Win−Win Coupling in Electrodialysis with Bipolar Membranes (EDBM

Jan 26, 2009 - The investors will benefit from allocation of investment and economies of scale as well as cleaner production. Nonetheless, this push p...
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Ind. Eng. Chem. Res. 2009, 48, 1699–1705

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Win-Win Coupling in Electrodialysis with Bipolar Membranes (EDBM) for Cleaner Production Chuanhui Huang, Tongwen Xu,* Haozhe Feng, and Qiuhua Li Laboratory of Functional Membranes, School of Chemistry and Materials Science, UniVersity of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China

An obstacle to the development of electrodialysis with bipolor membranes (EDBM) technologyshigh fixed costscan be cleared away by allocating the investment among factories or plants, but it requires that EDBM couple two processes inside and provide respective products cost-effectively. To assess the process coupling, piperazine sulfate (PzH2SO4) and sodium gluconate (NaGlu) were used as model agents for Pz regeneration and HGlu production, respectively. The results showed that the highest current efficiency was achieved at the highest current density, and the lowest energy consumption at the highest feed concentration. The process cost was estimated to be $0.80 kg-1 Pz and $0.17 kg-1 HGlu in the coupled operation, which were less than those in separate operationss$0.96 kg-1 Pz and $0.24 kg-1 HGlu. Apart from environmental benignity, the process coupling in EDBM can achieve a win-win economy due to allocation of investment and economies of scale. Introduction A bipolar membrane is a composite membrane consisting of a cation-exchange layer and an anion-exchange layer; under reverse potential bias, it can split water (or methanol) into H+ and OH- (or H+ and CH3O-) at a high efficiency and without gas emission. Having bipolar membranes integrated, electrodialysis can perform acid and/or base production or regeneration, acidification and/or alkalization, and some green chemical syntheses. This technology is named electrodialysis with bipolar membrane (EDBM), and its essential characteristic is direct conversion of salt and supply of H+ and OH-/alkoxide ions in situ without second salt pollution. Since EDBM can recycle resources from waste discharges and eliminate or alleviate pollution, it is classified as a sustainable technology and has found many applications in chemical synthesis, food processing, and environmental protection.1-5 Despite the technical advance, economical advantage, and environmental benignity, a high fixed cost of EDBM, specifically the bipolar membrane cost (ca. $1200 m-2 in current Chinese market), often keeps the investment away from the decision-making stages. Correspondingly, a vicious circle of economic activities will be formed if the application and manufacture of bipolar membranes both remain on a small scale. To make the stone roll, an increase in the total investment, together with a decrease in per capita investment, can be a strength-saving “push”, i.e., allocating the investment among those factories or plants which need EDBM technology and look for cooperation. The investors will benefit from allocation of investment and economies of scale as well as cleaner production. Nonetheless, this push poses a strict requirement regarding the adaptability of EDBM technology. To asses the adaptability, this work couples in EDBM two processes: regeneration of flue-gas desulfurizing agents and production of gluconic acid. The correspondent model agents used for experiments are (a) piperazine sulfate (PzH2SO4), a heat-stable salt formed in desulfurization of flue gas by using * To whom correspondence should be addressed. Tel.: +86-5513601587. Fax: +86-551-3601592. E-mail: [email protected].

piperazine (Pz),6 and (b) sodium gluconate (NaGlu), a raw material used to produce gluconic acid (HGlu) through ion exchange. Experimental Apparatus and Procedure Sample Preparation. PzH2SO4 was prepared by following the procedures reported in the literature.6 All the other chemicals were of analytical grade. Distilled water was used throughout. Apparatus. A laboratory-scale EDBM setup was used for process coupling. It was mainly comprised of four parts: (a) a direct current power supply (DF1731SD2A, Zhongce Electronics Co. Ltd.), (b) beakers to store the feeds, (c) submersible pumps (AP1000, Zhongshan Zhenghua Electronics Co. Ltd.) to circulate the solutions at the maximal speed of 27 dm3 h-1, and (d) an EDBM stack, as shown in Figure 1a. The stack adopted a BPA-BP-C (BP, bipolar membrane; C, cation-exchange membrane; A, anion-exchange membrane) configuration with one repeating unit. Specifically, the stack had (a) a cathode and an anode, both made of titanium coated with ruthenium; (b) Plexiglas spacers (thickness ) 9 mm) to separate the membranes with Viton gaskets as the seals; (c) an anion-exchange membrane (Neosepta AMX, Table 1), a cation-exchange membrane (Neosepta CMX, Table 1), and two bipolar membranes (Fumasep FBM, Table 1), all with an effective membrane area of 7.07 cm2; (d) supporting electrolyte solutions and electrode rinsing solutions, which were both prepared from sodium sulfate (Na2SO4, 0.35 mol dm-3). For industrialization, the unit can be repeated between a pair of electrodes to treat more feed solutions. In those multiunit stacks, electrode factors such as water decomposition and electrode electrical resistance have less influence on stack performances. As a comparison, two other stacks, as shown in Figure 1b, were used for Pz regeneration and HGlu production separately. The other conditions except configuration-related ones were identical with the process coupling experiments. All the experiments were conducted at a certain constant current intensity, and the voltage drop across the stack was measured with a digital multimeter (GDM8145, Good Will Instrument Co. Ltd.). Before a current was applied, the independent solutions were circulated for 30 min, and all

10.1021/ie801192k CCC: $40.75  2009 American Chemical Society Published on Web 01/26/2009

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Figure 1. Schematic of the EDBM stacks used for experiments: (a) coupled operation; (b) separate operations. A, anion-exchange membrane; C, cationexchange membrane; BP, bipolar membrane; Pz, piperazine; NaGlu, sodium gluconate. Table 1. Membrane Propertiesa membrane

ion exchange feature

thickness (µm)

IEC (mequiv g-1)

area resistance (Ω cm2)

selectivity (%)

Neosepta CMX Neosepta AMX Fumasep FBM

cationic anionic bipolar

140-200 120-180 200-250

1.5-1.8 1.4-1.7

1.8-3.8 2.0-3.5

>97 >95

a

voltage drop (V)

efficiency (%)

1.1

>98

Note: The data are collected from the product brochures provided by the corresponding companies.

the visible gas bubbles in every compartment were eliminated. The Pz concentration was determined by using UV spectrophotometry. The HGlu concentration was determined by titration with NaOH using phenolphthalein (pH 8.0-9.8) as indicator. Calculation of Current Efficiency and Energy Consumption. The current efficiency η was calculated as n)

(Ct - C0)zBF It

(1)

where C0 and Ct are the concentrations of Pz or HGlu at times 0 and t, respectively (C0 ) 0); z is the absolute chemical valence (2 for Pz and 1 for HGlu); B is the circulated volume of solution in the base or acid cycle; I is the current intensity (constant in each experiment); and F is the Faraday constant.7 In this work, t was equal to 1 h, and the change of fluid volume in each cycle was negligible; i.e., B ) 0.5 dm3.

The energy consumption E (kWh kg-1) was calculated as E)

∫ gUIdt C BM

(2)

t

where U is the voltage drop across the EDBM stack; I is the current intensity; Ct is the concentration of Pz or HGlu at time t; B is the circulated volume of solution in the base or acid cycle; M is the molar mass (86.14 g mol-1 for Pz and 196.16 g mol-1 for HGlu); and g is a factor dependent on operation modes, i.e., g ) 0.5 for coupled operation (the electricity consumed is allocated on both products) and g ) 1 for separate operation. All experimental data were determined through three independent measurements, and the uncertainty with those results was estimated to be approximately (5%. Results and Discussion System Overview. To have a better understanding of the complex results, here is an overview of the experimental

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Figure 2. Calculated ion distribution: I, the maximum OH- or H+ yield (0.0026 mol) at a current density of 10 mA cm-2 within 60 min; II, 0.0079 mol at 30 mA cm-2; III, 0.0132 mol at 50 mA cm-2. (a) 0.15 mol dm-3 PzH2SO4 and 0.30 mol dm-3 NaGlu; (b) 0.30 mol dm-3 PzH2SO4 and 0.30 mol dm-3 NaGlu; (c) 0.30 mol dm-3 PzH2SO4 and 0.15 mol dm-3 NaGlu; (d) trace species in PzH2SO4 or NaGlu aqueous solutions.

Figure 3. Schematic of species’ transport in the EDBM stack.

systems. As shown in Figure 1a, PzH2SO4 and NaGlu solutions are fed into the two compartments adjacent to a bipolar membrane, respectively. The bipolar membrane splits water into H+ and OH-: the H+ replaces Na+ in the NaGlu solution for HGlu production; the OH- replaces SO42- and HSO4- in the PzH2SO4 solution for Pz regeneration. Meanwhile, Na+, SO42-, and HSO4- migrate out through the cation-exchange and anionexchange membranes, respectively. Although H+ and OH- have much higher mobilities than other ions due to the tunneling effect, 15 they were far from the main current carriers through the cation-exchange or anion-exchange membranes since they were buffered to a trace level as compared to Na+, SO42- or HSO4-. Figure 2 presents a calculated ion distribution (based on dissociation constants, Table 2, 8-13) in the studied systems. The species of low concentration in Figure 2a-c can have a clear view in Figure 2d. Although PzH2SO4 and NaGlu are both buffers, they have distinctive buffering strategies and capacities.

For PzH2SO4, OH- is buffered by conversion of PzH22+ into monovalent cations: PzH+; for NaGlu, H+ is buffered by conversion of Glu- into molecules: HGlu. As for the buffering capacities at the same equivalent, PzH2SO4 has a larger one for OH- than NaGlu for H+ since Pz has smaller dissociation constants (Kb1 ) 10-4.27, Kb2) 10-8.66; Table 2). Extra attention should be drawn to the solubility parameter δsp in Table 2: 22.3 MPa0.5 for Pz and 50.9 MPa0.5 for HGlu. According to the principle “like dissolves like”, a certain amount of the regenerated Pz will be distributed into bipolar and monopolar membranes, while most of the produced HGlu stays in aqueous solutions. As a result, the determined Pz concentration will be less than the total since only solutions (no membranes) are used for Pz determination. Notably, the Pz concentration is larger in a 0.15 mol dm-3 PzH2SO4 solution than in a 0.30 mol dm-3 one since the latter has a larger buffering capacity. Consequently, the membranes adjacent to a 0.30 mol dm-3 PzH2SO4 solution will have less Pz distribution. As for the transport of species, there are four main aspects, as illustrated in Figure 3, to be considered. (a) Water SplittingsThe Source of H+ and OH-. With regard to the splitting, there exist two mechanisms: electrocatalysis and chemical catalysis. The former is the wellknown second Wien effect, and the latter is the catalysis of ionic groups or added chemicals at the interface of a bipolar membrane. Particularly, chemical catalysis is an effective means to decrease the voltage drop of water splitting and thus used to modify bipolar membranes. Moreover, in a weak direct current field, chemical catalysis plays a more important role in splitting water.

1702 Ind. Eng. Chem. Res., Vol. 48, No. 4, 2009 Table 2. Selected Properties of Model Agents

a The data are from literature.8,9 b The data are from literature.8,9 c Calculated by using the Fedors group contribution method.10 δsp(H2O), from literature.11 d Calculated by using the method reported in the literature.12 ∞, infinite dilution. e Calculated as λ0 ) D∞ziF2/RT: zi, charge; F, the Faraday constant; R, gas constant; T, absolute temperature. The data in remarks are collected from literature.13 e Measured with a digital conductivity meter (YEW Model SC51).

Figure 4. Performances of the coupled system: (a) voltage drop; (b) product yield; (c) current efficiency; (d) energy consumption.

(b) Counterion MigrationsSeparation of Impurity Ions. SO42- and HSO4- (the counterions for anion-exchange

membranes, and Na+ (the counterion for cation-exchange membranes) are the dominant current carriers and continu-

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Figure 5. Comparison between coupled and separate operations: (a) voltage drop; (b) product yield; (c) current efficiency and energy consumption. Current density i ) 50 mA cm-2; couple, 0.30 mol dm-3 PzH2SO4 and 0.30 mol dm-3 NaGlu.

ously migrate out of PzH2SO4 and NaGlu solutions, respectively. As aforementioned, OH- and H+ are buffered to a trace level and their competition with other counterions is negligible in this work. (c) Co-ion LeakagesConsequence of Membrane’s Incomplete Permselectivity. These co-ions are H+ and Na+ (for anionexchange membranes); OH-, SO42-, and HSO4- (for cationexchange membranes); Glu- (for the cation-exchange layer of bipolar membrane); PzH22+ and PzH+ (for the anion-exchange layer of bipolar membrane). These ions compete with counterions as current carriers; therefore, they decrease product yields and/or contaminate the products. (d) Molecular DiffusionsA Factor for the Decrease in Current Efficiency. Pz and HGlu, as neutral molecules, will diffuse through bipolar and monopolar membranes under the concentration gradient and thus reduce current efficiency. In comparison, a bipolar membrane has a larger thickness than each of the monopolar membranes, so the diffusion flux through bipolar membranes is less. Whether bipolar or monopolar membranes, an increase in current density will lead to a decrease in the flux ratio of diffusion/migration since diffusion is timedependent. Correspondingly, the current efficiency increases. Process Coupling in EDBM. Figure 4a shows the voltage drops across the EDBM stack at different feed ratios (0.15 and 0.30, 0.30 and 0.30, and 0.30 and 0.15; PzH2SO4 and NaGlu; mol dm-3) and current densities (10, 30, and 50 mA cm-2). Obviously, whatever the feed ratio, the voltage drop increases as current density increases and has a leap at the beginning. The leap is corresponding to (a) salt depletion and subsequent

water splitting at the interface of bipolar membranes14 and (b) generation of gas bubbles in electrode compartments.6 With water splitting undergoing, the generated H+ and OH- act as current carriers and decrease the electrical resistance of bipolar membranes. Meanwhile, the production of low-conductive moleculessPz and HGlusleads to an increase in the stack electrical resistance. Balanced by these factors, the voltage drop level off after the leap. As for the operations at the same current density, the voltage drop changes in different manners. In the case in which i ) 10 mA cm-2, the voltage drops have the following order: 0.30 and 0.15 > 0.15 and 0.30 > 0.30 and 0.30. That can be explained by the conductivities of PzH2SO4 and NaGlu (the former has a larger conductivity, Table 2). Nonetheless, for i ) 30 and 50 mA cm-2, the couples 0.30 and 0.15, and 0.15 and 0.30 have close voltage drops; i.e., the stack electrical resistance of the couple 0.30 and 0.15 increases by a similar amount when i increases from 10 to 30 or 50 mA cm-2. This can be explained by the affinity of Pz to membranes mentioned above. As current density increases and thus Pz yield increases, more Pz will be distributed into anion-exchange and bipolar membranes until saturation. These Pz molecules, though in a trace amount, will form a hydrophobic layer on membrane surfaces and increase the membrane electrical resistance dramatically. Consequently, the stack voltage drop increases. However, for the couple 0.30 and 0.30, the PzH2SO4 solution has a larger buffering capacity and thus less Pz is distributed into membranes. So it has the lowest voltage drop. As for NaGlu solutions, its strategy for H+ buffering is to increase molecule’s quantity (HGlu, high electrical resistance), so they have a higher

1704 Ind. Eng. Chem. Res., Vol. 48, No. 4, 2009 Table 3. Estimation of Process Cost for given product Pz

HGlu

Pz

HGlu

coupled 50 7.07 0.35 0.3 BP-A-BP-C 1 0.81 22.03

separate 50 7.07 0.35 0.3 BP-A 1 4.84 4.82

separate 50 7.07 0.35 0.3 BP-C 1 1.30 22.03

0.1 0.08 0.00 0.09

0.1 0.48 0.02 0.51

0.1 0.13 0.01 0.14

Operation Conditions operation mode current density, mA cm-2 effective membrane area, cm2 concentration of Na2SO4, mol dm-3 concentration of PzH2SO4 or NaGlu, mol dm-3 stack configuration repeating unit number energy consumption after allocation, kWh kg-1 process capacity, kg year-1

coupled 50 7.07 0.35 0.3 BP-A-BP-C 1 3.71 4.83

electricity charge, $ (kWh)-1 energy cost for the regeneration, $ kg-1 energy cost for the peripheral equipment, $ kg-1 total Energy cost, $ kg-1

0.1 0.37 0.02 0.39

membrane lifetime and the amortization of the peripheral equipment, year membrane price (monopolar membrane), $ m-2 membrane price (bipolar membrane), $ m-2 membrane cost, $ stack cost, $ peripheral equipment cost, $ total investment cost, $ amortization, $ year-1 interest, $ year-1 maintenance, $ year-1 total fixed cost, $ year-1 scale factor final total fixed cost, $ year-1 allocation factor allocated fixed cost, $ year-1 allocated fixed cost, $ kg-1

3

3

3

3

400 1200 2.26 3.39 5.09 8.48 2.83 0.68 0.85 4.36 0.90 3.92 0.5 1.96 0.41

400 1200 2.26 3.39 5.09 8.48 2.83 0.68 0.85 4.36 0.90 3.92 0.5 1.96 0.09

400 1200 1.13 1.70 2.55 4.24 1.41 0.34 0.42 2.18 1.00 2.18 1.0 2.18 0.45

400 1200 1.13 1.70 2.55 4.24 1.41 0.34 0.42 2.18 1.00 2.18 1.0 2.18 0.10

total process cost, $ kg-1

0.80

0.17

0.96

0.24

Energy Cost

Investment Cost

voltage drop than PzH2SO4 solutions. This is apparent for the NaGlu solution of a lower concentration as in the couple 0.30 and 0.15. The later increase in voltage drop of the couple 0.30 and 0.15 also confirms the larger increase in stack electrical resistance due to the formation of HGlu. Figure 4b shows the Pz or HGlu yields at different conditions. Generally, the product yields increase as current density increases, and Pz concentration is near half of HGlu concentration. The latter is because 2 mol of OH- are needed for production of 1 mol of Pz. Figure 4c shows the current efficiencies of coupling systems. Although the changes appear complex, two general trends can be found. One is that as current density increases, current efficiency increases; this can be explained by the molecular diffusion analysis aforementioned. The other is that current efficiency for Pz regeneration is lower than that for HGlu production at lower current densities. This can be explained by the distribution of Pz on membranes, which has a saturation amount and thus accounts for a lower proportion in the total Pz yield at higher current densities. Figure 4d shows the energy consumption of coupling systems. As current density increases, energy consumption increases. At the same current density, energy consumption has the following order: 0.30 and 0.15 > 0.15 and 0.30 > 0.30 and 0.30. This order can be explained by the trends regarding the voltage drop and product yields discussed above. Comparison between Coupled and Separate Operations. Figure 5a shows the voltage drop across the EDBM stack using different operation modes. The current density was set at 50 mA cm-2, and the couple 0.30 and 0.30 was used for

comparison. The voltage drop has the following order: (0.30 and 0.30 PzH2SO4 and NaGlu) > 0.30 NaGlu > 0.30 PzH2SO4. The separate operations use less compartments and membranes, so the stack electrical resistance is less than that in coupled operation. Furthermore, the separate operation for Pz regeneration has the lower voltage drop than that for HGlu production, and it is mainly because the latter has a higher electrical resistance. Figure 5b shows the product yields. There is no significant difference between coupled and separate operations. Figure 5c shows the current efficiency and energy consumption. Between coupled and separate operations, there is no significant difference of current efficiency but of energy consumption. The coupled operation has lower energy consumption than separate operations do. To sum up, the current efficiency for Pz regeneration is 98% for both coupled and separate operations, and that for HGlu regeneration is the same. The energy consumption is 5.5 kWh kg-1 of Pz for coupled operation and 8.5 kWh kg-1 of Pz for separate operation; and 1.2 kWh kg-1 of HGlu for coupled operation and 2.1 kWh kg-1 of HGlu for separate operation. Process Economics. The cost estimation is made on the basis of the laboratory-scale setup (Table 3), and the corresponding calculation was conducted using the method reported in the literature.15 Besides, the following modifications and hypotheses are considered for calculation. (a) Modification on Energy Consumption. For industrialization, an EDBM stack with more repeating units will be employed, and the electrode factors will have much less influence on energy consumption. To have a better estimation,

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the apparent electrical resistance of electrode pair (including electrical resistance of the electrode pair, thermodynamic potential required by water electrolysis, and overpotentials; 16.7 Ω; 298 K; 0.35 mol dm-3 Na2SO4; I ) 0.35 A) is subtracted from the stack electrical resistance. All of the data of energy consumption are recalculated. (b) Scale Factor. Considering economies of scale, the fixed cost reduces to a certain degree. In calculation, the scale factor is set at 0.9, i.e., 10% reduction. In fact, the scale factor can be much lower since the bipolar membrane price decreases from $1200 m-2 to $800 m-2 (scale factor ) 0.67) if membrane usage increases to a large scale in China. (c) Allocation Factor. For this work, two factories cooperate and share the operation cost and fixed cost. Correspondingly, the allocation factor is set at 0.5. According to calculation, the process costs for Pz regeneration and HGlu production in coupled operation are $0.80 kg-1 Pz and $0.17 kg-1 HGlu, respectively. The costs are both less than those in separate operations ($0.96 kg-1 Pz and $0.24 kg-1 HGlu). Obviously, the process coupling in EDBM can achieve a win-win economy due to allocation of investment and economies of scale. Note that this work is a preliminary research. There is much more work to do before bringing the process coupling to industrialization: high-conversion experiments, reduction of cross-contamination, selection of subjects for coupling, pilotscale tests, and simplification of operation, etc. Acknowledgment This research was supported by the National Science Foundation of China (Grant No. 20636050) and the Key Foundation of the Educational Committee of Anhui Province (Grant Nos. KJ2007A016 and KJ2008A69). Literature Cited (1) Bazinet, L.; Lamarche, F.; Ippersiel, D. Bipolar membrane electrodialysis: Applications of electrodialysis in the food industry. Trends Food Sci. Technol. 1998, 9, 107–113.

(2) Wilhelm, F. G.; Pu¨nt, I.; van der Vegt, N. F A. Asymmetric bipolar membranes in acid-base electrodialysis. Ind. Eng. Chem. Res. 2002, 41, 579–586. (3) Xu, F. N.; Innocent, C.; Pourcelly, G. Electrodialysis with ion exchange membranes in organic media. Sep. Purif. Technol. 2005, 43, 17– 24. (4) Huang, C. H.; Xu, T. W. Electrodialysis with bipolar membranes for sustainable development. EnViron. Sci. Technol. 2006, 40, 5233–5243. (5) Saxena, A.; Gohil, G. S.; Shahi, V. K. Electrochemical membrane reactor: Single-step separation and ion substitution for the recovery of lactic acid from lactate salts. Ind. Eng. Chem. Res. 2007, 46, 1270–1276. (6) Huang, C. H.; Xu, T. W.; Jacobs, M. L. Regenerating flue-gas desulfurizing agents by bipolar membrane electrodialysis. AIChE J. 2006, 52, 393–401. (7) Xu, T. W.; Yang, W. H. Effect of cell configurations on the performance of citric acid production by a bipolar membrane electrodialysis. J. Membr. Sci. 2002, 203, 145–153. (8) Hetzer, H. B.; Robinson, R. A.; Bates, R. G. Dissociation constants of piperazinium ion and related thermodynamic quantities from 0 to 50 °C. J. Phys. Chem. 1968, 72, 2081–2086. (9) Liu, S. J.; Qu, Q. S. Thermodynamic property of the protonation of gluconate ions. Nat. Sci. J. Xiangtang UniV. 1994, 16, 63–65, in Chinese. (10) Van Krevelen, D. W. Properties of polymers: Their estimation and correlation with chemical structure; Elsevier Scientific: AmsterdamOxford, U.K.-New York, 1976. (11) Fang, X. H.; Li, B. Q.; Sokolov, J. C.; Rafailovich, M. H.; Gewaily, D. Hildebrand solubility parameters measurement via sessile drops evaporation. Appl. Phys. Lett. 2005, 87, 094103. (12) La-Scalea, M. A.; Menezes, C. M. S.; Ferreira, E. I. Molecular volume calculation using AM1 semi-empirical method toward diffusion coefficients and electrophoretic mobility estimates in aqueous solution. J. Mol. Struct. 2005, 730, 111–120. (13) Dean, J. A. Lange’s handbook of chemistry; McGraw-Hill: New York, 1985. (14) Wilhelm, F. G.; van der Vegt, N. F. A.; Strathmann, H.; Wessling, M. Comparison of bipolar membrane by means of chronopotentiometry. J. Electroanal. Chem. 2002, 199, 177–190. (15) Strathmann, H.; Koops, G. H. In Handbook on bipolar membrane technology; Kemperman, A. J. B., Ed.;Twente University Press: Enschede, The Netherlands, 2000; pp191-220.

ReceiVed for reView August 2, 2008 ReVised manuscript receiVed December 18, 2008 Accepted December 21, 2008 IE801192K