
Hopping conductivity of a nearly 1D fractal: A model for conducting
polymers
A. N. Samukhin
A. F. Ioffe Physico-Technical Institute, 194021 St. Petersburg, Russia
Institute of Physics AS CR, Na Slovance 2, 180 40 Prague 8, Czech Republic
V. N. Prigodin
A. F. Ioffe Physico-Technical Institute, 194021 St. Petersburg, Russia
Department of Physics, The Ohio State University, Columbus, Ohio 43210-1106
L. Jastrabík
Institute of Physics AS CR, Na Slovance 2, 180 40 Prague 8, Czech Republic
A. J. Epstein
Department of Physics, The Ohio State University, Columbus, Ohio 43210-1106
(Received 19 May 1998)
We suggest treating a conducting network of oriented polymer chains
as an anisotropic fractal whose dimensionality D = 1 + is close to
1. Percolation on such a fractal is studied within the real space renormalization
group of Migdal and Kadanoff. We find that the threshold value and all
the critical exponents are strongly nonanalytic functions of as 0,
e.g., the critical exponent of conductivity is –2exp(–1 – 1/). The distribution
function for conductivity of finite samples at the percolation threshold
is established. It is shown that the central body of the distribution is
given by a universal scaling function and only the low-conductivity tail
of distribution remains dependent. Variable range hopping conductivity
in the polymer network is studied: both dc conductivity and ac conductivity
in the multiple hopping regime are found to obey a quasi-one-dimensional
Mott law. The present results are consistent with electrical properties
of poorly conducting polymers. ©1998 The American Physical Society
Limits for Metallic Conductivity in Conducting Polymers
R. S. Kohlman,1 A. Zibold,2 D. B. Tanner,2 G. G. Ihas,3 T. Ishiguro,4
Y. G. Min,5 A. G. MacDiarmid,5 and A. J. Epstein1,6
1Department of Physics, The Ohio State University, Columbus, Ohio 43210-1106
2Department of Physics, University of Florida, Gainesville, Florida
32611
3Center for Ultra Low Temperature Research, University of Florida,
Gainesville, Florida 32611
4Department of Physics, Kyoto University, Kyoto 606-01, Japan
5Department of Chemistry, University of Pennsylvania, Philadelphia,
Pennsylvania 19104-6323
6Department of Chemistry, The Ohio State University, Columbus, Ohio
43210-1106
(Received 25 July 1996)
The temperature (T) dependent dc conductivity (DC) (down to 20 mK) and
dielectric function at optical frequencies (0.002–6 eV) and 6.5 GHz are
used to probe the inhomogeneous disorder-driven insulator-metal transition
in conducting polymers. A correlation between large low T DC and the presence
to low T of a small fraction of the carrier density delocalized with long
transport times (> 10-13s) indicates that metallic DC is due to only a
small fraction of the charge carriers. The achievable DC for these systems
when the entire charge carrier density participates is estimated to surpass
that of copper.
Charge transport of the mesoscopic metallic state in partially crystalline
polyanilines
J. Joo
Department of Physics, The Ohio State University, Columbus, Ohio 43210-1106
Department of Physics, Korea University, Seoul 136-701, Korea
S. M. Long
Department of Physics, The Ohio State University, Columbus, Ohio 43210-1106
J. P. Pouget
Laboratoire de Physique des Solides, CNRS URA 02, Université
Paris-Sud, 91405 Orsay, France
E. J. Oh and A. G. MacDiarmid
Department of Chemistry, University of Pennsylvania, Philadelphia,
Pennsylvania 19104-6323
A. J. Epstein
Department of Physics and Department of Chemistry, The Ohio State University,
Columbus, Ohio 43210-1106
(Received 21 March 1997; revised 18 November 1997)
Charge transport properties, including temperature-dependent dc conductivity,
thermoelectric power, electron paramagnetic resonance,
microwave frequency dielectric constant and conductivity, and electric-field-dependent
conductance of partially crystalline ("physically"
cross-linked) HCl-doped polyaniline correlated with x-ray structure
studies, demonstrate that charge delocalization in physically cross-linked
polyaniline systems is structurally controlled. Further, we observe
a positive dielectric constant at room temperature which increases (to
values ³ 104) with increasing
percent crystallinity, the size of crystalline regions, and polymer chain
alignment in the disordered regions,
supporting the establishment of mesoscopic metallic regions. We propose
an inhomogeneous disorder model for this system in which ordered (crystalline)
regions, described by three-dimensional metallic states, are connected
through amorphous regions of polymer chains where one-dimensional disorder-induced
localization is dominant. We utilize the metallic box, interrupted metallic
strands, and Nakhmedov's
phonon-induced delocalization models to account for the temperature
dependence of charge transport properties of the various partially
crystalline polyanilines. Analyses for the sample and temperature-dependent
electron paramagnetic resonance linewidth and thermoelectric
power are presented.
Unusual semimetallic behavior of carbonized ion-implanted polymers
G. Du
Department of Physics, The Ohio State University, Columbus, Ohio 43210-1106
V. N. Prigodin
Department of Physics, The Ohio State University, Columbus, Ohio 43210-1106
A. F. Ioffe Physico-Technical Institute, 194021 St. Petersburg, Russia
A. Burns and J. Joo
Department of Physics, The Ohio State University, Columbus, Ohio 43210-1106
C. S. Wang
University of Dayton Research Institute, Dayton, Ohio 45469
A. J. Epstein
Department of Physics, The Ohio State University, Columbus, Ohio 43210-1106
(Received 16 December 1997)
We report a comprehensive charge transport study of ion-implanted rigid
rod and ladder polymers p-phenylenebenzobisoxazole,
p-phenylenebenzobisthiazole, and benzimidazobenzophenanthroline. The
three pristine materials are strong and stable polymers with a room
temperature conductivity sRT
~ 10–12 S/cm. After high dosage ion implantation
using Kr+, a carbonized and conducting
layer forms on the
surface of the film samples with sRT
> 102 S/cm. The experimental results suggest
that this carbonized layer is semimetallic with unusual
properties. The observed dc conductivity follows s(T)
= s0 + Ds(T),
where Ds(T) is weakly temperature dependent
and interpreted
within the model of weak localization and electron-electron interaction
effects. The model reveals that the interaction effect is three
dimensional for the experimental temperature range (3–300 K), whereas
the weak localization effect undergoes a dimensional crossover at ~
60 K from three to two-dimensions with decreasing temperature. The
magnetoconductance, thermoelectric power, and microwave dielectric
constant results are all in agreement with this semimetallic model.
In addition, all these results consistently point to an enhanced interaction
effect at low temperatures due to the reduced dimensionality of the
localization effect. It is concluded that a sp2
rich and three-dimensional
interconnected carbon network reformed upon ion implantation of the
densely packed pristine polymers is responsible for the semimetallic
behavior.
R.S. Kohlman and A.J. Epstein, Insulator-Metal Transition and Metallic State of Conducting Polymers, in Handbook of Conducting Polymers, Second Edition, edited by T.A. Skotheim, R.L. Elsenbaumer, and J.R. Reynolds (Marcel Dekker, Inc.), Chapter 3, 85-121 (1997).
R.S. Kohlman, A. Zibold, D.B. Tanner, G.G. Ihas, T. Ishiguro, Y.G. Min, A.G. MacDiarmid, and A.J. Epstein, Limits for Metallic Conductivity in Conducting Polymers, Physical Review Letters 78, 3915-3918 (1997).
Created by Darren Gebler. Maintained by John Rohrbacher. Last updated 5/23/00.