I've done this on other polymers. What worked for me was first dissolving the polymer in some solvent (perhaps toluene or methanol), then passing it through a column of weak base ion exchange resin like Amberlyst A21. The resin is basic enough to adsorb the BHT out of solution, but is unlikely to cause problems with the reactive groups. Flush the polymer off the column with more solvent.

FYI, BHT only quenches oxygen-based radicals, so if you polymerize using a carbon-based radical initiator like AIBN you shouldn't have to remove the BHT.

You can check the Aldrich catalog for "inhibitor removers". It is generally packed in a column. Just passing your reagent through it will remove the inhibitors.

Extract the PEG Ether with sodium hydroxide.

I agree with Charles. A column purification is the most simple way of removing your inhibitor. Usually basic alox (Al2O3) works quite well. Just flush your PEG monomer through a dry packed column. I would use a non-protic solvent like acetone as eluent.

Good luck!

Removing the inhibitor is often not necessary, but that does depend on the specific conditions. A column is a good idea, until the polymers get long and viscous in solution. For PEG longer than about 2-3k I would suggest precipitation in ether at –20ºC.

Be advised that unstabilized PEG-MEMA will start polymerizing on its own (thermally and photochemically) and will start oxidizing as well (which can lead to chain scission), so use it soon after. Otherwise keep it cold and dark.

I agree the column is best. The commercial ones (Aldrich, Polysciences) are good. I usually pass the monomer through neat ( no solvent), usually right into the measuring device (syringe). That minimizes handling, no solvent to remove. If you make your own column with alumina, use a dispo pipettes to use minimal alumina - you want to keep any loss ( column hang up ) small.

I recommend column or precipitation in ether or hexane. I usually use the precipitation method to remove BHT,