Electronic Excitations in Conjugated Polymers

Fixing to experimental values for the gap, of 1.7 eV and the bandwidth, of 12 eV, the value of X is required to be of order 0.2, rather larger than can be attributed to electron-phonon coupling alone [19,20], and it is widely held that the enhanced bond dimerisation is due to the effects of the on-site Coulomb repulsion energy, U . This is shown for example in the work on Baeriswyl and Maki [21], in which, for U small ( 4t), bond dimerisation is enhanced. It is possible to choose realistic values of X, (= 0.1) and U /4t (= 0.6-0.7) and to obtain a satisfactory value for the energy gap. 

In spite of the clear evidence for the importance of Coulomb interactions, and their role in determining the properties of conjugate molecules, the SSH model and its continuum version [18] are widely used, particularly for the modelling of polyacetylene in its excited states with the various parameters (bandwidth, electron-phonon coupling etc.) chosen empirically. This approach has been remarkably successful, and we follow it in the present work for the modelling of the effects of disorder on the chain. 

The fundamental excitations of the half-filled band Peierls distorted chain are known to be phase kinks, or solitons, in the pattern of the bond alternation. This was shown for polyacetylene [5,6] to take the form of the bond alternation defects shown in figure 2. An important insight into the nature of these excitations from the work of Su et al [6] is that the bond alternation defect is not localised at a single carbon site, as indicated for convenience in the schematic representation in figure 2, but is spread over some 10 to 15 carbon sites. This delocalisation is crucial to the energetics of the stabilisation of the soliton, and is clearly demonstrated experimentally. For this situation, it is possible to use a continuum model for the polyacetylene chain, within which various simple analytic results are found. Thus, the gap parameter, A varies through the soliton as 

A value of aUo/3 of about 0.4 eV is consistent with the measured values of AE obtained from photo-induced absorption measurements [25]. Associated with the formation of the mid-gap soliton absorption band is the loss of n and it band states and the bleaching of the n n interband transitions. 

In addition to the electronic excitations of the soliton, there are also new vibrational modes associated with translation of the soliton (T modes) and with shape or amplitude modes of the soliton (A modes). The T modes are associated with the coupling of those vibrational modes of the (CH)x unit cell that modulate the bond dimerisation amplitude to the translation of the soliton along the chain [22,27]. These modes appear as Raman-active modes fw the dimerised chain, with frequencies determined by the phonon response function. 

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Experimental studies of fundamental excitations in conjugated polymers are interpreted within the framework of current theoretical electronic structural calculations and physical structure characterizations. The instabilities peculiar to this class of materials that are responsible for their departure from metallic behavior are identified explicitly. 

For spin-1/2 excitations such as electrons and holes in normal semiconductors or polarons in conjugated polymers, a single resonance is found centered at the Field... 

After a photon has excited the conjugated polymer to form an exciton, the C60 accepts one electron due to its high electron affinity and establishes the anion Cg0. What is left on the polymer chain is a cation radical, i.e., a positive polaron, as depicted in Fig. 1.14, which is a mobile charge carrier that can move along the polymer backbone. This transfer is an exothermal reaction, where energy from the system is released. 

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