Critical cluster size cannot in practice be determined by slope analysis in atmospherically relevant applications

• We go through the assumptions used for deriving the first nucleation theorem.
• We simulate cluster formation in situations where these assumptions are not valid.
• We assess the effect of data analysis using simulated nucleation event data.
• We show that the nucleation theorem is not valid in realistic conditions.

The first nucleation theorem is the most widely used method to assess atmospheric new-particle formation mechanisms from particle formation rate measurements. The theorem states that the slope (∂logJ)/(∂logC) of the nucleation rate J versus the concentration C of a nucleating compound gives the number of molecules of that species in the critical cluster. In principle, the derivation of the theorem is solid, but it contains very restrictive assumptions, the validity of which is questionable in realistic situations. It applies only for systems where clusters grow by addition of single molecules, and there are no external losses. In addition, application of the theorem to experimental data requires that the nucleation rate can be determined from particle concentration observations. This work presents simulation results on particle formation rates in atmospherically relevant conditions. We show that the slope of the nucleation rate in realistic conditions differs from that in an ideal situation. The slope analysis can easily lead to erroneous conclusions on the critical cluster size, and should therefore not be used to interpret experimental data.