Polymer Diffusion in PBMA Latex Films Using a Polymerizable Benzophenone Derivative as an Energy Transfer Acceptor

Fluorescence resonance energy transfer (FRET) measurements were used to monitor polymer diffusion in poly(butyl methacrylate) latex films with a polymer molar mass of M w ≈ 125 000 ( M w / M n = 2.5). These experiments employed the nonfluorescent acceptor chromophore NBen, which allowed faster data acquisition at lower acceptor dye concentration (0.3, 0.5 mol %) than previous experiments with anthracene (1 mol %) as the acceptor. The data were analyzed in two distinct ways. Our traditional simplified approach involved calculating f m values for the quantum efficiencies of FRET (Φ ET ). Apparent diffusion coefficients D app were calculated by making rather severe assumptions about f m . In addition, we carried out mathematical simulations of diffusion which satisfied Fick's laws in a spherical geometry. The concentration profiles of donor and acceptor were introduced into equations that describe the rate for of energy transfer, and donor decay profiles were simulated ( t ). By comparing simulated and experimental decay profiles as a function of sample annealing time, optimum values of the mean diffusion coefficient 〈 D 〉 were obtained. A comparison of the two different methods of data analysis indicates that D app values are larger than 〈 D 〉 values by a factor of 2−4 but track the “true” diffusion coefficients rather well. From the temperature dependence of the diffusion coefficients, we found effective activation energies for diffusion of E a = 33.5 ± 2.5 kcal/mol from D app and 38 ± 5 kcal/mol from 〈 D 〉. These values are very similar to the value of E a = 39 kcal/mol from D app obtained in earlier experiments in which anthracene served as the acceptor chromophore.