Structure and Acoustic Properties of Hydrated Nafion Membranes

Jul 2, 2009 - A. Moro 2, I-00185, Roma, Italy, and Dipartimento di Fisica, Università di Perugia, I-06123 Perugia, Italy. J. Phys. ... Copyright © 2...
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J. Phys. Chem. B 2009, 113, 10121–10127

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Structure and Acoustic Properties of Hydrated Nafion Membranes M. Plazanet,*,†,‡ P. Bartolini,† R. Torre,† C. Petrillo,§ and F. Sacchetti§ European Laboratory for Non-Linear Spectroscopy and Dipartimento di Fisica, UniV. di Firenze, Via N. Carrara 1, I-50019 Sesto Fiorentino, Firenze, Italy, INFM-CRS-Soft Matter (CNR), c/o UniV. la Sapienza, Piaz. A. Moro 2, I-00185, Roma, Italy, and Dipartimento di Fisica, UniVersita` di Perugia, I-06123 Perugia, Italy ReceiVed: February 16, 2009; ReVised Manuscript ReceiVed: June 6, 2009

The propagation of acoustic waves in water-hydrated Nafion membrane has been monitored using heterodyne-detected transient grating spectroscopy. At room temperature, upon increasing the water content, the speed of sound drops to a value lower than the respective velocities of sound in pure Nafion and pure water. This counterintuitive effect can be explained by a simple calculation of the sound velocity in an effective medium made of water and Nafion polymer. Upon cooling, a phase separation occurs in the sample, and the formation of ice is observed (M. Pineri et al. J. Power Sources 2007, 172, 587-596). This phase transition is characterized via a second acoustic wave observed in the signal. Sound propagation and X-ray diffraction confirm the formation of crystalline ice on the membrane surface, that reversibly melts upon heating. The amount of ice that forms in the sample is monitored as a function of temperature and represents an order parameter for the transition. This parameter follows a power law with an exponent of 0.5, indicating the critical nature of the observed process. Introduction The confinement of a liquid into a small volume increases the surface/volume ratio and prevents the growth of correlation lengths, eventually leading to the modification of the properties of the liquid:1 shift of the melting point, slowing down of the dynamics, different structural organization... These phenomena, together with the development of well characterized porous solids, stimulated in the past decade an increasing number of studies on the properties of confined liquids. Most model systems used for this kind of studies are rigid matrixes filled with the liquid,2 such as porous silicate glasses (Vycor, MCM, or SBA). Other classes of materials provide soft confinement, like for example micelles that contain liquid droplets in the center3 or polymeric matrixes in which small volumes of liquid are trapped.4,5 Among liquids, water has a special place, due to its numerous anomalies and its omnipresence on Earth. Water is confined in numerous materials, such as clays, proteins, emulsions, and so forth, and its hydrogen bond network is strongly influenced by the hydrophilic or hydrophobic nature of the surface. In hydrophilic confinement, the mobility of water is reduced, mainly because of the presence of the immobile surface.6 The melting point is decreased when the confinement radius decreases, and the preferred crystal phase becomes cubic rather than hexagonal.2 The physics of water, still debated in bulk, becomes even more complex in a confined environment. The system investigated in the present study is a waterhydrated Nafion7 membrane. Nafion, which belongs to the family of perfluorosulfonated membranes, is a material with many potential applications on account of its ability to absorb * To whom correspondence should be addressed. E-mail: marie.plazanet@ ujf-grenoble.fr. † LENS and INFM. ‡ Current address: Laboratoire de Spectrometrie Physique, Universite Joseph Fourier et CNRS- UMR 5588, BP87, 38402 Saint Martin d’Heres Cx, France. § Universita` di Perugia and INFM.

a large quantity of water.8 The high water conductivity makes it a suitable material for fuel cells;9 the hydrophilic properties enable its use as an easily regenerative drying agent;10 surrounded by a metallic coating, the ionic displacements provide, under an electric field, controlled bending of the membrane, giving promising applications for artificial muscles.11 The polymer, that is the ionic form of the polytetrafluoroethylene (PTFE, Teflon), is a copolymer of tetrafluoroethylene and sulfonyl fluoride vinyl ether. The hydrophobic fluorocarbon backbone has regularly spaced hydrophilic ionic sulfonate groups (SO3- pending chains). These antagonistic properties lead to a material made of discrete regions, either formed by the polytetrafluoroethylene polymer or by the clustering of the ionic groups. In the presence of water, the hydrophilic clusters are readily saturated by water, which is confined in spheres of diameters varying from 20 to 60 Å. Upon increasing the water content, the water cavities swell and eventually percolate, forming water cylinders connecting the cavities.12,13 Many studies have been conducted on Nafion, and in particular, extensive studies were carried out on the structure and conductivity of water or mechanical properties.8,14 The microscopic dynamics of water in the membrane have been investigated by incoherent inelastic neutron scattering,15 while its collective dynamics, i.e., the acoustic propagation at high frequency (subnanometer length scale), has been studied by coherent inelastic neutron scattering.16 In the present work, we characterize the propagation of a longitudinal acoustic wave in the hydrated membrane using optical transient grating spectroscopy. We probe the system with an acoustic wavelength of a few micrometers, much longer than the nanometer inhomogeneities of the water/polymer system. The wave is therefore mainly sensitive to the average density and bulk/shear moduli of the water+Nafion system. After the technical description of materials and methods, we present in the first part measurements performed as a function of hydration at room temperature. The results are analyzed in terms of effective media. In the second part, we investigate the

10.1021/jp901406v CCC: $40.75  2009 American Chemical Society Published on Web 07/02/2009

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behavior of a fully hydrated sample in the temperature range 238-300 K. Below 271 K, the formation of ice is observed as the temperature decreases. The technique enables the phase transition to be followed and essential features to be characterized. Materials and Methods Samples. Nafion 112 was bought from Ion Power Inc. (USA). The membranes have an equivalent weight of 1100 (g of membrane/mol of sulfonic groups) and a thickness of 54 µm. The membranes were first cut into 10 mm diameter pieces, and treated according to the following procedure. Impurities were removed by boiling in a 3% H2O2 solution and rinsing with deionized water. In order to remove possible cations (K+, Na+) occupying the SO3- sites, the membranes were boiled in 0.5 M H2SO4 for 1 h and rinsed again. The sample was then sonicated for 2 h in a 50% ethanol solution to remove small polymers and fragments which remained from the synthesis. Finally, it was boiled three times for 1 h in H2O.17,18 The fully hydrated membranes were boiled in H2O for 15 min and immediately placed in the closed sample holder. By weighing the sample, it was found that the fully hydrated membrane contains about 0.5 g of H2O/g of dry membrane, corresponding to about 30 molecules of water per sulfonic group. This value is higher than previously obtained in other works (0.22 g/g19 or 0.36 g/g18). Nevertheless, as we will see in the next sections, no bulk water is present in the sample. This increased water content could be explained by the different treatment of the membrane or the higher temperature at which it was hydrated. D2O hydrated samples were obtained by soaking the membranes several times in D2O for a few hours. Lower hydration levels and dry samples are produced by pumping the water out. In this way, all of the water is removed except one molecule per sulfonic group.18,20 This corresponds to 0.016 g of H2O/g of dry membrane. The water content was determined by weighting of the samples; the total error on its determination was about (0.01 g of H2O/g of dry membrane. For the measurements, an adequate thickness is required and 10 layers were squeezed between optical quartz windows. Each layer is made of a 1 cm diameter sheet. The plane of the membranes was placed perpendicular to the optical axis; in this configuration, the sound wave propagates along the sheets. The stacking of the layers did not affect the sound propagation. Methods. HD-TG. The setup and principles of heterodynedetected transient grating (HD-TG), a four-wave mixing technique, have been described elsewhere in detail.21 The interference of two 20 ps pulses (1064 nm) creates in the sample a refractive index grating, due to light induced temperature and density variations. The density grating represents a standing acoustic wave, of wave vector Q defined by the wavelength of and angle between the excitation pulses: Q ) (4π/λ) sin(Θex). The grating is then probed at the angle that satisfies the phase matching condition. The time-resolved intensity of the diffracted probe monitors the characteristics (frequency and damping) of the photoinduced longitudinal sound wave. On a longer time scale, the thermal grating relaxes according to the thermal diffusivity of the material. Unless specified, the measurements have been performed at a momentum transfer of Q ) 1 µm-1, and the Q-dependence, when investigated, was measured at 0.6, 1, 1.4, 1.8, 2.1, and 2.5 µm-1. The analysis of the HD-TG signal was treated using the simplest solutions of the generalized hydrodynamic equations introduced by Yang et al.,22 also reanalyzed by Torre et al.21 This hydrodynamic model describes the HD-TG response function as

Plazanet et al.

R(t) ) A(e-ΓTt - e-Γt cos(ωt)) + Be-Γt sin(ωt)

(1)

where Γ and ω are the damping rate and frequency of the sound wave and ΓT is the thermal damping rate. The two oscillating terms account for the electrostrictive effect (sine) and thermal expansion (cosine) generating the acoustic wave, while the third term relates to the decay of the thermal grating. The fit of HDTG data enables the extraction of several parameters related to the acoustic propagation (sound velocity, c ) ω/Q, and damping rate, Γ), and the thermal diffusivity (χ ) ΓT/Q2). Due to the heterodyne detection, the signal-to-noise ratio is very high, and the data can be fitted with very good precision. The main source of errors in the data arises from the reproducibility of the measurements. For that reason, measurements were performed several times and all points are plotted on the figures, giving an estimation of the error bars. Brillouin. Brillouin scattering is, in the frequency domain, an analogous technique to the transient grating, and provides therefore directly comparable information. The Brillouin setup23 was used in near-backscattering configuration: the signal was measured at 174°, at a wavelength of λ ) 532 nm. The momentum transfer Q ) (4πn/λ) sin(Θ) depends on the refractive index (n) of the sample and was equal to 23.5 µm-1 in our measurements. All Brillouin measurements were performed at room temperature. In Figure 1, we present both the time-resolved HD-TG decay (top) and the frequency Brillouin spectrum (bottom), measured on 10 layers of fully hydrated Nafion. X-ray Diffraction. The X-ray diffraction data were recorded on a laboratory diffractometer using the radiation of the Cu kR (1.5418 Å). A clean incoming beam was obtained using a pyrolitic graphite monochromator which prevents the presence of the kβ line in the beam. Higher order wavelength contamination was avoided by the use of a scintillation detector having adequate energy resolution. The membranes were piled up as for the optical measurements (only six layers were used) and squeezed between two microscope coverslips of 120 µm thickness each. No background correction has been performed, as the signal arising from the sample, Nafion or ice, can be clearly distinguished from the glass signal. Elastic Moduli and Sound Velocity. For the convenience of the reader, we report here some basic definitions and relations between the various moduli that define the elastic properties of the solid (fluid). The different variables are the Young or tensile modulus Y, the Bulk modulus K, that is the inverse of the compressibility, the Shear modulus G that vanishes in a liquid, the Poisson ratio ν, the density F, and the longitudinal sound velocity c. These quantities are related as follows:

K)

Y , 3(1 - 2ν)

G)

Y , 2(1 + ν)

c)

 K +F4/3G

Sound Velocity upon Swelling of the Membrane At room temperature, we measured the longitudinal sound velocity in the membrane as a function of hydration. The sound wave was characterized at various hydration levels from 0.016 to 0.5 g of H2O/g of dry membrane. We observe a decrease of the sound velocity upon swelling of the membrane, from 1735 to 1345 ( 10 m/s. As the sound velocity in pure water is 1480 m/s, the values measured here are not limited by the speed of sound in pure water on one side and in the dry membrane on the other side. This counterintuitive behavior is however qualitatively easily explained: droplets in a non-miscible matrix, of respective densities F1 and F2 and compressibilities β1 and

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Figure 1. Measurement of acoustic wave in hydrated Nafion at room temperature: (top) in time domain using HD-TG at Q ) 1 µm-1; (bottom) in frequency domain with Brillouin scattering at Q ) 23.5 µm-1 (peaks at 7.1 GHz).

β2, with F1 > F2 and β1 < β2, can lead to such an effect in the sound velocity, c ) 1/(βF)1/2. In our study, we probe the system at a wavelength (∼µm) much longer than the heterogeneities of the sample (cavities e60 Å12). We are therefore sensitive to averaged properties of the composite material, in which the sound velocity can be calculated in an effective medium approximation. We perform the calculation of the sound velocity using the Maxwell-type approximation24 to first calculate the effective elastic moduli. For 3D spherical inclusions of bulk modulus K2 and shear modulus G2, in a matrix of bulk modulus K1 and shear modulus G1, the following expressions for the elastic moduli of the effective medium hold:

Ke - K1 K2 - K1 )φ 4 4 Ke + G1 K2 + G1 3 3

(2)

Ge - G1 G2 - G1 )φ Ge + H1 G2 + H1

(3)

and

Figure 2. Calculation of tensile modulus for an effective medium (Maxwell approximation) of spherical water inclusions in Nafion membrane. Solid line: experimental data from ref 25. Dashed line: FNafion ) 2.15, YNafion ) 237 MPa, ν ) 0.487.

Figure 3. Velocity of the longitudinal acoustic wave propagating in the membrane as a function of water content. Squares are experimental points. The calculations are performed for an effective medium (Maxwell approximation) of spherical water inclusions in the Nafion membrane. Dashed line: FNafion ) 2.15, YNafion ) 237 MPa, ν ) 0.487. Solid line: same parameters but with ν ) 0.493.

Y(0) ) 237 MPa for the tensile modulus of the pure polymer and ν ) 0.487 for the Poisson ratio, from which we deduced K1 and G1. This approach, or other more sophisticated approaches, was already used to compute the moduli of hydrated membranes.26-28 The density of the effective media formed by the inclusions of density F2 in the matrix of density F1 is

Fe ) (1 - φ)F1 + φF2

(6)

with and the longitudinal sound velocity is therefore given by

3 4 G1 K1 + G1 Y1 2 3 9 (1 - 2ν) H1 ) ) + K1 + 2G1 (4 - 5ν) 4 (1 + ν)

[

]

(

)

c)

(4) where φ is the volume fraction of the inclusion. The calculation of the bulk modulus of hydrated Nafion as a function of water content φ is compared with previous experimental measurements of the tensile modulus of the membrane.25 In this former study, the tensile modulus was found to follow the empirical behavior:

( (

Y(f) ) Y0 exp -R f +

1200 - EW 20

))

(5)

where Y0 ) 275 MPa is the tensile modulus, EW the equivalent weight, R ) 0.0294, and f ) 100∆m, where ∆m is the fractional weight change per 100 g of dry membrane. This empirical function is plotted in Figure 2, and is well represented by calculation using eqs 2 and 3. We used the values ENafion )



Ke + 4/3Ge Fe

(7)

Although the calculation of the tensile modulus was in good agreement with the experimental data from ref 25, the computation of the sound velocity (using the density of Nafion, F1 ) 2.15) does not reproduce our measurements (see dotted line in Figure 3). The sound velocity of 1735 m/s in dry Nafion implies a higher bulk modulus or Poisson’s ratio. A much better agreement is found in taking the Poisson ratio of 0.493, leading to a small decrease of the shear modulus G1 but an incease by a factor of 1.8 for the bulk modulus K1. This higher value can be assigned to the frequency dependence of the bulk modulus. Previous measurements25 probably used mechanical ways of measuring the tensile modulus and therefore probed a low frequency region, while the present study provides data in the GHz frequency range. The different curves are reported in Figure 3 together with our experimental data.

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Plazanet et al. fully hydrated sample was fitted in order to match the sound velocity obtained from the HD-TG data. The obtained value of 1.41 is in reasonable agreement with the refractive index of Teflon (1.29-1.38) and that of water (1.33, the Nafion is invisible in water). Moreover, the variation of the sound velocity between a fully hydrated and a dry sample is in agreement with the HD-TG measurements. It therefore fully confirms the variation of sound velocity with the water content in the Nafion membrane.

Figure 4. Brillouin spectra measured as a function of hydration in swollen Nafion. Hydration decreases from bottom to top. Pure water is reported at the bottom.

Figure 5. Variation of the Brillouin peak shift measured as a function of hydration. The corresponding sound velocity is calculated using n ) 1.41, and the error bars account for 10% variation in n.

The hydration of the membrane with heavy water leads to a decrease of the sound velocity, at full hydration, of about 30 m/s. This is in agreement with the prediction given by the previously described calculation, taking into account the density of D2O. Over a Q range varying between 0.6 and 2.5 µm-1, the sound velocity of the membrane slowly increases with Q, by 2.6 and 3.5% for the fully hydrated and dry membranes respectively. The damping of the acoustic wave increases by a factor of 2 from the hydrated to the dry membrane. Over the Q range investigated, the damping increases with Q as Q1.5, instead of the hydrodynamic prediction of Q2. Such a behavior has already been observed in porous silica glasses filled with CCl4 but could not be described by existing theories.29 The result could however be empirically interpreted by assuming an additional damping due to the scattering at the water boundaries. This disorder induced damping can be reasonably assumed to be proportional to Q, since the inverse of the wavelength is a measure of the number of boundaries interacting with the propagating wave. The total damping trend therefore is intermediate between Q1 and Q2, e.g., Q1.5. Brillouin Measurements. Brillouin spectra have also been measured as a function of hydration. Starting from a fully hydrated system, the water was simply pumped out of the sample while spectra were recorded. The spectra are shown in Figure 4, and for comparison, the spectrum of pure water is reported at the bottom. Although the signal-to-noise ratio in the spectra decreases as the sample dries, the increase of sound velocity is clearly indicated by an increase of the Brillouin shift, from 7.1 to 9 GHz. The small peaks at 5.5 GHz are assigned to an instrumental artifact, which is more pronounced when the signal gets very low (very low hydration). The variation of peak shift, directly related to the variation of the sound velocity, is plotted in Figure 5. The determination of the sound velocity depends, with this technique, on the knowledge of the refractive index. The refractive index of the

Water Behavior upon Cooling As mentioned in the Introduction, confinement prevents the growth of the correlation length, and is therefore expected to affect the phase transitions of the included water. The most obvious effect is that crystallization is prevented at least over a given temperature range. The melting point of the confined liquid is lowered with decreasing pore size, a well calibrated behavior that is used in thermo-porometry. Concerning the behavior of Nafion membranes, few studies have been conducted below 0 °C. Among them, calorimetric studies30-32 have shown that the melting of water spans a large temperature range, from -228 to nearly 273 K. Escoubes et al.30 assigned the peaks observed in calorimetry, upon heating, to water adsorption into the membrane, due to mechanical deformation of the polymer. These authors also observed, using NMR,31 a decrease of the number of mobile protons with the decrease of temperature. The same group recently completed the picture by performing X-ray microdiffraction analysis,34 showing that crystalline ice is formed outside of the membrane. With their experimental setup, the water migrates toward the coldest point to form ice crystallites. In this work, we present an investigation of the phase separation by monitoring the propagation of the longitudinal acoustic wave between 238 and 300 K, using the HD-TG technique. Reversible Phase Separation and Ice Formation. TG measurements were performed as a function of temperature, in order to investigate the behavior of water in the membrane below 0 °C. The sample was fully hydrated, and measurements were performed upon either cooling or heating. The cooling rate, in all experiments, was about 1°/min between two measurement points, at distances of 2 or 5°. It was checked that the sample had reached equilibrium before each measurement. The lower the temperature, the longer the equilibration takes (tens of minutes at 240 K). Because of the phase separation, below 267 K, distinct acoustic waves are observed for the Nafion matrix and ice crystallites, and give rise to two components in the signal. The data are therefore fitted with the following function:

R(t) ) A1(e-ΓT1t - e-Γ1t cos(ω1t)) + B1e-Γ1t sin(ω1t) + A2(e-ΓT2t - e-Γ2t cos(ω2t)) + B2e-Γ2t sin(ω2t) (8) Sound Velocity. The velocity of the new acoustic mode is ∼3840 m/s at 265 K, and increases upon cooling. The acoustic nature of the mode was established by changing Q to 0.63 µm-1 and obtaining the same velocity. This velocity is to be compared with the one of bulk ice, 3980 m/s. In parallel, the sound wave propagating in the Nafion matrix is observed; the temperature dependence of sound velocity changes slope without discontinuity. These phenomena are reversible upon heating, and only a small hysteresis can be observed in the temperature dependence of the sound velocity of the slow wave. The variation of sound

Structure and Acoustic Properties of Hydrated Nafion

Figure 6. Sound velocity of the two acoustic modes observed upon cooling the fully hydrated Nafion membrane (top, fast wave; bottom, slow wave). In the bottom panel is also reported (circles) the sound velocity of the single mode observed on a partially hydrated sample.

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Figure 8. Thermal diffusivity associated with the two components of the signal: (top) component associated with the fast acoustic mode; (bottom) component associated with the slow acoustic mode.

Figure 7. Damping of the acoustic waves in the fully hydrated Nafion membrane as a function of temperature: (top) damping associated with the fast mode; (bottom) damping of the slow mode.

velocity as a function of temperature for the two modes is represented in Figure 6. Sound Damping. At room temperature, the acoustic mode in hydrated Nafion is about 10 times more strongly damped than the sound in pure water. This was already observed in porous materials such as Vycor,29 where the heterogeneities of the sample, although much smaller than the wavelength, damp the acoustic wave. The damping of this mode is found to be fairly independent of temperature, down to 267 K, and exhibits a stronger temperature dependence below this point, when the water is expelled from the membrane. The damping of sound in the ice crystallites is smaller, as expected for an elastic solid like ice. Upon heating, the damping drastically increases as the component vanishes, an effect that is assigned to the reduction of the spatial extension of the crystallites. This is illustrated in Figure 7. Thermal DiffusiWity. Eventually, we report in Figure 8 the thermal diffusivity associated with the two components of the signal. The value extracted from the slow mode is close to the thermal diffusivity of water (0.13 mm2/s at 280 K), and the one associated with the fast one is close to the thermal diffusivity of ice: 1.27 and 1.48 mm2/s at 260 and 240 K, respectively. For the slow mode, an important perturbation is observed upon heating around 270 K, when the component vanishes, while, for the fast mode, two temperature regimes are observed, below and above 260 K. Structure. To confirm the formation of ice and determine the nature of the phase obtained, we performed X-ray diffraction as a function of temperature and time on a similar (six-layer)

Figure 9. Diffraction pattern of a fully hydrated sample measured by X-ray diffraction at λ ) 1.54 Å. The sample is first cooled to 267 K, several patterns are recorded, then down to 255 K, and heated to 273 K. One full spectrum is recorded in ∼30 min.

sample. The results are shown in Figure 9. Below 267 K, Bragg peaks appear in the spectrum at positions characteristic of the cubic and/or hexagonal phases of ice.2,33 The diffraction pattern is not stable in time, as indicated by the fluctuating intensities of the three peaks around 2θ ∼ 25° or the peak at 2θ ) 33° that grows after some time at 267 K. These fluctuations are probably due to the formation of small crystals with variable orientation. This continuous variation of the spectrum does not allow an analysis of the Bragg peak intensities, or to deduce the amount of ice formed in the sample as a function of time and temperature. Upon heating, the intensity of the Bragg peaks progressively decreases, until complete melting occurs, slightly below 273 K. It is easily conceivable that the crystallites exhibit broadened peaks due to poor quality of the stacking, and are partially oriented. The measured patterns can therefore not be identified either with pure cubic or hexagonal ice but probably with a complex mix of both phases slowly evolving with time. The results of diffraction measurements (temperatures, formation and melting of ice) are in very good agreement with these of sound wave propagation. Our data confirm the phase separation observed by Escoubes et al., and show its full reversibility. Only a small hysteresis between 267 and 271 K is observed. The momentum transfer

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used in this case, 1 µm-1, corresponds to a distance orders of magnitude larger than the heterogeneities of the sample (cavities e60 Å). The ice formation (crystalline or glass) within the membrane is not consistent with the values measured for sound speed and damping of the slow component, that would reflect the heterogeneous media composed of ice and polymer, and therefore give much higher values. The low cooling rate and the long breaks at constant temperature for measurements rule out the possibility of glassy ice formation ouside of the membrane. The size of the ice crystallites, in the plane of the sound propagation (the plane of the membrane), therefore has to be large enough so that the two contributions (membrane and ice) are separately measured, and not averaged as they are at room temperature. Ice crystals, of micrometer size, are expected to be formed between the membrane layers and/or between the membrane and the windows. The thickness of the crystals can however be much smaller than a micrometer. Escoubes et al. also observed that, for a water content lower than 8% of the full hydration level (e0.04 g of H2O/g of dry membrane), the membrane does not undergo desorption below 0 °C. This quantity of water directly hydrates the SO3- anion. We also performed HG-TG measurements on samples of intermediate hydration (sound velocity of 1550 m/s at 300 K, corresponding to a hydration of ∼0.05 g of H2O/g of dry membrane). The sound velocity, shown in Figure 6, increases linearly on cooling from 272 to 230 K, with the same slope as the slow mode of hydrated Nafion. The overall sound velocity is higher than that of the fully hydrated membrane at any temperature, corresponding to a lower water content (see the Sound Velocity upon Swelling of the Membrane section). No additional mode appears in the sample, down to 235 K. Our results are therefore in very good agreement with the previous studies. Acoustic Wave Intensity and Phase Transition. An issue of the phase transformation in the hydrated polymer is the understanding of the mechanism driving the desorption (and readsorption) of water with temperature. A thermodynamic model was proposed by B. Dreyfus,35 considering in a mean field approximation the adsorption of water by the ions in a deformable matrix. This approach, however, was not sufficient to quantitatively explain the data. The relative amount of desorbed water as a function of temperature gives information regarding this process. In the present measurement, this quantity is related to the ratio of the amplitudes of the two acoustic contributions, Afast/Aslow ) (A1 + B1)/(A2 + B2). The temperature dependence of the amplitudes is complex. For experimental reasons, one has to consider amplitude ratios in order to eliminate effects of laser power or scattering (changing turbidity). As previously stated in the section Materials and Methods, the data are analyzed within the framework of the hydrodynamic model. For bulk water, in contrast to most other materials, it was shown that both the density and temperature dependence of the dielectric constant had to be considered in the analysis of the HD-TG signal.37,36 In particular, close to 4 °C where the thermal expansion coefficient exhibits a sign inversion, the term arising from the density dependence of the dielectric constant ε is small and the one arising from the temperature dependence of ε becomes dominant. However, in our case, the data are well fitted by eq 1, and do not reflect the inversion of the thermal expansion coefficient of bulk water, the amplitude of the thermal signal being almost independent of temperature. A comparison can be made with the water/Vycor system, investigated by the same technique: the temperature dependence of ε was observed, but the inversion of the thermal

Plazanet et al.

Figure 10. (top) Normalized amplitudes of the two acoustic components. The temperature dependence can be fitted by a power law associated with an exponent of 0.32 ( 0.05. (bottom) Relative amplitudes of the two sound waves: Afast/Aslow. The ratio is 0 above ∼271 K. The fit by a power law yields a critical temperature of 271.6 ( 1.8 K and an exponent of 0.5 ( 0.1.

expansion was lowered by ca. 5°.38 In the hydrated Nafion, the averaging of the properties of water and polymer matrix might reduce the relative contribution of the thermal dependence of ε. Moreover, the confinement, that is of different nature of the Vycor because of the hydrophobic character of the matrix, might lower or even cancel the inversion of the thermal expansion of water. Therefore, none of these effects are observed. We consider here as the amplitude of the contribution, the sum of the thermal and electrostrictive terms (see the section Materials and Methods for details). Roughly, the amplitudes A and B as used in eq 1 are related to the thermodynamics parameters:37 A ∼ -R/cp and B ∼ Q/co, where R is the thermal expansion coefficient, Q is the momentum transfer, cp is the specific heat, and co is the sound velocity. Therefore, the ratio Afast/Aslow is related to the temperature dependence of the R, cp, and co values of ice on one side, and on the membrane on the other side. However, considering that the influence of the thermal expansion coefficient of water is not observed, none of these parameters exhibit a strong temperature dependence within the given range. Moreover, the X-ray diffraction data also indicate the increasing amount of ice on cooling (or better observed as a decrease of intensity on heating). We can therefore consider the amount of ice to be the main contribution to the temperature dependence of the amplitude ratio. The temperature dependence of each component, and their ratio, is plotted in Figure 10. The amplitude of the slow component decreases with the temperature, in favor of the fast one. This one-to-one compensation of the amplitudes supports the previous assumption that the temperature dependence of Afast/ Aslow is related to the quantity of sample contributing to each component. As for other properties of the acoustic wave (velocity, damping), the transition is reversible. The regular growth of the ice component indicates a smooth temperature dependence of the mechanisms responsible for the phase separation. The large temperature spread of the transition could arise from the pore size distribution. In silica-based porous glasses,2 the crystallization temperature decreases linearly with the inverse of the pore diameter. However, even a sufficiently large range pore size distribution (from 20 to 200 Å for melting points distributed between 235 and 270 K) should not follow a regular

Structure and Acoustic Properties of Hydrated Nafion trend without any plateau or peak. Another reason for the phase separation could be the difference in thermal expansion between water and membrane. This difference also leads to the expulsion of water from the membrane, as the result of matrix contraction and water expansion. However, once again, by considering the well characterized thermal expansion of water, and a thermal expansion coefficient of Nafion of 123 × 10-6 K-1, we would get, at 235 K, a maximal amount of 10% of ice in the sample. Moreover, this amount would grow roughly as T2.5, and would not reproduce the data. We therefore postulate the existence of a second-order phase transition, driving the water out of the membrane. The amplitudes, Afast/(Afast + Aslow) or Afast/Aslow, both follow a power law (271.6 - T)β, the first one with an exponent of β ) 0.32 ( 0.05, close to the d ) 3 Ising model,39 and the second one with an exponent of β ) 0.5 ( 0.1, close to the mean field critical exponent. Because of large uncertainties on the measurements, the present study does not enable discrimination on the dimensionality of the lattice, but T0 ) 271.6 ( 1.8 K is interpreted as the critical temperature. Conclusion We have presented in this paper the first transient grating and Brillouin scattering measurements in a hydrated membrane of Nafion. In the investigated frequency range (GHz), the propagation of the acoustic wave is affected by the hydration of the membrane. Because the differences in density and compressibility between water and polymer have opposite signs, the sound velocity exhibits a minimum as a function of hydration that is lower than the sound velocity of both pure water and polymer. The hydration dependence of the sound velocity can be qualitatively explained by a mean field approximation for the bulk modulus and density. This behavior is expected to be observed for any low frequency wave. When the frequency becomes high enough so that the distance probed is smaller than the heterogeneities, one observes the propagation in confined water.16 Upon cooling below 0 °C, the HD-TG data reveal a second contribution to the signal, all characteristics of which are consistent with the propagation of sound and heat in ice. In agreement with X-ray diffraction data, and with prior studies on this system,31,34 this signal is assigned to the formation of ice following the water desorption from the membrane. We could observe the full reversibility of the phase transition with temperature: the ice progressively melts and reintegrates the membrane as the temperature rises. The ratio between the amplitudes of the two components follows a power law, with an exponent of 0.5, equal to the critical exponent of the order parameter in the mean field approximation. This ratio reflects the amount of ice formed as a function of temperature, that is an order parameter for the phase transition. This suggests a critical nature for the observed process. In order to get better insight into this parameter, neutron reflectrometry and/or diffraction measurements of D2O hydrated membranes could give a quantitative indicator of the amount of ice forming during the process.

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