## The Mechanism of Water Dissociation in Bipolar Membranes

The water dissociation rate in the bipolar membrane determines the overall efficiency of the process. It can easily be shown, however, that the dissociation rate constant of pure water is much too low to explain the experimentally determined high acid and base generation rate in bipolar membranes.

As indicated earlier, a bipolar membrane consists of a laminate of cation and anion exchange layers. The specific resistance a of a strong acid or base ion exchange layer is in the order of 50-100 Q cm. Assuming a thickness of 100 |im each for the cation and anion exchange layers, the total area resistance r of the ion exchange layers of the bipolar membrane is in the order of 1-2 Q cm2.

The electrical resistance of the interphase layer of a bipolar membrane which is assumed to consist of deionized water can be calculated by:

by the electric current across the bipolar membrane are replenished by the water dissociation. This means that the ion fluxes from the bipolar membrane into the outer phases cannot exceed the rate of their generation in the interphase. Thus, the maximum flux of H+ and OH~ ions of the bipolar membrane is given by:

where J is the maximum ion flux from the bipolar membrane into the outer phases, kd is the water dissociation rate constant, CH2O is the concentration of water in the interphase and X is the thickness of the interphases. The subscripts H +, OH~ and H2O refer to H + , OH~ ions and water, respectively.

The water dissociation rate constant kd for pure water at 25°C is given in the literature as 2.5x10~5s~1.

According to eqn [4], the maximum fluxes JH# and JOH- from a bipolar membrane that has a 1 nm thick interphase of pure water would be 1.4 x 10~13 mol cm~2s~\

The electrical current I through the bipolar membrane is proportional to the sum of all ion fluxes and is given by:

where rin is the area resistance, X the thickness, and k is the specific conductivity of the interphase layer. If the interphase layer contains only pure water, its specific resistance is approximately 18 x 106 Q cm. Thus, the area resistance of a 1 nm thick interphase is approximately 1.8 Q cm2. The above argument however is only correct if the ion concentration in the interphase is constant and all ions which are removed

Thus, the maximum current density through a bipolar membrane is, according to eqns [4] and [5], approximately 1.4 x 10 "8 Acm~2. A current density exceeding this value would lead to a depletion of ions in the interphase and thus to a drastic increase in its electrical resistance. In practice, however, bipolar membranes can be operated at current densities in excess of 0.1 A cm~2, as demonstrated in Figure 3A, which shows the current through a bipolar membrane as a function of the applied voltage. When an increasing voltage difference across a bipolar membrane is established, the current hardly increases until the voltage drop reaches a value of about 0.8 V, corresponding to the concentration potential calculated by eqn [2] for a pH value difference between the two solutions outside the bipolar membrane of about 14. A further small increase in the voltage then leads to a drastic increase in the current density to values in excess of 0.2Acm~2. Thus, the current-voltage curves determined with bipolar membranes show two plateau values that indicate a limitation in the current with increasing voltage drop across the membrane, as depicted in Figure 3B. The first plateau value indicates a limitation of the current density due to a limitation of ions in the interphase. However, at 0.8 V accelerated water dissociation begins and the current

Figure 3 Schematic diagram of the current density as a function of the applied voltage (A) determined with a typical commercially available bipolar membrane and (B) three distinct areas of operation with bipolar membranes.

is no longer limited by a lack of ions until the second plateau value is reached at ca. 0.2 A cm~2. Water dissociation is then limited by the supply of water to the interphase.

Thus, there are three distinct regions in the operation of a bipolar membrane. In the first region the current is very low and mainly transported by salt ions. In the second region, high water dissociation occurs and the current is transported by protons and hydroxide ions generated in the interphase. In the third region the production rate of protons and hydroxide ions is limited by the water transport rate into the interphase. Operation of bipolar membranes at current densities that exceed the second plateau value leads to destruction of the membrane.

The experimentally determined current densities indicate that the simple model of a bipolar membrane depicted in Figure 1 is incorrect. Either the water dissociation rate is faster by several orders of magnitude in the bipolar membrane than in free solution or the interphase is much thicker. A thick interphase, however, would lead to a high area resistance of the interphase, which is not the case. From scanning electron microscope photographs and calculations based on the Poisson and Bolzmann relation for the space charge at an interphase between differently charged ion exchange membranes, it can be concluded that the thickness of the interphase is less than 5 nm. This means that, in bipolar membranes the water dissociation is at least 106 times faster than in free solution.

Various mechanisms have been suggested to explain the accelerated water dissociation in bipolar membranes. One possible explanation, suggested by Wien, is that at high electric field densities the ion mobility as well as the degree of dissociation of weakly dissociated electrolytes increases with increasing field density. The increase in the dissociation constant of weak electrolytes by the electric field effect can be expressed by an increase in the water dissociation rate constant, assuming that the recombination rate of H+ and OH~ ions is unaffected.

Other theoretical considerations and experimental evidence support a hypothesis that the accelerated water dissociation is caused by a reversible proton transfer reaction between charged groups and water. This means that, in the presence of certain ionic groups, the water dissociation rate constant may be several orders of magnitude higher than in pure water. In the case of the bipolar membrane the anion exchange groups of the membrane polymer adjacent to the interphase layer are assumed to react with the water molecules at the membrane surface as follows:

where B is a neutral base, e.g. a tertiary ammonium group.

Both models can explain the acceleration of the water dissociation in the interphases between the anion and cation exchange layer of the bipolar membrane and serve as theoretical basis for the development of bipolar membranes.

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