Mercaptopurine (6-MP), a cancer medication limited by its hydrophobic properties, was studied using molecular dynamics simulations with biodegradable copolymers (PLA-PEG, PLA-PEG-PLA, PEG-PLA-PEG) as drug carriers. The influence of PEG concentration in copolymers on drug release was examined. Results revealed that blending PEG with PLA or copolymerizing them affected hydrogen bond numbers and mixing energy in the drug carrier, dependent on copolymer type and PEG concentration. Introducing PEG into PLA chains increased hydrogen bonds and energy, but copolymerizing PLA and PEG did not consistently enhance hydrogen bond energy (PLA-PEG-PLA > PEG-PLA-PEG > PLA-PEG). Mixing energy was consistently elevated by PEG-PLA copolymerization, ranked PEG-PLA-PEG > PLA-PEG > PLA-PEG-PLA. The fastest drug release was observed with the PLA&PEG-10.9 carrier, attributed to weak PLA-PEG chain connections facilitating water access to PEG. Increasing PEG content reduced chain mixing energy, slowed drug release via stronger chain hydrogen bonding. Notably, PEG-PLA-PEG-8.7 exhibited the highest drug release rate due to quicker water penetration. The copolymer type and chain length were found to impact water molecule access to PEG and drug release rate significantly.