Derivation of Particle Number Concentration from the Size Distribution: Theory and Applications.

Area of Science:

• Nanotechnology
• Materials Science
• Analytical Chemistry

Background:

• Particle number concentration (PNC) is crucial in nanotechnology.
• PNC is often derived from mass concentration and per-particle mass.
• Per-particle mass calculation typically uses particle diameter and density.

Purpose of the Study:

• To evaluate the accuracy of different methods for calculating PNC from particle size distributions.
• To identify and quantify errors associated with using arithmetic mean diameter (AMD) for volume calculation.
• To propose a more accurate method for PNC determination.

Main Methods:

• Theoretical analysis of particle size distribution statistics.
• Comparison of PNC calculations using arithmetic mean volume (AMV) versus arithmetic mean diameter (AMD).
• Validation using experimental data from gold nanoparticles and polystyrene standards, employing techniques like spICP-MS and SEM.

Main Results:

• Using AMD for volume calculation leads to significant PNC overestimation, increasing with coefficient of variation (CV).
• Errors can reach 12% at CV=0.2 for normal distributions and exceed 35% for CV > 0.3.
• AMV provides accurate PNC, showing ±1.1% consistency with direct spICP-MS measurements.

Conclusions:

• Arithmetic mean volume (AMV) is the correct parameter for deriving accurate PNC from size distributions.
• Arithmetic mean diameter (AMD)-based calculations introduce substantial errors, particularly for polydisperse nanoparticles.
• Accurate PNC determination is vital for applications in nanomedicine, environmental monitoring, and food safety.