Developing Random Network Theory for Carbon Nanotube Modified Electrode Voltammetry: Introduction and Application to Estimating the Potential Drop between MWCNT−MWCNT Contacts

Abstract

A theoretical model of carbon nanotube (CNT)-modified electrodes is introduced to explain the observed increase in the effective electroactive area of such electrodes when formed by the casting of CNT films on top of an electrode of finite size. The model proposes that a fraction of the CNTs deposited form a conducting network that extends beyond the electrode area and onto the insulating surround. Critical parameters for this situation to occur are described. The random network of conducting CNTs is described by the size of the largest “connected component” and is considered in terms of the minimum number of CNT-CNT connections required to travel a given distance through the network. As such, this approach can be used to describe multilayers of CNTs, provided that the film extends in the radial direction as well as normal to the electrode surface, and also CNTs in contact with more than one neighboring CNT within the mesh. The theoretical predictions were experimentally validated by performing a series of voltammetric experiments. These were conducted using electrodes modified with multiwalled-CNT (MWCNT) films produced by the casting method, so as to deliberately extend the MWCNT film beyond the electrode area. Thus, we determined the magnitude of the potential drop between the first MWCNT-MWCNT contacts to be 20-50 mV. Here we also describe the distribution of potentials throughout the CNT network

Connectivity percolation of polydisperse anisotropic nanofillers

“…17 We speculate that the few size distributions available in the literature [37][38][39][40][41][42][43][44] are not representative of the ones that have been used in the production of the percolating networks in CNT composites. Although a speculation, we feel it is plausible because sonication and, in some preparation procedures, screw extrusion 54 causes a larger skewness toward short lengths.…”

“…Based on the very few available experimental measurements of the length distribution of CNTs, we choose a Gamma distribution and the related Weibull distribution. [39][40][41][42] A limiting case of both of these distributions is the exponential distribution with a probability density function (PDF) f e (L) = η exp(−ηL), 43,44 for which φ p (η)/φ p (η 0 ) = 1/2, with η 0 = η/2, irrespective of the value of the distribution parameter η that takes the form of the inverse mean length. 45 So, an exponential distribution reduces the PT by a factor of 2 (relative to the equivalent monodisperse case).…”

Quantifying Single-Carbon Nanotube–Electrode Contact via the Nanoimpact Method

“…Although indicative of a large contact resistance between the carbon nanotubes and the electrode, the above interpretation is subject to a number of assumptions. Specifically the potential drop between the CNT-CNT contacts 13 and the orientation of the tubes will be influential.…”

Do Carbon Nanotubes contribute to Electrochemical Biosensing?

“…While microspotting, electrodeposition and direct growth enable a more precise localization of CNT on the working electrode, it has been shown that drop casting may further extend the electro-active area by creating a sort of conducting CNT forest in the insulating area surrounding the WE [56]. Also for this reason, we decided to use the drop casting technique in this study.…”