# Particle and Particle Agglomerate Size Monitoring by Scanning Probe Microscope
## 1 Introduction  
The physical and chemical properties of nanoparticles are mainly determined by their sizes. Size monitoring is an important component of the process of nanoparticles production [1, 2]. The monitoring is the formation of the particle-size sampling followed by the analysis of the particle-size distribution. The analysis is of importance for the evaluation of the sizes of particles themselves and for the evaluation of particle-based products, for example, of the dispersity evaluation of powders containing particles under study. For the data acquisition and formation of the particle-size distribution such methods as laser diffraction [3, 4], dynamic light scattering [5, 6] and acoustic spectroscopy [7, 8] are more widely used. The methods are mainly suitable for controlling particles in solutions. The disadvantage of these methods is measurement results distortion, which can occur with a significant difference in the particles size present in the solution. In this study, we consider the case when nanoparticles are deposited on a substrate before research and size monitoring, carried out by images. An overview of deposition methods and a description of the simplest one can be found in [9]. Deposition is widely used for particles obtained in the liquid phase and in the form of powders. In the latter case, a suspension or colloidal solution is prepared from the particles. Traditional photography [10] or various microscopes and diffractometers [11, 12, 13, 14, 15, 16, 17] are widely used to obtain particles images on substrates. One of the most powerful tools among them is a scanning probe microscope (SPM). In comparison with other devices such as an electron microscope, forexample, the SPM has the following advantages: variety of sample types, functionality in air and liquid, relative simplicity of sample preparation, direct topographic measurements and the presence of nanolithography functions permitting to mark studied regions during monitoring. Since the lifetime of particles on the substrate can be limited, and the execution time of one scan can reach 5-10 min, significant efforts of developers are aimed at time reduction and automating the monitoring of particle sizes. One of the ways to reduce monitoring time is to substitute sequential uniform scanning [18] with tracking scanning. Automation is possible due to additional image processing and the determination of tracking scan parameters based on the results of this processing. Direct topographic measurements in SPM allow to use the conventional image processing methods. As a rule, SPMimages are processed with the use of conventional algorithms [19] presented in OpenCV and FLANN libraries [20; 21; 22]. Commercial universal SPM [23] software, as well as specialized software (Image), MountainsSPIP) widely use the methods (binarization, segmentation, contour analysis) implemented in the mentioned libraries. However, it is further shown that in some cases it is reasonable to use specialized methods for image processing. There are various special-purpose SPMs that can be used for nanoparticle size monitoring such as a multi-probe scanning microscope (an AFM with parallel active cantilevers) and large-sample SPM. The multi-probe scanning microscope can be used for fast investigation (several minutes) of a large area (several mm\({}^{2}\)). However, it has a low resolution of about 40-50 nm [24], which makes it impossible to monitor nanoparticles with a diameter smaller than 40-50 nm. A large-sample SPM can also be used for nanoparticle size monitoring. Such an SPM is equipped with advanced sample-positioning systems, which leads to an increase in the effectiveness of size monitoring. The use of a large-sample SPM is economically sound for monitoring nano-objects in mass-production items such as silicon wafers, catalysts, membranes, or filters.