You are using vinyl monomers with an initiator! So, the polymerization is based on free radical and quite sensitive to dissolved O2. Hence, I recommend to properly degas the solution with N2 gas, and then seal the solution under the inert atmosphere. The free space of the reaction vessel should be as small as possible.
To do so, you can use a screw cap vial with a rubber septa fixed on the cap (like Penicillin vial!). Insert a large needle beneath the solution through the septa for feeding the vial with N2 gas, and use another small needle as an outlet. Degas the solution for about 10 min. If the solvent is volatile, put the vial in an ice bath while degassing.