J. Phys. Chem. B 2001, 105, 7979-7983
7979
Kinetics of Water Sorption in NafionThin Films - Quartz Crystal Microbalance Study Petr Krtil,* Antonı´n Troja´ nek, and Zdeneˇ k Samec J. HeyroVsky´ Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, DolejsˇkoVa 3, CZ 18223, Prague, Czech Republic. ReceiVed: NoVember 10, 2000; In Final Form: June 6, 2001
Quartz crystal microbalance measurements are used to investigate the water sorption in the cast Nafion films exposed to water vapor. Equilibrium and kinetic sorption data are reported for H- and Na-form Nafion films of a thickness ca. 0.02 µm. Water sorption isotherms obtained agree well with the literature data for Nafion117. However, the water diffusion coefficients evaluated from the initial sorption and desorption rates by using the theory of diffusion in a plane sheet are ca. 7 orders of magnitude lower than those obtained from sorption measurements in ca. 200 µm thick Nafion117 membranes. It is concluded that the kinetics of water sorption (desorption) in the partially hydrated Nafion exposed to water vapor is controlled by the first-order process of water transfer in and out of the nanoscopic hydrophilic regions (ion clusters) for membranes thinner than 10 µm. On the other hand, the linear diffusion is the rate-determining step of water transport in thick Nafion membranes and in fully hydrated thin Nafion films.
Introduction Practical utilization of ion conducting polymers (ionomers) as solid polymer electrolytes, e.g., in industrial electrolysis1 or polymer electrolyte fuel cells2-4 boosted the interest in detail understanding the transport properties of these materials. Research has focused on the transport behavior of perfluorosulfonate polymers, such as Nafion (DuPont) and related materials.5 A series of measurements of ion diffusion coefficients indicated that the transport properties of Nafion are closely related to the polymer microstructure and are strongly influenced by the polymer hydration (water to exchange site mole ratio)6-15, which in turn depends on the nature of the cation present.16,17 Transport properties of polymer electrolytes exposed to water vapor are of particular interest for fuel cell applications.18-20 Systematic data are available mainly for proton conducting polymers, e.g., H-form Nafion. Conductivity,19,21 radiotracer,11,22 and NMR19 measurements of the proton diffusion coefficient provided consistent results. On the other hand, there exits significant discrepancy between water diffusion coefficient in partially hydrated Nafion (measurements in vapor phase) and in fully hydrated Nafion (water immersion measurements).9,26 The sorption23-25 and permeation24 measurements in vapor phase give the values of water diffusion coefficient in Nafion D by orders of magnitude lower than water immersion data.9,26 In earlier experiments comprising water immersion, the D was reported to be in the range of 1.32-1.65 × 10-6 cm2 s-1 depending on the nature of the cation present;9 an exponential function was found to describe the temperature dependence of diffusion coefficient D ) 6.0 × 10-3 exp(-20.2 × 103/RT) cm2 s-1,26 i.e., D ) 1.7 × 10-6 cm2 s-1 at 25 °C. Comparable values 1.3-1.6 × 10-6 cm2 s-1 were obtained also by radiotracer, pervaporation, and dimensional variation methods.24 In contrast, water diffusion coefficients evaluated from classical sorption and permeation experiments involving water vapor fall in the range from 2 × 10-8 to 4 × 10-7 cm2 s-1.23-25 In addition to * To whom correspondence should be addressed.
the effect of Nafion hydration,24,25 a significant difference between the sorption and desorption rates was noted.23,25 The difference between water sorption and immersion data was ascribed to the two-phase structure of Nafion comprising hydrophilic and hydrophobic regions and the dimensional changes associated with the swelling, which results in a higher water diffusion coefficient.25 However, NMR measurements of water self-diffusion in Nafion equilibrated with water vapor also provided high values of the water diffusion coefficient D ranging from 1.3 × 10-6 to 4.2 × 10-6 cm2 s -1, after correction for the variation of water activity coefficient with water content.4 It has been proposed that the hydrophobic membrane surface could introduce a barrier to the water transport and thereby control the flux observed in the sorption experiment.27 To clarify this discrepancy, we have used quartz crystal microbalance (QCM) measurements to follow kinetics of water sorption in a thin Nafion film. Because the film thickness (L < 80 nm) estimated from AFM measurements was about 3 orders of magnitude lower than that of the commercially available Nafion membranes (ca. 200 µm), we have expected about the same order of magnitude higher water sorption rates. Surprisingly, despite the comparable water sorption isotherms, the water sorption in the cast Nafion film is about as slow as that in the Nafion 117 membrane.25 Because this result casts doubts on the interpretation of sorption kinetic data24,25 in terms of the classical diffusion model,28 a modified transport model was considered. Experimental Section Materials. Reagent grade HCl, LiCl, NaCl, KCl, MgCl2, Mg(NO3)2, Nafion perfluorinated powder (5 wt. % solution), and Nafion 117 perfluorinated membrane (0.007 in. thick, Lot No. JX-0862KW) were purchased from Aldrich. The water used in all experiments was of Millipore-MilliQ quality. Synthetic air was supplied by Messer Technogas, Ltd. (Czech Republic). The gas phase with controlled water partial pressure pw (or relative humidity RH) was prepared by purging compressed air
10.1021/jp004162t CCC: $20.00 © 2001 American Chemical Society Published on Web 07/27/2001
7980 J. Phys. Chem. B, Vol. 105, No. 33, 2001
Krtil et al.
Figure 1. AFM image of the cast Nafion film.
through the saturated solutions of LiCl (pw ) 396 Pa, RH ) 11%), MgCl2 (pw ) 1188 Pa, RH ) 33%), Mg(NO3)2 (pw ) 1908 Pa, RH ) 53%), NaCl (pw ) 2700 Pa, RH ) 75%), and KCl (pw ) 3060 Pa, RH ) 84.5%) or through liquid water (pw ) 3600 Pa, RH ) 100%). Gas phase with RH ) 0% was obtained by passing the air through a column packed with P2O5. Preparation of the Nafion Film. A Nafion solution (Aldrich, 5 wt %) was diluted by methanol to the concentration of 40 mg/L. The Nafion film with the mass of 1 µg was prepared by casting 25 µL of the diluted solution on a piezoactive area (0.2 cm2) of a silver contact of an AT-cut 10 MHz quartz crystal (ICM, Oklahoma, USA). The film was converted to the H or Na form by bathing in a 0.1 M solution of HCl or NaCl for 30 min, washed with water, and dried in the stream of dry air. The frequency shift ∆f caused by the film deposition was about 1.176 kHz, in an agreement with the value of 1.219 kHz that can be inferred from the Sauerbrey equation
∆f )
( ) 2nf02
F1/2µ1/2
∆m
described elsewhere30 was used as a mass sensing device in water sorption experiments. The analogue data output of the QCM was logged using a National Instruments PCI MIO16E-4 DA/AD converter card. The Nafion film was placed in a sealed plexiglass chamber, which was purged with the gas of controlled humidity. The film was first equilibrated in the stream of air of RH ) 11% until the film showed a constant mass. The relative humidity of the air stream was then stepped successively to 0, 33, 53, 75, 80, or 100% and, after the new steady-state was reached, back to 11%. The flow rate of the air was kept between 10 and 15 mL/ s. The QCM reading under these conditions is independent of the actual flow rate. Water content in Nafion 117 dried over P2O5 was determined by employing a Karl Fischer titrator (Diram, Czech Republic). All measurements were carried out at the ambient temperature i.e., 23 ( 2 °C. Results and Discussion
(1)
where n ) 1 is the order of harmonics, f0 ) 10 MHz is the fundamental frequency of the crystal oscillation, and F or µ represent the density and shear modulus of the quartz crystal, respectively. This indicates that the viscoelastic properties of the film do not contribute significantly to the changes in the frequency measured. Crystallinity of the cast film was checked by XRD measurements (Siemens 500 series). Thickness of the film, as estimated from its mass, the density of the recast Nafion (1.8 g cm-3),29 and the exposed piezoactive area, was 0.02 µm. A similar value of about 0.08 µm was determined by AFM microscopy (Nanoscope IIIsDigital Instruments). Mole amount Ns of the fixed -SO3- groups in the film was estimated from the film mass and the nominal equivalent mass (1100 g mol-1) of Nafion 117. Water Sorption Measurements. A custom-made quartz crystal microbalance (QCM) designed according to the circuitry
Surface and Bulk Morphology of the Film. Typical topography mode AFM image of the cast Nafion film is shown in Figure 1. AFM imaging did not reveal any pinholes or open pores. Morphology of the Nafion film was similar to that of the substrate surface, as it can be expected for relatively thin films. Lack of the crystalline structure, as evidenced by X-ray diffraction, indicates the favorable water uptake capability.31 Equilibrium Water Sorption. Figure 2 shows typical mass change ∆m vs time t curves of the water sorption by a thin Nafion film upon a step change in the water vapor pressure (relative humidity). The mass change was recalculated from the recorded frequency shifts according to eq 1. The observed mass changes were reversible; that is, the same amount of water which enters the film leaves it when the vapor pressure is stepped back to its initial value. The stationary film mass reached in ca. 2001200 s should correspond to the water sorption equilibrium established after the vapor pressure step. Hence, the mass change data were used to evaluate the equilibrium mole amount of water Nw (or the water to exchange site mole ratio λ ) Nw/Ns) in the
Quartz Crystal Microbalance Study
Figure 2. Time dependence of the mass change ∆m for the thin H-form Nafion film upon a step increase in the relative humidity of the gas phase from 11 to 33% (1), 53% (2), 75% (3), or 85% (4) and the reverse. The dry-membrane mass was 1320 ng.
J. Phys. Chem. B, Vol. 105, No. 33, 2001 7981
Figure 4. Relative mass change ∆m/∆m∞ of the thin H-form Nafion film upon a step increase in the relative humidity of the gas phase from 11 to 75% vs square root of time t. The dashed line shows the initial slope.
shape and time scale. Small difference in the water sorption rate between these two plane sheets is quite surprising. The sorption data have been analyzed24,25 by using the linear diffusion model,28 which refers to the second Fick’s diffusion equation, i.e.
∂c ∂2c )D 2 ∂t ∂x
(2)
where c is the volume water concentration and x is the coordinate perpendicular to the plane of the sheet. Expression for the initial fraction uptake by the plane sheet, of which one face is not permeable, is analogous to that for the symmetric case, i.e.28 Figure 3. Water sorption isotherms of the thin Nafion films in the H (O) or Na (b) form. The dashed line shows the data for the H-form Nafion 117 membrane at 25 °C taken from ref 25.
Nafion film by taking the water content of the dry Nafion 117 as a reference. The amount of water retained in Nafion 117 dried over P2O5 was determined by Karl Fischer titration, yielding λ ) 1.3 and 0.6 for H- and Na-form samples, respectively. A comparable value of 1.58 was reported for the H-form Nafion 117, which was dehydrated under vacuum (0.01-1 Pa) at 150 °C.25 Water sorption isotherms of the H- and Na-form Nafion films are shown in Figure 3. Data for the H-form Nafion film and Nafion11725,32 exhibit a very good agreement, cf., empty points and the dashed line in Figure 3, except for the region of high vapor pressures. Because the torsion balance measurements25,32 are not affected by the viscoelastic properties of the Nafion sample, we conclude that changes in these properties, e.g., due to swelling,33 play a role in the QCM measurements, perhaps except for the relative humidities approaching 100%. Water sorption by Nafion 117 was found to follow the sequence H+ > Li+ > N(CH3)4+ > Cs+.33 Such behavior is apparently related to the relative degree of hydration of these ions, which is mainly responsible for water uptake at low and medium vapor pressure.32 Our sorption data for Na-form Nafion film are consistent with this observation, as they fall between those for Li- and Cs-form Nafion117,32 cf., solid points in Figure 3. Kinetics of the Water Sorption. The sorption curves for thin Nafion film displayed in Figure 2 are comparable with those measured for thick (ca. 200 µm) Nafion membrane25 in both
2 Dt 1/2 ∆m ) ∆m∞ L π
( )
(3)
where ∆m∞ is the value of the mass change at time t f ∞ and L is the sheet thickness. The application of eq 2 to the present sorption data yields extremely low values of the water diffusion coefficient D. Typical curve of the fraction uptake as a function of t1/2 is illustrated in Figure 4. The initial slope of this curve, which is indicated by the dashed line, corresponds to D ) 5 × 10-14 cm2 s-1 for L ) 0.02 µm. This value is ca. 7 orders of magnitude lower than the values derived from sorption measurements in Nafion 117.23-25 Slow water transport across the gas phase/solid polymer boundary has been proposed to explain the difference in the water diffusion coefficients obtained from sorption and immersion and NMR experiments.27 The sorption curves corresponding to the process controlled by both diffusion and interfacial kinetics should have a sigmoid shape.28 Besides of it, as follows from the mass balance, the change of water concentration in the polymer film is always inversely proportional to the film thickness 1/L
∂c ) (A/V)J0 ) (1/L)J0 ∂t
(4)
where J0 is the interfacial flux. The experimental results, however, contradict both the expected shape of sorption curves (cf. Figure 2 and ref 25) and the independence of sorption kinetics of the film thickness. That rules out the slow transport across the gas phase/polymer interface as the rate-determining step of the water sorption in Nafion.
7982 J. Phys. Chem. B, Vol. 105, No. 33, 2001
Krtil et al.
A more general description of the water sorption process can be obtained by taking into account the microporous structure of Nafion, which can be represented, e.g., by a network of spherical ion clusters (approximately 5 nm in diameter, hydrophilic region) connected by 1 nm diameter channels (hydrophobic region).34 Because the water mobility in these two regions ion is likely to be different, the rate-determining step can eventually be the water transfer in and out of the ion clusters, which primarily accumulate water at low and medium water vapor pressures.20 Therefore, we shall assume that the water volume concentration c′ outside the ion clusters is governed by the water partial pressure pw, whereas the water volume concentration c . c′ inside the clusters is influenced by the kinetics of the water transfer in and out of the clusters. A plausible model of the macroscopic water transport across a Nafion plane sheet would be then a combination of the linear diffusion and the first-order water transfer reaction, i.e.
∂c ∂2c ) D 2 + k′c′ - kc ∂t ∂x
(5)
where x is the coordinate perpendicular to the plane of the sheet and k′ and k are the rate constants of the water transfer in and out of the clusters, respectively. The solution of the diffusion problem described by eq 5 has been obtained for a solute, which is absorbed and becomes immobilized in a plane sheet as diffusion proceeds.28 Although the present model is somewhat different, i.e., water cannot be considered as being immobilized in the film, the role of the kinetic term can be discussed on the basis of the conclusion drawn.28 Essentially, two limiting cases can be distinguished depending on the value of the dimensionless parameter kL2/D. If this parameter is sufficiently large, i.e., kL2/D . 1, a local equilibrium can be assumed to exist between water outside and inside the clusters. Because water accumulates mainly inside the clusters, the corresponding equilibrium constant K ) k/k′ , 1. The solution of eq 5 is then analogous to that for eq 228
∂2 c ∂c ∂c )D 2-K ∂t ∂t ∂x D ∂2c ∂c ∂ 2c ) ≈ D ∂t K + 1 ∂c2 ∂c2
(
)
(6)
Figure 5. Comparison of the relative mass change ∆m/∆m∞ of the thin H-form Nafion film upon a step increase in the relative humidity from 11 to 33% (A) and the reverse (B) with the exponential fit (dashed line) to eqs 8 and 9, respectively.
[ ( ) ]
λ ) λ∞ 1 - 1 -
λ0 -kt e λ∞
(9)
where λ0 and λ∞ represent the initial and the final (t f ∞) value of λ. As follows from eq 7, the time dependence of the mass change ∆m has the simple form
∆m ) 1 - e-kt ∆m∞
(10)
On the other hand, if kL2/D , 1, the water distribution over x should be homogeneous and the overall sorption process is controlled by the kinetic term,28 i.e.
it relates the sorption rate to the rate constant k of the water transfer out of the ion clusters. The same rate constant controls the water desorption rate upon a step decrease in the water vapor pressure
∂c ≈ k′c′- kc ∂t
∆m ) e-kt ∆m∞
(7)
The dimensionless form of eq 7 is obtained by multiplying both sides by the factor VMw/Ns (Mw is the water molar mass)
dλ ≈ k′λ′ - kλ ) a(1 - bλ) dt
(8)
where a ) k′λ′ and b ) k/a. The equilibrium state is reached when dλ/dt f 0, the corresponding sorption isotherm has the general form λ )1/b ) a(pw)/k. Theoretical dependence of the water to exchange site mole ratio λ on time upon a step increase in the water vapor pressure from an initial value pw0 to pw is obtained by an integration of eq 6
(11)
with ∆m and ∆m∞ < 0. Apparently, the value of k determines the initial slope of the sorption or desorption curve, i.e., k ) [d(∆m/∆m∞)/dt]tf0. Figure 5 shows that the water sorption or desorption in a thin Nafion film can indeed be fitted to the exponential dependence described by eq 10 or eq 11, respectively. The rate constant k obtained from this analysis is plotted in Figure 6 as a function of the water to exchange site mole ratio λ for both H- and Na-forms Nafion films. Figure 6 shows that this rate constant is practically independent of the nature of the cation present. Values up to 5 times higher of k obtained in water desorption experiments (at λ > 4, cf., Figure 6) indicate
Quartz Crystal Microbalance Study
J. Phys. Chem. B, Vol. 105, No. 33, 2001 7983 of the Nafion swelling at λ > 4. In turn, the linear diffusion is the rate-determining step of water transport in the Nafion membranes thicker than 10 µm and fully hydrated Nafion immersed in liquid water. Acknowledgment. The study was supported by the Grant Agency of the Czech Republic under Contract No. 203/99/0575. The authors also thank Dr. Kocˇirˇk of the J. Heyrovsky´ Institute for stimulating discussion. References and Notes
Figure 6. Rate constant k of the water transfer out of the water clusters vs the water to exchange site mole ratio λ for the H- (O,0) and Naform (b,9) thin Nafion films, as evaluated from the sorption (b,O) and desorption (0,9) measurements.
asymmetry of the sorption/desorption process. The difference in water sorption and desorption rates of a Nafion thin film is quite analogous to behavior observed for Nafion117, though in the latter it was interpreted as a change in the water diffusion coefficient.24,25 Its origin is probably in the cluster size increasing with water content as a result of swelling,26,35 which enables a faster release of water from ion clusters. The difference in the sorption and desorption kinetics indicates that the swelling of Nafion is a relatively slow process. The apparent difference in the mechanism of water sorption in thin and thick24,25 Nafion membranes can be explained keeping in mind that eqs 6, 10, and 11 represent the limiting solutions of eq 5. As a matter of fact, water sorption by a Nafion plane sheet can be controlled either by linear diffusion, or by kinetics of water transfer inside the ion clusters depending on the actual sheet thickness L. Kinetic control prevails when k < D/L2. Because the diffusion coefficient of water in Nafion is of the order of 10-7 cm2s-1,23-25 and the experimental value of k is of the order of 10-1 s-1, cf., Figure 6, the kinetics of water transfer inside the ion clusters can influence the water sorption rate only if the thickness of the sheet L is less than 10 µm. Conclusions The transport model comprising both linear diffusion and the first-order bulk reaction provides an explanation for the discrepancy between the water transport data inferred from the measurements of Nafion plane sheets of different thickness. If the film thickness does not exceed 10 µm, the kinetics of water sorption (desorption) in the partially hydrated Nafion exposed to water vapor are controlled by the first-order water transfer in and out of the nanoscopic hydrophilic regions (ion clusters), rather than by linear diffusion. The water desorption from thin Nafion films is kinetically favored over water sorption because
(1) Bergner, D. J. Appl. Electrochem. 1982, 12, 631. (2) Lemons, R. J. Power Sources 1990, 29, 251. (3) Yeo, R. S.; McBreen, J. J. Electrochem. Soc. 1979, 126, 1682. (4) Zawodzinski, T. A., Jr.; Springer, T. E.; Uribe, F.; Gottesfeld, S. Solid State Ionics 1993, 60, 199. (5) Heither-Wirguin, C. J. Membr. Sci. 1996, 120, 1. (6) Lopez, M.; Kipling, B.; Yeager, H. L. Anal. Chem. 1976, 48, 1120. (7) Lopez, M.; Kipling, B.; Yeager, H. L. Anal. Chem. 1977, 49, 629. (8) Yeager, H. L.; Kipling, B. J. Phys. Chem. 1979, 83, 1836. (9) Yeager, H. L.; Steck, A. J. Electrochem. Soc. 1981, 128, 1880. (10) Herrera, A.; Yeager, H. L. J. Electrochem. Soc. 1987, 134, 2446. (11) Verbrugge, M. W.; Hill, R. F. J. Electrochem. Soc. 1990, 137, 893. (12) Yeo, R. S. J. Electrochem. Soc. 1983, 130, 533. (13) Pourcelly, G.; Oikonomou, A.; Gavach, C.; Hurwitz, H. D. J. Electroanal. Chem. 1990, 287, 43. (14) Millet, P. J. Membr. Sci. 1990, 50, 325. (15) Samec, Z.; Troja´nek, A.; Samcova´, E. J. Phys. Chem. 1994, 98, 6352. (16) Yeager, H. L.; Steck, A. Anal. Chem. 1979, 51, 862. (17) Steck, A.; Yeager, H. L. Anal. Chem. 1980, 52, 1215. (18) Springer, T. E.; Zawodzinski, T. A., Jr.; Gottesfeld, S. J. Electrochem. Soc. 1991, 138, 2334. (19) Zawodzinski, T. A., Jr.; Neeman, M.; Sillerud, L. O.; Gottesfeld, S. J. Phys. Chem, 1991, 95, 6040. (20) Zawodzinski, T. A., Jr.; Derouin, C.; Radzinski, S.; Sherman, R. J.; Smith, Van T.; Springer, T. E.; Gottesfeld, S. J. Electrochem. Soc. 1993, 140, 1041. (21) Rieke, P. C.; Vanderborgh, N. E. J. Membrane Sci. 1987, 32, 313. (22) Verbrugge, M. W.; Hill, R. F. J. Electrochem. Soc. 1990, 137, 1131. (23) Takamatsu, T.; Hashiyama, M.; Eisenberg, A. J. Appl. Polym. Sci. 1979, 24, 2199. (24) Zelsmann, H. R.; Pineri, M.; Thomas, M.; Escoubes, M. J. Appl. Polym. Sci. 1990, 41, 1673. (25) Morris, D. R.; Sun, X. J. Appl. Polym. Sci. 1993, 50, 1445. (26) Yeo, S. C.; Eisenberg, A. J. Appl. Polym. Sci. 1977, 21, 875. (27) Zawodzinski, T. A., Jr.; Gottesfeld, S.; Shoichet, S.; McCarthy, T. J. J. Appl. Electrochem. 1993, 23, 86. (28) Crank, J. The Mathematics of Diffusion, 2nd ed.; Clarendon Press: Oxford, U.K., 1975. (29) Paik, W.; Springer, T. E.; Srinivasan, S. J. Electrochem. Soc. 1989, 136, 644. (30) Bruckenstein, S.; Michalski, M.; Fensore, A.; Li, Z. Anal. Chem. 1994, 66, 1847. (31) Ludwigsson, M.; Lindgren, J.; Tegenfeldt, J. J. Electrochem. Soc. 2000, 147, 1303. (32) Pushpa, K. K.; Nandan, D.; Iyer, R. M. J. Chem. Soc., Faraday Trans. 1 1988, 84, 2047. (33) Buttry, D. A. In Electroanalytical Chemistry; Bard, A. J., Ed.; Marcel Dekker: New York, 1991; Vol. 17, p 1. (34) Gierke, T. D.; Munn, G. E.; Wilson, F. C. J. Polym. Sci. Polym. Phys. Ed. 1981, 19, 1687. (35) Gierke, T. D.; Hsu, W. Y. In Perfluorinated Ionomer Membranes; Eisenberg, A., Yeager, H. L., Eds.; ACS Symp. Ser. No. 180; American Chemical Society: Washington, DC, 1982; pp 283-307.
