Polarization, energetics, and electrorheology in carbon nanotube suspensions under an applied electric field: An exact numerical approach

We theoretically investigate the polarization, aggregation, and yield stress in carbon nanotube suspensions under an electric field. The nanotubes are modeled as solid rods with hemispherical ends. An exact numerical approach, which includes self-consistent Coulomb interactions within classical electrostatics, is employed to derive nanotube surface charge densities. Two essential nanotube characteristics, i.e., large aspect ratios and end contributions, are included together. The reliability of the model is demonstrated by comparing the calculated emerging yields against experimental data. The onsets of system parameters can be used to control the phase transition in nanotube suspensions.

Figure 1

Schematic of a dispersed solution of nanotubes (a). Upon application of an electric field, the nanotubes become polarized, align with the applied field (b), and subsequently aggregate in chainlike structures (c).

Figure 2

Surface charge density along metallic nanotubes with different radii (a). The nanotube stems (excluding the ending hemispheres) extend from $-250$ to 250 nm. Surface charge density along metallic (b) and semiconducting (c) nanotubes with different stem lengths and a fixed radius of 0.5 nm. The applied electric field of 1 kV/mm is parallel to the nanotube’s axis, and the solvent for semiconducting nanotubes is water.

Figure 3

Pair interaction potential (in units of $kT$ with $T=300\text{K}$) (a), attractive internanotube force (b), and the (continuous) half-nanotube charge (c) for different internanotube distances in an aggregated chain. The applied electric field is fixed at 1 kV/mm.

Figure 4

Upper bounds for the yield stress in nanotube solutions consisting of different nanotube chains under a fixed electric field of 1 kV/mm.