# Recycled PP for 3D Printing: Material and Processing Optimization through Design of Experiment
## 2 Materials and Methods
### Characterization Methods  
Differential scanning calorimetry (DSC) analyses were performed using a Q20, TA Instruments (New Castle, DE, USA) apparatus. The samples were placed in aluminum crucibles and subjected to the following thermal treatment: (i) a first heating ramp from \(-50\) to \(300\)\({}^{\circ}\)C, (ii) a cooling ramp from \(300\) to \(-50\)\({}^{\circ}\)C, and (iii) a second heating ramp from \(-50\) to \(300\)\({}^{\circ}\)C. For all the ramps, the heating/cooling rate was maintained at \(10\)\({}^{\circ}\)C/min.  
The rheological behavior of all the investigated materials was investigated using an ARES (TA Instrument, New Castle, DE, USA) strain-controlled rheometer, equipped with a parallel plate geometry (plate diameter = 25 mm, typical gap imposed during the tests = 1 mm). Frequency sweep tests were performed at 230 and 260 \({}^{\circ}\)C, from 100 to 0.1 rad/s and using a strain amplitude of 5% (which preliminary strain sweep tests demonstrated to be in the linear viscoelastic range of the tested materials). The obtained complex viscosity curves were then fitted using the following models to evaluate the yield stress value of the tested materials:  
\[\eta^{*}=\frac{\eta_{0}^{*}}{1+\lambda\omega^{n}} \tag{1}\]  
\[\eta^{*}=\frac{\eta_{0}^{*}}{\left[1+\lambda\omega^{2}\right]^{\frac{n-1}{2}}} \tag{2}\]  
\[\eta^{*}=\frac{\eta_{0}^{*}}{\left[1+\lambda\omega^{2}\right]^{\frac{n-1}{2}}} \tag{3}\]  
\[\eta^{*}=\frac{\sigma_{y}}{\omega}+\frac{\eta_{0}^{*}}{1+\lambda\omega^{n}} \tag{4}\]  
\[\eta^{*}=\frac{\sigma_{y}}{\omega}+\frac{\eta_{0}^{*}}{\left[1+\lambda\omega^{ 2}\right]^{\frac{n-1}{2}}} \tag{5}\]  
\[\eta^{*}=\frac{\sigma_{y}}{\omega}+\frac{k_{1}n\left(\lambda\omega\right)^{n} }{\left[1+\left(\lambda\omega\right)^{n}\right]^{2}} \tag{6}\]  
where \(\eta^{*}\) is the complex viscosity, \(\omega\) is the frequency, \(\eta_{0}^{*}\) is the zero-shear complex viscosity, \(\lambda\) is the characteristic relaxation time, \(n\) is the power-law exponent, \(a\) is a corrective factor, \(\sigma_{y}\) is the yield stress, and \(k_{1}\) is the shear stress at infinite shear rate. The main difference between the selected models is the presence or not of a term accounting for the occurrence of an apparent yield stress behavior at low frequencies. In particular, the models that were described by Equations (1)-(3), are able to predict the rheological behavior of linear viscoelastic fluids (presenting either a Newtonian or a non-Newtonian behavior) which do not possess yield stress. At variance, models that are presented in Equations (4)-(6) contain the term \(\sigma_{y}/\omega\) accounting for yield stress. Apart from the presence of this term, the selected models differ from some details allowing a better fitting of the shear thinning region or of the so-called transition zone of the complex viscosity curve, registered at intermediate frequencies (between the low frequency region and the shear thinning zone). All the models that are presented in Equations (1)-(6) were used to fit the experimental data; however, for each studied formulation the model allowing minimizing the cost function was selected. To this purpose, Matlab software was used as a computational resource.  
The morphology of the produced filaments (in terms of both external surfaces and internal microstructure) was evaluated using a scanning electron microscope (SEM) EVO 15 by Zeiss (beam voltage: 20 kV working distance: 8.5 mm). To evaluate the microstructure of the filaments, the samples were fractured in liquid nitrogen and the obtained fracture surfaces were covered with a sputtered gold layer.  
The mechanical properties of the 3D printed specimens were evaluated through tensile tests, using an Instron(r) 5966 (Norwood, MA, USA) equipped with 2 kN load cell. Thecrosshead speed was set at 1 mm/min until 0.25% of deformation was reached, and then at 10 mm /min. A total of five specimens for each formulation were tested.