume
ratio λa
SPI-2 0.2 0.8 SPI 23222.7 1 83.2 80.0 13.0
water 18 260 16.8 20.0
SPI-3 0.3 0.7 SPI 24023.3 1 82.4 78.7 9.5
water 18 286 17.7 21.3
SPI-4 0.4 0.6 SPI 24823.8 1 81.5 77.2 7.9
water 18 314 18.6 22.8
main chain block
copolymer
SPI-5 0.5 0.5 SPI 25624.4 1 80.3 75.7 7.0
water 18 350 19.7 24.3
SPI-6 0.6 0.4 SPI 26425 1 77.4 72.8 7.5
water 18 450 22.6 27.2
SPI-7 0.7 0.3 SPI 27225.6 1 68.0 61.3 10.2
Water 18 713 32.1 38.7
SPI-8 0.8 0.2 SPI 28026.1 1 54.2 47.1 16.4
water 18 1314 45.8 52.9
side chain grafting
polymer
Nafion-8 n/a n/a Nafion 22922.1 1 88.6 80.0 8.0
water 18 160 11.4 20.0
Nafion-16 n/a n/a Nafion 22922.1 1 79.8 67.0 16.0
water 18 320 20.2 33.0
aλ: the number of water molecules per sulfonic acid group.
Phase Separation and Water Channel Formation in SPI J. Phys. Chem. B, Vol. 114, No. 37, 2010 12037

weighed in air and deionized water at room temperature. The
density was calculated using the following equation
where Wair and Wwater are the weights of samples in air and water,
respectively.
Water uptake was measured using a dynamic vapor sorption
analyzer (DVS- 1000, Surface Measurement System Ltd.,
London, U.K.) under 90% relative humidity (RH) at 25 °C (298
K). Water uptake (%) was obtained from the following equation
where Wwet and Wdry are weights of fully hydrated and dried
membranes, respectively.
Proton conductivity was measured at 25 °C (298 K) and under
95% RH conditions by a four-probe AC impedance method.42
The ohmic resistance (R) of membrane films was measured
using an impedance/gain-phase analyzer (Solatron 1260; ONR,
UK) and an electrochemical interface (Solatron 1287; ONR,
UK). Proton conductivity (σ) was calculated using the following
equation
where Ris the ohmic resistance, lis the distance between
reference electrodes, and Sis the cross-sectional area of the
membrane.
3. Simulation Procedures
3.1. Model Construction and Parametrization. Figure 1
shows the chemical structures and 3D models of the repeat units
of Nafion and SPI. Specifically assigned charge and force field
typing procedures for each atom are described in Figure S1 of
the Supporting Information. The commercial force field COM-
PASS was used, and their potential parameters were listed in
the literature.19,43,44 All of the molecular simulations were carried
out using a Hewlett-Packard workstation and the Material
Studio software package (Accelrys Inc., CA, U.S.A.).
SPIs chains with 50 repeat units and Nafion chains with 20
repeat units were built with varying compositions of hydrophilic
and hydrophobic segments. For example, the SPI-2 chain
consists of 10 sulfonated repeat units (the hydrophilic block)
and 40 nonsulfonated repeat units (the hydrophobic block).
Amorphous models were constructed at 298 K with one polymer
chain to represent the nonhumidified condition or with one
polymer chain and the corresponding hydronium/water mol-
ecules to represent the humidified condition under periodic
boundary conditions using Amorphous Cell modules in Material
Studio. Table 1 outlines the model construction parameters, such
as the mole ratio and compositions for polymer chain building
and amorphous cell generation. The initial target densities of
Nafion and SPI cells were 1.5 and 1.2 g cm-3, respectively.
For SPI cells, the option of ramp density from an initial value
of 0.3 g cm-3was selected to avoid cell generation failure due
to the rigid structure of polyimide. Each cell was followed by
the energy minimization step via the smart minimizer method,
which is a combination of the steepest descent, conjugated
gradient, and Newton methods in a cascade, where the conver-
gence levels were set to 1000 kcal mol-1Å-1, 10 kcal mol-1,
and 0.1 kcal mol-1, respectively.
3.2. Molecular Dynamics (MD) Simulation. Using energy-
minimized amorphous cells of Nafion and SPIs, molecular
dynamics (MD) simulations were performed using a time step
of 1.0 fs for equilibrating the cells and obtaining the final
densities. The Ewald summation method was used to calculate
the nonbond interactions (electrostatic and van der Waals) with
an accuracy of 0.001 kcal mol-1. The Berendsen algorithm set
to a decay constant of 0.1 ps was used to control the temperature
and pressure of each cell. Specific MD simulation procedures
Figure 1. Chemical structures and 3D models of (a) Nafion and (b) SPIs.
Density(g cm-3))F
waterWair/(Wair -Wwater)(1)
Water uptake(%) )(Wwet -Wdry)/Wdry ×100 (2)
σ(S cm-1))l/(RS)(3)
12038 J. Phys. Chem. B, Vol. 114, No. 37, 2010 Park et al.

are as follows: (1) NPT (a constant particle number, pressure,
and temperature) MD simulation at 400 K and 1 bar for 50 ps,
(2) NPT MD simulation at 298 K and 1 bar for 50 ps, and (3)
NVT (a constant particle number, volume, and temperature) MD
simulation at 298 K for 10 ps. After comparing the simulated
and the experimental densities, most SPIs had about 7% lower
values, and therefore, further MD simulations were performed:
(4) NPT MD simulation at 298 K and 10000 bar for 50 ps, (5)
NVT MD simulation at 600 K for 20 ps, (6) NVT MD
simulation at 298 K for 20 ps, and (6) NPT MD simulation at
298 K and 1 bar for 50 ps. Steps 4-7 were repeated until the
simulated density and density changing rates had converged to
within 3%. Finally, NVT MD simulation was carried out at 298
K for 10 ps for production of the SPI models. To evaluate the
mobility of sulfonic acid groups and the proton in the hydronium
form, NPT MD simulation was performed at 298 K at 1 bar for
1.2 ns.
We were unable to obtain experimental densities for humidi-
fied models due to limitations of the buoyancy method for
density measurement that we used in this study. Accordingly,
MD simulations for the humidified model were performed
following the procedures described above without comparison
of densities.
3.3. Model Analyses and Property Calculations. Structural
analyses were performed using the trajectory files of the final
NVT MD simulations. The fractional free volume (FFV)45 was
calculated according to the following equation
where Vtotal is the total volume of the unit cell and VvdW is the
van der Waals volume of the polymer chain, with both values
obtained from the simulated models with the lowest energy.
Diffusivities (D) were calculated using the Einstein equation16,46
where ri(t) and ri(0) are the position vectors of atom Rat time
tand 0, respectively. Here, mean-square displacement (MSD),
∑i)1
NR〈[ri(t)-ri(0)]2〉, represents the average of all chosen atoms
of time origin in a dynamics trajectory, which was also used to
compare the motilities of functional groups as well as to
calculate diffusivities of protons.
4. Results and Discussion
4.1. Model Verification and Structural Properties. Nafion
and SPIs have different polymer structures, as shown in Figure
1. As mentioned above, the main backbone of Nafion is a linear
perfluorinated alkyl chain, and the sulfonic acid groups are
located at the end of the side chain (Figure 1a), whereas SPIs
have rigid aromatic backbones containing six-membered rings
in the repeat unit, and the sulfonic acid groups are directly
attached to phenyl rings in the main chain (Figure 1b). These
structural distinctions affect not only properties that can be
observed during experiments but also the model construction
procedure that enables one to obtain reasonable properties for
simulation studies.
The experimental and simulated densities of Nafion and SPIs
are shown in Table 2. For Nafion, the simulated density quickly
converged within a reasonable range, 3% of the experimental
density, after simple NPT MD simulation steps at 400 and 298
K. However, for SPIs, large differences (over 7%) remained
between simulated and experimental densities even after the
same MD steps were applied due to rigidity and ring catenation
and spearing problems. To minimize these errors in density,
the compression and relaxation algorithm for packing models
used by Dr. Hofmann’s group16,18 was modified and applied.
Finally, the simulated densities of SPIs were in good agreement
with the experimental ones, within a 3% deviation.
The degree of sulfonation (DS) and density are known to
exhibit a proportional relationship in sulfonated polymers.33,47,48
Our results are consistent with this observation, as shown in
Table 2, but do not have the completely linear correlation
between densities and the DS that is demonstrated in Figure 2,
in which the density increases linearly with the increase in DS
and then its rate of increase is reduced after a certain point,
SPI-5. To explain this unexpected trend, the structural properties
were further analyzed using the simulated results presented in
Table 2. In general, the density of the polymer is initially
affected by the atomic weights of constituent atoms. For
example, Nafion consisting of fluorine atoms with heavy atomic
weight has about 50% higher density than SPI-2 that has similar
molecular weights (about 23 kDa; Table 1). However, as shown
in Figures 2 and 3, although the molecular weights of SPIs
increase linearly according to increases of the number of sulfonic
acid groups, their densities show two different slopes at around
a 0.5 molar ratio of hydrophilic content due to nonlinear
increases of total volumes of simulated unit cells. Accordingly,
other factors affecting volume should be investigated, such as
the strength of interactions like hydrogen bonding between
FFV )(Vtotal -1.3VvdW)/Vtotal (4)
D)1
6NR
lim
tf∞
d
dt∑
i)1
NR
〈[ri(t)-ri(0)]2〉(5)
TABLE 2: Model Verification and Structural Properties
IEC
(meq g-1)aDensity
(g cm-3)
name measured measured simulated error
(%) # H bondb
(ea) S atomc
(ea)
SPI-2 0.8 1.39 1.35 2.88 21.85 20
SPI-3 1.16 1.4 1.36 2.86 34.08 30
SPI-4 1.5 1.42 1.39 2.11 46.23 40
SPI-5 1.82 1.45 1.42 2.07 59.49 50
SPI-6 2.13 1.46 1.43 2.05 70.41 60
SPI-7 2.41 1.49 1.45 2.68 80.37 70
SPI-8 2.68 1.49 1.45 2.68 91.17 80
Nafion 0.98 1.98 2.03 -2.53 22.24 20
aIEC (ion exchange capacity): the equivalent weights of sulfonic
acid groups per polymer gram. b# H-bond: the average number of
hydrogen bonds in simulated cells. Acceptor: N, O, S, and halogen
atoms. Maximum hydrogen-acceptor distance: 2.5 Å. cS atom: the
number of sulfonic acid groups in the simulated cells.
Figure 2. Simulated density comparison of SPIs.
Phase Separation and Water Channel Formation in SPI J. Phys. Chem. B, Vol. 114, No. 37, 2010 12039

constituent molecules or atoms. Hydrogen bonding plays a
particularly important role as strong physical interaction among
the inter- or intramolecular interactions in molecules with polar
atoms.23,24,29,49 As a result, the consideration of hydrogen bonding
in SPIs having sulfonic acid groups can provide valuable
information in understanding the contribution of a second factor
on their densities. Figure 4 shows the number of hydrogen
bondings per sulfonic acid group (#H-bondings/SO3H) in PEMs.
At first, #H-bondings/SO3H increases as the number of sulfonic
acid groups increases. However, after SPI-5, as the number of
hydrophilic segments becomes greater than that of hydrophobic
segments in a polymer chain, #H-bondings/SO3H decreases due
to the saturation of hydrogen bondings between sulfonic acid
groups, which in turn weakens intermolecular interactions
limiting the expansion of total volume. As a result, the increase
in densities (molecular weight/total volume) of SPIs decelerates
after SPI-5. In particular, this peculiar behavior about the
reduction of #H-bondings/SO3H gives very interesting informa-
tion about water uptake of SPIs, which will be further discussed
in the following section 4.2.
4.2. Water Uptake. Water uptake is one of the most
important macroscopic properties of PEMs because water
channel formation is essential for proton transportation. Gener-
ally, PEMs with high water uptake exhibit good proton
conduction. However, excessively swollen membranes are too
weak to be employed in fuel cell system. Moreover, when the
membranes are used in the system, it is impossible to obtain
high electrochemical fuel cell performances for a long time
because of the critical delamination in the interfaces between
those membranes and electrodes. It indicates that water uptake
level control is an important issue to develop high-performance
PEM materials.
The water uptakes for the PEMs examined under 90% RH
at 25 °C in this study, according to ion exchange capacities
(IECs) and the distributions of water molecules, are shown in
Figure 5. IECs are proportional to the number of sulfonic acid
groups due to their definition (i.e., the mole equivalent of
sulfonic acid groups per polymer gram).50 However, water
uptake increases gradually from SPI-2 to SPI-5, and then
increases drastically for SPI-7 and SPI-8, as shown in Table 1.
The mass ratio of water is about 17% higher at SPI-5 than that
at SPI-2, but the ratios drastically increase by 35, 91, and 173%
at SPI-6, SPI-7, and SPI-8, respectively, as compared to SPI-2.
We studied the distributions of sulfonic acid groups to
elucidate the relationships between water uptakes and PEM
structures because water molecules are usually located in the
vicinity of sulfonic acid groups in PEM chains and make
hydrogen bonds with the fixed charged ions. Figure 6 shows
the intermolecular pair correlation functions of sulfur atoms in
SPIs without water molecules for nonhumidified conditions. The
pair correlation function, also called the radial distribution
function, indicates the probability of finding a particle A at a
certain distance rfrom another particle B, which can give useful
information about the distribution of particles such as atoms or
molecules.20,51 As shown in Figure 6, the distances between
sulfur atoms located in another polymer chain decrease from
SPI-2 to SPI-5 since more sulfonic acid groups occupy the
simulated cells. However, as the ratio of hydrophilic segments
with sulfonic acid groups becomes higher than that of hydro-
phobic segments, the distances between sulfur atoms can no
longer be closer (less than 3.5 Å). Instead, sulfonic acid groups
acting as water attractive sites become more uniformly distrib-
uted through the SPI cells, as indicated in Figure 6, where the
graphs become flatter after SPI-5. Consequently, after hydration,
the denser packing of water/sulfonic acid group clusters indu-
ces the percolation behavior of water uptake,52,53 which explains
the resulting exponential shape observed in Figure 5. Moreover,
as #H-bondings/SO3H decreases after SPI-5 (as discussed in
section 4.1), more sulfonic acid groups are available in SPI-6,
SPI-7, and SPI-8 to interact with water molecules through
hydrogen bondings.
4.3. Phase Separation and Water Channel Morphology.
Phase separation between hydrophilic segments including water
molecules and hydrophobic segments in PEMs and the resulting
water channel morphology are the most important factors
controlling macroscopic characteristics such as water uptake,
water swelling, and proton conductivity, which in turn are
significantly affected by microscopic PEM structures such as
constituent atoms, backbone structures, and the locations of
sulfonic acid groups.
Figure 7 shows the distribution of water molecules in Nafion
and SPIs according to their λvalues (i.e., the number of water
molecules per sulfonic acid group). Here, two absorbed water
models with similar λvalues (about 8 and 16) were selected
among the respective SPI and Nafion models. Nafion-8 and
Nafion-16 have the same structure, including the same number
of sulfonic acid groups, but the only difference is the ratio of
water molecules and Nafion, λ)8 (partially hydrated) and 16
(fully hydrated), respectively. When comparing Nafion and SPIs
with similar λvalues, we observe a remarkable contrast in water
channel morphology. For λ)∼8, as shown in Figure 7a, Nafion
(λ)8) forms strong phase separation and well-defined water
channels despite having a relatively low λvalue, whereas SPI-6
Figure 3. Gravimetric and volumetric analysis of SPIs.
Figure 4. Number of hydrogen bondings per sulfonic acid group in
SPIs.
12040 J. Phys. Chem. B, Vol. 114, No. 37, 2010 Park et al.

(λ)7.5) cannot form such distinct water channels despite
higher mass and volume ratios of water molecules in the cell.
The trends described above become even clearer when the λ
value increases to 16, as shown in Figure 7b. For fully hydrated
Nafion (λ)16), stronger phase separation and more separated
water channels are observed than even those for Nafion (λ)
8). However, water molecules are distributed through the SPI-8
cell in a disordered fashion, despite over 200 and 60% higher
mass and volume ratios of water molecules in SPI-8 (λ)16.4)
than those in Nafion (λ)16), respectively. The difference in
water channel formation can be observed more conspicuously
with expanded multicells (3 ×3×3) of Nafion and SPI.
In addition to the above morphological differences, Figure 8
shows the intermolecular pair correlation function of all atoms
in the water channel in Nafion and SPIs cells under humidified
conditions. In this paper, water channels in PEMs are supposed
to consist of water molecules and hydronium ions, which means
that the probability of finding other water molecules or
hydronium ions is strongly related to their density distribution
in water channels. For example, if water molecules and
hydronium ions form water channels or clusters with a diameter
of r, the probability of finding another becomes higher and more
concentrated over the range. Hydronium ions, H3O+, are one
of the complex forms of water molecules and protons and play
an important role in proton transport, which will be further
discussed in section 4.4. As shown in Figure 8, all peaks show
their highest value within a range of 1.5-4 Å, irrespective of
PEM types, which represents the distance from atoms in water
molecules or hydronium ions to the atoms in the second
coordinated ones. However, for SPIs, the probability becomes
rapidly lower and flatter after 4 Å. In particular, the differences
in peak intensities before and after 4 Å were significantly
reduced in SPIs as water uptake increased exponentially, which
means that water molecules and hydronium ions were uniformly
distributed through the SPI cells without distinct water channel
formation. In contrast, for Nafion, the probability was slowly
reduced after4Åtoover 12 Å, indicating that a higher ratio of
water molecules and hydronium ions is located within a distance
of about 12 Å in Nafion than that in SPIs, as shown in Figure
7b, not uniformly distributed through the cell.
One of the possible explanations for the strong phase
separation in Nafion is the mobility of sulfonic acid groups.
Figure 9 shows the MSD of sulfur atoms in Nafion and SPIs,
indicating the mobility of sulfonic acid groups or hydrophilic
moieties containing the sulfonic acid groups in the each system.
Under humidified conditions, the sulfur atoms in Nafion-16 and
even those in Nafion-8 have much higher mobility than those
in SPIs, although SPI-8 has many more water molecules which
can act as plasticizers. In particular, the slope in Nafion 16 is
almost five times higher than that in SPI-8 under humidified
conditions. This slow polymer chain movement limiting the
mobility of sulfonic acid groups in the SPI system is owed to
Figure 5. Experimental water uptake and simulated water molecule distribution in SPIs. Colors: red (O), white (H), blue line (hydrogen bonding).
Figure 6. Intermolecular pair correlation function of sulfur atoms in
nonhumidified SPIs.
Phase Separation and Water Channel Formation in SPI J. Phys. Chem. B, Vol. 114, No. 37, 2010 12041

its rigid chemical architecture as shown in Figure 1b. All SPIs
are composed of rigid aromatic rings including naphthalene
rings. The sulfonic acid groups were directly attached to the
phenyl rings. Thus, the mobility of sulfonic acid groups in SPIs
was severely hindered as compared to that in Nafion with
sulfonic acid groups located at the terminal ends of its flexible
aliphatic side chains, as shown in Figure 1a.
The constituent atoms that strengthen or weaken the interac-
tions with water molecules also affect phase separation behavior
in PEMs. For strong phase separation, interactions between
atoms and water molecules are favorable in hydrophilic seg-
ments but not in hydrophobic segments. For Nafion, Devanathan
et al. demonstrated that the water molecules were inaccessible
to the hydrophobic segment.54 The atoms in the backbone have
much less affinity to water molecules due to the symmetrical
arrangement of fluorine atoms around the carbon backbone (i.e.,
net dipole moment is 0), whereas oxygen atoms and some
fluorine atoms in the hydrophilic side chains can form hydrogen
Figure 7. Comparison of the water molecule distributions in Nafion and SPIs with the similar λvalues; (a) λ)about 8 and (b) λ)about 16.
Colors: red (O), white (H), blue line (hydrogen bonding).
Figure 8. Intermolecular pair correlation function of all atoms in water/
hydronium molecules in humidified Nafion and SPIs.
12042 J. Phys. Chem. B, Vol. 114, No. 37, 2010 Park et al.

bonds with water molecules. In contrast, SPIs have oxygen
atoms even in the hydrophobic segments due to imide linkages
and ether linkages, which can interact with water molecules via
hydrogen bonds, as shown in Figure 10.
The effects of these structural differences are investigated
more specifically in Figure 11. The probability of finding water
molecules in the hydrophobic segments of SPIs rapidly increases
to 4 Å and then shows almost saturated values regardless of
their sulfonation levels, whereas the probability of finding water
molecules in the hydrophobic segments of Nafion slowly
increases and reaches the highest value at 11 Å. Consequently,
there are much fewer water molecules penetrating into hydro-
phobic segments in Nafion, and therefore, Nafion shows much
stronger phase separation behavior than SPIs.
4.4. Proton Transport Behavior. Figure 12 illustrates the
proton conductivity and water uptake properties of SPIs. In many
cases, the diffusion or transport properties are explained by
percolation theory.52,53 Here, proton conductivity of SPIs also
shows percolation behavior, drastically increasing at a certain
point, SPI-6, with the increase of DS, as shown in Figure 12.
However, although water uptake has a strong relationship with
proton conductivity and also shows percolation behavior as
discussed in section 4.2, its trend is very different from that of
proton conductivity, particularly from SPI-5 to SPI-8, where
the number of hydrophilic segments is higher than that of
hydrophobic segments. To explain these behaviors, an under-
standing of proton transport mechanisms is required. There are
two mechanisms, the vehicle mechanism and the hopping (or
Grotthus) mechanism, that are widely accepted to explain proton
transport behavior in PEMs.55-57 In the vehicle mechanism,
protons are transported through water channels in complex forms
with water molecules such as H3O+,H
5O2+, and H9O4+.
Accordingly, the effects of water uptake on proton conductivity
can be explained via the vehicle mechanism. The hopping (or
Grotthus) mechanism postulates that protons are transported by
bond making and breaking with proton carriers such as sulfonic
acid groups and water molecules via hydrogen bonding.
Figure 13 shows the simulated diffusivities of hydronium ions
in SPI cells. In this simulation, a classical MD method was
adopted using nondissociable hydronium ions (H3O+) as rep-
resentatives of the complex forms of protons and water for the
purposes of simulation. Here, the diffusivities of hydronium ions
Figure 9. Mobility comparison of sulfur atoms in the sulfonic acid
group of Nafion and the SPI under humidified conditions.
Figure 10. Snapshot of water molecules coordinated with the
hydrophobic block in humidified SPIs. Colors: gray (C), red (O), white
(H), blue (N).
Figure 11. Intermolecular pair correlation function of all atoms in
water/hydronium molecules and all atoms in hydrophobic blocks in
humidified Nafion and SPIs.
Figure 12. Comparison of experimental proton conductivity and water
uptake of SPIs at 25 °C (298 K).
Figure 13. Diffusivity of hydronium ions in SPIs at 298 K.
Phase Separation and Water Channel Formation in SPI J. Phys. Chem. B, Vol. 114, No. 37, 2010 12043

in Nafion (2.6 ×10-6cm2s-1in Nafion (λ)16)) were included
as references, which are reasonably similar to the previously
reported simulation results (0.68 ×10-6cm2s-1at 300 K (λ)
16)20 and 1.15 ×10-6cm2s-1at 300 K (λ)15)58). As shown
in Figure 13, the diffusivity of hydronium ions exhibits similar
trends to water uptake behavior because the proton transport
mechanism in classical MD simulations is based on the vehicle
mechanism. Actually, classical MD simulations have limited
abilities to describe the hopping mechanism in which proton
transport occurs via bond making and breaking because they
do not adequately model electron-level reactions (i.e., bond
making and breaking).20,59 As discussed in the Introduction,
many studies were performed to describe the hopping mecha-
nism and obtained reasonable results.26-30 However, because
this study mainly focuses on the PEM morphology under
hydrated conditions, such a model using excess protons is not
applied. As a result, the diffusivity of Nafion in simulations is
lower than that from the experimental results (about 7 ×10-6
cm2s-1at 303.15 K60) due to the absence of the additional
driving force of the hopping mechanism. Accordingly, further
analyses should be performed to explain the differences between
proton conductivity and water uptake.
Intermolecular pair correlation functions of sulfur atoms in
humidified SPIs are shown in Figure 14. In the hopping
mechanism, as the hydrogen bonding acceptable sites such as
sulfonic acid groups play an important role as proton carriers,
their location is thought to affect proton transport significantly.
As the DS increases, the distances between sulfur atoms become
closer from SPI-2 to SPI-6 because water uptake increases more
slowly than does the number of sulfonic acid groups. However,
as water uptake drastically increases after SPI-6, the distance
also increases, and the distribution of sulfur atoms becomes
homogeneous. As a result, with SPI-6 as a critical point, sulfonic
acid groups distribute more closely and more homogeneously
than in SPI-5, enabling a percolation jump in proton conductivity
between SPI-5 and SPI-6 via the hopping mechanism.
5. Conclusions
On the basis of experimental data for Nafion and the SPIs,
molecular simulations were successfully performed to study
structure-property relationships in PEMs, demonstrating density
deviations within 3%. The constituent atoms and the number
of hydrogen bonds were found to be very important factors
governing densities. The water uptake of SPIs increases drasti-
cally after SPI-6, probably due to the distribution of sulfonic
acid groups in SPIs. Nafion has stronger phase separation than
SPI, and the resulting water channel formation facilitated by
the higher mobility of sulfonic acid groups and water inacces-
sibility to hydrophobic segments is a key factor explaining the
differences in proton transport between Nafion and SPIs. We
observed that proton transport shows percolation behavior, and
this observation may be explained via the hopping mechanism
as well as the vehicle mechanism.
Acknowledgment. This research was supported by the WCU
(World Class University) program through the National Re-
search Foundation funded by the Ministry of Education, Science
and Technology (R31-2008-000-10092).
Supporting Information Available: Force field typing and
partial charge assignment of Nafion and sulfonated block
copolyimides (SPIs). This material is available free of charge
via the Internet at http://pubs.acs.org.
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