Water Sorption Behavior in Different Aromatic Ionomer Composites

Article pubs.acs.org/Macromolecules

Water Sorption Behavior in Different Aromatic Ionomer Composites Analyzed with a “New Dual-Mode Sorption” Model Yongli Li,* Quang T. Nguyen, Kateryna Fatyeyeva, and Stéphane Marais Laboratoire Polymères, Biopolymères et Surfaces, UMR 6270 & FR 3038, CNRS-Normandie Université-Université de Rouen, Bd. Maurice de Broglie, 76821 Mont Saint Aignan, France S Supporting Information *

ABSTRACT: A new dual-mode sorption model (NDMS) was applied to sigmoid-shaped isotherms of water vapor sorption in composites of sulfonated or nonsulfonated polysulfones with a sulfonic-modified laponite clay and in blends of sulfonated poly(ether ether ketone) with sulfonated polyether sulfone cardo, respectively. The three NDMS parameters, Cp, A′, and k′ can be correlated to the amount of water molecules sorbed in the first hydration shell, the subsequent sorption on the sulfonic-sites and the tendency for water molecules to form clusters at very high water activities, respectively. The fitted values were used to study the relationship between sorption behaviors and component structure or organization in the composites. The analysis of the sorption−desorption cycles shows that the sorption hysteresis increases with the ionomer chain rigidity. An analytical expression for the mean cluster size (MCS) as a function of activity was deduced and validated by correlating to sorption kinetics. It has been shown that MCS increases with chain flexibility at high water activities.

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INTRODUCTION Solid polymer electrolytes (SPEs) are polymer systems with complex structures. They generally consist of a dense matrix of ionomers, i.e., highly polar ionizable groups covalently attached to an aromatic polymer backbone, which is mainly hydrophobic in nature. The aromatic polymer matrix which remains in a glassy state even at large water sorption extent on ionic sites, imparts the mechanical stability to the materials. Such a structure of SPE systems provides insoluble ionic systems (or polymer electrolytes) in aqueous media, making SPE suitable for uses in electrolyzers or fuel cells.1 The properties of SPEs in fuel cells depend largely on water diffusion and water sorption, which are characterized by the water sorption isotherms.2−5 In fact, the water states and their morphological transitions affect numerous system properties6 such as surface wettability and free volume or pore size (i.e., heterogeneous structure in the matrix). The water sorption isotherms in ionomer systems, such as polyelectrolytes, generally have a sigmoid shape, i.e., concave to the water activity axis at low activity values and convex to the same axis at high activity values.7 The sigmoid-shaped isotherm has generally been observed for natural polymer systems such as starch,8 cellulosic materials,9 and complex foodstuffs10 and has often been simulated by specifically designed models for that type of isotherm, i.e. BET type II equation, Guggenheim− Anderson−de Boer (GAB) equation, or Park equation. Feng11 has recently developed a new vapor sorption model that describes well all types of isotherms of vapor sorption in glassy polymers. The new dual mode sorption (NDMS) model has three parameters based on multilayer theory. The NDMS model has been tested by its author on several series of vapor © 2014 American Chemical Society

sorption data reported in the literature on different types of isotherms,11 mainly for the fitting quality aspect. It appears to be better than other models for the fitting of sigmoid-shape isotherms,11,12 keeping in mind that only three adjusting parameters have to be determined. The main aim of the present paper is to analyze the water vapor sorption behavior of polymer nanocomposites (sulfonated polysulfones (SPSU) or polysulfones (PSU) with a sulfonic-modified laponite clay (SLp)) and polymer blends (sulfonated poly(ether ether ketone) (SPEEK) with sulfonated polyether sulfone cardo (SPESc)), with the NDMS model. The sulfonated polymer−inorganic particles composites are attractive as solid electrolytes for proton exchange membrane fuel cells or direct methanol fuel cells, since the inorganic particles can increase the water sorption extent at relatively high temperature and reduce the methanol crossover.13−15 For all composite systems, the component compatibility is considered to be the main requirement for obtaining homogeneous and defect-free materials with interesting properties. For the ionomer blends, we used two acid ionomers, SPEEK and SPESc due to their good compatibility in the entire composition range.16 For the composites with laponite clay, the latter was modified by surface grafting with styrenesulfonate after remote-plasma activation of the clay surface to improve its compatibility with sulfonated ionomers and water adsorption.2 With such a surface-modified laponite, the composite ionomers exhibited improved proton conductivities at high temperatures, Received: May 27, 2014 Revised: August 31, 2014 Published: September 9, 2014 6331

dx.doi.org/10.1021/ma501097k | Macromolecules 2014, 47, 6331−6342

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which were attributed to water sorption onto laponite particles.15,17,18 By analyzing the data of water sorption and desorption in these polymer composites, we expect to get a better insight into the influence of the chemical nature and the physical structure on the sorption and desorption of water at different activities. The sorption behavior of these composites is compared with that of a block copolyimide12 and with that of Nafion 117 ionomers whose structures in both dry and humid forms at different water activities are the best known.

The sorption is a contribution of two modes, as shown in Figure 1, one occurs in the matrix region of the glassy polymers

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THEORETICAL BACKGROUND The first theoretical equation for sigmoidal sorption isotherms is the well-known BET (Brunauer−Emmett−Teller model) relationship.19 The BET type II sorption isotherm is a combination of Langmuir (the first part of the curve, i.e. concave to the activity axis) and Flory−Huggins isotherms (the second part, i.e. convex to the activity axis).20 It was established to describe the adsorption phenomena at the surface of very diverse materials, inorganic and organic systems.21,22 The BET model considers that water molecules condense in several layers on adsorption surfaces and assumes that beyond the second layer, their evaporation−condensation properties are the same as in the liquid state. This model is limited to water activities up to about 0.4−0.5.23 The GAB model also considers the assumption of localized physical adsorption into a multilayer (the number of layers being limited) with no lateral interactions.24 The molecules in the so-called multilayer have interactions with the penetrant which range in energy levels somewhere between those of the monolayer molecules and the bulk liquid. Successive layers of water molecules increasingly exhibit bulk liquid properties. The GAB model represents a refinement over the BET type II model, shares with it the two original BET constants and owes its major versatility to the introduction of a third constant.19 The water molecules beyond the monolayer are not structured in a multilayer, but have the same characteristics as the molecules in the bulk liquid. The GAB equation is thus reduced to the BET equation for sorption. The monolayer value is a measure of the availability of active sites for water sorption by the material.24 The Park model for sigmoidal isotherms of water vapor25 considers three mechanisms: Langmuir’s sorption on special sites (the first part of the curve), nonspecific sorption of Henry’s type (the second part) and water-molecule aggregation or clustering (the third part, i.e., convex to the activity axis) at high water activity based on the equilibrium nH2O ⇆ (H2O)n. This model for multimode sorption fits sigmoid isotherms very well. Since it requires a large number of adjustable parameters (five), the interpretation of the values of the parameters on the basis of physicochemical interactions is rather difficult. The NDMS model is deduced from the GAB equation and is thus based on multilayer sorption theory. Four assumptions are made for this new model: (i) the sorption site in a glassy polymer material can be divided into two different species, one is located in the matrix region of the polymer and the other in the microvoids; (ii) all the molecules in the matrix region of the polymer have the same partition functions; (iii) there is GAB sorption in the microvoid region of the polymer; (iv) the molecules in the layers other than the first layer in the microvoid region have the same partition function as those in the matrix region.

Figure 1. Representation of NDMS model.11

and follows C1 that has an upward curve similar to that in rubbery polymers; the other occurs in the microvoids and follows C2 that has a downward trend. The penetrant concentration in the polymer is given by C = C1 + C2 = Cp

k′aw (A′ − 1)k′aw + Cp 1 − k′aw 1 + (A′ − 1)k′aw

(1)

where Cp is the weighted mean value of the sorption capacity of the polymer for the penetrant (a constant at a given temperature); it mainly depends on the structure and the state of the polymer. k′ is the difference between the interactions of vapor molecules with each other and with a polymer molecule segment; it is essentially an indication of the interaction between the penetrant molecules in the polymer matrix. Large k′ indicates preferential interactions between penetrant molecules compared to the penetrant-polymer ones; thus, the isotherms shows a stronger exponential increase at higher water activities where the amount of the new-sorbed water molecules are only due to the interactions between them and the already absorbed water molecules, and not due to the interactions between them and the ionomers. A′ is the difference between the interactions of a microvoid with the penetrant molecules sorbed on the first layer and those of the microvoid with the penetrant molecules sorbed later in the subsequent layers; in other words, it indicates the material capacity of absorbing the penetrant molecules that come into the polymer after the sorption of penetrant molecules of the first layer on the Langmuir sites.11 The NDMS model leads to a shape for the sigmoidal sorption isotherms that is similar to the original GAB model. The GAB equation assumes that all the sorption sites are equivalent, while there are two different types of sorption sites in the NDMS model. From the physical viewpoint, the NDMS model is more appropriate to polymer systems in which there are different phases/sites with which the sorbate molecules can interact. The NDMS model is compatible with sigmoidal isotherms, concave isotherms (i.e., Langmuir’s or classical dualmode type), or convex isotherms (i.e., Flory−Huggins’ type) for vapor sorption in polymers. Henry’s isotherm is the limiting case of very low interactions between the vapor and the polymer (k′ ≪ 1, C1 = CpA′k′a), while the concave isotherm is the limiting case where the vapor-microvoid interactions are strong (A′ >1) and the convex isotherm is the limiting case of a rubbery polymer without microvoids (A′ = 1, C = C1). The most complex one is the sigmoidal isotherm that exhibits different patterns according to the range of the sorbent activity. 6332


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For the ionomers, the two populations of penetrant inside the solid polymer considered in the NDMS model takes into account the particularity of glassy polymers, which are known to have “frozen holes” between the polymer chains at temperatures lower than the glass transition temperature of the penetrant-polymer system. The sorption at low penetrant (water) activities has been suggested to be of the Langmuir type which occurs as a result of the insertion of the penetrant molecules into a finite “number of these pre-existing gaps in the polymer matrix”.26 The sorption of water is easier in these holes than in the matrix, so that it occurs at low water activities. At high activities, sorption of gases was found to obey to Henry’s law of gas dissolution,27 and this model of isotherms in the whole activity range was named “dual-mode model”. However, sorption of vapors in polymers often involves strong positive deviations from Henry’s law. Berens28 used the Flory−Huggins equation for such a deviation in the case of vapors. Stannett et al.29,30 found that for water, such a modified dual-mode model was not adequate due to a marked penetrant clustering in the polymer matrix. The NDMS model, which derives from the GAB model of multilayer sorption, postulates the presence of a first layer of strong sorption on the fixed Langmuir sites which correspond physically to the “frozen holes” glassy polymer. The second population of sorbed species was postulated to be in the matrix to include the general case of multiphase/site materials, but was not exclusive to the matrix. In the case of ionomers, this second population was shown to be in subsequent layers of the first layer of water molecules on the sulfonic sites.31 The NDMS model implicitly postulates more negative sorption energy per sorbed molecule at low penetrant activities due to stronger interactions involved in the Langmuir-type sorbed population, if there are any molecules in this. However, the model is compatible with a continuous distribution of sorption energy, as one can expect, the dual population in the case of water sorption in ionomers is in agreement with the data of sorption energy measured in different ranges of water activities, with a highly negative sorption at low activities that switched to a less negative at a certain activity.7,32 The NDMS model appears not only a convenient model from the engineering viewpoint due to its good fitting ability with few adjustable parameters but also a sound model from the physical viewpoint, otherwise it would fail to fit all types of isotherms over the whole penetrant activity range,11 no matter what type of mechanism of interaction between the penetrant and the polymer species.

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Scheme 1. Surface Grafting Process for Laponite Clay

of all the basic materials are summarized in Table S1 of the Supporting Information. The composite membranes prepared from SPSU or PSU and SLp are named SPSU-1% SLp, SPSU-3% SLp, SPSU-5% SLp, PSU-3% SLp, and PSU-5% SLp according to the mass fraction of SLp. The blend membranes prepared from SPEEK and SPESc are named SPEEK100-SPESc0, SPEEK80-SPESc20, SPEEK60-SPESc40, SPEEK50-SPESc50, SPEEK40-SPESc60, SPEEK20-SPESc80, and SPEEK0-SPESc100 according to the mass fractions of SPEEK and SPESc. As reference, the sulfonated polyimide (SPI),33 Nafion 117 (film used as provided) and a lab-made Nafion-3% SLp composite17 were also produced. The detailed membranes preparations were described elsewhere.16−18,20 All films with the thickness in the range of 100−200 μm, were put in the acid form by treatment in 1 M hydrochloric acid solution for at least 12 h (except for Nafion, which was treated in more concentrated acid). Water Vapor Sorption Measurement. The ionomer samples in acid form were dried under vacuum at 80 °C before its mounting in the microbalance. DVS electronic microbalance (Cahn D200 with a mass resolution of 0.1 μg, from Surface Measurement Systems Ltd., London, U.K.) was used for the kinetics data collection. A typical sorption protocol consists of two steps: the sample is first placed in drying the sorption chamber where it is suspended on the microbalance beam, and it is dried by dry nitrogen flushing until a constant sample weight reaches; then, a vapor at a constant vapor pressure was admitted in the sorption chamber whose temperature was controlled by enclosing the entire system in a temperaturecontrolled incubator where the partial vapor pressure in the sorption chamber is controlled by mixing water-saturated nitrogen and dry nitrogen using electronic mass flow controllers. The sorption kinetics were obtained from the mass gain versus time and the sorbed amount at equilibrium was obtained from the extrapolated value for infinite time of the sorption curve. The sorption measurements were performed around 25 °C. The vapor pressure was then increased stepwise (at values corresponding to increments of 0.05 or 0.10 in water activity) and the sorption curve was recorded up to a pressure close to the saturation pressure. Care was taken to avoid vapor condensation for vapor pressures close to saturation. The measured mass of sorbate ws was converted to the number of sorbed molecules per ion pair with eq 2:

EXPERIMENTAL SECTION

MATERIALS In this work, polysulfone, poly(ether ether ketone), polyether sulfone cardo, and polyimide were selected and sulfonated to have the ion exchange capacities (IEC) of 1.41, 1.83, 0.94, and 1.26 mequiv/g, respectively, to get good compromise in mechanical properties. The syntheses of these polymer materials were detailed in previous work.16−18,33 The laponite powder was first activated by a He plasma with a flow of 125 sccm, and then underwent the grafting process by immediate immersion in a 3% (w/v) solution of p-styrenesulfonate in DMF (Scheme 1). After the grafting process, the SLp was filtered, washed and dried at 100 °C. The chemical formulas of these polymers are presented in Chart 1 and the characteristics

λ=

ws /Ms IEC × m

(2)

where Ms is the sorbate molecular-weight (g/mol), IEC is the SPE ion-exchange capacity (equivalent ion/g of dry membrane) and m is the mass of the dry membrane sample. The “λ versus solvent activity” isotherms were fitted with Feng’s equation by Gauss−Newton method by using Matlab. Sorption Kinetics. By applying Fick’s laws to dense membranes that are considered as a plane sheet material of 6333


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Chart 1. Repeat unit of SPEEK, SPSU, SPESc, Nafion, and SPI

Such an assumption would hold for the majority of ionomer systems, which generally have a matrix formed of hydrophobic segments that do not absorb any significant amount of water. The Cp parameter in the NDMS model has the same unit as λ, i.e., the molar ratio of water to sulfonic in the dry polymer. Depending on the water−ion pair interactions and the water activity in the external phase, there could be two populations of water molecules around the ionic site in the polymer, those that are strongly bound to the acid site of the polymer and those that are more weakly bound to the ionic sites. The former corresponds to the value of the Cp parameter, which represents the water molecules strongly sorbed (in a Langmuir-site sorption way), while the latter corresponds to those sorbed in subsequent layers on the first-sorbed water layer.31 We further assume, in the discussion, a biphasic structure with hydrophilic and hydrophobic domains for ionomer composites.37 Study on Water Sorption Isotherms of SPSU Composites. To improve further the water retention capacity of the laponite clay, it was treated by a surface grafting process. The water sorption isotherms for Lp and SLp are given in Figure 2 and the values of parameters fitted with NDMS are presented in Table 1. Figure 2 shows that the sorption isotherms of SLp and Lp are almost indiscriminable at low activities, however, the quantity of sorbed water molecules by SLp increases significantly at higher activities (>∼ 0.8). The values of Cp and A′ of SLp are not much higher compared to those of Lp. The reason is that the surface grafting can only take place on the extreme surface and not in the particle bulk, so that the amount of grafted sulfonic group is limited. X-ray photoelectron spectroscopy investigations show that the laponite interlamella distance was increased from 1.25 nm (the case of Lp) to 1.53 nm (the case of SLp) due to the grafting of styrenesulfonic chains inside the lamellas.17 Such

thin thickness and assuming that the mass transfer occurs in the perpendicular direction to the plane sheet,34 the determination of diffusion coefficients from sorption kinetic measurements was done.35 The diffusion coefficient corresponding to the early time period (first half-sorption) of diffusion (D) and the diffusion coefficient corresponding to late-time period (second half-sorption) of diffusion (D′) can be calculated by35 ⎛ π 1/2L ⎞2 ⎛ dm(t ) ⎞2 D=⎜ ⎟⎜ ⎟ ⎝ 4 ⎠⎝ d t ⎠

(3)

⎛ L ⎞2 d[ln(1 − m(t ))] D′ = −⎜ ⎟ ⎝π ⎠ dt

(4)

where L is the membrane thickness, t is the sorption time and m(t) (=ΔM/ΔMeq) is the mass gain of the membrane at the time t and normalized with the mass gain at the equilibrium state.

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RESULTS AND DISCUSSION The water sorption isotherms are generally expressed as the content of water in the considered polymer as a function of water vapor activity.36 To compare different categories of ionomer systems on the basis of the affinity of their hydrophilic sites with water, we prefer to use the parameter λ that represents the number of water molecules per sulfonic site in the dry material. By referring the water sorption to this parameter, we are free from the effect of the content in sulfonic sites, which changes with the composite system. In assuming that the water sorption occurs preferentially around the highly hydrophilic ionic sites and that there is a negligible sorption elsewhere into the polymer matrix, the water sorption per sulfonic site reflects the intrinsic water sorption properties of the sulfonic-sites in their specific environment. 6334


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Table 2. Values of NDMS model parameters for λ versus activity isotherms of water vapor sorption for SPSU composites (Figure 3), Nafion composites, SPI, SLp and Lp membranes

Cp (mol/equiv)

k′

A′

R2

SPSU SPSU-1% SLP SPSU-3% SLp SPSU-5% SLp Nafion 117 Nafion-3% SLp SPI

2.72 2.86 2.89 2.97 2.28 + 1a 2.50 + 1a 4.30

0.72 0.72 0.69 0.73 0.80 0.84 0.72

3.42 3.01 3.91 5.27 16.12 23.30 14.40

0.999 0.999 0.998 0.998 0.998 0.999 0.999

Figure 2. Water vapor sorption isotherms (mass gain versus water activity) for SLp and Lp: SLP (○) and Lp (■). Experimental points (markers) and best-fit curves with NDMS model (dotted lines).

“+1” in the Cp values represents the water molecule that remains bound to the sulfonic group of the starting materials.

Table 1. Values of the NDMS Model Parameters for Mass Gain versus Activity Isotherms of Water Vapor Sorption for PSU Composites (Figure 4), SLp, and Lp (Figure 2)

sorption cycle; this quasi-chemically sorbed water molecule can only be removed at high temperatures (ca. 180 °C).7 The lower Cp value for the SPSU-based materials compared ̀ with that for Nafion-based materials can be explained by the stronger interactions of the hyperacidic fluorosulfonic sites in Nafion with water compared with those of aromatic sulfonic sites. The weaker interactions of the latter limit more the water sorption of the Langmuir-type sorption into the hydrophilic sites confined by the hydrophobic chains in the glassy hydrophilic domains of the polysulfone matrix. If we admit a value of three water molecules for the spontaneous dissociation of proton in model sulfonic acid structures determined from ab initio electronic structure calculations,38 the mean values of less than three water molecules indicate that part of the sulfonic sites in SPSUbased materials do not absorb enough water for their full dissociation, while the sulfonic sites in Nafion still have enough interaction power to absorb almost one more water molecule per site in the first hydration layer (i.e., strongly bound water on the sites) after the sulfonic dissociation. The Cp values for the composites of SLp with SPSU or with Nafion are higher than that for the pure SPSU or Nafion ionomers (Table 2). The similar trend in Cp changes for the two ionomer systems suggests similar effects of the sulfonic-grafted laponite particles on the Cp value of the glassy ionomer. At higher vapor activity, the long-range electrostatic field of the hydrated sulfonic ion pairs drives additional water molecules sorbed onto the first hydration layer of the ion pairs into subsequent layers. Although the higher values of either k′ or A′ parameters indicate both higher interactions of additional water molecules with those of the first hydration layer, a higher k′ value corresponds particularly to a stronger sorption increase at very high water activities, as it characterizes the interactions between the sorbed water molecules compared with those between water and polymer sites. Such k′ effect is mostly visible in the sorption simulation with the NDMS model (not shown) at very high penetrant activities in the external phase, while an increase in the A′ value leads mainly to a larger penetrant sorption in the intermediate range of water activities. For the SPSU-SLp (Figure 3) or the PSU- SLp (Figure 4) composites, the larger values of both A′ and k′ parameters observed for the composites with increasing SLp contents in 1−5 wt % (Table 2) or 3−5 wt % range of SLp content (Table 1) indicate larger multilayer sorption onto the sulfonic sites, at intermediate and at high water activities. Table 1 shows that the addition of SLp into PSU causes slight or moderate increases in Cp or A′ values, but significant increases in k′ values, which can be assigned to the contribution of SLp because of its high k′

membranes

Cp (g/g)

k′

A′

R2

PSU PSU-3% SLp PSU-5% SLp SLp Lp

0.0096 0.0096 0.0097 0.0722 0.0715

0.41 0.50 0.60 0.93 0.84

3.39 3.41 3.62 5.38 5.35

0.999 0.999 0.998 0.998 0.994

a

clay-lamella expansion would make it possible for more water molecules to be sorbed at high activities, where the larger sorption driving forces favor more the interactions between incoming water molecules than those between water and the sites in the clay structure (reflected by much larger increase in k′ value for SLp compared with Lp, Table 1). The sorption isotherms for SPSU-based composites and for Nafion-based composites were obtained under identical measurement conditions. All the isotherms were well fitted with the NDMS model (Figure 3). Cp values of 2.7 to 3.0 water

Figure 3. Water vapor sorption isotherms (λ versus activity) for SPSUbased composites: SPSU-5% SLp (black, ■), SPSU-3% SLp (purple, ×), SPSU-1% SLp (red, △) and SPSU (blue, ○). Experimental points (markers) and best-fit curves with NDMS model (dotted lines).

molecules per acid site corresponds to the mean number of water molecules strongly sorbed in the first hydration shell of a sulfonic acid group in a SPSU-based composites. The steady increase in Cp value with SLp contents indicates an increase in the number of water molecules that absorb on the sulfonic sites due to the dispersed laponite particles (Table 2). For the Nafion-based materials, the true Cp values are those measured in our standard measurement conditions plus one water molecule that was quasi-chemically sorbed on each sulfonic site, and was already in the materials at the beginning of the 6335


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Figure 4. Water vapor sorption isotherms (mass gain versus activity) for PSU-based composites: PSU-5%SLp (□), PSU-3%SLp (▲), and PSU (○). Experimental points (markers) and best-fit curves with NDMS model (dotted lines). Figure 5. Water vapor sorption isotherms (λ versus activity) for SPEEK-SPESc blends: SPEEK20-SPESc80 (green, □), SPEEK40SPESc60 (purple, ▲), SPEEK50-SPESc50 (orange, ×), SPEEK60SPESc40 (blue, ○), SPEEK80-SPESc20 (red, ◆) and SPEEK100SPESc0 (black, △). Experimental points (markers) and best-fit curves with NDMS model (dotted lines).

value (0.93). Apparently, by the intrinsic capacity for its sulfonic-graft sites to absorb water, SLp imparts its own water sorption power to the polymer matrix, however, in the case of SPSU-SLp composites, this effect would be partly compensated by the interactions between the sulfonic sites of laponite particles and the SPSU ionomer, which make the composite cross-linked via the laponite particles. The same effect of the sorption capacity imparted by the modified laponite particles to the composites provides a direct basis for the explanation of the improved proton conductivity for SPSU-SLp and for Nafion-SLp composites determined at high water activities or in aqueous media.15,17,18 The much higher k′ and A′ values for the Nafion-SLp composite than those for SPSU-SLp composites (Table 2) indicate a much larger gain in water sorption at medium and very high water activities for the Nafion-SLp composite compared with the SPSU-SLp composites. Such a behavior can be attributed to an easier plasticization by sorbed water molecules for less rigid Nafion matrix than for SPSU, as reflected by their respective glass transition temperature, the higher Tg value for SPSU (190 °C) than that for Nafion (125 °C) (Table 3).

Table 4. Values of the NDMS Model Parameters for λ versus Activity Isotherms of Water Vapor Sorption for SPEEKSPESc Blends of Different Compositions (Figure 5) membranes

Cp (mol/equiv)

k′

A′

R2

SPEEK0-SPESc100 SPEEK20-SPESc80 SPEEK40-SPESc60 SPEEK50-SPESc50 SPEEK60-SPESc40 SPEEK80-SPESc20 SPEEK100-SPESc0

6.66 4.42 4.13 3.81 3.34 3.09 2.60

0.46 0.59 0.62 0.64 0.67 0.70 0.77

2.54 4.95 4.32 3.68 2.80 2.79 2.77

0.998 0.999 0.999 0.999 0.999 0.998 0.999

Table 3. Tg of the Studied Membranes membranes

Tg (°C)

Nafion 117 SPEEK SPSU SPI SPESc

125 175 190 >250 265

Figure 6. Mass gain (aw = 0.1 and 0.9) and Cp values (fitted by using NDMS model) versus IEC for SPEEK-SPESc blends. Unfilled markers for mass gain (□ assigned for aw = 0.9; △ assigned for aw = 0.1) and filled markers (●) for Cp.

Study on Water Sorption Isotherms of SPEEK-SPESc blends. The isotherms of SPEEK-SPESc blends are studied with the NDMS model (Figure 5) and the fitted parameters values are shown in Table 4. A′ is the difference between the interactions of the water molecules that sorb in the successive layers and those of water molecules on the Langmuir sites (the first layer). The decrease in Cp values with the increase of the SPEEK content in the blend membrane (Table 4) can indicate a change in the space in the vicinity of the sulfonic groups that is available for water sorption (sorption capacity of each Langmuir−sulfonic site), or a decrease in the hydrophilicity of sulfonic sites. However, the latter is unlikely since the sulfonic groups are linked to aromatic rings in both the ionomer components, thus, they must have equivalent hydrophilicity. As the IEC increases with the increase in SPEEK content (due to the higher IEC for SPEEK than for SPESc), we plot in Figure 6 the Cp and water sorption extents at 0.1 and 0.95 water

activities as a function of the IEC of the ionomer blends. The steady Cp decrease with increasing IEC in the ionomer blends can be attributed to a decrease in the space available on the sulfonic site for water sorption in blends of increasing SPEEK contents. Such a change in the space available for water sorption around the sulfonic site can be explained by the absence of the bulky cardo ring in SPEEK, while it is present in SPESc polymer (Chart 1). As a consequence, the chain packing in the glassy ionomer is looser for SPESc due to steric effects of the cardo ring on the ionomer main chain, leading to a larger frozen voids around the sulfonic sites, i.e. a higher water number absorbed in the first hydration layer (Cp) without 6336


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requiring volume increase in the blends of higher SPESc contents. In a similar way, one can interpret the much larger Cp value for SPESc than that for SPEEK by the existence of larger frozen voids around the sulfonic sites in the rigid SPESc ionomer compared with those in the more flexible SPEEK ionomer. The increase in the k′ parameter value with the SPEEK content reflects an increase in the multilayer water sorption at high water activities aw. Figure 5 shows effectively a large increase, at aw > 0.95, in the water sorption in blends of IEC values larger than 1.5 mequiv/g (i.e., of SPEEK contents larger than ca. 60 wt %). Such an increase in water sorption under high water activities, while the number of water absorbed by each sulfonic group in the first hydration layer decreases, suggests an enhanced capacity of the hydrophilic domains (with sulfonic groups) to uptake water in multilayers at increasing SPEEK contents. This may be caused by the higher SPEEK chain flexibility compared with that of SPESc (the measured SPEEK Tg value, 175 °C, much lower than that of SPESc, 265 °C16) in agreement with the base-polymer Tg values given in Table 3. This makes larger local plasticization for SPEEK-richer blends at high water activities, leading to easier chain reorganization in response to the multilayer water sorption around sulfonic-bound water molecules in the first hydration layer. We will come back to this point in the next subsection. The A′ value is more related to the water molecules sorbed in the “second” hydration layer (bound to those in the first hydration) at intermediate water activities. Its maximal value at 20 wt % of SPEEK in the ionomer blends has no clear explanation. We speculate that the blend at this composition has the loosest chain structure in the hydrophilic domains around the sulfonic sites. In fact, we showed that the two ionomer components are compatible, with a unique Tg value for the blend, but the blend Tg value does not exactly obey the Flory−Fox equation.16 The negative deviation of the blend Tg from the Flory−Fox equation suggests the presence of larger free volume in the blend composition range than that given by a volume additivity law. In this case, we expect that there is a blend composition where the free space available for molecular motions achieved a maximal value that should correspond to the blend of 20 wt % of SPEEK. Hystereses in Sorption Isotherms. We studied the hysteresis phenomenon in sorption−desorption cycles for Nafion, SPSU composites, and for an aromatic copolyimide ionomer. Hystereses were observed by other researchers with both Nafion39,40 and SPEEK ionomers.41,42 However, we did not observe any significant hysteresis with Nafion samples (Figure 7) in the sorption−desorption experiments by performing differential sorption experiments (on different samples), as did Hallinan and Elabd43 who compared integral sorption data, where large-steps in water activities were used, with those where small steps were successively applied (differential sorption). They found that only integral sorptions led to isotherm hystereses. One can infer that the swelling stresses are so small under small changes in chemical potentials in differential sorption that the relatively flexible fluorocarbon segments in Nafion have enough time to reversibly relax. On the contrary, the large swelling stresses generated in integral sorption can cause relaxation of longer polymer segments, which takes longer time. Contrary to the Nafion ionomer, SPSU composites with modified laponite particles exhibited large hystereses in the sorption−desorption cycle. The water-uptake values are

Figure 7. Hystereses in water vapor sorption−desorption isotherms (λ versus activity) for SPI (purple, ■ or □), SPSU (black, ● or ○) and Nafion117 (blue, ▲ or △). Experimental points (filled markers for sorption, unfilled markers for desorption) and best-fit curves with NDMS model (solid lines for sorption, dashed lines for desorption).

significantly higher in desorption compared with those in sorption for all SPSU composites (with and without modified laponite). In fact, the desorption isotherm pattern of SPSU is very similar to those of its composites with 1, 3, and 5 wt % SLp (Figure 8). We suggest that the hysteresis in these materials is

Figure 8. Water desorption isotherms (λ versus activity) for SPSUbased composites: SPSU-5% SLp (purple, ■), SPSU-3% SLp (red, ○), SPSU-1% SLp (blue, +) and SPSU (black, ▲). Experimental points (markers) and best-fit curves with NDMS model (dotted lines).

mainly due to the sole behavior of SPSU. It is interesting to note that the hydrophobic polymer of the same base-structure (i.e., nonsulfonated PSU) showed no sorption hysteresis, whereas its composites with the same laponite starts to impart a slight deviation of the water uptake in desorption only at 5 wt % SLp (Figure 9). This behavior confirms the above suggestion, i.e., the polymer matrix imparts its sorption hysteresis to the laponite-composite systems. The hysteresis is logically clearer in hydrophilic polymers (e.g., SPSU compared with the hydrophobic one, PSU), for which the larger affinity to water of the sulfonated polymer induces larger swelling (Figure 9). Finally, the SPI ionomer, with its highly rigid backbone due to the presence of imide rings on the main chain, shows a large hysteresis in water sorption (Figure 7). Berens et al.44 and Wessling et al.45 interpreted the sorption hysteresis as the induction of new free volume sites and subsequent filling of the extra free volume during the sorption cycle. According to Rivin et al.,39 the sorption hysteresis can be 6337


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Table 5. Values of the NDMS Model Parameters for the λ versus Activity Isotherms of Water Vapor Desorption for SPSU Composites (Figure 8), Nafion 117, and SPI membranes

Cp (mol/equiv)

k′

A′

R2

SPSU SPSU-1% SLp SPSU-3% SLp SPSU-5% SLp Nafion 117 SPI

4.56 4.73 4.75 4.82 2.75 + 1a 6.62

0.56 0.58 0.54 0.58 0.75 0.64

5.22 3.99 5.27 6.09 9.20 10.10

0.994 0.996 0.994 0.992 0.999 0.998

“+1” in the Cp values represents the water molecule that remains bound to the sulfonic group of the starting materials. a

Figure 9. Hystereses in water vapor sorption−desorption isotherms (mass gain versus activity) for SPSU-5% SLp (black, ● or ○) and PSU-5% SLp (purple, ▲ or △). Experimental points (filled markers for sorption, unfilled markers for desorption) and best-fit curves with NDMS model (solid lines for sorption, dashed lines for desorption).

plasticization by water molecules penetrated into the matrix in the sorption experiments, while the reverse situation occurs in desorption (i.e., deplasticization). Macroscopically, there is a chain mobility increase by ionomer swelling beyond a certain value of water uptake (i.e., for a sufficient increase in system volume due to the free volume of absorbed water molecules). Zhao et al.49 showed an increase in the free volume of water per mole of sorbed water with the increase of λ beyond four water molecules per sulfonic site in Nafion. Li et al.31 interpreted such an increase beyond a minimum as a result of chain relaxation at the glass−rubber transition in the ionomer. However, this plasticization effect is probably localized in different ioniccluster domains depending on the ionomer structure, when the amount of penetrant (water) is high enough for their dilation to occur. If one accepts the biphasic ionomer structure in which all the absorbed water molecules are confined in the hydrophilic domains of fraction (without affecting the hydrophobic domains), then the glassy-rubber transition would occur in these domains even at a lower water content than the one calculated from the total weight fraction ww measured for water absorbed in the ionomer as a whole, and Fox−Flory’s equation50 can be modified to take into account the water confinement in the hydrophilic domains of fraction f as follows:

explained by the slow volume relaxation of the hydrophilic clusters in response to the change in vapor activity, resulting in higher swelling of membrane at a given activity. In other words, desorption of the already-absorbed penetrant occurs more rapidly than the collapse of the free volume, leaving a larger amount of free volume available for water molecules, resulting in higher water vapor concentration during desorption.44−46 Observing infrared spectrum changes for Nafion ionomer surface during drying, Nguyen and Vanderborgh47 came to the conclusion that the sorption hysteresis is due to a “skin effect” whose origin is a migration of the sulfonic acid group away from the surface during the ionomer drying. In the sorption experiments, water molecules have more limited hydration ability because of accessibility restriction to the sulfonic acid sites in the collapsed network. In the experiments of water desorption from the copolyimide ionomer and SPSU composites, we observed a significant absorbed-water amounts at zero water activity. This observation suggests that appreciable times must be required to restructure the network in the decrease of the water activity. Indeed, the glassy ionomers that contained free volumes created by water absorption at high water activity would need some time for their segments to reorganize themselves in response to a lower water activity in the external phase. The lower the water activity is, the more glassy behavior the polymer shows and the slower the chain reorganization is. Following the same trend, one can infer that the amplitude of the sorption hysteresis must be larger for polymers with more rigid backbone. Among different ionomers studied here, the order of the amplitude for the sorption hysteresis follows the order of chain rigidity decreasing based on their glass transition temperature: SPI (Tg > 250 °C48) > SPSU (Tg ∼ 190 °C) > Nafion (Tg ∼ 125 °C). The values of the NDMS model parameters for the desorption isotherms are collected in Table 5. The higher Cp values for the desorption isotherms compared with those for sorption correspond to the extra water-molecules per sulfonic group kept in the larger free volumes that remain in the matrix due to slow relaxation, as mentioned above. The above-given interpretation can also be used here for the A′ and k′ values that reflect the isotherm pattern at higher water activities. It is also interesting to note a slightly lower fitting quality for all desorption isotherms compared with that for the sorption ones, suggesting the more random nature (i.e., more scattered desorption data). This is understandable if one considers the facilitated chain reorganization that results from the ionomer

⎛ w W ⎞ 1 1 1 = w × + ⎜1 − w ⎟ × Tg f Tgw f ⎠ Tgp ⎝

(5)

where Tgw and Tgp the glass transition temperatures for water (134 K) and for the ionomer, respectively. Depending on the values of f, the calculated Tg for the hydrophilic domain can be significantly reduced compared to that calculated without taking into account the water confinement in the hydrophilic domains. The confinement of absorbed water molecules in the sole hydrophilic domain is proven and well accepted, however, whether the confinement affects only the Tg value of the hydrophilic domain or that of the entire ionomer system is not known. In fact, without the water-induced plasticization of the hydrophilic domains there would be no swelling. We showed in a previous work51 that a glassy poly(vinyl alcohol) can become highly swollen by water (0.45 g/g dry polymer) in a network after water-induced plasticization by absorbed water, whose Tg value was lowered by more than 150 °C. Such a large fall in the system Tg value obeyed well the Flory−Fox equation. Potreck et al.41 used this equation to estimate the Tg decrease in SPEEK ionomers, whose Tg values may fall below room temperatures in liquid water, even without taking into account the biphasic nature of the ionomer material. 6338


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It is worth discussing the isotherm portions after the similar Langmuir-mode part of the NDMS and Park’s model. In the latter, the Henry-mode is a limit for an isotherm model based on a statistical mechanics, i.e., with the water molecules that do not experience any effect of the other water molecules. At high concentrations, water molecules tend to form clusters inside the polymer. The tendency to form clusters of penetrant molecules is accounted in Park’s model by an equilibrium constant K for the clustering reaction and a water activity raised to the nth power, where n is assumed as the mean number of water molecules per cluster. In NDMS model, after the saturation of the Langmuir sites, the additional water molecules are absorbed sequentially in successive layers that pile up on the first layer. One of the base assumption of the NDMS model11 is that the molecules in all the layers other than the first one (on Langmuir sites) have the same partition function, or have the same heat of sorption, as those in the “matrix” (i.e., the hydrophilic domains outside the first hydration layer). The NDMS model parameters are shared into two terms for the entire water activity range, but affect differently the water uptake according to the target water activity. Under the assumption of preferential water sorption into hydrophilic domains of the ionomer biphasic structure, k′ and A′ parameters affect more the isotherm portion related to the multilayer sorption onto the first hydration layer, i.e., to the water molecule−molecule interaction, or water molecular cluster−cluster interaction in a polymer. This effect is wellknown and has been attributed to self-hydrogen bonding clustering of water molecules. Zimm and Lundberg52 have developed a method to analyze water clustering from the experimental isotherms. The clustering function G11/v1̅ considers the statistical molecular distribution in the polymer component and water in the system: ⎡ aw ⎢ ∂ φw G11 = −φp⎢ v1 ⎢ ∂aw ⎣

( ) ⎤⎥⎥

⎥ ⎦ p,T

Figure 10. G11/v1̅ calculated with values of NDMS parameters fitted from the isotherms of water vapor sorption for SPSU (dotted line) and Nafion 117 (solid line).

The quantity of (φwG11/ v1) is the mean number of penetrant molecular in the neighborhood of a given molecule in excess of the mean concentration of penetrant in the polymer. Thus, the mean cluster size (MCS) can be evaluated by MCS = 1 +

φwG11 v1

(8)

The combination of eqs 7 and 8 gives a general expression of (MCS − 1) or φwG11/v1̅ as a function of aw: MCS − 1 =

φwG11 v1

⎛ C ⎞ ⎟ = −⎜ ⎝1 + C ⎠

⎧ ⎤ ⎪⎛ 1 ⎞ ⎡⎢ −2(A′ − 1) × k′aw + A′ − 2 ⎥ ⎜ ⎟ × 1 ×⎨ + ⎪ CpA′ ⎦⎥ ⎩⎝ 1 + C ⎠ ⎣⎢ ⎫ ⎪ ⎬ + 1⎪ ⎭

−1

(9)

The plots of (MCS − 1) versus water activity for SPSU and its composites with 1, 3, and 5 wt % of SLp (Figure 11) show practically the same mean cluster size for the water activities exceeding ∼0.7, which reaches a value of ca. 1 when aw is close to 1. We find here again the prevailing role of SPSU in the behavior of the water sorption isotherm in SPSU composites.

(6)

where aw and φw are the activity and the volume fraction of component 1 (water), respectively, and φp is the volume fraction of component 2 (polymer), with φp = 1 − φw. By deducing from NDMS (eq 1) and eq 6, G11/ v1 can be expressed as ⎛ 1 ⎞ ⎡ −2(A′ − 1) × k′aw + A′ − 2 G11 ⎟ × ⎢ = −⎜ ⎝ 1 + C ⎠ ⎢⎣ v1 CpA′ ⎤ + 1⎥ − 1 ⎥⎦

(7)

where C is the penetrant concentration (in m3 water/m3 polymer, its expression is shown by eq 1) and Cp has the same unit as C. G11/ v1 > −1 indicates that the water concentration is greater than the average in the vicinity of a given water molecule, which denotes the nonrandom distribution of water molecules (clustering). Figure 10 shows clearly that water molecules tend to cluster more and more in Nafion 117 and SPSU ionomers when the water activity increases beyond a value of ca. 0.6 (Figure 10).

Figure 11. (MCS − 1) calculated with values of NDMS parameters fitted from the isotherms of water vapor sorption for SPSU-based composites: SPSU (black, solid line), SPSU-1% SLp (purple, dashed line), SPSU-3% SLp (blue, dashed line), and SPSU-5% SLp (red, dashed line). 6339


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al.30) dominant region at lower activities and the clustering dominant region at higher activities. The increase of D at lower activities can be explained by the double sorption mode: first, some water molecules are sorbed on hydrophilic sites or at the surface of the micro cavities (these sorbed molecules have limited mobility); then, more water molecules dissolve and diffuse in the matrix (the population of these molecules increases with aw and thus facilitates diffusion). The decrease of D at higher activities is likely due to the association into largesize clusters by hydrogen bonding of the water molecules, which have to be dissociated to migrate in the matrix. The presence of nanoclays induces a change in diffusion pathways so that water molecules can diffuse more easily in clay−SPSU interfacial areas, which explains the increase of the apparent diffusion coefficient in the “simple dual mode dominant” range at lower activities. However, this enhancement is not observable in the “clustering dominant” range at higher activities. This is because the larger-size water clusters having slower dynamics govern water molecule diffusion and the influence of SLp content is so negligible. On the basis of the above-analyzed Tg changes that may accompany water sorption, we attribute such an increase in water molecular clustering in the ionomers with the water activity by an increase in water absorption that plasticizes more and more the hydrophilic domains, making easier and easier the water clustering in the increasingly deformable matrix. The MCS values at high water activities for different ionomer structures, especially the SPEEK-SPESc blends, can be interpreted on the same basis; i.e., the more rigid the ionomer chains at a fixed temperature, the less they can be plasticized at fixed water activity and the higher the water activity required for the chains to be plasticized. The same order of the ionomers according to their decreasing MCS value calculated at unit water activity (Table 7) as that of increasing Tg value (Table 3)

It is well-known that for systems in which clustering occurs without significant plasticization of the matrix, the effective diffusion coefficient calculated from the sorption kinetics show a decreasing trend with increasing water activity. The study of sorption kinetics will be helpful to valid our analysis with eq 9. In previous works,18 the sorption kinetics of the SPSU-based composites was studied. D and D′ were found almost equal, which indicates that there was no significant plasticization. In the current work, only the D values will be presented for discussion. Figure 12 shows that D increases with aw at low activities; D reaches the maximum at activities near 0.5 or 0.6 (named as

Figure 12. Diffusion coefficients determined from sorption kinetics for SPU-based composites: SPSU (black, ×), SPSU-1% SLp (red, □), SPSU-3% SLp (blue, ○), and SPSU-5% SLp (purple, △).

aw_max); then, D decreases with aw at high activities. The aw_max values were determined from the data shown in Figure 12, and presented in Table 6. The activity values corresponding to the Table 6. Correlations between aw_onset and aw_max membranes

aw_onset

aw_maxa

SPSU SPSU-1%SLp SPSU-3%SLp SPSU-5%SLp

0.58 0.58 0.60 0.67

0.5 0.6 0.5 0.5

Table 7. MCS (aw = 1) Calculated with Values of NDMS Model Parameters from the Fitted Isotherms of Water Vapor Sorption for Nafion 117, SPSU, SPEEK, SPI, and SPESc

a

The maximal measurement step of water activity for studying sorption kinetics was taken by every 0.1, so the uncertainty for the determination of aw_max is ±0.1.

starting of clustering of water molecules (named as aw_onset), were determined from Figure 11 and also added into Table 6 for comparison. These results show that the aw_max coincide approximately with the aw_onset in the cases of SPSU and its composites with SLp except for the one with highest SLp content (SPSU-5%SLp). The deviation in the MCS behavior as a function of the water activity for the composite with 5 wt % SLp content, may correspond to the content at which the composites become more heterogeneous due to SLp aggregates. It should be noted that D values were determined in the transient regimes of sorption between two values of water activities while the MCS values correspond to equilibria at precise water activity values. In spite of this difference, it is very comforting to notice the close water activity values for the onset of clustering and the maximum value of the apparent diffusion obtained with the composite materials. One can easily deduce that beyond the water activity value for the clustering onset, the increasing size of water aggregates hinders water diffusion. As suggested by Stannett et al.,29 Figure 11 can be divided into two parts, the simple dual mode (named by Ranade et

membranes

MCS (for aw = 1)

Nafion 117 SPEEK SPSU SPI SPESc

2.08 1.85 1.81 1.31 1.02

suggests that the ionomer with more rigid chains is less plasticized, i.e., less able to dilate for accommodating larger clusters, the low MCS values (smaller than 2.08) for all the studied ionomers indicate the strong limitation of the material dilation, which can be attributed to the presence of the hydrophobic domains. In the series of SPEEK-SPESc blends of different compositions, the maximal (MCS − 1) value increases with the SPEEK content, i.e., the content in the more flexible ionomers (Figure 13). For copolyimides, there were no precise values given in the literature due to their thermal degradation temperature starting at 250 °C, which is usually lower than their glass transition temperature. The MCS value significantly larger than one was obtained for our SPEEK sample; however, Potreck et al.41 showed that the water molecules in their SPEEK films remain isolated in the quasi-entire water activity range, and that the cluster formation did not influence the 6340


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The sorption hysteresis gave an idea about the amplitude of the deviations from the theoretical equilibrium state at the Langmuir sites in the desorption experiments at low water activities and eventually about the glass−rubber transition in the materials at high water activities. During the desorption run, the more rigid is the ionomer chains, the less the dilated ionomer structure relaxes at high water activities, leading to more ample hysteresis; the sequence of increasing chain rigidity is the same as that of increasing hysteresis: Nafion 117 < SPSU < SPI. Similarly, the plasticization extent that is revealed by the calculated mean cluster size at the highest water activity has the same the same sequence as the chain flexibility: Nafion 117 > SPEEK > SPSU > SPI (or SPESc).

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Figure 13. (MCS − 1) calculated with values of NDMS model parameters fitted from the isotherms of water vapor sorption for SPEEK-SPESc blends: SPEEK100-SPESc0 (black, solid line), SPEEK80-SPESc20 (black, dashed line), SPEEK60-SPESc40 (orange, dotted line), SPEEK50-SPESc50 (blue, dashed line), SPEEK40SPESc60 (black, dotted line) and SPEEK20-SPESc80 (purple, dashed line).

ASSOCIATED CONTENT

S Supporting Information *

Characteristics of the basic materials studied in the current work. This material is available free of charge via the Internet at http://pubs.acs.org.

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sorption kinetics of water vapor molecules in the SPEEK films. The Tg value, which is a macroscopic measure, may not take into account all the subtle changes in the systems involved in water sorption into ionomers. Finally, we would like to emphasize that our paper is focused on the macroscopic aspect of the water sorption in ionomers, where the behaviors are analyzed in the “mean field sense”. In fact, the situation is very complex on the microscopic scale,53 in which water molecules can be in many different states, i.e., in equilibrium or in nonequilibrium between each other, depending on time, structure of the ionomers, temperature, and local water content. In our opinion, the water uptakes obtained in our gravimetric determination represent situations approximately close to the thermodynamic equilibrium state, but the departure from the equilibrium state depends on the systems and their history in sorption.

AUTHOR INFORMATION

Corresponding Author

*(Y.L.) E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Smith, B.; Sridhar, S.; Khan, A. A. J. Membr. Sci. 2005, 259, 10− 26. (2) Helfferich, F. G. Ion Exchange; McGraw-Hill: New York, 1962. (3) Tant, M. R.; Mauritz, K. A.; Wilkes, G. L. Ionomers: synthesis, structure, properties and elasticity; Chapman and Hall: London, 1997. (4) Eisenberg, A.; Kim, J. S. Introduction to ionomers; John Wiley and Sons: New York, 1998. (5) Bass, M.; Freger, V. Polymer 2008, 49, 497−506. (6) Mauritz, K. A.; Moore, R. B. Chem. Rev. 2004, 104, 4535−4585. (7) Escoubes, M.; Pineri, M. In Structure and properties of ionomers; Pineri, M., Eisenberg, A., Eds.; Reidel Publishing Co.: Dordrecht, The Netherlands, 1987; p 341. (8) Masclaux, C.; Gouanvé, F.; Espuche, E. J. Membr. Sci. 2010, 363, 221−231. (9) Belbekhouche, S.; Bras, J.; Siqueira, G.; Chappey, C.; Lebrun, L.; Khelifi, B.; Marais, S.; Dufresne, A. Carbohyd. Polym. 2011, 83, 1740− 1748. (10) Furmaniak, S.; Terzyk, A. P.; Gołembiewski, R.; Gauden, P. A.; Czepirski, L. Food Res. Int. 2009, 42, 1203−1214. (11) Feng, H. Polymer 2007, 48, 2988−3002. (12) Li, Y.; Nguyen, Q. T.; Lixon-Buquet, C.; Marais, S. IET Nanobiotechnol. 2014, 8, 51−58. (13) Zaidi, S. M. J. In Polymer Membranes for Fuel Cells; Zaidi, S. M. J., Matsuura, T., Eds.; Springer: New York, 2009; Chapter 2, p 7. (14) Sharma, S.; Mohanty, K. In Membrane Technologies and Application; Mohanty, K., Purkait, M. K., Eds.; CRC Press: Boca Raton, FL, 2011; Chapter 25, p 461. (15) Bébin, P.; Caravanier, M.; Galiano, H. J. Membr. Sci. 2006, 278, 35−42. (16) Li, Y.; Nguyen, Q. T.; Lixon-Buquet, C.; Schaetzel, P.; Colasse, L.; Marais, S. Electrochim. Acta 2013, 111, 419−433. (17) Fatyeyeva, K.; Chappey, C.; Poncin-Epaillard, F.; Langevin, D.; Valleton, J. M.; Marais, S. J. Membr. Sci. 2011, 369, 155−166. (18) Lixon-Buquet, C.; Fatyeyeva, K.; Poncin-Epaillard, F.; Schaetzel, P.; Dargent, E.; Langevin, D.; Nguyen, Q. T.; Marais, S. J. Membr. Sci. 2010, 351, 1−10. (19) Brunauer, S.; Emmett, P. H.; Teller, E. J. Am. Chem. Soc. 1938, 60, 309−319.

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CONCLUSION The NDMS model was proved to be highly suitable for sigmoidal isotherm fittings and convenient to account for the behavior of ionomer composites in the water sorption and desorption. The Cp value, which characterized the sorption capacity in the microvoid region in the original model, gives here the mean number of water molecules in the first hydration layer of the sulfonic groups, the hydrophilic sites of the ionomers or its composites. We found that (i) the k′ parameter gives the tendency for water (penetrant) molecules to cluster together at very high water activities, and (ii) the A′ value gives the affinity of the penetrant to the hydrophilic domain of the ionomer, beyond the first hydration layer, in the intermediate water activity range. The values of these three parameters depend on the rigidity of the ionomer segments/chains. The lower the rigidity, which determines the space readily available for the water absorption without requiring energy for volume dilation, the larger the mean number of the sulfonic-sorbed water molecules in the first hydration layer. The higher rigidity of the chains in the hydrophilic domain also makes it more difficult for the hydrophilic-domain to dilate and accommodate incoming water molecules at higher water activities. The magnitude of the A′ reflects such an ionomer dilatability (after Langmuir void filling) under the osmotic stress due to the change in water activity. 6341


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