Generally, the polymerization of multifunctional monomer give gel-network polymers. However, it is possible to get soluble and linear-like polymeric products under the controlled synthetic conditions.
The question is how to get linear-like polymer from the polymerization of multifunctional ( tri-, four-functional) compounds. The synthesis of hyperbranched polymer well-known in elsewhere, no mention about controlled polymer topology.
i work on polymer synthesis by microwave assisted polymer synthesis and also refluks. I think it depend on precursor for monomer and nitrogen gas controled
I would wage on the introduction of monofunctional, adequately reactive group bearing molecules in hopes of moderating and steering the polymerization. It is difficult to know the outcome, because the reaction path would be a matter of different combinations between the moderators and the monomers.
I am assuming you are dealing with step-growth polymerization. If this is the case, the slow conversion can be put to good use. If you plan an array of experiments varying the molar amount of moderators and the moment of their introduction in the reaction vessel, you can pinpoint the better reaction parameters to give you the desired architecture.
For hyperbranched polymers obtained by polycondensation of an ABf type of monomer a suitable pathway is to protect (f-1) of the B-groups, resulting in an ABB*(f-1) type of monomer where only the A and the B groups can react (B* hinderd on reaction by the protective Group). After polymetrization, have a linear polymer with protected B-Groups.(B*) deprotect and you have your linear analogon of the hyperbranched polymer.
t should way in an analogous way for polycondensates of A2 wit Bf Monomers
See e.g.
Khalyavina, A.; Lederer, A.; Schallausky, F.; Komber, H.; Al Samman, M.; Radke, W.
Aromatic-aliphatic polyesters with tailored degree of branching based on AB/AB2 and ABB*/AB2 monomers mehr
Good question- there are many things which need to control in such a complicated polymerisation. To avoid branching by side reactions - always carry reaction in presecene of nitrogen atmosphere. Multifunctional monomer is the other difficulty which can be overcomed by adjusting stoichiometric amount of reactant and controlling extent of reaction. The detail information can be received from "principles of polymerisation" George Odian, Wiley book.
I know my suggestions may not solve your problem 100 but will help you to proceed in the right direction.