## 3 Results
### SOA Formation Study  
In Figure 5, the size distribution of particles is shown in terms of the normalized particle number, \(d\)N/\(d\)logDp, and mass, \(d\)M/\(d\)logDp. As depicted in Figure 5a, shortly after the beginning of the Cl reaction (at \(t\) = 2 min), the appearance of a high concentration (in terms of number) of ca. 20-nm particles was observed. At subsequent times, the diameter of the particles increased, being centered at ca. 100 nm at \(t\) = 60 min, while the number of particles decreased. Figure 5b shows that the maximum mass of the first formed particles was centered at a ca. 30 nm diameter, reaching a value of around 10 \(\mu\)g m\({}^{-3}\). As Cl reaction continued, the maximum of the mass increased up to 200 \(\mu\)g m\({}^{-3}\) and was centered at 130 nm. Both graphs indicate that the formation of a big number of small particles took place 2 min after Cl reaction started and this formation was due to a nucleation process. It was followed by the growth of the particles due to coagulation, which caused that the number of particles was reduced at longer times even though the mass kept increasing.  
Figure 5: Evolution of the size of the secondary organic aerosol (SOA) generated in the Cl reaction of T2M2B in terms of the normalized particle number (**a**) and mass (**b**). Reaction starts at \(t\) = 0 min and ends at \(t\) = 60 min.  
The SOA yield, \(Y_{\text{SOA}}\), was determined under different conditions from the slope of the plot of \(M_{\text{SOA}}\) versus \(\Delta\)[T2M2B] (Figure 6). The correction of \(M_{\text{SOA}}\) was done considering the rate coefficient for the loss of particles determined in each experiment (average value: \(k_{\text{loss\,particle}}=4.2\times 10^{-2}\) s\({}^{-1}\)). The rate coefficient for the dark loss of T2M2B was also determined at the beginning of each experiment and was used for correcting its concentration at each reaction time. This rate coefficient averaged \(k_{\text{loss}}=3.4\times 10^{-3}\) s\({}^{-1}\). The results of \(Y_{\text{SOA}}\) are listed in Table 3 together with the conditions used in this research.  
The gas/particle absorption model proposed by [PERSON] [26; 27] can describe the mechanism of SOA formation accordingly to the relationship between \(Y_{\text{SOA}}\) and the maximum value of \(M_{\text{SOA}}\) reached in every experiment [28]:  
\[Y_{\text{SOA}}=M_{\text{SOA}}\sum_{i}^{\text{n}}\frac{\alpha_{i}K_{\text{p},i} }{1+K_{\text{p},i}M_{\text{SOA}}}, \tag{5}\]  
where \(\alpha_{i}\) is the mass-based stoichiometric coefficient and \(K_{\text{p},i}\) is the gas/particle partitioning coefficient of the \(i\) semi-volatile species formed. In this research, data could be fitted to a one-product model (\(i=1\)), as can be seen in Figure 7, yielding \(\alpha=(2.4\pm 0.2)\%\), and \(K_{\text{p}}=(2.7\pm 0.5)\times 10^{-3}\) m\({}^{3}\) mg\({}^{-1}\). These parameters indicate, respectively, that \(Y_{\text{SOA}}\) tends towards 2.4% at very high \(M_{\text{SOA}}\) values and  
Figure 6: Some examples of the plots of SOA mass (\(M_{\text{SOA}}\)) versus \(\Delta\)[T2M2B] used to determine the SOA yield (\(Y_{\text{SOA}}\)).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**[T2M2B]\({}_{0}\)/10\({}^{14}\) molecule cm\({}^{-3}\)** & **[Cl\({}_{2}\)/10\({}^{14}\) molecule cm\({}^{-3}\)** & **M\({}_{\text{SOA}}\)/\(\mu\)g m\({}^{-3}\)** & **Y\({}_{\text{SOA}}\) (\%)** \\ \hline
5.62 & 4.46 & 27.4 & \(0.26\pm 0.01\) \\
6.79 & 2.54 & 52.9 & \(0.27\pm 0.01\) \\
5.99 & 2.67 & 60.9 & \(0.33\pm 0.01\) \\
7.17 & 5.96 & 191 & \(0.68\pm 0.01\) \\
6.31 & 6.93 & 244 & \(0.96\pm 0.01\) \\
7.79 & 9.53 & 441 & \(1.42\pm 0.03\) \\
7.58 & 12.6 & 491 & \(1.49\pm 0.04\) \\
7.39 & 15.0 & 580 & \(1.44\pm 0.02\) \\
6.74 & 17.0 & 764 & \(1.56\pm 0.03\) \\
7.10 & 19.9 & 863 & \(1.65\pm 0.03\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Results of \(Y_{\text{SOA}}\) under different conditions. Errors are \(\pm 2\sigma\).  
that the semi-volatile product that causes the SOA formation is mostly in the vapor phase rather than in the condensed phase.