First choose the area in polymer chemistry for example polymer modification, polymer synthesis and its application in different fields like biomedical, liquid crystal, conductiong materials in which you are interested but you need to focous on any one area for your better thesis.
It is better to choose an area of application which is of high value like adsorption of CO2 or degradation of dye effluents with visible radiation and you can synthesize the new polymers which does the job.
I think it is good to choose phd topic of your interest or topic which you know better with some research experience like polymer synthesis, modification, etc. after you choose your desired phd topic search for research groups in that field with decent publications.
As you are reading many publications according polymers try to find unresolved problem. It may be related with any field (medicine for example). Performing you research you can choose a suitable polymeric material or develop a new one.
As far as I know, PhD students normally decide which field they want to study. From there, they will choose a supervisor. The supervisor normally has a certain area / scope of study that he is familiar with. Once you have decided the area, e.g. synthesis, characterization, or modification, it is more important to get a good supervisor who can spend time on guiding you. From my experience, the choice of supervisor is more important than single polymer / multi plymers. After all, it is the training experience that counts, not so much of the content
It depends on the facilities and materials available with your lab. Further, the research problem is generally decided both by the Supervisor and the student.
If you have carried out prior experiments and confident you can choose a specific polymer for your Ph.D. Otherwise it is safe to choose a broad area. It is better to study a host of polymers falling under any one category.