A Stochastic FRET Study on the Core Dimension of Polystyrene-block-Poly(Polyethylene Glycol Monomethyl Ether Acrylate) Micelles

Polystyrene-b-poly(polyethylene glycol monomethyl ether acrylate) (PSt-b-PPEGA) copolymers featuring pyrene and perylene as the Förster resonance energy transfer (FRET) donor (denoted as D-BCP) and acceptor (denoted as A-BCP), respectively, were synthesized via the reversible addition and fragmentation chain transfer (RAFT) polymerization. These copolymers were then used to form DA-mixed micelles via a dialysis method. The micelles consisted of D-BCP (mole fraction f_D = 0.04), A-BCP (f_A = 0.04), and label-free PSt-b-PPEGA (f_N = 0.92). The decrease in fluorescence intensity of pyrene in the micelles confirmed the occurrence of FRET, with an observed efficiency of 0.32. A Monte Carlo approach was employed to estimate the expected FRET efficiency, assuming the random fractional distribution of D-BCP and A-BCP, along with the random spatial distribution of pyrene and perylene within the micellar core. The observed FRET efficiency suggested a core radius (R_c) of 0.95R₀, where R₀ was the Förster critical distance. With R₀ calculated to be 3.2 nm based on Förster theory, R_c was determined to be approximately 3.0 nm, aligning closely with the dried-out core radius estimated from aggregation number and polystyrene density. This stochastic FRET methodology was further applied to investigate the swelling behavior of the polymer micelles in a mixture of N,N-dimethylformamide (DMF) and water. Dynamic light scattering analysis revealed minimal change in core dimension below 60 vol % DMF content. However, FRET analysis provided a deeper insight, showing an increase in core radius with DMF content up to 20 vol %, followed by saturation up to 50 vol %, offering a more comprehensive understanding of the micelle swelling behavior.