An Experimental Approach to the Percolation of Sticky Nanotubes

Abstract

Percolation is a statistical concept that describes the formation of an infinite cluster of connected particles or pathways. Lowering the percolation threshold is a critical issue to achieve light and low-cost conductive composites made of an insulating matrix loaded with conductive particles. This has interest for applications where charge dissipation and electrical conductivity are sought in films, coatings, paints, or composite materials. One route to decreasing the loading required for percolation is to use rod-like particles. Theoretical predictions indicate that this may also be achieved by altering the interaction potential between the particles. Although percolation may not always respond monotonically to interactions, the use of adhesive rods can be expected to be an ideal combination. By using a system made of carbon nanotubes in an aqueous surfactant solution, we find that very small attraction can markedly lower the percolation threshold. The strength of this effect can thereby have direct technological interest and explain the large variability of experimental results in the literature dealing with the electrical behavior of composites loaded with conducting rods.

Continuum percolation of carbon nanotubes in polymeric and colloidal media

“…By contrast, even very weak attractive interactions, caused, e.g., by the presence of the matrix material (21), significantly lower the PT, although we cannot rule out the existence of a regime outside the range of validity of our approach, where attraction might do the opposite (22). We confirm earlier speculation that there are two different regimes with a different local structure depending on the strength of the attractive interactions (11,23), but in addition we make plausible the existence of two additional regimes at higher interaction strengths where the percolating network is either built up from nanotube bundles or is kinetically frozen and no longer in equilibrium.…”

“…As is well known, the PT of conductive filler particles decreases in inverse proportion to their aspect ratio, a rule of thumb that is generally valid for elongated and flat particles alike (9,10). Recent experiments on the percolation of singlewalled carbon nanotubes (SWNTs) in aqueous dispersions (11,12) have also shown that a remarkable lowering of the PT can be achieved by making use of weak attractive interactions between the SWNTs (11).…”

“…In an attempt to come to a more realistic description, we focus attention on the effects of nonideality characteristic of real CNTs and apply the continuum percolation theory of physical clusters to elongated particles in an effective medium. The effective medium describes the presence of the host material, e.g., a polymer melt or an aqueous dispersion containing depletants such as surfactant micelles or polymer latex particles (11,12).…”

Empirical evaluation of attractive van der Waals potentials for type-purified single-walled carbon nanotubes

“…61 Equilibrium statistical mechanics predicts an exponential decrease in φ c at moderate attraction. 63,64,67 For strong attraction (w p ≃ 20-40k B T ) and large aspect ratio (λ ≃ 500-1000) such theories predict unphysical values for φ c , many orders of magnitude too small. This is not surprising, since the SWCNTs of interest are not in thermal equilibrium but form a glassy network.…”

Modelling percolation in fibre and sphere mixtures: Routes to more efficient network formation

“…The formation of extended networks of particles dispersed in a fluid gives rise to a discontinuous change in the rheological [1][2][3][4][5] and electrical [6][7][8][9] properties of the dispersion at concentrations around the so-called percolation threshold. Historically, percolation theory was first used by Flory [10] to explain the phenomenon of gelation in thermosetting polymers.…”