2007-JMaterials Chem 37_3255-3268_Main-Chain, Statistically Sulfonated PEM Proton Mobility to Water

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Main-chain, statistically sulfonated proton exchange membranes: therelationships of acid concentration and proton mobility to water content andtheir effect upon proton conductivity{

Timothy J. Peckham,a Jennifer Schmeisser,{a Marianne Rodgersab and Steven Holdcroft*ab

Received 15th February 2007, Accepted 8th March 2007

First published as an Advance Article on the web 3rd April 2007

DOI: 10.1039/b702339a

An in-depth analysis has been developed for proton exchange membranes to examine the effect of

acid concentration and effective proton mobility upon proton conductivity as well as their

relationship to water content. The analysis was carried out on a series of main-chain, statistically

sulfonated polymers with varying ion-exchange capacities. These polymer systems consisted of:

sulfonated poly(ether ether ketone) (1), poly(ethylenetetrafluoroethylene-graft-polystyrenesulfonic

acid) (2), sulfonated polyimide (3) and BAM1 membrane (4) with Nafion1 (5) as baseline. They

represent membranes comprising polyaromatic polymers (1and3), one of which is also a rigid-rod

polymer (3), vinylic polymers (4) and a vinylic polymer polymerized inside a polymer matrix ( 2). In

order to remove the differences in acid strength for the membranes, proton mobility values atinfinite dilution (Xv = 1.0)and 25uC were calculated and found to be 3.2 (0.4)6 10

23 cm2

s21

V21

(1), 2.9 (0.4) 6 1023 cm2 s21 V21 (2), 1.6 (0.7) 6 1023 cm2 s21 V21 (3) and 2.1 (0.2)6

1023 cm2 s21 V21 (4). These were then compared with the theoretical value for the mobility of a free

proton at infinite dilution. Significant deviations from this value were theorized to be due to possible

differences in tortuosity and proximity of acid groups.

1.0 Introduction

Research on proton exchange membrane fuel cells (PEMFCs)

has been an area of active interest since the 1960s but more

so over the last decade. This has been partially the result of

increasing demands from the public for zero-emission vehicles

and power sources that lead to the reduction of greenhouse

gases. However, the major impetus, particularly for auto-

motive manufacturers, has been government-funded initiatives

such as legislation enacted in California to achieve significantly

lower automotive emissions,1 the FreedomCar and Fuel

Partnership program initiated by the U.S. government through

the U.S. Department of Energy (DOE)2 and an initiative by

the European Union through the Commission of the European

Communities.3

As a key component in PEMFCs, the proton exchange

membrane (PEM) and its development have attracted parti-

cular interest in commercial, government and academic institu-

tions. Nafion1 membranes have been at the forefront of this

development, offering to date the best combination of

performance, durability and reliability. Nevertheless, as the

technological requirements for automotive and stationary

applications are becoming increasingly rigorous,4 there is a

growing need for PEMs that have improved properties over

those offered by Nafion1 membranes.4,5 As an iterative or

random hit and miss approach to membrane development is

generally not very effective, a more desirable way to system-

atically develop new PEMs would be first to obtain a funda-

mental understanding of the structureproperty relationships

for these materials before attempting to design a new PEM.

One of the most important properties of a PEM is its ability

to provide an ionic path for protons to travel from the anode

to the cathode.6 In the case of Nafion1 and the majority of

other PEMs, water-saturated channels are believed to form

due to the phase separation of the normally hydrophobic

polymer backbone from the hydrophilic, bound sulfonic acid

groups. Proton conduction is thought to occur through these

channels, mediated by the sulfonic acid groups and in

conjunction with water that is either closely associated with

the acid groups or present as bulk water in the channels.79 If

the level of proton transport is insufficient, a resistive (Ohmic)

loss will be observed along with a concomitant negative impactupon the performance of the fuel cell.6,10 Factors such as

density of acid-containing groups within the membrane,

polymer structure and morphology, in combination with water

content, have an impact upon the observed level of proton

conduction. In order to design new membranes with improved

levels of proton conduction, it is therefore important to learn

from existing materials exactly how these factors influence

proton conductivity. This attempt to better understand the

structureproperty relationship for proton conductivity in

PEMs has been a core focus of our research1123 on PEMs as

well as that of several other groups.2443 Some of this work will

be highlighted in the following paragraphs.

aDepartment of Chemistry, Simon Fraser University, Burnaby, BritishColumbia, V5A 1S6, CanadabInstitute for Fuel Cell Innovation, National Research Council Canada,3250 East Mall, Vancouver, British Columbia, V6T 1W5, Canada{ This paper is part of a Journal of Materials Chemistrytheme issue onNew Energy Materials. Guest editor: M. Saiful Islam.{ Current address: Department of Chemistry and Biochemistry, 273-1Essex Hall, 401 Sunset Avenue, University of Windsor, Windsor,Ontario N9B 3P4, Canada.

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Not surprisingly given its position as a standard for fuel cell

research, Nafion1 has been particularly well studied to better

understand its structureproperty relationships. The micro-

structure of this membrane has been extensively analyzed using

both small-angle X-ray scattering (SAXS) and small-angle

neutron scattering (SANS) with a wide range of polymer-to-

solvent ratios as well as using different types of solvents with

much of the primary studies having been conducted by Gebelet al.4447 In Nafion1, as with other PEMs, nanoseparation of

the hydrophobic and hydrophilic portions of the polymer leads

to the formation of interpenetrating domains wherein proton

transport occurs via the hydrophilic domains.31,34 In compar-

ing the microstructure of Nafion1 to that of sulfonated

poly(ether ether ketone), SPEEK, Kreuer et al. noted that the

hydrated channels in Nafion1 are larger and exhibit better

connectivity than those in SPEEK. With smaller channels, the

protons in SPEEK are in closer proximity to the tethered

SO32 groups and thus experience a higher degree of

attraction, more so magnified by the stronger basicity of the

sulfonate anion in SPEEK relative to the analogous site in

Nafion

1

. Protons in SPEEK, therefore, exhibit lower mobilityvalues. With less connectivity, the mean free path for protons

in SPEEK is also longer, thereby further reducing the overall

mobility in comparison to the situation in Nafion1. These

differences have thus been used to explain the deleterious effect

of lower water contents on conductivity in SPEEK whereas the

result is not as severe for Nafion1.5

Investigating structureproperty relationships in PEMs

has also been a strong focus of the research in our group

on fuel cells. The proton conductivity of BAM1 membranes

(4), sulfonated styrene-(ethylene-butylene)-styrene triblock

copolymers (DAIS-Analytical), ETFE-g-PSSA (2) and N117

(5) were measured and the microstructures analyzed

by SAXS.11

Whereas 5 showed clear signs of microphaseseparation in the form of ionic aggregates, most ionic sites

were homogeneously distributed in the case of2. For 4, there

was evidence for some degree of ionic aggregation but with the

aggregates widely and homogeneously dispersed, unlike the

channel structure observed for 5. Additional TEM studies on 4

confirmed that localization of ionic domains was not as well

developed as in the case of5.

Another study comparing the more structured PS-g-PSSA

with PS-r-SSA found that the former exhibited significantly

higher conductivity values than the latter for a similar degree

of ion content.1214 TEM analysis revealed clear signs for

microphase separation and a continuous network of ionic

channels in PS-g-PSSA whereas PS-r-SSA showed a lack ofphase separation. It was thus surmised that the higher conduc-

tivity of PS-g-PSSA was due to its more organized micro-

structure. More recently, our group has investigated systems in

which the presence of fluorinated blocks in a sulfonated

copolymer has led to varying degrees of microphase separa-

tion.16,1820 These systems and others are currently under

investigation to try and determine how the morphology of the

microphase-separated structure affects proton conductivity.

A number of other groups have also been actively involved

in studying structureproperty relationships on PEMs. In the

interest of space, only a few, more recent examples will be

highlighted here. Elabd et al., for example, have studied

sulfonated poly(styrene-b-isobutylene-b-styrene) and examined

the effect of polymer morphology26 and the increased align-

ment of ionic domains24 on its properties. In the former study,

it was found that a 3-fold decrease in transport properties

could be achieved by changing the solvent used to cast the

membranes from toluene to a tolueneethanol mixture

with observable differences in morphology between the two

membranes as determined by SAXS measurements. In the

latter study, it was found that up to a 6-fold improvement in

conductivity could be achieved by aligning the ionic domains

perpendicular to the casting plane of the membrane in

comparison to the isotropic analogue.

Structureproperty relationships in PEMs have also been

investigated for sulfonated polyimides (4). Okamoto et al.

observed that a microphase-separated structure for polyimides

could be achieved by separating the sulfonic acid group from

the polymer backbone by means of a short graft chain.42

Improvements in both conductivity and resistance to hydro-

lysis over main chain-sulfonated polyimides were attributed

to the microphase-separated structure. Watanabe et al. also

performed a similar study on polyimides with sulfonic acid-bearing side chains and observed improvements in proton

conductivity.43

Overall, it appears that the general approach in the literature

to study the efficiency of proton transport for a series of new

materials is to interpret proton conductivity data (as measured

by ac impedance spectroscopy) as a function of ion-exchange

capacity (IEC) or water uptake. Using supporting data

obtained from supplementary analytical techniques (e.g.,

TEM, XRD), the results are then usually explained and

correlated to the connectivity and size of the water-saturated

channels that result from the phase separation of the

hydrophobic polymer backbone from the hydrophilic sulfo-

nate side chains in order to explain differences observed inproton conductivity between different materials. While useful

information can certainly be obtained from this approach, we

have found in our group that a more in-depth, systematic

analysis of proton conductivity data also provides additional,

useful information that could potentially lead to further

understanding of proton conduction in PEMs and thus

hopefully aid in the design of new materials with improved

levels of proton conductivity.

In this paper, we would like to report both this method as

well as present examples of its application to a number of

different sulfonic acid-bearing polymer systems. Generally, it is

difficult to compare literature data in a systematic manner as

frequently not all the required information is presented. Inaddition, measurement techniques are not consistent through-

out the literature. In order to circumvent these issues, all the

data on the PEMs that we present in this paper were obtained

in our own laboratory, thereby ensuring that measurements,

treatments and data acquisition were kept consistent.

2.0 Results and discussion

2.1 Approach to proton conductivity data analysis

The observed proton conductivity for a PEM is intimately

linked to both its water content and its acid content. The

approach for the expanded analysis examines in detail the

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relationships amongst these properties as well as a deeper

examination of proton conductivity itself. By carrying out this

analysis, it was hoped that additional information could be

gained from proton conductivity data alone that could

complement other techniques (e.g., TEM) currently employed

to explain observed trends in proton conductivity. The analysis

itself is divided into four sections: a) proton conductivity,

b) effective proton mobility, c) acid concentration in themembrane and d) water content. Fig. 1 shows the various

component plots for each section.

2.1.1 Proton conductivity. Although both water content and

the density of acid groups have an effect upon the conduction

of protons through a PEM, only the density of acid groups

remains consistent within a membrane, irrespective of the

membrane environment. Thus, the relationship between

proton conductivity (s) and the density of acid groups (i.e.,

IEC) at a fixed temperature and humidity is an effective

starting point for an analysis.

As proton conductivity is also related to water content,

however, determining the relationship between water contentand proton conductivity is required. Water content of a PEM

is commonly described in terms of water uptake (weight%

increase for PEM from dry to wet state). Water uptake as a

volume percentage, also described as the water volume fraction

(Xv),48

is used as a replacement here for water uptake as a

weight percentage.Xv is generally a more useful measure that,

in addition to indicating how much water a membrane is

capable of absorbing, also gives the actual percentage of the

volume of the membrane occupied by water. This is

particularly useful for membranes with very high water

uptakes, as will be seen in the discussion on BAM1

membranes. With extrapolation to Xv= 1.0, use of this factor

also potentially shows how close proton conductivity in themembrane approaches that in pure water. As increasing IEC

for all PEMs generally leads to an increase in water content, it

is also convenient to standardize water content for acid

content and thereby permit comparisons between PEMs with

different IEC values. This factor, l (moles of water per mole of

acid), will also be used in the analysis.

2.1.2 Proton mobility. Mobility is defined as the rate

of transport of a species under an applied electric field

(cm2 s21 V21). Upon examination of the general definition of

electrical conductivity, se, it can seen that it is simply a

function of the quantity of charge carriers in a given volume, g,

and the mobility of those charge carriers, me (eqn (1)):

se = geme (1)

This general relationship is easily extended to ionic systems

where the transference number of an ion is equal to one

(eqn (2)):

s = Fai|Zi|m (2)

where s is the specific conductivity of the ion, F is Faradays

constant,aiis the activity of the ion, and Ziis the charge on the

ion. The activity, ai, itself can be defined by the following

equation:

ai = fiCi (3)

wherefidescribes the degree of dissociation of the ion andCiis

the analytical concentration of the ion.

This relationship is applicable for an estimation of proton

mobility from proton conductivity in PEMs as the negatively

charged SO32 counter-ions are tethered to the backbone, thus

resulting in a transference number of one for the positively

charged protons (eqn (4)):

sH+ = F[H+]mH+ (4)

In fact, a more correct description of eqn (3) is to replace

[H+] with the activity value for H+. This requires accurate

knowledge of the activity coefficient of H+, which is

concentration dependent and an unattainable value in these

systems. The activity, as previously shown in eqn (3), is related

tof, the degree of dissociation (dependent upon both the pKaof the acid group and the water content of the PEM) and is

thus a factor in the mobility of the proton. In fact, proton

mobility in the aqueous phase of a PEM does not fall into the

Fig. 1 Analysis of proton conductivity data.


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classical view of mobility of free ions in solution. For example,

strong binding of a proton to the tethered anion (or anions) as

it traverses the membrane should be considered as an

impediment to its mobility. Hence, the calculated proton

mobility is an effective mobility that includes the uncertainties

of the activity coefficient(s) for H+. In the extreme, if all the

acid groups in the membrane remain undissociated, the

effective mobility value is zero. The titration measurement,

however, measures the concentration of SO3H groups in the

membrane rather than an actual free proton concentration,

thus combining both bound and unbound protons (eqn (5)):

SO3H = SO32 + H+ (5)

Given that the analytical acid concentration, rather than

proton concentration, is the quantity measured by titration,

we have substituted acid concentration for proton concentra-

tion into the equation for proton conductivity as seen in

eqn (6). Calculation of proton mobility, therefore, allows a

normalized proton conductivity to be determined; i.e., acid

concentration effects are removed. By doing this, it is possible

to view the relative contributions of both proton mobility and

acid concentration (itself consisting of contributions from

both acid and water contents) to the experimentally measured

proton conductivity.

In addition to the effect dissociation and tethered anionic

groups have on mobility, there are additional effects that

further remove the mobility of protons in a PEM from the

classical picture. One of these relates to the connectivity and

effective mean-free path for protons. This is schematically

illustrated in Fig. 2 in which A is characterized as having a

more tortuous conduction pathway, with a series of dead ends,

compared to the conduction pathway in B which is more

linear. The supposition, therefore, is that proton mobility will

be effectively greater in B relative to A. In fact, Kreuer has

previously invoked these concepts of smaller conduction

channels and dead ends in order to explain the lower proton

mobility in SPEEK compared to Nafion1.5

The distance between acid groups may also play a role in the

mobility of protonspores having different distances between

acidic groups are shown schematically in Fig. 3. As the proton-

bearing, positively charged species (e.g., H3O+, H2O5

+ and/or

H4O9+ ions)34 are transported between the negatively charged,

tethered SO32 groups, it may be expected that it will be more

difficult for a proton to be transported over the larger

distances between SO32 in A in comparison to the shorter

distances between SO32 groups in B. Therefore, it might be

expected that this would lead to a lower proton mobility in A

in comparison to B.5,49,50

The effective proton mobility, m9H+, as derived from the

proton conductivity data using eqn (6), therefore, incorporates

terms that relate to acid dissociation (eqn (5)), tortuosity (Fig. 2)

and spatial proximity of neighbouring acid groups (Fig. 3).

sH+ = F[SO3H]m9H+ (6)

Calculations based on perfluorinated triflic acid (as a small

molecule analogue for 5) and the hydrocarbon-based p-tolue-

nesulfonic acid (as a small molecule analogue of 1) with pKavalues of26 and 22 respectively51 suggest that dissociation of

the proton occurs when l = 3, forming a hydronium ion.52

However, it has also been calculated that complete separation

of the proton-bearing species from the tethered SO32 anion

does not occur forl , 6.53 In the case of the PEMs examined

in this study, the samples were allowed to equilibrate in water.

Thus, all possessed a l value 10 and relatively completedissociation may be assumed for all the membranes. However,

calculations comparing triflic acid and p-toluenesulfonic

acid suggest that a greater separation distance between the

hydrated proton and the sulfonate group exists in the triflic

acid case due to its greater acidity.52 At the theoretical infinite

dilution limit (i.e., Xv = 1.0), it is reasonable to assume that

differences in acid strengths might have a minimal effect on

m9H+at Xv= 1.0. If the only significant contributing factor for

a series of given PEMs is the acid strength, this effect should be

removed at infinite dilution. All things being equal, the effec-

tive proton mobility of PEMs at Xv= 1.0 should be equivalent

to the theoretical mobility value for a single, free proton at

infinite dilution (3.66 1023 cm2 s21 V21).54 If, however, thereare also other contributing factors such as tortuosity,55

different pore sizes and/or dead end channels, these manifest

themselves as a deviation for proton mobility of the PEM at

Xv = 1.0. If this information could then be attributed to the

chemical structures of the membranes, the resultant structure

property relationships could then be potentially exploited to

design new PEMs with increased values of proton conductivity.

2.1.3 Acid concentration. Acid concentration is determined

as shown in eqn (7):

SO3H ~moles ofSO3H

Vwet membrane(7)

Fig. 2 Connectivity of aqueous domains in PEMs (white = aqueous

domains) where the degree of tortuosity of proton conduction pathway

is greater inA than in B.

Fig. 3 Spatial proximity of neighbouring acid groups within an

aqueous channel where the distance between acid groups is greater in A

than inB.


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where SO3H refers to bound sulfonic acid moieties in the

PEM, moles of SO3H = IEC 6 dry mass of polymer and Vwetis the wet volume of the polymer. Although these two

latter parameters are determined experimentally, the value of

[SO3H] represents the overall concentration of protons in the

membrane without distinguishing between those protons that

are mostly associated with the sulfonic acid groups and those

that are fully dissociated and thus mainly present in the bulkwater. Nevertheless, as acid concentration (see eqn (4) and (6))

has an important influence on proton conductivity, it is of

interest to note how this parameter itself is affected by changes

in acid and water content. Hence, [SO3H] is plotted as a

function of IEC, Xv and l and this will show whether acid

concentration remains constant or whether it varies (e.g., at

high IEC values, water uptake may be very high, leading to

an overall dilution of available acid sites, thus having a

detrimental effect upon proton conductivity).

2.1.4 Water content. Water content was examined both as a

volume percentage (Xv) and as a ratio of moles of water to

moles of sulfonic acid (l). These were determined as per eqn (8)and eqn (9) respectively:

Water content vol% ~Xv~Vwater

Vwet membrane(8)

l~moles H2O

moles SO3H (9)

In the case of eqn (5), the volume of water was calculated by

considering all of the water in the membrane as bulk water

(rather than a combination of bulk and bound or non-

freezable water) and assuming a water density of 1 g mL21.48

As water content tends to vary as a function of acid content,

bothXvand l are plotted as a function of IEC and allow for a

determination of whether water content increases steadily as a

function of acid content or whether there are any sudden,

sharp increases. In the latter case, this is a sign of increased

swelling and is an important point to note due to the strong

effect it will have upon [SO3H] and, hence, upon proton

conductivity.Another important plot is to see how l varies as a function

ofXv. In common with determining how water content varies

as a function of acid content, this plot also will show if swelling

occurs at a consistent rate (lincreases steadily as a function of

Xv) or there are sudden increases (l increases suddenly as a

function ofXv). There is also a third case where swelling is very

limited (i.e. l remains the same over a wide range of Xv).

Finally, a plot ofl as a function of Xv also permits relative

comparisons between different PEMs and will show whether

certain membranes are able to achieve a given l value at lower

Xv values than for other membranes.

2.2 Approach to proton conductivity data analysis: applicationexamples

In order to demonstrate the usefulness of this approach, four

different PEM systems were chosen and compared against the

standard, Nafion1 N117 (IEC = 0.91 mmol g21). They are: i)

sulfonated poly(ether ether ketone), SPEEK (1); ii) poly(ethyl-

enetetrafluoroethylene-graft-styrene sulfonic acid), ETFE-g-

PSSA (2); iii) linear sulfonated polyimide, sPI (3); (iv)

substituted, sulfonated poly(trifluorostyrene), BAM1 mem-

brane (4). The structures for these systems can be seen in Fig. 4.

For each of the four systems (i.e., not including Nafion1),

samples with a minimum of three different IEC values were

Fig. 4 PEM systems used in this study: SPEEK (1), ETFE-g-PSSA (2), sPI (3), BAM1 membrane (4) and Nafion1 membrane (5).


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used. In addition, the sulfonic acid groups were statistically

distributed and attached directly to the main chain of the

polymer (vs. a sulfonic acid-bearing side group). The polymer

systems were synthesized via step-growth polymerization (1

and 3) or chain-growth polymerization (2, 4 and 5). The

analyses of each system (with the analogous results for

Nafion1 N117 (5) shown for comparison) are discussed in

the following sections. As previously mentioned, in order toensure consistency for all the data collected, all samples were

tested under identical conditions in our laboratory.

2.2.1 Proton conductivity as a function of acid and water

content.The plot shown in Fig. 5 (sH+vs. IEC) is the one most

frequently used to present the results of proton conductivity

studies on new membranes. A linear relationship is often

observed forsH+as a function of acid content (i.e., IEC). This

can be seen in the results for our study for both1(conductivity

values consistent with literature results)56 and 2 as well as to

some degree for 3 and at lower IEC values in the case of 4.

Within this range of IEC values, the acid content in these

systems is sufficiently high to have reached the percolationthreshold; i.e., the point at which there is a sufficiently high

enough degree of connectivity between ionic domains for the

transport of protons and water through the membrane.

Comparing 1 with the baseline, 5, this percolation threshold

is reached at a considerably lower IEC value for 5 versus 1 as

evidenced by the high conductivity value of5. As the sulfonic

acid groups in 5 are separated from the polymer backbone via

a flexible spacer unit, microphase separation of the hydrophilic

portion of the polymer from its hydrophobic portion is more

readily achieved than in the case of the main chain sulfonated

1. Therefore, this enables 5 to form broad, continuous

channels for proton transport through the membrane. In the

case of1, the channels are more narrow with a greater numberof discontinuities, thereby leading to less effective proton

transport, as previously reported by Kreuer.5

Beyond the percolation threshold, the trend generally

observed for the majority of PEMs is an increase in sH+ with

increasing IEC. This is normally assumed to be a result of an

increasing concentration of sulfonic acid groups and increased

water content, water being necessary to ensure the protons are

sufficiently dissociated for mobility. By analyzing the proton

conductivity behaviour of 1 as a function of water content,

however, a linear trend is not observed. Instead, sH+appears tobe reaching a maximum with increasing water content. This

can be seen clearly in Fig. 6 (sH+vs.l) and even more clearly in

Fig. 7 (sH+vs. Xv). In addition, it can be seen that 5 exhibits a

similar degree of conductivity to 1 for the same water content

(virtually identical values in Fig. 6 and slightly higher for 5

in Fig. 7). Moreover, it can be seen from Fig. 10 (later) that 5

(Xv = 0.41, l = 19.6) is able to achieve a higher l value as a

function ofXv in comparison to 1 (Xv = 0.40, l = 14.7).

Of all the PEMs examined here, 2 displays the highest

average IEC value (2.65 meq g21) and exhibits the highest

proton conductivity (0.20 S cm21). Although this is signifi-

cantly higher than the value observed for5, an extrapolation of

the data to lower IEC values suggests that a sample of2 withan IEC value equivalent to that of5 would display a similar

conductivity value. In comparison to 1,2 displays significantly

higher conductivity values over the IEC range 2.02.6 meq g21

(e.g., sH+ = 0.17 S cm21 at IEC y 2.5 meq g21 versus sH+ =

0.12 S cm21 for1). Also, in contrast to1, the data for2 do not

appear to be approaching a maximum in the case ofsH+ vs.

IEC,sH+vs. l and sH+vs. Xv(Fig. 57 respectively). However,

Fig. 5 Proton conductivity of15 as a function of IEC.

Fig. 6 Proton conductivity of15 as a function ofl.

Fig. 7 Proton conductivity of15 as a function ofXv.


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given the more limited data set available for 2, it is unclear

whether this is reflective of a definite trend or not.

The higher conductivity values for 2 in comparison to 1 are

achieved for similar l values (Fig. 6) and Xv (Fig. 7). Anexplanation for this observation can be found in section 2.2.2.

The relationship between water content, l and Xv, and IEC

can be more easily seen in Fig. 8 and 9. At IEC , 2.4 meq g21,

2possesses both greater l and Xvvalues for a given IEC than

1. However, this begins to change at IEC y 2.5; the l values

for 1 and 2 at IEC = 2.45 meq g21 are both y24 whereas

the respective Xv values are 0.53 and 0.62.57 Also, whereas at

IEC = 2.56, 1 possess a significantly higher l value in

comparison to 2 (42 and 24, respectively), both 1 and 2 have

almost the same Xv value (0.66 and 0.63, respectively). This

means that the wet volume of2, given the same approximate

volume of water (e.g., at IEC = 2.45 meq g21, both polymers

have l y24 and assuming that water has the same density in

both membranes), is smaller than for the wet volume of1. This

is most likely due to a higher density of2 in comparison to1.58

There also does not appear to be any change in the amount of

water taken up as function of IEC for 2 whereas significantly

higher amounts of water are being absorbed by 1 at IEC .

2.5 meq g21 versus the initial trend over the range of IEC =

2.02.5; i.e., the amount of swelling exhibited by 2 appears to

be considerably smaller than observed for 1. This difference in

swelling behaviour can be seen in the plot ofl vs.Xv(Fig. 10):

whereas a linear extrapolation of the data for2suggests similarl values would be found over the Xv range of 0.30.5, the l

values for 1 are much higher than those for 2 when Xv . 0.5.

Given the differences in the chemical structures of 1 and 2,

the presence of a preformed matrix in 2 (wherein there are

crystalline regions that do not swell, thereby acting as physical

cross-links) and the chemical cross-linking that may occur

during the irradiation grafting process used to obtain 2, it is

perhaps not surprising that 2 is unable to swell as easily as 1.

PEMs designated as 3 are prepared from sulfonated

polyimides in which the polymer assumes a linear backbone.

Derivatives of3with an angled backbone have been previously

reported by our group59 and a more detailed analysis of the

proton conductivity results for this system will be reported at alater date. Structurally, 3 is more similar to 1 than to 2 or 4.

Thus, as might be expected on this basis, the conductivity

data for 3 exhibits similar behaviour to that of 1; i.e., at

IEC , 2.5 meq g21, lower conductivity values are generally

seem in comparison to 2 or 4. At IEC . 2.5 meq g21, 3

continues to exhibit lower conductivity values than the other

PEMs with the exception of4.

More information about the conductivity behaviour of 3

can be gained by examining its relation to water content. As a

function of water content (Fig. 6 and 7), the proton conduc-

tivity of3 does not exhibit any apparent sign of approaching a

maximum as in the case of1. Examining the water content as a

function of IEC (Fig. 8 and 9), it can be seen that 1 and 3have similarXvandl values until IEC y 2.3 meq g

21 at which

point the value for 1 increases to a much higher value than

seen for 3. The latter system does exhibit a similar water

content at IEC = 2.7 meq g21 (Xv = 0.62) that 1 exhibits at

IEC = 2.6 meq g21 (Xv = 0.62). However, given that 3 does

not appear to show signs of a significant increase in Xv as a

function of IEC (Fig. 9) as does 1, it is likely that at the same

IEC (i.e. 2.7 meq g21),1 would actually exhibit a significantly

higherXvvalue in comparison to3. It thus appears that, like 2,

3experiences less swelling in water than does 1 even at higher

IEC values. This can be clearly seen in Fig. 8 and 10 where

it can be seen that the value of l in the case of 3 remains

Fig. 10 l of15 as a function ofXv.Fig. 8 l of15 as a function of IEC.

Fig. 9 Xv of15 as a function of IEC.


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relatively consistent across a wide range of IEC and Xv. Such

behaviour is in sharp contrast to 1, 2 and 4 for which l is

continually increasing as a function of IEC and Xv.

BAM1 membrane (4) is an experimental, a,b,b-trifluoro-

styrene-based copolymer developed by Ballard Advanced

Materials, consisting of a perfluorinated polymer backbone

with the sulfonic acid groups bound to the benzene ring.60

Structurally, it is more similar to2than any of the other PEMsexamined in this study although it does not possess either the

macrophase separation or the potential cross-linking of 2.

Therefore, in some respects, 4 might be anticipated to display

some similarities in its conductivity behaviour to that of 2.

However, in contrast to both 1 and 2 where conductivity

was always seen to be increasing as a function of IEC, Fig. 5

clearly shows that conductivity of 4 reaches a maximum

around IEC = 2.0 meq g21 and then decreases rapidly

such that at IEC = 2.2 meq g21, the observed value is 30%

lower than seen at IEC = 2.0 meq g21. This significant

decrease in sH+ as a function of increasing Xv and l is also

clearly visible in Fig. 6 and 7, respectively. PEM 4 can also be

seen to exhibit similar conductivity values to 1 at Xvy

0.6and over the range ofl y 1030 but significantly lower than

observed for 2.

In sharp contrast to any of the other PEMs, however, 4

exhibits much higher water contents as observed in Fig. 8 and

9. Even at IEC = 2.2 meq g21,4has already achievedXv= 0.82

andl = 76 whereas1 only achievesXv= 0.66 and l = 42 even

at IEC = 2.6 meq g21

and2reachesXv= 0.73 andl= 29 at the

considerably higher IEC value of 3.3 meq g21. It appears clear

that4absorbs significantly larger amounts of water than either

1or2at high IEC values. Relating these data to the discussion

on the water contents of 1 vs. 2, 4 appears to be moving

towards the opposite extreme in comparison to 2; i.e., 4

appears to be able to swell more easily than 1. This higherdegree of swelling is probably related to a more flexible

backbone for 4 in comparison to 1 as well as the absence of a

matrix polymer and/or cross-linking that are present in 2.

Furthermore, 4 is able to hold a high water content (e.g.,

Xv= 0.85 at IEC = 2.5 meq g21) without completely losing its

mechanical integrity (i.e., the sample will return to its original

dimensions upon drying to ambient conditions) or dissolving.

Nevertheless, it can be seen that higher water content does not

necessarily lead to higher conductivity values, the reasons for

which will be discussed in the following section.

2.2.2 Proton mobility and acid concentration as a function of

acid and water content. Additional information can be gleanedfrom examining the conductivity results in greater detail

for the studied polymer systems. The effective proton mobility

for 1 is seen to increase steadily over the IEC range until

IEC . 2.5 meq g21 at which point m9H+ exhibits an even

greater increase. The increase inm9H+ could be due to at least

two factors: a) increasing water content leading to increased

dissociation of the protons from the SO32 groups; b)

increasing water content changes the size and shape of the

hydrophilic channels through which proton transport occurs,

thereby leading to higher m9H+ values. As water content

generally increases with increasing IEC, the observed trend in

m9H+ would thus generally be expected.

At a first approximation, [SO3H] might similarly be

expected to increase with increasing IEC since this also means

that there are a greater number of sulfonic acid groups

available. However, as can be seen in Fig. 14 (later), [SO3H]

of 1 actually decreases with increasing IEC (for IEC .

2 meq g21). When the water content of1 as a function of IEC

is taken into account (Fig. 8 and 9), the explanation for this

observation becomes apparent. Water content increases as afunction of IEC with an even larger increase seen where IEC .

2.5 meq g21. Although higher water content enables greater

dissociation of protons and hence higher mobility, the effect on

[SO3H] of a significant increase in water content is a dilution

of the available sulfonic acid groups and thus a decrease in the

observed values of [SO3H].

One parameter for PEMs such as1 that is frequently altered

in the hope of achieving greater levels of conductivity is the

IEC. Given the clear effect of water content on proton

mobility and concentration and hence on the observed value of

conductivity, however, it is important to study the effect that

water content has on the available iterations of a PEM and

then attempt to extrapolate this information to determinewhether significantly higher IEC PEMs of that polymer system

would be a worthwhile undertaking. Looking at the available

data for1, it was already previously noted that it appears that

conductivity is approaching a maximum as a function ofl. As

m9H+is increasing while [SO3H] is decreasing as a function ofl

(see Fig. 12 and 15 respectively, later), it would therefore

appear that a balance is achieved for conductivity as a function

of water content. In other words, water content must achieve a

level at which proton dissociation is sufficiently high enough

for good mobility and yet there must be not too much water

because this leads to dilution of those protons. For the series of

1 that were available for this study, conductivity is still

increasing as a function of IEC and though, based on the datain Fig. 6, a maximum conductivity appears to exist, there is no

definite indication that higher water content would actually

lead to lower proton conductivity unlike the situation observed

in the case of4.

Although a higher conductivity is generally a desirable

quantity in a PEM, achieving this via an increase in IEC may

not be necessarily the best method. Higher IEC values are

generally accompanied by increases in water content. Given

that mechanical stability is also a requirement of a good PEM

for FC applications, too much water can lead to large and

undesirable volume changes during humidification/dehumidi-

fication cycles under FC operating conditions. In Fig. 8 and 9,

both Xv and l are seen to increase as a function of IEC, moresharply for IEC . 2.5 meq g21. It should be noted that 1 is

known to exhibit poor chemical stability in water at sulfona-

tion levels greater than 70% and temperatures greater than

50 uC (i.e., within the typical PEMFC operating temperature

range).61,62 Even if the stability of the polymer could be

increased (e.g.,viacross-linking), the data in this study suggest

that1at sulfonation levels in excess of those obtained with our

samples (i.e. .95%) will undergo considerable swelling and

thus, in this respect, would be unsuitable for application in a

PEMFC.

In common with 1,2 also shows a trend towards increasing

mobility with increasing IEC, Xv and l values (Fig. 1113) as


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well as decreasing [SO3H] with increasing IEC, Xv and l

(Fig. 1416 respectively). These observed behaviours are most

likely due to the same reasons discussed for 1; i.e., increasing

water content leads to increasing proton mobility but also to

dilution of available acid sites. In comparison though, 1 has a

considerably higher m9H+ value (1.67 6 1023 cm2 s21 V21) at

IEC = 2.56 meq g21 (Fig. 11) whereas the analogous value

for 2 is only 1.18 6 1023 cm2 s21 V21 even though both

membranes have similar water contents at this IEC (Xv= 0.67

and 0.63 for 1 and 2 respectively). In contrast, however, 1

exhibits a lower value for proton conductivity (0.14 S cm21 vs.

0.17 S cm21 for2 at IEC = 2.56 meq g21). This situation arises

due to dilution of the protons as evidenced by the higher l

value of 1 (42 vs. 24 for 2) and also its considerably lower

[SO3H] (0.88 M for 1 vs. 1.46 M for 2). The higher effective

acid concentration of 2 is likely due to its restricted swelling

which limits the amount of water that the membrane can

uptake and thus helps mitigate against dilution of protons.

On the other hand, 2 also benefits from an uptake of water

that is sufficient to maintain a high enough proton mobility

and, therefore, leads to a higher level of conductivity for 2

relative to 1.

Of the PEMs used in this study, 3exhibits some of the lowest

m9H+ values as a function of IEC. For example, while the

respectivem9H+ values for 2 and 4 at IEC y 2.0 meq g21 are

8.47 6 1024 cm2 s21 V21 and 1.30 6 1023 cm2 s21 V21

respectively, the corresponding value for 3 is 6.01 6

1024 cm2 s21 V21. Only the value for 1 (2.56 6

1024 cm2 s21 V21) is lower. However, at higher IEC

(2.62.7 meq g21), proton mobility for 1 increases to 1.66 6

1023 cm2 s21 V21 whereas little change is observed in the case

Fig. 11 Effective proton mobility of15 as a function of IEC.

Fig. 12 Effective proton mobility of15 as a function ofl.

Fig. 13 Effective proton mobility of15 as a function ofXv.

Fig. 14 Acid content of15 as a function of IEC.

Fig. 15 Acid content of15 as a function ofl.


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of3 (m9H+= 8.336 1024 cm2 s21 V21). As the mobility of the

protons in a PEM is directly related to the degree of

dissociation from the bound SO32 counter-ions and the degree

of dissociation is directly related to water content, this result

can be interpreted as a result of the restricted swelling of these

PEMs. With l values remaining, for the most part, in the

region ofy1520 water molecules per sulfonic acid group in

the case of 3, the mobility of the protons is similarly kept

below y8.36 1024 cm2 s21 V21. The restricted water uptake

of3, however, does have the added benefit that the available

protons are not dilutedhence the conductivity values of3are

more dependent upon [SO3H] than for the other PEMs.

As was shown earlier, 4 at high IEC levels is capable of

absorbing enormous amounts of water without dissolving.

However, this ability to absorb greater amounts of water does

not appear to be an advantage as the conductivity of4actually

starts to decrease beyond IEC = 2.0 meq g21. The effect of

this high water content on the contributing factors to sH+

can be seen in the plots ofm9H+vs. IEC,m9H+vs.l,m9H+vs.Xv,

[SO3H]vs. IEC, [SO3H]vs.l and [SO3H]vs.Xvas shown in

Fig. 1116, respectively. At IEC y 2.5 meq g21, m9H+ values

for 4 (1.75 6 1023 cm2 s21 V21) are higher than for either 1

(1.67 6 1023 cm2 s21 V21) or 2 (1.19 6 1023 cm2 s21 V21).

However, acid concentrations are considerably lower in the

case of4 (0.56 M) versus either 1 (0.88 M) or 2 (1.28 M), as

would be expected based on the very high l value (85) for

4, thereby leading to lower conductivity values at IEC .

2.0 meq g21

than might be anticipated based on the resultsfrom1and2. Thus,4is a good example of how increasing IEC

for a given PEM can actually lead to lower conductivity values

due to the ability of the polymer to absorb excessive volumes

of water, resulting in the dilution of the available protons.

2.2.3 Proton mobility at infinite dilution. In order to remove

the effect of the different acid strengths for 14 fromm9H+, the

effective proton mobility was calculated for 14 at Xv= 1.0 by

performing linear regressions for the data in Fig. 13 (plots of

m9H+vs. Xv). The calculated infinite m9H+values can be seen in

Table 1. In all cases except 3, the data appeared to be relatively

linear (R2 . 0.98). For 3, the correlation of the data to

linearity was somewhat low (R2 = 0.89) and this is reflected in

the high standard deviation (44%) for the calculatedm9H+value

at infinite dilution (cf. standard deviations for 1, 2 and 4

average y12%). Nevertheless, for the sake of comparison and

keeping the large standard deviation in mind, this value for 3

will still be used for comparison with those calculated for the

other membranes.

For 1, the linear regression analysis gives value of 3.2 6

1023 cm2 s21 V21 at 25 uC for m9H+at Xv = 1.0. This mobility

value is similar, within y10%, to the calculated mobility

of a free proton in water at infinite dilution of 3.63 6

1023 cm2 s21 V21 at 25 uC.54 The slightly lower value in the

case of 1 might be due to the immobility of the bound SO 32

counter-ion, thus restricting the mobility of the proton.

However, the standard deviation for this value brings the

calculated value at Xv= 1.0 for1 to the calculated mobility of

a proton at infinite dilution and thus, for 1, there do not

appear to be any significant contributions due to tortuosity or

proximity of acid groups.

A similar approach to determine the mobility of protons at

Xv = 1.0 was carried out by Kreuer for Nafion1 and

sulfonated poly(ether ether ketone ketone) (SPEEKK) mem-

branes.5,30,34 In his study, proton conductivity measurements

were carried out on an SPEEKK sample with a 70% degree of

sulfonation and where varying levels of water content were

achieved by varying relative humidity. This differs from our

study in which the proton conductivity values of our samples

with varying IEC values and hence varying water contents

were measured in the fully wet state (i.e., membrane was

immersed in water prior to measurement). In both studies, the

resultant values for proton mobility at Xv= 1.0 determined for

this type of polymer were within y10% of the calculated

mobility of a free proton at infinite dilution. However, whereas

the value for m9H+at Xvobtained from our study is lower than

3.66 1023 cm2 s21 V21, the value derived by Kreuer is higher

(estimated to be y3.86 1023 cm2 s21 V21 from the literature

extrapolation to Xv = 1.0 plot of proton diffusion rate vs.Xv).

5,63 The different values for m9H+at Xv = 1.0 from the two

studies may be in part due to the different methods employed.

Although we have not to date carried out a similar study ( i.e.,

proton conductivity as a function of relative humidity) for 1,

this study has been done for polymers 2 and 4. These results

will be reported in a subsequent publication, thus enabling a

comparison of the two methods for obtaining a value ofm9H+

at Xv = 1.0.

In contrast to the value for 1, the theoretical maximum

mobility for 2 is 2.9 6 1023 cm2 s21 V21. This is lower than

both estimated values for1as well as the calculated mobility of

a proton in water at infinite dilution. In the case of the

Fig. 16 Acid content of15 as a function ofXv.

Table 1 Calculated proton mobility values at infinite dilution(Xv = 1.0)

Polymer m9H+ at Xv = 1.0/1023 cm2 s21 V21

1 3.2 0.42 2.9 0.43 1.6 0.74 2.1 0.2


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comparison with 1, the standard deviation range suggests that

the differences are not significant but in the case of2versusthe

mobility of a proton in water at infinite dilution, the standard

deviation for2still predicts a lower value. As was theorized for

1, this may be due in part to the bound SO32 groups restricting

the mobility of the protons. This effect could be potentially

further magnified by the potentially cross-linked nature of2,

leading to increased tortuosity and thereby decreasing theoverall mobility of the protons.

For 3, the calculated value for m9H+ value at Xv = 1.0 was

found to be approximately 1.66 1023 cm2 V21 s21. This is the

lowest calculated value for m9H+ at Xv = 1.0 for all of the

studied PEMs, even when taking the large standard deviation

of the value into account. Again, as previously discussed for 1

and 2, this is probably due in part to the bound sulfonate

counter-ions. Also, this observed result potentially arises due

to the restrictions imposed on the protons due to the relative

inflexibility of the polymer backbone in comparison to 1and4.

In the case of 2, cross-linking is potentially present in the

hydrophobic region of the membrane and hence possibly does

not have as much influence on proton mobility, as does arelatively inflexible polymer where the sulfonic acid groups are

present on the polymer backbone.

In the case of4, the estimated value for m9H+at Xv = 1.0 is

2.1 6 1023 cm2 s21 V21. This value is lower than the range

observed for 1 and 2 ((2.93.2) 6 1023 cm2 V21 s21) and

considerably lower than the theoretical value for a free proton

at infinite dilution (3.66 1023 cm2 V21 s21). In common with

the previous examples, this deviation from the theoretical

value at infinite dilution may be partially explained by the

restriction imposed on the protons by the bound anionic SO32

groups. However, the explanation used for the lower m9H+

value atXv= 1.0 of2in comparison to1cannot be applied at4

as it seems very unlikely that there are any potential cross-linkspresent in 4. Furthermore, given that 4 appears to swell in

the presence of water even more readily than does 1, it may

have been anticipated that this PEM would more closely

approach the infinite dilution value than either 1 or 2. At this

point, it is not clear what the nature of the tortuosity and/or

proximity of acid groups might be in the case of4 to cause the

observed low value.

3.0 Conclusion

A more in-depth analysis of the proton conductivity data has

been developed and provided additional information on the

observed proton conductivity behaviour for a series of main-chain, statistically sulfonated PEMs. The analysis has shown

the strong links between conductivity and the combination of

acid and water content. In addition, it has been shown that at

least in the case of one polymer system (4), higher ion content

actually leads to lower values for proton conductivity due to

very high water uptakes and a resultant dilution of available

protons. In order to remove the effect of differing acid

strengths of the PEMs, values for proton mobility at infinite

dilution (Xv= 1.0) have also been estimated for 14. Whereas

the calculated value for 1 and 2 are close or within error

identical to the value for the mobility of a free proton at

infinite dilution, the corresponding values for 3 and 4 were

found to be significantly lower. The differences in mobility at

infinite dilution were considered as being potentially a

consequence of the different chemical structures for these

systems that give rise to different levels of tortuosity and

proximity of acid groups.

In comparing the sulfonated derivatives of an aromatic

polymer (1), a polyaromatic rigid rod polymer (3), a vinylic

polymer (4) and a vinylic polymer polymerized inside apreformed matrix (2), the preformed PEM (2) possesses higher

Xvand, therefore, higher [SO3H] at higher IEC but at the cost

of lower m9H+ values. In contrast, 1 and 4 swell excessively at

higher IEC such that [SO3H] is diluted although m9H+ values

are higher. Overall, m9H+ values loosely vary linearly with Xvover the range 0.3 A 1.0, and linearly with l over the range

10 A 30. Subsequent publications will detail results of this

analysis as applied to other PEM systems (e.g., block

copolymers and side-chain sulfonated polymers) as well as

PEMs in which ion content is fixed and water content is varied

as a function of relative humidity.

4.0 Experimental

4.1 Membranes

As received Nafion1 117 (Du Pont) (5) and BAM1 membrane

(4) (supplied by Ballard Advanced Materials) were used in this

work. Nafion1 membrane was supplied as a single sulfonic

acid content polymer whereas a five membrane series of

BAM1 membrane was supplied with a wide range of sulfonic

acid contents. Dry BAM1 membranes were first hydrated in

Milli-Q (18 MV) water (Millipore Systems) for 24 hours,

protonated by submersing in 0.5 M H2SO4 for 48 hours at

room temperature, and subsequently rinsed and stored in

Milli-Q water for at least 24 hours prior to use. Impurities in

Nafion were cleaned by boiling in a 3 vol% H2O2solution for

2 hours, boiling in Milli-Q H2O for two hours, boiling in 0.5 M

H2SO4 for two hours and finally boiling in Milli-Q H2O for

2 hours. Nafion1 membranes were stored in Milli-Q water

prior to use. The synthesis and preparation of sulfonated linear

polyimide membranes (4) has been described previously.59

Radiation-grafted ETFE-g-PSSA membranes (2) were pro-

vided by K. Lovell and co-workers (Cranfield University,

UK). A detailed description of the synthesis of ETFE-g-PSSA

membranes is described elsewhere.64 SPEEK was obtained

from PEEK (Victrex, Mn y 110000) using a literature

procedure.62

4.2 Water content analysis

Circles (8.48 mm diameter) were cut from fully hydrated sheets

and soaked in Milli-Q water for a minimum of 12 hours prior

to use. Wet weights,Wwet, were obtained after blotting with a

Kimwipe to remove surface water. This was carried out on as

short a time scale as possible (,30 s) to avoid water loss to the

atmosphere. Dry weights, Wdry, were obtained after mem-

branes were vacuum (1 mmHg) dried to constant weight

(0.0005 g) at 80 uC and cooled in a desiccator. For all

samples, constant weight was achieved after drying for 2 hours.

Membrane volumes were obtained for both wet, Vwet, and

dry, Vdry, samples by measuring diameter, d, with a caliper


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(0.1 mm) and thickness, h, with a micrometer (0.001 mm)

and applying the following relationship (eqn (10)):

Volume = 0.25pd2h (10)

Membrane water content was calculated as a weight

percentage (eqn (11)):

Water Content wt% ~Wwet{Wdry

Wdry(11)

4.3 Ion exchange capacity

Ion exchange capacity (milliequivalents per dry gram of

polymer), IEC, is used to describe sulfonic acid content. It

was determined using a direct titration method. Circular

samples were cut and placed in 2 M HCl and stirred for

12 hours. The membrane was then transferred to a new beaker

containing Milli-Q water and stirred for 30 minutes, after

which the water was decanted and replaced with fresh water

and stirred for another 30 minutes. This process was repeated

two more times. The acidified membranes were then immersedin 50 mL of NaCl (2.0 M) solution for 2 hours, with occasional

agitation, and titrated with standardized NaOH (0.025 M) to

the phenolphthalein endpoint. After titration the membranes

were placed for 1 hour in 0.1 M HCl, rinsed with distilled

water and dried under vacuum (1 mmHg) at 80 uC t o a

constant weight. The ion exchange capacity was calculated as

follows (eqn (12)):

IEC mmol SO3H g{1

~

vol:NaOH, mL | conc:NaOH, M

dry wt:of membrane, g

(12)

4.4 Proton conductivity

Proton conductivity was measured using AC impedance

spectroscopy with a Solartron 1260 frequency response

analyzer (FRA) employing a transverse two-electrode con-

figuration. Rectangular samples (y1 6 2 cm) of hydrated

membranes were cut to the required dimensions (length,L, and

width,W, measured using a calliper, 0.1 mm, and thickness,

h, using a micrometer, 0.001 mm). To ensure complete

protonation samples were soaked in 0.5 M H2SO4for 24 hours

followed by soaking in Milli-Q water for a minimum of

12 hours prior to use.

Samples were removed from water, blotted with a Kimwipe

to remove surface water, and laid across two Pt electrodes(0.56 1 cm) 1 cm apart fixed in place by attaching to an inert

Teflon block (26 2 cm). Another Teflon block was placed on

top and four nylon screws were used to hold the probe together

during measurement. Both blocks have identical 1 6 1 cm

holes cut out of the centre to allow for membrane equilibration

with the atmosphere where necessary (see Fig. 17).

Two wires fitted with alligator clips connected the probe to

the FRA and ionic resistance was measured by applying a

100 mV sinusoidal AC voltage between the two platinum

electrodes over a 10 MHz100 Hz frequency range and

measuring the AC resistance (i.e., impedance). Probe assembly

was carried out on as short a time scale as possible (,1 min) to

keep the samples from losing water to the atmosphere before

completion of the measurement.

Data were analyzed using Zplot software (Scribner) and a

detailed explanation of the analysis (using BAM1 membranes

as examples) is included in the next section.

Fig. 18 shows typical complex-plane plots of the imaginary

impedance (Z0) versus real impedance (Z9) for 5 BAM1

membranes of various sulfonic acid contents (IEC 1.36, 1.86,1.96, 2.20, 2.46 mmol g21). Nafion1 is included for com-

parison. A series of semi-circles is the result where the size of

the semi-circle varies with IEC and membrane dimensions.

The complex-plane plot for BAM1 membrane (IEC = 2.46)

(Fig. 19) is highlighted as an example of how ionic resistance

was abstracted from the impedance data. Fitting was per-

formed by non-linear least squares regression to a Randles

equivalent circuit model. It consists of the membrane

capacitance, Cm, acting in parallel with the membrane ionic

resistance, Rm. A contact resistance, Rc, arising from the

membrane/electrode interface acts in series with the above. In

essence, the data can be approximated by taking the difference

between the high frequency and low frequency x-intercepts,i.e., semi-circle diameter.

All BAM1 membrane complex-plane plots fit near perfect

semi-circles indicating that the Randles equivalent circuit

model was a reasonable choice for this system. The low values

of contact resistance measured, Rc, compared to that of

Fig. 17 Pt/Teflon1 conductivity probe.

Fig. 18 Complex-plane plots obtained by AC impedance spectro-

scopy for BAM1 membranes with various IEC values.


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membrane resistance (,1%) indicate that there is sufficient

contact between the Pt electrodes and membrane surface.

The ionic resistance was used to calculate proton conduc-tivity,sH+, according to the following relationship (eqn (13)):

sHz~L

RmA (13)

whereL is the spacing between the Pt electrodes (1.0 cm),A is

the cross-sectional area of the membrane (W6 h), and Rm is

the ionic resistance of the membrane.

4.5 Linear regression analysis

Linear regression analyses for m9H+ as a function of Xvwere performed using Microsoft1 Excel1 2004 for Mac

Version 11.3 to fit the data to eqn (14):

y = mx + b (14)

wherey = m9H+,x = Xv,m = slope of line and b = y-intercept.

Standard deviations for the residuals (sy), m (sm) and b (sb)

were determined using eqn (15), (16) and (17) respectively:

sy~

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiSyy{m2Sxx

N{2

r (15)

sb~sy

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

N{P xi 2

Px2i

vuuut

(16)

sm~sy

. ffiffiffiffiffiffiffiSxx

p (17)

where N= number of data points and where Sxx and Syy aredefined as follows by eqn (18) and (19) respectively:

Sxx= S(xi2 x)2

(18)

Syy = S(yi2 y)2

(19)

The results of the regression analysis can be found in Table 2.

A summary of all the data used in Fig. 516 can be found in

Table 3.

Acknowledgements

We would like to thank Mr Keith Lovell and Dr JackieHorsfall of Cranfield University for providing the samples of

ETFE-g-PSSA (2) and Dr Ana Siu for determining its

conductivity data. We are also grateful to Ballard Advanced

Materials for providing the samples of BAM1 membrane (4)

used for our conductivity studies. Finally, we would like to

thank the Natural Sciences and Engineering Research Council

of Canada for providing the funding for this project.

References

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Fig. 19 Complex-plane plot for BAM1 membrane (IEC = 2.46).

Table 2 Results of linear regression analysis (m9H+ as a function ofXv) for 14

Polymerm/cm2 s21

V21s.d./cm2 s21

V21b/cm2 s21

V21s.d./cm2 s21

V21 R2

1 4.6 6 1023 3 6 1024 21.4 6 1023 2 6 1024 0.9842 4.8 6 1023 4 6 1024 21.9 6 1023 3 6 1024 0.9913 2.0 6 1023 7 6 1024 24 6 1024 3 6 1024 0.8904 2.3 6 1023 2 6 1024 22 6 1024 1 6 1024 0.985

Table 3 Summary of data for Fig. 516

Polymer IECa lb Xv sH+c m9H+

d [SO3H]e

1 1.99 13 0.35 0.038 0.26 1.522.14 15 0.40 0.066 0.45 1.522.30 19 0.49 0.098 0.73 1.402.45 24 0.53 0.12 1.02 1.222.56 42 0.66 0.14 1.67 0.88

2 2.13 22 0.58 0.15 0.85 1.782.56 24 0.63 0.17 1.19 1.463.27 29 0.73 0.20 1.59 1.28

3 1.36 14 0.29 0.057 0.50 1.191.85 24 0.55 0.12 0.97 1.271.96 31 0.62 0.14 1.30 1.122.20 76 0.82 0.10 1.74 0.602.46 84 0.85 0.095 1.74 0.56

4 1.77 15 0.29 0.014 0.14 1.121.95 24 0.42 0.059 0.61 0.942.70 26 0.62 0.11 0.83 1.41

5 0.91 20 0.41 0.093 0.87 1.11a mmol g21. b mol H2O mol

21 SO3H.c S cm21. d 1023 cm2 s21 V21.

e mol L21.


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63 The extrapolation of the proton diffustion rate of SPEEKKto infinite dilution given by Kreuer5 is approximately 1 61024 cm2 s21. However, with the available data points, itappears to us a more accurate extrapolation is approximately 8 61025 cm2 s21 which is more in agreement with our results.

64 C. Chuy, V. I. Basura, E. Simon, S. Holdcroft, J. Horsfall andK. V. Lovell, J. Electrochem. Soc., 2000, 147, 4453.

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2007-JMaterials Chem 37_3255-3268_Main-Chain, Statistically Sulfonated PEM Proton Mobility to Water