Structures

Figure 1: Structures and charge densities for the carbon polymers PPP (top-left) and PPV (top-right) and their BN analogues PBZ (bottom-left) and PVB (bottom-right).

The structures we chose are the analogues of poly(p-phenylene) (PPP) and poly(p-phenylenevinylene) (PPV), which are shown in Fig. 1. When made of BN, they become poly(p-borazylene) (PBZ) and poly(p-vinyleneborazylene) (PVB) respectively. As PPP is a sequence of concatenated benzene rings, PBZ is a sequence of concatenated borazine rings. An analogous substitutional process leads to the creation of PVB from PPV. The charge densities in Fig. 1 clearly show the effects of the polar B-N bonds in comparison to the homonuclear C-C bonds. This is certainly related to the improved solubility of BN polymers compared to their organic counterparts: in fact, PBZ was found to be soluble in ethers [41] whereas PPP is insoluble. Side chains are usually attached to the backbones of insoluble polymers to make them soluble, leading to complex systems which are difficult to process. If BN polymers are soluble without the need to complicate their structures with side chains, they might be more easily processed to form films from solutions. Moreover, the absence of side chains would facilitate polymer alignment resulting in sharper features in the electronic spectra and enhanced mobility.

Figure 2: Comparison of the geometries of carbon and BN structures: (a) benzene and borazine; (b) PPP and PBZ; (c) PPV and PVB; (d) graphite and graphitic BN. All bond lengths are in Å and angles in degrees.

The calculated bond lengths and angles are reported in Fig. 2. An important difference between the geometries of the carbon and BN polymers is the twisting angle between monomers. The bonds linking the monomers together are not necessarily rigid and therefore the monomer planes need not align. The torsion angle between the monomers measures the deviation from the planar configuration. In carbon polymers, the twisting is induced by the significant charge transfer in C-H bonds. In fact, because of the different electronegativities of the two atoms (2.2 for hydrogen versus 2.55 for carbon on the Pauling scale), the carbon atoms are negatively charged, whereas the hydrogen atoms are positively charged. Using Mullikan population analysis, we estimate the positive charge on the hydrogen to be around 0.3 electron charges. Taking PPP as an example, the close positively charged hydrogens attached to adjacent monomers will repel one another. To minimize the repulsion, they will try to maximize their distance by inducing a torsion between the monomers, with $90^{\circ}$ as the most effective value. On the other hand, the overlap of the $\pi$-orbitals on neighbouring carbons belonging to adjacent monomers will be maximal when the polymer configuration is perfectly planar: there would be no overlap for $90^{\circ}$ torsion. The energy gain arising from the $\pi$-electron delocalization depends on this overlap: it is at its maximum in the planar configuration. Hence there are two competing contributions to the total energy, resulting in an equilibrium angle between 0 and $90^{\circ}$. For the isolated PPP chain, we obtained a torsion angle of about $26^{\circ}$, which compares well with a previously reported value [19]. In BN polymers, the situation is different. The electronegativities on the Pauling scale are 2.04 for boron and 3.04 for nitrogen. Since the hydrogen electronegativity lies in between these values, in the N-H bond the nitrogen will be negatively charged and the hydrogen positively charged, while the opposite will hold in the B-H bond. In PBZ for example, the hydrogen atoms facing each other on adjacent monomers have opposite charge and therefore tend to attract each other: this has the effect of reinforcing the planar structure. The variations of the total energies of PPP and PBZ as a function of the twisting angle between monomers is shown in Fig. 3.

Figure 3: Energy differences vs twisting angle for PPP (squares) and PBZ (circles).

This difference, induced by polarity, between the carbon and BN polymers, will certainly manifest itself in the excited state behaviour. By comparing the absorption and emission spectra of carbon polymers like PPP, a strong Stokes shift is observed, which is a signature of the different atomic arrangements in the ground and excited states. A relevant component of the excited state geometry relaxation is related to the change of the torsion angle towards a more planar configuration. Since the BN polymers are already planar in the ground state, the torsion angle should not change upon excitation. For simplicity, especially in the case of copolymers and crystals, we have enforced the planar configuration in the calculations that will be presented in the rest of the paper.