The water content of an IEM is an important property because both the effective charge density and electric resistance of the membrane depend on the water content. Figure 2 shows the water content of the AEMs prepared in this study as a function of C_pc. Here C_pc is identified as a molar percentage of cation-exchange groups in the membrane. Data obtained for the polymer blend-type AEMs quoted from our previous study [18] are also shown in order to compare the characteristics of them. The water content increased with increasing C_pc, because the osmotic pressure in the membranes increased with an increase in the number of charged groups in the membranes. Further, the water content decreased with increasing glutaraldehyde (GA) concentration, C_GA, because of the increase in the number of chemical cross-linking points with increasing C_GA. A comparison of the water content of the random-type AEMs with that of the polymer blend-type AEMs at the same C_pc shows that the water content of the polymer blend-type AEMs is lower than that of the random-type. For example, in AEMs with C_pc = 5.4 mol %, the polymer blend-type AEMs showed smaller water content than the random-type AEMs although C_GA of the former was higher than that of the latter. This difference is attributed to the difference in the morphology among AEMs. The random-type AEM has a uniform morphology because the ion-exchange groups randomly connect to PVA chains. On the other hand, the blend-type AEM has a phase-separated morphology at large sizes because it consists of two different kinds of polymers, PVA and poly(allyl amine). Hence some parts of the poly(allyl amine) chains dissolve into the cross-linking solution during the cross-linking process. Therefore, the water content of the blend-type AEMs is almost independent of the C_pc content as shown in Figure 2.

Table 1 shows the molar percentage of the anionic-exchange groups, C_pc, and IEC of the AEMs (RPA-X) along with the values for a commercially available AEM, Neosepta AMX (ASTOM Corp.: Tokyo, Japan). The experimental IEC values are about 30%–40% of the calculations. This might be attributed to the fact that the same part of the charged groups in the random-copolymer were enclosed with the crystal regions in the random-type AEMs, and that the counter-ion of the enclosed charged groups may not be able to exchange ions with that of the external solution. The IEC of the commercial AMX is 1.4 meq/g dry AEM. Hence, the IEC of RPA-4 is about one third of that of AMX.

The permselectivity of an IEM is best determined via membrane potential measurements as effective charge density, because the higher the effective charge density of a membrane, the higher the counter ion permselectivity. Figure 3 shows the effective charge density of the membranes as a function of C_pc. The effective charge density increased with C_pc and reached a maximum value. The effective charge density is proportional to the charge density, which is defined as the division of IEC by the water content, H: (1)

IEC was almost proportional to C_pc as shown in Table 1. The water content also increased with C_pc as shown in Figure 2. Hence, in the first stage of the effective charge density-C_pc curves, the effective charge density increases with increasing C_pc because of the increase in IEC. At high C_pc, the effect of the increase of water content on the effective charge density is larger than that of the increase in IEC. As a result, the effective charge density decreased after reaching a maximum value. The maximum value of the effective charge density increases with increasing C_GA because the water content decreases with increasing C_GA. The maximum value of the effective charge density was 0.42 mol/dm³ for the random-type AEM having C_pc = 4.2 mol % and C_GA = 0.15 vol %. The effective charge density of AMX measured under the same conditions is 1.6 mol/dm³. Thus, the effective charge density of the random-type AEM was almost one fourth of that of the commercially available AEM.

The membrane resistance is important for energy-saving electrodialysis. Figure 4 shows the membrane resistance as a function of C_pc. The membrane resistance decreased with increasing C_pc because of the increase in the water content and IEC with increasing C_pc. The resistance increased with increasing C_GA because of the decrease in the water content. The lowest membrane resistance of 1.4 Ω cm² was obtained for the random-type AEMs at C_pc = 6.0 mol % and C_GA = 0.01 vol %. A comparison of the membrane resistance of the random-type AEMs with that of the polymer blend-type ones at the same molar percentage of C_pc showed that the membrane resistance of the random-type AEMs was lower than that of the blend-type ones. For example, in AEMs with C_pc = 6.0 mol %, the membrane resistance of the blend-type AEMs was far larger than that of the random-type AEMs although C_GA of the random-type AEM was higher than that of the blend-type one. This difference also indicates that the distribution of the ion-exchange parts is different among AEMs. In the case of polymer-blend AEMs some portion of the polycation chains located on the membrane surfaces will be dissolved in solution and leaked out from the membrane. This will cause high electrical resistance near the membrane surfaces.

The membrane resistance depends on the mobility and concentration of ions in an IEM. It is difficult to measure experimentally the ionic mobility in a water-swollen membrane. To estimate the ionic mobility, many authors have replaced the mobility as a function of both the mobility in an aqueous solution, w_i and factors such as membrane geometry. Mackie and Meares [19] stochastically dealt with these factors as a function of the water content of a swollen-membrane. Consequently the dependence of membrane resistance on water is given as the following equation: (2)

Figure 5 shows the membrane resistance as a function of water content, (2 − H)²/H³, where the resistances of all the random-type AEMs are almost linear. This means that the resistance of the random-type AEMs can be estimated from the value of the water content.

The dynamic state transport number relates to the counter-ion permselectivity of an IEM in electrodialysis. An IEM with a transport number of 1.0 can allow the permeation of only the counter ions in an electrodialysis system. Figure 6 shows the dynamic state transport number of the AEMs as a function of C_pc. The transport number of the random-type AEMs increased with increasing C_pc, and then decreased after reaching a maximum value at C_pc ≈ 4.2 mol %. As mentioned above, this trend is attributed to the fact that the effective charge density has a maximum value at C_pc = 4.2 mol %. The transport number increased with increasing C_GA. These results indicate that the transport number of the membranes can be controlled by changing the cross-linking conditions. The dynamic transport number of the random-type AEM with C_pc = 4.2 mol % and C_GA = 0.15 vol % is 0.85, while that of AMX is 0.98 under the same conditions (0.5 mol/dm³ NaCl), indicating that the random-type AEM applies to desalination under lower salt concentration than 0.5 mol/dm³ NaCl.

An ion exchange membrane having both high ion permselectivity and low membrane resistance is desirable in electrodialysis processes. Figure 7 shows the relationship between the membrane resistance and dynamic state transport number of the membranes. The membrane placed on the upper left-hand side of the figure has a high performance for electrodialysis processes. The membrane resistance decreases and the dynamic state transport number increases with increasing C_pc. The transport number of the membrane increases with increasing C_GA. The dynamic transport number and membrane resistance of the random-type AEM at C_pc = 6.0 mol % and C_GA = 0.15 vol % were 0.83 and 4.8 Ω cm², respectively, while those of AMX were 0.98 and 2.5 Ω cm², respectively. This means that the random-type AEMs have lower ionic selectivity than AMX at high concentration of saline solutions.

Figure 8 shows the dynamic state transport number as a function of the effective charge density. The transport number increased with increasing effective charge density and was almost on a curve independent of the other membrane parameters: IEC and C_GA.

The Donnan theory on an IEM gives the relationship between the transport number and effective charge density as [20]: (3) where C_s is the NaCl concentration at the transport number measurement (0.5 mol/dm³). (4) where α_i is the correction factor of the i-th ion in the Mackie and Meares theory; w_Na and w_Cl are the mobilities of Na⁺ and Cl⁻ ions in the membrane, and Q_i is the factor related to the standard chemical potential difference and the activity coefficient as (5) (6) where Δμ0 i is the standard chemical potential difference of the ion, respectively, between the membrane and an aqueous solution; and γ_i are the corresponding activity coefficients in the membrane and the solution. The values of the mobility of Na⁺ and Cl⁻ ions in an aqueous solution are 5.4 × 10⁻¹³ mol m² J⁻¹ s⁻¹ and 7.9 × 10⁻¹³ mol m² J⁻¹ s⁻¹, respectively [21]. Hence, the ratio of w_Na to w_Cl is 0.66. In the case of assuming that α_Na/α_Cl = 1 and Q_Na/Q_Cl = 1, the calculation of β = 0.66 is lower than the experiments as shown in the broken curve in Figure 7. The calculation of β = 0.46 as shown in the solid curve is in good agreement with the experiments. This means that the ratio of the correction factor, α_Na/α_Cl, and/or the ratio, Q_Na/Q_Cl, is less than 1.0. The correction factor of the highly hydrated ion Ca²⁺ in PVA-based membranes is smaller than that of the Cl⁻ (α_Ca = 0.60, α_Cl = 0.94) [21]. The radius of the hydrated Na⁺ is lower than that of the Cl⁻. Hence, α_Na/α_Cl is lower than 1.0. The result indicates that the transport number can be estimated from the value of the effective charge density.

PVA117 (degree of hydrolysis: 98.5 mol %, viscosity-average degree of polymerization: 1700) and poly(vinyl alcohol-co-methacryloyl aminopropyl trimethyl ammonium chloride: MAPTAC) (degree of MAPTAC modification: 4 mol %, degree of hydrolysis: 98.5 mol %, viscosity-average degree of polymerization: 1700) were obtained from Kuraray Co., Ltd.: Tokyo, Japan. Glutaraldehyde (GA) (25 wt % solution in water) was of analytical grade and was obtained from Wako Pure Chemical Industries. Sulfuric acid and sodium sulfate were of analytical grade and were obtained from Nakarai Tesque.

Self-standing base membranes, BM-X (X = 1–4) for random-type AEMs were prepared by casting an aqueous solution of a mixture of PVA and PVA-co-MAPTAC on a plastic plate and then drying the mixture over a hot stage (NISSIN, NH-45N) overnight at 50 °C. The thickness of the base membranes was ca. 0.1 mm. The weight percentage of PVA-co-MAPTAC to PVA in the mixture solution was varied to control the molar percentage of anion-exchange groups to vinyl alcohol groups (C_pc) in BM-X, as shown in Table 1. The random-type AEMs, RPA-X, were prepared by annealing BM-X at 160 °C for 30 min under vacuum to induce physical cross-linking between the PVA chains because PVA is a semi-crystalline polymer and the crystalline region acts as a physical cross-link point [22]. Chemical cross-linking was induced by immersing the membranes in an aqueous solution of various concentrations of GA, 0.05 mol/dm³ of H₂SO₄ (pH = 1), and 2.0 mol/dm³ of Na₂SO₄ at 25 °C for 24 h to control the water content of the membranes in the equilibrium swelling state in deionized water. Figure 9 shows the chemical cross-linking mechanism of PVA and GA.

The water content, H, of the membranes was measured as follows: A base membrane was weighed in the dry state after annealing and chemical cross-linking. The membrane was immersed in deionized water at 25 °C for 7 days. The membranes were removed from water, dabbed with a filter paper to remove excess water on the membrane surfaces, and weighed in the wet state. For the sake of simplicity, we assume the volume between the water phase and the polymer phase of a swollen membrane to be additive. The volumetric water content, H, is calculated from the weights in the wet state, W_w, and in the dry state, W_d, as shown below: (7) where 1.0 and 1.3 are the densities of water and PVA [23], respectively.

The ion-exchange capacity (IEC) of an AEM is an important parameter because the ionic transport properties of the AEM depend on the amount and species of the ion exchange groups. IEC is expressed as milliequivalent per gram of membrane (meq/g dry AEM) and was determined as follows: A sample membrane was immersed in 0.10 mol/dm³ KCl solution for 3 h before measuring IEC. The membrane was rinsed with deionized water to remove non-exchange KCl electrolyte adsorbed on the membranes and was then immersed in 0.20 mol/dm³ of NaNO₃ with a volume of 50 cm³ under stirring for 12 h to achieve the complete exchange of Cl⁻ ions in the membrane with NO₃⁻ ions in the solution. The concentration of Cl⁻ ions in the solution, C_Cl was determined by using an ion chromatograph (Dionex ICS-1500). The membrane was dried under vacuum for 24 h and was weighed in the dry state, W_d. IEC of the base membrane was calculated using the following equation: (8)

Membrane effective charge density is one of the most important factors for estimating the permselectivity between ions with different charge and valence in an ion exchange membrane. In order to estimate the effective charge density, the membrane potentials, Δϕ, were measured as a function of the KCl concentration in the two chambers of the apparatus described elsewhere [18]. One chamber of the cell was filled with KCl solution of various concentrations, C_o, while the other chamber was filled with KCl solutions with concentration, C_d, which is five times higher than that in the former (r = C_d/C_o= 5). The membrane potential between the solutions in the two chambers was measured at 25.0 ± 0.5 °C using Ag/AgCl electrodes (TOA HS- 205C) with a salt bridge (3.0 mol/dm³ KCl) and a voltmeter HM-20E (TOA Corp.: Tokyo, Japan). The membrane effective charge density, C_x, was calculated from the measured membrane potential using the following equation [24,25]: (9) where W ≡ (w_k - w_Cl ) / (w_k + w_Cl ); w_k and w_Cl are the K⁺ and Cl⁻ mobilities in a membrane, respectively; F, R and T are the Faraday constant, gas constant and the absolute temperature, respectively. Parameters W and C_x are adjusted so that the left-hand side of Equation (9) fits the experimental data at various KCl concentrations.

The electrical resistance of a sample membrane was measured by using a handmade acrylic plastic cell composed of two parts separated by the membrane, as described elsewhere [18], with an LCR meter AD-5827 (A&D Corp. Ltd.: Tokyo, Japan) operated at 10 KHz AC. An amount of 0.5 mol/dm³ of NaCl solution was poured into the two cell compartments, after which the electrical resistance, R_o, was measured at 25.0 ± 0.5 °C in a water bath. Subsequently, a sample membrane was set in the cell and the resistance, R_s, was measured again under the same conditions. The difference between R_s and R_o gives the membrane resistance, R_m.

The dynamic state transport number, t_d−, of a membrane was determined by electrodialysis carried out using the handmade acrylic plastic cell with two parts separated by the membrane as shown in Figure 10.

The amount of ions transported through the membrane during electrodialysis was measured using a conductivity meter (HORIBA 3552-10D). The dynamic state transport number was obtained using the following equation: (10) where ∆C, V and q are the concentration change of the transported ions, the volume of the measurement solution, and the amount of electricity passing through the membrane during the electrodialysis, respectively.