A Birds Eye View of Ionic Transport

In the section on diffusion (Section 4.2), we were concerned with the random walk, but we learned that because this type of movement is purposeless in direction, it causes particles to spread out in all available directions. To bring about a diffusional flux in a given direction, all one has to do is to introduce a concentration gradient into the system and, although the movement of each particle is random, the fact that there are fewer ions in one direction than in others means that the random walk gradually raises the concentration in the dilute parts of the solution until all is uniform. In this sense, there is a directed diffusion flux down the concentration gradient. 

Then we discussed the idea that this randomness can have superimposed upon it an electrical field that does indeed have a direction, so that there are still random motions by cations and the anions, but a little less randomness for the positive ion in the direction of the negative electrode and for the negative ion in the direction of the positive electrode. There thus arises a net drift of ions in the direction of the field. 

In the phenomenological treatment of the directed drift that the field brings, we take the attitude that there is a stream of cations going toward the negative electrode and anions going toward the positive one. We now neglect the random diffusive movements they do not contribute to the vectorial flow that produces an electrical current. 

This discussion then follows on to give rise to the idea of a transport number. This is a term that describes the fact that when we talk about the drift velocity, cations and anions of equal but opposite charge do not have the same speed although the applied field is the same. On the whole, cations tend to be smaller than anions and we show that the drift velocity is inversely proportional to the radius of the solvated ion, so that transport numbers tend to be larger for the cation and smaller for the anion in an electrolyte. 

This brings us to an apparent dilemma because, according to laws first laid down by Faraday himself, when one passes a certain amount of electricity through a solution for a certain time, the number of cations and anions carrying the same numerical charge put on the cathode and anode, respectively, is the same. 

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