We sucessfully banned ants from our home by using baking powder .
Unlike us ants will explode from bubbles produced in their intestines when eating baking powder.
But this will take enough time for them to carry soda fragments to their mates and their breed which will then effectively kill those as well.
The place we put quite huge piles of baking powder (2-3 spoons) was where their trails came out of the wall.
We repeated the procedure for 2 times until no more ants were visible.
Years later we still don't have any more ants which makes us believe that traces of powder they carried away still serves as an effective biological ant-blocker, provided there is no moist in the regions they carried it to.
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You could try: Diatomaceous Earth -
The particles basically get inside of their bodies and cut them up.
Sprinkling this stuff down wherever the ants are sited works and wherever they go.
I have heard that borax works as well.
Essential oils-
Using a strong oil like peppermint, Tea Tree oil, etc around where the ants are sited works.
It suffocates the ants(It may suffocate them, all I know is that it kills them) and works on other bugs.
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Treat them with liquid soap containing SLS (Sodium Lauryl Sulfate) -
controversial toxin available in most commercial hand/shower gels and shampoos.
It is toxic to bacteria and animals.
Just spill a lot of some cheap SLS in the areas you don't want them to be and leave it to dry.
They'll avoid it as hell.
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We use a homemade version of Terro to kill ants.
It works slowly but kills the entire colony as they take it back.
Commercial Terro is 5.4% borax in a sweet solution.
My homemade Terroid is 25 grams of borax in a 16 ounce bottle of store brand Karo, so it makes a lot.
We also have termites and the borax I use is Timbor
but I think any drugstore boric acid or 20 Mule Team works.
25 grams is a little less than an ounce
but I don't think the amount is critical, in fact, mine doesn't all dissolve.
It helps to warm it to dissolve it.
I just put the bottle into hot water.
Very Important Step 1 : deface label of the Karo
so it can't be confused and write poison on it.
I find it easiest to decant some into a dropper bottle.
For inside use, where I don't want this sticky goo on things, I put it onto an old CD near their trail with drops at the edge
so they find it.
Then if it dries too much for them to eat it
I just wash the CD and dot it again.
Ants don't seem to mind stepping onto a CD (there are some things they don't like, foil, oily surfaces, etc.)
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Ants apparently won't cross a line of chalk / powder.
If you use a standard block of chalk for a black board you can draw a nice solid line on the ground and it will stop them completely in their tracks.
You have to make sure that there isn't any gaps in the chalk line as they will find it and go through it
but so long as your line is solid they'll be kept at bay.
You can also use a powder in the place of the chalk which will have the same effect (baking powder tends to work well)
Another option is you can apply double sided sticky tape, or you can get special tape designed for stopping ants and other critters and this will literally stop them in there tracks and they will be stuck there until you decide to do what you will with them
- gives you the nice sense of being God in the world of ants.
On a side note - if spiders are also a problem, if you know where they come in (cracks in the wall or doors) if you place a nice pile of conkers in the way they'll be deterred from coming in.
Works and can look like some decorations if you're into that natural decor type stuff.
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I know you said no pesticides, but there is a little box called a bait box that works like a miracle.
I have used these a few times in the past.
The ants have to walk into the box, eat the food inside, and carry it back to their nest.
Once in the nest the food is poisonous to the Queen.
Within a couple of days the ants will be gone, and they will not come back.
These have worked VERY well for me in the past, and I like them because you don't have to spray poison that you could breathe or get on you.
You just put out the little plastic boxes.
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Destroy the Ant

We have some ants ramping up their annual activity here in beautiful Arizona. I want to control them without using any pesticides. In the past I have just destroyed their nests using a hose and basically strip mining them to their demise. I don't want to manually do that this year and if/when they can penetrate the home security system and get into the abode it's a completely ineffective strategy.

How do I dominate this situation without bringing the badness of a chemical company into the solution?
Pest Control - Natural Method of Ant Control - Howto
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There are a number of ways to control ants getting into the home, and a popular one is to use baking powder, diatomacecous earth or Borax. It is also possible that ants won't cross a line of chalk. Another creative method is to lay down strips of double-sided sticky tape to trap the ants. The options are to sprinkle baking powder or Diatomaceous Earth or make your own Terro using 25g of borax in a 16 ounce Karo bottle, lay down a line of chalk or use a plastic bait box.
Use baking powder where the trails come out of the wall. Try Diatomaceous Earth - sprinkle it wherever the ants are located Make your own version of Terro using 25 grams of borax in a 16 ounce bottle of Karo. Lay down a line of chalk powder to stop the ants. Use a plastic bait box to avoid spraying poisons.