Up: Material design from first
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
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.
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  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.
Structures and charge densities for the carbon polymers PPP (top-left)
and their BN analogues PBZ (bottom-left) and PVB (bottom-right).
The calculated bond lengths and angles are reported in
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 as the most
effective value. On the other hand, the overlap of the -orbitals
on neighbouring carbons belonging to adjacent monomers will be maximal
when the polymer configuration is perfectly planar: there would be no
overlap for torsion. The energy gain arising from the
-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 . For the isolated PPP chain, we obtained a
torsion angle of about , which compares well with a previously
reported value .
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.
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.
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.
Energy differences vs twisting angle for PPP (squares) and PBZ
Up: Material design from first
Peter D. Haynes