You can omit the article sometimes before nouns that are describing generic roles that can apply to any situation. Articles try to answer the question "which" for a noun X, but in cases where nouns are used abstractly, this question doesn't need to be answered (because there is no X).
John as manager took great pride in his employee's work.
So here, we mean John as a manager in general. "Which manager" is not answered because it's not important to the speaker/writer. The speaker/writer is trying to convey you could stick John in any management role and he would take pride in his employee's work. Contrast with the below:
John as the manager took great pride in his employee's work.
which means John as a manager - which manager? - likely the one of his current workplace with his current employees. Here the question of "which manager" is answered (don't forget the relies on previous sentences/context to work).
So in your original sentence, sulfur is acting as a cathode, but not a cathode in a specific reaction or whatever.