To first order the equatorial structures, perpendicular to the polymer chain
axis, can be treated independent from that parallel to the polymer chains. Two
very different structural motifs, channels and layers, are characteristically
seen. The most commonly reported channel structures for small dopants are
characterized by a single, quasi-one-dimensional array of the guest specie
enclosed by some number of polymer main
as shown in Fig. 8. This phase transformation is often dominated by
cooperative rotational motions of the host polymer chains about their chain
axes to form the individual channel sites. Fig. 9 is arranged so that the
sequential evolution of three fold and four fold channel structures,
appropriate for intercalation of alkali-metal ions into PA, PPV and PPP, can be
clearly viewed. Panels 9(a) and 9(d) show the herringbone lattice of the
undoped polymer in juxtaposition with the various degenerate candidate channel
sites for three fold and four fold structures respectively. Panels 9(b) and
9(e) depict two intermediate structures which form when only a single channel
sublattice is filled. The relative polymer chain to ion channel ratios are 3:1
and 4:1, respectively. Panels 9(c) and 9(f) contain the subsequent structural
phases that form when a second sublattice site becomes filled. Thus these
polymer chain/ion channel ratios are twice those of the previous two panels.
Example scattering spectra for intercalation of alkali-metals into PPV are
shown in Fig. 10.
The actual local structural details are found to be extremely sensitive to the specific treatment, host polymer and guest specie. For instance, the ``stage 2'' structure of Fig. 9(e) has only been clearly observed during electro-chemical dedoping of K-PA. The reported structural phases for crystalline PANI doped with halogen acids are significantly different those just introduced in the preceding paragraphs. The template structures of Fig. 9 also ignore much of the self-consistent structural relaxation by the polymer host. While Fig. 9(e) identifies the major translational response of the polymer lattice, a majority of these structural phases[65,72,73,74,75] have been shown to exhibit either symmetry-lowering distortions of the unit cell or pronounced displacements of the various unit cell constituents away from high symmetry positions. In one instance there is experimental evidence for the presence of even more complex ordering phenomenon. In addition, these doped structures often contain further structural ordering between guest ions in the immediately adjacent channels to give tetragonal[68,69,76], trigonal or orthorhombic 3D structures.
To compliment these experimental studies there has been an effort to develop an understanding from a theoretical perspective. The large number of atomic constituents in combination with complexity of the structures that characterize the experimental systems precludes the use of realistic models in theoretical treatments except in certain limiting cases. Hence a true fundamental understanding of the full range of structural behavior is lacking. It is possible, however, to reproduce much of the complexity in this structural phase behavior using much simplified models[78,79,80]. Choi et al.[79,81] have studied a model Hamiltonian which embodies many essential aspects of the competing guest-host interactions that exist within the conducting polymer matrix. In their work the polymer host is reduced to a 2D triangular lattice of interacting planar rotors and the dopants are allowed to occupy the high-symmetry sites similar to the model of Fig. 9(a). Depending on the relative strengths of the interaction energies and that of the dopant chemical potential, a rich array of equilibrium structures are possible.