## 2 Materials and Methods
### Controlling the Particle Size Distribution  
Filler particle size was controlled using a wet grinding process by dispersing the calcium carbonate feed in demineralized water at a solids content of 25 \(w\)/\(w\)%. Chemical-free grinding was applied using an agitator ball mill (Dyno(r)-Mill KDL-Pilot from Willy A. Bachofen AG Maschinenfabrik, 4132 Muttenz, Switzerland) adopting zirconium dioxide grinding beads of 0.7-1.4 mm diameter. Grinding was pursued to different levels of particle fineness. The ground suspensions were subsequently spray-dried in a \"GEA Niro MOBIE MINORT(tm)\" nozzle spray dryer (GEA Group, Peter-Muller-Strasse 12, 40,468 Dusseldorf, Germany) exposed to an atomization temperature of 200 \({}^{\circ}\)C at 3 bar, and expelled eventually at 90 \({}^{\circ}\)C.  
Specific surface area (SSA) was determined using the gas adsorption BET-Method recording the adsorption cycle of nitrogen as a function of applied partial pressure (ASAP 2460 Surface Area and Porosity Analyzer, Micromeritics(r), 4356 Communications Drive, Norcross, GA 30093-2901, USA) [13]. The particle size distribution of the derived filler was determined in suspension using time-average laser light scattering (Malvern Instruments Mastersizer 3000, Malvern Panalytical Ltd., Enigma Business Park, Grovewood Road, Malvern WR14 1 XZ, United Kingdom) recording the particulate scattering volume adopting the Fraunhofer particle scattering model. To provide the necessary colloidal stability, and hence the required particle-particle separation, the suspension was further diluted with demineralized water and the addition of approximately 500 ppm of polyacrylate dispersing agent. The dispersant was used only for particle size determination, and that filler used in the polyamide 12 composite samples was maintained dispersant-free. To be able to combine the beneficial effect of both the marked increase in the melting rate, caused by the coarse fraction, i.e., thermal conductivity and capacity-related, as well as the stabilizing of the melt flow by the sub-micrometer fraction, two functional fillers were produced. Table 2 shows an overview of the resulting volume-based 50 \(v\)/\(v\)% less than (median) particle size \(d_{v50}\) and specific surface area properties of the processed functional filler particle after the drying step. As suggested in the previous publication [1], the greatest influence on the melting properties of a final compound was achieved by an implementation of approx. 10 to 20 m\({}^{2}\) per 100 g polyamide 12 of a coarse filler fraction of approximately 5 \(\upmu\)m in \(d_{v50}\) \begin{table}
\begin{tabular}{c c c} \hline \hline
**Omyacarb 10-AV** & **PA2200** \\ \hline Producer/supplier & Omya International & EOS e-Manufacturing \\ Volume-based median Particle size, \(d_{v50}\) & 9 \(\upmu\)m & 60 \(\upmu\)m \\ Particle shape & irregular & spherical \\ Approx. thermal Conductivity at 298 K & 1.3 Wm\({}^{-1}\) K\({}^{-1}\) & 0.2 Wm\({}^{-1}\) K\({}^{-1}\) \\ Approx. specific heat & 0.8 kJkg\({}^{-1}\) K\({}^{-1}\) & 1.2 kJkg\({}^{-1}\) K\({}^{-1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material specification. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Filler** & \(d_{v10}\)/\(\upmu\)m & \(d_{v50}\)/\(\upmu\)m & \(d_{v90}\)/\(\upmu\)m & **Specific Surface Area/m\({}^{2}\)g\({}^{-1}\)** \\ \hline A & 0.99 & 6.34 & 18.9 & 1.9 \\ B & 0.24 & 0.56 & 1.16 & 23.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Resulting filler particle data after drying step. An increased amount of sub-micrometer filler particles should result in an increased tendency for nucleation without having a significant influence on the melt flow. The two functional fillers of different particle sizes were combined in specific ratios to optimize the precise thermal response parameters. Table 3 gives an overview of all tested ratios, as well as the resulting carbonate surface. Figure 1 shows the individual particle size distribution of each of the final combined functional fillers.