Influence of polyaniline intercalations on the conductivity and permselectivity of perfluorinated cation-exchange membranes

Journal of Membrane Science 318 (2008) 255–263

Contents lists available at ScienceDirect

Journal of Membrane Science journal homepage: www.elsevier.com/locate/memsci

Influence of polyaniline intercalations on the conductivity and permselectivity of perfluorinated cation-exchange membranes ˜ a,∗ , E. Riande b , F.J. Fernandez-Carretero a , N.P. Berezina c , A.A.-R. Sytcheva c V. Compan a

Departamento de Termodin´ amica Aplicada, ETSII, Universidad Polit´ecnica de Valencia, 46022 Valencia, Spain Instituto de Ciencia y Tecnolog´ıa de Pol´ımeros (CSIC), 28006 Madrid, Spain c Department of Physical Chemistry, Kuban State University, 149 Stavropolskaya Street, Krasnodar 350040, Russia b

a r t i c l e

i n f o

Article history: Received 16 November 2007 Received in revised form 11 February 2008 Accepted 22 February 2008 Available online 29 February 2008 Keywords: Perfluorinated sulfocationic membrane Polyaniline Conductivity Transport numbers

a b s t r a c t This work describes the effect of polyaniline intercalations, produced by polymerization in situ of aniline in perfluorinated sulfocationic polymer templates, on the electrochemical properties of the resulting composite membrane. During the polymerization in situ process, the color of the template evolves rapidly from white to blue and then to emerald green. After 5 h of aniline polymerization, both pristine and composite membranes exhibit higher protonic conductivity than aqueous sulfuric acid solutions with concentrations lower than 0.1 M. After a polymerization time of 30 days, intercalations made up of a mixture of emeraldine and pernigraniline are formed that reduce the conductivity to one-third of that corresponding to the pristine acid membranes. The electroosmotic water transport number across both the pristine and composite acid membranes is about 3 mol/Faraday, a rather low value explained by the high protonic conductivity of the membranes. Apparent cation transport numbers determined from electromotive forces of concentration cells are little affected by the polyaniline intercalations and their values are rather close to those calculated taking the membranes as reference frame. © 2008 Elsevier B.V. All rights reserved.

1. Introduction In the last decades, the development of ion-exchange membranes to be used as polyelectrolytes for fuel cells, batteries, electrodialyzers, sensors, etc., has become a flourishing field of research. From a practical point of view, good performance ion-exchange membranes for a variety of applications should exhibit high ionic conductivity and high permselectivity, low permeability to free diffusion of electrolytes, low water transport through osmosis and electroosmosis, chemical stability, high mechanical resistance, high flexibility and good dimensional stability at working conditions [1,2]. Moreover, membranes to be used as electrolytes in fuel cells should exhibit low permeability to fuel and oxidant [3]. Perfluorinated polyelectrolytes, such as Nafion® , are up to date the best proton carriers for low temperature fuel cells because of their relatively high conductivity combined with good chemical and mechanical stability [4,5]. However, the rather poor thermal properties of the membranes at temperatures above 80 ◦ C, and the need for operating at temperatures above 120 ◦ C to minimize platinum catalyst poisoning by carbon monoxide, has led to the search for new ways to improve the thermal stability of ion-exchange

∗ Corresponding author. Tel.: +34 96 3879328; fax: +34 96 3877329. ˜ E-mail address: [email protected] (V. Compan). 0376-7388/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.memsci.2008.02.048

membranes used as electrolytes for fuel cells [3]. On the other hand, diminution of the hydration of the membranes by both electroosmotic and evaporation processes, that increases their protonic resistance, renders necessary the search for polyelectrolytes that exhibit an acceptable protonic conductivity under low humidity conditions. To meet some of these requirements, a variety of perfluorinated polyelectrolytes have been synthesized [6,7]. Other route has been the modification of Nafion® using inorganic fillers [8,9], inorganic acids [10,11], a polymer coating and/or filler such as polyvinylidene fluoride [12], protonated poly(vinylimidazole) [13], etc. Polyaniline exhibits unique electrical, electrochemical and optical properties, which enable this polymer to be used in storage systems [14], electronics [15], electrochromic devices [16], sensors [17], separation science ranging from gas separation and pervaporation to electrodialysis [18]. A variety of studies have been made concerning the use of polyaniline as support for catalyst platinum particles in direct methanol fuel cells (DMFC) [19,20] and as co-catalyst of platinum plates for methanol electro-oxidation [20,21]. Recently, extensive work has been focused on Nafion® membranes modified with conducting polymers, such as polyaniline [22], polyaniline/silica [23] paying special attention to the methanol crossover in the composite membranes. It is worth noting that the mix of electronic conductivity of polyaniline with the ionic conductivity of cation-exchange membranes has also pro-

256

V. Compa˜ n et al. / Journal of Membrane Science 318 (2008) 255–263

moted the study of these composites for electrode modifications [24–28]. This work studies the effect of intercalations of the emeraldine form of polyaniline on the permselectivity of perfluorinated sulfocationic membranes. Earlier studies have shown that the deposit of a polyaniline layer on the surface of commercial cation-exchange membranes may improve their selectivity for specific ion transport [28,29]. Moreover, the permselectivity of the membranes seems to depend on the location of the polyaniline layer on the membrane matrix [30]. In any case, one would expect that the presence of protonated polyaniline in cation-exchange membranes would decrease cations transport thus reducing the permselectivity of the membranes. Therefore, this work is mainly focused on the study of the electrochemical performance of perfluorinated sulfocationic membranes modified by chemical polymerization in situ of aniline. The electromotive force of concentration cells is measured, and special attention is paid to the effect of aniline polymerization time on the conductivity of membranes equilibrated with distilled water and with dilute acid solutions. 2. Experimental 2.1. Materials A Nafion-type perfluorinated sulfocationic membrane (MF4SC) produced by “Plastpolymer” (St.-Petersburg, Russia) was used as a template matrix for composites preparation. The thermalconditioning technique of the membrane includes sequential boiling of films in 5% HNO3 , 10% H2 O2 and distilled water for 3 h in each solution. 2.2. Template synthesis of polyaniline A template synthesis of polyaniline in the MF-4SC matrix is described in detail elsewhere [27,31,32]. Briefly, a vertically fixed MF-4SC membrane was placed between solutions of 0.01 M FeCl3 in 0.5 M H2 SO4 (oxidant), and 0.01 M aniline in 0.5 M H2 SO4 . The polymerization of aniline was carried out in the membrane by a counter diffusion method. After a certain polymerization time, the membrane turns blue and then, rapidly evolves to emerald-green. As a result, membranes with different color intensity can be prepared by simply varying the oxidation time of aniline. The polymerization time of the membranes used in this study was 5 h and 30 days. The mass fraction of polyaniline was 12% and 17%, for polymerization times of 5 h and 30 days, respectively. The acronyms used for these composite membranes will be PAni-5H/MF-4SC and PAni-30D/MF4SC, respectively. It is worth noting that polyaniline intercalations in the PAni-5H/MF-4SC membranes are in the emeraldine form.

Scheme 1. Redox reactions of aniline polymerization.

ion-exchange processes are a limiting stage of the aniline polymerization in the membrane’s template matrix [34], as established by electrochemical methods. Usually, the sorption and exchange of Fe3+ ions from a 0.01 M FeCl3 + 0.5 M H2 SO4 solution occurs via the equation: 3RSO3 − H+ + Fe3+ → (RSO3 − )3 Fe3+ + 3H+

(3)

Fe3+

ions act as a redox-catalyst oxidizing aniline, and the polymerization process proceeds as indicated in Scheme 1. The color intensity depends on the balance between oxidized (doped) and reduced (undoped) forms of polyaniline and the exposure duration in working solutions [35]. Anions A− in the scheme are –SO3 − groups of the MF-4SC template matrix. Chemical forms of polyaniline are described in detail elsewhere [36,37]. The thickness of the membranes used, equilibrated with distilled water, was 0.22, 0.29, and 0.31 mm for MF-4SC, PAni-5H/MF-4SC and PAni-30D/MF-4SC, respectively. 2.4. Water uptake Weighed pieces of acidic dry membranes were submerged in distilled water. The kinetics of water sorption was obtained by removing the pieces from water at different time ranges, superficially dried by gently blotting with filter paper and weighed. From the weights of the dry and wet pieces, the water content of the membranes as a function of time was obtained. The water sorption increases very rapidly at short times reaching equilibrium in less than 30 min. These experiments were repeated three times and the pertinent results concerning the water uptake are collected in Table 1. 2.5. Ion-exchange capacity The membranes were equilibrated in a 2 M HCl solution overnight. The acidic membranes were further washed several times with distilled water and then equilibrated with a 2 M sodium chloride solution. The protons delivered after the exchange reaction R–SO3 H + Na+ → R–SO3 Na + H+ were titrated with a 0.01 M sodium hydroxide solution. The values of the ion-exchange capacities of the membranes are given in Table 1.

2.3. Aniline polymerization mechanism in the MF-4SC matrix

2.6. Experimental measure of electromotive forces

A template synthesis involves several stages [33]. In an acid medium, aniline exists as phenylammonium cations acting as counterions for the –SO3 − fixed groups of the MF-4SC membrane:

Experimental electrochemical potential measurements were performed in an experimental device made up of two compartments separated by the membrane. Each compartment was provided with a reversible Ag/AgCl electrode. The configura-

(1) In the course of the cation-exchange process, protons are exchanged in the membrane with An+ cations −

+

+

−

+

+

RSO3 H + An → RSO3 An + H

Table 1 Water uptake and ion-exchange capacity (IEC) of perfluorinated sulfocationic MF4SC, PAni-5H/MF-4SC and PAni-30D/MF-4SC membranes Membrane

Water uptake (kg water/kg wet membrane)

IEC (equiv. H+ /kg wet membrane)

Moles H2 O/equiv. fixed ionic groups

MF-4SC PAni-5H/MF-4SC PAni-30D/MF-4SC

0.22 0.22 0.20

0.86 0.93 1.11

14.2 13.1 10.0

(2)

Non-exchange sorption of phenylammonium ions in the membrane may simultaneously take place. The diffusion and accumulation of An+ in the membrane matrix at the expense of sorption and

V. Compa˜ n et al. / Journal of Membrane Science 318 (2008) 255–263

257

high frequencies [38]. An alternative method to obtain R0 is the Bode diagram [39] where the modulus of the complex impedance |Z*| is plotted vs. ω. As frequency increases the modulus increases reaching a plateau, whereas the out of phase angle  = tan−1 (Z /Z ) reaches a maximum. Since lim|Z*| → R0 and  = 0 at ω → ∞, the proton resistance is R0 = |Z*| at tan−1 (Z /Z ) = 0. 3. Basic aspects of ion transport and selectivity

Fig. 1. Equivalent electric circuit of the acidic membranes in the impedance measurements.

tion of the cell was: Ag/AgCl|solution (cL )|membrane|solution (cR )|AgCl/Ag. The potential generated in the configuration indicated was measured with a high-impedance pH meter (Z > 1014 ), model Crison 2002, at 25 ◦ C. Electromotive forces (emf) of the concentration cells were recorded via a PC every 10 s. The measurements were performed under strong stirring to minimize concentration polarization effects. All measurements were performed by keeping one of the compartments of the cell, for example the left one, filled with a 0.01 M XCl (X = H, Na and K) solution whilst the concentration of the solution in the right compartment was allowed to vary from 0.001 M to 1 M. Prior to a new experiment, the membrane was equilibrated with a 0.01 M XCl solution for at least 24 h. Before starting and after finishing each experiment, the asymmetry potential of the electrodes was checked in a 10−3 mol/L solution of XCL, and the mean value of these measurements was subtracted from the emf of the cell. When the asymmetry potential of the electrodes exceeded 2 mV, the AgCl layer of the electrodes was refreshed by electrolysis. If this procedure did not work, new electrodes were used. 2.7. Impedance spectroscopy measurements The resistance R0 of the membranes in the acidic form was measured at 25 ◦ C by complex impedance spectroscopy. The membranes previously equilibrated with water or dilute acid solutions were placed between two gold electrodes coupled to a Novocontrol broadband dielectric spectrometer. The results were interpreted in terms of the equivalent circuit of Fig. 1 that comprises a protonic resistance R0 in series with a circuit made up of an element Rp representing the charge transfer resistance at the membrane/electrode interface in parallel with a constant phase element representing the membrane/electrode double layers connected in series. By assuming that the phase element admittance is Y* = Y0 (jω)n , 0 < n ≤ 1, the complex impedance of the circuit is given by Z ∗ (ω) = R0 +

Rp 1 + Y0 (ω0 )n jn

(4)

where j = (−1)1/2 . Hence the real and imaginary components of the complex impedance of the equivalent circuit are 

Z = R0 +

Rp [1 + Rp Y0 (ω0 )n cos(n/2)] 1 + Rp2 Y02 (ω0 )2n + 2Rp Y0 (ω0 )n cos(n/2)

Z  = −

1 + Rp2 Y02 (ω0 )2n + 2Rp Y0 (ω0 )n cos(n/2)

0 0 0 −T s˙ = jw ∇w + j+ ∇ ˜ + + j− ∇ ˜−

(7)

where,  ˜ k and w (k = +, −) are, respectively, the electrochemical and chemical potentials of ions and water, respectively, and jk0 (k = +, −, w) the flux of cations, anions and water. The superscript zero means that the membrane is taken as reference frame for the fluxes. If reversible electrodes to one of the ions are used, i.e. to the anion, the gradient of the electric potential at equilibrium is related to the chemical gradient of the anions at the electrodes/solution interfaces by ∇

=

1 ∇ ˜− z− F

(8)

where F (=96,480 C/equiv.) denotes the Faraday constant. If the driving forces acting on the transport are unidirectional, for example in the x-direction perpendicular to the surface of the membrane, Eqs. (7) and (8) lead to 0 −T s˙ = jw ∇w +

0 j+ ∇ + i∇ +

(9)

0 + z j0 ) and  =   where i = F(z+ j+ ˜ − are, respectively, − − + ˜ + + −  the electric current density and chemical potential of the electrolyte. Notice that in the deduction of Eq. (9) the electroneutrality principle + z+ + − z− = 0 was used. By combining Eq. (9) with the Gibbs-Duhem’s equation, cw dw + cd = 0 where cw and c are, respectively, the concentration of solvent and electrolyte, the following expression for the dissipation function rate is obtained [41–43]:

−T s˙ =

1 d d j+ +i + dx dx

(10)

where (5)

and Rp2 Y0 (ω0 )n sin(n/2)

Flows of solvent and electrolyte across ion-exchange membranes separating two electrolytic solutions may arise from gradients of the so-called forces: concentration, temperature, electrical potential and pressure. Let us consider a concentration cell with the following configuration: Ag|AgCl aqueous electrolyte solution (cL )|membrane|aqueous electrolyte solution (cR ) AgCl|Ag. Let us assume that the electrolyte dissociates as C+ A− = + C z+ + − Az− . It is assumed that the two adjacent boundary layers flanking the membrane are included in the system. The local dissipation function rate at every point of the membrane system is given by [40]:

(6)

where ω is the angular frequency of the electric field and  0 is a characteristic relaxation time. Notice that at the limits ω → ∞ and ω → 0, Z → R0 and Z → R0 + R1 , respectively. Moreover, Z → 0, at the limits ω → 0 and ω → ∞. The Z vs. Z plot, called Nyquist diagram, gives a curve that intersects the abscissa axis at Z = R0 , at

0 − j+ = j+

v+ c 0 j cw w

(11)

In this expression, j+ is the flux of cations taking the center of mass of the moving liquid as reference frame. For isobaric and isothermal conditions, the linear relationship between fluxes (j+ , i) and forces (d/dx, d /dx) leads to the general expression: −

d t+ d i = + z+ + F dx dx

(12)

where (=−i/(d /dx)) is the specific conductivity, and t+ is the cation transport number taking the center of mass of the moving

258

V. Compa˜ n et al. / Journal of Membrane Science 318 (2008) 255–263

liquid as reference frame. The pertinent expression for t+ is t+ =

Fz+ j+ i

(13)

In the case of zero current density (i = 0), Eq. (12) leads to the electromotive force of the concentration cell, E, which coincides with the electric potential . The pertinent expression for E is 1 E=− z+ + F



l

t+ (x, c) 0

d dx dx

(14)

where l is the membrane thickness. For homogeneous membranes, the counterion transport number only depends on the solution concentration c in the membrane phase and Eq. (14) becomes 1 E=− z+ + F



l

t+ (x, c) 0

Since  = 0 + RT E=−

1 z+ + F



d dx dx

ln(a+ a− ),

(15) Fig. 2. Nyquist diagram for the MF-4SC (squares) and PAni/MF-4SC (triangles) membranes equilibrated with water. Lines represent the fit of the Z vs. Z impedance obtained from Eqs. (5) and (6).

Eq. (15) yields

l

t+ (c) d ln a±

(16)

0

where 2 = + + − and aL (aR ) denote the electrolyte activity in the left (right) compartments of the concentration cell. 4. Water transport numbers determination The experiments were carried out by using an experimental device, provided with Ag/AgCl electrodes, that allows to measure in horizontal capillaries the water dragged by the transport of a known amount of electricity across the membranes. The interval of concentrations used was 0.05–3 M of HCl. More details on the experimental set up are given elsewhere [44,45]. 5. Results and discussion 5.1. Protonic conductivity The results obtained for the water uptake, given in Table 1, show that this parameter is practically independent on the aniline content of the composite membranes. Similar results have recently been reported for Nafion/polyaniline composites [23], suggesting favorable interactions between polyaniline and water in the membrane composites presumably favored by the polarity of the polyaniline. Preliminary impedance experiments in which the membrane was sandwiched between electrodes gave very low values for the resistance that led to significant errors. To enhance the resistance, impedance experiments were carried out in a 10 mm × 10 mm rectangular membrane strips tightly held between two Teflon® semicylinders of radius 5 mm and length 10 mm. Complex plots of the components of the complex impedance obtained using this

latter configuration for the MF-4SC and PAni-5H/MF-4SC membranes equilibrated with distilled water are shown in Fig. 2. Usually, the equivalent circuit utilized to model the conductivity of cationexchange membranes in the acidic form is made up of a resistance that accounts for the protonic resistance in series with a RC parallel circuit accounting for the relaxation processes taking place in the membrane. The real and imaginary components of the complex impedance for this circuit can be obtained making n = Y0 = 1 in Eqs. (4) and (5), respectively. In this case, the Nyquist diagrams are semicircles intersecting the abscissa axis in the high frequency region at Z = R0 . Departure from semicircles is observed in experimental Nyquist diagrams as a result of polarization processes and other phenomena taking place in the membrane electrode interface. To account for the departure of the experimental results from a semicircle the condenser in the RC circuit is replaced by a constant phase element (see Fig. 1). Fitting Eqs. (4) and (5) to the experimental complex Z vs. Z plots in a relatively wide range of the high frequency region is accomplished using for Y0 and n the values given in Table 2. Using several circuits in series with different phase elements, the experimental Nyquist plot in the whole frequency range could be reproduced. However, the experimental results over a wider frequencies range do not affect the estimation of the protonic resistance and therefore we did not proceed with this analysis further. Alternative Bode diagrams are shown in Figs. 3 and 4, respectively, for MF-4SC and PAni-5H/MF-4SC membranes equilibrated with distilled water, hydrochloric acid 1 M and sulfuric acid 1 M solutions. The plots show a plateau at high frequencies coexisting with the peak of the phase angle, . The modulus of the impedance at the peak maximum was taken as the protonic resistance R0 of the membrane. Values of R0 for the MF-4SC and PAni-5H/MF-4SC membranes equilibrated with water, and with 1 M HCl and 1 M H2 SO4 solutions

Table 2 Values of the protonic resistance and conductivity of the MF-4SC and PAni-5H/MF-4SC membranes equilibrated with HCl and H2 SO4 solutions, 1 M, obtained from Nyquist and Bode diagrams Membrane

Solution

n

Y0 (×105 )

Nyquist plot R0 ()

Bode diagram (S/m)

R0 ()

(S/m)

MF-4SC PAni-5H/MF-4SC

HCl HCl

0.60 0.94

4.15 7.12

7.50 6.31

4.61 5.43

7.32 6.35

4.73 5.40

MF-4SC PAni-5H/MF-4SC

H2 SO4 H2 SO4

0.71 0.45

43.6 8.70

10.8 9.05

3.21 3.79

10.8 9.50

3.21 3.61

MF-4SC PAni-5H/MF-4SC

Water Water

0.47 0.35

8.28 3.88

14.8 54.9

2.34 0.62

15.0 56.6

2.31 0.61

V. Compa˜ n et al. / Journal of Membrane Science 318 (2008) 255–263

Fig. 3. Bode diagrams for the MF-4SC membrane equilibrated with distilled water (squares), 1 M hydrochloric acid (circles) and 1 M sulfuric acid (triangles). Filled and open symbols represent, respectively, the impedance modulus and the out of phase angle.

are shown in Table 2. The proton conductivity of the membranes was obtained from the proton resistance by means of the following expression: =

l R0 S

(17)

where S and l are, respectively, the area and thickness of membrane in contact with the electrodes. The results obtained for the proton conductivity of the membranes are also collected in Table 2. In general the values of the conductivities obtained from the Nyquist and Bode diagrams are in rather good agreement. Had polyaniline intercalations formed an electronic percolation path the electric circuit of measurement would be shortcircuited. This was not detected during the measurements, and the conductivity of the composite membranes measured is exclusively of ionic character. The PAni-5H/MF-4SC membrane equilibrated with water exhibits protonic conductivity nearly 4-fold below that corresponding to the pristine membrane. Similar results have been reported by Chen et al. [23] who found conductivities nearly 3–5-fold below that of Nafion. The strong interaction with the ionomers via the positively charged polyaniline in the emeraldine form and the negatively charged sulfonic groups presumably hinder the pro-

Fig. 4. Bode diagrams for the PAni/MF-4SC membrane equilibrated with distilled water (squares), 1 M HCl (circles) and 1 M H2 SO4 (triangles). Filled and open symbols represent, respectively, the impedance modulus and the out of phase angle.

259

Fig. 5. Dependence of the conductivity, in S/m, for the original membrane (MF4SC) and for the composite membranes equilibrated with different concentrations of aqueous solutions of H2 SO4 . Curves 1, 2, and 3 represent, respectively, the conductivity of MF-4SC, PAni/MF-4SC (after 5 h of aniline polymerization), and PAni/MF-4SC (after 30 days of aniline polymerization) membranes. The straight line 4 represents the evolution of the conductivity of H2 SO4 solutions with concentration. Error bars are included.

ton transport mechanisms [46]. On the other hand, the lower hydrophilic properties of the polyaniline layers also contribute to the reduction of the conductivity. As shown in Table 2, the values of the conductivity of the pristine membranes equilibrated with acid solutions are slightly higher than those obtained equilibrated with water. However, the conductivity of the PAni-5H/MF-4SC equilibrated with a 1 M acid solution undergoes a significant increase attributed to the presence of free electrolyte in the membrane that facilitates current transport. This assumption is supported by the fact that the conductivity of the membranes equilibrated with hydrochloric acid is higher than that of the corresponding membranes equilibrated with sulfuric acid. One should remind in this regard that the mobility of the bulky sulfate anion is more restricted than that of the chloride anion. On the other hand, the fact that as we shall see later the proton transport number for dilute solutions is somewhat lower than the unit suggests that free electrolyte is present in the membranes equilibrated with acid solutions that contribute to transport, thus increasing the conductivity. Increasing the polymerization time up to 30 days, the limiting saturation degree of the membrane by polyaniline is reached. At this stage, the polyaniline is a mixture of emeraldine and pernigraniline (non-protoned form), the membrane becoming black with lower elasticity. Values of the conductivity of the membranes equilibrated with acid are shown as a function of the concentration in Fig. 5. To obtain the curves of this figure, the resistance of the membranes equilibrated with acid was taken as the real component of the impedance for the membrane sandwiched between electrodes, at 105 Hz. An inspection of the variation of the conductivity with concentration of sulfuric acid shows that the conductivity of the PAni-30D/MF-4SC membrane is roughly one-third of that corresponding to the MF-4SC and PAni-30D/MF-4SC membranes. These results may be due to morphological changes in the cluster zones of the composite membranes arising from the transition of nanosize polyaniline clusters in PAni-5H/MF-4SC to microsize polyaniline clusters in PAni-30D/MF-4SC membranes [47]. The nanosize particles of emeraldine dispersed in the membranes does not seem to affect the protonic percolation path of the MF-4SC membranes as the microsize domains formed by the mixture of pernigraniline and emeraldine do.

260

V. Compa˜ n et al. / Journal of Membrane Science 318 (2008) 255–263

Table 3 Variation of the electromotive force of concentration cells with the concentration of hydrochloric acid

Table 5 Variation of the electromotive force of concentration cells with concentration of potassium chloride

cL

cL

0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100

cR

0.0001 0.0005 0.0010 0.0050 0.0500 0.1000 0.5000 1.0000

PAni/MF-4SC

MF-4SC

Emf (mV)

t¯+

Emf (mV)

t¯+

−224.5 −141.6 −105.4 −24.80 90.10 124.8 202.7 231.4

0.973 0.961 0.947 0.931 0.926 0.924 0.920 0.917

−228.2 −145.3 −108.2 −25.70 91.70 126.0 204.1 233.2

0.989 0.986 0.972 0.965 0.942 0.933 0.926 0.923

0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100

cR

0.0001 0.0005 0.0010 0.0050 0.0500 0.1000 0.5000 1.0000

PAni/MF-4SC

MF-4SC

Emf (mV)

t¯+

Emf (mV)

t¯+

−210.5 −130.6 −97.40 −21.90 79.50 108.9 177.3 201.4

0.912 0.886 0.875 0.822 0.817 0.806 0.805 0.798

−212.2 −133.3 −101.2 −21.90 80.70 110.5 180.3 203.9

0.920 0.904 0.909 0.822 0.829 0.818 0.819 0.808

The results of Fig. 5 show that the conductivity of the membranes in presence of electrolyte undergoes a slight increase with concentration in the region of low concentrations, and then remains roughly constant for concentrations higher than 0.1 M. In the same figure, and for comparative purposes, the conductivity of sulfuric acid solutions is plotted as a function of concentration. It can be seen that at low and moderate concentrations the conductivity of H2 SO4 solutions is a linear function of the concentration. Below the concentration at which the membranes and the acid exhibit the same conductivity, the membranes are more conductive than the sulfuric acid solutions. The intersecting concentration for MF-4SC and PAni-5H/MF-4SC membranes is higher than that found for PAni30D/MF-4SC membranes. It is worth noting that the small change in conductivity with the concentration of sulfuric acid exhibited by the membranes suggests that the potential zeta of the double layer of the pores of the membrane excludes the existence of free sulfuric acid in the percolation protonic path of the membranes.

Interchanging the solutions concentration in the compartment cells, the absolute values of the electric concentration potentials remain invariant, a fact that guarantees the homogeneity of the membranes. Values of emf for the MF-4SC and PAni-5H/MF-4SC membranes flanked by HCl solutions are shown in the third and fifth columns of Table 3. The corresponding values for sodium chloride and potassium chloride solutions are presented in Tables 4 and 5, respectively. The results show that for similar concentrations, the emf of the concentration cell containing hydrochloric acid is somewhat larger than that of the cells containing sodium chloride and potassium chloride. Moreover, the emfs of sodium chloride and potassium chloride concentration cells are rather similar. In all cases, straight lines fit fairly well the plots of the electromotive force against the logarithm of the activity of the electrolyte on the right side of the membranes (see Fig. 6). Taking into account that according to Eq. (16) the emf can be expressed by

5.2. Electromotive forces and transport numbers

E=−

A thorough study was carried out on the permselectivity of PAni-5H/MF-4SC membranes which was extended to the pristine MF-4SC membranes. According to Eq. (16), the emf of concentration cells is governed by the counterion transport number that depends on the concentration of free electrolyte inside the membrane. As concentration increases, a concentration profile of free electrolyte develops across the membrane in such a way that co-ions intervene in the transport of current, and the permselectivity of the membrane decreases. The effect of concentration on the permselectivity of PAni5H/MF-4SC and MF-4SC membranes was studied by measuring electromotive forces of concentration cells where a electrolyte concentration cL = 0.01 M was kept on the left compartment side of the cell. The concentration on the right compartment was allowed to vary in a wide range. Values of the different cR /cL ratios used are given in the first column of Tables 3–5. Chloride acid, sodium chloride and potassium chloride solutions were used as electrolytes.

where t¯+ is the average counterion transport number inside the membrane, the rough fit of a straight line to the E vs. ln(aR /aL ) plots covering a wide range of concentrations suggests that counterion transport numbers are nearly independent on electrolyte concentration. The values of t¯+ in the MF-4SC membrane, obtained from Fig. 6 are 0.950, 0.875 and 0.858 for H+ , Na+ and K+ , respectively,

2RT aR t¯+ ln F aL

(18)

Table 4 Variation of the electromotive force of concentration cells with the concentration of sodium chloride cL

0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100

cR

0.0001 0.0005 0.0010 0.0050 0.0500 0.1000 0.5000 1.0000

PAni/MF-4SC

MF-4SC

Emf (mV)

t¯+

Emf (mV)

t¯+

−211.5 −131.6 −98.40 −22.30 80.10 109.8 178.7 203.4

0.917 0.893 0.884 0.837 0.823 0.813 0.811 0.806

−214.2 −135.3 −102.2 −22.50 81.70 112.0 182.0 205.0

0.928 0.918 0.918 0.845 0.840 0.829 0.826 0.812

Fig. 6. Variation of the electromotive force of the concentration cells with the logarithm of the ratio of concentrations of the hydrochloric acid solutions. Open squares and filled circles represent the emfs of the MF-4SC and PAni/MF-4SC membranes, respectively.

V. Compa˜ n et al. / Journal of Membrane Science 318 (2008) 255–263

261

Table 6 Variation of the water transport number with the concentration of HCl for the MF-4SC and PAni/MF-4SC after 5 h HClc (mol/L)

0.05 0.1 0.5 1

MF-4SC

PAni-5H/MF-4SC

t¯+ (equiv. H+ /Faraday)

0 tw

0.942 0.933 0.926 0.923

3.3 3.0 2.9 2.2

(mol H2 O/Faraday)

t¯+0 (equiv. H+ /Faraday)

t¯+ (equiv. H+ /Faraday)

0 tw (mol H2 O/Faraday)

t¯+0 (equiv. H+ /Faraday)

0.945 0.938 0.952 0.959

0.926 0.924 0.920 0.917

3.3 3.2 3.1 2.7

0.929 0.929 0.948 0.971

which amount to 0.940, 0.852 and 0.846, respectively, for the PAni5H/MF-4SC membrane. Values of t¯+ for H+ in the PAni-5H/MF-4SC and the MF-4SC membranes, for different concentration ratios, are shown in the fourth and sixth columns of Table 3. The same results are given in Tables 3 and 5, respectively, for the transport number of Na+ and K+ , respectively. In general, the transport numbers are dependent on the counterion size following the trends t¯+ (H+ ) > t¯+ (Na+ ) ≥ t¯+ (K+ ). The slightly larger values of t¯+ in the MF-4SC samples may depend on the distribution of electrolyte domains in the membranes. For the MF-4SC membrane, ionic clusters formed by fixed ionic groups and the corresponding counterions coexist with hydrophobic domains in which fixed ions are nearly absent. Ionic transport in these membranes mainly occurs across the hydrophilic clusters. Polyaniline intercalations presumably are mainly distributed in the hydrophilic domains in the case of the PAni-5H/MF-4SC membrane. Initially, positively charged emeraldine intercalations should promote co-ions transport across the membrane thus decreasing the counterions permselectivity of the membrane composite. However, the rather low sensitivity of the permselectivity of the membranes to polyaniline intercalations suggests that some sort of special interactions between the positive charges of emeraldine and the associated co-ions take place which restrict transport of these latter ionic species across the membrane composite. It should be stressed in this regard that recent reports [48] show that the transport number of protons across cation-exchange membranes based on polynorbornenes functionalized with imide side groups decreases as the concentration of hydrochloric acid increases. However, a concentration is reached at which the proton transport undergoes a sharp increase attributed to the protonation of the imide groups by the high concentrated hydrochloric acid solution. In principle, the positive imide groups in the polynorborneno/imide membranes should facilitate co-ions transport, thus decreasing the protons transport number. The only way of interpreting these experimental results is to postulate that co-ions presumably form some sort of pair ions with protonated imide groups that restrict their mobility across this kind of membranes [48]. 5.3. Electroosmosis and transport numbers Electroosmosis arises from the motion of charged liquid in the pores of the membranes under the action of an electric force field, d /dx. The electroosmotic permeability, Pe , can be expressed by [3]: Pe =

(dVl /dt)c εu0 = i i

membrane. Then 0 u0 +

XF d =0 ε dx

(20)

where F is Faraday’s constant, 0 in kg/(m3 s) is the specific friction coefficient between the moving liquid and the walls of the pores of the membrane and X is the concentration of fixed ionic groups in the cation-exchange membrane in equiv./m3 of wet membrane. Hence, the electroosmotic permeability can finally be written as Pe =

XF 0

(21)

where is the ionic conductivity. Finally the water transport number is given by 0 = tw

FPe V¯ w

(22)

where V¯ w represents the partial molar volume of water. Accordingly, the electroosmotic permeability is directly proportional to the concentration of ionic fixed groups and to the reciprocal of the product of the conductivity times the specific friction coefficient. 0 at different concentrations for the MF-4SC and PAniValues of tw 5H/MF-4SC membranes are shown in Table 6. It can be seen that 0 is both rather small and little sensitive to the concentration of tw polyelectrolyte. Since the electroosmotic permeability is proportional to the reciprocal of the conductivity (see Eq. (21)), the low osmotic flow is explained by the high conductivity exhibited by the 0 with conmembranes. On the other hand, the low variation of tw centration of the acid electrolyte arises from the small sensitivity of the conductivity to the concentration of sulfuric acid flanking the membranes, made evident in Fig. 6. As indicated above, the reference frame for t¯+ is the center of mass of the moving liquid in the membrane. The relationship between t¯+ and the counterion transport number referred to the 0 , can straightforwardly be obtained from Eq. (11). membrane, t+ Actually, by multiplying the two sides of Eq. (11) by Fz+ /i, the fol0 is obtained: lowing expression relating t¯+ and t+ 0 t+ = t+ −

z+ + c 0 t cw w

(23)

0 = Fz j0 /i and t 0 = Fj0 /i. Values of t¯ 0 and t¯ at differwhere t+ + + + + w w ent concentrations are shown in Table 4. It can be seen that as a consequence of the low values of the water transport numbers, the counterion transport numbers determined from electromotive forces are close to those calculated taking the membranes as reference frame.

6. Conclusions (19)

where Vl is the volume of liquid flowing across the membrane for area unit, ε and u0 are, respectively, the volume fraction and velocity of liquid in the membrane. In steady-state conditions, the acceleration of the charged liquid promoted by the electrical potential driving force, d /dx, is dissipated by the friction between the moving liquid and the walls of the porous of the

The influence of polyaniline intercalations on the permselectivity and conductivity of perfluorinated sulfocationic membranes is studied. The emeraldine form of polyaniline should decrease the counterions transport numbers across the composite membranes. The fact that this does not occur implies that some sort of interaction between the positively charged emeraldine and the negative mobile ions (Cl− ) takes place, which restricts the motion of the

262

V. Compa˜ n et al. / Journal of Membrane Science 318 (2008) 255–263

anions across the membranes, preserving the high permselectivity of the composites. The protonic conductivities of the PAni-5H/MF-4SC membrane are similar to that of the MF-4SC membrane, 4–5 S/m. The critical analysis of these results shows that emeraldine intercalations do not form a percolation path through which electronic conductivity occurs. The higher conductivity of the membranes equilibrated with hydrochloric acid in comparison with that of those equilibrated with sulfuric acid may be a consequence of the bulkiness of the sulfate anion that hinders its motion in the membranes. This fact suggests that free electrolyte in the membrane may take part in ionic transport. The conductivity of the PAni-5H/MF-4SC membrane is roughly three times that of the PAni-30D/MF-4SC membrane. Morphological changes taking place in polyaniline cluster zones may be responsible for this behavior. Acknowledgements This work was supported by the Comunidad de Madrid (CAM) through the Program Interfaces (S-0505/MAT-0227), Fondo Europeo de Desarrollo Regional (F.E.D.E.R.) and Fondo Social ´ General de Investigacion ´ Europeo (F.S.E.). Support by the Direccion ´ Cient´ıfica y Tecnica (DGICYT), Grant MAT-2005-05648-C02-01, and from IMPIVA of Generalitat Valenciana through project IMCITA/2006/030 is gratefully acknowledged. The co-authors from Russia are grateful to the Russian Foundation for Basic Research for the financial support (Grant RFBR 06-08-01424).

Nomenclature List of symbols a activity coefficient c electrolyte concentration (molal) cw water concentration in the electrolyte solution (molal) E electromotive force (V) F Faraday’s constant, 96,480 C/equiv. i current density (A/m2 ) j+ flux density of cations referred to the center of mass of the moving liquid (mol/(m2 s)) ji0 flux density of anions (i = −), cations (i = +) and water (i = w) referred to the membrane (mol/(m2 s)) l thickness of the membrane (m) n exponent/factor lying in the range 0 < n ≤ 1 in Eqs. (4)–(6) Pe electroosmotic permeability (m3 of water/C) R gas constant (8.314 J/(mol K)) R0 protonic resistance () Rp polarization resistance () s energy dissipation (J/mol) S area of the membrane (m2 ) transport number of cations taken the center of t+ mass of the moving liquid as reference frame (equiv./Faraday) 0 t+ transport number of cations referred to the membrane (equiv./Faraday) 0 transport number of water taken the membrane as tw reference frame (mol water/Faraday) 0 t¯+ average transport number of cations referred to the membrane (equiv/Faraday)

t¯+ T u0 Vl V¯ w X Y0 Y* zi Z* Z Z

average transport number of cations referred to the center of mass of the moving liquid (equiv./Faraday) absolute temperature (K) velocity of moving liquid in the pores of the membrane (m/s) volume of electroosmotic flow per area unit of membrane (m3 /m2 ) molar volume of water (m3 /mol) concentration of fixed groups (equiv/m3 of wet membrane) admittance for n = 0 (−1 ) complex admittance (−1 ) valence of cations (i = +) and anions (i = −) of the electrolyte complex impedance () real component of the complex impedance () imaginary component of the complex impedance ()

Greek symbols ε volume fraction of water in the membrane (m3 water/m3 wet membrane) proton conductivity, −1 m−1 (S/m)  chemical potential of electrolyte (J/mol) electrochemical potential moles of cations (k = +)  ˜k and anions (k = −) per mol of electrolyte (J/mol) 0 standard chemical potential of the electrolyte (J/mol) chemical potential of water (J/mol) w  total moles of cations and anions per mol of electrolyte i moles of cations (i = +) and anions (i = −) per mol of electrolyte 0 characteristic relaxation time (s)  out of phase angle in impedance measurements 0 specific friction coefficient of the moving liquid in the membrane (kg/(m3 s)) electrical potential (V) ω angular frequency (s−1 )

References [1] N. Lakshminarayanaiah, Transport Phenomena in Membranes, Academic Press, London, 1967. [2] E. Riande, Physics of Electrolytes, vol. 1, Academic Press, 1972 (Chapter 11). [3] T. Sata, Ion Exchange Membranes, RSC, 2004. [4] B. Smitha, S. Sridhar, A.A. Khan, Solid polymer electrolyte membranes for fuel cells applications, Rev. J. Membr. Sci. 259 (2005) 10. ´ [5] S. Tan, D. Belanger, Characterization and transport properties of Nafion/ polyaniline composite membranes, J. Phys. Chem. 109 (2005) 23480. [6] M.M. Nasef, H. Saidi, M.A. Yarmo, Surface investigations of radiation grafted FEP-g-polystyrene sulfonic acid membranes using XPS, J. New Mater. Electrochem. Syst. 3 (2000) 309. [7] Q.F. Li, R.H. He, J.O. Jensen, N. Bjerrum, The CO poisoning effect in PEMFCs operational at temperatures up to 200 ◦ C, Chem. Mater. 15 (2003) 4896. [8] N. Miyake, J.S. Wainright, R.F. Savinell, Evaluation of a sol–gel derived Nafion/silica hybrid membrane for polymer electrolyte membrane fuel cell applications. II. Methanol uptake and methanol permeability, J. Electrochem. Soc. 148 (2001) A905. [9] B. Baradie, J.P. Dodelet, D. Guay, Nafion–inorganic membrane with potential applications for polymer electrolyte fuel cells, J. Electroanal. Chem. 489 (2000) 101. [10] S. Malhotra, R. Datta, Membrane-supported non-volatile acidic electrolytes allow higher temperature operation of proton-exchange membrane fuel cells, J. Electrochem. Soc. 144 (1997) L23. [11] P. Dimitrova, K.A. Friedrich, U. Stimming, B. Vogt, Nafion-based membranes for use in direct methanol fuel cells, Solid State Ionics 150 (2002) 115.

V. Compa˜ n et al. / Journal of Membrane Science 318 (2008) 255–263 [12] M.K. Song, Y.T. Kim, J.M. Fenton, H.R. Kunz, H.W. Rhee, Chemically-modified Nafion/poly(vinylidene fluoride) blend ionomers for proton exchange membrane fuel cells, J. Power Sources 117 (2003) 14. [13] B.C. Bae, H.Y. Ha, D.J. Kim, Preparation and characterization of Nafion/poly(1vinylimidazole) composite membrane for direct methanol fuel cell application, J. Electrochem. Soc. 152 (2005) A1366. [14] P. Novak, K. Muller, K.S.V. Santhanam, O. Hass, Electrochemically active polymers for rechargeable batteries, Chem. Rev. 97 (1997) 2007. [15] G. Gustafsson, Y. Cao, J.-M. Treacy, F. Klavetter, N. Colaneri, A.J. Heeger, Flexible light-emitting diodes made from soluble conducting polymers, Nature 357 (1992) 477. [16] N. Leventis, Y.C. Chung, Polyaniline–Prussian blue novel composite material for electrochromic applications, J. Electrochem. Soc. 137 (1990) 3321. [17] P.N. Bartlett, P.R. Birkin, E.N.K. Wallace, Oxidation of beta-nicotinamide adenine dinucleotide (NADH) at poly(aniline)-coated electrodes, J. Chem. Soc., Faraday Trans. 93 (1997) 1951. [18] J.A. Conklin, T.M. Su, S.C. Huang, R.B. Kaneer, in: T.A. Skotheim, R.L. Elsenbaumeer, J.R. Reynolds (Eds.), Handbook of Conducting Polymers, 2nd ed., Dekker, New York, 1998 (Chapter 33, p. 945 and references therein). [19] A. Kitani, T. Akashi, K. Sugimoto, S. Ito, Electrocatalytic oxidation of methanol on platinum modified polyaniline electrode, Synth. Metals 121 (2001) 1301. [20] L. Niu, Q. Li, F. Wei, X. Chen, H. Wang, Electrochemical impedance and morphological characterization of platinum-modified polyaniline film electrodes and their electrolytic activity, J. Electroanal. Chem. 544 (2003) 121. [21] K. Rajendra Prasad, N. Munichandraiah, Electrooxidation of methanol on polyaniline without dispersed catalyst particles, J. Power Sources 103 (2002) 300. [22] T. Shimizu, T. Naruhashi, T. Momma, T. Osaka, Preparation and methanol permeability of polyaniline/Nafion composite membrane, Electrochemistry 70 (2002) 991. [23] C.-Y. Chen, J.I. Garnica-Rodriguez, M.C. Duke, R.F. Dalla Costa, A.L. Dicks, J.C. Diniz da Costa, Nafion/polyaniline/silica composite membranes for direct methanol fuel application, J. Power Sources 166 (2007) 324. [24] V.N. Andreev, V.I. Zolotarevski, Structure and properties of the polyaniline– Nafion–Pd composite electrodes, Russ. J. Electrochem. 41 (2005) 189. [25] N. Li, J.Y. Lee, L.H. Ong, Polyaniline and Nafion composite film as a rechargeable battery, J. Appl. Electrochem. 22 (1992) 512. [26] C. Barthet, M. Guglielmi, Mixed electronic and ionic conductors: a new route to Nafion-doped polyaniline, Electrochim. Acta 41 (1996) 2791. [27] P. Aldebert, P. Audebert, M. Armand, G. Bidan, M. Pineri, New chemical synthesis of mixed conductivity polymers, J. Chem. Soc., Chem. Commun. (1986) 1636. ´ [28] S. Tan, A. Laforgue, D. Belanger, Characterization of a cation exchange/ polyaniline composite membrane, Langmuir 19 (2003) 744. ´ [29] S. Tan, V. Viau, D. Cugnod, D. Belanger, Chemical modification of a sulfonated membrane with a cationic polyaniline layer to improve its permselectivity, Electrochem. Solid State Lett. 5 (2002) E55. ´ [30] S. Tan, J.H. Tieu, D. Belanger, Chemical polymerization of aniline on a poly(styrene sulfonic acid) membrane: controlling the polymerization site using different oxidants, J. Phys. Chem. B 109 (2005) 14085.

263

[31] M. Fabrizio, G. Mengoli, M.M. Musiani, F. Paolucci, Electrochemical characterization of PANI–Nafion membranes and their electrocatalytic activity, J. Electroanal. Chem. 300 (1991) 23. [32] N.P. Berezina, A.A-R. Kubaisy, Peculiarities of electrotransport characteristics of composite membranes PAni/MF-4SK in sulfuric acid solutions, Russ. J. Electrochem. 42 (2006) 81. [33] N.P. Berezina, A.A.-R. Kubaisy, N.M. Alpatova, V.N. Andreev, E.I. Griga, Composite polyaniline/MF-4SC membranes: a chemical template synthesis and the sorption and conduction properties, Russ. J. Electrochem. 3 (2004) 286. [34] N.P. Berezina, A.A. Kubaisy, S.V. Timofeev, L.V. Karpenko, Template synthesis and electrotransport behavior of polymer composites based on perfluorinated membranes incorporating polyaniline, J. Solid State Electrochem. 11 (2007) 378. [35] E.K.W. Lai, P.D. Beattie, F.P. Orfino, E. Simon, S. Holdcroft, Electrochemical oxygen reduction at composite films of Nafion, polyaniline and Pt, Electrochim. Acta 44 (1999) 2559. [36] J.-C. Chiang, A.G. Macdiarmid, Polyaniline: protonic acid doping of the emeraldine form to the metallic regime, Synth. Metals 13 (1986) 193. [37] M.R. Tarasevich, E.I. Khrushcheva (Eds.), Elektrokhimiya Polimerov (Electrochemistry of Polymers), Nauka, Moscow, 1990. [38] H. Nyquist, Thermal agitation of electric charge in conductors, Phys. Rev. 32 (1928) 110. [39] W.W. Bode, Network Analysis and Feedback Amplifier Design, Van Nostrand, Princeton, NJ, 1956. [40] R. Haase, Thermodynamics of Irreversible Processes, 2nd ed., Dover, New York, 1990. ˜ M.L. Lopez, ´ [41] J. Garrido, V. Compan, D.G. Miller, Phenomenological equations with observable electric potentials applied to non-equilibrium binary electrolyte solutions, J. Phys. Chem. 101 (1997) 5740. ´ ˜ J. Garrido, E. Riande, J.L. Acosta, Proton transport [42] M.L. Lopez, V. Compan, in membranes prepared from sulfonated polystyrene–poly(vinylidene fluoride)blends, J. Electrochem. Soc. 148 (2001) E372. ˜ F.J. Fernandez-Carretero, ´ [43] V. Compan, E. Riande, A. Linares, J.L. Acosta, Electrochemical properties of ion-exchange membranes based on sulfonated EPDM–polypropylene blends, J. Electrochem. Soc. 154 (2007) B159. [44] N.P. Berezina, N. Gnusin, O.A. Dyomina, S. Timofeyev, Water electrotransport in membranes systems. Experimental and model description, J. Membr. Sci. 86 (1994) 207. [45] N.P. Berezina, E.N. Komkova, A comparative study of the electric transport of ions and water in sulfonated cation-exchange polymeric membranes of the new generation, Kolloid Zh. (Russ. Colloid J.) 65 (2003) 5. [46] N.M. Alpatova, V.N. Andreev, A.I. Danilov, E.B. Molodkina, Y.M. Poukarov, N.P. Berezina, S.B. Timofeeb, L.P. Bobrova, N.N. Belova, Electrochemical template synthesis of an polyaniline composite with polymeric perfluorinated sulfo cationite, J. Electrochem. 38 (2002) 913. [47] N.P. Berezina, A.A.-R. Kubaisy, I.A. Stenina, R.V. Smolka, S.V. Timofeev, Protonelectron conductivity and structure of composite membranes MF-4SC modified by polyaniline or platinum, Membr. Ser. Crit. Technol. 32 (2006) 48–55 (in Russian). ´ ´ [48] J. Vargas, M. Tenklopatchev, M.-F. Laguna, M.M. Lopez-Gonz alez, E. Riande, Gas transport and ionic transport in membranes based on polynorbornenes with functionalized imide side groups, Macromolecules 40 (2007) 563.