On the diffusion-controlled rate coefficient for chemical reactions and collisions of nano-particles

•Collisions of chemical reactants and nanoparticles are very important.•Smoluchowski's collision rate coefficient is questioned.•An equation for estimating the collision rate coefficient kc was proposed.

In this work, the validity of the Smoluchowski collision rate coefficient (SCRC) to describe random collisions of nano-particles and molecules is questioned and an alternative equation for this purpose is proposed. This latter is based on geometric considerations and basic concepts of diffusion. The proposed equation agrees, at least qualitatively, with experimental data of the coagulation rate coefficient reported in the literature for particle radii <50 where the SCRC equation deviates by up to three orders of magnitude. To quantitatively validate the proposed equation more experimental data is needed. Implications of these findings on chemical kinetics are briefly discussed.

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