Diameter measurements of polystyrene particles with atomic force microscopy

The size of (nano) particles is a key parameter used in controlling their function. The particle size is also important in order to understand their physical and chemical properties and regulate their number in health and safety issues. In this work, the geometric diameters of polystyrene spheres of nominal diameter 100 nm are measured using atomic force microscopy. The measurements are based on the apex height and on the average distance between neighbouring spheres when they form a close-packed monolayer on a flat mica substrate. The most important influence parameters for the determination of the geometric diameter are the lateral air gaps and deformation of the spheres. The lateral air gaps are caused by significant size variations of the individual spheres, and a correction is calculated based on the simulation of packing of spheres. The deformation of the spheres is caused mainly by capillary forces acting when they are in contact with each other or with the mica substrate. Based on calculated capillary forces and the literature values of the elastic properties of the polystyrene and mica, the deformation is estimated to be 2 nm with a standard uncertainty of 2 nm. The geometric diameter of the polystyrene spheres was measured with a combined standard uncertainty of ≈3 nm. The measured vertical diameter of 92.3 nm and the certified mobility equivalent diameter measured by differential mobility analysis (DMA) are marginally consistent at a confidence level of 95%. However, the measured lateral geometric diameter was 98.9 nm and is in good agreement with DMA.