..where i need to describe a technique (synthetic methods) that could produce polystyrene with lower polydisperisty ?
With a lower PD than what? Free Radical polymerisations (FRP) give tighter PDs than the ionic ones. You can get PDs down to 1.5 with FRP using AIBN initiator in toluene solvent. If you use a 'living' FRP using TEMPO as a mediator then you can get lower than 1.5 - typically about 1.02 to 1.3 - depending on the method and amount of washing and reprecipitating of your product. (I managed to get a PD of 1.02 like this with a dimethylstyrene and chloromethylstyrene copolymer of Mn around 10,000). You can now do funky ATRP and RAFT type FRPs which can give you tighter control, but I haven't done too many of these personally.