Ferydon Babaei-Taleshi Not sure I fully understand your question but the mode will invariably be smaller than the average if a few large particles are present. One example. Imagine a company with 50 workers. 49 of them earn $50000 per year and the President ‘earns’ $1 million. The mode (most common value) will be $50000 but the average will be ((49*50000)+ 1000000)/50 or 3450000/50 or $69000 - way higher than the mode.

Thanks Prof.Rawle.

But I see that for metal nanoparticles, especially metal nanoparticles with corners and ends, the electric fields outside the nanoparticle are stronger, and to calculate the volume of the electromagnetic mode, more energy is located outside the nanoparticle, and the integral must be carried out far away from the nanoparticle. considered. This causes the volume of the model to be calculated to be greater than the volume of the nanoparticle itself.

Ferydon Babaei-Taleshi I still don't really understand your question. However, if we look at nano or colloidal particles in suspension then their innate charge leads to a strongly absorbed counter ions on the surface and these counter ions lead to a decrease in charge as the distance increases from the surface to the fluid bulk ions. The charge measured at the slipping plane is known as the zeta potential. Thus, the effective size in the way that the particle interacts with its environment is larger than the core particle itself. This is easily seen where if the apparent size of a metal colloid is measured by DLS, it is larger than that measured by electron microscopy (EM) as the latter only responds to the electron-rich part of the system i.e. the metal. The protective layer and ions are invisible to the EM but the particle's properties in suspension are those of the core plus the protective ions which is larger.

Using DLS and EM together can provide a more comprehensive understanding of the physicochemical properties of nanoparticles or colloids. DLS provides information on the dynamic behavior of particles in solution, while EM provides a direct image of the core structure and morphology of the particles. Understanding the differences between these measurement techniques can help to correctly interpret the behavior and properties of nanoparticles or colloids under different environmental conditions.