Killing worker ants has little effect, because the queens can produce more workers. The best way to eradicate them is to set up baits with slow acting poison that worker ants carry back to the nest and feed the queens. When all the queens die, the colony is destroyed. It is important to get the right concentration of the poison. Too low will have no effect, too high will kill the workers too soon, and the ants may abandon the trail.
One of the best ways to eradicate Argentine ants may be a simple home-made bait made of boric acid, sugar and water.
You can buy boric acid in a drug store e.g. Longs Drugs, about $2 a bottle.
Boric acid is used as an ingredient in eye drops.
To prepare the bait solution, pour 1/4 l (250 ml) of hot tap water into a jar.
Hot water makes it easier to dissolve sugar and boric acid.
Add 8 teaspoons of sugar.
Add 1 teaspoon of boric acid.
Mix well until all solids dissolve.
Mark the jar clearly that it contains poison, and store it for future use out of reach of children.
For bait stations you can use some small glass jars.
Remove the labels if you want to see the ants clearly inside.
Mark the jars clearly that they contain poison.
Make a small hole in the jar lids, just enough for ants to enter.
A tool with a sharp tip and a hammer are useful for this.
Put some cotton balls inside.
They make it easier for ants to access the bait solution.
Pour some bait solution into the jars, and soak the cotton balls.
Put the bait stations on ant trails, so that ants can find them easily.
Avoid direct sunshine, and cover if needed.
If the ants don't find the baits, move them to a better place.
Every few days check them and add more bait solution if needed.
You may see some dead ants inside or carried by other workers.
The ants are expected to disappear after several weeks.
Let's see what happens.