Configurational dependence of the optical properties of π-conjugated polymers. I. Strong disorder limit

The dependence of the optical properties (ππ* energy gap, polarizability, oscillator strength) of polyenes on chain length, degree of bond alternation, and backbone configuration are studied theoretically. For all-trans polyenes a modified form of Hückel theory is proposed which is analytically simple and well behaved in the high polymer limit. Comparison with exact valence bond calculations for short polyene chains and the infinite chain limit reveals that the method is quantitatively accurate for the polarizability and qualitatively reliable for other properties and degrees of bond alternation. Modification of the optical properties by the presence of conjugation-disrupting defects along the polymer backbone is addressed by combining molecular orbital and statistical mechanical techniques. The specific case when the rotational defects severely localize the π electrons (strong disorder) is treated in detail. The disordered polymer configurations are classified by the defect density or mean conjugation length as the primary order parameter. The effects of conjugation length fluctuations and both long and short range defect interactions on the optical properties are determined. Experimental implications for π-conjugated polymers in condensed phases are briefly discussed.