Localization of excitons by molecular layer formation in a polymer film

Spin coated films of atactic polystyrene of two different molecular weights have been studied with uv spectroscopy and x-ray reflectivity, the film thickness (d) varying from similar to 2R(g) to similar to 12R(g) where R-g is the unperturbed radius of gyration of the polymer. uv extinction due to the pure electronic singlet (1)A(1g)-> E-1(1u) is seen to increase with d(-1) for 4R(g)<= d <= 12R(g) (region 1). This suggests excitonic interaction along d. The variation of total exciton energy (E) of the A(1g)-> E-1u singlet with d in region 1 can be well explained by formation of linear J-aggregates of polystyrene molecules, in a lattice with spacing "a" (in A) R-g < a < 2R(g), along d. Atomic force microscopic images of the films show the presence of "spheres" distributed randomly on film surfaces with in-plane dimensions matching a. From the variation of E with d(-2) the effective mass (m(eff)) of the exciton is also determined. For R-g < d < 4R(g) (region 2) the extinction and E become essentially independent of d, indicating exciton localization along d, and the value of m(eff) becomes very large. This enhancement in the effective mass maybe used to quantify localization. The variations of electron density (rho) with d, i.e., the electron density profiles (EDPs) of the films extracted from x-ray reflectivity studies, indicate formation of layers with period "b" (in A), R-g < b < 2R(g) parallel to substrate surface in region 2 and a constant rho film in region 1. On raising the temperature of a typical film to 60 degrees C, the layering was seen to almost vanish, as obtained from both the EDP and the Patterson function of the reflectivity profile. The close correspondence between "a" and "b" indicates that the molecules forming the J-aggregates form the layers, too. The average difference in rho between successive extrema in the EDPs in region 2, denoted by delta, can be used as the order parameter for the layering transition. For PS-5, delta>0 at d similar or equal to 4R(g), where the exciton is still delocalized. Layering reduces the Hamaker constant (A(H)), deciding the cohesive force, between the layers and this reduction, Delta A(H), is found to be less than A(e) at d >= 4R(g), where iA(e)/h is the amplitude for exciton transfer between neighboring molecules in the excitonic lattice of region 1. On the other hand, Delta A(H) in region 2 starts from a value larger than A(e). This indicates that Delta A(H) acts as a barrier between the layer, which localizes the exciton within the layers.