Analysis of equations of state for polymers

Júnior, Erlí José Padilha; Soares, Rafael de Pelegrini; Cardozo, Nilo Sérgio Medeiros

doi:10.1590/0104-1428.1621

Cited by 19 publications

(5 citation statements)

References 31 publications

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“…The critical temperature of PLA, which defines the transition from solid to liquid when heating is applied and from liquid to solid when the molten material is cooled down, is generally expressed by the Tait equation for the solid state (just below the melting point) https://doi.org/10.37358/MP.20.2.5369 (11) where b5 is the glass transition temperature for P = 0 and b6 is the rate of change of glass transition temperature with pressure; they describe the change of transition temperature with pressure. According to Padilha [25] and Chang [26] the estimated values for b5 and b6 are 440.44 K, respectively 0.0048 K/MPa.…”

Section: Figure 7 Sparkling Appearance Of the Area Melted By Laser Rmentioning

confidence: 99%

Laser Marking of PLA FDM Printed Products

Savu¹,

Savu²,

Sîrbu³

et al. 2019

Mater. Plast.

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The paper aimed to reveal, qualitatively and quantitatively, the modifications suffered by the PLA during the complex heating cycle specific to the 3D printing followed by laser marking. The obtained results showed that the melting point of the PLA decreases from 162.2oC (which is specific to PLA filament) to 153.1oC after the 3D printing process and to 149.7oC after the laser heating. The glass transition suffered the same lowering after the printing process but an important increasing after the laser heating. The elastic modulus evolution proved a decreasing of the plasticity and that is hapenning when the material suffers an increasing of its rigidity. The elongation viscosity was analyzed and its values were decreasing with the increasing of the temperature that happened on the material. The decreasing was produced by the reduction of the elasticity, when the chain branches are decreasing their length. The decreasing is more pronounced with the increasing of the temperature. The ratio between the loss modulus to the storage modulus and quantifies the way in which the PLA absorbs and disperses energy moves its peak from 65oC (curve specific to the PLA filament) to 45oC (curve specific to the last layer deposited by 3D printing process and re-heated by laser beam for marking). The peak means the lowest storage modulus, which is a measure of elastic response of a material, so the transition from glass to high elasticity moves to the lower temperatures.

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Section: Figure 7 Sparkling Appearance Of the Area Melted By Laser Rmentioning

confidence: 99%

Laser Marking of PLA FDM Printed Products

Savu¹,

Savu²,

Sîrbu³

et al. 2019

Mater. Plast.

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“…where T is the exact temperature. It was noted that the equation, T = T − d 1 , has been used in the two-domain Tait EoS in many publications [11,22,30,42]. However, it will cause large deviations without the dependency on pressure [34], because d 1 only represents the transition temperature at zero pressure, which cannot combine the pressure effects.…”

Section: Continuous Two-domain Eosmentioning

confidence: 99%

“…Various theories have been developed to describe the pvT properties of polymer solutions, including the cell model [12][13][14], the hole model [15], the lattice-fluid model [16], and the statistical-mechanical EoS [17][18][19][20]. These theoretical models have been modified and extensively used [21,22]. However, the solid state is a quasi-equilibrium state, which is dependent on the conditions of pressure and cooling…”

Section: Introductionmentioning

confidence: 99%

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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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“…The Tait model is widely used for polymers because of its high fit accuracy and simple form [5][6][7][8][9]. It is used in commercial simulation software, such as Moldflow (Autodesk, Inc., Mill Valley, CA, USA), Moldex 3D (CoreTech System Co., Ltd., Zhubei City, Taiwan), Sigmasoft (SIGMA Engineering GmbH, Aachen, Germany) and Cadmould (Simcon kunststofftechnische Software GmbH, Würselen, Germany).…”

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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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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Analysis of equations of state for polymers

Cited by 19 publications

References 31 publications

Laser Marking of PLA FDM Printed Products

Laser Marking of PLA FDM Printed Products

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

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

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