The influence of absorbed methanol on the swelling and conductivity properties of cation-exchange membranes

Journal of Membrane Science 323 (2008) 167–175

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The influence of absorbed methanol on the swelling and conductivity properties of cation-exchange membranes Evaluation of nanostructure parameters Lobna Chaabane a , Gérard Bulvestre a , Christian Larchet a , Victor Nikonenko b,∗ , Claude Deslouis c , Hisasi Takenouti c a

LMEI – Université Paris-Est. 61, Avenue du Général de Gaulle, 94010 Créteil,France Department of Physical Chemistry, Kuban State University. Stavropolskaya Street 149, 350040 Krasnodar, Russia c LISE – Université P. et M. CURIE, Case courrier 133. 4, Place Jussieu, 75252 Paris Cedex 05, France b

a r t i c l e

i n f o

Article history: Received 31 March 2008 Received in revised form 9 June 2008 Accepted 9 June 2008 Available online 24 June 2008 Keywords: Cation-exchange membrane Nafion CM2 Nanostructure Conductivity Methanol Model Swelling

a b s t r a c t In this work, we have measured the swelling properties (thickness, area, density, solvent content), and the conductivity of two different cation-exchange membranes (Nafion® 117 and CM2), as functions of methanol content (XMeOH ) and LiCl concentration in the external solution. The volume fraction of electroneutral solution in the membrane (f2 ) was found by using the microheterogeneous model of Gnusin. The values of f2 as well as the porosity of Nafion® 117 obtained as functions of the methanol content are compared with those calculated on the basis of the nanostructure model developed by Haubold et al. Generally a good agreement is noticed. It is found that the volume of regions occupied by side chains with fixed ion-exchange groups increases with methanol content, that determines the total swelling and growth in porosity of Nafion® 117. This swelling is accompanied however by a small decrease in the pore core region volume, free of polymer chains. The latter results in a decrease in f2 , found also from conductivity measurements. The lower ionisation of the inner solution caused by the presence of less polar and less ionising solvent, such as methanol, produces a decrease in the membrane conductivity, which is partially compensated by swelling of side-chain regions. The conductivity (*) of CM2 membrane, which is reticulated and swells only slightly in the presence of methanol, decreases much more in comparison ∗ with non-reticulated and strongly swelled Nafion in pure methanol solution: CM2 ≈ 0.05 mS cm−1 and ∗ Nafion ≈ 6 mS cm−1 . © 2008 Elsevier B.V. All rights reserved.

1. Introduction The understanding of relationships between the behaviour of ion-exchange membranes (IEMs) and their structure is important for improving the membranes and various membrane techniques. The effect of organic solvents present in aqueous solutions produced on membrane properties and structure is of particular interest taking into consideration such applications as electrodialysis treatment of water–organic solutions [1–3] or direct methanol or ethanol fuel cells [4,5]. Many studies [6–10] showed that the structure of IEMs is very sensitive to the presence of organic solvents. It is well known that the functional properties of IEMs are determined by their nano-scale structure. Effectively, due to phase separation within such membranes occurring even in dry state and

∗ Corresponding author. E-mail addresses: [email protected] (L. Chaabane), v [email protected] (V. Nikonenko), [email protected] (C. Deslouis). 0376-7388/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.memsci.2008.06.044

becoming much stronger when swelling, ion and solvent conducting channels of 1–4 nm in diameter are formed. The morphology of these channels is very important, and a number of structural models were developed in order to interpret membrane properties [6,11–18]. The basic model was proposed by Gierke and Hsu [11]. It consists in representing the membrane as a periodic structure. A structural unit is of 4–10 nm size and includes a region usually named cluster, which contains functional sites attached to the macromolecular chains as well as mobile solvent molecules and ions. The mobile particles are inside the cluster while the fixed solvated ions form its walls (Fig. 1, [16]). The clusters are linked between them by more or less wide channels (1–6 nm in diameter) thus making a connected network. Generally, the membrane contains also hydrophobic domains, enveloping the clusters and channels, and formed by bundles of chains devoid of charged sites. The models developed or applied by different authors [12–18] differ by details, sometimes important, such as the geometrical shape of clusters and channels and their spatial distribution [12,13]; they specify the morphology at dry state [14] and its evolution when

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Fig. 1. Schematic representation of the microstructure of Nafion® 117 derived from SAXS experiments (Kreuer et al.).

hydration [15], the effect of different solvent [6,16–18], the role of side polymer chains [6]. The most studies cited above concern the perfluorosulfonated membranes of Nafion-type (Gierke’s, Haubold’s, and others). The structure of other type of membranes is less studied. However, it is known that IEMs with hydrocarbon matrix are more hydrophilic; the range of pore radius is more large with higher mesopore contribution [9,19–21], in comparison with perfluorosulfonated IEMs. Heterogeneous membranes prepared from a mixture of ion-exchange resin and polyethylene particles [22–24] are characterized by bi-porous structure: microand mesopores with radius 2–10 nm are related to ion-exchange resin particles, and macropores with the radius of the order of 1 ␮m are confined between the resin and/or polyethylene particles [9,19–21]. Consider the nanostructure 3D model of Nafion membranes by Haubold et al. [6], which will be used in this study (Fig. 2a and b). The phase separation in Nafion results in formation of a hydrophobic fluorocarbon backbone phase non-accessible to water and methanol, and a hydrophilic region containing the side chains with fixed ionic groups on their edge [6]. Thus the side-chain region is detached; it constitutes a new structure element having a thickness s/2. These regions form the “shell” of a transport channel. The “core” of the channel is either empty (in dry state) or flooded by water–methanol solution. A basic structure unit (Fig. 2b) is characterized in addition to s by three other parameters: the distance, c, between two parallel planes passing through fixed ions belonging to opposite side-chain regions; and the lateral dimensions, a and b, which determine the cross-section of the structure unit. Note that in this model, the thickness of core region, c, does not vary with coordinates (thus being an average size) whereas in Gierke’s and other similar models the spacing between the opposite pore walls is different in the clusters and channels.

Generally, one can distinguish two approaches to describe quantitatively membrane macro-properties starting from the membrane structure image and parameters describing this structure. In the first one, the ion and water transport is considered within the solution filling the pores/channels (charged space models) [25–27]. In the second approach, which is discontinuous, the membrane is presented as a microheterogeneous multiphase system and the transport modelling consists in describing the physicochemical properties of the entire membrane as functions of the properties of different phases and of their relative disposition [28–32]. Within the first approach, different types of modelling are developed, especially in the last 10 years [17,18]: atomic and molecular dynamics simulations [33], statistical mechanics modelling [34], application of Poisson–Boltzmann equations taking into account the interactions between individual ions, fixed and/or mobile, and solvent [27]. Between the numerous results giving a more comprehensible understanding of transport in nano-dimensional pores, it is found that the internal solution possesses bulk properties (at least, the dielectric permittivity, ε, reaches its bulk value (81) in the centre of pore), when the water content is higher than 10 water molecules per sulfonic acid group [16,17,27]. For lower degrees of hydration, ε is lower than 81 even in the pore centre. Gnusin et al. [28,35,36] have developed, in the framework of the second approach, a “microheterogeneous model”, which gives relatively simple relationships between some membrane macroproperties (such as the electrolyte uptake, the conductivity and the permeability towards electrolyte diffusion) and its structural parameters. In the microheterogeneous model, three phases are distinguished: (1) the electroneutral electrolyte solution filling central regions of the pores, (2) the gel phase containing the charged hydrophilic polymer domains (i.e. the side polymer chains with fixed sites present at the pore’s walls) surrounded by the charged regions of the internal solution compensating the charge of the fixed sites, and (3) the hydrophobic domains of polymer chains free of functional sites. Taking into account the small dimensions of these three regions (often lower than 5 nm), that means they are only quasihomogeneous, one can consider them as continuous and use the term “phase” with a great reserve. Mafé et al. [37] have developed a two-region model that can be considered as intermediate between continuous (space charge models) and discontinuous (multiphase models) approaches, thus giving a certain theoretical background for the latter when starting from the former. In the mathematical description of ion and water transport, the gel phase can be joined together with the hydrophobic phase to form a “joint-gel” phase [28]. In this way, only two pseudo-phases are considered: the joint-gel phase and the electroneutral solution filling the spaces between different elements of the joint-gel phase. When assuming that the volume fractions of these two phases is given as well as the disposition of the one in relation to the other, the microheterogeneous model allows the calculation of the electrolyte uptake, membrane conductivity and diffusion permeability as functions of ion concentrations an diffusivities within the phases. In particular, if the external solution concentration is not too far from the so-called isoconductance concentration, ciso , at which the conductivity of all membrane phases and the membrane as a whole are the same, the membrane specific conductivity, *, may be approximated by the following equation: ∗ = ¯ f1 sf2

(1)

where ¯ and s are the specific conductivity of the joint-gel phase and internal electrolyte solution, respectively; f1 and f2 are the volume fractions of the joint-gel and solution phases, f1 + f2 = 1; s is

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Fig. 2. Haubold’s model.

assumed the same as the conductivity of the external equilibrium solution. In practice, the condition of closeness of the external concentration, c, to the isoconductance point ciso may be expressed as 0.1 ciso < c < 10 ciso [28]. As it was mentioned above, the electroneutral solution phase represents the bulk of pores, the properties of which are close to those of a free solution [17,25,37]. Thus, both the cations and anions contribute here to the conductivity. However, in the gel phase, almost exclusively the counterions assure the conductivity. The co-ions are present there in a very low amount, increasing with bulk concentration, but negligible in the case of diluted water solutions (up to 1 M) and relatively high local concentration of fixed charges, as in the case of considered Nafion and CM2 membranes. Besides, with increasing solution concentration, the water uptake decreases that can result in a decrease of the counterion mobility [36]. For these reasons, the specific conductivity of the gel (or joint-gel) phase, in the indicated cases, varies only slightly with the external solution concentration; hence, ¯ can be considered as constant. Then, if the membrane conductivity is presented as a function of the equilibrium solution conductivity in log (*) – log (s ) coordinates, a straight line should be obtained, in accordance with Eq. (1), and its slope is equal to f2 . Eq. (1) was verified in a number of papers [28,29–31,36] and used later [23,24] for simple and efficient characterization of membrane structure. The aim of this paper is to determine, starting from the conductivity measurements and by using the microheterogeneous model, the f2 value for Nafion® 117 and CM2 membranes as a function of the external water–methanol solution composition, and to try to interpret the results on the basis of existing structural models. In such a way, certain parameters describing the nanostructure of these membranes will be found. Their evolution with increasing methanol volume fraction in the external solution will be discussed when considering the interaction of three kinds of forces: osmotic, electrostatic and mechanic forces, the latter expressing the tendency of the expanded matrix to contract. 2. Experimental part 2.1. Membranes Two sulfonic cation-exchange membranes were chosen to study their properties as functions of methanol content in equilibrium solution: Nafion® 117 (DuPont® ) as being a reference in researches devoted to fuel cells, and CM2 (Neosepta® , Tokuyama Soda) widely used in electrodialysis [22].

Nafion® 117 is a copolymer of tetrafluoroethylene and perfluorinated vinylether containing terminal sulfonic fluoride groups (Fig. 1). Its ion-exchange capacity is relatively low (Table 1) and the matrix is not reticulated. CM2 is a hydrocarboned membrane; it has a high concentration of sulfonic grafted sites in a structure containing divinylbenzene reticulated polystyrene and amorphous PVC. According to Goering et al. [38], some zones correspond to crystallized PVC, and others, of smaller size, contain all the functional sites and the mobile ions with their hydration shells. In a polar solvent, the ionised zones become more voluminous and their number decreases until a threshold of percolation allowing a continuous junction between the two faces of the membrane to be established. The both membranes were pre-treated before their use according to the French standard NF X 45-200 [39]. 2.2. Membrane conductivity The experimental device was described in a previous paper [10]. It is composed of a clip-type conductivity cell developed at the LMEI, Paris 12 university [10,36], a conductimeter (CDM 92, Radiometer-Analytical) and a thermo-regulated bath. Measurements were realized under an ac at 1 kHz frequency and at 25.0 ± 0.1 ◦ C. Before the measurements, the electrodes of the clip were platinized in a 1% platinum (IV) chloride solution [8]. The choice of the frequency (1 kHz) was justified by the measurements of the impedance spectrum of Nafion® 117 membrane under various physicochemical conditions by using the experimental device described in [40,41]. The particularity of the cell used [40,41] is that it allows the membrane to be taken out without disturbing the measuring (Ag/AgCl) electrodes. For given experimental conditions, two series of measurements have been realized: one with a membrane between the measuring electrodes, and the other without membrane. The obtained curves are shown in Fig. 3a–c with a frequency varying from 10 mHz to 10 kHz. These curves show first, that the real part of the impedance (Z ) is almost constant between 200 Hz and 10 kHz, and second, that the imaginary part (Z ) is almost zero. Finding the difference between the two values of impedance, with and without membrane, and taking into account the contribution of the solution layer replacing the membrane after taking out it from the cell (the thickness of this layer is the same than that of the membrane), we can determine the membrane conductivity. The comparison of the conductivity values determined by the LMEI clip cell and by the impedance measurements showed a small difference (less than 10%). This comparison as well as literature data

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Table 1 Main properties of Nafion® 117 and CM2 membranes in a 0.1-M LiCl solution

Nafion® 117 CM2

Specifications

Water content (gH2 O /gLi+ form wet membrane )

Exchange capacity (mequiv./gLi+ form wet membrane )

Thickness (␮m)

Perfluorinated, sulfonic, non-reticulated Hydrocarboned sulfonic, reticulated

16 23

1.01 2.12

217 129

[21,42] lead to conclude that the frequency of 1 kHz is appropriate to measure the membrane conductivity by the LMEI clip cell. The membranes were equilibrated in their electrolyte solutions before and during the conductivity measurements. For each studied composition and concentration, we carried out 10 measurements and calculated the average value. The curves of the Nafion® 117 and CM2 conductivity vs. the methanol volume fraction in different lithium chloride solutions are represented in Fig. 4a and b, respectively.

The results of thickness, surface, wet mass and density measurements for Nafion® 117 and CM2 membranes, as functions of methanol volume fraction and LiCl and HCl concentration, were reported in our precedent paper [43]. 3. Results and discussion 3.1. Membrane swelling Table 2 gives Nafion® 117 and CM2 membranes swelling properties measured at different lithium chloride concentrations and methanol contents. The reference states (notated with subscript “0”) correspond to the aqueous solutions. The measurement details and the absolute values are given in a previous paper [43]. 3.2. Membrane and solution conductivity Fig. 4a and b shows the membrane conductivity vs. the LiCl concentration in the external solution at different methanol contents. As it can be seen, the membrane conductivity increases slightly with the electrolyte concentration, while one observes a rather strong decrease in membrane conductivity as soon as a small quantity of methanol is introduced into the solution. Note also that the conductivity value in presence of pure methanol is very low for

Fig. 3. Bode diagram for Nafion® 117 membrane. (a) XMeOH = 0% and [LiCl] = 0.1 M, (b) XMeOH = 40% and [LiCl] = 0.1 M, and (c) XMeOH = 40% and [LiCl] = 1.0 M. : Real part of impedance (Z ) with membrane; ♦: real part of impedance (Z ) without membrane; : imaginary part of impedance (Z ) with membrane; : imaginary part of impedance (Z ) without membrane.

Fig. 4. Variation of membrane conductivity vs. methanol fraction and LiCl concentration. (a) Nafion® 117 and (b) CM2.

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Table 2 Membrane properties related to those measured in LiCl solutions at different methanol contents Nafion® 117

Experimental conditions Electrolyte

LiCl

CM2

C (M)

XMeOH (vol.%)

e/e0

S/S0

m/m0

e/e0

S/S0

m/m0

0.1

0 20 40 60 80 100

1.000 1.010 1.030 1.118 1.122 1.204

1.000 1.088 1.155 1.341 1.378 1.433

1.000 1.033 1.096 1.198 1.226 1.330

1.000 1.017 1.031 1.030 1.020 1.004

1.000 1.010 1.020 1.017 1.004 0.999

1.000 1.014 1.018 1.015 0.988 0.968

0.5

0 20 40 60 80 100

1.000 1.052 1.069 1.133 1.160 1.234

1.000 1.075 1.154 1.257 1.318 1.363

1.000 1.035 1.029 1.105 1.142 1.229

1.000 1.013 1.015 1.013 1.005 0.998

1.000 1.013 1.024 1.023 1.009 1.004

1.000 1.012 1.016 1.010 0.988 0.970

1.0

0 20 40 60 80 100

1.000 1.052 1.084 1.126 1.156 1.225

1.000 1.072 1.142 1.206 1.286 1.315

1.000 1.030 1.040 1.094 1.141 1.205

1.000 1.006 1.013 1.008 1.002 0.994

1.000 1.011 1.023 1.022 1.008 1.003

1.000 1.014 1.026 1.008 0.997 0.976

e = thickness, e0 = thickness in aqueous solution, S = area, S0 = area in aqueous solution, m = weight, m0 = weight in aqueous solution

the CM2 membrane, but it remains relatively high (5 mS cm−1 ) for Nafion® 117. The decrease in membrane conductivity with increasing methanol content in solution is generally explained [16–18,44] by the fact that the methanol is less polar and less ionising solvent in comparison with water. Hence, in presence of methanol, ion pairs form and the degree of electrolyte dissociation becomes lower that results in decreasing concentration of current carriers. The behaviour of lithium chloride conductivity (s ) in water–methanol solutions is shown in Fig. 5. The shape of curves s vs. the LiCl concentration in the presence of methanol is characteristic for weak electrolytes in water solutions: the slope of conductivity vs. concentration curve decreases with the LiCl concentration; this effect grows with an increase in the methanol content in the solution (XMeOH , in vol.%). 3.3. Determination of the intergel solution volume fraction According to the microheterogeneous model, the main reason of increasing membrane conductivity (*) with rising external elec-

Fig. 5. Water–methanol solution conductivity s vs. LiCl concentration at different methanol fractions (temperature: 25.0 ◦ C).

trolyte solution concentration (c) is the increase in the conductivity of electroneutral solution filling the intergel spaces. Effectively, in the case of strong electrolyte aqueous solutions, the conductivity of this phase () increases nearly linearly with c when assuming  to be the same as in free solution. At the same time, the conductivity of gel phase () ¯ increases only slightly with the external concentration; this increase is due to co-ion penetration into this phase. The role of co-ion transport is very weak in Nafion® 117 and CM2 membranes in the considered range of concentrations (less than 1.0 M), if methanol is absent. It can be estimated from the fact that the Na+ transport number in the CM2 membrane equilibrated with 1.0 M NaCl solution is higher than 0.99 [45]. When assuming ¯ constant, the slope of straight line that one should obtain when presenting the experimental data in log (*) – log (s ) coordinates is equal, according to Eq. (1), to the volume fraction (f2 ) of the solution filling the intergel spaces. However, when the fact of invariability of ¯ is not established, this method may give only apparent value of f2 . Effectively, we should expect that ¯ increases with increasing LiCl concentration when methanol is present in the solution in a considerable content. The reason is a higher uptake of electrolyte by the membrane in the presence of methanol in the solution [44]. By taking experimental data on membrane and solution conductivity as functions of LiCl concentration in external solution, it is possible to build log (*) vs. log (s ) plots (Fig. 6a and b). The apparent values of f2 for Nafion® 117 and CM2 membranes as functions of XMeOH are presented in Fig. 7 (curve 1 for Nafion® 117; curve 3 for CM2). It can be seen that in absence of methanol, the experimental log (*) vs. log (s ) points follow well the linear dependence with a slope f2 ≈ 0.065 for Nafion® 117 and f2 ≈ 0.05 for CM2. These values seem reasonable taking into account relatively small water content in these membranes and the fact that only a part of this water is present in the electroneutral solution localized within the central zones of clusters. Besides, these values are in a good agreement with the results of other authors [21,28–31] obtained with homogeneous membranes. For instance, Berezina et al. [46] have reported for Nafion 117 the values of f2 to be in the range 0.05–0.12 depending of the conditioning procedure: f2 increases with boiling and thermal pre-treatment of the membrane. Nikonenko [31] have found f2 = 0.07 for a CM2 membrane in NaCl solutions. The heterogeneous membranes have higher values of f2 because of a relatively great

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Fig. 6. Log (*) vs. log (s ) curves for Nafion® 117 (a) and CM2 (b) membranes in equilibrium with LiCl water–methanol solutions. The methanol content is shown (temperature: 25.0 ◦ C).

volume of macroporous cavities separating different particles of ion-exchange resin and inert filling material, often polyethylene, in this kind of membranes: for MK-40, MA-40 and MA-41 membranes, f2 is about 0.2 [21,28]. When the methanol content increases, the apparent value of f2 decreases firstly, then passes through a minimum and grows (curves 1 and 3 in Fig. 7). There is an apparent contradiction in the fact that f2 decreases with increasing methanol content in the external solution, whereas the total amount of internal solution increases in this case, as Fig. 3 shows, and it is reported by other authors [47]. However, this contradiction can be explained from Haubold’s nanostructure model. Table 3 shows the evolution of the model parameters found [6] on the basis of small angle X-ray scattering (SAXS) measurements as functions of the methanol content in the external equilibrium solution. As it follows from Table 3, the product of lateral dimensions (a and b), i.e. the cross-section of the structure unit, as well as the length of the side chains in the shell region (s) increase with increasing methanol content that determines the fact that the overall amount of solution increases in this case. However, the thickness of the core zone of the pore (c) decreases that explains the decrease in f2 . The sum (c + s) increases only slightly, thus the side-chain swelling occurs at the expense of available volume for the core region. Apparently, this behaviour may be interpreted by the actions of three main forces: the osmotic pressure and electrostatic repulsion forces are balanced by the mechanical force tending to contract expended matrix [44]. The polarity of methanol is only slightly lower than that of water (1.68 Debye and 1.84 Debye, respectively [44]). This results in decreasing solvation tendency of ions and in osmotic pressure, however moderate. At the same time, the dielectric constant of the two solvents is rather different: 81 for water and 32 for methanol. Hence, a noticeable increase in the repulsion between neighbouring charged sites should be expected when passing from water to methanol solutions. That should lead to an increase in the cross-section of structure unit decisive for the increase in membrane volume. The distance between the sites belonging to opposite pore walls seems too high to induce a noticeable repulsion force [25]. The increase in side-chain length (parameter s in Haubold’s model [6]) with increasing methanol content is probably due to growing mobility of chains caused by an increase in general swelling and enlarging spaces between them. It can be considered that the water–methanol solution fills the core of the pores (of thickness c, Fig. 2) as well as the spaces between the side chains (of total thickness s) in the shell region. In this case the volume accessible for solution within one structure unit will be: Vpore = a × b × (c + s)

(2)

Let us introduce one more parameter in addition to those used in Haubold’s model [6]. It will be the thickness of hydrophobic backTable 3 Structural parameters of Haubold’s nanostructure model (see Fig. 2a and b) as functions of the external solution methanol content, XMeOH (vol.%), found on the basis of SAXS measurements [6]

Fig. 7. Variation of the volume fraction of the intergel electroneutral solution, f2 , vs. the methanol content (vol.%) in LiCl solutions, for Nafion® 117 and CM2. (1) Apparent values for Nafion® 117 found from conductivity measurements, (2) calculated values for Nafion® 117 with help of Haubold’s nanostructural model, and (3) apparent values for CM2 found from conductivity measurements.

XMeOH (%)

a (Å)

b (Å)

c (Å)

s (Å)

a × b (Å2 )

c + s (Å)

0.0 9.3 19.5 25.8 33.1 50.8 70.3 89.8 100.0

22.4 22.0 21.6 21.6 21.6 22.8 21.2 18.0 14.4

28.6 28.4 34.0 35.6 36.4 37.2 40.8 46.4 44.8

27.7 26.9 24.4 23.6 23.2 22.3 15.7 14.5 12.4

34.8 35.2 38.5 39.3 39.7 41.0 49.2 49.2 49.2

641 625 734 769 786 848 865 835 645

62.5 62.1 62.9 62.9 62.9 63.3 64.9 63.7 61.6

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et al. [6] have used a more radical method of pre-treatment: cleaning Nafion in hot H2 O2 and water. Hence, it is possible that the real porosity of the sample studied in [6] at low methanol contents was even higher than that in [47].

Fig. 8. Nafion® 117 porosity vs. methanol content.

bone chain region (h), which is inaccessible for water and methanol solutions. Then the total volume of the structure unit will be: Vtot = a × b × (c + s + h)

(3)

Thus the porosity of the membrane is: p=

Vpore c+s = Vtot c+s+h

(4)

3.3.1. Porosity of Nafion® 117 The results of calculation of p with Eq. (4), as a function of methanol content are presented in Fig. 8. The values of c and s, as functions of XMeOH , for Nafion® 117 are taken from paper [6] by Haubold et al. The value of h = 60 Å (not varying with methanol content) is fitted in order to make an accordance with our experimental data as well as with those taken from paper by Villaluenga et al. [47]. In experiments, p was found after measuring the masses of wet (mw ) and dry (md ) membrane samples [47]: p=

(mw − md )dm (mw − md )dm + md s

(5)

where dm and s are the density of dry membrane and water–methanol internal solution, respectively. For Nafion® 117, dm was taken as 1.98 g cm−3 [47], s was calculated by assuming that the composition of the internal solution is the same as external one. The density of water–methanol mixtures is taken from handbook [48]. As it can be seen from Fig. 8, the total porosity of the membrane increases with increasing XMeOH in our experiment and in that of Villaluenga et al. [47]. However, the calculation with Eq. (4), when the microscopic parameters are taken from [6], shows a constant value of p. The difference in values of p at low methanol contents is apparently due to the difference in the membrane pretreatment prior measurements. Villaluenga et al. [47] has dried the membrane sample in a vacuum oven at 100 ◦ C during 24 h. We have not heated the sample, and applied the French standards [39] as described above. It is well known that a treatment of Nafion at elevated temperatures (100 ◦ C and higher) results in better evacuation of secondary synthesis products and in larger opening of pores. Thus, it can be assumed that a part of pore volume was not accessible for solution in the case of pre-treatment as applied in our laboratory, while the pre-treatment of Villaluenga et al. [47] was more efficient. However, as far as the membrane swelled more in solutions containing more methanol, the pores became more open that facilitated their purgation. In pure methanol solutions, the porosity found in both cases was the same. Note that Haubold

3.3.2. Volume fraction of electroneutral solution It is possible now to evaluate f2 , the volume fraction of electroneutral solution in Nafion® 117 starting from Haubold’s model and found nanostructure parameters [6]. The electroneutral solution occupies a part of the pore core region beyond the electric double layer (EDL) surrounding charged sites at the edge of side chains. The solution occupying the shell region of the pore (Fig. 2) relates to the gel phase, in terms of microheterogeneous model [28]. The EDL consists of two parts: the Helmholtz dense layer, of thickness Helm , and the diffuse layer, of thickness D . The outer Helmholtz plane passes through the centres of the closest solvated counterions [49]. Thus the thickness of the Helmholtz layer is equal to the sum of solvated radii of fixed ion and mobile counterion. While the number of solvating molecules for Li+ in water solutions is about 7 [50], in methanol solution this number is close to 5 [51,52]. In highly hydrated state, the radius of Li+ is equal to 3.7 Å [50]; it decreases in concentrated solutions such as in the EDL near fixed ions of Nafion membrane. As well it decreases in the presence of methanol. The hydration number of fixed SO3 − ion found by molecular simulation [18] is close to 5. The radius of fixed hydrated sulfonate ion can be probably evaluated as 3.3 Å. This distance corresponds to a hydroxonium-sulfonate bound state, as it follows from molecular dynamics simulations [33]. In our estimations, in the presence of water solution within the pore, Helm is taken equal to 6 Å. We have assumed that Helm decreases linearly with increasing methanol content: from Helm = 6 Å when XMeOH = 0, to 5 Å when XMeOH = 100% in the external solution. It is taken into account that the solvent absorbed in Nafion® 117 has approximately the same composition as the solvent outside the membrane [7,53]. The diffuse part of EDL (D ) is evaluated as Debye thickness [44]: εε0 RT/2c0 F 2 calculated at bulk concentration c0 = 1.0 M. D = The results of calculation of the dielectric constant (assumed varying linearly with the methanol content) as well as the thicknesses of different parts of EDL at the internal interfaces are presented in Table 4. The volume of the electroneutral solution within a structure unit of Haubold’s model is calculated as Velectroneutral = a × b × [c − 2(Helm + D )]

(6)

The results of calculation of the volume fraction of the electroneutral solution, f2 = Velectroneutral /Vtot are shown by curve 2 in Fig. 7. The parameters of Haubold’s model [6] were taken from Table 3, additional parameter h fitted to the porosity measurements is equal to 60 Å.

Table 4 Dielectric permittivity of inner bulk solution, thicknesses of the Helmholtz and the diffuse parts of EDL, and total EDL thickness at inner interfaces in Nafion® 117 calculated as functions of the methanol contain XMeOH (%)

a (Å)

Helm (Å)

D (Å)

tot (Å)

0.0 9.3 19.5 25.8 33.1 50.8 70.3 89.8 100.0

80.0 75.5 70.6 67.6 64.1 55.6 46.2 36.9 32.0

6.0 5.9 5.8 5.7 5.7 5.5 5.3 5.1 5.0

3.1 3.0 2.9 2.8 2.7 2.6 2.3 2.1 1.9

9.1 8.9 8.7 8.6 8.4 8.1 7.6 7.2 6.9

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As it was noted above, the reason for an increase in the gel phase conductivity, , ¯ with increasing external electrolyte solution concentration, is the penetration of electrolyte inside this phase, more precisely inside the EDL, which encloses a part of core and shell regions of pores. In the case of water solutions, this penetration is very weak (the Donnan exclusion is strong), and ¯ may be assumed constant. Then it can be expected that the treatment of conductivity data in log (*) vs. log () coordinates gives a value close to the real volume fraction of the intergel electroneutral solution, f2 . However, in the presence of methanol, the penetration of electrolyte inside the joint-gel phase is stronger due to formation of ion pairs. The higher presence of co-ions in this phase is favoured also by increased distance between fixed ions. The latter can also give rise to an increase in ion mobility. Thus, at elevated methanol contents, ¯ should increase with increasing LiCl concentration that will result in a higher slope of the log (*) vs. log () curve, with the same f2 . This explains the growth in apparent value of f2 found as the slope of the log (*) vs. log () curves at methanol contents higher than 60% (Fig. 7). The CM2 membrane reveals a similar behaviour in the presence of methanol. However, this membrane is cross-linked; hence, the increase in its swelling in the presence of methanol is lower. As Nafion® 117 swells more in methanol, the distance between neighbouring chains becomes higher that reduces the hindrance effect for conductivity and facilitates the penetration of ions and solvent inside the side-chain regions. As a result, the decrease in conductivity in the case of Nafion is less important: at 100% of methanol ∗ ∗ Nafion ≈ 6 and CM2 ≈ 0.05 mS cm−1 .

4. Conclusion A good agreement is found when comparing the estimation of some nanostructure parameters of Nafion® 117, starting from the electrical conductivity (*) data, with that by Haubold et al. resulted from SAXS measurements. The volume fraction of electroneutral solution (f2 ) occupying the central region of the pores was found by applying the microheterogeneous model to * vs. LiCl water–methanol solution concentration dependence. It was established that f2 decreases with increasing methanol content (XMeOH ) in external solution, at least at XMeOH < 60 vol.%. The same result was obtained by evaluating f2 with help of Haubold’s model and parameters resulted from SAXS measurements. The decrease in f2 with growing methanol content is explained in the framework of Haubold’s model by the reduction of pore core region caused by an increase in the length of side chains delimiting the shell region of pore. The increase in the shell region volume conditions the additional swelling of the membrane in the presence of methanol. This increase should be due to increasing repulsion force between neighbouring fixed sulfonic ions caused by lower dielectric constant of the methanol solution. The growing repulsion increases the distance between neighbouring fixed ions and the spaces between the side chains (shell regions), by decreasing in this way the hindrances to ion and solvent transfer in these regions. As the methanol is less polar and less ionising solvent than water, its presence in the inner solution induces formation of ion pairs and facilitates penetration of electrolyte (favoured by swelling) into the charged part of inner solution (into the gel phase, in the terms of the microheterogeneous model). The lower ionisation produces a decrease of the membrane conductivity in the presence of methanol, which is partially compensated by swelling of shell regions. Thus, the conductivity of CM2 membrane, which is reticulated and swells only slightly in the presence of methanol, decreases much more in comparison with non-reticulated and strongly ∗ swelled Nafion, in pure methanol solution: CM2 ≈ 0.05 mS cm−1

∗ and Nafion ≈ 6. On the other hand, elevated electrolyte sorption results in higher dependence of the gel phase conductivity () ¯ on the external electrolyte solution concentration. In particular, the increase of ¯ with external concentration explains the growth in the apparent value of f2 with increasing methanol content at XMeOH > 60 vol.%.

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