Polyacene crystals

SUinsh, E.A., Khmkans, A., Larsson, S., and Capek, V., Molecular polaron states in polyacene crystals. Eormation and transfer processes, Chem. Phys., 198, 311, 1995. 

Qualitatively, the dynamic properties of different polyacene crystals are similar, since both the intermolecular van der Waals forces and also the molecular masses are to first order proportional to the number of C atoms per molecule. Therefore, for example all the sound velocities are of the same order of magnitude (Table 5.4). The same is true for the maximum frequencies of the optical phonons and of the intramolecular osdUations. A clear and general difference is however to be found between smaller and larger molecules in terms of the lowest frequencies of the intramolecular modes with increasing molecular mass, the frequency of the low-energy intramolecular vibrations shift towards lower values. These molecular excitations are either bending or torsional oscillations. This frequency shift can cause the gap and the strict separation of internal and external modes to become less sharp. 

The values of AT in the MN crystals are nearly as large as that for benzene (Sect. 5.8.2). This result is also typical the order of magnitude of the van der Waals interactions is similar in all the polyacene crystals. A typical correlation time tc at room temperature can be found e.g. for 1,5 DMN from the values in Table 5.6 and Eq. (5.23) to be (1,5 DMN, 300 K) = 2.4 10 s. Compared with the period of rotation of a free CH3 group around its threefold symmetry axis, similarly to the case of benzene, the corresponding rotational frequency is much lower than that of the free groups or molecules [30]. The reorientation motions of the CH3 groups are thus hindered rotations. 

The dibromonaphthalene (DBN) crystal differs in its crystal structure (Fig. 2.14) considerably from the structure of the polyacene crystals (Fig. 2.10) the unit cell of DBN contains eight molecules, which belong to two non-equivalent sublattices I and II. The excitation energies of the triplet excitons in the sublattices I and II differ by 50 cm. At low temperatures, therefore, only the excitons in one of the sublattices are excited. Each sublattice consists of linear stacks of DBN molecules along the c axis of the crystal. The exciton transport along this stacking axis is also predominant the triplet excitons in in DBN crystals are quasi-one-dimensional excitons. 

Fig. 8.8 A comparison of the term diagrams of the ionised states of the polyacene crystal series benzene, naphthalene, anthracene, tetracene, and pentacene, with the levels of the isolated molecules. Notation as in Fig. 8.6. From [19].

A typical bandwidth of the charge-carrier bands VB and CB in the polyacene crystals is of the order of 0.1-0.5 eV (see Sect. 8.5.4), i.e. r > 10 s must hold if one wants to describe the conductivity in terms of a band model. The states of the charge carriers in a band extend coherently over at least several unit cells. Therefore, for a description within a band model, the mean free path X of the charge carriers must be long in comparison to the lattice constant ... 

With Eqns. (8.69) to (8.72), the band structures for excess charge carriers in several different polyacene crystals were calculated numerically [42]. As an example. 

The bandwidths of the all together sixteen subbands in the monocUnic crystals (or twenty in the triclinic crystals) - both for electrons and for holes, there are two bands each, F+ and F, for each of the five directions of k calculated, of which two are degenerate in the monocUnic crystals - vary between 4meV and 500 meV, depending on the direction and the crystal (cf. Fig. 8.38). The overaU bandwidths W vary, depending on the crystal and the LUMO or HOMO band (CB or VB) between 372 meV (naphthalene, LUMO) and 738 meV (pentacene, HOMO). Table 8.3 Usts the values of the overall bandwidths for the polyacene crystals naphthalene, anthracene, tetracene, and pentacene. 

Table 8.3 Overall bandwidth W for holes in the LUMO and electrons in the HOMO in polyacene crystals. From [42].

Petelenz, P. and M. Slawik. 1991. 2-Dimensional model of charge-transfer excitons in polyacene crystals. Chem Phys 157 169. 

SUinsh, E.A., Shlihta, G.A., Juigis, A.J. A model description of charge carrier transport phenomena in organic molecular crystals. 1. Polyacene crystals. Chem. Phys. 138, 347-363 (1989)... 

Calorimetric measurements of the heat evolved from the reactions of sodium polyacene dianion salts with water afforded the determination of thermodynamic parameters 70). For all the polyacene dianion salts, the heats of formation were found to be negative. Crystal lattice energies between 400 and 440 kcal/mol were found. These studies add a very important insight into the properties of 4nrc conjugated polycyclic dianions (Sect. 6.4). The measurements were carried out on solvent free dianions in a colimeter... 

Experimentally, crystals of polyacenes have been studied by absorption and reflection spectroscopy. The pioneering work by Clark and his students, using a microtome to deliberately cut specific crystal faces of organic crystals which were then studied by reflection spectroscopy was very important. The corresponding absorption spectra have been derived by Kramers-Kronig analysis (63) (equa-... 

Table 2.1 Melting points (°C) of some molecular crystals. Van der Waals forces are determined by the polarisabilities of the molecules. Thus, cyclooctatetraene, with the same number of carbon atoms (8), has a higher melting point than o-xylol, because it has more polarisable Jt electrons. The same holds for benzene in comparison to n-hexane and for the series of polyacenes from benzene to hexacene.

The aromatic compounds are of special interest. As an example, we show here the crystal structure of the very intensively investigated molecule anthracene (Fig. 2.10). The molecular structure, with the charge clouds of the n electrons perpendicular to the molecular plane (compare Fig. 1.2), shows in an understandable way that the polarisability is strongly anisotropic and has by far its largest value in the molecular plane. From the conditions of maximum dispersive interactions and optimum packing in space, the herringbone structure seen in Fig. 2.10 is most favourable in a monodinic crystal lattice with two molecules in the unit cell. Fig. 2.10 also shows the structiures and Table 2.3 the structural data for the other crystals of polyacene molecules, i.e. for naphthalene, tetracene and pentacene with 2, 4 or 5 aromatic rings. All of these substances crystallise like many others also in the same pattern. Table 2.3 also contains data about the orientations of the individual molecules in the unit cell for these crystals. 

Draw a band structure for polyacene, using butadiene as the unit cell. Describe the origin of each band, and sketch the crystal orbital at the zone center and the zone edge for each band. Rationalize in as quantitative a way as possible the zero band... 

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