Interchain overlap

The above considerations apply to isolated polymer chains in solution, i.e. at very low polymer concentrations or volume fractions, < >p (i.e. in the limit < >p - 0). As p increases, interchain interactions becom important. Indeed, at a critical polymer concentration, second critical concentration, the chains are so overlapped... 

This chapter has summarized some of the recent trends in thiophene polymers. The key factors determining the bandgap are connectivity, bond alternation and the effect of conjugation over the sulfur n-centers. Copolymers frequently have electronic structures that are not intermediate between those of the component repeat units. Calculations can help to select systems for synthetic targets whether the aim is a small bandgap or a particular specific bandgap value. Naturally, one has to bear in mind that the theoretical calculations refer to periodic, defect-free and very long polymers and thus the actual polymers may differ in essential ways from this ideal. Further uncertainty results from the usually unknown interchain overlap, which tends... 

It is clear that the ability to design and control conjugated 77 architectures is the key to creating new materials. Synthesis can determine the magnitude of 77 overlap along the backbone and eliminate structural defects. Materials assembly (and/or processing) determines interchain overlap and dimensionality. Together these... 

Ladder polymers have been of interest for many years, and an early paper on poly(per/-naphthalene) (49) using the VEH method combined with crystal packing calculations provided a band gap of 0.44 eV. With interchain overlap the calculated band gap decreases to 0.29 eV [81,82], The synthesis of polymer 49 by pyrolysis of 3,4,9,10-perylenetetracarboxylic dianhydride at temperatures between 530 and 900°C gave very highly conducting undoped films (a up to 15 S/cm) that were probably not the simple polymer 49 [82]. 

Now we assume that the inter and the intrapart are additive in a way that the inter chain interaction is given by the pairwise overlap of the ellipsoids of the different chain. Since each mass tensor corresponds to a density distribution we can describe the interchain free energy contribution of the pair ij ... 

---