Making silica aerogel at home - YouTube

He followed instructions in the silica TMOS recipe from http://www.aerogel.org and successfully produced some small pieces of aerogel in my home shop.

The two main difficulties are: 1. Getting TMOS or TEOS (the key chemical ingredient), and 2. Building a supercritical drying chamber. The components for the chamber can be bought from http://www.mcmaster.com or another source of industrial pipe fittings.

You'll also need a supply of liquid carbon dioxide. I used a 20-lbs cylinder, which I bought from a local welding store. Most of the cost is in the cylinder itself, since a refill costs only $20 to $30. You may find a welding supply shop that will rent the cylinder.

Getting the TMOS is difficult since chemical suppliers are generally unwilling to sell to individuals.

The process to make aerogel is:

1. Mix TMOS, methanol, and ammonium hydroxide. Pour this mixture into molds, and wait for a gel to form.
2. Submerge the gel in methanol, and wait a day for the remaining water in the gel to diffuse into the methanol.
3. Discard the methanol, and replace with fresh methanol. Wait a day, and repeat. Repeat this process a few times over three days.
4. Transfer the gel into the supercritical drying chamber, and fill the chamber with methanol.
5. Add liquid CO2, then open the chamber's bottom valve to remove the methanol. Make sure the gels are always covered with liquid CO2.
6. Wait a day for methanol to diffuse into the liquid CO2.
7. Open the bottom valve and remove more methanol.
8. Repeat the methanol draining procedure while making sure the gels stay submerged in liquid CO2. Repeat the CO2 draining/exchange a couple times over 2-3 days.
9. Raise the chamber temperature to cause the CO2 to become supercritical. Slowly vent the chamber while applying heat to ensure the CO2 moves from the supercritical phase to the gas phase. 
10. Continue venting the chamber slowly, then remove the finished aerogels.