7866
J. Phys. Chem. B 1998, 102, 7866-7870
Current-Voltage Curves of Composite Bipolar Membrane in Alcohol-Water Solutions Tzu-Jen Chou and Akihiko Tanioka* Department of Organic and Polymeric Materials, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152, Japan ReceiVed: May 27, 1998; In Final Form: July 31, 1998
The current-voltage curves of a composite bipolar membrane (CBM) were experimentally measured for the various mole fractions of methanol-water, ethanol-water, and n-propanol-water mixed solution systems. In each solution system, 0.1 mol/L LiCl was used as the electrolyte. The experimental results showed that a CBM has the characteristics of a bipolar membrane. The current-voltage characteristics were analyzed using Mafe´ and Ramı´rez’s ion transport theory by applying the chemical reaction model in the intermediate region, and the theoretical calculations were able to well explain the experimental results. The currentvoltage curves show that the maximum local effective value of a CBM resistance will increase with an increase in the mole fraction of alcohol. This phenomenon is due to the fact that the dissociative ability of an alcohol is much weaker than that of water; thus, the current is mainly induced by the water splitting. However, methanol splitting was observed in the case of the LiCl-methanol solution because of its somewhat large autoprotolysis constant.
1. Introduction A bipolar membrane, which has a sandwich-like structure involving a negatively charged layer, N, and a positively charge layer, P, has been studied for application to bioreactors or biosensors,1 a model of biophysical systems,2 both acid and base production,3-6 and treatment of saltwater effluents.7-10 The characterization of bipolar membranes has been carried out for aqueous solution systems by studying the current-voltage curves,11-18 membrane potential,19-24 and ac impedance spectra.25-27 One of the main interests in bipolar membranes is their water-splitting property. Water splitting has to be accompanied by water dissociation into hydrogen and hydroxide ions at the boundary surface between anionic and cationic layers and successive ion diffusion through charged layers. Ohki predicted the rectification effect by consideration of the Donnan equilibrium and the Nernst-Planck equation.28 It was strongly affected by the fixed charge densities in the cationand anion-exchange layers. Anyway, the water-splitting effect cannot be explained based solely on their theory. Mafe´ and co-workers theoretically derived an equation to explain the experimental results of the current-voltage curve for different bipolar membranes at different temperatures.11-13,16 In their deduction, the Donnan equilibrium and the Nernst-Planck equation were employed for the ion fluxes, and the watersplitting phenomenon was accounted for by means of either the Onsager theory of the second Wien effect29 or the chemical reaction model.30 Their equation can explain well the currentvoltage characteristics by the selection of several appropriate unknown parameters. However, the coupling of water splitting with ion transport is still poorly understood from the viewpoints of basic materials science, chemistry, and physics. A CBM consisting of a layered structure involving a cation selective membrane joined to an anion selective membrane is used for the analysis, because the physicochemical properties * To whom correspondence should be addressed. Tel +81-3-57342426, Fax +81-3-5734-2876, E-mail
[email protected].
of both monopolar membranes (water content, fixed charge density, and ionic mobility ratio) can be separately obtained. The current-voltage curves of the CBM were measured for the various mole fractions of methanol-water, ethanol-water, and n-propanol-water mixed solution systems. In each solution system, LiCl was used as the electrolyte because of its large solubility in the pure alcohol. The experimental results were analyzed using Mafe´ and Ramı´rez’s ion transport theory by applying the chemical reaction model in the intermediate region.16 It is confirmed that the water-splitting phenomenon occurs in the LiCl alcohol-water mixed solutions, and the local effective value of the CBM resistance increases with an increase in the mole fraction of alcohol. These phenomena can be explained due to the fact that the dissociative ability of alcohol is much weaker than that of water.31 The measurements of the current-voltage curve show that a CBM has the characteristics of a bipolar membrane and can significantly contribute to a better electrochemical characterization of the CBMs in the electrolyte organic aqueous solutions. 2. Experimental Section 2.1. Materials. A cation-exchange membrane (K-101, Asahi Chemicals), which is composed of poly(divinylbenzene-costyrene) containing sulfonic acid groups in a polymer matrix, and an anion-exchange membrane (A-201, Asahi Chemicals), which is composed of poly(butadiene-co-styrene) containing quaternary amine groups in a polymer matrix, were used for the measurements. Both membranes were supported by woven polymer fiber cloth in order to prevent the swelling caused by the organic solvents. The thickness, water content, and fixed charge density of both membranes are given in Table 1. Prior to the measurements being carried out, both membranes were immersed in 3 mol/L LiCl aqueous solution for 3 days to ensure that the counterions were exchanged for the same species. After both membranes were thoroughly washed with ion-exchanged water, they were immersed in ion-exchanged water for 3 days to remove the excess ions in the membrane matrices. Finally,
S1089-5647(98)02375-X CCC: $15.00 © 1998 American Chemical Society Published on Web 09/11/1998
Composite Bipolar Membrane
J. Phys. Chem. B, Vol. 102, No. 40, 1998 7867 surfaces in order to minimize the ohmic potential drops in the bulk solutions. Prior to the measurements being carried out, the effect of bulk solutions on the ohmic drops was examined. In this case, the resistance from the bulk solutions was below 0.1% of the total resistance. Also, the distances between the Ag/AgCl electrode wires and the CBM surfaces were kept approximately constant during all the experimental runs. Under reverse bias conditions, the current and voltage are definitely the negative values which appear in the third quadrant. However, in this work, the measured current and voltage are multiplied by -1 in order to have them appear in the first quadrant. 3. Results and Discussion
Figure 1. Schematic diagram of current-voltage measurement apparatus.
TABLE 1: Physicochemical Properties of the Studied Ion-Exchange Membranes membrane
thickness (mm)
water content (wt %)
fixed charge density (mol/L)
K-101 A-201
0.22 0.23
27 26
5.0 4.2
both membranes were immersed in the various mole fraction of alcohol (purity >99.0 mol %)-water mixed solvents for a week to ensure that the mixed solvents were sorbed in the membrane phase. The CBM, which consisted of a layered structure involving K-101 joined to A-201, was used for the measurement of the current-voltage curves in this study. 2.2. Measurement of Current-Voltage Curves under Reverse Bias Conditions. The current-voltage curves under reverse bias conditions across the CBM were measured for the various mole fractions of LiCl alcohol-water solutions at 20.0 ( 0.5 °C. Figure 1shows the schematic diagram of the currentvoltage measurement apparatus. The CBM was placed between two electrodialytic half cells, which had a cross-sectional area equal to 0.79 cm2. Methanol, ethanol, and n-propanol were used as the alcohol, and the salt-free mole fractions of alcohol in mixed alcohol-water solutions were 0.0, 0.25, 0.5, 0.75, and 1.0. When the entire electrodialysis cell was reverse biased (see Figure 1) using the working electrodes, the large electric field appearing at the CBM junction produced an excess of H+ and OH- ions due to the electric field-enhanced water dissociation reaction. These water ions permeated the corresponding ion-exchange layers of the CBM and entered the adjacent LiCl solutions. The microtube pumps (EYELA, MP-3) maintained a continuous cyclic flow of the solutions to ensure that the concentration of LiCl in the electrodialysis cell was equal to 0.1 mol/L during the measuring period. Before the actual experiment, all compartments were filled with the corresponding solutions for a couple of hours in order to produce an equilibrium state between the CBM and the solutions. The current-voltage curves were obtained by applying a potential difference to the system via a dc signal source (HIOKI, 7011) and allowing the current to reach a steady state. Nickel (cathode) and platinum (anode) electrode plates were used, and the cross-sectional area of both electrodes was 3.14 cm2. The potential drop across the CBM was measured using two Ag/AgCl electrode wires (diameter equal to 1.0 mm) which were laid on both surfaces of the CBM and connected to a digital voltmeter (HIOKI, 7011). Special care was taken in placing these Ag/AgCl electrode wires close to the CBM
The experimental results for the current-voltage curves of the CBM in LiCl methanol-water, LiCl ethanol-water, and LiCl n-propanol-water solutions are shown in Figures 2, 3, and 4, respectively. The various salt-free mole fractions of alcohol in the mixed solvents were used for the measurements of the current-voltage curves. As previously described, the measured current and voltage are multiplied by -1 in order to have them appear in the first quadrant. Except for the systems that do not contain water, the electric field-enhanced water dissociation can be observed for sufficiently high applied voltages. Ordinary water dissociation cannot explain the magnitude of the electric current. It is generally believed that the H+ and OH- ions originate in a very thin region at the interface between the two ion-exchange layers. Nevertheless, it is not known exactly which mechanism is responsible for this enhanced dissociation. One possible explanation was suggested by Wien and Schile.32 They pointed out that the ion mobility increases with increasing electric field in weakly dissociated electrolytes. This effect has been called the second Wien effect, and the theory was developed by Onsager.29 Water is a weakly dissociated electrolyte; thus, this theory can be applied to a bipolar membrane. A high electric field is generated at the space charge region with a p-n junction. Because the structure of the bipolar membrane resembles that of a semiconductor, such a high electric field may be produced. Orsager’s theory gives an exponential dependence of the water dissociation rate on the electric field and assumes that the water recombination rate remains unaffected. However, Mafe´ and Ramı´rez have pointed out that some limitations exist in this model, and these limitations will cause the model to fail in some systems.16 Simons30 suggested that the H+ and OH- ions may be generated from protonation-deprotonation reactions between some membrane fixed charge groups and the water molecules in the anion-exchange layer and proposed the following mechanism for the water dissociation reaction:
B + H2O h BH+ + OHBH+ + H2O h B + H3O+
(1)
where BH+ refers to the catalytic active center for the protontransfer reactions. There are two reasons why the protontransfer reaction accelerates the water splitting at bipolar membranes. The first is the influence of the electric field, which causes the orientation of the water molecules to take an optimum position for the reaction with a fixed charge group. The second is the influence of the counterion on the fixed charge group in the space charge region. The concentration of the counterion is very low in this region, because it is extracted from the
7868 J. Phys. Chem. B, Vol. 102, No. 40, 1998
Chou and Tanioka
Figure 2. Current-voltage curves for the composite bipolar membrane. The curves have been measured at the mole fractions of methanol: x1 ) 0.0 (O), 0.25 (0), 0.5 (]), 0.75 (4), and 1.0 (3). Solid lines show the calculated results using eq 4.
Figure 3. Current-voltage curves for the composite bipolar membrane. The curves have been measured at the mole fractions of ethanol: x1 ) 0.0 (O), 0.25 (0), 0.5 (]), 0.75 (4), and 1.0 (3). Solid lines show the calculated results using eq 4.
membrane to an electrode. Therefore, the fixed charge group without a counterion simultaneously reacts with water, as shown in eq 1. Mafe´ and co-workers reported the ion flux in bipolar membranes for different bipolar membranes at different temperatures.11-13,16 They used the chemical reaction model to quantify the efficiencies of water splitting. In their papers, the dissociation constant of water, kd, is written in the following form16,33,34
E [RF RT ]
kd ) k0d exp
(2)
where R is the gas constant, T is the absolute temperature, F is Faraday’s constant, E is the electric field, R is a microscopic parameter having the dimensions of length, and k0d is the effective dissociation rate for water which results from the protonation-deprotonation reactions of eq 1 in the absence of an external electric field. k0d is a function of temperature and can be expressed by the following Arrhenius relationship
[ ]
Ea k0d ) A exp RT
(3)
where A is the preexponential (frequency) factor and Ea is the activation energy of the process. Figure 5shows the bipolar membrane separating two solutions of the same uni-univalent electrolyte. The cation-exchange layer extends from -dN to 0 and has the concentration Cx,N of the negatively charged fixed groups. The anion-exchange layer lies between 0 and dP and has the concentration Cx,P of the positively charged fixed groups. The entire system formed by the membrane and the bathing electrolyte solutions is assumed to be isothermal and at a steady state. Solvent flow is neglected. The bias voltage, V, dependence of the current, I, using the space charge model can be written in the form16
- 1] - I [ (FV RT)
I ) (ILS + ILW) exp
d
where the constants ILS and ILW are defined in the form
(4)
Figure 4. Current-voltage curves for the composite bipolar membrane. The curves have been measured at the mole fractions of n-propanol: x1 ) 0.0 (O), 0.25 (0), 0.5 (]), 0.75 (4), and 1.0 (3). Solid lines show the calculated results using eq 4.
[
ILS ≡ F
[
]
D2,NC2,N(-dN) D1,PC1,P(dP) + dN dP
ILW ≡ F D3,PC3,P(dP)
(5)
x (x ) x ( x )] χP coth dP D3,P
D4,NC4,N(-dN)
χP + D3,P
χN coth dN D4,N
χN D4,N
(6)
and can be interpreted respectively as the limiting current densities carried by the salt ions and by the H+ and OH- ions generated when no external electric field is applied. Di,K represents the diffusion coefficient of the ith species (i ) 1 for salt cations, i ) 2 for salt anions, i ) 3 for H+ ions, and i ) 4 for OH- ions) in layer K (K ) N and P which refer to the cationic and anionic layers of the bipolar membrane, respectively), and χP and χN can be defined by
Composite Bipolar Membrane
J. Phys. Chem. B, Vol. 102, No. 40, 1998 7869
TABLE 2: Values of the Parameters nA and r for the Mole Fractions of Alcohol Equal to 0.0, 0.25, 0.5, 0.75, and 1.0 methanol mole fractions of alcohol
nA × 10-7 (mol m-3 s-1)
0.0 0.25 0.5 0.75 1.0
2.64 2.52 4.91 5.53 5.88
ethanol
R × 1010 (m)
nA × 10-7 (mol m-3 s-1)
10.3 8.8 6.7 5.9 5.1
2.64 3.08 3.49 3.61 4.77
Figure 5. Schematic diagram of the composite bipolar membrane considered under reverse bias conditions. The region from -λN to λP corresponds to the space charge layer.
χN ≡ k0r C3,N(-dN)
(7)
χP ≡ k0r C4,P(dP)
(8)
where k0r is the recombination rate constant of water when no electric field is applied. Ci,K represents the concentration of the ith species in region K (K ) L, R, N, and P which refer to the left and right bulk solutions and to the cationic and anionic layers of the bipolar membrane, respectively) and can be expressed by
Ci,N(-dN) )
[x
Cx,N2
Ci,L C1,L + C3,L Ci,P(dP) )
4
[x
Ci,R C1,R + C3,R
+ (C1,L + C3,L)2 +
Cx,P2
]
(-1)i+1Cx,N (9) 2
]
(-1)iCx,P (10) + (C1,R + C3,R) + 4 2 2
The term Id in eq 4 is the current density due to the electric field-enhanced water dissociation and can be written in the form
Id ≡ Fkdnλ
(11)
where n is the concentration of active sites in the depleted layer where the reaction is taking place, and kd is given by eqs 2 and 3. The electric field at the junction, E, and the thickness of the space charge region, λ, are
E)
[
]
Cx,NCx,P 2F (-V) r0 Cx,N + Cx,P
λ ≡ λN + λP )
[
1/2
(12)
]
2r0 Cx,N + Cx,P (-V) F Cx,NCx,P
1/2
(13)
where 0 is the vacuum electric permittivity and r is the dielectric constant.
n-propanol R × 1010 (m)
nA × 10-7 (mol m-3 s-1)
R × 1010 (m)
10.3 7.8 6.4 5.1 2.1
2.64 3.59 3.62 3.64 3.64
10.3 7.1 5.7 4.2 1.3
Although eq 4 was derived for the electrolyte aqueous solution systems, it can also provide a good fit for the experimental results of the electrolyte alcohol-water solution systems in this study by adjusting the unknown parameters. The experimental results of the current-voltage curves have been fitted using eq 4, and the theoretic curves are shown in Figures 2-4 as lines. According to Bruggeman’s equation,35 the local dielectric constant r in the membrane only slightly varies with the dielectric constant of the solvent. Thus, we took the typical value, r ) 20, for all of the systems,36 and the error caused by this assumption can be compensated by the regressing process. Other parameters required in the calculation procedure took the typical values: Ea ) 30 kJ/mol, Di,K ) 10-9 m2/s (i ) 1, 2; K ) N, P), and Di,K ) 10-8 m2/s (i ) 3, 4; K ) N, P). The unknown parameter, R, whose physical meaning is not completely clear, can be considered as a characteristic length (R ≈ 1 Å) for the chemical reaction taking place between the membrane groups and the water molecules.16 Unfortunately, it is not clear how to estimate reliable values for this length in each experimental case, and to make matters worse, eq 2 is very sensitive to the R value. Therefore, nA and R were took as adjustable parameters in this study, and the values of these parameters are given in Table 2. In Figures 2-4, the current-voltage curves show the typical behavior associated with an electric field-enhanced water dissociation caused by a chemical reaction for the LiCl-water solution,37 and the water-splitting phenomenon can be also observed for the electrolyte alcohol-water mixed solutions. The experimental results show that, with an increase in the mole fraction of alcohol, the water splitting will become less obvious. This phenomenon can be explained due to the fact that the dissociative ability of alcohol is weaker than that of water. Thus, the existence of alcohol will decrease the concentration of water in the space charge region of the membrane and cause the decrease in the water-splitting effect. The dissociation of methanol is also observed for the LiClmethanol solution in Figure 2. If the phenomenon was mainly caused by the existence of the impurity of water, we would also find the obvious dissociation that occurred for the LiClethanol and LiCl-n-propanol solutions in Figures 3 and 4 at the same applied voltage region. However, such dissociation cannot be found in these two figures. Like water, methanol is a very weak electrolyte. For pure methanol, the equilibrium for the ionization reaction lies in the following equation38
CH3OH + CH3OH h CH3O- + CH3OH2+
(14)
Thus, we can expect that the dissociation of methanol occurred in the CBM. According to eqs 1 and 14, a similar mechanism for the methanol dissociation reaction is supposed to be written as follows
B + CH3OH h BH+ + CH3OBH+ + CH3OH h B + CH3OH2+
(15)
7870 J. Phys. Chem. B, Vol. 102, No. 40, 1998
Chou and Tanioka LiCl-ethanol solution. This phenomenon is due to the fact that the dissociative ability of ethanol is weaker than that of water; thus, the existence of ethanol will cause the increased resistance. Acknowledgment. The authors’ appreciation is expressed for the financial support given by the Salt Science Research Foundation. They also express special appreciation to Mr. M. Hamada and Mr. K. Yamamura at Asahi Chemicals Co. for providing us with the samples and for helpful suggestions. References and Notes
Figure 6. Local effective value of the composite bipolar membrane resistance, R′, vs the applied voltage at various mole fractions of ethanol: x1 ) 0.0 (O), 0.25 (0), 0.5 (]), 0.75 (4), and 1.0 (3). Solid lines represent the theoretical results.
The catalytic active center, B, may be the quaternary amine groups of the anion-exchange membrane16,30 in this study. The dissociation phenomenon for the LiCl-ethanol and LiCl-npropanol solutions cannot be obviously observed due to the fact that the autoprotolysis constants of ethanol and n-propanol (pKSH ) 19.1 and 19.4, respectively) are smaller than that of methanol (pKSH ) 17.2).30,31 However, we believe that the dissociation of ethanol and n-propanol can also occur when the applied voltage becomes sufficient large. For an aqueous methanol solution, the equilibrium for the ionization reaction also lies on the following reaction38
CH3OH + H2O h CH3O- + H3O+
(16)
It is assumed that the reactions in eqs 1 and 15 are mixed in the CBM. pKa in dilute aqueous methanol solution is 15.5, which approximates the pKSH value of water; thus, the simultaneous reactions of eqs 1 and 15 are reasonable. On the other hand, pKa is close to the pKSH of methanol when the concentration of methanol is high. This implies that the dissociation of methanol will play an important role at this moment. These results indicate that the application of the bipolar membrane can be extended to produce the organic salt. Finally, a local effective value of the CBM resistance, R′, defined as the quotient, V/I, is presented in Figure 6for the LiCl ethanol-water solutions. The experimental data are those shown in Figure 3. It can be observed that the resistance first increases with the bias voltage, reaches a maximum value, and finally decreases toward very low values at higher voltages. This can be interpreted by considering that when a low voltage is applied, the rectification properties dominate. The maximum value of the resistance gives the voltage from which the watersplitting effects become dominant. In Figure 6, the resistance increases with an increase in the mole fraction of ethanol, and the dissociation of ethanol is not obviously observed for the
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