Systems Polyacetylene-Based Lattices

Their calculated mean square displacement P t) and the self-diffusion coefficient D for the carbon and hydrogen atoms defined in Section 3.3.1 [Eqs. (24) and (25)] show that PAc chains undergo diffusional motion mainly along their axial (c) 

With the two Li ions in as widely separated positions as the simulation box allows, the dynamics were initiated and equilibrated for the same thermodynamic conditions as in pristine PAc. By artificially constraining the diffusive motion of polymer chains, the motion of Li ions was monitored through the radial distribution function g(r) [Eq. (28)]. The gcxiC ) 9h,u( ) were found to describe a liquid-like motion for Li ions, while Qu,u( ) was almost featureless except for a very small range of dopant separations. This indicates that in agreement with the results of the static lattice calculations (Section 5.3), the motion of the ions was rapid along the chain directions, but correlated by the dominant interionic Coulomb repulsions, so that they maintained (on average) the maximum distance apart permitted by the simulation box. 

The highly doped structures referred to in the description of static lattice simulations (Section 5.3) as PAKl and PAK2 have also been investigated by MD by Sese and her colleagues. As in the static studies the electronic charge transferred from the dopant atoms was distributed uniformly on the carbon atoms, which therefore bear net charges of -0.25e and -0.125e, respectively in the two species. 

The dynamics of PAKl and PAK2 were investigated using a 432-atom and a 408-atom simulation box under the same 300K thermodynamic conditions that were applied to the pristine and lithium-doped lattices. Some of the liquid-like features of the Li ions in lightly doped PAc also appear in the PAK systems, but as seen in Fig. 5.23 the gKjc( ) shape resembles the radial distribution functions in solids. In PAKl there are peaks at r values corresponding to dopant site separations in the static lattice. This indicates that the dopant sublattice of the initial (static) 

FIGURE 5.23. Radial distribution functions gxY(r) in potassium (a) fully-doped and (b) semi-doped  

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The step-potential model is the conceptually simplest approach to treating electron-phonon coupling in tt-electron systems and is the logical extension of the free electron model. Scaled to the experimental bond lengths of butadiene and benzene, the static properties of nonlinear excitations in /ran5-polyacetyIene are well described. Based on standard adiabatic approximation, the extension of the step-potential model to the study of the dynamical behavior of nonlinear excitations in trans-polyacetylene is straightforward. The time unit is scaled to the frequency of the in-phase stretching mode of the polyene lattice. However, this does not affect the course of the dynamics shown. 

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