Gas-to-particle formation Homogeneous nucleation

Interestingly, it has been found that the formation of SOA is accelerated in the presence of SO2 and sulfuric acid (Jang et al. 2002, Edney et al. 2005, Surrat et al. 2007). The first step in atmospheric SO2 oxidation is OH addition (Chapter 5.5.2.1) and this radical can react with alkoxy radicals (RO) to form sulfonic acid and further with organic peroxo radicals to form dialkyl sulfates  

The main concern of the classical homogeneous nucleation theory has been a thermodynamic description of the initial stage of nucleation from embryo to nucleus with a little larger size over the critical one (Seinfeld 1986, Pruppacher and Klett 1997, Seinfeld and Pandis 1998, Kulmala et al. 2000). The change of the free enthalpy of the cluster is at first positive because the decrease of entropy is initially larger (regular structure formation) than the decrease in enthalpy  

Applying Eq. (4.226) as a special case for T,n = constant (see also Eq. 4.75 concerning volume-pressure change)  

Now transferring from infinitesimal to difference expressions, we integrate dpip (= dhip) and replace plp°° by the saturation term (see Kelvin equation)  

Finally, using the standard expression for the surface (of the cluster) and replacing ds, we get (V is the molar volume of the cluster phase)  

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