FRACTIONAL DIMENSIONALITY ON SELF-TRAPPED FRENKEL EXCITONS IN MOLECULAR CRYSTALLITES

Abstract

Self-trapped exciton characteristics in microcrystallites are discussed in terms of the fractional dimension. The concept of the fractional dimension is introduced since microcrystallites are formed with various side lengths where the concept of the integral dimensions (1D, 2D and 3D) are not significant. The theory is based on the tight-binding approach. Uniqueness in self-trapping appears in the magnitude of the fractional dimension. Exceptionally high threshold for self-trapping is found when (1) a thin crystallite is made of two layers, or (2) a crystallite is formed by two molecular chains, or (3) a linear molecular chain is made of four molecules. The fractional dimension analysis thus offers a wider overview of the self-trapped exciton character than the analysis that can be done using intergral dimensions only.