THEORY OF ELECTRONIC EXCITATION TRANSFER IN POLYMER MICELLES AND LAMELLAE

We have developed a theoretical description of energy-transfer between chromophores in various geometries which correspond to actual configu rations of polymers in a variety of materials. These include micelles with chromophores in the core or in the corona, such as one might obta in with a diblock copolymer in which chromophores are incorporated in one block, micelles with chromophores at the surface or at the interfa ce between blocks, lamellae, and balls. The distribution of chromophor es in this model can be random or described by a variety of functions to investigate situations such as the packing of diblocks at the inter face between two homopolymeric phases and the expansion, contraction, or redistribution of micelle coronae which often accompanies changes i n solvent characteristics. The calculated quantity, G(S)(t), is the pr obability of finding an initially excited chromophore still in the exc ited state at time t, and is directly related to fluorescence depolari zation. The behavior of G(S)(t) in the cases of chromophores randomly distributed in an infinite plane and on a sphere is compared with anal ytical expressions in closed form for G(S)(t) in those configurations; in the case of a ball, G(S)(t) is compared with a previously reported expression(4) for energy-transfer in that geometry, and exact agreeme nt is obtained. The sensitivity of this method is explored by examinin g G(S)(t) as a function of the shape and volume of the chromophore dis tribution.