Using High-Resolution Microscopies and Dedicated Sample Preparation to Determine Particle Concentration in Liquid Suspension

Beside the measurement of particle size and shape distribution, accurate determination of particle number concentration is essential for many applications [1]. Widely used methods for the measurement of particle number concentration, such as MADLS, SAXS, spICP-MS, rely on material specific input parameters, modelling assumptions, or calibration strategies, which contribute to measurement uncertainty, making absolute quantification challenging and limiting direct metrological traceability [2]. In the framework of the European project ConcenSus (https://www.bam.de/Content/EN/Projects/Concensus/Concensus. html), a new experimental approach to determine (nano)particle number concentration is being studied. This includes a dedicated sample preparation from liquid suspension onto a substrate for analysis of the particles with an imaging technique such as SEM, TEM or AFM by counting the deposited particles. Imaging methods such as electron microscopies and AFM are well established for characterising the size and shape of (nano)particulate matter with ISO standards in place: ISO 21363:2020 for TEM and ISO 19749:2021 for SEM. However, no corresponding standard operating procedures exist for the measurement of (nano)particle number concentration using imaging methods. Avoiding agglomeration and coffee-ring effect by conventional drop-casting from liquid suspension is a challenging task [3], as shown in Figure 1a, however, some solutions have been partly found in the recent years [4,5]. This work presents a proof-of-principle study for determining the particle number concentration using SEM by employing a special sample preparation procedure developed recently in our laboratory. This allows the deposition of isolated particles within a small, see Figure 1b, localised spot on the substrate for further imaging [6], see the measurement workflow detailed in Figure 2. In a first stage, relatively simple particulate materials such as Ag and Pd nanoparticles with monodisperse size distribution have been tested. The performance of our counting-by-imaging approach has been assessed by evaluating the main sources of uncertainties along the measurement workflow, i.e. sample inhomogeneity, (nano)particle deposition efficiency, spot area estimation, counting inaccuracy, uncertainty in droplet-to-suspension volume extrapolation, etc. A measurement uncertainty budget in the range of 40% to 80% has been calculated for the approach as applied at this stage. Further, the results obtained by counting through imaging have been compared with concentrations measured with MADLS, but in liquid suspension. The results obtained with both methods for both types of samples are in the same order of magnitude, i.e. 1011 particles/mL. This demonstrates the strong potential of SEM combined with dedicated sample preparation as a powerful approach for the measurement of number concentration of (nano)particles. This approach is independent of material-type and theoretical assumptions, focusing mainly on direct particle counting. Future project work will include other material types, for example, liposomes, quantum dots, mesoporous SiO2, etc with increasing particle complexity. Further optimisation of the sample preparation, measurement, and data analysis will enable an automated workflow for the measurement of particle number concentration by imaging as an accurate, fast, easy and standard method for quality assurance [7]. SEM micrographs of Pd nanoparticles on TEM grid showing (a) agglomeration after preparation by conventional drop-casting, and (b) homogeneously distributed and isolated particles after optimized sample preparation. Measurement workflow of particle number concentration by electron microscopy (here SEM) including dedicated sample preparation, imaging sequence, data analysis and extraction of the particle concentration in liquid suspension from the number of all particles counted by imaging within a well-defined deposition spot.