J. Phys. Chem. 1996, 100, 16361-16364
16361
Thermoosmosis and Transported Entropy of Water across Poly(4-vinylpyridine/styrene) and Poly(N-vinyl-2-methylimidazole/styrene) Type Membranes in Electrolyte Solutions Masayasu Tasaka,* Takashi Suzuki, Ryotaro Kiyono, Masato Hamada,† and Kiyotaka Yoshie† Department of Chemistry and Material Engineering, Faculty of Engineering, Shinshu UniVersity, Wakasato, Nagano 380, Japan ReceiVed: June 20, 1996X
Poly(4-vinylpyridine/styrene) and poly(N-vinyl-2-methylimidazole/styrene) type membranes (SA-14 and SA15) were prepared as weak-base anion-exchange membranes, and strong-base anion-exchange membranes (SA-14(4) and SA-15(4)) were prepared by quaternizing them with CH3I. Solvent transport across the membranes was measured in electrolyte solutions under a temperature difference. Thermoosmosis toward the cold solution side was clearly observed for membranes SA-14 and SA-15 in KCl and HCl solutions. However, the direction of thermoosmosis was toward the hot side in H2SO4 solutions because the membrane is considerably ionized with H2SO4 and the water in the membrane is more stabilized than that in the external solutions. Thermoosmosis across the quaternized membranes SA-14(4) and SA-15(4) occurred toward the hot side in KCl and KIO3 solutions. The difference between the mean transported entropy of water in the membrane, cs0, and the partial molar entropy of the external solution, s0, was estimated from the thermoosmotic data by combining the experimental data of water flux under an osmotic pressure difference. The values of (sc0 - s0) in KCl solutions were positive for membranes SA-14 and SA-15 and negative for membranes SA14(4) and SA-15(4). Lp ) -V0D*
Introduction Thermoosmotic volume flux across a membrane is observed when there is a temperature difference on both sides of the membrane separated in a solution. Solvent flux is then called thermoosmosis. The direction of thermoosmosis can reverse only if a hydrophilic membrane is exchanged with a hydrophobic membrane even if the two external solutions on both sides of the membrane are kept constant.1 Volume flux, Jv, under a temperature difference, ∆T, can be expressed by eq 1:
-Jv ) De∆ln T ) D∆T
(1)
D ) De/Tm ) D*[(ej0/Tm) - s0] ) D*(sc0 - s0)
(2a)
je0 ) cs0Tm
(2b)
Tm ) ∆T/∆ln T
(2c)
where
The D and De are the thermoosmotic coefficients, D* is a coefficient related to the hydraulic permeability, Lp, as shown in eq 4, je0 is the transported energy per mole of water in the membrane, cs0 is the mean transported entropy per mole of water in the membrane, s0 is the partial molar entropy of water in the external solution, and Tm is the mean temperature in the membrane.1-5 Volume flux under a difference in osmotic pressure, ∆π, can be expressed by eq 3:
-Jv ) Lp∆π
(3)
where † Membrane R & D Department, Ion-Exchange Administration, Asahi Chemical Industry Co., Ltd. 1-3-2 Yakoh, Kawasaki-Ku, Kawasaki 210, Japan. * Corresponding author. Phone: +81-26-226-4101. Fax: +81-26-2284295. Email:
[email protected]. X Abstract published in AdVance ACS Abstracts, September 15, 1996.
S0022-3654(96)01850-3 CCC: $12.00
(4)
If we obtain the values of D and Lp from experiments of thermoosmosis and hydraulic permeation, we can estimate the value of the entropy difference (sc0 - s0) from eqs 2 and 4:
(sc0 - s0) ) V0D/Lp
(5)
For hydrophobic polyethylene and polytetrafluoroethylene membranes thermoosmosis appears from the hot to the cold side just as in distillation.6 This is because the interfacial water structure near hydrophobic surfaces is similar to that at the airwater interface7 and the state of water near the hydrophobic surface resembles that in gas phase.8 Water in the hydrophobic membranes is unstable, and the value of (sc0 - s0) is positive.6 It is known that for cation-exchange membranes the direction of thermoosmosis changes with the counterions.4 However, it has been observed that thermoosmosis across anion-exchange membranes, in general, appears from the cold to the hot solution side except for some membranes with low water content.5,9 For strong-base anion-exchange membranes, both fixed charges of quaternized ammonium and hydrophobic membrane matrix surrounding the fixed charges would act in ordering the solvent water structure, as is known for aqueous solutions containing alkylammonium ions.10,11 Therefore, in general, the mean transported entropy of water in the membranes, cs0, will be lower than the partial molar entropy of the external solution, s0, regardless of the variety of anions. In this study, weak-base anion-exchange membranes were prepared with poly(4-vinylpyridine/styrene) and poly(N-vinyl2-methylimidazole/styrene), which is expected to act as a hydrophobic polymer membrane. In order to analyze the effect of the strongly charged groups on the water structure, anionexchange membranes having the same membrane matrix but containing strong basic groups were prepared by quaternizing the above two membranes with CH3I. In thermoosmotic experiments, for the weak-base anion-exchange membranes KCl, HCl, and H2SO4 solutions were used as the external solutions, © 1996 American Chemical Society
16362 J. Phys. Chem., Vol. 100, No. 40, 1996 and for the strong-base anion-exchange membranes KCl and KIO3 solutions were used as the external solutions. Experimental Section Membranes and Electrolytes. Poly(4-vinylpyridine/styrene) type (SA-14) and poly(N-vinyl-2-methylimidazole/styrene) type (SA-15) membranes cross-linked by divinylbenzene were prepared. The two types of membranes were dipped into a mixture of 1 part methyl iodide and 9 parts acetone to quaternize them at 313 K for 18 h. After that the membranes were washed several times with acetone to remove the methyl iodide sorbed in the membranes. Moreover, the quaternized membranes SA14(4) and SA-15(4) were washed with pure water to remove the sorbed acetone. The membrane thickness was measured for the Cl- form membranes equilibrated with pure water. A special grade of HCl, KCl, KIO3, and H2SO4 was used without purification to prepare the external solutions. Measurements of Ion-Exchange Capacity and Water Content. Ion-exchange capacity was measured by weighing the membranes with the Cl- and the IO3- form using the gravimetric method.12 The ion-exchange capacity is expressed by the unit mmole of ion-exchange groups per gram of the dry membranes without anhydrous counterions. A membrane equilibrated at 0.01 mol kg-1 of electrolyte solution was sandwiched between additional two pieces of wet filter paper equilibrated with the same solution, and then the excess solution on the surface of two wet filter papers on both sides of the membrane was blotted with dry filter paper. The weight of the wet membrane was measured as soon as the wet filter paper was separated from the membrane.13 For quaternized membranes SA-14(4) and SA-15(4) the water content is also expressed by the unit excluding the weight of counterions: grams of water per gram of the dry membranes without anhydrous counterions. However, for membranes SA-14 and SA-15 the water content was estimated from the weight of sorbed solution by neglecting the weight of the solute. Measurements of Thermoosmosis. The volume flux under a temperature difference was measured using the same cell as that used in a previous paper.9 The upper hot 1500 cm3 chamber was separated by a membrane from the lower 96 cm3 cold chamber. The effective area of the membrane was 28 cm2. The two temperatures in the cold side and in the hot side were controlled to fix the mean temperature at 308.2 K. The ratio of the effective temperature difference across the membrane, ∆T, to the temperature difference of two bulk solutions, ∆Tb, was about 0.7.9 All measurements were carried out at 0.01 mol kg-1 of electrolyte solutions. Measurements of Osmotic Volume Flux. The volume flux under an osmotic pressure difference was measured using the same cell as that used in the previous paper.5 The effective area of the membrane was 2.54 cm2. The osmotic pressure difference was applied using the difference in concentrations of sucrose. For membranes ionized by acids, in order to keep the degree of ionization under the same acidity, the osmotic pressure difference was applied using the solutions prepared by adding sucrose to 0.01 mol/kg of acid solution. The osmotic pressure coefficient of mixtures was assumed to be the same as that of pure sucrose solutions containing no acid, for the lack of data. Measurements of Membrane Resistance. Membranes were equilibrated at 0.01 mol kg-1 of the electrolyte solutions. Two flat, impervious carbon electrodes were directly connected to both sides of the membrane equilibrated with the solution, and the membrane resistance was measured at 298 K with 10 kHz
Tasaka et al. TABLE 1: Thickness and Ion-Exchange Capacity of Membranes membrane
thickness mm
SA-14 SA-14(4) SA-15 SA-15(4)
0.181 0.191 0.180 0.188
ion-exchange capacity mmol/g dry membrane 1.66 1.64
TABLE 2: Properties of Membranes
membrane SA-14 SA-14(4) SA-15 SA-15(4)
electrolyte KCl HCl H2SO4 KCl KIO3 KCl HCl H2SO4 KCl KIO3
membrane resistancea/ Ω cm2
transport number of anionsb
water content g H2O/g dry membrane
2160 82.02 16.00 7.53
0.98
2040 126.0 18.91 8.76
0.97
0.10 0.16 0.23 0.32 0.41 0.09 0.15 0.16 0.30 0.39
0.98
0.97
a Measured in 0.01 mol kg-1 solutions at 10 kHz. b Calculated from the membrane potential in 0.1 mol kg-1/membrane/0.2 mol kg-1 of KCl solutions.
using a low-frequency impedance analyzer 4192A (YokogawaHewlett-Packard, Ltd., Japan). The effective area of membrane was 1 cm2. Results and Discussion The thickness and the ion exchange capacity of the membranes are listed in Table 1. The thickness of weak-base anionexchange membranes SA-14 and SA-15 was about 0.18 mm and that of the corresponding strong-base anion-exchange membranes SA-14(4) and SA-15(4) was slightly thicker to about 0.19 mm because the membranes were swollen owing to the quaternization. Membrane resistance decreasd with the series RKCl > RHCl > RH2SO4 for membranes SA-14 and SA-15 because of the increase in the degree of ionization by acids as shown in Table 2. Moreover, the membrane resistance of the quaternized membranes SA-14(4) and SA-15(4) in KCl solutions was lower than those of SA-14 and SA-15 in acid solutions. The water content of quaternized membranes SA-14(4) and SA-15(4) with the IO3- form was larger than that with the Cl- form because of the larger radii of the hydrated IO3- ions. Transport numbers of anions estimated from the concentration membrane potential in 0.01//0.02 mol kg-1 of KCl solution systems were 0.970.98 for all membranes as shown in Table 2. Therefore, these membranes can be considered to be ideally perm-selective for counterions under the experimental conditions. Figure 1 shows the thermoosmotic volume flux against the temperature difference of bulk solutions for poly(4-vinylpyridine/styrene) membranes SA-14 and its quaternized membrane SA-14(4) at 0.01 mol kg-1 of electrolyte solutions. For the untreated weak-base membrane SA-14 the direction of thermoosmosis was from the hot to the cold solution side in KCl solutions. This is because membrane SA-14 was hydrophobic in KCl solutions as expected from the high membrane resistance and the low water content as shown in Table 2. In HCl solutions membrane SA-14 will be fairly ionized by HCl. The membrane resistance of SA-14 in HCl solutions was lower than that in KCl solutions. But thermoosmosis occurred toward the cold solution side in HCl solutions as well as in KCl solutions. For membrane SA-14 in KCl and HCl solutions, the values of thermoosmosis were similar, although the membrane
Entropy of Water
Figure 1. Dependence of thermoosmotic volume flux, JV, on the temperature difference of bulk solutions, ∆Tb, for membrane SA-14 in KCl, HCl, and H2SO4 solutions and for membrane SA-14(4) in KCl and KIO3 solutions.
Figure 2. Dependence of thermoosmotic volume flux, JV, on the temperature difference of bulk solutions, ∆Tb, for membrane SA-15 in KCl, HCl, and H2SO4 solutions and for membrane SA-15(4) in KCl and KIO3 solutions.
resistance in the HCl solution was lower than that in the KCl solution. Similar phenomena were observed for the poly(Nvinyl-2-methylimidazole/styrene) membrane SA-15 as shown in Figure 2. However, for membrane SA-15 the absolute value of thermoosmosis in HCl solutions is larger than that in KCl solutions. It may be considered from the data of membrane resistance in H2SO4 solutions that membranes SA-14 and SA-15 are considerably ionized and the state of water in the membrane is stabilized. Thermoosmosis in H2SO4 solutions occurred from the cold to the hot side. For quaternized membranes SA-14(4) and SA-15(4) thermoosmosis occurred toward the hot solution side in both KCl and KIO3 solutions. If there are hydrophilic ion-exchange groups to act in ordering the structure of water in the membrane, the hydrophobic membrane matrix will be able to cooperate to act in ordering the water structure, as is known for aqueous solutions of alkylammonium ions.10,11 If there are little hydrophilic ion-exchange groups in the membrane, just as SA-14 and SA-15 in KCl solutions, the hydrophobic membrane matrix will act in disordering the water structure, as is known for hydrophobic polyethylene and polytetrafluoroethylene membranes.6 Figure 3 shows the relationship between the osmotic pressure difference and the volume flux for membrane SA-14 in KCl, HCl, and H2SO4 solutions and for membrane SA-14(4) in KCl and KIO3 solutions. For membrane SA-14 the flux increased
J. Phys. Chem., Vol. 100, No. 40, 1996 16363
Figure 3. Dependence of osmotic volume flux, JV, on the osmotic pressure difference of external solutions, ∆π, for membrane SA-14 in KCl, HCl, and H2SO4 solutions and for membrane SA-14(4) in KCl and KIO3 solutions.
Figure 4. Dependence of osmotic volume flux, JV, on the osmotic pressure difference of external solutions, ∆π, for membrane SA-15 in KCl, HCl, and H2SO4 solutions and for membrane SA-15(4) in KCl and KIO3 solutions.
TABLE 3: Values of D, D*, (sc0 - s0), and cs0 membranes SA-14
SA-14(4) SA-15
SA-15(4) a
electro- D × 108 lytes cm K-1 s-1 KCl HCl H2SO4 KCl KIO3 KCl HCl H2SO4 KCl KIO3
1.3 1.4 -3.9 -5.1 -11.4 3.8 7.3 -4.0 -2.9 -4.2
D* × 108 cm mol J-1 s-1
(sc0 - s0) J K-1 mol-1
cs0a J K-1 mol-1
1.0 2.1 4.4 8.7 9.1 1.2 3.6 3.8 9.1 8.3
1.3 0.68 -0.87 -0.59 -1.3 3.2 2.0 -1.1 -0.32 -0.51
5.4 4.8 3.2 3.5 2.8 7.3 6.1 3.0 3.8 3.6
Assumed s0 ) 4.1 J K-1 mol-1 at 308.2 K.14
with the order of electrolytes KCl < HCl < H2SO4, which corresponds to the order of the membrane conductance. The osmotic volume flux for SA-14(4) was fairly larger than that for SA-14 because of the large difference in water content. Figure 4 shows the osmotic volume fluxes for membranes SA15 and SA-15(4), which are similar to those for SA-14 and SA14(4) shown in Figure 3. The values of D, D*, and (sc0 - s0) estimated from the data shown in Figures 1-4 are listed in Table 3. The mean molar transported entropy of water in the membranes was estimated and listed in Table 3, assuming the partial molar entropy of water at 0.01 mol kg-1 of electrolyte solutions equals 4.1 J K-1
16364 J. Phys. Chem., Vol. 100, No. 40, 1996 mol-1 of the molar entropy of pure water at 308 K.14 For weakbase membranes SA-14 and SA-15 the values of (sc0 - s0) or cs0 decrease with the order of the electrolytes KCl > HCl > H2SO4, and for strong-base anion-exchange membranes SA-14(4) and SA-15(4) the values of (sc0 - s0) or cs0 in KCl solution were larger than those in KIO3 solution. For KCl solutions the value of (sc0 - s0) or cs0 of the weak-base anion-exchange membranes is very much larger than that of the strong-base anion-exchange membranes because of the difference in hydrophobicity. Conclusions 1. For hydrophobic anion-exchange membranes containing weak-base groups, thermoosmosis in KCl and HCl solutions occurred clearly toward the cold solution side. 2. For weak-base anion-exchange membranes strongly ionized by H2SO4 and for strong-base anion-exchange membranes quaternized by CH3I, the direction of thermoosmosis turned toward the hot solution side. 3. For KCl solutions the mean transported entropy of water in weak-base anion-exchange membranes is larger than that in strong-base anion-exchange membranes. Acknowledgment. The authors thank Mr. M. Shibata for his technical assistance in measuring the volume flux under an osmotic pressure difference.
Tasaka et al. References and Notes (1) Tasaka, M. Pure Appl. Chem. 1986, 58, 1637. (2) Tasaka, M.; Nagasawa, M. Biophys. Chem. 1978, 8, 111. (3) Tasaka, M.; Suzuki, T.; Kiyono, R. Membr. Symp. (Japan) 1994, No. 6, 53. (4) Tasaka, M.; Suzuki, T.; Kiyono, R.; Sekiguchi, O. Proc. Int. Symp. Membr. Membr. Processes 1994, 86. (5) Suzuki, T.; Kiyono, R.; Tasaka, M. J. Membr. Sci. 1994, 92, 85. (6) Tasaka, M.; Mizuta, T.; Sekiguchi, O. J. Membr. Sci. 1990, 54, 191. (7) Du, Q.; Freysz, E.; Shen, Y. R. Science 1994, 264, 826. (8) Kusanagi, H. Kobunshi High Polym. Jpn. 1993, 42, 314. (9) Tasaka, M.; Urata, T.; Kiyono, R.; Aki, Y. J. Membr. Sci. 1992, 67, 83. (10) Nightingale, E. R., Jr. In Chemical Physics of Ionic Solutions; Conway, B. E., Barada, R. G., Eds.; John Wiley & Sons, Inc.: New York, London, Sydney, 1966; Chapter 7. (11) Uedaira, H.; Uedaira, H. Zh. Fiz. Khim. 1968, 42, 3024. (12) Bunzl, K.; Sansoni, B. Anal. Chem. 1976, 48, 2279. (13) Kiyono, R.; Tanaka, Y.; Sekiguchi, O.; Tasaka, M. Colloid Polym. Sci. 1993, 271, 1183. (14) Lentz, B. R.; Hagler, A. T.; Scheraga, H. A. J. Phys. Chem. 1974, 76, 1531.
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