Effect of Ion Exchange Capacity and Water Uptake on Hydroxide Transport in PSU-TMA Membranes: a DFT and Molecular Dynamics Study

Javier Luque Di Salvoa,b, Giorgio De Lucab*, Andrea Cipollinaa*, Giorgio Micalea

aDipartimento di Ingegneria (DI), Università degli Studi di Palermo– viale delle Scienze Ed.6, 90128 Palermo (PA), Italy.

bInstitute on Membrane Technology, ITM-CNR, Via P. Bucci 17/C, 87036 Rende (CS), Italy.

Supplementary Information

S1. Force Field calibration

In order to choose a suitable force field potential, a model system, used in Merinov and Goddard [1] work,

and composed of three PSU-TMA chains with an IEC of 1.95 meq/g corresponding to all monomers functionalized

with one TMA group, and 14% WU was considered. The annealing procedure was adapted from the one used in ref.

[1] while production runs were extended from 50 ps as [1] to 1 ns. Three force fields (OPLS-AA [2,3], UFF [4], and

DREIDING [5]) with four water models (SPC, TIP3P, TIP4P and TIP5P) at 300 K, 360 K, 400 K and 450 K, were

tested. Production runs should be extended for longer simulation times to guarantee a diffusive regime; however, 1

ns was considered sufficient to give a first insight since much simulations were necessary. Each simulation was

repeated four times, resulting in 176 production runs of 1ns. The combination OPLS/TIP5P does not give good

results because water molecules escaped away from the polymer during the NPT annealing procedure, leading to a

system with very low density. The force field and water model that yielded the best agreement with previous works

on OH- diffusion in PSU (or similar polymers) as well as the better linearity of MSD(t) was the DREIDING and

TIP5P model. Results of the OH- diffusion coefficients, obtained during the calibration procedure and the R2

coefficients are shown in Fig. S1.

Although the DREIDING/TIP5P force field resulted in the highest DOH, the self-diffusion coefficients were

lower with respect to the values reported in the Merinov and Goddard [1] work. In this regard, it is worth noting that

the MD performed in the ref. (1) used very short simulation times for the production runs, which makes a direct

comparison difficult. Similar low hydroxide diffusion coefficients (DOH) were also reported by Han et al. in an MD

work of a similar system (PSU functionalized with a TMA derivative) [6]. Since the tested bulk PSU-TMA has high

ionic concentration, this may explain the lower diffusion coefficients.

Furthermore, the partial charges, used to describe the Coulomb interaction in the selected FF, were

explicitly parametrized by applying high-level single-point DFT calculations on the fully hydrated PSU-TMA-

(H2O)13-OH systems, as detailed in section 3.2 of the article.

0.0E+00

2.0E-07

4.0E-07

6.0E-07

8.0E-07

1.0E-06

SPC TIP-3P TIP-4P TIP-5P

D (c

m2 /s

)

Water model

UFF

300K 360K 400K 450K

0.80

0.85

0.90

0.95

1.00

SPC TIP-3P TIP-4P TIP-5P

R2

Water Model

UFF 300K 360K400K 450K

0.E+00

2.E-07

4.E-07

6.E-07

8.E-07

1.E-06

SPC TIP-3P TIP-4P TIP-5P

D (c

m2 /s

)

Water model

DREIDING

300K 360K 400K 450K

0.80

0.85

0.90

0.95

1.00

SPC TIP-3P TIP-4P TIP-5P

R2

Water Model

DREIDING 300K 360K400K 450K

0.0E+00

2.0E-07

4.0E-07

6.0E-07

8.0E-07

1.0E-06

SPC TIP-3P TIP-4P

D (c

m2 /s

)

Water model

OPLS

300K 360K 400K 450K

0.80

0.85

0.90

0.95

1.00

SPC TIP-3P TIP-4P

R2

Water Model

OPLS 300K 360K400K 450K

Figure S1. Left: Diffusion coefficients for various force field/water model combinations at different Temperature. Error bars are standard deviation for the four independent production runs at the same conditions. Right: Media of

R2 coefficients referred to linear regressions of the MSD curves for the four independent production runs.

S2. Molecular Dynamics equilibration protocol

The annealing procedure was adapted from the Merinov and Goddard’s work [1]. It consisted in the application of

subsequent heating-cooling cycles performed in the isothermal-isobaric (NPT) ensemble. Two annealing phases

were defined: (i) umbrella constraints between water oxygens and nitrogen were applied to the system to prevent

water molecules to escape during equilibration; (ii) all constraints were turned off when a stable response on density

was obtained. A single heating-cooling cycle had a duration of 250 ps and consisted in the following annealing

cycle: the firsts 50 ps at constant temperature (300 K), then a linear increase of the temperature of 300-450 K for 50

ps, further 50 ps at constant T (450K), a linear temperature decrease of 450-300 K for 50 ps, and final 50 ps at

constant T (300 K). The annealing cycles were repeated until the linear chain self-compressed inside the initially

large box. Then, box vectors were re-scaled to fit the system size and the annealing cycles were repeated until a

stable response on density was achieved, which was around 0.8 g/cm3 (at 300K) for all systems. At this point,

constraints to water molecules were turned off and further heating-cooling cycles were applied until a stable

response on density, potential and kinetic energy was obtained as shown in Figures S2 and S3. A final 3 ns NPT

simulation (300 K) with the Nosè-Hoover thermostat and Parrinello-Rahman barostat was performed to set the new

heath and pressure coupling baths. Figure S2 shows a representative example of the response of density during the

annealing procedure.

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4 5 6 7 8 9 10

dens

ity (

g/cm

3 )

t (ns)

Box re-scale

Constraints turned off

Switch to Parrinello-

Rahman NPT

a) IEC = 1.04 meq/g

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8 10 12 14 16 18

dens

ity (

g/cm

3 )

t (ns)

Box re-scale

Constrainsturned off

Switch to Parrinello-Rahman NPT

b) IEC = 1.34 meq/g

Figure S2. Variation of density during an equilibration procedure according to the described MD simulated annealing procedure, for representative cases of a) 1.04 meq/g and b) 1.34 meq/g.

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

0 1 2 3 4 5 6 7 8 9 10

E (k

cal/m

ol)

x 10

000

t (ns)

E_totalE_kineticE_potential

a) IEC = 1.04 meq/g

-4

-3

-2

-1

0

1

2

3

4

5

0 2 4 6 8 10 12 14 16 18

E (k

cal/m

ol)

x 10

000

t (ns)

E_kineticE_potentialE_total

b) IEC = 1.34 meq/g

Figure S3. Variation of total, kinetic and potential energy during equilibration procedure of the systems

according the described MD simulated annealing procedure (corresponding to the same systems of Fig. S2).

S3. Cluster analysis

0

0.01

0.02

0.03

0.04

0.05

0 0.2 0.4 0.6 0.8 1

Cou

nt (a

rbitr

ary

units

)

θ

0.81 meq/g

0

0.01

0.02

0.03

0.04

0.05

0 0.2 0.4 0.6 0.8 1

Cou

nt (a

rbitr

ary

units

)

θ

1.04 meq/g

0

0.01

0.02

0.03

0.04

0.05

0 0.2 0.4 0.6 0.8 1

Cou

nt (a

rbitr

ary

units

)

θ

1.34 meq/g

Figure S4. Clusters’ size distribution for the IEC systems studied, accumulated during the 100 ns NVT

trajectories, in terms of the fraction of water and hydroxide oxygens belonging to a cluster (θi), as defined by

equation 7 of the article.

S4. Radial distribution functions

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6 7 8 9 10 11 12

g (r)

r (Å)

0.81 a0.81 b0.81 c1.04 a1.04 b1.04 c1.34 a1.34 b1.34 c

N-NIEC (meq/g)

Figure S5. RDFs of the Nitrogen – Nitrogen pairs for all the systems simulated in the work.

0

1

2

3

4

5

6

7

0 1 2 3 4 5 6 7 8 9 10 11 12

g (r)

r (Å)

0.81 meq/g; C.N.=1.75@5.99 Å0.81 meq/g; C.N.=0.79@5.73 Å1.04 meq/g; C.N.=1.69@5.92 Å1.04 meq/g; C.N.=0.96@5.85 Å1.34 meq/g; C.N.=0.71@5.71 Å

N-OH

Figure S6. RDFs of the Nitrogen – Oxygen (hydroxide) pairs, corresponding to the same systems plotted in Fig. 7. Coordination numbers are reported as C.N.@ rmin (Å).

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6 7 8 9 10 11 12

g (r)

r (Å)

S (all), C.N. 1.99@4.64 Å

S (PSU-TMA), C.N. 1.90@4.65 Å

S (PSU), C.N. 2.10@4.64 Å

S-OW0.81 meq/g

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6 7 8 9 10 11 12

g (r)

r (Å)

S (all), C.N. 1.98@4.64 Å

S (PSU-TMA), C.N. 2.04@4.63 Å

S (PSU), C.N. 1.92@4.66 Å

S-OW1.04 meq/g

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6 7 8 9 10 11 12

g (r)

r (Å)

S (all), C.N. 2.86@4.62 Å

S (PSU-TMA), C.N. 2.85@4.64 Å

S (PSU), C.N. 2.87@4.62 Å

S-OW1.34 meq/g

Figure S7. RDFs of the Sulphur–Oxygen (water) pairs for different IEC cases, showing all S atoms of the polymer chain, S atoms of the functionalized PSU-TMA monomer (S (PSU-TMA)) and S atoms of the not-functionalized

PSU monomer (S (PSU)). Coordination numbers are reported as C.N.@ rmin (Å).

S5. Mean Square Displacement curves

Figure S8. MSD curves obtained from the NVT production runs used to calculate the hydroxide diffusion coefficient. Solid lines correspond to ‘normal’ OH- solvation patterns, dashed lines correspond to OH- solvation

profiles with the presence of a shoulder between the first and second peaks of the OH-OW g(r) curves shown in Fig. 7b.

References cited in the Supplementary Information

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[4] A.K. Rappé, C.J. Casewit, K.S. Colwell, W.A. Goddard III, W.M. Skiff, UFF, a Full Periodic Table Force Field for Molecular Mechanics and Molecular Dynamics Simulations, J. Am.Chem. Soc. 114 (1992) 10024–10035. doi:10.1021/ja00051a040.

[5] S.L. Mayo, B.D. Olafson, W.A. Goddard III, DREIDING: A Generic Force Field for Molecular Simulations, J. Phys. Chem. 9 (1990) 8897–8909. doi:10.1021/j100389a010.

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