Journal of Membrane Science 431 (2013) 79–85
Contents lists available at SciVerse ScienceDirect
Journal of Membrane Science
journal homepage: www.elsevier.com/locate/memsci
Computational modeling of structure and OH-anion diffusion in quaternary
ammonium polysulfone hydroxide – Polymer electrolyte for application
in electrochemical devices
Boris V. Merinov n, William A. Goddard III
Materials and Process Simulation Center (139-74), California Institute of Technology, Pasadena, CA 91125, USA
a r t i c l e i n f o
abstract
Article history:
Received 25 May 2012
Received in revised form
3 December 2012
Accepted 7 December 2012
Available online 20 December 2012
Using computational approaches we predict the microstructure of high-performance alkaline polymer,
quaternary ammonium polysulfone hydroxide (QAPS-OH) membranes, dry and with 14 wt% water
uptake. The microstructure can be described as a hydrophobic polymer backbone penetrated by a
network of three-dimensional interlinked hydrophilic channels of different diameters. Mobile
OH-anions are distributed inside the channels. OH diffusion coefficients and corresponding activation
energy were calculated from our molecular dynamics simulations of the QAPS-OH membrane at
different temperatures. The predicted values are consistent with available experimental data. Possible
mechanisms of the OH-anion diffusion have been discussed.
& 2012 Elsevier B.V. All rights reserved.
Keywords:
Alkaline membrane
Modeling
Microstructure
Diffusion
1. Introduction
Despite the significant progress made in reducing cost of
Polymer Electrolyte Membrane Fuel Cells (PEMFCs) due to
improving their performance and decreasing Pt loading, it is
becoming clear that to reach further progress in commercialization of the fuel cell technology, the focus should be moved to
other types of fuel cells which do not require expensive Pt as
catalysts. Alkaline fuel cells (AFCs) are more efficient than the
acid-based PEMFCs and can operate with cheaper non-precious
metal catalysts such as Ni. However, the current AFC technology
uses the corrosive liquid electrolyte (e.g. KOH) which raises issues
related to safety, reliability and durability of AFC systems.
Electrolyte is a critical component of fuel cell systems. Synthesis
of polymer alkaline membranes that have high hydroxide-ion
conductivity might eliminate this serious disadvantage of AFCs.
During last two-three years, new high-performance alkaline
polymers, such as quaternary ammonium polysulfone hydroxide
(QAPS-OH) and tris(2,4,6-trimethoxyphenyl)polysulfone-methylene quaternaryphosphonium hydroxide (TPQP-OH), have successfully been designed and synthesized [1–5].
QAPS-OH is thermally stable up to 120 1C and can be dissolved in
certain solvents. This allows preparation of Membrane-Electrode
Assemblies (MEAs) of required thickness and size. The hydroxide-
ion conductivity of QAPS-OH is 10 2 S/cm at room temperature
and meets the basic requirement for fuel cell applications [1–3].
TPQP-OH can also be successfully used as a soluble hydroxideconducting ionomer. It turns out that TPQP-OH polymer with a
degree of chloromethylation of 152% has excellent hydroxide-ion
conductivity, 0.05 S/cm at room temperature, and stability.
A fuel cell based on the TPQP-OH electrolyte shows the highest
power density (258 mW cm 2) and lowest cell resistance
(0.210 O cm2) reported and has the potential to achieve cell
performances of state-of-the-art Nafion-based PEMFCs [4,5].
Despite the great promise, the polymer AFC technology has
several technical issues which need to be solved before this
technology would be utilized for applications. One of them is
identifying polymer backbones and side chains that could form
chemically and mechanically stable polymer membranes with
high ionic conductivity suitable for employment in fuel cells.
However, this process is hindered by lack of information about
the structure and structural characteristics that provide the
desirable properties. Using computational techniques is an efficient way to advance this issue.
In our paper, we focus on modeling of the structure and
hydroxide-ion diffusion of QAPS-OH membranes at different
temperatures and water contents.
2. Simulation details
n
Corresponding author. Tel.: þ1 626 395 2754; fax: þ 1 626 585 0918.
E-mail address: [email protected] (B.V. Merinov).
0376-7388/$ - see front matter & 2012 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.memsci.2012.12.010
The initial QAPS-OH structure was constructed using the
Amorphous Builder of Cerius2 [6]. It uses Monte Carlo techniques
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B.V. Merinov, W.A. Goddard III / Journal of Membrane Science 431 (2013) 79–85
to build an amorphous structure with a three-dimensional periodic
cell. We followed this Monte Carlo build with an extensive series of
annealing simulations in which the volume and temperature are
varied systematically to achieve a fully equilibrated system at the
target temperature and pressure. The QAPS-OH predicted structure
was not biased by imposing any particular geometry, density or
packing. To build the structure, we used 3 chains with a degree of
polymerization of 16. The total number of atoms in the system is
3414 including 48 OH-anions. To describe inter- and intramolecular interactions, and water, we applied the DREIDING [7]
and F3C [9] force fields which were successfully used before to
study a Nafion system [8]. The standard geometric combination
rules of Dreiding were employed in mixing these force fields.
The initial QAPS-OH structure was relaxed by applying the
following annealing procedure. First, the structure was gradually
expanded by 50% of its initial volume over a period of 50 ps, while
the temperature was simultaneously increased from 300 to 600 K.
Next NVT molecular dynamics (MD) simulations were performed
at 600 K with the expanded volume for 50 ps. Then the structure
was compressed back to the initial volume over 50 ps, while
cooling the temperature down to the target temperature, 300 K.
This procedure was alternated with a conventional annealing that
included heating from 300 to 600 K and cooling back to 300 K
with a temperature step 50 K and 10 ps of NPT dynamics at each
temperature. We repeated this operation until the structure
showed no significant changes (this requires to repeat the cycle
5 times). The calculated density of such a way prepared structure
was 0.89 g/cm3. Then we added 200 water molecules, which
approximately correspond to 14 wt% water uptake, into the
channels and larger voids and equilibrated this structure by
repeating the procedure described above. Our approach of
temperature-pressure MD annealing allows us to obtain an
equilibrated distribution of water in an equilibrated polymer
system. The two final structures (dry and with the 14 wt% water
uptake) were used for MD simulations at 300, 360, 400, and 450 K
to study the dynamic properties of the QAPS-OH membrane. At
each temperature we first performed a 10 ps NPT dynamics
continued with a 100 ps NVT dynamics.
Diffusion coefficients were calculated based on the mean
square displacement (MSD) (see Supplementary material)
n
D
E
X
2
2
MSD ðmÞ ¼ 9rðtÞr9 ¼ 1=n
9r ðm þ iÞrðiÞ9
i1
where r is the position of the particle, t is the time, k is the total
number of snapshots (k¼m þn 40), m is the maximum number
of points allowed for the MSD calculation (m ¼k/2 in our calculations), n is the number of data points used for averaging, and i is
the step counter.
The self-diffusion constant is obtained using the Einstein
relation
D¼
1
2
/9r ðt Þr9 S
6Nt
where N is the number of atoms. We fitted the temperature
dependence of the diffusion coefficient to
DðTÞ ¼ Do exp Ea =kT
where Ea is the activation enthalpy.
Conductivity can be calculated from diffusion coefficient using
the Nernst–Einstein equation
s¼
DczF
RT
where D is the diffusion coefficient, c the charge carrier concentration, z the carrier charge, F the Faraday constant, R the gas
constant, and T is the temperature.
3. Results and discussion
3.1. Microstructure of dry QAPS-OH membrane
Fig. 1 shows the QAPS-OH chemical formula (a) and structure
unit (b), which were used for our MD simulations to build and
optimized the dry microstructure of the QAPS-OH for our MD
simulations to build and optimized the dry microstructure
of the QAPS-OH membrane (c). This microstructure can be
described as a hydrophobic polymer backbone penetrated by a
network of three-dimensional interlinked hydrophilic channels
of different diameters. The presence of channels containing
mobile charge carriers is an important characteristic feature of
solid state ionic conductors [10]. According to our results, N(CH3)3
functional groups are mostly located along walls of the
channels. The predicted distances between the nearest N atoms,
which can be considered as side chain distances, vary from 6 to
12 Å (see Fig. 2), which are similar to distances between
side chains in Nafion [8]. Predicted distances between N atom
Fig. 1. The QAPS-OH chemical formula (a), structure unit (b) and dry microstructure, 2 2 1 unit cells (c) obtained from our MD simulations.
B.V. Merinov, W.A. Goddard III / Journal of Membrane Science 431 (2013) 79–85
81
3.2. Microstructure of QAPS-OH membrane with 14 wt%
water uptake
To build the hydrated microstructure of QAPS-OH, we used the
method described in Section 2 and carried out a 100 ps MD
simulation on this structure at 300 K. Fig. 3 shows the corresponding microstructure (4056 including 200 H2O and 48
OH-anions) and water distribution in a QAPS-OH membrane with
the 14 wt% water uptake. Radial distribution functions (RDF) can
be seen in Fig. 4. The QAPS-OH microstructure keeps the features
earlier observed for the dry membrane, i.e. it can be described
as a hydrophobic polymer backbone penetrated by a network of
three-dimensional interlinked hydrophilic channels. N(CH3)3
functional groups occupy positions on walls of the channels.
The distances between the nearest N atoms remain varying
from 6 to 12 Å, which are similar to distances between
side chains in the dry QAPS-OH membrane and Nafion [12].
The mobile OH ions are mostly distributed inside the channels
and the OH–OH distances, as well as N–OH, close to those in the
dry membrane. However, the coordination number corresponding
to the distance between the nearest OH groups ( 3 Å) is
significantly lower, 0.1, in the hydrated membrane compared
to that of the dry membrane ( 0.5). The lower hydroxide ion CN
in the hydrated membrane is most probably due to adding
water molecules which results in swelling of the microstructure
Fig. 2. Radial distribution functions g(r) of N–N (a), N–OH (b), and OH–OH (c),
distances and their integration (CN) for the dry QAPS-OH membrane.
and the nearest OH group is 5 Å with a coordination number
of 1. This indicates that each N(CH3)3 functional group is
coordinated with one OH-ion. Mobile OH ions are distributed
inside the channels. The distance between the nearest OH
groups is 3 Å with a coordination number of 0.5. This
geometry is favorable for the OH diffusion, because it suggests a
presence of vacant positions close to the OH groups to which they
can jump.
In addition to the channels in the QAPS-OH microstructure, there exist cavities that also contain hydroxide
ions. However, mobility of these ions is limited to local
diffusion that does not contribute to the long-range diffusion.
However in hydrated membranes, some of these cavities
may unite and form new channels due to following water
uptake and swelling. A void analysis, which was performed
according to the procedure reported in Ref. [11], estimates the
void volume as being equal to 20% of the total volume of the dry
membrane.
Fig. 3. The QAPS-OH microstructure (2 2 1 unit cells) with the 14 wt% water
uptake (a) and corresponding water distribution in the microstructure (b).
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B.V. Merinov, W.A. Goddard III / Journal of Membrane Science 431 (2013) 79–85
Fig. 4. Radial distribution functions g(r) of N–N (a), N–OH (b), OH–OH (c), OH–H2O (d), and H2O–H2O (e) distances (Å) and their integration (CN) for the QAPS-OH
membrane with the 14 wt% water uptake.
and formation of the water shapes around hydroxide ions.
The OH–H2O and H2O–H2O intermolecular distances (between
oxygen atoms of corresponding molecules) are close to each
other and equal to 2.9 Å, which is in good agreement with
other computational works (see, for example, [13]). From
Fig. 4e, which shows RDF and CN of water, it is clear that the
QAPS-OH membrane with the 14 wt% water uptake is far
enough from to be considered as fully hydrated. It should be
noted that the calculated ion-exchange capacity (IEC) of our
QAPS-OH membrane is 1.9 which allows significantly
higher water uptake for the fully hydrated membrane than
14 wt%.
According to [3], the 14 wt% water uptake of the QAPS-OH
membrane corresponds to the ion-exchange capacity (IEC) of
Table 1
Diffusion coefficients (cm2/s) of dry and hydrated (14 wt% water uptake) QAPS-OH
membranes.
Membrane
QAPS-OH, dry ( 10 5)
QAPS-OH, 14 wt% H2O ( 10 4)
Temperature (K)
300
360
400
450
0.12
0.16
0.22
0.34
0.44
0.54
0.68
0.56
1.04 and swelling degree (SD) of about 5%. From our MD
simulation of the dry and 14 wt% water uptake QAPS-OH membranes, SD can be estimated, using the corresponding microstructure
B.V. Merinov, W.A. Goddard III / Journal of Membrane Science 431 (2013) 79–85
volumes. We found that SD is equal 7% which is close to the
experimental value of 5%.
In general, the QAPS-OH microstructure looks similar to that of
Nafion in which hydrophilic clusters connected by channels are
embedded into a hydrophobic matrix [14,15].
Fig. 5. Calculated OH-diffusion coefficients of QAPS-OH as a function of temperature and 1000/T.
83
3.3. OH-diffusion in QAPS-OH membrane
In order to estimate the hydroxide-ion diffusion and its
activation energy, we modeled the OH-transport in the dry and
hydrated QAPS-OH membranes at different temperatures (300,
360, 400, and 450 K). The calculated diffusion coefficients and
corresponding activation energies are listed in Table 1 and their
temperature dependences are shown in Fig. 5. We find our
computational results are consistent with experiment. The calculated conductivity that corresponds to the diffusion coefficient at
T¼300 K is 0.7 10 2 S/cm (the experimental value is about
10 2 S/cm for the membranes with a very low water-uptake
degree) and activation energy is exactly the same as in experiment,
Ea ¼0.14 eV [3].
In the hydrated membrane with the 14 wt% water uptake, the
OH diffusion coefficient increased by 1 order of magnitude and
reached the value of D ¼0.16 10 4 cm2/s at room temperature,
which is similar to the value of en masse diffusion in Nafion,
0.17 10 4 cm2/s [16] calculated using the Stokes–Einstein equation, and predicted activation energy is Ea ¼0.10 eV. This is
consistent with experimental results observed [1–3].
It is well-known that water has ability to transport charge
species, such as H þ and OH . To present, the OH-anion structural
diffusion is much less studied than the proton diffusion. There is
no experimental technique that can provide necessary data
for the firm conclusion about the detailed mechanism of the
Fig. 6. The Grotthuss-type OH-anion diffusion mechanism with the 4-coordinated OH-anion (a–c) and with the overcoordinated ( 4.75) OH-anion (d–h).
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B.V. Merinov, W.A. Goddard III / Journal of Membrane Science 431 (2013) 79–85
hydroxide-ion diffusion. According to neutron scattering experiments [17,18], the hydroxide-ion can accept between 3 and
4 hydrogen bonds and donate one in aqueous environment. 2D
infrared (IR) and pump-probe (PP) spectroscopies confirm this
result and indicate formation of a Zundel-like configuration,
wherein a proton is delocalized between a water molecule and
hydroxide ion [19]. The authors of the latter publication [19]
came to conclusion that the motion of the proton is coupled to the
surrounding solvent environment through dielectric fluctuations
that originate in hydrogen bond rearrangements.
Ab initio MD generally suggests two possible scenarios: (1) the
hydroxide ion accepts three hydrogen bonds and is able to donate
one [20], and (2) the hydroxide ion is overcoordinated and the OHtransport is driven by first solvation shell reorganizations [21–23].
Here we consider two mechanisms for the OH-diffusion which
are related to the above-mentioned mechanisms. Fig. 6a shows a
configuration where the hydroxide ion accepts three hydrogen
bonds from water molecules and donates one. In process of
thermal fluctuations, the proton can move from one of the water
molecules towards the hydroxide ion to form, first, a Zundel-like
ion (Fig. 6b), and then move further to transform the hydroxide
ion to the water molecule (Fig. 6c). This mechanism is similar to
the Grotthuss mechanism for the proton transport in water [24].
Thus, if only this mechanism is realized, we might expect that the
corresponding OH-diffusion coefficient should be close to the
proton diffusion coefficient in water. However, it is well-known
that the OH-diffusion in water is almost twice slower than the
proton diffusion [25,26], which makes the mechanism to be
inconsistent with experiment.
In the second mechanism, the hydroxide ion is overcoordinated accepting four hydrogen bonds from water molecules and
donating one (Fig. 6d). The latter hydrogen bond is most probably
longer and weaker, than the first four. A possible scenario for the
OH-diffusion might be the following. In process of fluctuations,
the proton can move from one of the water molecules towards the
hydroxide ion to form a Zundel-like ion. Simultaneously, the
adjacent accepted hydrogen bond elongates, while the donated
one becomes shorter and stronger (Fig. 6e). The proton continues
moving towards the hydroxide ion and transforms it to the water
molecule, breaking one of the accepting hydrogen bond (Fig. 6f).
This configuration is identical to the configuration shown in
Fig. 6c. At this point, next steps of the OH-diffusion might be
similar to those described for the first Grotthuss-type mechanism,
or another water molecule comes closer to the hydroxide ion and
then two situations are possible: (1) this water molecule forms a
hydrogen bond with the hydroxide ion (the fourth accepted
hydrogen bond) and the donated hydrogen bond will elongate,
but not break (Fig. 6g) and (2) the donated hydrogen bond breaks
and reorients to form a new donated weak hydrogen bond with
the coming water molecule (Fig. 6h). The broken hydrogen bond
will transform to the accepted one with the same water molecule
or with a new one. The rate-determining step for this mechanism
is breaking of a hydrogen bond. The newly formed configuration
is again overcoordinated with four accepted and one donated
hydrogen bonds of water molecules. This mechanism is consistent
with the neutron scattering data [17,18], indicating that a hydroxide ion can accept between 3 and 4 hydrogen bonds and donate
one in aqueous environment, and theoretical results [22,26,27]
which provide evidence that OH favors four accepted hydrogen
bonds and is able to donate a fifth one.
The OH-diffusion in a dry QAPS-OH membrane is a proper OHanion diffusion similar to that of other ions such as Li þ , Na þ or Cl .
In hydrated membranes, the OH-diffusion probably combines both
the en masse, also called the vehicle [28], (OH-anion diffusion of
an aggregated [OH (H2O)n] species) and Grotthuss-type proton
diffusion mechanisms. The hydroxide ion water coordination
number might be different for low- and fully hydrated membranes
and increases with increasing the water contents in a membrane.
It should be noted that conventional non-reactive force fields such
as Dreiding, can be used for studying en masse OH-anion diffusion,
while modeling of the Grotthuss-type proton diffusion needs application of a reactive force field, such as ReaxFF [29]. This will allow the
relative contributions of these two mechanisms to be estimated.
4. Concluding remarks
Using MD simulations, we predicted the microstructure and
OH-diffusion in high-performance alkaline polymer, quaternary
ammonium polysulfone hydroxide membranes, dry and with
14 wt% water uptake. The microstructure can be described as
a hydrophobic polymer backbone penetrated by a network of
three-dimensional interlinked hydrophilic channels of different
diameters. N(CH3)3 functional groups are mostly located along
walls of the channels. The mobile OH-anions are distributed
inside the channels. In consistent with experiment, the calculated
hydroxide-ion diffusion coefficient is by 1 order of magnitude
higher for the hydrated membrane with the 14 wt% water uptake
compared to that of the dry membrane. It should be noted that
the relatively small system used in our MD simulations may have
channels that would be closed in larger systems, and therefore the
‘‘density’’ of the channels and OH-diffusion would be lower in
such systems. Also, for more accurate estimation of diffusion
parameters, longer simulation times are typically required. MD
simulations on much larger ( 6 times) systems and for significantly longer time (several nanoseconds) are now in progress. Our
preliminary results of such simulations show that the geometric
characteristics (RDF) of the microstructure remain similar to
those described here. However, OH-diffusion coefficients are
about one order of magnitude lower than reported in this paper.
We discussed possible mechanisms of the OH-anion diffusion in
a QAPS membrane. In the hydrated membranes, the OH-diffusion
probably combines both the en masse (vehicle) and Grotthuss-type
proton diffusion mechanisms. Development of the ReaxFF reactive
force field will allow us to perform reactive MD simulations to
estimate the relative contributions of these two mechanisms to the
total hydroxide-ion diffusion in QAPS membranes.
Acknowledgments
This work was supported by SAMSUNG under the Global
Research Outreach (GRO) Program. The facilities of the Materials
and Process Simulation Center used in this study were established
with grants from DURIP-ONR, DURIP-ARO and NSF-CSEM.
Appendix A. Supporting information
Supplementary data associated with this article can be found in
the online version at http://dx.doi.org/10.1016/j.memsci.2012.12.010.
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