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actual membrane potential and the theoretical one given by the Nernst equation (5) for 𝛼 = 1, i.e. 𝛼 = 2 𝑡 − 1 (see eq. (4)). It should be noted that the transport number (and thus the permselectivity) evaluated with this simple method is generally underestimated. In fact, this measurement leads to an apparent transport number that should be corrected by the water transport number. A more detailed discussion of this issue can be found in [61]. By a more rigorous definition, the permselectivity can be expressed as [49, 66]: 𝑡 −𝑡 𝛼 = 1 − 𝑡 (6) where 𝑡 and 𝑡 the different permselectivity values in the whole operational range. The membrane electrical resistance (ER), inversely related to the electrical conductivity, generates Ohmic potential drops when an electrical current passes through the membrane pile, thus dramatically affecting the process energy consumption. As in the case of permselectivity, electrical resistance is influenced by solutions concentration [60, 75, 142]. This dependence can be explained with the typical multiphase structure of IEMs, widely reported in the literature [60, 73, 143]. In order to characterise membranes ER, direct current (DC) or alternating current (AC) measurements can be carried out. The simplest method consists of estimating ER from the slope of an I-V (current-potential) curve in DC mode, limited to the region where a linear relationship between voltage and current is maintained. This curve can be obtained using a test-cell with two chambers separated by one membrane [144] or by chronopotentiometry in a six-cell compartment device [75, 140]. Another option involves the use of a clip cell, composed by two black graphite electrodes fixed on Plexiglas plates and used to “clip” a conditioned wet membrane [145, 146]. ER can thus be measured by the previously mentioned DC method but also by means of AC methods (as described in the following lines). It should be noted that I-V curves (and, more generally, the use of DC methods) give reliable results only when IEMs are placed in contact with a sufficiently concentrated solution. The reason is that this method is not suitable for low concentrations as it cannot separate the effects of electric double are the counter-ion transport numbers in the membrane and in the solution, respectively. In particular, it is possible to experimentally estimate transport numbers using Hittorf’s method [61, 66, 134, 135] or by chronopotentiometric measurements [136–140]. One of the most critical aspects is that the concentration of electrolytes in solution affects permselectivity [5, 141]. For this reason, multiple measurements at different concentrations are necessary in order to get 19PDF Image | Electrodialysis for water desalination
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