(174bo) Maxwell-Stefan Modeling and Experimental Study on the Ionic Resistance of Nafion 117

Membrane resistance
is a key parameter for electrochemical membrane-based technologies, such as
water electrolysis and chlor-alkali electrolysis.

In modern electrochemical
cells with a zero gap configuration, membrane resistance is considered the main
contributor to the overall ohmic resistance of the cell.

Measuring the
membrane resistance remains a challenge as various reported methods and
operating conditions lead to different results. Galama et al. [1]
discussed different approaches and possible flaws in measuring membrane
resistance. The resistance strongly depends on operating
conditions such as the type of electrolyte, electrolyte concentration, membrane
thickness, and temperature. It has also been suggested that applied current
densities can affect the membrane resistance, which would result in non-ohmic
behavior [2–4].

In this work, we present new
experimental data and modeling results on the resistance of a Nafion membrane
as a function of temperature. We have obtained the experimental results for
Nafion 117 with a setup, in which flaws in measuring membrane resistance are
avoided (Figure 1). Most important is the measurement of temperature close to
the membrane and the fixed distance between the Luggin-Haber capillaries and
the membrane. The temperature measurement is especially important since at high
current densities a significant difference between the bulk and membrane
temperatures is observed.   

Figure 1:
Schematic view of the experimental setup to measure the membrane resistance.

Both the Direct
Current (DC) and the Electrochemical Impedance Spectroscopy (EIS) methods were
applied. Figure 2 shows the measured resistance of NaOH 15 wt% without the
membrane with different current densities and capillary distances. The capillary
distances were determined by comparing the measured solution resistance with
the conductivity data in the literature for NaOH 15 wt% [5].  It can be seen from Figure 2 that the
distances between the tips of capillaries are 2 mm and 10 mm respectively. As
expected, the solution resistance follows Ohm‘s law as it is independent of current
density. DC method enables to record the resistance as a function of the
temperature while heating the solution with heating oil.

Figure 3: Measured
resistance of  NaOH 15wt% using Direct Current (DC) method (a) and Electrochemical Impedance Spectroscopy  (EIS)
method (b) as a function of the average value of the O-ring stack temperature with
different current densities.

When the membrane was inserted in
the experimental setup with a fixed capillary distance of 2 mm, the
measured resistance was not stable. A possible explanation could be that the
tips of the capillaries touch the membrane or disturb the current flow distribution.
Therefore the distance between capillaries was kept between 6 – 10 mm. As shown
in Figure 3, no electrical boundary layer is observed in the results of the EIS
method even at a high current density of 20 kA/m². The
membrane resistance is a function of temperature but is independent of current
density. To conclude, for a highly concentrated solution, Both DC and EIS
methods are applicable and show similar results. Moreover, the membrane
resistance shows an ohmic behavior. It is important to note that having a bigger distance between the capillary tips leads to a higher
solution resistance. Therefore measuring a very low ionic membrane resistance might
be challenging due to a higher standard error of the solution resistance.

Figure 3: Measured
resistance of  Nafion 117 + NaOH 15wt% using Direct Current (DC) method (a) and Electrochemical Impedance Spectroscopy  (EIS)
method (b) as a function of the average value of the O-ring stack temperature with
different current densities.

We also introduce a newly
developed Maxwell-Stefan model for alkali water electrolysis using concentrated
sodium hydroxide solution (NaOH 15 wt%) at both sides to predict the ionic
resistance of a monolayer Nafion 117 as a function of temperature. We have
previously already used this model to successfully predict membrane resistance
for chlor-alkali applications [6].
A significant difference from the chlor-alkali system is that no chloride ion
is present in the alkali water electrolysis. Figure 4 shows that the predicted
value of the Maxwell-Stefan model matches the experimental data very well. Maxwell-Stefan
diffusivities play a significant role in the model and the values of
diffusivities are temperature dependent. Similar to the chlor-alkali system, the
semi-empirical correlations for the Maxwell-Stefan diffusivities based on the
bulk diffusivities are also suitable for the alkaline electrolysis system. The
model also predicts a constant membrane resistance as a function of current
density. Zhang et al. [4]
derived the equation using the Ohm’s law to relate the ionic resistance of the
membrane with the conductivity and needed the membrane perm-selectivity as an input
parameter of their model. However, the values membrane perm-selectivity are not
generally available for different operating conditions. The Maxwell-Stefan
model, on the other hand, can predict both the membrane resistance and membrane
perm-selectivity including water transport number without using Ohm’s law to
derive the potential gradient explicitly.  

Figure 4: Modeled and measured areal membrane resistance of Nafion 117 as
a function of the average value of the
O-ring stack temperature using NaOH 15 wt% as anolyte and catholyte. Input
parameters based on known membrane properties: void fraction = 0.27 [-];
membrane thickness; 0.183 mm, EW = 1100 [-].

At last, we used
the Maxwell-Stefan model to predict the membrane resistance when the
concentration of NaOH is varied at the cathode compartment keeping the anolyte
concentration constant at 15 wt% (Figure 5a). The result shows a lower membrane
resistance at higher catholyte concentration and in line with the measured
resistance of NaOH 15wt% as anolyte and NaOH 32 wt% as catholyte. Varying the
fixed ionic group of the membrane in Figure 5b, the model suggests that the
membrane resistance increases slighly at higher fixed group membrane
concentration. There is a maximum resistance around 6 M. In this case,
mathematical modeling can be a more powerful approach than the experimental
studies in understanding the fundamental transport phenomena of the
ion-exchange membrane as the model can theoretically predict the membrane
resistance based on different operating conditions.

Figure 5: Modeled and measured areal membrane resistance of Nafion 117 as
a function of catholyte concentration while keeping the anolyte concentration
constant at NaOH 15 wt% (a) and as a function of fixed ionic group of the membrane
using NaOH 15wt% at both sides (b). Temperature is 80 ^oC. Input
parameters based on known membrane properties: void fraction = 0.27 [-];
membrane thickness; 0.183 mm, EW = 1100 [-] (a)

References

[1]      A. H. Galama, N. A. Hoog, and D. R. Yntema,
“Method for determining ion exchange membrane resistance for electrodialysis
systems,” Desalination, vol. 380, pp. 1–11, 2016.

[2]      S. Moshtarikhah, M. T. de Groot, and J. van der
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1, pp. 51–62, 2017.

[3]      E. J. Taylor, N. R. K. Vilambi, R. Waterhouse, and
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21, no. 5, pp. 402–408, 1991.

[4]      B. Zhang, J. G. Hong, S. Xie, S. Xia, and Y. Chen,
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362–369, 2017.

[5]      T. F. O’Brien, T. V. Bommaraju, and F. Hine, Handbook
of Chlor-Alkali Technology Volume I : Fundamentals. Springer, 2005.

[6]      R. R. Sijabat, M. T. de Groot, S. Moshtarikhah, and
J. van der Schaaf, “Maxwell–Stefan model of multicomponent ion transport inside
a monolayer Nafion membrane for intensified chlor-alkali electrolysis,” J.
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