AALTO UNIVERSITY
School of Chemical Technology
Department of Chemistry
CHEM-E4100 Laboratory projects
Determination of the diffusion coefficient of methanol
in Nafion 115 ion-exchange membrane
1 Introduction
Fuel cells are power sources, which transform the chemical energy of the fuel into
electricity, via an electrochemical reaction. Fuel cells can be categorized by the
electrolyte used in them. For applications below 100 °C the most common fuel cell
type is polymer electrolyte membrane fuel cell (PEMFC), where the electrolyte is a
polymer membrane. Different fuels can be used in a PEMFC, provided that it is
possible to oxidize them in low temperatures into protons and electrons. Commonly
used fuels include hydrogen gas or small organic molecules such as alcohols or acids.
The PEMFC can be seen as an electrochemical cell, where anode and cathode are
separated by a solid polymer electrolyte (Figure 1). The fuel, i.e. methanol diluted in
water, is fed to the anode, where it is oxidized (methanol oxidation reaction) on the
surface of noble metal catalyst particles into protons, electrons and CO2. The
electrolyte is a good ionic conductor but a poor conductor of electrons, which is why
protons are transported from the anode to the cathode directly through the electrolyte,
whereas electrons have to travel via metallic end-plates and an external circuit. The
electric power created by the movement of electrons in an external circuit can then be
utilized. Oxygen is fed to the cathode, where it reacts with the electrons and protons,
forming water (oxygen reduction reaction, ORR).
e-
e-
Anode
Cathode
H+
O2 + 4 H+ + 4 e-
CH 3OH + H2O
CO2 + 6 H+ + 6 e-
2 H 2O
H+
Total: CH3OH + 3/2 O2
CO2 + 2 H2O
Figure 1. The operating principle of a direct methanol fuel cell.
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All galvanic cells, including fuel cells, have different factors which decrease the output
voltage and power of the cell. Fuel cell technology is still developing as these factors
still significantly decrease the performance, and the components in the cells are
expensive or not durable enough. The electrolyte is a key factor in the durability of a
fuel cell. The polymer membrane in a PEMFC commonly consists of a hydrophobic
perfluorinated hydrocarbon backbone to maximize its mechanical and chemical
durability. The backbone is crosslinked with hydrophilic sulfonic acid groups. When
the membrane gets wet, the hydrophobic parts come together and the hydrophilic parts
form channel-like structures throughout the membrane. The channels allow the
transport of water and protons, which means that in order for the membrane to
function, the membrane has to be wet. The structure of the membrane is shown in
Figure 2.
Figure 2. The structure of perfluorinated Nafion®-membrane, m = 6 - 10, n = 1.
Methanol fuel molecule is water-like for it is small, polar and neutral, which means
that it easily diffuses through the water channels. If methanol is present at the cathode,
its oxidation reaction competes with the reduction of oxygen, decreasing the cell
voltage. These unwanted side reactions thus decrease the efficiency of the fuel cell.
Therefore, methanol diffusion in the electrolyte membrane should be minimized.
2 Theory
Diffusion describes the spontaneous leveling out of differences in concentration (or
chemical potential) of a substance i towards an equilibrium concentration. It can be
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thought as the net movement of substance through random collisions caused by
thermal motion, which through time cause the substance to become more evenly
distributed in space. Diffusion coefficient D essentially describes how fast the process
is.
To analyze diffusion rate through a membrane, it is convenient to study a setup shown
in Figure 3. There are two solutions, I and II, separated by the membrane with a
thickness of L. If the methanol concentration in solution I is higher than the methanol
concentration in solution II, there will be a flux of methanol J from I to II. This flux
can be expressed with Fick’s first law of diffusion [1]
=
Where
d
d
=
d
d
(1)
is the total volume of solution II, A is the surface area of the membrane in
contact with the solution
and
are the concentrations of methanol in cell II and
the membrane, respectively, t is time, D is the diffusion coefficient and S is the surface
area of the membrane in contact with the cell. The flux takes place in the positive
direction x from I to II normal to the membrane.
x
Figure 3. Transport of methanol through a membrane.
The concentration gradient can be approximated to be linear over the membrane,
which leads to
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where
and
d
d
=
Δ
Δ
−
=
=
( −
)
(2)
are the methanol concentrations on the interfaces of the membrane
and the solutions I and II, L is the thickness of the membrane, and
=
/
is the
partition coefficient, which accounts for the differences in the solute environment
between the solution phase and the membrane phase. These include different water
concentrations, dielectric constants and short-range interactions [3]. If the volume of
the membrane is negligible when compared to the volume of the surrounding solutions,
the methanol balance can be expressed as
where
=
+
(3)
is the initial concentration of methanol in side I. With eqs. (2) and (3), the
methanol concentration gradient is
d
Eqs. (1) and (4) yield
Where
=
=
/(
d
d
=
=
−
−
1+
1+
(4)
=
−
(5)
is the permeability of methanol through the membrane,
) and
the initial condition
=
(
+
( = 0) = 0:
)/(
d
−
). Eq. (5) can now be integrated with
=− d
ln 1 −
=−
4
(6)
(7)
( )=
=
From (8) it can be seen that
[1 − exp(− )]
+
1 − exp −
+
(8)
approaches exponentially the value (
)/(
+
).
For ≪ 1/ (few hours), eq. (8) can be linearized with the Taylor series expansion at
t = 0, also known as the Maclaurin series expansion:
( )≈
(9)
This is a model for steady-state diffusion, which shows that the increase in the
methanol concentration of solution II is linear in the early stages of the experiment, to
a good approximation. Figure 4 shows the exponential equation (8) and the linearized
equation (9). When t increases to a point where the concentrations of volumes I and II
significantly start to change, the dependence deviates from linear behavior.
1
cII(t)/c0
0.8
0.6
0.4
0.2
0
0
10
20
Figure 4. Equation (8) approaches the value
t [h]
30
( )/
40
50
(solid line). The linearization
is a good approximation when t is small, but deviates when t increases.
The weakest point of the model is that the concentration profile is considered to be
established immediately, even though the membrane does not have a concentration
profile when t = 0. In reality, methanol first has to diffuse through the membrane,
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which is seen as a lag time
under which no methanol permeates the membrane. A
more thorough analysis of the problem is shown in e.g. [3], which results in
/6 . Introducing the lag-time to eq. (9) results in
( )≈
−
6
=
(10)
Equation (10) shows that the partition coefficient can be determined from the intercept
and the diffusion coefficient from the slope.
3 Experimental
The work is carried out with a diffusion cell (Permegear ® Side-bi-Side) with
temperature control and mixing, which consists of two half-cells with round apertures
between which the studied membrane can be clamped. The studied ion-exchange
membrane (Nafion® 115) has been pretreated so that the ion-exchange groups are in
proton form.
To clean the membrane, Nafion® 115 membrane was kept in boiling 5 mass% H2O2
for 30 minutes followed by rinsing with water. Afterwards, the membrane was kept in
boiling 0.5 M H2SO4 for 30 min to make the Nafion membrane in proton form and
again rinsing twice (each for 30 min) with hot deionized water.
Before the experiment, the diameter of the aperture in the diffusion cell and the
thickness of the wet membrane is measured, and the temperature of the thermostat is
set to 30 °C. A methanol solution of 1 mol/L is prepared to a 10 mL volumetric flask.
The cell is assembled accordingly and the left side of the cell is filled with 3 mL of the
methanol solution, whereas the right side is filled with 3 mL of ion-exchanged water.
The mixing is turned on and samples are taken at t = 15, 30, 45, 60 and 120 min.
The sample volume is 30 µL. To the sample, 10 µL of 0.5 mol/L 1,4-dioxane is added
in the fumehood after which the cap of the sample bottle is sealed tightly.
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The samples are analyzed with a gas chromatograph with a polyethylene glycol
column (Innowax, HP). Each sample is measured twice. Due to the small number of
samples, it is best to inject the samples into the gas chromatograph manually. 2 µL of
the sample is injected with a syringe into the chromatograph, after which the program
for methanol is run: Initial temperature is 40 °C, and it is ramped up with a rate of 4
°C/min until the methanol-solution vaporizes. The boiling point of pure methanol is
64.5 °C. With the described temperature program, the methanol peak is visible after
ca. 2.7 minutes, and the dioxane peak after ca. 5 minutes, but the exact retention times
depend on the time between injection and the beginning of the experiment. After these
two peaks are clearly visible, the measurement can be stopped. Now the column will
cool down to the initial temperature, after which a new measurement can be taken. The
last measurement should be let to run until the end of the program (230 °C) to remove
any impurities in the column.
4 Results
The results will be tabulated and the average value of the parallel measurements should
be used in the calculations. For the column used in this work, a standard series has
been measured for methanol, which yields the following relationship for the
concentration of the methanol and the area of the peak:
mol/L
= 7 ∙ 10
∙
.
(11)
where A is the methanol peak area divided by the area of the inner-standard (expressed
as percent %). Equation (11) is used to formulate the concentration profile in time, and
with the use of eq. (10), the diffusion coefficient of methanol in the membrane can be
determined. Compare your result with a literature value [4].
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5 Analysis of error
The error from the concentration measurements is estimated with regression analysis.
An estimate for the total error for the diffusion coefficient is carried out with the total
differential method, taking into account the errors from preparation of the solutions,
filling of the cells, membrane thickness and exposed membrane area. What is the
dominant source of error? How could the precision of the measurement be enhanced?
References
1. Z Wu, G. Sun, W. Jin, H. Hou ja S. Wang, J. Memb. Sci. 325 (2008) 376-382.
2. M.M. Nasef, N.A. Zubir, A.F. Ismail, M. Khayet, K.Z.M. Dahlan, H. Sairi, R.
Rohani, T.I.S. Ngah ja N.A. Sulaiman, J. Membr. Sci. 268 (2006) 96-108.
3. K. Kontturi, L. Murtomäki, J.A. Manzanares, Ionic Transport Processes,
Oxford University Press, Oxford, 2008.
4. T. Kallio, K. Kisko, K. Kontturi, R. Serimaa, F. Sundholm ja G. Sundholm,
Fuel Cells, 4 (2004) 328-336.
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