Lattice Vibrational Analysis Of Elementary Excitation In Conjugated Polymers

Conjugated polymers have been the new organic functional materials with good development foreground owing to their unique properties, such as they can luminesce and conduct, and have advantages of simple technology, flexibility, low cost etc.. There is different from inorganic materials. The carriers in polymers are not traditional electrons and holes, but with internal lattice structure of the nonlinear elementary excitations, such as soliton, polaron, bipolaron and trion etc..The static state and dynamic properties about various kinds of nonlinear elementary excitations play a very important role in understanding of the conjugated polymers, such as luminescence, transport, and so on. In addition, these elementary excitations have their own unique localized vibrational modes, so the localized vibrational modes can be regarded as the "fingerprint" of these nonlinear elementary excitations. We can identify the type of the elementary excitations through these localized vibrational modes. It’s very interesting to investigate the vibrational modes in order to understand dynamic properties of various nonlinear elementary excitations in conjugated polymers.In the first part of this article, we have calculated the lattice configuration and electronic state of trion based on the Su-Schrieffer-Heeger(SSH) and the extend Hubbard model. Using the equations of vibrational modes, the localized vibrational modes of trion can be obtained. The effects of electron-electron interaction on the lattice configuration and electronic state and localized vibrational modes of trion are studied. The study found that: the on-site electron-electron interactions and the nearest electron- electron interactions make the trion lattice configuration more localized and changed the electronic state of trion. The on-site electron-electron interactions and the nearest electron-electron interactions don’t change quantity and parity of the localized vibrational modes, just make their frequency drift, but changed their localization.In the second part of this article, we have investigated the localized vibrational modes of two excitons and two polarons. How does the length of the chain affect the vibrational modes of two excitons and two polarons. The results show that: the two excitons have sixteen localized vibrational modes which can be divided into two sets, one is symmetric, and the other is antisymmetric. When the chain length is long enough, there is no interaction between the two excitons, the local energy level is degenerate, and the frequency of the symmetric and antisymmetric localized vibrational modes take the same value. The two excitons will interact with each other when the length of the chain is short, which leads to the local energy level splitting and the frequencies of the symmetric and antisymmetric localized vibrational modes are non-degenerate. The difference of the two frequencies value increases with the chain length decreasing. It is found the critical length of the two modes is different. Furthermore, we found that the dependence of the chain length to the localized vibrational modes of two polaron’s is the similar as that of the two exciton’s.