Silica nanoparticles possessing three different diameters (23, 74 and 170 nm) were used to modify a piperidine-cured epoxy polymer. Fracture tests were performed and values of the toughness increased steadily as the concentration of silica nanoparticles was increased. However, no significant effects of particle size were found on the measured value of toughness. The toughening mechanisms were identified as (i) the formation of localised shear-band yielding in the epoxy matrix polymer which is initiated by the silica nanoparticles, and (ii) debonding of the silica nanoparticles followed by plastic void growth of the epoxy matrix polymer. These mechanisms, and hence the toughness of the epoxy polymers containing the silica nanoparticles, were modelled using the Hsieh et al. approach (Polymer 51, 2010, 6284-6294). However, it is noteworthy that previous modelling work has required the volume fraction of debonded silica particles to be measured from the fracture surfaces but in the present paper a new and more fundamental approach has been proposed. Here finite-element modelling has demonstrated that once one silica nanoparticle debonds then its nearest neighbours are shielded from the applied stress field, and hence may not debond. Statistical analysis showed that, for a good, i.e. random, dispersion of nanoparticles, each nanoparticle has six nearest neighbours, so only one in seven particles would be predicted to debond. This approach therefore predicts that only 14.3% of the nanoparticles present will debond, and this value is in excellent agreement with the value of 10-15% of those nanoparticles present debonding which was recorded via direct observations of the fracture surfaces. Further, this value of about 15% of silica nanoparticles particles present debonding has also been noted in other published studies, but has never been previously explained. The predictions from the modelling studies of the toughness of the various epoxy polymers containing the silica nanoparticles were compared with the measured fracture energies and the agreement was found to be good.@en

Measuring quantitatively the nanoparticle dispersion of a composite material requires more than choosing a particular parameter and determining its correspondence to good and bad dispersion. It additionally requires anticipation of the measure's behaviour towards imperfect experimental data, such as that which can be obtained from a limited number of samples. It should be recognised that different samples from a common parent population can give statistically different responses due to sample variation alone and a measure of the likelihood of this occurring allows a decision on the dispersion to be made. It is also important to factor into the analysis the quality of the data in the micrograph with it: (a) being incomplete because some of the particles present in the micrograph are indistinguishable or go unseen; (b) including additional responses which are false. With the use of our preferred method, this article investigates the effects on the measured dispersion quality of nanoparticles of the micrograph's magnification settings, the role of the fraction of nanoparticles visible and the number of micrographs used. It is demonstrated that the best choice of magnification, which gives the clearest indication of dispersion type, is dependent on the type of nanoparticle structure present. Furthermore, it is found that the measured dispersion can be modified by particle loss, through the limitations of micrograph construction, and material/microscope imperfections such as cut marks and optical aberrations which could lead to the wrong conclusions being drawn. The article finishes by showing the versatility of the dispersion measure by characterising various different spatial features.@en