Advanced quantitative analysis of colloidal solution of metal nanoparticles produced by laser ablation in liquids

Abstract

The diameter of laser synthesized colloidal nanoparticles can be derived from a volume of ablated material and absorbance at surface plasmon resonance wavelength. The origin of such nanoparticles’ diameter is studied in this work. The study is based on Beer-Lambert law where nanoparticle size-distribution and UV-Vis photoabsorbance data are used. Theoretically modeled diameter is verified by independent integral approach proving that simple model derived in our previous work is by most means usable for determination of diameter of laser synthesized nanoparticles in colloidal solution with sizes less than SPR wavelength. Here is also presented the mathematical proof which indicates that in monodisperse limit, under assumption that size-distribution of synthesized nanoparticles can be described by log-normal function, diameter obtained by simple analytical model is in fact mode diameter (most frequent diameter) of size-distribution. Furthermore, it is shown that mode diameter of size-distributions can be obtained from volume average diameter of nanoparticles over experimentally determined diameter distribution as well as from number average diameter of nanoparticles over the same diameter distribution by multiplication of those diameters with shift factors depended only on standard deviation of log-normal distribution. This is verified for size-distributions obtained independently by AFM, TEM and DLS techniques and is proposed to be universal property of log-normal distribution function.