Molecular dynamics simulations of substrate hydrophilicity and
confinement effects in capped nafion films
Citation for published version (APA):
Sengupta, S., & Lyulin, A. V. (2018). Molecular dynamics simulations of substrate hydrophilicity and confinement effects in capped nafion films. Journal of Physical Chemistry B, 122(22), 6107-6119.
https://doi.org/10.1021/acs.jpcb.8b03257
Document license: CC BY-NC-ND
DOI:
10.1021/acs.jpcb.8b03257
Document status and date: Published: 07/06/2018
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Accepted manuscript including changes made at the peer-review stage
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S1
SUPPORTING INFORMATION
Molecular Dynamics Simulations of Substrate
Hydrophilicity and Confinement Effects in Capped
Nafion Films
Soumyadipta Sengupta1,*, Alexey V. Lyulin 1,2
1Theory of Polymers and Soft Matter, Department of Applied Physics, Eindhoven University of
Technology, Eindhoven 5600 MB, The Netherlands
2Center for Computational Energy Research, Department of Applied Physics, Eindhoven
University of Technology, Eindhoven 5600 MB, The Netherlands
I. Model Construction
The Nafion chains were constructed using Materials Studio1. The molecular structure of Nafion is
shown in Figure 1 [main document]. The value of n is taken as 7 for this study, corresponding to
an equivalent weight (EW) of 1100. An equivalent weight of 1100 represents common varieties
of Nafion like Nafion-117 and Nafion-112. The value of m represents the degree of
polymerization and this has been taken as m=10. Polyelectrolytes like Nafion2, Aciplex3 and
PFSI4, which have a PTFE backbone, have been previously modelled using 10 monomers in a
S2
Three different simulation boxes were constructed corresponding to the three different
thickness values (6.3nm, 8.7nm, 11.5 nm) using the Amorphous Cell module of Materials
Studio1. The different simulated thickness values represent varying nanoparticle filler fractions,
i.e., the thinner the film, the higher the filler fraction could be. Each simulation box had 17
Nafion chains, 170 hydronium ions and 2380 water molecules. The simulation box was confined
in the Z direction and was periodic in the X and Y directions. A fixed boundary was used for the
Z direction. The corresponding lateral (X and Y directions) dimensions varied from 6 nm (the
thinnest film) to 4.5 nm (the thickest film).
Bulk Nafion simulations were also performed in 3D periodic boxes at the same hydration level
λ=15 for two different system sizes of 7 and 17 Nafion chains. No finite size effects have been
observed on comparing the density, radial distribution functions (RDFs) and water diffusion
coefficients.
All the simulation results for bulk and interfacial models shown in the present paper are for a
17 chain Nafion system.
II. Simulation Protocol
Each of the simulation boxes were energy minimized using the conjugate gradient algorithm in
LAMMPS5. Two different temperatures of 300 K and 353 K were chosen for the present
simulations (300 K is the room temperature and 353 K is the average operating temperature for
PEMFCs).
The equilibration and production runs were also carried out using LAMMPS software5. For a
S3
walls with both 𝜖𝑝ℎ𝑜𝑏 and 𝜖𝑝ℎ𝑦𝑙 fixed at 0.25 kcal/mol. Then, the simulation box was subjected to a NVT run of 0.2 ns at T=300 K/353 K. After that, the simulation box was subjected to an
annealing sequence in which the sample was heated up from 300 K/353 K to 600 K in 50 ps,
maintained at 600 K for additional 50 ps and cooled down from 600 K back to 300 K/353 K in
another 50 ps. This cycle was repeated for five times. After the annealing cycles were completed,
the sample was simulated in the canonical NVT ensemble at T=300 K/353 K for 0.2 ns. After
that, the sample was simulated under NpT conditions for another 7 ns at p=1 atm (in the lateral
periodic dimensions) and T=300 K/353 K. The density of the sample has been stabilized after
about 1.5 ns of NpT simulations. The final configuration after 7 ns of NpT simulations was used
as a starting configuration for simulations with five different 𝜖𝑝ℎ𝑦𝑙 values at a fixed film
thickness. Then, each of these different 𝜖𝑝ℎ𝑦𝑙 value simulation boxes underwent the same simulation protocol as mentioned above (in this paragraph). For a fixed film thickness, different
initial configurations were also implemented to increase the statistics and to confirm the accuracy
of the simulations.
The Nose-Hoover style thermostat and barostat6,7 in LAMMPS5 were used for maintaining the
temperature and pressure, as imposed during the NVT/NpT simulation. The Verlet integration
algorithm8 was used for time integration of the equations of motion. The slab PPPM9 solver was
used for solving electrostatic interactions in the Nafion film simulations while the normal PPPM
solver was used for bulk Nafion simulations. The cutoff for non-bonded interactions was set at 10
Å. The time step was 1 fs for all the simulations.
The density of the samples has been stabilized at around 1.5 ns (Fig. S1) from the start of the
NpT simulations for both T=300 K/353 K. The last 3 ns of the NpT simulation was used for
S4
analysis. The RDFs and average water cluster sizes did not show any significant variation during
this time.
III. Force Field Validation
Bulk Nafion was simulated at T =300 K and 353 K and at p = 1 atm to ascertain the validity of
the force field. The density at λ= 15 at T=300 K was 1.83 g/cc and at T=353 K was 1.79 g/cc.
These density values were within 5% of previously observed experimental Nafion density at
T=300 K10,11 and simulated Nafion density at T=363 K12. The radial distribution functions
(RDFs) for sulfur-oxygen (water) and sulfur-oxygen (hydronium) for bulk Nafion are shown in
Figure S1. The peak distances for these RDFs also agree well with previous simulations13,14. The
first peak of sulfur-sulfur (S-S) radial distribution function, as seen in Figure S2 , was at 4.4 Å
which is within the range of the first peak distances observed in previous simulation studies2,14.
The oxygen (water) - oxygen (water) first peak, as seen in Figure S3, was at 2.9 Å which is also
quite similar to the previous simulation studies2,15.
The diffusion coefficient of water in Nafion at λ= 15 for T=300 K was 0.98*10-5 cm2/s and at
T=353 K was 1.93*10-5 cm2/s. These values were within the range of the previous simulation
data14,12 and the experimental16 water diffusion coefficient values at λ= 15. The diffusion
coefficient for hydronium was 0.25*10-5 cm2/s (T=300 K) and 0.48*10-5 cm2/s (T=353 K) which
agreed well with the previous simulation14 and experimental values17,18,19.
The density of bulk hydrated Nafion has been decreased with increasing hydration levels and
with increasing temperature. The water and hydronium diffusion coefficient values have been
increased with increasing hydration levels and with increasing temperature. This is consistent
S5
The sulfur-sulfur radial distribution function (RDF) (Figure S2), sulfur-sulfur coordination
number (CN) (Figure S3), sulfur-oxygen (water) CN (Figure S4), oxygen (water) - oxygen
(water) RDF (Figure S5), layer resolved side chain orientations (Figure S6), water cluster
distributions (Figure S7), film averaged in-plane water mean square displacement (Figure S8) and
layer resolved in-plane water diffusion coefficients (Figure S9) have been shown below.
IV. Sulfur-Sulfur Radial Distribution Functions
Figure S2. Sulfur-Sulfur radial distribution functions (RDF) for different wall
hydrophilicity values for (a) 8.7nm film (b) 11.5 nm film. The RDF values for bulk Nafion
are also shown
(a) (b)
Figure S1. Radial distribution functions for bulk Nafion. S-
S6 V. Sulfur-Sulfur Coordination Number
VI. Sulfur-Oxygen (Water) Coordination Number
Figure S4. Sulfur-Oxygen (water) coordination numbers (CN) for different wall
hydrophilicity values for (a) 8.7nm film (b) 11.5 nm film. The CN values for
bulk Nafion are also shown
(a) (b)
Figure S3. Sulfur-Sulfur coordination numbers (CN) for different wall hydrophilicity
values for (a) 8.7nm film (b) 11.5 nm film. The CN values for bulk Nafion are also
shown
S7 VII. Side Chain Orientation
(a) (b)
(c)
Figure S5. Side chain orientation with respect to Z-axis for different film thickness values for (a)
𝜖𝑝ℎ𝑦𝑙 = 0.50 kcal/mol wall (b) 𝜖𝑝ℎ𝑦𝑙= 1.20 kcal/mol wall (c) 𝜖𝑝ℎ𝑦𝑙 = 1.50 kcal/mol wall. Relative
S8 VIII. Oxygen (Water) – Oxygen (Water) Radial Distribution Functions
(a) (b)
(c)
Figure S6. Radial distribution functions (RDF) for Ow-Ow for different wall hydrophilicity values for (a)
S9 IX. Water Cluster Distribution
(a)
(b)
Figure S7. Water cluster distributions for cluster sizes from 100 to 2380 for
different wall hydrophilicity for (a) 8.7 nm film (b) 11.5 nm film. Bulk Nafion
S10 X. Mean Square Displacement
(a) (b)
(c)
Figure S8. Mean square displacement (MSD) vs time plots for water in the planar direction (X
and Y direction combined) for different wall hydrophilicity values (in kcal/mol) for (a) 6.3 nm
film (b) 8.7nm film (c) 11.5 nm film. Bulk Nafion MSD is also shown. The dotted line denotes a
S11 XI. Layer Resolved Diffusion Coefficients
Figure S9. Layer resolved in-plane water diffusion constants (D) normalized by two
dimensional water diffusion constant (Dbulk) at λ=15 for bulk Nafion. Results are
shown for (a) 8.7 nm and (b) 11.5 nm film for varying wall hydrophilicity. Relative
distance (t/T) is defined as the distance (t) from a wall divided by the film thickness
(T).
(b) (a)
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