Quantifying the dispersion of carbon nanotubes in thermoplastic-toughened epoxy polymers

The distribution of particles within modern materials must be defined to understand the change in properties attained by their addition. Two methods of analysis, which use different size scales, are presented here. These methods are applied to characterise the dispersion of multi-walled carbon nanotubes in a thermoplastic-toughened epoxy polymer. First, the greyscale method uses transmission optical micrographs, and calculates the ratio of the variance/mean of the greyscale values. Higher values indicate a greater degree of clustering; lower values may be described as showing a ‘better’ distribution of nanotubes, hence allowing the results to be ranked. This method is relatively easier to carry out, but care must be taken to use a consistent small thickness of sample. Secondly, the quadrat analysis uses transmission electron micrographs of the same materials, after identifying the centre of each nanotube observed. This defines the distribution on the scale of the nanotubes. Peaks in the relationship between the ratio of the variance/mean and cell size are related to microstructural features such as agglomeration. This scale is expected to be related to the scale of microstructural deformation mechanisms which determine global material properties.