Developing random network theory for carbon nanotube modified electrode voltammetry: Introduction and application to estimating the potential drop between MWCNT-MWCNT contacts

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.