Polylactide (PLA) (Ingeo biopolymer 2003D, 4.3 mol% D-lactide content, specific gravity: 1.24, tensile strength: 53 MPa, melting temperature: 151˚C) was purchased from NatureWorks, USA. Azodicarbonamide (ADA, CELOGEN 754A, density: 1.68 g/cm³ at 25˚C, decomposition temperature: 164˚C - 180˚C) was purchased from CelChem, USA.

First, PLA was dried under vacuum for 12 h at 50˚C using a Shel Lab oven, model 1445. Then, it was mixed for 3 min with ADA added at different weight concentrations (see Table 1), using a Hamilton Beach Single-Serve Blender (model 51101BZ). The PLA/ADA mixture was then placed into the mold cavity (0.3 cm × 6 cm × 6 cm) placed between the plates of an automatic compression press (Carver, Model: Auto series 3893). For all of the samples, the compressing pressure was maintained constant at 12 MPa and the compression (foaming) time was varied from 5 to 15 min, depending on the experiment, as shown in Table 2. Foamed PLA samples were then obtained by reducing the temperature of the mold to the mold opening temperature (values are shown in Table 1). Finally, the mold was opened, and the foamed sample was cooled down to room temperature. Scheme 1 shows a sketch of the different steps of the foaming process.

PLA foam samples were first frozen in liquid nitrogen to ensure a brittle fracture [19]. Magnified pictures of the fractured surfaces were then acquired using a stereomicroscope (Model: SZ-PT 126x) and the average cell size was obtained using the image processing, Image J, software (at least three measurements per cell were done and their average value is reported). The final average cell size was calculated from the results of at least three different samples for each run.

The central composite design (CCD) technique was used in this work to design the three levels (low-level: −1, mid-level: 0, and high-level: +1) of the three independent processing parameters shown in Table 1, which are the foaming time under compression, X₁ (min), the mold opening temperature, X₂ (˚C), and the ADA blowing agent weight concentration, X₃ (wt%). The mold opening temperature is the temperature at which the mold is opened following a rapid cooling upon the end of the foaming time.

As reported in literature, the decomposition temperature of ADA is between 165˚C and 180˚C [20], and the melting temperature of PLA is 150˚C [21]. Using ADA as a foaming agent, Luo, Zhang, Qi, Lu, Hu and Jiang [21] reported that the optimum foaming temperature for PLA is 180˚C during a foaming time under compression of 10 min. Based on this study, the foaming temperature was maintained constant at 180˚C and the foaming time X₁ (min) was considered as an independent parameter for cell size optimization. Its minimum and maximum limits were taken at equal intervals from the foaming time of 10 min used by the above authors (X_1min = 5 min, X_1max = 15 min).

To get an adequate foam, the mold must be cooled quickly after PLA foaming to increase the PLA viscosity and consequently avoid cell collapse. Mold opening should be performed at a temperature that is between the glass transition temperature (T_g) and the melting temperature of PLA, which are 58˚C and 151˚C, respectively [21]. It was found that when the mold opening temperature was higher than 120˚C, bubbles were ruptured due to the low PLA viscosity; on the other hand, when the temperature was lower than 80˚C, not enough bubbles were formed. Based on these observations, the mold opening temperature was set between X_2min = 80˚C and X_2max = 120˚C for cell optimization.

To study the effect of the ADA blowing agent concentration on the average cell size, preliminary tests were performed at 180˚C to determine the minimum and maximum ADA concentrations needed to obtain a foam with an open-cell structure. For a mold opening temperature of 100˚C and a foaming time of 10 min, the ADA concentration was slowly increased until the formation of an open cell structure, which was obtained at 4.2 wt% ADA. On the other hand, foam collapse was observed for ADA weigh concentrations higher than 7.7 wt%. Based on these results, the ADA concentration was set between 4.2 wt% and 7.7 wt%.

Knowing the minimum and maximum values of the three independent parameters X₁, X₂ and X₃, the calculation of their corresponding low-level (−1), mid-level (0), and high-level (+1) values is done using the CCD technique (Figure 1) and the corresponding values are shown in Table 1. As an example, the following steps show how to find the corresponding values for the foaming time, X₁ (min): 1) First, the minimum and maximum values of X₁ corresponding to −α and +α are respectively 5 min and 15 min, as mentioned above in this section; 2) the mid-level (0), which is the center between −α and +α, is then equal to (5 + 15)/2 = 10 min; 3) Equation (2) is then used to get the low and high level settings of X₁, which are respectively:

{ Low-level ( − 1 ) = ( ( 1.682 − 1 ) × 15   min   + ( 1.682 + 1 ) × 5   min ) / ( 2 × 1.682 ) = 7.03   min High-level ( + 1 ) = ( ( 1.682 − 1 ) × 5   min   + ( 1.682 + 1 ) × 15   min ) / ( 2 × 1.682 ) = 12.97   min

The low, mid, and high levels for X₂ and X₃ are calculated in the same manner and their corresponding values are shown in Table 1.

Figures 2(a)-(c) show SEM micrographs corresponding to foamed samples respectively obtained from the runs 11, 1 and 6, presented below in Table 2. Their corresponding foaming time and blowing agent concentration were kept constant at 10 min and 5.95 wt% and their mold opening temperature was varied [80˚C (level: −α) (Figure 2(a)), 100˚C (level: 0) (Figure 2(b)), and 120˚C (level: +α) (Figure 2(c))]. As shown, closed cell structure was obtained under a mold opening temperature of 80˚C and larger cells were obtained with increasing the mold opening temperature, leading to an open cell structure at 120˚C. The corresponding results are presented in Table 2 and Figure 3(a). An increase of the mold opening temperature from 80˚C to 120˚C is accompanied by a respective increase in the average cell size from 136 µm to 326 µm. Because of PLA matrix viscosity decrease and gas diffusion increase inside the PLA matrix with increasing the temperature, this leads to an increase in the formation and growth

of bubbles [21].

Keeping the foaming time and mold opening temperature constant at 10 min and 100˚C, respectively, the ADA weight concentration was varied from 4.2 wt% to 7.7 wt% and the corresponding results are presented in Table 2 (runs 1, 2, and 14) and Figure 3(b). The results show that an increase in ADA concentration is accompanied by an increase in cell size due to the higher gas concentration/amount generated inside the PLA matrix during ADA degradation, [21].

The effect of the foaming time on the average cell size was studied under a constant mold opening temperature (T = 100˚C) and ADA concentration (5.95 wt%) (i.e., X₂ and X₃ = 0: runs 8, 9, 7). As shown in Figure 3(c), an increase of the foaming time from 5 min to 15 min leads to a respective increase of the average cell size from 209 µm to 294 µm. This is because there is enough time for the generated smaller bubbles to expand and in many cases meet each other due to the high pressure gases [22].

The Minitab 17.0 software was used to randomize the 20 experimental runs shown in Table 2, and the polynomial model used by the software for the calculation of the cells average size, Y, as a function of the three significant factors X₁, X₂, and X₃, and their combinations, is given by Equation (3):

Y = a + b × X 1 + c × X 2 + d × X 3 + e × ( X 1 × X 1 ) + f × ( X 2 × X 2 )     + g × ( X 3 × X 3 ) + h × ( X 1 × X 2 ) + i × ( X 1 × X 3 ) + j × ( X 2 × X 3 ) (3)

where the parameters a to j are adimensional fitting parameters.

The coefficient of variation (CV) shown in Table 2, which is the ratio between the standard deviation and the average cell size, gives an indication about the level of dispersion around the average cell size. Lower CV means a lower level of dispersion around the average cell size. Distributions with a coefficient of variation (CV) less than 1 are considered to be low-variance distributions, whereas those with a CV higher than 1.0 are considered to be high-variance distributions [23].

The analysis of variance (ANOVA) was used to find the best dimensional fitting parameters a to j of Equation (2), based on the experimental data of Table 2 obtained for the 20 experimental runs. The final form of this equation with the calculated fitting parameters is as follows (Equation (4)):

Y = − 2352 + 72.2 × X 1 + 26.1 × X 2 + 189 × X 3 − 0.006 × ( X 1 × X 1 )     − 0.0515 × ( X 2 × X 2 ) + 1.26 × ( X 3 × X 3 ) − 0.375 × ( X 1 × X 2 )     − 4.13 × ( X 1 × X 3 ) − 1.252 × ( X 2 × X 3 ) (4)

The statistical significance of the fitting parameters of the above regression model used to estimate the average cell size was based on their probability values (P-values) presented in Table 3. These P-values indicate if the regression model

fails to sufficiently describe the functional relationship between the average cell size and the three studied parameters (foaming time, X₁, mold opening temperature, X₂, and ADA blowing agent concentration, X₃). The fitting parameters are considered significant if their corresponding P-values are less than 0.05, and not significant if their P-values are greater than 0.05 [24]. As shown in Table 3, the P-values corresponding to the linear interaction between the cell size (Y) and the foaming process parameters X₁, X₂, and X₃ were all significant(their corresponding p-values are less than 0.05). However, their corresponding square and 2-way interactions were insignificant (corresponding P-values where higher than 0.05). Finally, the P-value for the lack of fit was 0.273 (i.e., higher than 0.05), which means that there is no lack of fit and the regression model sufficiently describes the functional relationship between the average cell size (Y) and the independent processing parameters X₁, X₂, and X₃.

The regression analysis of the 20 runs presented in Table 2 also provides various residual plots and two of them are shown in Figure 4 (the normal probability plot, Figure 4(a), and the residuals versus associated fitted values, Figure 4(b)). The normal probability plot of the residuals displays the residuals versus their expected values when the distribution is normal. Ideally, this plot should approximately follow a diagonal straight line (fitted values). Figure 4(a) clearly shows a normal distribution of the residuals. The difference between the observed values (round symbols) and their corresponding diagonal fitted values (continuous line), is relatively small. On the other hand, the residuals should ideally fall randomly around the center (zero) line, which is the case, as shown in Figure 4(b). This indicates a high degree of correlation between the observed and predicted residual values.

Figure 5 shows the optimization curves for the average cell size maximization (i.e., the maximization of the response Y) obtained using the “response optimizer” in the Minitab software. To do this, the three independent parameters X₁, X₂ and X₃ were respectively varied from 5 to15 min (Figure 5(a)), 80˚C to 120˚C (Figure 5(b)), and 4.2 to 7.7 wt% (Figure 5(c)). As shown, the maximum average cell size of 392.4 μm was obtained at a foaming time of 5 min, and a mold opening temperature of 120˚C.

Figure 6 presents the contour plots showing the evolution of the average cell size (µm) with the variation of two of the three independent processing parameters, while maintaining the third one constant. Figure 6(a) shows that, for a constant ADA weight concentration of 5.95 wt%, the average cell size increases from 125 µm to about 375 µm with increasing the foaming time from 5 min to 15 min (X-axis) and the mold opening temperature from 80˚C to 120˚C (Y-axis). So, the average cell size can be tailored by varying one or both of the two processing parameters, mold opening temperature or the foaming time. For example, a narrow average cell size ranging between 275 and 300 µm can be obtained under a foaming time of 8 min and a mold opening time ranging between 106˚C and 112˚C, or a mold opening temperature of 109˚C and a foaming time ranging between 6 and 11 min. Figure 6(b) shows that, for a foaming time maintained constant at 10 min, the average cell size increases from 100 µm to about 400 µm with increasing the mold opening temperature from 80˚C to 120˚C (X-axis) and the ADA weight concentration from 4.2 wt% to 7.7 wt% (Y-axis). So, a narrow average cell size ranging between 275 and 300 µm can be obtained using 7.0 wt% ADA and a mold opening time ranging between 91 and

101˚C. Finally, Figure 6(c) shows that, at a constant mold opening temperature of 100˚C, the average cell size varied from 150 µm to about 375 µm with increasing the foaming time from 5 min to 15 min (X-axis) and ADA concentration from 4.2 wt% to 7.7 wt% (Y-axis). The same narrow average cell size ranging between 275 and 300 µm can be obtained using 6.8 wt% ADA and a foaming time between 7.2 min and 11.6 min.