## 4 Results and Discussion
### General Results  
In this section, the results of a typical time-resolved measurement of the dust particle size and dust density using the method proposed in this work are discussed. Using the developed optimization procedure explained in Section 3.3, the fitted dust particle radius \(a\) and the dust density \(n_{\mathrm{d}}\) are shown in Figure 5. After igniting the plasma at \(t=0\,\mathrm{s}\), the dust particles will be generated through the polymerization of precursor species. The lower detection limit of the method is determined by the sensitivity of the extinction measurement; at early times, the dust particle size and/or density is too small to cause sufficient extinction of the laser light (i.e., \(\hat{T}\approx 1\)). Therefore, the fitting procedure is started when \(\hat{T}\leq 0.99\), i.e., from \(t=34\,\mathrm{s}\) onward, resulting in a detection limit for particles with a radius of \(a_{\mathrm{min}}=59\,\mathrm{nm}\). As soon as the particles can generate enough extinction, a linear increase in the particle radius and a decrease in the dust density are observed. The growth rate in this linear regime is determined to be \(1.30\,\mathrm{nm}/\mathrm{s}\), which lies in the same range as the experiments performed in C\({}_{2}\)H\({}_{2}\) reported elsewhere [50,73]. Figure 5: General result from the optimization procedure. The dust particle radius \(a\) is shown in panel (**a**) and the dust density \(n_{\mathrm{d}}\) in panel (**b**). The gray-shaded area indicates the time period after discharge ignition during which the transmittance remains similar to a pristine plasma, which inhibits the proper determination of the dust particle size and density. The red lines mark the appearance of the void region, after which the path length \(L\) is no longer constant. A constant value of the electron temperature \(T_{\mathrm{e}}=3\,\mathrm{eV}\) and the negative ion density \(n_{\mathrm{i-}}=4n_{\mathrm{e,initial}}\) are assumed. At around \(t=83\,\)s, the dust density transitions into a sharper decrease. This coincides with the turning point of the transmittance (see panel (b) in Figure 3 and is indicated with the red vertical lines in Figure 5), which signifies the appearance of the void. It should be noted that this implies that with the presence of the void the path length \(L\) (in Equation (11)) is overestimated, which eventually underestimates the quantity \(a^{2}n_{\rm d}\). From this moment on, the interpretation of the dust particle size and the dust density is complicated, since the path length is no longer fixed and since dust particles from two subsequent generations coexist, implying two different dust size distributions [51]. Therefore, the results shown in the following sections will be limited to the first growth cycle, and before the appearance of the void. It is interesting to note that the mean dust charge \(Q_{\rm d}\) also becomes available as soon as the dust particle radius and the dust density have been determined. Using Equations (5) and (10), the total (negative) dust particle charge is shown to become more negative over time, ranging from \(-50\) elementary charges at \(t=34\,\)s to \(-130\) elementary charges at \(t=83\,\)s.  
Several other researchers focused on the growth of dust particles in low-pressure nanodusty plasmas. In order to get a sense of whether the retrieved dust particle size is consistent with literature, an overview of the methods, precursor gases, and operating conditions have been provided in Table 1. The table indicates that under low-pressure conditions dust particles are produced with a typical radius of \(a=100\) nm to \(300\) nm, depending on the pressure, plasma power, and reactor geometry. Even though this range of dust particle sizes matches the retrieved particle size from the fitting procedure, a direct comparison is difficult. Therefore, in Appendix A.1, the method has been applied to MCRS and extinction data from previous work [31]. which could be directly compared to SEM images of the dust particles collected during the same measurement.