Supplementary Material
Nanophase Segregation and Water Dynamics in Hydrated
Nafion: Molecular Modeling and Experimental Validation
Kourosh Maleka,*, Michael Eikerlinga,b, Qianpu Wanga, Zhongsheng Liua, Shoko
Otsukac, Ken Akizukic, Mitsutaka Abec
a
National Research Council of Canada, Institute for Fuel Cell Innovation, 4250 Wesbrook Mall,
Vancouver, BC, Canada, V6T 1W5
b Department
c
of Chemistry, Simon Fraser University, Burnaby, BC, Canada V5A 1S6
Fuel Cell Laboratory, Nissan Research Center, Nissan Motor Co. Ltd., Kanagawa 237-8523,
Japan
Introduction
Atomistic molecular dynamics simulations were used to rationalize the effect
of the monomeric sequence of the ionomer on nanophase-segregation and water
and proton transport properties over a wide range of  and temperature.
Vishnyakov and Neimark
2,3
1
inferred from their simulations that as the water
content increased, temporary bridges between water clusters formed and broke
apart dynamically on a time scale of 100 ps instead of forming permanent water
channels. MD simulations performed by Elliott et al.
4
showed that water can be
divided into bound water that strongly interacts with the sulfonate groups and
freezable-bound or free water that is only weakly more correlated with the
1
5
polymer matrix. Urata et al.
showed that at low  , the sulfonate groups
aggregate and formed clusters with water molecules that are held together by
strong hydrogen bonds, while at high  , frequent exchange occurred between
bound and free water molecules.
In a series of recent papers, Devanathan et al
6,7
and Venkatnathan et al
8
simulated the effect of temperature and membrane hydration on membrane
nanostructure and mobility of water and hydronium ions using classical MD
simulations with DREIDING
9
and modified AMBER/GAFF
10
force fields. They
found that increasing  causes the sulfonate groups to drift apart. At   7 , most
of the water molecules and hydronium ions were bound to the sulfonate groups.
Cui et al. 11 performed similar analyses to obtain qualitative features of sidechainsidechain interactions. Radial Distribution Functions (RDFs) reported by Cui et al.
show remarkable deviation from those reported in Ref.[8].
Jang et al.
12
employed an all-atom approach in their MD simulation of
nanophase segregation and transport in Nafion at   16 . They showed that
blocky Nafion ionomers with highly non-uniform distributions of sidechains on the
polymer backbones form larger phase-segregated domains compared to systems
with uniform distributions of sidechains on the backbones. They found that water
transport depended strongly on membrane nanostructure. The calculated water
diffusion coefficients at 300 and 353 K were in good agreement with
experimental values. In a recent effort, Elliot and Paddison
calculations (using the ONIOM
14
13
applied QM/MM
method) to understand the effects of hydration
on the local structure of PFSA membranes.
2
Computational Methods
Dissipative Particle Dynamics (DPD) simulations
In an independent set of calculations, the average water cluster diameters were
calculated by Dissipative Particle Dynamics (DPD)
J-OCTA package.
22
15, 16, 17
using COGNAC in the
In our DPD simulations, Nafion was coarse-grained in a
slightly different way than in our CGMD simulations, in order to be consistent with
the previous DPD simulation of hydrated Nafion
17,
Scheme S1. Units of -[-CF2-
CF2-CF2-]-were coarse-grained as spherical beads of radius r = 0.30 nm and
perfluorinated ether and sulfonic side groups were coarse-grained separately by
two spherical beads of radius r=0.30 nm. In our CG mapping strategy, F atoms
were attached to the CF2 groups in the end of each -[-CF2-CF2-CF2-]- unit to
cap the chain, as shown in Scheme S2. The volume of each CG segment was
defined as 0.12 nm3 similar to the volume of two water molecules. One Nafion
polymer was composed of four monomers and 1000-2300 particles were initially
positioned randomly inside a 101010 nm3 simulation box. Details are given in
Table S1.
The Flory-Huggins  parameters of each particle were calculated by a
Monte-Carlo method at 298 K. Here, the direction and position of the segments
were assigned randomly, based on the number of neighbouring segments and
the contact energy:

Z 
1

 E12  ( E11  E22 )
RT 
2

(S1)
where Z is number of possible arrangements of neighbouring segments, E12 is
contact energy between segment 1 and segment 2, R is the gas constant, and T
3
is the temperature. The calculated values of  are shown in Table S2. We have
adjusted the  parameter between the charged sidechain bead 2 and water from
1.6 to -6.0, where the cluster-size converged with the variations of Particle
density was set at  = 3.0 particle/nm3. The dimensionless parameters for DPD
simulations were 0.02 for time step, 0.65 for dissipative parameter, 4.0 for bond
parameter, and 0.86for equilibrium length. The conservative force was adapted
from that reported in Ref. [17].
Atomistic molecular dynamics simulations
As a reference for CGMD and DPD simulations, we have also performed
atomistic simulations. These simulations were carried out based on a fullatomistic model for Nafion chain using a modified version of GROMOS96 force
field by adapting the charges and nonbonding and bonding parameters from the
DREIDING potential.
9
Charges on Nafion atoms were obtained using GAMESS
at the B3LYP-6-31G/ESP level.
18
In the force field used, interactions between
atoms are divided into non-bonded interactions, that exist between any pair of
atoms within a given cut-off radius, and bonded interactions between atoms in
the ionomer that are connected by chemical bonds. The bond stretching potential
and bond angle bending were expressed in terms of simple harmonic potentials.
The torsional rotational potential for the dihedral angle is a periodic function with
a 3-fold barrier. A typical effective potential is of the form:
4
V 
1
2k
b
ij
( rij  bij0 ) 2
bond


1 
kij ( ij   ij0 ) 2
angles 2

 k  {(1  cos[n(  
0
(S2)
)]}
dihedrals
A

B
erfc( rij )
   ij  6ij 
qi q j 
rij
40 rij
i j 

 Bij
To avoid the artefacts associated with truncation of electrostatic forces,
electrostatic interactions in our simulations were calculated using the ParticleMesh Ewald (PME) method with a grid spacing of 0.12 nm and fourth order
interpolation. PME improves the performance of calculations of electrostatic
interactions by applying a Fourier transformation on the grid. An inverse
transformation and interpolation factors provide the potential and forces on each
particle. When Ewald summation is used for long-range interactions, the shortrange columbic potential has to be modified. The last term in equation (3) shows
the short-range electrostatic potential that has been used in our simulations.
During the MD simulations, the potential energy and the total energy were
monitored in order to check whether the system has approached equilibrium.
Moreover, the temporal evolution of the root mean square deviation of the
particle position from the initial configuration was used in order to assess the
approach to equilibrium and the stability of the system.
Atomistic MD simulations were performed in a NVT ensemble at 298 K. A
cut-off of 1.0 nm was used for van der Waals interactions in our simulations,
comparable to what it was assumed originally in the force field. The integration
5
time step was 0.002 ps. After that the systems were equilibrated for 500 ps using
harmonic position restraints (1000 kJ mol-1 nm-2) and employing a similar
annealing procedure to that in CGMD simulations. This annealing procedure was
followed by production runs of 2 ns, the last 1.75 ns of which were used for the
analysis. The temperature was controlled by the Berendsen thermostat.
19,20
In
our MD simulations, the weak coupling algorithm was applied separately for each
group (polymer, water, hydronium ions) with a time constant 0.1 ps and a
temperature of 298 K. During the production run, structures were saved every
step (1 ps) and used for the analysis. Visualization was done by using the VMD
v1.8.1 commercial package. 21
Employing the structures obtained from our DPD simulations, we performed
atomistic MD simulations to calculate the diffusion coefficient of water. The initial
molecular arrangement for these MD calculations was chosen from the
equilibrated final morphology in our DPD simulations, using ZOOM option in the
J-OCTA package.
22
The MD simulation box included two polymers,
each composed of four monomers, and a varying number water molecules that
were placed between the polymer walls. 23,24 After the equilibrium structure was
obtained, we conducted MD runs at 298 K for a period of 500 ps in an NVT
ensemble and trajectories were sampled every 1 ps. The Nose-Hoover
thermostat was used to control the temperature.
6
Experimental methods
To understand the relationship between mass transport and microstructure
in the membrane, we employed small-angle X-ray scattering (SAXS).
25,26
The
formation and size of water clusters are studied by SAXS experiments and are
correlated to the diffusivity of water, measured by Pulsed Field Gradient NMR
(PFG-NMR).
Sample preparation. The NRE211-CS (DuPont), with equivalent weight 1100,
thickness of 25 m, and the density of around 2.0 g/cm3 in the dry state was used
for analysis. The membrane (as received) was cut out to adequate rectangular
pieces to be inserted into a test tube. The hydration state of the membrane was
controlled by a globe box where the test tube was placed with saturated salt
solution. After equilibration, the test tube was sealed.
SAXS measurements. SAXS experiments were carried out using a Nano
STAE/U/TXS (BRUKER AXS, USA) at 25 oC. The Cu K X-rays were generated
by a rotating copper anode generator source. The wavelength of the X-ray beam
was 1.54 nm. A two-dimensional position-sensitive proportional counter collected
SAXS images. The distance between the sample and the detector was 670 mm.
The beam line was perpendicular to the membrane surface. The mean intercluster spacing was estimated from the Bragg spacing
d
2

q





7



where q 
4 sin 

where q is the scattering vector, with wavelength ,
scattering angle The scattering angle varied in the range
0.23    4.4
corresponding to 40 nm  d  2.1 nm .
PFG-NMR. PFG-NMR experiments were carried out using a JNM LA-400 NMR
spectrometer (JEOL, Japan) at 25°C. The pulse gradients were applied along the
NMR tube axis, which was parallel to the membrane surface. A typical pulsed
field gradient sequence was used
27
and the self-diffusion coefficient of water,
Ds , was determined from
 A( g ) 
 2 Ds g 2 2 (4   )
ln 



2
 A(0) 
(S4)
where A(g) is the signal intensity observed with the applied field gradient, A(0) is
the signal intensity in the absence of a gradient, g is the gradient strength with a
pulse duration ,  is the nuclear gyromagnetic ratio, and  is the diffusion time.
The experimental conditions were δ = 0.05 – 2.45 ms, Δ = 50 ms, and g = 4.7
T/m.
8
main chain
-(CF2)3-(CF2)3-(CF2)3-(CF2)3-(CF2)3
side
chain1 side chain2
|
OCF2CFO-(CF2)2SO3H
CF3
Scheme S1
Scheme S2
9
Table S1. Specification of simulation boxes used for DPD calculations.
Corresponding relative humidity [%]
33
58
90
Volume fraction of water [%]
9.2
13.2
24.2
mol-H2O/mol-SO3H ()
2.8
4.3
8.9
Number of Nafion particles in DPD box
272
257
227
Number of water particles in DPD box
767
1094
2029
Distance between water clusters
2.7
3
3.3
Table S2. Flory-Huggins 
for each pair of particles calculated by
Monte-Carlo method at 298K. The  parameter between side chain 2 and water
was adjusted from 1.6 to -6.0.
Main chain
Main chain
Side chain 1
Side chain 2
-
-
-
Side chain 1
-0.56
-
-
Side chain 2
2.3
2.1
-
Water
7.7
7.7
1.6 (-6.0)
10
10n
m
3.30nm
2.25nm
Figure S1. Atomistic model of water channel in Nafion membrane based on the equilibrated
mesoscopic structure, obtained by DPD calculations. The rectangle shows the region, from which
the atomistic model was reconstructed.
11
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