Study On Conducting Polymers In Condinate Space

Organic conjugated polymers have unique properties quite different from that of inorganic semiconductors. In the first place, organic molecular chains are in one-dimensional structure with weak interchain interaction. In the second place, owing to the strong electron-lattice couplings, the electronic states can interact with the lattice in organic materials. In other words, lattice distortions can be induced by injected charges or photoexcitations, and inversely the distortions will impact on the electronic structure of the system. Different from saturated polymers, conducting polymers is conductive as the backbone consists of carbon atoms with not only localizedσelectrons to bond with other atoms but also delocalizedπelectrons, created by the overlap between p_z electrons, to itinerate freely in the chain through s-p or s-p~2 orbital hybridization.The charge carriers in polymers are self-trapped excitations, e.g., solitons and polarons, rather than electrons or holes. These self-trapping states to a great extent determine the polymer properties, such as charge transport and luminescence, etc, and play fundamental roles in the understanding of polymers.It was found in 1977 that the conductivity of trans-polyacetylene can be greatly enhanced by tens of magnitudes by doping. Thereafter, great interests have been attracted into the study of conducting polymer. As a new species of functional materials, conducting polymers hold general properties of polymers, such as easy processibility, flexibility, and low cost, as well as similar electronic properties of metals or semiconductors. Therefore, conducting polymers have greatly focused on in recent years by researchers. Furthermore, as polymers are typical samples of soft condensed matter, the understanding of organic and life materials has also been enhanced by the extensive study of polymers.The current researches on excitations in polymers are mainly based on the SSH model, founded by Su, Schrieffer and Heeger. The electronic structure and optical properties of polymers were then successfully studied by this semiempirical tight-binding method. Then after, extended SSH models were founded separately by Bishop, Sun, Conwell, Xie, et al., to study different kinds of excitations and their dynamical evolution processes. These work play important roles in the microcosmic understanding of conjugated polymers.In this thesis, a Hamiltonian for one-dimensional conducting polymers is founded based on the Kronig-Penny square potential well model. The total energy of the system is the functional of lattice site displacements treated as slight fluctuations by perturbation theory. The properties of different excitations of degenerate and nondegenerate conducting polymers, such as the electronic structure, the charge density and the lattice configurations, are simulated and compared with results from the SSH model in order to propose new method in studying polymers and obtain universal results. The results of the study are mainly as follows:1. The foundation of Kronig-Penny square potential model.Elementary excitations in the degenerate polymer trans-polyacetylene are studied by using the Kronig-Penny model with tunable potential width, depth and elastic coefficient. By introducing a degenerate-breaking term, a Kronig-Penny model with unequal potential barriers is founded to describe cis-polyacetylene with nondegenerate ground state. Different band gap can be obtained by tuning the magnitude of the degenerate-breaking term. The model will return to the Kronig-Penny model with equal potential barrier for the trans-polyacetylene when the degenerate-breaking term is zero.2. Study on elementary excitations in degenerate polymers in coordinate space. Based on the Kronig-Penny model and the perturbation theory, the ground state ofone-dimensional molecular chain of Jraws-polyacetylene is studied. Soliton state is found to exist in a chain with odd site number. Excitations, e.g., charged solitons, polarons, soliton pairs, and soliton lattice can be obtained by doping. Results of this model in terms of the level structure of excitations, the density of electronic states, lattice configurations and charge density distributions are compared with that derived from the discrete SSH model and the continuous TLM model. It is found that the creation of elementary excitations and their lattice configurations is the same among these models. The differences from the SSH model are that: Firstly, the level structure is asymmetry and the electronic density of state (DOS) decreases with increasing the energy, in accordance with relation between the electronic DOS and the energy in one-dimensional system; Secondly, charges are distributed in the whole chain, both the lattice sites and the bonds there between.3. Study on elementary excitations in nondegenerate polymers in coordinate space.By using the Kronig-Penny model with unequal potential barriers, the typical nondegenerate polymer ds-polyacetylene is studied in coordinate space. By introducing a degenerate-breaking term into the Hamiltonian, two phases with different energy in the ground state, i.e., the A phase and B phase, is obtained. The A phase is focused on by studying the ground state, the polaron state and the exciton state in terms of the level structure, the electronic density of states, the lattice configuration and the charge density . By comparing with the results from the tight-binding model with secondary quantization, it is found to be more accurately to study some properties, e.g., the electronic density of states and the charge density distribution in coordinate space.