Analytical review of some relevant methods and devices for the determination of the specific volume on thermoplastic polymers under processing conditions

Suarez, Sergio Aguilera; Naranjo, Alberto; López, Iván; Ortiz, J.

doi:10.1016/j.polymertesting.2015.10.009

Cited by 13 publications

(9 citation statements)

References 20 publications

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“…Since temperature conditions in injection moulding processes are mainly non-isothermal and cooling rates reach from 3000 °C/min at the mould walls to 60 °C/min near the core of the part, it is necessary to have a model predicting the crystallisation behaviour at a wide range of cooling rates [ 11 ].…”

Section: Discussionmentioning

confidence: 99%

“…The CTD is an empirical model, which was fitted to pvT data measured on an isotactic polypropylene applying pressures from 200 to 2200 bar and cooling rates up to 20 °C/min. This is problematic for modelling injection moulding processes since large cooling rates up to 3000 °C/min close to the mould walls and 60 °C/min near the centre of the part are usually experienced [ 11 ]. Since the cooling rate has a clear influence on the pvT behaviour of polymers and their solidification process, it is important to have an accurate description of the pvT behaviour at process-relevant cooling rates [ 9 , 12 , 13 , 14 , 15 , 16 ].…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2020

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The modelling of the correlation between pressure, specific volume and temperature (pvT) of polymers is highly important for applications in the polymer processing of semi-crystalline thermoplastics, especially in injection moulding. In injection moulding, the polymer experiences a wide range of cooling rates, for example, 60 °C/min near the centre of the part and up to 3000 °C/min near the mould walls. The cooling rate has a high influence on the pvT behaviour, as was shown in the continuous two-domain pvT model (CTD). This work examined the Hoffman–Lauritzen nucleation and growth theory used in the modified Hammami model for extremely high cooling rates (up to 300,000 °C/min) by means of Flash differential scanning calorimeter (DSC) measurements. The results were compared to those of the empirical continuous two-domain pvT model. It is shown that the Hammami model is not suitable to predict the crystallisation kinetics of polypropylene at cooling rates above 600 °C/min, but that the continuous two-domain pvT model is well able to predict crystallisation temperatures at high cooling rates.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2020

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“…It should be noted that the maximum cooling rate in injection molding can be as high as 3000 • C/min [41]. Several laboratories have reported that they can realize equally high cooling rates [36,41,45], but no commercial pvT instrument is available with such abilities. This further indicates the necessity of predictive models to extrapolate pvT data for higher cooling rates.…”

Section: Influence Of the Ccooling Ratementioning

confidence: 99%

“…Even a small discontinuity in the specific volume can cause large errors in the shrinkage estimates [35].The cooling rate has an obvious influence on the pvT behavior of polymers [34,[36][37][38][39][40]. In injection molding mainly non-isothermal conditions for polymer solidifications are found, with large cooling rates up to 3000 • C/min close to the mold walls and 60 • C/min near the center of the thickness [41]. Therefore, the prediction of pvT data of polymers considering the cooling rate is important.…”

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confidence: 99%

Continuous Two-Domain Equations of State for the Description of the Pressure-Specific Volume-Temperature Behavior of Polymers

et al. 2020

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The two-domain Schmidt equation of state (EoS), which describes the pressure-specific volume-temperature (pvT) behavior of polymers in both the equilibrium molten/liquid state and non-equilibrium solid/glassy state, is often used in the simulation of polymer processing. However, this empirical model has a discontinuity problem and low fitting accuracy. This work derived a continuous two-domain pvT model with higher fitting accuracy compared with the Schmidt model. The cooling rate as an obvious influencing factor on the pvT behavior of polymers was also considered in the model. The interaction parameters of the equations were fitted with the experimental pvT data of an amorphous polymer, acrylonitrile-butadiene-styrene (ABS), and a semi-crystalline polymer, polypropylene (PP). The fitted results by the continuous two-domain EoS were in good agreement with the experimental data. The average absolute percentage deviations were 0.1% and 0.16% for the amorphous and semi-crystalline polymers, respectively. As a result, the present work provided a simple and useful model for the prediction of the specific volume of polymers as a function of temperature, pressure, and cooling rate.Polymers 2020, 12, 409 2 of 18 rate, and therefore is difficult to model by an analytical approach [21]. The semi-empirical model of Hartmann-Haque (HH) [23,24], on the other hand, showed satisfactory results for amorphous polymers but difficulties for semi-crystalline polymers [21]. Additionally, the specific volume is not a dependent variable in these theoretical and semi-empirical models, leading to difficulties in simulation or prediction. In comparison, empirical models are often convenient to represent pvT data on polymers in analytical form, by only giving the parameters in the correspondent equations [25]. Empirical pvT models include the Spencer-Gilmore model [26], the Schmidt model [27,28], and the Tait model [29,30], which are used in commercial software, e.g., by Moldflow (Autodesk, Inc.), Moldex 3D (CoreTech System Co., Ltd.), Sigmasoft (SIGMA Engineering GmbH) and Cadmould (Simcon kunststofftechnische Software GmbH). The Spencer-Gilmore model is quite simple but less accurate. The Tait model has been widely used for polymers [21,22,31,32], because of its simple form, convenient application, and high precision. The two-domain Tait EoS has much more fitting accuracy, especially in the solid state. The Schmidt model was developed by T.W. Schmidt at the Institute for Plastics Processing (IKV) in 1986 [28]. The two-domain Schmidt EoS is similar to the two-domain Tait EoS, although simpler, and it is primarily used in German-speaking countries [7,8,10]. The Tait model uses a volume-pressure relationship, while the Schmidt model considers a volume-temperature relationship. The Schmidt model has less accuracy than the Tait model [33], and fitting problems occur regularly. Furthermore, another important problem for the two-domain Tait EoS and the Schmidt EoS is the discontinuity of the models. Because the EoS describes the pvT behavior of...

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“…8,9 Especially, the cooling rate (dT/ dt) has a significant effect on the pvT behavior of polymers. 10,11 Most polymer-forming processes such as extrusion, injection molding, additive manufacturing, and polymer welding are rapid cooling processes. The control of the crystallization or shrinkage and resultant stress depends on the level of control of the cooling rate through the entire part.…”

Section: Introductionmentioning

confidence: 99%

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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Analytical review of some relevant methods and devices for the determination of the specific volume on thermoplastic polymers under processing conditions

Cited by 13 publications

References 20 publications

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

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

Continuous Two-Domain Equations of State for the Description of the Pressure-Specific Volume-Temperature Behavior of Polymers

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

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