Chains trans-polyacetylene

In the following Section we present results of the application of the method to two model prototype systems, namely molecular hydrogen chains and all-trans polyacetylene. 

The charge transport in a conjugated chain and the interchain hopping is explained in terms of conjugation defects (radical or ionic sites), called solitons and polarons. Several possible conjugation defects are demonstrated in Fig. 5.33 on the example of trans-polyacetylene. 

The crystallinity of m-polyacetylene has been estimated to be 76-84% by x-ray diffraction while trans-polyacetylene is 71-79 %6). Observations on Durham polyacetylene 445) showed that the diffraction peak narrowed, and the interchain -spacing decreased, during isomerization and annealing. The x-ray coherence length, a measure of the crystallite size perpendicular to the chains, increased from 2.6 nm to 7.1 nm, compared with 30 nm for polyethylene. 

When two trans-polyacetylene chains with different phases are put together, an obvious disturbance occurs in the standard conjugation pattern. The bond alternation defect that appears is known as a neutral soliton (Fig. 1.7). This kind of quasi-particle has an unpaired electron but is electrically neutral and is isoenergetically mobile along the polymer chain in both directions. This soliton gives rise to a state in the middle of the otherwise empty energy gap that can be occupied by zero, one or two electrons (Fig. 1.8). 

The experiments showed clear differences of behavior between polyacetylene in the cis and trans forms. Namely, SEE and OE are obtained in the cis and trans forms, respectively. In other words, the electronic spins are fixed in ds-polyacetylene, and they become mobile in the trans form. This result is quite consistent with the soliton picture. In cw-polyacetylene, a bond alternation defect divides the chain into two parts ds-transoid and frans-cisoid, whose energies are different (Fig. 8a). Thus, to minimize energy, the spin defect will be trapped at one end of the chain (Fig. 8b). On the other hand, in trans-polyacetylene the chain is divided into two degenerate parts. The defect should therefore be free to move (Fig. 9). 

Trans-polyacetylene, tra 5-(CH) was the first highly conducting organic polymer [1,2]. The simple chemical structure, -CH- units repeated (see Fig. IVB-la), would imply that each carbon contributes a single p electron to the tr-band. As a result, the rr-band would be half-filled. Thus, based upon this stmcture, an individual chain of neutral polyacetylene would be a metal since the electrons in this idealized metal could move only along the chain, polyacetylene would be a one-dimensional (Id) metal. However, experimental studies show clearly that neutral polyacetylene is a semiconductor with an energy gap greater than 1.5 eV. Rudolf Peierls [86] showed many years ago that Id metals are... 

The Pariser-Parr-Pople Hamiltonian for the description of the 7i-electrons in trans-polyacetylene is reparametrized using ab initio Coupled Cluster Doubles calculations based on a Restricted Hartree Fock reference on trans-butadiene. To avoid the spin contaminations inherent in Unrestricted Hartree Fock (UHF) type calculations on polymethine chains in the doublet state the Annihilated Unrestricted Hartree Fock (AUHF) model is applied in our PPP calculations (tPA (CH) , polyenes H-(CH)2N-H, polymethines H-(CH)2N+1-H). In geometry optimizations on polymethine chains it is shown that in contrast to results from Hiickel type models the width of neutral solitons is strongly... 

Figure 4 Ln-Ln plot of the average polarizability (a) in units of esu versus chain length L in A for Hubbard chains of up to 20 sites in all — trans polyacetylene configuration for (a) <5 = 0 and (b) 6 — 0.09, for three different values of Ult.

In the case of defect-free trans-polyacetylene chain, a charge transfer directly between doping agents and valence and conduction band, respectively, will produce an ion radical in the chain, i.e., a defect pair instead of an isolated defect. Figme 5.21 shows the mechanism of p-doping of fra/is-polyacetylene. 

It must be noted that the values reported in the literature vary over broad ranges. Therefore, the values listed here reflect only the general behavior of several classes of compounds. It can be seen in Table 3.5 that trans-polyacetylenes (PAs) and polydiacetylenes (PDAs) exhibit the largest third-order NLO susceptibilities. The x value of cis-PA (not shown) is more than an order of magnitude smaller than that of trans-PA. Derivatives of poly-p-phenylene, poly(phenyl-ene vinylene), and polythiophene also exhibit NLO activity, but to a much lesser extent than PAs and PDAs. As pointed out above, polysilanes also possess quite large x values. This is explained by the cr-conjugation of the silicon chain, which implies a pronounced delocalization of cr-electrons. A very large x value... 

FIGURE 15.48 Real and imaginary parts of the dielectric functions (solid lines) and loss function Imf-l/s) (dotted line) from Kramers-Kronig analyses of the reflectance spectra for light polarized parallel to the chain direction for highly oriented AsFs doped trans-polyacetylene. (From Leising, G., Phys. Rev. B, 38, 10313, 1988. Reprinted from the American Physical Society. With permission.)... 

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