Polymer nanotubes by wetting of ordered porous templates

We have developed a simple technique for the fabrication of polymer nanotubes with a monodisperse size distribution and uniform orientation. When either a polymer melt or solution is placed on a substrate with high surface energy, it will spread to form a thin film, known as a precursor film, similar to the behavior of low molar mass liquids. Similar wetting phenomena occur if porous templates are brought into contact with polymer solutions or melts: A thin surface film will cover the pore walls in the initial stages of wetting. This is because the cohesive driving forces for complete filling are much weaker than the adhesive forces. Wall wetting and complete filling of the pores thus take place on different time scales. The latter is prevented by thermal quenching in the case of melts or by solvent evaporation in the case of solutions, thus preserving a nanotube structure. If the template is of monodisperse size distribution, aligned or ordered, so are the nanotubes, and ordered polymer nanotube arrays can be obtained if the template is removed. Any melt-processible polymer, such as polytetrafluoroethylene (PTFE), blends, or multicomponent solutions can be formed into nanotubes with a wall thickness of a few tens of nanometers. Owing to its versatility, this approach should be a promising route toward functionalized polymer nanotubes.

A Maxwell relation for current-induced forces

A Maxwell relation is presented involving current-induced forces. It provides a new physical picture of the origin of current-induced forces and in the small-voltage limit it enables the identification of a simple thermodynamic potential which drives electromigration. The question of whether current-induced forces are conservative or non-conservative is discussed briefly in the light of these insights.

Are current-induced forces conservative?

The expression for the force on an ion in the presence of current can be derived from first principles without any assumption about its conservative character. However, energy functionals have been constructed that indicate that this force can be written as the derivative of a potential. On the other hand, there exist specific arguments that strongly suggest the contrary. We propose physical mechanisms that invalidate such arguments and demonstrate their existence with first-principles calculations. While our results do not constitute a formal resolution to the fundamental question of whether current-induced forces are conservative, they represent a substantial step forward in this direction.

Reply to comment on 'Counterbalancing forces in electromigration'

Reply to comment by K-H W Chu.

Counterbalancing forces in electromigration

In electromigration (EM) experiments on metallic wires, a flux of atoms can lead to motion of the centre of mass (COM) of the wire. Hence, it may be tempting to assume that the flow of current produces a net force on the wire as a whole. We point out, on the basis of known momentum-balance arguments, that the net force on a metallic wire due to a passing steady-state current is zero. This is possible, because in addition to EM driving forces, acting on scattering centres, there are counterbalancing forces, acting on the rest of the system. Drift of the COM in EM experiments occurs inevitably because the substrate keeps the crystal lattice of the wire fixed, while allowing diffusion of defects in the bulk of the wire. This drift is not evidence for a net force on the wire.

Current-induced forces in atomic-scale conductors

We present a self-consistent tight-binding formalism to calculate the forces on individual atoms due to the flow of electrical current in atomic-scale conductors. Simultaneously with the forces, the method yields the local current density and the local potential in the presence of current flow, allowing a direct comparison between these quantities. The method is applicable to structures of arbitrary atomic geometry and can be used to model current-induced mechanical effects in realistic nanoscale junctions and wires. The formalism is implemented within a simple Is tight-binding model and is applied to two model structures; atomic chains and a nanoscale wire containing a vacancy.