Is autocorrelation image analysis the proper method in nanoparticle sizing?

Nanomaterials display a range of properties which are completely different to those of bulk materials. This unexpected behaviour is particularly apparent when the size of objects reaches the nanometre scale. A wide range of methods are currently used to characterize the properties of nanoparticles. The aim of this work is to analyse the application of image autocorrelation of atomic force microscope samples in determining the distribution of nanoparticle sizes. We propose a model of cross-correlation, which expands upon a recently published model and which further allows us to determine the limits of the image autocorrelation method. Numerical simulations of different configurations of positions, sizes and shapes of particles were used to study the impact of these parameters on the computation of particle size distribution. The precision of the method was found to be strongly dependent on the shape of particles and thus approximate corrections of the model autocorrelation function are limited in terms of validity. Furthermore, the omission of the cross-correlation component during analysis of very dense particle distributions causes a deformation of the central part of the autocorrelation function and a significant increase in errors. Taking the basic principles of auto correlation into consideration, it is clear that this method is very sensitive to any disturbance of the topographic surface of the distribution. Therefore, we suggest that data obtained using image autocorrelation particle distribution analysis should be interpreted very carefully and that the limits presented in this paper should be taken into consideration in such an interpretation.