Machine learning assisted optimization of blending process of polyphenylene sulfide with elastomer using high speed twin screw extruder

Random forest regression was applied to optimize the melt-blending process of polyphenylene sulfide (PPS) with poly(ethylene-glycidyl methacrylate-methyl acrylate) (E-GMA-MA) elastomer to improve the Charpy impact strength. A training dataset was constructed using four elastomers with different GMA and MA contents by varying the elastomer content up to 20 wt% and the screw rotation speed of the extruder up to 5000 rpm at a fixed barrel temperature of 300 °C. Besides the controlled parameters, the following measured parameters were incorporated into the descriptors for the regression: motor torque, polymer pressure, and polymer temperatures monitored by infrared-ray thermometers installed at four positions (T1 to T4) as well as the melt viscosity and elastomer particle diameter of the product. The regression without prior knowledge revealed that the polymer temperature T1 just after the first kneading block is an important parameter next to the elastomer content. High impact strength required high elastomer content and T1 below 320 °C. The polymer temperature T1 was much higher than the barrel temperature and increased with the screw speed due to the heat of shear. The overheating caused thermal degradation, leading to a decrease in the melt viscosity and an increase in the particle diameter at high screw speed. We thus reduced the barrel temperature to keep T1 around 310 °C. This increased the impact strength from 58.6 kJ m−2 as the maximum in the training dataset to 65.3 and 69.0 kJ m−2 at elastomer contents of 20 and 30 wt%, respectively.

2 S1. Changes in the measured parameters Figure S1. Motor torque current as a function of the elastomer type, elastomer content, and screw rotation speed.

S2. Melt viscosity as a function of the shear rate
Melt viscosity of polymer is a function of the shear rate. Figure S9 shows the melt viscosity of PPS measured with a plunger-type capillary rheometer (Toyo Seiki, Capillograph 1D; inner diameter and length of the capillary were 1 and 40 mm, respectively) at various shear rates and 300 ºC. The melt viscosity of PPS was a decreasing function of the shear rate, as is generally observed for other polymers. The change in the melt viscosity (Pa s) with the shear rate (s -1 ) can be expressed by the power function: where the exponent is a constant and was 0.177 for PPS. For quantitative discussion, therefore, the melt viscosity should be compared at a constant shear rate. In the present study, in contrast, the melt viscosity was measured at a constant pressure of 4.9 MPa with a constant-force-type capillary rheometer (Shimadzu, CFT-500D). Thus, the viscosity change presented in this paper is an apparent one. We can estimate, however, the real viscosity change from the apparent one and can expect that the real viscosity change is qualitatively similar to the apparent one enough to discuss the increase and decrease in the molecular weight, as explained in the following.

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In the measurement with a capillary rheometer, the melt viscosity (Pa s) is obtained by , where (Pa) is the pressure, (m) and (m) are the inner diameter and length of the capillary, (s -1 ) is the shear rate, and (m 3 s -1 ) is the volume flow rate. Equation (S2) shows that the melt viscosity is inversely proportional to the shear rate , when the pressure is fixed.
Let us suppose that the melt viscosity measured at a constant shear rate varies from to ′ , while the apparent melt viscosity measured at a constant pressure varies from to ′ , as illustrated in Figure S10. Assuming that the shear rate dependence of the melt viscosity ∝ is negligibly affected by the viscosity change (otherwise the comparison at a constant shear rate is also meaningless), the apparent shear rate ′ is related to the corresponding shear rate ′ by Since the melt viscosity is inversely proportional to the shear rate at a constant pressure, Combining these equations, we can estimate the real change in the melt viscosity ⁄ from the apparent one ⁄ by ⁄ ⁄ (S5) Figure S10. Relationship between the apparent melt viscosity change and the real one.
In Figure S11, the real melt viscosity calculated with Equation (S5) using = 0.177 and = 130.2 (Pa s) is compared with the apparent one. The real melt viscosity shows qualitatively similar behavior to the apparent one, although the magnitude of the change is overestimated in the apparent melt viscosity. In Section 3.4, we reduced the barrel temperature to avoid the degradation of polymer so that the polymer temperature T1 was within 310 ± 5 °C at each screw rotation speed. The change in the barrel temperature and the resultant change in the polymer temperature T1 are plotted in Figure S12 as functions of the screw rotation speed. Figure S12. Change in the polymer temperature T1 (: red → blue) upon the reduction in the barrel temperature (: red → blue) at various screw rotation speeds for the PPS/BF-7L blend at the elastomer content of 20 wt%.