Hello,
You'd be lucky to find branches the size you want without paying an arm and a leg. I've found what works best is to simply collect your large branches from the woods being sure not to collect from an area that has restrictions on removing materials (i.e. forest preserves, state parks, etc.). Hose off excess dirt and debris than treat with a uniformly heavy spraying of Provent-a-Mite. Leave treated branches out of cages for several hours to a day or more.
Provent-a-Mite is an acaricide (kills mites and ticks), but will kill other invertebrates. So, obviously you don't want to use in cages that will house invertebrates and you don't want to put it into cages with insectivorous lizards or other animals for at least two weeks. The two week time frame gives enough time for the chemical to kill any hitch-hikers and enough time for it to degrade to a harmless level which the product is designed to do.
You can get Provent-a-Mite from www.pro-products.com or possibly searching other herp supplies dealers. It's around $20 a can which sounds expensive but then again you're talking about the only USDA approved chemical for treating mites and ticks on reptiles. You can also feel free to contact the company president Bob Pound. He's always been very helpful to those with questions.
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Matt Campbell
Animal Keeper, Small Mammal/Reptile House
Lincoln Park Zoo Chicago, Illinois
Assistant Curator
Wildlife Discovery Center at Elawa Farm
Lake Forest, Illinois