The Open-Access Journal for the Basic Principles of Diffusion Theory, Experiment and Application

Time-dependent Diffusion Coefficient of Proton in Polymer
Electrolyte Membrane
Takahiro Ohkubo, Koh Kidena, Akihiro Ohira
Polymer Electrolyte Fuel Cell Cutting-Edge Research Center (FC-Cubic), National Instituteof Advanced Industrial Science and Technology (AIST), 2-41-6 Aomi, Koto-ku, Tokyo 1350064, Japan
Corresponding author: Takahiro Ohkubo, E-Mail: ookubo-takahiro@aist.go.jp(received ??
11 July
July 2008,
01 ??
March(received2008,acceptedacceptedJuly2009)200?)

Abstract
We investigated the time-dependent self-diffusion coefficients of water,, inpolymer electrolyte membranes at 278 K. The
was measured from
0.7 to
100 ms by field gradient NMR techniques. The results showed that the self-diffusion
coefficients of water were dependent on
less than 2 ms due to restricted diffusion, andwere constant beyond 3 ms. The tortuosity and surface-to-volume ratio related to water
diffusion were also estimated from. The obtained values revealed the existence oflarge-scale restricted geometry compared with well-known nanometer-sized domain inpolymer electrolyte membranes.

Keywords
Polymer electrolyte membrane, Oscillating gradient, time-dependent diffusion

1. Introduction
Polymer electrolyte membranes (PEMs) are currently the object of intense interest due totheir potential use in fuel cells. Many studies have been carried out to investigate electrical
proton conductivity and its mechanism. Since a part of the proton conduction is caused bymass transport of water, the understanding of the water diffusion path is one of the subjects toclarify the proton transport mechanisms. Nano-scaled analyses of water path in PEMs havebeen achieved mainly by X-ray and neutron scattering techniques. However, little is known
about long-range order (up to micrometer) structure in PEMs. In this study, we attempt todetect the micron-scale restricted structure from the observation of the restricted diffusion ofwater through field gradient NMR techniques.

2. Methods and Materials
Sulfonated poly(4-phenoxybenzoyl-1,4-phenylene) (SPPBP), whose preparation andcharacterization were found in the literature[1] as S-PPBP, and commercial perfluorinated© 2009, Takahiro OhkuboDiffusion Fundamentals 10 (2009) 21.1 - 21.3

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membrane, N112 and NRE212CS of DuPont (Wilmington, De), were used as PEMs. The
membrane was cut into thin 2.5 mm 5 mm rectangular strips. Pieces of the cut membrane
were immersed in 1.0 M H2SO4 aqueous solution for 12 hours, and rinsed with deionizedwater at 353 K for 1 hour. After removing surface water by filtration paper, approximately 10cut pieces of membrane are put into glass tube (4 mm od, 40 mm length). To control the watercontent of membrane, we employed humidity chamber (Tabai Espec Corp, Osaka, Japan).
The atmosphere was controlled at 40 °C on 50 %RH. Equilibrium was achieved with glass
tube for 5 days at least. After reaching equilibrium, the glass tube was sealed with silicone
rubber plugs to avoid change of the water content during NMR measurements.
All measurements were carried out on a JEOL ECA-500 at 11.7 T, narrow-bore NMR
spectrometer equipped with maximum gradient strength of 1330 G/cm. The 4 mm od glass
tube including samples was sealed, inserted into 5 mm od NMR glass tube. Two pulse
sequences as shown in Fig. 1, oscillating gradient spin echo (OGSE) and 13 interval bipolar
pulse stimulated echo (13BPP), were employed to measure the 1H self-diffusion coefficient.
The observable NMR signal,, are expressed as a function of spin dephasing,where
is the self-diffusion coefficients, is the gyromagnetic ratio,is the NMR
echo intensity without field gradient andis the applied effective field gradient. The value andof two pulse sequences are given in Table 1.
Fig. 1: Two pulse sequences were employed tomeasureonfrom 1 ms to 100 ms.
(a)OGSE; the was fixed to 20 ms. The isadjusted in changing n and . (b)13BPP; Theis adjusted in changing T.

bOGSETable. 1:
factor and, for
OGSE and 13BPP. Each symbol
corresponds to that of thesequences in Fig. 1.

13BPP

We have measured
for eight linearly spaced values of for a maximum value
corresponding to the maximum signal attenuation of about 20 %. It is assured thatis
still in the Gaussian regime, and the self-diffusion coefficients can be obtained from eq. (1)for 13BPP and OGSE sequences, respectively. This procedure was performed by a linear
regression analysis onversus .

3. Results and Discussions
Figure 2 indicatesof N112, NRE212CS, SPPBP membranes and 5 mM CuSO4
aqueous solution at 278 K. On the calculation of the self-diffusion coefficients, the signal
attenuation with applied field gradient can be expressed by eq. (1) as a single diffusioncomponent. It is well-known that there are several kinds of proton species in PEMs such as
SO3 H+, H3O+ and H2O. However, since the exchange process among these species occurs
rapidly compared with the time scale of the NMR diffusion measurement, the obtained selfdiffusion coefficients cannot be identified these species individually. We thus should regard© 2009, Takahiro Ohkubo
Diffusion Fundamentals 10 (2009) 21.1 - 21.3

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the measured values as weight-average of these species. The self-diffusion coefficients in
5 mM CuSO4 were 1.31 10-9 m2/s on all over the diffusion time. This value is appropriate ascompared with the result of water[2]. On the other hand, The 1H self-diffusion coefficients inall membranes clearly depended onless than 2 ms at least. These results demonstrated
that there is restricted structure for these membranes on the length scale probed by thisexperiment. The self-diffusion coefficients for>3 ms were nearly independent on
andseem to be approaching a constant. The tortuosity, , related to tortuous diffusion path can bedetermined in this time scale of=100 ms.
where,is bulk diffusion coefficients of water (=1.3 10-9 m2/s). In addition, toextract surface-to-volume ratio, S/V, Mitra equation[3] was applied to thefor theshort diffusion time region less than 2 ms,

whereis the bulk diffusion coefficient. Theare plotted as a function of square rootof, are fitted by Mitra equation with the straight lines. The S/V andare provided fromthe slope and the intercept of the straight lines as shown Fig. 2. These values are summarized
together with in Table 2. The values ofobtained from Mitra equation are quite lower
than the bulk diffusion coefficients of water. It is thought that the values ofreflect thediffusion within the homogeneous network of cavities and so contains the transfer effectthrough the tortuous water path. In our results, the pore size (=6V/S for spherical pore) is
micrometer order, and is quite large compared with well-known hydrophilic domain size[4](nanometer size in Gierke model). A feasible interpretation for the obtained S/V is the density
fractionation of cavities resulting from heterogeneous distribution of cavity. The existence ofheterogeneous cavity distribution may produce restricted wall for water diffusion.
Fig. 2: Measured
versusthe square root of. The
data for N112, NRE212CS andSPPBP were fitted by eq. (3) atthe range ofms. The
straight lines show fittedresults.

Table. 2: Estimated values of,and in membranes. Errors reported
here are the standard error of thefitting lines to experimental data.

References[1] M. Rikukawa, K. Sanui, Prog. Polym. Sci. 25 (2000) 1463-1502.
[2] W. S. Price, H. Ide. Y. Arata, J. Phys. Chem. A 103 (2005) 448-450.
[3] P. P. Mitra, P. N. Sen, L. M. Schwartz, P. Le Doussal, P. Phys. Rev. Lett 68 (1992) 35553558.
[4] W. Y. Hsu, T. D. Gierke, J. Membr. Sci. 13 (1983) 307-326.
© 2009, Takahiro Ohkubo
Diffusion Fundamentals 10 (2009) 21.1 - 21.3

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