C O M M U N I C A T I O N S
(σAC) of this pristine film exhibited a behavior which can be fitted
by a power law with an s value in the range of ∼0.8 (Figure 2b).
This value for s suggests that the dominant mechanism of transport
is a polaron hopping mechanism and may be related to the
disordered dielectric effects in the system.15 From our results on
this and similar systems we have found that the polaron hopping
can be relatively fast.9 For example, with the use of time-resolved
spectroscopy we have found that the hopping time can be as fast
as ∼1 ps.9 Such a fast hopping would suggest a relatively strong
long range interaction of the branched structure and this is an
intrinsic effect. It is interesting to note that this was not the case
for the pressure compressed pellet samples of the hyperbranched
Pc, where a value of s greater than unity was obtained and this
may be related to the fabrication procedure used to make the
samples.
In conclusion, we have found a novel organic branched Pc
dendrimer system which shows impressive dielectric properties with
very low loss at high operational frequencies. Compared to
percolative systems, this dendritic system shows very low loss at
higher frequencies and a small dispersion, as well as improved
stability and flexibility. Measurements were carried out with both
pressure compressed pellets and thin films of the Pc dendrimer
system. The mechanism for this impressive high-frequency response
with relatively small dispersion is suggested to be due to a long-
range polaron hopping mechanism accompanied by strong intra-
molecular interactions in the branched system.
Figure 2. (a) Dielectric dispersion curves and (b) AC conductance of the
branched Pc film.
loss, as previous results for Pc related polymers and oligomers had
shown losses (tan δ) up to 0.7 for the polymer composite and above
1.0 for the Pc oligomers.6,8,11 For the purpose of comparison, we
also examined the dielectric properties of the Pc monomer: the
dielectric constant was relatively small (∼5) and the dielectric loss
was high (up to 0.3). Although other results have been reported
with the Pc oligomers and polymers, these results with the dendritic
Pc system present a major improvement which we attribute to the
long-range interactions in the hyperbranched structure.
To probe the transport mechanism which yields this impressive
dielectric response in the dendritic Pc system, we carried out the
analysis of the AC conductance. The AC conductance was analyzed
by the expression given as σAC ) ꢀ0ꢀr tan δ ω, where ꢀ0 is the
permittivity of the vacuum, ꢀr is the real part of the dielectric
constant, tan δ is the dielectric loss, and ω is the angular frequency.
Measurements with the AC conductivity of the Pc samples showed
a frequency dependent conductivity which could be fitted by a
power law given as σAC ) A + Bωs, where A and B are constants
related to the DC (zero frequency conductivity) and s is a fitting
parameter. The AC conductance of the pressure compressed pellet
with a thickness of 76 µm showed the super-linear power law
dependence with an s value of ∼1.70. It has been suggested that
the s parameter may give an indication of the charge transport
mechanism in the system. For example, a value of the s parameter
of 1.75 was obtained for a metallorgano Pc film.12 Also, low
temperature measurements of CuPc oligomers have found a
superlinear dependence as well.11 The explanation common to both
of these cases in regards to the transport mechanism was heavily
based on polaron tunneling in the system. However, for this situation
the tunneling of polarons occurs on a relatively short length scale
(short range interactions).12 For the case of the compressed pellet
sample of the dendritic Pc system, the contribution from a polaron
tunneling mechanism is reasonable in describing the transport
properties. It should be mentioned that in the case of the dendritic
structure we have found that the interactions may extend over a
number of repeat units and thus over larger length scales.13 This
effect may be sensitive to the macromolecular order exhibited in
the dendritic system which may be a function of the fabrication
(packing) of the solid-state system (compressed pellet or thin film).
To probe the importance of the morphology of the system once
fabricated in the solid-state, we also carried out measurements of
films of various thicknesses and concentrations of the branched Pc
system. Shown in Figure 2 is the result for a film of the branched
Pc coating on an Al substrate. This system also showed a very
small dispersion and the dielectric constant was close to ∼15 at 1
MHz. A very small dielectric loss (on the order of 0.001) was
obtained at high frequencies (Figure 2a). Compared to TiO2
functionalized polystyrene nanocomposites (ꢀr ) 6∼10),14 the
dielectric performance of the hyperbranched Pc films meets the
stiff requirements for gate dielectrics and of organic transistor
applications. Our measurements of different film’s AC conductance
showed no apparent thickness dependence. The AC conductance
Acknowledgment. This work is supported by the Office of
Naval Research.
Supporting Information Available: Synthesis and characterization
of the hyper-branched Pc polymer. This material is available free of
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