Biomedical Engineering Reference
The sketch of Fig. 4 b summarizes the conceptual simplifi cation that we adopt
here for describing the effective electron transport properties of the CNT meshwork,
deposited on a planar substrate, constituting a growth surface for ex vivo networks
of dissociated neurons. The branched outline depicted in Fig. 4 b is a 2-dimensional
reconstruction of the actual morphology of a cultured hippocampal neuron, dissoci-
ated from rat brain and developing in vitro on an adhesion substrate made of nano-
tubes as in Fig. 3 (see also Lovat et al. 2005 ). We hypothesize that most of the
neuronal cellular processes grow in close proximity of the heterogeneous mesh-
work, largely composed of resistive links. While such a cartoon accounts for the
lateral conduction within the meshwork, it leaves unspecifi ed the details related
both to the substrate-electrolyte and to the substrate-neuronal membrane physical
interfaces (modeled in Fig. 4c-d ). Indeed, charge carriers in an electrolyte are not
free electrons as in the nanotubes.
Carbon Nanotube Electrodics
The electrical properties of the interface CNT-electrolyte have been characterized,
mostly in the context of biosensing and electrodics (Czerw et al. 2006 ; Crespo et al.
2008 ), by electrochemical impedance spectroscopy (see Girault 2004 , for an introduc-
tion). Although most of the current literature focuses on the CNTs' excellent ampero-
metric properties when functionalized with polymers and enzymes (see, e.g., Sinha
et al. 2006 ; Zhang et al. 2007 ; Male et al. 2007 ; Muguruma et al. 2008 ; Roy et al.
2008 ; Crespo et al. 2008 ), very few investigators fully realized the great potential of
CNTs as novel materials for (neuroprosthetics) electrodes (Phely-Bobin et al. 2006 ;
Gabay et al. 2007 ; Mazzatenta et al. 2007 ; Li and Andrews 2007 ; Keefer et al. 2008 ) .
The nanoscale sizes of individual CNTs as well as their considerable mechanical
rigidity suggest replacing large metal electrodes with nanostructures comparable in
size with subcellular neuronal details ( see, e.g., Fig. 3 ) while exploiting the electrical
properties of the large exposed surface (i.e., electrical capacitance).
Since CNTs are inert in saline solutions, electrical fl ow at the interface between a
saline solution and CNTs ideally occurs as a capacitive current only, as charge carriers
in the solutions (i.e., ions) and charge carriers in the CNT (i.e., electrons) cannot be
directly exchanged. Instead, at the equilibrium, a redistribution of charge carriers in
both the CNT and the electrolyte occurs at the interface as in a capacitor, forming what
is called the electric double layer (see Geddes 1972 ; Robinson 1968 ; Bockris et al.
2000 ). The electric double layer approximates literally an electrolytic capacitor, and
for CNT dispersions with high surface area it results into a large effective capacitance,
compared, e.g., to gold electrodes. Faradaic reactions at the interface are limited to
oxygen chemisorptions (Girault 2004 ), causing conduction leakage current passing
through the interface at very low frequencies and large electric fi elds. Figure 4c-d
sketches an equivalent electrical circuit model, describing effectively the electrochem-
ical impedance at the CNT-electrolyte interface. Such a model is employed in the
next sections, when a biophysical model of the CNT-neuron junction is introduced.