10166
J. Phys. Chem. B 2007, 111, 10166-10173
Water-Nafion Equilibria. Absence of Schroeder’s Paradox Lisa M. Onishi,*,† John M. Prausnitz,‡ and John Newman† Department of Chemical Engineering, UniVersity of California, Berkeley, California 94720-1462, and Lawrence Berkeley National Laboratory (LBNL), Berkeley, California 94720 ReceiVed: April 27, 2007; In Final Form: June 27, 2007
Water-Nafion phase equilibria and proton conductivities were measured in two ways. First, Nafion was in contact with saturated water vapor. Second, Nafion was in contact with liquid water at the same temperature. At 29 °C, for preboiled, vapor-equilibrated Nafion exposed to water with an activity ) 1 and air pressures ranging from 0 to 0.96 bar, the water content was λ ) 23 ( 1 mol H2O/mol SO3-. For the preboiled, liquidequilibrated membrane, λ ) 24 ( 2. At 100% relative humidity (RH), the water content of preboiled Nafion decreased as the temperature rose from 30 to 80 °C but did not recover its initial water content when the temperature returned to 30 °C. The water content of predried Nafion at 1 atm and 30 °C was λ ) 13.7 ( 0.2 when vapor-equilibrated and λ ) 13.1 ( 0.5 when liquid-equilibrated. A Nafion membrane originally boiled in water had much higher liquid- and 100% RH vapor-equilibrated proton conductivities than the same membrane originally dried at 110 °C with a RH less than 2%. The liquid-equilibrated and 100% RH vaporequilibrated membrane conductivities were the same when the membrane had the same thermal history. The conductivity data was fit to a model, and the water content was determined at different temperatures. The predried membrane water content increased with temperature, and the preboiled membrane’s water content changed slightly with temperature. Both water sorption and proton-conductivity data do not exhibit Schroeder’s paradox. These studies and previous results suggest that Schroeder’s paradox is resolved when attention is given to the thermal history of the absorbing polymer.
I. Introduction In 1903, Schroeder reported that gelatin had less water uptake from 100% relative humidity (RH) water vapor than from liquidwater immersion at the same temperature.1 This observation, known as Schroeder’s paradox, is inconsistent with thermodynamics because the chemical potential of saturated water vapor is equal to that of liquid water at the same temperature; therefore, at equilibrium, the water content of gelatin in contact with saturated water vapor should be the same as that when in contact with liquid water. In this work, we investigate Schroeder’s paradox with new experimental data using water and a polymer, Nafion, which is used extensively in electrochemical devices. Nafion has a repeating backbone structure with side chains terminating in a sulfonic acid group
Nafion 117 is a random copolymer with x ) ∼1 and y ) ∼7. As indicated by Curtin et al.,2 the equivalent weight is 1100 g dry polymer/mol SO3-, and the molecular weight is 105 g/mol. At ordinary temperatures, Nafion has ionic domains and low crystallinity. Nafion swells with water uptake. The SO3H group * To whom correspondence should be addressed. E-mail: onishil@ berkeley.edu. Phone: 510-643-1972. † Environmental Energy Technologies Division, LBNL. ‡ Chemical Sciences Division, LBNL.
in Nafion is associated with the hydrophilic and ionic regions, and the backbone is associated with the hydrophobic regions.3 Currently, Nafion is used as a proton-conducting membrane in fuel cells. Water management is critical to fuel cell operation because, on the one hand, too much water slows oxygen transport to the reaction sites and, on the other, too little water causes low proton conductivity, both resulting in reduced power output. Because fuel cell membranes are exposed simultaneously to vapor and liquid water, understanding the Schroeder’sparadox phenomenon is important for developing an accurate fuel-cell model. The purpose of the current study is to investigate the effect of thermal history on Nafion-water equilibria and proton conductivity. Transport properties and water content in Nafion depend on polymer morphology. However, little is known about Nafion morphology,3 despite numerous studies using small-angle X-ray scattering (SAXS),4-18 small-angle neutron scattering (SANS),7,8,14,19-25 wide-angle X-ray diffraction (WAXD),4-6,9,10,16-20,25-27 tensile drawing with SAXS, WAXD, and SANS,5,20,24,28-36 atomic force microscopy (AFM),37-39 and transmission electron microscopy (TEM).20,40-42 Since SANS and SAXS show only one peak, the structure of the repeat unit is unknown. TEM is conducted in a vacuum, and therefore, only dry membranes have been examined; AFM has probed the structure only near the surface. SAXS and SANS’s single peaks indicate that Nafion has only local order, not long-range order.3 This peak corresponds to the repeat unit that includes the water domain in the polymer; the repeat unit is approximately 5 nm when fully humidified.3 The literature is rich in water-uptake studies on Nafion between 30 and 80 °C,43-51 indicating that membrane water content is a nonlinear function of water activity. For Nafion,
10.1021/jp073242v CCC: $37.00 © 2007 American Chemical Society Published on Web 08/09/2007
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TABLE 1: Vapor-Equilibrated and Liquid-Equilibrated Membrane Water Content, Where All Membranes Have the Same Thermal Historya nafion
water content at 30 °C (moles H2O/mol SO3-)
pretreated, vapor-equilibrated membrane III pretreated, liquid-equilibrated membrane III pretreated, vapor-equilibrated membrane IV pretreated, liquid-equilibrated membrane IV predried, vapor-equilibrated membrane III predried, liquid-equilibrated membrane III predried, liquid-equilibrated membrane IV
23 ( 1 23.33 25.3 26.66 13.71 13.10 12.42
a Pretreated: membrane boiled in 3% H2O2, DI water, 0.5 M H2SO4, and DI water for 1 h each. Then, the water and submerged membrane were cooled to 30 °C. Predried: pretreated membrane dried at 105 °C under high vacuum for 24 h. Then, the membrane was cooled to 30 °C.
Schroeder’s paradox was reported; at 30 °C, the liquidequilibrated water content was 22, and the 100% RH vaporequilibratedwatercontentwas14molH2O/molSO3-.43-45,48,50,52-56 Proton conductivity is related to the Nafion water content. Previous authors have measured Nafion conductivity near room temperature and at elevated temperatures.43-47,54,57-63 In their conductivity studies, Nafion had different thermal histories.23,43-45,47,50,54,57-59,61,63,64 Other studies reported results that, perhaps, were not under equilibrium conditions46,58,59 or not at 100% RH.46,57,59,62 Similar uncertainties appear with water-uptake studies: different thermal histories,48,49,51,65-67 different membrane morphology,66 uncertain experimental conditions,46,53,59 environmental effects,2-4,6,9,12,13,23 and perhaps, experiments conducted at nonequilibrium conditions.46,49,53,59 Numerous published experimental results show differences in the liquid- and vapor-equilibrated water content and conductivity; these differences were attributed to Schroeder’s paradox. Table 5 summarizes possible reasons why the apparent Schroeder’s paradox may have appeared in these studies. Sone et al.58 showed that vapor-equilibrated Nafion conductivity changes with thermal history. Membrane conductivity was largest when Nafion was first boiled in water, called the expanded (E) form, also referred to as pretreated. Conductivity was lower for Nafion originally dried at 80 °C, the normal (N) form, and lower for Nafion originally dried at 105 °C and 120 °C, the shrunken (S) and further-shrunken (FS) forms. The suggested reason for this conductivity difference was that the water channels or clusters collapsed when the membrane was dried at high temperature. For the membrane to achieve high conductivity after such a collapse, it is necessary to expand the collapsed channels by boiling in water. Nafion conductivity κ was modeled using eq 1, shown below,56 where f is the water volume fraction in Nafion, f0 ()0.06) is the water volume fraction at the percolation conductivity, V0 is the water molar volume, Vm is the dry-Nafion molar volume, Ea is the activation energy, R is the gas constant, T is the Nafion temperature, Tref is 303 K, and λ is the water content in mol H2O/mol SO3-. Exponent 1.5 follows from an empirical relation that represents the tortuosity of the polymer conductive pathways
[(
κ ) κ0(f - f0)1.5 exp f)
Ea 1 1 R Tref T
λV0 Vm + λV0
where subscript 0 refers to pure water.
)]
(1)
(2)
Figure 1. Nafion is between BekkTech conductivity clamps. (a) Shown unassembled, Nafion lies across the Teflon bottom piece, contacting platinum mesh and platinum wires. Platinum mesh attaches to platinum wires. The top Teflon piece sits on top of Nafion and the bottom part, and the top and bottom are screwed together. Current passes through the left-most and right-most wires. Inner wires’ potentials characterize membrane conductivity. (b) The conductivity clamp hangs inside of a closed conductivity apparatus containing water for equilibration with liquid or vapor.
Figure 2. The membrane hangs on a spring inside a water-uptake apparatus with water in the bottom. The glass apparatus seals and connects to a vacuum pump. A valve in line opens or closes to pull vacuum or seal the system, and a pressure gauge measures the total pressure in the line. The line disconnects after the valve; atmospheric air flows into the water-uptake apparatus when the valve is open and the pump is not connected. A cathetometer outside of the constanttemperature chamber measures spring extension through the chamber window.
II. Experimental Section Experiments were carefully designed and conducted to avoid problems encountered in previous studies. Nafion 117 was pretreated using the standard procedure in the literature: by boiling, in succession, in 3% aqueous H2O2 to remove organic impurities, in distilled and deionized (DI) water from a Milli-Q Academic System, in 0.5 M H2SO4 to remove ionic impurities, and in DI water for 1 h each. The membrane was then stored in DI water before insertion into a conductivity clamp, shown in Figure 1, or in a water-content apparatus, shown in Figure 2. The important last step of pretreatment is boiling in DI water for 1 h. A membrane of this type is referred to as preboiled. Four membrane samples, I, II, III, and IV, were cut from preboiled Nafion 117. Some literature studies used membranes dried at different temperatures. In this study, a preboiled membrane that was subsequently dried near 105 °C is called predried. Membrane conductivity was obtained from four-probe ACimpedance measurements. The impedance was measured using a Schlumberger 1254 potentiostat and a Schlumberger 1286 frequency-response analyzer that passed an AC current between counter and working electrodes (platinum gauze) from 1 to 65000 Hz, set at a 5 mV alternating voltage at open circuit. The membrane alternating potential was measured using the two inner platinum wires contacting the membrane, shown in Figure 1a. For Nafion membranes I and II, the membrane resistance was the real impedance of the high-frequency
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intercept of the data. The scatter in the real impedance was used to calculate conductivity uncertainty. Conductivity, κ, was obtained from
1 rA ) κ w
(3)
where A is the membrane’s cross-sectional area, r is the real impedance intercept at high frequency, and w is the distance between the inner platinum wires. To determine liquidequilibrated or vapor-equilibrated conductivities, the conductivity clamp containing the membrane was either submerged in or elevated above DI water or Burdick and Jackson high-pressureliquid-chromatography (HPLC) water inside a closed vessel, as indicated in Figure 1. Preboiled membrane I was submerged in HPLC water in the conductivity cell and liquid-equilibrated from 6 to 80 °C. The conductivity was measured after several hours of equilibration at each temperature. The conductivity clamp with membrane I was then removed from the cell and heated to 108 °C at less than 2% RH and held for 30 min. The conductivity cell was cooled, and the clamp was then placed into the cell and vaporequilibrated for 5 days at each temperature with DI water in the bottom of the cell. (There was no flowing gas stream.) For conductivity measurements, the temperature varied from 5 to 80 °C, in increasing order. Membrane II was preboiled, and the conductivity clamp containing the membrane was exposed to 30 °C ambient air until water loss caused the conductivity to drop to 1/10 of its liquid-equilibrated value. Then the membrane was vaporequilibrated with DI water in the bottom of the cell at 30 °C for 5 days. Later, the membrane in the conductivity clamp was removed from the cell, heated to 113 °C, held at this temperature for 30 min, and cooled to 30 °C in an Aroma Mfg. Company Aromatic Model ASD850 constant-temperature chamber exposed to ambient humid air. Predried membrane II was then submerged in DI water at 30 °C. The conductivity was measured at 30, 6, 18, 30, 50, 65, and 80 °C in that order, after equilibrating at each temperature for 1 day. Our water-uptake apparatus was specifically designed and fabricated for Nafion-water equilibria. The apparatus was used to measure the membrane mass inside of the vessel, while the membrane was equilibrated at a set water vapor pressure. To compare water uptake at different temperatures, at different relative humidities, and at different air partial pressures, a membrane can be equilibrated with water vapor in the absence of air (two-component system: water vapor and membrane) or water vapor in the presence of air (three-component system: water vapor, membrane, and air). Since the membrane mass is measured in situ, that is, in the apparatus under a set environmental condition, our method eliminates significant error from water loss that would occur if the membrane were exposed to a different temperature or a different water partial pressure during the weighing process. Figure 2 shows our water-uptake apparatus. A glass chamber (set inside of an Associated Testing Laboratory Model SK-3105 constant-temperature chamber) contains a membrane hanging on a fused-quartz spring. Spring extension was calibrated with several masses at temperature Tcal. The extension was also adjusted for temperature using LC ) LM[1 + 1.35 × 10-4(T Tcal)], where LC is the temperature-corrected spring extension, LM is the measured spring extension, T is the temperature measured in the glass chamber, and Tcal is the calibration temperature, here taken as 19.6 °C.
After a vacuum pump connected to the glass chamber evacuated air and evaporated water vapor, the chamber was closed, and preboiled membrane III was allowed to equilibrate with water vapor. Total pressure of water vapor and air inside the glass chamber was measured with a vacuum gauge. The membrane mass was determined by measuring the spring extension with a cathetometer outside of the constant-temperature chamber. Air pressure was increased by opening a valve on the side of the apparatus. Afterward, membrane III was dried at 105 °C and high vacuum for 2 days to determine the dry membrane mass. The predried membrane was cooled to 30 °C and then vapor-equilibrated for 2 days. The membrane was subsequently dried at 105 °C and high vacuum for 1 day and cooled to 30 °C, before submersion into DI water for 1 h. The predried membrane was blotted with a KimWipe and weighed on a balance. In a separate experiment, preboiled membrane IV was exposed to air for about 10 min before it was placed in the cell. The purpose was to partially remove water from the membrane before starting the water vapor sorption experiment. The initial water content λ ) 16 and the spring extension was monitored until it did not change. At each temperature, the membrane was vapor-equilibrated at 30, 50, 65, and 80 °C for 2 weeks to 1 month until equilibrium was established. Both membranes were submerged in liquid water to obtain water-uptake data; the mass of each liquid-equilibrated membrane was measured. After conducting water sorption measurements on preboiled membranes III and IV, the dry membrane mass was found by drying the membranes at 105 °C and high vacuum for 2 days and then measuring the spring extension. The membrane was cooled to 30 °C and immersed in DI water for 2 days. The predried membrane was blotted with a KimWipe and weighed on a balance. The enthalpy of vaporization of water in Nafion was found by
1 ) γwf ∆hH2O vaporization in Nafion ) ∆hpure H2O vaporization - R
(4) ∂ ln γH2O ∂
(T1) (5)
where γH2O is the water activity coefficient, wf is the weight fraction of water in Nafion, ∆hH2O vaporization in Nafion is the molar enthalpy of vaporization of water in Nafion, ∆hpure H2O vaporization is the molar enthalpy of vaporization of pure water, R is the ideal gas constant, and T is the temperature. These equations are derived in the appendix. III. Results and Discussion III.1 Water Content. Figure 3 shows that, for the vaporsaturated membrane, the water uptake is unaffected by air pressure. At 100% RH, the vapor-equilibrated water content was λ ) 23 ( 1 mol H2O/mol SO3-, as indicated in Table 1. Droplets were not seen on the membrane. For liquid-equilibrated Nafion, λ ) 23 ( 0.1. Therefore, the water content for the vapor-equilibrated membrane is the same as that for the liquidimmersed membrane. There was no Schroeder’s paradox. In these measurements, the membrane thermal history was the same in both cases; a preboiled membrane was used. For the liquidequilibrated membrane III, λ ) 13.1 ( 0.5 near 30 °C after the membrane was dried under vacuum at 105 °C, in essential agreement with the vapor-equilibrated membrane III water
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Figure 3. Air pressure has no effect on water content at 29 °C when pretreated Nafion is in contact with saturated-water vapor. The partial pressure of water is 0.04 bar.
Figure 4. Nafion water content at increasing (2) and decreasing (9) temperature between 30 and 80 °C for Nafion in contact with saturatedwater vapor; (0) shows the water content after 2.5 months at 30 °C.
TABLE 2: Vapor-Equilibrated Membrane Water-Content Hysteresis from 30 to 80 °C and Back to 30 °C; Membrane Held at 30 °C for 2.5 Months water content (moles H2O/mol SO3-) rising T decreasing T hold at T
30 °C
50 °C
65 °C
80 °C
25.3 23.3 23.9
24.6 23.0
23.8 22.4
22.2 22.2
content λ ) 13.7 ( 0.2 at 30 °C after it was dried under the same conditions. Further, to investigate Schroeder’s paradox and the effect of thermal history, water contents were measured for 100% RH vapor-equilibrated preboiled membrane IV from 30 to 80 °C and back to 30 °C. The measured water content had a 0.1% uncertainty for separate water-uptake measurements at each temperature after the sample was equilibrated for 2 weeks or 1 month. In the current work, the water content of the liquidequilibrated membrane IV was λ ) 26 after pretreatment at 30 °C, in good agreement with λ ) 25 for the vapor-equilibrated membrane IV. Water content decreased with rising temperature, as shown in Figure 4. When the temperature decreased from 80 to 30 °C, the water content rose, but it did not recover its initial value, as indicated in Table 2. After decreasing the temperature from 80 to 30 °C, the membrane was held at 30 °C for 2.5 months. The water content increased from λ ) 23.3 to 23.9 with a 0.8% uncertainty, between the third week and 2.5 months, indicating that the membrane was relaxing slowly to its equilibrium state. This relaxation time is expected to decline at higher temperatures. The predried membrane IV
Figure 5. Liquid-equilibrated and 100% relative humidity vaporequilibrated conductivities in the presence of air. Liquid-equilibrated conductivities for membrane I after boiling in DI water (0) and vaporequilibrated conductivity for membrane II after boiling in DI water (2). Vapor-equilibrated conductivities for membrane I after heating to 108 °C (4) and liquid-equilibrated conductivities for membrane II after heating to 113 °C (9). The line shows a fit of liquid-equilibrated conductivities.
liquid-equilibrated water content was 12.4, in good agreement with predried membrane III. Our experimental results suggest that the thermal history of the membrane is responsible for any reported water-content difference between the vapor-equilibrated membrane and the liquid-equilibrated membrane, previously attributed to Schroeder’s paradox. The decrease in water content after increasing the temperature to 80 °C indicates that, because the polymer had lost water at the high temperature, the polymer morphology changed. Since water acts as a plasticizer, it is possible that the morphology was more rigid after exposure to 80 °C. This lessplasticized morphology may not have been able to absorb in the polymer as much water at lower temperatures as had been absorbed previously. Dynamic mechanical analysis on dry Nafion shows chain movement down to 0 °C, which declines as water content rises, indicating that Nafion is viscoelastic above 0 °C and depends on water content.68 Previous vapor-equilibrated water uptake and conductivity studies used membranes initially exposed to even higher temperatures (such as 150 °C under high vacuum), thereby setting a membrane morphology that allows a water uptake smaller than those for preboiled liquid-equilibrated membranes. To determine the enthalpy of vaporization of water in Nafion, the polymer must be relaxed and in its equilibrium state with water. This requirement comes from ∆G ) 0 in the ClausiusClapeyron equation. The preboiled vapor-equilibrated membrane in the increasing temperature study gave an enthalpy of vaporization of water in Nafion of 2454 kJ/kg, similar to 2370 kJ/kg in pure water. The enthalpy of vaporization of water in Nafion was found from the slope of the natural log of the activity coefficient versus 1/T graph and the mean average of the vaporization of pure water between 30 and 80 °C. Since relaxation takes a long time, it is possible that the preboiled vapor-equilibrated membrane may not have been in its equilibrated state, even though the membrane was initially relaxed by being preboiled, and the water content was measured after having been equilibrated for several weeks to a month. III.2 Conductivity. Nafion proton conductivity was measured between 0 and 80 °C for both vapor-equilibrated and liquidequilibrated membranes at atmospheric pressure. Figure 5 and Table 3 show conductivities for liquid-equilibrated and for 100% RH vapor-equilibrated Nafion. The conductivities have a 0.1% uncertainty, as indicated in Figure 5. The conductivity of a
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TABLE 3: Vapor-Equilibrated and Liquid-Equilibrated Membrane Conductivities, Where All Membranes Have the Same Thermal Historya conductivity (S/cm) 5 °C membrane I; pretreated, liquid-equilibrated membrane II; pretreated, vapor-equilibrated membrane I; predried, vapor-equilibrated membrane II; predried, liquid-equilibrated
18 °C
0.085 0.049 0.050
20 °C
30 °C
50 °C
65 °C
80 °C
0.111
0.121 0.118 0.083 0.078
0.160
0.199
0.223
0.120 0.108
0.159 0.159
0.201 0.185
0.064 0.059
a Pretreated: membrane boiled in 3% H2O2, DI water, 0.5 M H2SO4, and DI water for 1 h each. Then, the water and submerged membrane were cooled to 30 °C. Predried: pretreated membrane heated to 108 °C at less than 2% RH and held 30 min. Then, the membrane was cooled to 30 °C.
Figure 6. Liquid-equilibrated and 100% relative humidity vaporequilibrated water content in the presence of air in conductivity experiments. Liquid-equilibrated membrane I after boiling in DI water (0) and vapor-equilibrated membrane II after boiling in DI water (2). Vapor-equilibrated membrane I after heating to 108 °C (4) and liquidequilibrated membrane II after heating to 113 °C (9). Hinatsu et al.’s predried membrane at 105 °C in vacuum for 24 h (+) and Hinatsu et al.’s predried membrane at 80 °C in vacuum for 24 h (×).49
preboiled liquid-equilibrated membrane has an Arrhenius-type dependence on temperature, with a 10.7 kJ/mol activation energy; our high-temperature data agree well with those in the literature.58,69,70 Table 3 and Figure 5 show that the predried membrane conductivity was lower than the preboiled membrane conductivity. After heating a membrane (originally boiled in water) to 108 °C at less than 2% RH, the resulting vaporequilibrated and liquid-equilibrated conductivities at 30 °C were the same, indicating no Schroeder’s paradox. For a membrane originally boiled in DI water, the vapor-equilibrated and liquidequilibrated conductivities were the same at 30 °C, again indicating no Schroeder’s paradox. Conductivity data were fit to an empirical equation to show how conductivity is related to temperature and to water content from 0 to 80 °C. Preboiled liquid-equilibrated membrane conductivity data were fit to
the conductivity model given in eqs 1 and 2. Water content was set to 24 mol H2O/mol SO3-, obtained in our water-uptake study. From our data, the activation energy is 10.7 kJ/mol, and κ0 is 0.337 S/cm. Model results are shown as a line in Figure 5. The model was used to determine the predried membrane water content from the predried conductivity data. Figure 6 and Table 4 compare water content in preboiled and predried membrane I and II to literature values. In the current study, the preboiled membrane water content changed very little with temperature, in agreement with the preboiled water-uptake experiment, showing that the water content decreased slightly with rising temperature. However, the predried Nafion water content increased dramatically with temperature from λ ) 15 to 21 mol H2O/mol SO3- from 5 to 80 °C, in agreement with literature that shows a similar trend.73 Hinatsu found Nafion predried at 105 °C under vacuum for 24 h (S form) increased the liquid-equilibrated water content from λ ) 11 to 21 mol H2O/mol SO3- as the temperature rose from 25 to 100 °C.73 Between 25 °C and 100 °C, their membrane, predried at 80 °C and vacuum for 24 h (N form), had a water content approximately 2 mol H2O/mol SO3- higher than that of a membrane predried at 105 °C. The differences between the current work’s water-uptake values and those of Hinatsu et al. were most likely due to several factors. First, this study’s membranes were exposed to 105 °C and less than 2% RH for 30 min, which was less severe than 105 °C and vacuum for 24 h. Second, this study’s conductivity experiments had much longer equilibration times to permit more polymer relaxation and water uptake. The predried Nafion water content increased with temperature because the membrane was initially constrained. As water absorbed into the predried polymer and plasticized it, the polymer relaxed. This relaxation time decreased, and water absorption rose with increasing temperature. Therefore, the predried Nafion water content increased with temperature. On the other hand, preboiled Nafion was already expanded by boiling and did not relax as the temperature rose, and the water content remained relatively constant.
TABLE 4: This Study’s Vapor-Equilibrated and Liquid-Equilibrated Membrane Water Contents from Conductivity Data, Where All Membranes Have the Same Thermal History, and Water-Uptake Literaturea model water content (moles H2O/mol SO3-) 5 °C membrane I; pretreated, liquid-equilibrated membrane II; pretreated, vapor-equilibrated membrane I; predried, vapor-equilibrated membrane II; predried, liquid-equilibrated Hinatsu et al.; predried S form, liquid-equilibrated73 Hinatsu et al.; predried N form, liquid-equilibrated73
18 °C
24 15 15
20 °C
25 °C
24
30 °C
40 °C
23 23 16 16
15 14 11 13
12 14
50 °C
65 °C
70 °C
80 °C
23
24
23
18 16 13 16
20 20
21 20 18 21
17.5
15 19
a Pretreated: membrane boiled in 3% H2O2, DI water, 0.5 M H2SO4, and DI water for 1 h each. Then, the water and submerged membrane were cooled to 30 °C. Predried: pretreated membrane heated to 108 °C at less than 2% RH and held 30 min. Then, the membrane was cooled to 30 °C. Hinatsu et al.’s predried S and N forms: dried under vacuum for 24 h at 80 and 105 °C, respectively, then cooled and liquid-equilibrated with increasing temperature.49
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TABLE 5: Previous Nafion Water Sorption, Conductivity, and Schroeder’s Paradox Studies authors Schroeder1
Pushpa et al.48 Hinatsu et al.49
Legras et al.51 Morris and Sun52 Takamatsu et al.66
Pineri and Volino67 Meyers53
Anantaraman and Gardner46
Sumner et al.59
Zawodzinski et al.43-45,50,54
Fontanella et al.47 Fontanella et al.61 Edmondson et al.63 Rieke and Vanderborgh57
Sone et al.58
Cahan and Wainright62 Halim et
al.60
McLean38
Zawodzinski et al.71
Weber and Newman55,56
Choi and Datta72
experimental details water sorption Mass increased when gelatin was removed from either 1 × 10-5 or 1 × 10-6 equiv sulfate solution and equilibrated with the water vapor above the solutions. water sorption Predried membrane at 150 °C under vacuum. water sorption Predried membranes for liquid sorption studies. Predried membranes were further dried at 80 °C under vacuum before vapor sorption; waited up to several hours for equilibrium. water sorption Predried membranes under vacuum. water sorption Predried membrane at 150 °C under vacuum. Equilibration time not given. water sorption Predried membrane at 150 °C under vacuum. Removed surface water with KimWipe. Membrane exposed to ambient air to weigh. water sorption Predried membrane at 100 °C under vacuum. water sorption Equilibrated with humidified air for 1 h and water vapor without air for 24 h. Humidity was not measured. Removed surface water with KimWipe. Water sorption was measured while exposed to ambient air. water sorption and conductivity Waited 30 min for vapor equilibration. Removed membrane from humidification to weigh. Dried membrane in a vacuum chamber at 80 °C for 2 h and 105 °C for 30 min. Equilibration time not stated for conductivity. Coaxial probe might have provided a leak for humidification. water sorption and conductivity Flowing air humidity at 60 and 105 °C was not measured. Predried membranes for water sorption. Waited 4 h for sorption vapor equilibrium, but conductivity equilibration time was not given. water sorption and conductivity The liquid-equilibrated membrane was pretreated in boiling water. The vapor-equilibrated setup was possibly heated above and then lowered to the equilibration temperature to humidify the gas faster and to lower vapor-equilibration time.64 Removed surface water with KimWipe. Conductivity was measured with a two probe AC-impedance method. conductivity Membrane was predried under vacuum for 24 h before exposure to 100% RH vapor. conductivity Membrane was initially autoclaved at 20 psi and 127 oC or to 150 °C in distilled water. The humidity level was not measured. The two probe AC impedance was used. conductivity Membrane was predried before exposure to saturated gas. The equilibration time was between 30 min and several hours. Assumed constant membrane thickness. Vapor-equilibrated membrane in an environmental chamber. conductivity Unclear whether samples were liquid-equilibrated or vapor-equilibrated. Applied unknown pressure on the membranes in the conductivity experiment. morphology Membranes were predried at 130 °C under vacuum. Membrane was exposed to ambient humidity in the AFM study, suggesting a fluoride layer on the surface. contact angle Seal was punctured during experiment. The membrane surface was wiped with a KimWipe to remove surface water. Modeling Proposed membrane channels between clusters opened when liquid-equilibrated and closed when vapor-equilibrated. modeling Assumed channel geometry in the membrane and contact angle for water in pores.
comments The humidity of the vapor may have been lower than 100%, or gelatin may have changed morphology when immersed in different salt solutions. Predrying set a different membrane morphology from that when pretreating in boiling water, causing lower water sorption. Predrying set membrane morphology, affecting water sorption. Possibly needed more time for vapor equilibration. Predrying set membrane morphology, affecting water sorption. Predrying set membrane morphology, affecting water sorption. Possibly needed more time for vapor equilibration. Predrying set membrane morphology, affecting water sorption. KimWipe could have removed additional water. May have lost water while weighing. Predrying set membrane morphology, affecting water sorption. Humidified air may not have been at 100% RH. Possibly did not wait long enough in humidified air. KimWipe may have removed more than surface water, and water may have evaporated while weighing membrane. Possibly did not wait long enough for vapor equilibrium. Water may have been lost during weighing. Perhaps they did not remove all water from the membrane during drying.
Predrying set membrane morphology, affecting water sorption and conductivity. Air may not have been at 100% RH. Perhaps needed more time for equilibrium. Liquid- and vapor-equilibrated membranes may have had different thermal histories. The vapor-equilibrated membrane was possibly heated above the equilibration temperature, changing membrane morphology and water sorption. A KimWipe could have removed more than surface water. The two probe AC impedance includes contact and wire resistance in membrane resistance. Predrying set membrane morphology, affecting water sorption and conductivity. Set membrane morphology, affecting conductivity. Membrane may not have equilibrated with 100% RH vapor. The two-probe AC-impedance method includes contact and wire resistance in membrane resistance. Predrying set membrane morphology, affecting water sorption and conductivity. Possibly needed a longer equilibration time. Different pretreatments change membrane thickness. Vapor may not have been at 100% RH since humidity chamber can control only to about 98% RH. Applied pressure affects conductivity.
Predrying set membrane morphology. Membrane was exposed to ambient air. Surface structure may reflect a dried membrane with low water content, rather than one fully humidified. Advancing and receding angles are sensitive to surface roughness and contamination. Membrane water content may have changed due to Parafilm seal leaks, causing internal and surface morphology changes. KimWipe may have left a residue, affecting the water contact angle. Since SAXS and WAXS have a single peak, exact structural information cannot be determined.3 Channels have not been shown experimentally. Structural geometry is not known.3 Contact angle inside the pore cannot be measured.
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IV. Conclusions The experimental results given here show that, at a fixed temperature, the water content of Nafion depends only on the activity of water, regardless of whether the equilibrium phase is liquid water or a saturated water vapor. When exposed to a water activity of unity, the Nafion water content was λ ) 23 ( 1 mol H2O/mol SO3- at 30 °C, independent of air pressure in the range of 0-0.96 bar. The liquid- and vapor-equilibrated water content was the same for the same membrane-pretreatment process. For a preboiled membrane, the 100% RH vaporequilibrated water content decreased with rising temperature but did not recover the initial water content when the temperature declined. The water content of a predried membrane was λ ) 13.7 ( 0.2 when vapor-equilibrated and λ ) 13.1 ( 0.5 when liquid-equilibrated. These results show that the thermal history of the Nafion is very important. For membranes with the same thermal history, the vapor-equilibrated proton conductivity, in the presence of air, increased with rising temperature and was the same as that for liquid-equilibrated conductivity. The preboiled Nafion water content in conductivity experiments changed slightly with increasing temperature, but the predried Nafion water content rose dramatically with temperature. Our water-content and conductivity data show no evidence for Schroeder’s paradox, provided that the thermal history of Nafion is kept constant. Acknowledgment. The authors thank Pat Hagans, John Kerr, Gao Liu, Brian Pivovar, Mukundan Rangachary, Yu Seung Kim, Kendra Krutilla, Francesco Fornasiero, Adam Weber, and Tom Zawodzinski for helpful discussions. The authors gratefully acknowledge collaborations with Los Alamos National Lab, UTC Fuel Cells, and United Technologies Research Center. This work was supported by the Assistant Secretary for Energy Efficiency and Renewable Energy, Office of Hydrogen, Fuel Cells and Infrastructure Technologies Program, by the Office for Basic Sciences of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231, and by a University of California Berkeley Graduate Opportunity Program Fellowship. Appendix In a closed container filled with pure water, Nafion is equilibrated with water vapor L fH0 2O ) f pureH ) f0 2O
(A1)
L f pureH ) fHV2O ) fHM2O ) γwf f0 2O
(A2)
1 ) γwf
(A3)
L where f H0 2O is standard state fugacity of pure water, f pureH is 2O the fugacity of pure liquid water in the container, f 0 is the reference fugacity, f HV2O is the fugacity of water vapor in the container, f HM2O is the fugacity of water in the membrane, γ is the activity coefficient of water in the membrane, and wf is the weight fraction of water in the membrane. The enthalpy of vaporization of water in Nafion, ∆hH2O vaporization in Nafion, is the difference between the enthalpy of water in Nafion, hLH2O, and the enthalpy of water vapor, hHV2O. The enthalpy of water in Nafion is the sum of the L hE enthalpy of pure water, hpure H2O, and the excess enthalpy, h
∆hH2O vaporization in Nafion ) hHV2O - hLH2O
(A4)
L hhEH2O ) hLH2O - h pureH 2O
(A5)
The activity coefficient of water in Nafion at a given concentration and temperature is related to the excess enthalpy by equation A673
∂ ln γH2O ∂
1 T
()
)
hhE R
(A6)
Substituting eq A5 into eq A4 L - hhEH2O ) ∆hH2O vaporization in Nafion ) hHV2O - h pureH 2O
∆hpure H2O vaporization - hhEH2O (A7) Substituting eq A6 into eq A7
∆hH2O vaporization in Nafion ) ∆hpure H2O vaporization - R
∂ ln γH2O ∂
(T1(A8) )
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