I saw discussion of the relationship between the concentration and temperature or something else, but is there any quantitative evidence better than just discussion.
There is much quantitative evidence in peer-reviewed literature but nothing that provides a universal answer. The reason is that the diurnal change in ambient particle (number) concentration is strongly dependant on local ambient parameters and sources, and both vary significantly. Consider for instance factors like new particle formation from gaseous pre-cursors in the presence of sun-light, or hot vehicle emissions (with a local dependance on diesel vs gasoline engines) in wintertime, or seasonal sources such as the use of domestic fire places. Of course, these are just three examples to illustrate that there is no simple answer to your question.
I was asking what kind of ambient parameters are causing the diurnal change of particle concentration. But you are right, any local emission events will affect the pattern.
I just saw a paper discussing the relationship between the ambient parameters and PM2.5 using 6-year data. "Long-term measurements of Planetary Boundary Layer height and interactions with PM2.5 in Shanghai, China" Atmospheric Pollution Research DOI: 10.1016/j.apr.2019.01.007