We have no more information about the requirements of the end-use application, please consider only a short answer to your question:
You need PE microspheres (of 4 microns diameter/ or lower diameter/ nanospheres). My first suggestion is to look on the offers of some suppliers of PE microspheres/nanospheres for biomedical applications. Hereinafter there is some information to help you.
3. Attention, due to the low density of PE micro/nano beads you can have problems of dispersion, e.g., in applications such as microcarriers for biomedical use...but I will refrain from more comments.
What about functionalized polystyrene microspheres/nanospheres ?