theory of interfacial proton transport in polymer...

Theory of Interfacial Proton Transport

in Polymer Electrolyte Membranes

Anatoly Golovnev and Michael Eikerling

Simon Fraser University, Burnaby, BC, Canada

SSPC16. September 13, 2012

Outline

• Importance of surface proton transport

• Model of the surface (interface)

• Mechanism of surface proton transport

• Mathematical description and results

• Conclusion/Prospective

2

Motivation

Our main research focus is on polymer electrolyte membrane (PEM) fuel cells

Operation relies on the proton conducting PEM which conductivity is mainly

due to a network of water filled pores

At T>90 oC the water starts to evaporate which leads to a significant decrease

of PEM conductivity

Since the bulk water transport is out of game, one has to count on the surface

proton transport

Aim: to understand the mechanism of surface proton transport and, based on that, link surface structure with proton mobility

3

Experimental Evidences

Can the surface transport provide high enough mobility? Yes!

J. Matsui, H. Miyata, Y. Hanaoka, and T. Miyashita, ACS Appl. Mater. Interfaces, 3, 1394-1397 (2011) 4

• J. Zhang, and P. Unwin, J. Am. Chem. Soc., 124, pp 2379-2383

(2002)

• S. Serowy, S. Saparov, Yu. Antonenko, W. Kozlovsky, V. Hagen, and

P. Pohl, Biophys. J. 84,1031-1037 (2003).

Experimental Evidences

Can the surface transport provide high enough mobility? Yes!

J. Matsui, H. Miyata, Y. Hanaoka, and T. Miyashita, ACS Appl. Mater. Interfaces, 3, 1394-1397 (2011) 5

• J. Zhang, and P. Unwin, J. Am. Chem. Soc., 124, pp 2379-2383

(2002)

• S. Serowy, S. Saparov, Yu. Antonenko, W. Kozlovsky, V. Hagen, and

P. Pohl, Biophys. J. 84,1031-1037 (2003).

Model Surface

6

A. Roudgar, S.P. Narasimachary, and M. Eikerling, J.

Phys. Chem. B, 110, 20469-204777 (2006)

up-right and tilted structures (top view)

−− 33 SOCF

−3SO

+OH3

Proton Transport

Vertices: SG

Triangles: H3O+

Vertices: SG

Triangles: H3O+

Activation energy of a single hop is 0.6 eV

A. Roudgar, S.P. Narasimachary, and M. Eikerling, Chem. Phys. Lett., 457, 337-341 (2008)

Such a large value is due to uneven distribution of

hydrogen bonds

7

Solution: to keep the number of HB at each surface group constant

Concerted Motion (Soliton)

S. Vartak, A. Roudgar, A. Golovnev, and M. Eikerling, submitted to the Journal of Physical Chemistry C

Hydrogen bonds

distributed evenly

Activation energy is 0.3 eV

8

Mathematical Description

( )∑ +−+

= +

i

iiii uVuu

k

dt

dumH )(

22

2

1

2

?)( =iuV

Hydronium ions move in the potential created by surface groups

What should look like?

• Periodic

• Harmonic for small displacement

• Steep ascending and descending flanks; plateau between wells

• Asymmetric

Exact potential profile is unknown. How to model it then?

is the hydronium ion displacement

iu

1+iuu

)(uV

9

Potential Profile

How does the hydronium motion depend on the potential profile?

)(cosh)(2

1 uuV λε−−=

)(cos)( 22 ua

uVπ

ε−=

Two extreme cases of the considered potentials

Different potentials offer different behaviour of hydronium ions.

But what about soliton energy and mobility? 10

(Strong HB)

(Weak HB)

Energy and Mobility

2

0

2

2)1(

1

2

v

v

kaE

−

=ε

εµ

2

1 2)1( ka

b=

)(1 uV )(2 uV

steep wells, large plateau slanting wells, minor plateau

2

0

2

2)2(

1

22

v

v

kaE

−

=ε

π

m

kav

22

0 ≡

ε

πµ

2

1

2

2)1( ka

b=

is the maximal soliton velocity

2)2(

)1(

)1(

)2( π

µ

µ==

E

E

b is the viscous friction coefficient

introduced to derive mobility

Consider a soliton travelling with a velocity v

11

100)1(

)2(

≈N

N

Soliton size ratio

Energy and Mobility

2

0

2

2)1(

1

2

v

v

kaE

−

=ε

εµ

2

1 2)1( ka

b=

)(1 uV )(2 uV

steep wells, large plateau slanting wells, minor plateau

2

0

2

2)2(

1

22

v

v

kaE

−

=ε

π

ε

πµ

2

1

2

2)1( ka

b=

Consider a soliton travelling with a velocity v

Only two (three?) parameters define the dynamics:

ε2

ka

b

- potential well depth. Already calculated! S. Vartak, A. Roudgar, A. Golovnev, M. Eikerling, submitted to the Journal of Physical Chemistry

- hydronium ion – hydronium ion interaction.

- viscous friction coefficient12

Conclusion

• A mechanism of soliton proton transport on a surface

• The particular potential profile has a minor influence on soliton’s

energy and mobility

• A complete description of single soliton properties

Prospective

• Numerical calculation of the constants to evaluate mobility

• The step from a single soliton to soliton statistics to find conductivity

13

Acknowledgements

14

Thanks to:

•NSERC for financial support

•Michael Eikerling

•Swati Vartak

•Ata Roudgar

15

3-Step Mechanism

In 2D one can avoid

overcoming large

potential barriers

16

Constants

k

b

hydronium ion – hydronium ion interaction.

- viscous friction coefficient. Where does it come from?

( )∑

−−+−+

= +

i

iii qu

a

qq

quu

k

dt

dumH ),

)(K2(dn1

22

22

2

2

1

2ε

ε

To evaluate results one has to calculate the constants used

- potential well depth. Already calculated!S. Vartak, A. Roudgar, A. Golovnev, M. Eikerling, Collective proton dynamics at highly charged

interfaces studied by Ab Initio Metadynamics, submitted to Chemistry of Materials .

17

Quest for Conductivity

µσ qn≡

probability density for creation of a soliton

A step from one soliton consideration to a soliton statistics

?=n

dvTk

vEEdvvvW

B

d

+−=+

)(exp

2);(

π

ω

−−≡

Tk

EEE

B

T

)0()(exp)(

δδ

18

Solutions

Narrow potential wells correspond to narrow solitons with a smaller

number of participants but a higher level of collectiveness of the motion

εξ

2

)1(2

0

22

)1( v

vka

a

−

=

vtx −=ξ

19