Honestly, I don't think Intelligence can intimidate anyone. Either they ignore you or they get pissed off, but they won't be scared. Maybe you could persuade someone to listen to reason and back down, but that's more like Intelligence-based Diplomacy than Intimidation.
If you're using Intelligence, you're basically handing someone a post-it note or a printed thesis, and hoping they agree with what evidence you present. But if you're saying anything, speaking at all, that's Charisma.