Linear Unsubstituted Polymers

Figure 1 sketches the chemical structures for a number of prototypical linear unsubstituted electroactive polymers. Nearly all of these polymers crystallize into tightly packed herringbone structures characterized by two-dimensional p2gg symmetry as seen in Fig. 2. This packing is also widely seen in saturated hydrocarbon polymers[8] such as polyethylene and polypropylene. The only consistent exception to this base structure, in regards to the $\pi $-conjugated examples of Fig. 1, is in the case of PANi. Polyaniline exhibits a number of structural forms[9] and this complexity is likely traceable to the increased torsional and angular flexibility surrounding the phenyl-amine (or quinoidial-imine) linkage in combination with a strong tendency to form hydrogen bonds.

Figure 2: Views of the prototypical herringbone packing in poly($p$-phenylene vinylene) and often seen in many crystalline unsubstituted $\pi $-conjugated polymers.

The well-defined periodicity and knowledge of the underlying unit cell structure has enabled detailed calculations of band structure[10,11], electron transport[12] and optical properties[13,14]. Depending on the chain setting angle, $\theta$, and the relative axial chain to chain position[15], parallel to the chain axis, there can be significant interchain $p_z$ orbital overlap and the development of three-dimensional (3D) bands and transport. Continuing advances in quantum chemical ab initio methods and other theoretical approaches have dramatically improved our understanding of these materials at the molecular level[16,17,18].

Beyond the seeming near universality of the herringbone motif there are still significant differences relating to the exact molecular structure. A key component in determining both intrachain and interchain transport and photophysics is the C-C torsion angle ($\phi$ or as $2\phi_\tau$ in Fig. 2) across C-C ``single'' bonds along the skeletal backbone. In a very basic interpretation this torsional degree of freedom leads to site-specific variations in the transfer integrals consistent with a $\cos 2\phi$ functionality[19,20]. Thus if two adjacent molecular units have orthogonal p$_z$ orbitals this completely disrupts conjugation to the same extent that chain ends or chemical defects will also terminate $\pi $-conjugation.

From this perspective the differences between the various homopolymers shown in Fig. 1 becomes readily apparent. For example in PPP, as seen in Fig.1(b), every phenylene ring is affected by two pairs of hydrogen-hydrogen repulsions. Gas phase studies[21] of biphenyl, consisting of just two para-linked phenylene rings, report a large 45$^\circ $ twist between planes of the two benzene rings. For PPP in the solid state interchain interactions become important and as a result of packing constraints this angular torsion angle alternates between approximately $\pm 18^\circ$ from the ideal case of a trans planar backbone[22]. Non-planarity is generally associated with increasing interband transition energies, narrowing of the band width and a reduction of intrachain charge transport[23]. A full accounting requires detailed knowledge of both the ground state and excited states because there are often changes in the local bond alternation. This latter effect can strongly alter other aspects of the geometrical construction[24,14].

In contrast both polyacetylene and PT include much weaker repulsive steric interactions between neighboring monomer units and so these polymers are reported to be planar or very near planar[25,26]. In these cases $\pi $-conjugation will be measurably enhanced. A secondary effect arises from the non-collinearity between the chain axis and the C-C bond direction. Torsional twists around a single C-C bond would in principle produce large scale translational motions and so that deviations from planarity are necessarily small and involve changes in both bond angles and correlated motion of neighboring units. These low energy torsional modes can be clearly observed by inelastic neutron scattering measurements[27,28]. A peculiar structural consequence of this behavior is that increasing temperature does not directly correlate with an approach to a rotator phase[29] in which orientational ordering is lost but the underlying translation symmetry of the underlying lattice is retained.

Intermediate between these two extremes are polymers like PPV in which there is only one pair of somewhat weaker alpha H repulsions per phenylene ring. This leads to a torsional potential well which is very nearly flat and includes only a small barrier between positive and negative torsion angle minima (of approximately $\pm10^\circ$ from planarity[30,31]). Room temperature NMR experiments[32] have resolved very strong librational motions between the two minima and, in addition, sudden ring flips of nearly 180$^\circ $ degrees. PPV has the added advantage over the other $\pi $-conjugated materials so far discussed in that it also has a significant photoluminescence yield[33] and can be prepared in a wide variety of thin film forms[34,35,36]. This has enabled a large number of photophysics studies[37,38,39] in addition to more basic transport measurements[40].

Unfortunately even these crystalline materials are far from perfect and crystallite coherence lengths rarely exceed 250 Å. Charge transport over any but the smallest distances invariably involves traversing both ordered and disordered regions. Thus there is a continuing need to accurately assess and quantify the impact that disorder has on device properties[41]. One well-known characteristic, termed inhomogeneous broadening, is reflected in the strong asymmetry between optical absorption and the emission spectra[42]. This property originates from the fact that the interband LUMO-HOMO transition (typically $\pi-\pi^*$ or $\sigma-\sigma^*$) is sensitive to the effective conjugation length and so absorption can always occur if the incident light has energy in excess of a threshold dictated by the local segment specific intraband transition energy. Because of strong coupling to a quasi-one-dimensional lattice relaxation along the polymer chain there is rapid interconversion to a bound positive/negative charge excitation termed an exciton if intrachain or an excimer if interchain. These excitations can undergo large scale intrachain (i.e., migration) and interchain (i.e., energy transfer) displacement over their lifetimes (typically tens to hundreds of picoseconds in the case of singlet excitons) to regions of lower energy or, equivalently, greater effective conjugation length where, depending on the system specific details (intersystem crossings, triplet-triplet annihilation, local traps, etc.) these excitations can recombine luminescently. Thus optical absorption can occur just about anywhere but emission is always highly site selective. In a polymer light emitting diode device (PLED) this implies that luminescence originates preferentially at a very limited number of chain chromophores. In crystalline materials the presumption is that the core of the crystallite contains the most well ordered and extended conformations and so acts as a deep trap for exciton recombination. A more general implication is that structural heterogeneity will strongly affect device performance. Similar arguments can be forwarded for charge transport in transistor devices based on these aforementioned polymers and the somewhat more exotic materials that are introduced in the next section.

Winokur 2004-01-28