Disjoined Quranic letters (muqatta'at)

Twenty-nine surahs open with bare letters of the alphabet, recited by their names — alif-lam-mim, not 'alam'. Grammatically the safest classical statement is negative: they are not nouns, verbs or particles in construction; they are mabni and have no place in i'rab. As for meaning, the soundest position is the famous الله أعلم بمراده — Allah knows best His intent — though many scholars note the pointed challenge in them: the Quran is woven from the very letters on every tongue, yet stands inimitable. Fourteen distinct letters appear, exactly half the alphabet.

Do the disconnected letters have a grammatical role?

They take no place in i'rab, which is the grammarian's way of saying the question does not apply to them. They are recited letter by letter rather than read as words, and no analysis of their meaning is agreed on.