I am trying to work out costs and order parts for a small liquid fuelled rocket I have designed. My oxidiser is liquid oxygen but I can’t seem to find anywhere to purchase it on the internet. Does anyone know where to buy liquid oxygen?
In general, you can't buy cryogens on the internet because they're both hazardous, and perishable (as they boil off). This goes double for LOX, which does things like turn leather gaskets and asphalt road surfaces into a shock-sensitive explosive. This caused the Bell X-1 Rocket Plane to mysteriously explode at least once.
The vendors would be those such as Airgas, Linde, and Praxair, which also sell various compressed industrial gases and liquid nitrogen. However, you can expect to need a lot more credentials and restrictions than you would for the everyday gaseous oxygen, acetylene, argon, CO2, or even liquid nitrogen.
It is likely that they will require a DOT-certified dewar to put it in, or that they will want to deliver one of those big ~50 gallon dewars with all the valves and hose fittings on the top. It is likely that they will impose other restrictions or want to see the kind of paperwork, training, etc that a business regulated under OSHA would be required to have. They may be flatly unwilling to deliver it anywhere that is not a business address -- and it is probably both illegal and unwise to carry any quantity of liquid oxygen in a passenger automobile.