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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The demand of precise injection-molded parts is steadily increasing and is today one of the most relevant challenges, due to local variations in temperature and pressure during the production of the part. These variations can lead to a significant change of the local specific volume, shrinkage potential, and inner stress, which ultimately results in part warpage. By homogenizing the local specific volume over the part according to the specific pvT-behavior of the polymer, warpage is expected to be reduced. The following work describes a new approach to control the local specific volume by a newly developed segmented and highly dynamic mold temperature control based on rapid heating ceramics and CO 2 evaporation chambers. Since injection molding is a dynamic process and heat transfer inside the mold is comparably slow, a special control strategy is necessary to activate the heating and cooling elements in advance. For this, a novel prediction strategy based on a discretization of the onedimensional heat equation has been developed. Experimental trials including a classical PID controller and a model predictive control approach (MPC) show that the MPC is superior regarding the process stability.

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