# Solid-State Foaming Process Optimization for the Production of Shape Memory Polymer Composite Foam
## 3 Results and Discussion
### Foaming Ratio and Density  
The foaming ratio is defined as the ratio between the foam height and the initial tablet height. Both heights were measured using a digital caliper to ensure accuracy. The density was calculated using the formula below:  
\[\rho=\frac{m}{V} \tag{4}\]  
where \(\rho\) is the density of the foam, \(m\) is the mass of the foamed sample, and \(V\) is the measured volume of the foamed sample. Additionally, the results of pycnometric test are shown in Table 2 above. Prior to designing a Taguchi plan and selecting the foaming temperature levels, three samples were prepared from every set of experiments to determine the best parameters required in order to obtain the highest foaming ratio and lowest foam density. The average foaming ratio and density were calculated using Excel software for each experiment. The results were later analyzed using Minitab software. The samples' foaming ratios and densities can be found in Table 3 below. An analysis of the data showed that regardless of the parameters, a high foaming ratio resulted in a low density. This inverse relationship between foaming ratio and density is logical, because a higher foaming ratio in a sample means it has better foamability, resulting in greater pore formation and ultimately an increased volume of the foamed sample, thus lowering its density. The more nanoparticles introduced into the polymer matrix, the higher the foaming ratio. This results in a lower foam density. Therefore, the addition of NP% had a positive impact on the foamability of the samples. The CC polymer had better  
Figure 13: Stress–strain curves of the pure polymers and their composites. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Run \#** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** \\ \hline Average foaming ratio & 5.43 & 5.54 & 3.18 & 3.96 & 6.21 & 5.79 & 2.56 & 2.9  
foaming potential, as it had a much higher foam ratio and a much lower foam density when compared to the JSD polymer. Moreover, as more packing pressure was applied while making the tablets, a higher foaming ratio was obtained with a lower foam density. This trend is also noticeable regarding holding time, foaming temperature, and foaming time (see Figures 14 and 15). All of the parameters exhibited higher foaming ratios and lower foaming densities at their higher levels. The process parameters were expected to have the same effect on the foaming ratio and density, as increasing foaming ratios lead to a decrease in density. This is valid unless NPs are added. If the polymer contains NPs, the foaming ratio is improved, but the density does not necessarily decrease just because the NP density increases the composite density. The polymer type and packing pressure were the most influential factors for both the density and foam ratio in the samples. This indicates that these properties depend on the material being used, as well as how much that material has been compressed. More  
Figure 14: Effect of all of the parameters on the foam density. Figure 15: Effect of all of the parameters on the foaming ratio. pressure causes the powder to be more compacted and connected, thus resulting in better heat transfer within the structure itself. The NP% showed a significant impact (10%) on the foam density, as well as on the observed foaming ratio, when added to CC. It was expected that any increment in NP% would improve the heat transfer within the CC polymer matrix and thus give a higher foam ratio and a lower density. However, the same significance level was not obtained when NPs were added to JSD. The CC polymer showed very high ratios of 5.95 when NPs were added as compared to 5.44 at 0% of NPs (see Table 2). On the contrary, the JSD showed lower ratios of 2.75 as compared to 3.54 at 0% of NPs. This result is not consistent with the expected outcome, as the addition of NPs is supposed to improve formality. A careful investigation of this phenomenon suggested that the foaming temperature working range was dependent on polymer type.