Polymers coherence lengths

In their neutron diffraction studies of p-type doping of PPP, Stamm and Hocker [179] have determined the setting angle (p of the chains in the pristine polymer to be 57° 3°. In this refinement, the authors started from the data by Kovacic et al. [169], but assumed a monoclinic P2i/a structure with /i=I00°. While a number of later studies by others confirm that the value of 4> is around 57°, Stamm et al. [180] find a much lower value of 45° in their electron diffraction work. The neutron study yields lateral coherence lengths L of 60 A for Kovacic PPP and 150 A for Yamamoto PPP. 

This aspect of polymer-dopant interaction has been the subject of a more detailed study by Chen et al. [104]. PPV-Cs has been compared with rubidium-doped polyacetylene, for which the guest/host size ratio is very nearly the same (Table 1.7). Whereas poly-acetylene-Rb has an intrachannel coherence length of 25 A for the ion sublattice, the coiresponding value is 70 A in the case of PPV-Cs the ion siiblattices are incommensurate for both at the compositions studied. Such intriguing differences can only be understood by considering, in a more polymer-specific manner, the character of the chain and the guest-host interactions. 

The elastic moduli of an extruded PLC are largely determined by its molecular orientation, so we first consider the orientation parameters calculated from the observed meridional X-ray reflections. For liquid crystalline copolyesters and copolyesteramides, the sharpness of these reflections gives an indication of the coherence length, a value corresponding to 10 monomers being typical. Therefore, the orientation parameter obtained from the meridional reflection is not specific to the crystalline regions but instead reflects the average orientation of all the chains in the polymer. 

When the concentration of chain interruptions is sufficiently high such that the left hand side of equation 1.3 is small, then the wave function will be localised. The possible limits for the conductivity arise from the chain interruptions and/or phonon scattering. All the above factors suggest that in high-quality conducting polymers the electronic mean free path could be much larger than the structural coherence length and real metallic features could be observed. 

---