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Encyclopedia of Physical Science and Technology En012j-597 July 26, 2001 11:8

Polymers, Electronic Properties 647

cepts of band theory may have validity for these poly-
mers. These considerations are further amended if, as is
the case in reality, the polymer materials are not ordered as
in single crystals. Any variation in the energy of a molec-
ular orbital due to disorder (compositional, translational,
or rotational) can impede band formation by the disrup-
tion of the required periodicity. Experimental values for
mobilities in pendant-group polymers reveal values much
2
lower (∼10 −4 cm V −1 sec −1 or less), which reflects the
consequences of strong electron–phonon interactions rel-
ative to bandwidths together with substantial effects of
disorder.
The conventional method of experimentally studying
electronic states in polymers is that of optical absorption,
including increasingly sophisticated techniques such as
low-energy electron-loss spectroscopy and synchrotron
radiation source spectroscopy. These techniques allow
such optical properties as absorption, reflectivity, and di-
electric loss to be measured over an energy range from
0.2 to 1000 eV with a resolution of 0.1 eV. With these
FIGURE 2 Examples of a saturated polymer (a) without pendant energies, it is also possible to do core-level spectroscopy
groups, polyethylene, and (b) with a pendant group, poly(N-vinyl in which the very narrow deep-lying atomic levels, by act-
carbazole), and associated energy level picture. ing as a source of electrons of well-defined energies, can
be used to probe the structure in the broader, higher ly-
of polymers with the bonds saturated (i.e., complete bond ing empty extended states. Photoemission spectroscopy,
satisfaction) or unsaturated but no pendant groups. Exam- in which electrons are excited out of the polymer, can
ples of these are polyethylene and polyacetylene, respec- give complementary information regarding filled-valence
tively. The second class comprises polymers with satu- molecular states.
rated backbones with appended aromatic chromophores
that project out of the polymer chain. Polystyrene and
A. Pendant-Group Polymers
poly(N-vinyl carbazole) (PVCA) are representative ex-
amples. Figure 2 schematically represents examples of The extension of the pendant group perpendicular to
these two polymer classes together with the appropriate the chain direction and its typically planar character can
electronic energy level picture. As alluded to above, the lead to very little overlap and therefore interaction even
strong intrachain covalent bonding leads to wide bands between adjacent pendant groups. Amorphous pendant-
of states with an energy gap, ε g between the last-filled grouppolymersarethereforesimilartoarandomassembly
and first empty band. This is applicable even for amor- of isolated pendant molecules. This fact has several far-
phous polymers because of the maintenance of periodic- reaching consequences. The electronic states of pendant-
ity in the chain direction. An important requirement for group polymers bear a remarkable resemblance to those
the applicability of the band theory relates the strength of the isolated pendant group. Similarly, the aromatic pen-
of any electron–phonon interaction with the width of the dant groups give rise to electronic states in the gap between
energy band. In order for a carrier to remain within an the valence and conduction band and play a dominant role
energy band of width W after a phonon-scattering event, in the static and dynamic electrical properties, as is dis-
the Heisenberg uncertainty principle states that W τ > h, cussed in Sections III and V.
where τ is the electron–phonon scattering time. Since The most obvious feature of their electronic absorption
µ = eτ/m (m is the effective mass of the carrier), then spectra is the close similarity to those of the effectively
∗
∗
µ must be >he/m W. For reasonable choices of m ,a isolated chromophores, which can be observed in the gas
∗
∗
2
minimum mobility of ∼0.2 cm V −1 sec −1 is required for phase. Figure 3 shows a typical energy-loss function and
the valid application of band theory. This value is typical its derivative for polystyrene. The features indicated by the
of those experimentally measured for molecular crystals arrows, covering the range from 9 to 19 eV on the rising
such as anthracene. By contrast, calculations for polyethy- edge of the plasmon peak, correspond to strong peaks in
lene and polyacetylene predict mobilities considerably the ultraviolet absorption spectrum of benzene, which is
higher than this minimum value and suggest that the con- closely related to the styrene chromophore.