Polyacetylene linear absorption

V-UV Application First Excited State of Linear Polyenes. The first electronic absorption band of perfect linear aromatic polyenes (CH)X, or perfect polyacetylene shifts to the red (to lower energies) as the molecule becomes longer, and the bond length alternation (BLA) would be zero. This was discussed as the free-electron molecular orbital theory (FEMO) in Section 3.3. If this particle-in-a-box analysis were correct, then as x > oo, the energy-level difference between ground and first excited state would go to zero. This does not happen, however first, because BLA V 0, next, because these linear polyenes do not remain linear, but are distorted from planarity and linearity for x > 6. 

For long (infinite) trani -polyacetylene chains, the treatment of quantum lattice fluctuations is very complicated, because many lattice degrees of freedom couple in a non-linear way to the lowest electronic transitions. We have recently shown that for chains of up to 70 CH units, the amount of relevant lattice degrees of freedom reduces to only one or two, which makes it possible to calculate the low-energy part of the absorption spectmm in an essentially exact way [68]. It remains a challenge to study models in which both disorder and the lattice quantum dynamics are considered. 

Under the conditions used for the electro-optical measurements on the various device structures that are reported in sections S and 6, we will expect to see a substantial electric field applied across at least a fraction of the polyacetylene layer, and we need to characterise the modulation of the %-n absorption edge with electric field. This electromodulation response is the Franz-Keldysh effect, and arises through modulation of the electron states near the band edge in the applied field. It is found to be very large in Shirakawa polyacetylene [54,55] and it has been pointed out that this is due to the strong non-linear electronic response that characterises the conjugated polymers [55]. In the low field limit, we expect to see a response that varies quadratically with the applied electric field, and that is proportional to the second differential of the absorption coefficient, a, 92a/aE2 [54]. 

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