Fractional dimensionality on self-trapped Frenkel excitons in molecular crystallites

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 signif icant. The theory is based on the tight-binding approach. Uniqueness in sel f-trapping appears in the magnitude of the fractional dimension. Exceptiona lly high threshold for self-trapping is found when (1) a thin crystallite i s made of two layers, or (2) a crystallite is formed by two molecular chain s, or (3) a linear molecular chain is made of four molecules. The fractiona l dimension analysis thus offers a wider overview of the self-trapped excit on character than the analysis that can be done using intergral dimensions only.