Alternating current ͑ac͒ and direct current ͑dc͒ conductivities have been measured in polymer-nanotube composite thin films. This was carried out for a range of concentrations of multiwall nanotubes in two polymer hosts, poly͑m-phenylenevinylene-co-2,5-dioctyloxyp-phenylenevinylene͒ ͑PmPV͒ and polyvinylalcohol ͑PVA͒. In all cases the dc conductivity DC was ohmic in the voltage range studied. In general the ac conductivity displayed two distinct regions, a frequency independent region of magnitude 0 at low frequency and a frequency dependent region at higher frequency. Both DC and 0 followed a percolation scaling law of the form ϰ(pϪp c ) t with p c ϭ0.055% by mass and tϭ1.36. This extrapolates to a conductivity of 1ϫ10 Ϫ3 S/m for 100% nanotube content. Such a low value reflects the presence of a thick polymer coating, resulting in poor electrical connection between tubes. This leads to the suggestion that charge transport is controlled by fluctuation induced tunneling. In the high frequency regime the conductivity increases with frequency according to an approximate power law with exponent sϷ0.92, indicative of hopping transport. The onset of this frequency independent conductivity scales with mass fraction for the PmPV composite due to the variation of correlation length with nanotube content. This behavior is discussed in terms of a biased random walk in three dimensions. In addition ac universality is demonstrated by the construction of a mastercurve.

We study the optimal packing of hard spheres in an infinitely long cylinder, using simulated annealing, and compare our results with the analogous problem of packing disks on the unrolled surface of a cylinder. The densest structures are described and tabulated in detail up to D/d = 2.873 (ratio of cylinder and sphere diameters). This extends previous computations into the range of structures which include internal spheres that are not in contact with the cylinder.

Single-wall carbon nanotubes are severely restricted by the fact that they exist in bundles. In addition, their interaction with other materials is poorly understood. In this work a new spectroscopic method is described to measure the ratio of free polymer to nanotube-bound polymer in SWNT/polymer solutions. This ratio is highly nonlinear and can be described by a model based on polymer−nanotube adsorption/desorption kinetics. In combination with the experimental data, this model shows that the nanotube bundles decrease in size as the concentration is reduced. Individual nanotubes are stable at low concentration, as supported by atomic force microscopy data. In addition, the model allows the indirect measurement of the polymer−nanotube binding energy at 1.1 eV per molecule. In principle, this method is generic and can be used to monitor dispersions of any metallic nanomaterials in suitable, luminescent organic solutions.

This article focuses on foams, which consist of gas bubbles surrounded by liquid and closely packed together so that they are in contact with each other. As a mixture of two fluids, a foam is paradoxically a solid, at least under a small enough stress — surface tension and gas pressure maintain it in equilibrium when deformed. The corresponding mixture of two liquids is an emulsion, rendered stiff by surface tension under low stress. After explaining what a foam is, this article discusses various applications of foams. It then considers the statics and dynamics of foams, the simple rules that govern local equilibrium, and the structure of foams. It also examines the key properties of foams, such as coarsening due to diffusion, coalescence, drainage, foamability, rheology and rheometry, shear localization, conductivity, and light scattering. Finally, it describes the role of surfactants in foam stability and evaluates analogous systems such as emulsions.

The two-dimensional viscous froth model is a simple tractable model for foam rheology and coarsening. It includes, but is not confined to, the quasistatic regime. Here we present a detailed analysis and implementation of the model, illustrated with various examples. With certain simplifying assumptions, it provides significant insight into strain-rate-dependent effects in foam rheology and elsewhere, particularly in relation to recent experiments.