## 3 Results and Discussion
### Flammability Test
\begin{table}
\begin{tabular}{c c c c c} \hline
**Sample Series** & **R** & **R-2L** & **R-HY** & **R-2T** \\ \hline Material & Radel R & Radel R double layer & Ceramer-coated Radel R & Radel R \\ \# of samples & 4 & 3 & 3 & 4 \\ dimensions (mm) & 300 \(\times\) 64 \(\times\) 6 & 300 \(\times\) 64 \(\times\) 12 & 300 \(\times\) 64 \(\times\) 6 * & 300 \(\times\) 64 \(\times\) 6 \\ \multicolumn{4}{c}{flame time (s)} & 12 & 12 & 24 \\ smokes length (mm) & 163 & 70 & 208 & 225 \\ damage length (mm) & 11 & 17 & 42 & 26 \\ char length (mm) & 4.5 & 8.4 & 4.6 & 11.2 \\ char width (mm) & 24.4 & 30.0 & 21.5 & 15.1 \\ after flame time (s) & 1.1 & 1.4 & 1.1 & 0.9 \\ after glow time (s) & no glow & no glow & no glow & no glow \\ material spread & N & N & Y & N \\ \hline \end{tabular}  
* The thin thickness of the coating is not taken into account. R, as-received Radel R; R-2L, double-layered Radel R; R-HY, Ceramer-coated Radel R; R-2T, Radel R double duration test.  
\end{table} 
Table 1: Flammability test: main characteristics of samples classes and experimental setup (upper box), and experimental results (lower box). The measured smoke lengths indicate that only R-2L test series satisfied the abovementioned condition of damaging propagation limited to one half of sample height (150 mm) for the scheduled time of flame exposure (12 s). The correspondent results obtained by analyzing the base PSU in shorter and longer tests allow us to gain insights about the damage evolution, in order to estimate an optimal thickness and envisage the material performance for prolonged flame exposures. Experimental data of smoke length measured at four/two flame-times for Radel R/R-2L specimens are reported in Figure 4, where the curves estimating the effective behavior of single and double-layered material are obtained by simple physical modeling. A generic power law regression based on a functional behavior as  
\[l(t)\propto t^{\alpha} \tag{1}\]  
leads to an optimal value of the exponent \(\alpha\sim\) 0.52, which meaningfully suggests an effective quadratic dependence between the variables. Such a finding can be easily retrieved by assuming a schematic framework where the damaging progression \(\Delta l(t)\) may be expressed as follows:  
\[\Delta l=\frac{k}{l\cdot S^{2}}\Delta t \tag{2}\]  
Figure 3: Flammability test: pictures of specimen charred area (left) and damaged surface (right) from (**a**) R, (**b**) R-2L, (**c**) R-HY and (**d**) R-2T testing series. where the parameter \(k\) is characteristic of the specific material, having considered that the damage forward is doubly retarded by the surface (\(S\)) heat dissipation and due to the distance from the burning point. By imposing trivial initial conditions, the differential relationship (2) leads to the functional expression:  
\[l(t)=\frac{1}{S}\sqrt{2k\cdot t} \tag{3}\]  
which is in agreement with the above considerations and is used to fit the experimental data, giving an optimal value for the coefficient \(k\sim\) 1.54 \(\times\) 10\({}^{-1}\)0 m\({}^{6}\)/s. In such a framework, it can be thus established that a slab specimen of the analyzed PSU material should fulfill the damaging propagation constraint with a thickness around 6.5 mm, while the double-layered component is believed to provide flame retardant effective behavior up and beyond 40 s of fire exposition, as far as the adopted setup is concerned. To summarize, Radel R material showed to be non-combustible, well resistant to flame exposure and to keep visible transparency. As expected, the thicker the material slab, the lower the flame damaging, whereas a sharper degradation occurs for prolonged exposures. Thus, this kind of thermoplastic material provides an acceptable performance within the scenario of polymeric flame-retardant solutions. On the other hand, the hybrid coating seems to worsen the Radel properties, with particles emission during the melting, thus resulting in a non-admissible material for anti-flame applications.