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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In the market of lighting technologies, light-emitting diodes (LEDs) gradually substitute conventional light sources. Because of their high energy efficiency and long lifetime, they are increasingly used in consumer products, interior and exterior lighting applications in the home and mobility sector as well as in industrial applications. The material properties in the surrounding area of the light-emitting semiconductor chip are crucial to the performance of LED. Although the energy efficiency of LED is higher compared to conventional light sources, temperatures exceed about 150°C close to the semiconductor chip. Especially in combination with high amounts of blue ultraviolet (UV) radiation, the materials for encapsulation cannot meet the requirements and reduce the lifetime of an LED significantly. Contrary to conventional materials, high transparent liquid silicone rubber (LSR) can resist high temperatures as well as UV radiation and offer a great freedom in design. This enables the combination of the encapsulation (primary optics) and the secondary optics in one component. The objective of an ongoing joint research project with various partners from the industry is the development of an innovative injection moulding process for high precision optics in LED applications made of LSR, which is analysed at the Institute of Plastics Processing (IKV), Aachen, Germany. Therefore, the LED board is placed in the injection mould and overmoulded with LSR. The goal is a highly integrated process with major emphasis on the reduction of components, mounting steps and costs. Furthermore, the combination of primary and secondary optics promises an improved effectiveness because losses in light power due to the transition of the primary and secondary optics are reduced.