I'm not aware of any way that ants will harm your sunflowers but they might be farming aphids. They drink the fluids the aphids produce. I'd look close to see if you have an aphid problem. You may need to treat for aphids, not ants.
All my container have ant nest in them. Go to plant something and you find a swarm running away carrying eggs. I always wonder if they meet up somewhere after,, or just carry the egg till tired.
Greetings Mary Catherine, Ant milk aphids and take them to plants to graze like cows.
My folks use to paint a ring around the trunk of fig trees, with this black sticky stuff, I hated it when I was a kid, got it all over myself, anyway: the ants couldn't cross the sticky line. That, the black sticky line, should work for you, maybe that sticky mouse pads or than again maybe we can find a sticky something to paint a ring around the bottom of your sunflowers.
Our Sunflowers were 10' or taller, are yours the big plants? Best of luck with what you choose.