A Stochastic FRET Study on the Core Dimension of Polystyrene‑<i>block</i>-Poly(Polyethylene Glycol Monomethyl Ether Acrylate)\nMicelles

Polystyrene-<i>b</i>-poly(polyethylene\nglycol monomethyl\nether acrylate) (PSt-<i>b</i>-PPEGA) copolymers featuring\npyrene and perylene as the Förster resonance energy transfer\n(FRET) donor (denoted as D-BCP) and acceptor (denoted as A-BCP), respectively,\nwere synthesized via the reversible addition and fragmentation chain\ntransfer (RAFT) polymerization. These copolymers were then used to\nform DA-mixed micelles via a dialysis method. The micelles consisted\nof D-BCP (mole fraction <i>f</i><sub>D</sub> = 0.04), A-BCP\n(<i>f</i><sub>A</sub> = 0.04), and label-free PSt-<i>b</i>-PPEGA (<i>f</i><sub>N</sub> = 0.92). The decrease\nin fluorescence intensity of pyrene in the micelles confirmed the\noccurrence of FRET, with an observed efficiency of 0.32. A Monte Carlo\napproach was employed to estimate the expected FRET efficiency, assuming\nthe random fractional distribution of D-BCP and A-BCP, along with\nthe random spatial distribution of pyrene and perylene within the\nmicellar core. The observed FRET efficiency suggested a core radius\n(<i>R</i><sub>c</sub>) of 0.95<i>R</i><sub>0</sub>, where <i>R</i><sub>0</sub> was the Förster critical\ndistance. With <i>R</i><sub>0</sub> calculated to be 3.2\nnm based on Förster theory, <i>R</i><sub>c</sub> was\ndetermined to be approximately 3.0 nm, aligning closely with the dried-out\ncore radius estimated from aggregation number and polystyrene density.\nThis stochastic FRET methodology was further applied to investigate\nthe swelling behavior of the polymer micelles in a mixture of <i>N</i>,<i>N</i>-dimethylformamide (DMF) and water.\nDynamic light scattering analysis revealed minimal change in core\ndimension below 60 vol % DMF content. However, FRET analysis provided\na deeper insight, showing an increase in core radius with DMF content\nup to 20 vol %, followed by saturation up to 50 vol %, offering a\nmore comprehensive understanding of the micelle swelling behavior.