Non-Isothermal Crystallisation Kinetics of Polypropylene at High Cooling Rates and Comparison to the Continuous Two-Domain pvT Model

Alms, Jonathan; Hopmann, Christian; Jian, Wang; Hohlweck, Tobias

doi:10.3390/polym12071515

Cited by 8 publications

(8 citation statements)

References 37 publications

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“…The values for T t at much higher cooling rates (600, 3000, 6000, 60 000, and 300 000 °C/min) under atmospheric pressure were obtained by a flash DSC device (Flash DSC 2+, Mettler Toledo, Columbus, Ohio). 42 The temperature changed between 10 and 260 °C. A holding time of 5 min was used after each cooling process.…”

Section: Methodsmentioning

confidence: 99%

“…T t in this work is the crystallization temperature of the semicrystalline polymer PP. The values for T t at much higher cooling rates (600, 3000, 6000, 60 000, and 300 000 °C/min) under atmospheric pressure were obtained by a flash DSC device (Flash DSC 2+, Mettler Toledo, Columbus, Ohio) . The temperature changed between 10 and 260 °C.…”

Section: Methodsmentioning

confidence: 99%

“…Figure a,b shows the curves of DSC and flash DSC measurements. The T t which is the crystallization temperature for semicrystalline polymers can be obtained from the peak points of the DSC curves.…”

Section: Methodsmentioning

confidence: 99%

“…To confirm the extrapolative accuracy, the used data of T t were calculated by a regression equation which is based on the experimental data of T t from the pvT measurements at high pressure but low cooling rates and the differential scanning calorimetry (DSC) tests at atmospheric pressure but high cooling rates. 42 In a preliminary hyperparameter search, different hyperparameter sets were probed and optimized, including the variation of the optimizers such as Adadelta, Adagrad, Adam, Adamax, Nadam, and RMSprop. We used the data of T t from DSC at atmospheric pressure and high cooling rates to indirectly validate the prediction accuracy and the extrapolation ability of the ANNs.…”

Section: Introductionmentioning

confidence: 99%

“…Besides the data of p , T , and time ( t ), phase-transition temperature ( T t ) and cooling rate (d T /d t ) were also considered as features of the input data to improve the extrapolation ability of the ANNs. To confirm the extrapolative accuracy, the used data of T t were calculated by a regression equation which is based on the experimental data of T t from the pvT measurements at high pressure but low cooling rates and the differential scanning calorimetry (DSC) tests at atmospheric pressure but high cooling rates . In a preliminary hyperparameter search, different hyperparameter sets were probed and optimized, including the variation of the optimizers such as Adadelta, Adagrad, Adam, Adamax, Nadam, and RMSprop.…”

Section: Introductionmentioning

confidence: 99%

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Prediction of Specific Volume of Polypropylene at High Cooling Rates by Artificial Neural Networks

Jian

Hopmann

Liu

et al. 2021

Ind. Eng. Chem. Res.

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The specific volume of polymers is a critical parameter that has offered many highly promising applications in focus as a basic material property. The specific volume (v) as a function of commonly pressure (p) as well as temperature (T), however, does not satisfy accuracy requirements with respect to experimental results. In addition, polymer forming is a rapid cooling process, and the cooling rate (dT/dt) has a significant effect on the pvT behavior of polymers. However, today’s commercial testing devices cannot obtain the pvT data for high cooling rates. Hence, the prediction of specific volume of polymers for rapid cooling applications remains a challenge. This work deals with the potential application of artificial neural networks (ANNs) to model the v in dependence of p, T, and dT/dt within their experimental uncertainty. The experimental pvT data of the semicrystalline polypropylene (PP) at the temperature range of 40–240 °C, the pressure range of 200–2200 bar, and the set cooling rate range of 2–20 °C/min were used for the ANN training. Besides the data of p and T, time (t) and phase-transition temperature (T t) were also used as input features of the training datasets to improve the extrapolation ability for high cooling rates. A hyperparameter search was conducted to identify the optimized hyperparameter sets. The experimental values of T t at atmospheric pressure (1 bar) and cooling rates (2–300 000 °C/min) obtained through differential scanning calorimetry (DSC) and flash DSC were used to indirectly validate the prediction accuracy of the ANNs. The newly developed continuous two-domain equations of state (EoS) were also applied in comparison. The ANN approach showed the most reliable predicting results both for interpolations and extrapolations when trying to predict the specific volume beyond the pvT measurement range (the cooling rate is up to 6000 °C/min and the pressure is the atmospheric pressure of 1 bar).

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Prediction of Specific Volume of Polypropylene at High Cooling Rates by Artificial Neural Networks

Jian

Hopmann

Liu

et al. 2021

Ind. Eng. Chem. Res.

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Injection molding of semi‐crystalline polymers in a space‐time framework

Fabón

Alms

Behr

et al. 2023

Proc Appl Math and Mech

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The challenges in the numerical simulation of the polymer injection molding process are manifold. Such simulation involves a two‐phase flow formulation and the physical modeling of complex material, i.e., molten polymer. This paper presents a complete macroscale simulation approach for the filling stage of injection molding with semi‐crystalline polymers, applied on polypropylene as example. Accurate and efficient results are obtained using a space‐time finite‐element discretization. Heading towards more efficient computations, we search for a reduction of the polymer's physical model, which includes variable viscosity, density, and several crystallization models. The final contribution of the present work is a model sensitivity analysis, which evaluates the relevance of each material model during the filling stage of injection molding.

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High‐resolution numerical simulations of polymer injection molding: Analysis of mesh size and refinement

Ferrer‐Fabón,

Alms,

Behr

et al. 2023

Proc Appl Math and Mech

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Accurate and high‐resolution numerical simulations are crucial for preventing manufacturing defects during polymer injection molding. However, achieving efficient and precise simulations in this field remains a subject of ongoing research. In this study, we develop a macro‐scale numerical model to describe the behavior of melted polymer during the filling phase. Employing our in‐house finite‐element solver, XNS, we simulate the polymer and air flows as a two‐phase flow using the level‐set method. This formulation involves significant discontinuities across the interface, therefore a high mesh resolution along the interface becomes necessary. Furthermore, to accurately capture the polymer behavior along the wall, we apply a variable Navier slip condition that is dependent on the mesh size. To assess the impact of mesh size on the solution, we compare the results obtained with different levels of mesh refinement. Additionally, we investigate the effects of localized mesh refinement at the wall boundary and conclude that refinement in the interior of the channel is also required. Through our analysis, we highlight the importance of high‐resolution meshing and appropriate wall boundary conditions in achieving accurate simulations of polymer injection molding. This research contributes to the ongoing efforts in improving the understanding of the complex phenomena involved in this manufacturing process.

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Non-Isothermal Crystallisation Kinetics of Polypropylene at High Cooling Rates and Comparison to the Continuous Two-Domain pvT Model

Cited by 8 publications

References 37 publications

Prediction of Specific Volume of Polypropylene at High Cooling Rates by Artificial Neural Networks

Prediction of Specific Volume of Polypropylene at High Cooling Rates by Artificial Neural Networks

Injection molding of semi‐crystalline polymers in a space‐time framework

High‐resolution numerical simulations of polymer injection molding: Analysis of mesh size and refinement

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