The role of microcrystalline structure on optical scattering characteristics of semi-crystalline thermoplastics and the accuracy of numerical input for IR-heating modeling
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Infrared (IR) heating is widely used for thermoforming of thermoplastic polymers. The key benefit of radiation heating is that a significant amount of the radiative energy penetrates into the polymers thanks to their semi-transparency. For the case of heating unfilled semi-crystalline polymers, the relation between their microcrystalline structure and optical properties is the key to develop a predictive IR-heating model as microcrystalline structure introduces an optically heterogeneous medium. In this study, a relation between the microcrystalline structure of a polyethylene (PE) and its effect on the thermo-optical properties was experimentally analyzed considering a two-step analysis. At very first step, the relation was analyzed considering samples with identical thicknesses and different morphologies, characterized here in terms of degree of crystallinity (Xc (%)). Using Fourier Transform Infrared (FT-IR) spectroscopy and integrating sphere, optical characteristics of the PE samples were analyzed in near-infrared (NIR) and middle-infrared (MIR) spectral ranges. The analyses showed that a slight variation in Xc (%) has a great effect on the optical characteristics of PE, particularly the transmission characteristics in NIR range. The wavelength-dependent effect of Xc (%) on the transmission behaviors opened a discussion about the fact that the microcrystalline structures -in particular spherulites or their substructures such as lamellae- are responsible for optical scattering. Using the optical properties obtained from the two-step experimental analyses, two different thermo-optical properties were calculated, namely extinction and absorption coefficients, and used as a numerical input for the parametric numerical studies. The numerical studies were performed using an in-house developed radiation heat transfer algorithm -RAYHEAT-. Both the experimental and numerical analyses demonstrated the importance of the optical scattering regarding the identification of thermo-optical properties, used as a numerical input for radiation heat transfer models.
KeywordsInfrared heating Semi-crystalline thermoplastics Thermo-optical properties Optical scattering Crystallinity Radiation heat transfer modeling
The major advantage of IR radiation heating is that a portion of the radiative energy penetrates directly into the bulk of thermoplastic polymer because of its semi-transparency where high heat flux densities can be used to decrease the heating time without causing thermal damage to the polymer surface . Polymer structures used in thermoforming processes are heated prior to forming stage. The temperature profile at the end of the heating stage has therefore a great effect on viscoelastic properties and thus on the mechanical behavior of polymers during forming. As a consequence, it is crucially important to have an extensive knowledge on the temperature distributions throughout the bulk volume of a polymer.
A numerical radiative heat transfer model may be helpful to predict temperature distributions and to optimize the heating conditions such as reducing the heating time and the input of energy. However, physical background of the radiation heat transfer into the bulk polymer needs to be understood adequately in order to develop a predictive model. In the last decade, several authors developed such radiative thermal models for various thermoplastic polymers at which the amount of absorbed radiation  or temperature fields [3, 4, 5, 6, 7] on the studied thermoplastics were predicted closely. The radiation heat transfer models used in those studies adopted the Beer-Lambert law, assuming an optically homogenous and non-scattering medium for bulk material so that the radiation attenuation through a medium was only the function of absorption. For amorphous or semi-crystalline thermoplastics with a low Xc (%), where the crystalline content in such polymers is much lower than their amorphous content, the optical scattering may be negligible. However, it may be an ill-defined assumption considering the radiation propagation inside of an optically heterogeneous medium. Basically, the term -optically heterogeneous medium- represents the discontinuities existing inside of a heated medium that causes to change the direction of propagated radiation, named optical scattering. These discontinuities -also called scatterers- may be fiber-matrix interface in thermoplastic composites [8, 9], filled particles [10, 11] or microcrystalline structure of semi-crystalline polymers [10, 12]. Considering optically heterogeneity of a medium, some numerical models were proposed for simulating laser transmission welding (LTW) of filled thermoplastics [11, 13] and laser-assisted tape placement (ATP) processes of thermoplastic composites . In those studies, the relation between the scatterers (filled particles or fiber) and the scattered radiation was established. Such a relation between optical scattering and microcrystalline structure is required to be established for building an accurate radiation heat transfer for unreinforced or unfilled semi-crystalline thermoplastics. Although some effort given to establish a relation between microcrystalline structure of such type of polymers and its optical scattering effect, those proposed relations were limited to Xc (%) where no detailed explanation was introduced for scatterers that may be related to the morphological characteristics [15, 16]. Lebaudy et al.  developed a radiation heat transfer model for poly(ethylene terephthalate) (PET) considering its cold crystallization behavior under heating. Their model was based on both scattering and absorption characteristics of the studied material where the change in the direction of radiation propagation caused by optical scattering was taken into account. In their study, it was concluded that Xc (%) was the main factor that causes optical scattering during cold-crystallization of PET. Those analyses were extended by Denis et al.  where the optical scattering characteristics of the PET polymers with different degrees of crystallinity were experimentally analyzed. Based on the analyses, an empirical law was established between the Xc (%) and the scattering coefficient of PET. Although the experimental analyses in  also revealed that the scattering characteristics of the material with the same Xc (%) changes dramatically in the spectral range of 0.4–1 μm, no explanation was given why the optical scattering behavior changes under varying wavelength and at a constant crystallinity. A similar wavelength-dependent optical scattering relation was observed in [17, 18] where it was proposed that the microcrystalline structure, particularly spherulites or their substructures such as lamellae, are responsible for the optical scattering.
In our study, the effect of the microcrystalline structure on thermo-optical properties of PE was studied. As a first step, the PE samples were prepared with identical thickness and cooled down under two different cooling conditions so that two groups of samples with different morphologies were introduced and characterized in terms of different degrees of crystallinity obtained via Differential Scanning Calorimetry (DSC). The effect of microcrystalline structure on the thermo-optical characteristics of PE was initially analyzed comparing the bi-directional transmittance and reflectance of the samples obtained via FT-IR spectroscopy and integrating sphere respectively. The analyses revealed a strong coupling between crystallinity and the thermo-optical properties of PE, especially in the range of NIR. The analyses were extended adopting a comparative experimental analysis on the transmission characteristics of the polymer. Bi-directional and directional-hemispherical transmittances of the identical samples were determined and the amount of the scattered radiative flux was estimated. These measurements also allowed estimating the extinction and absorption characteristics of the polymer that were calculated based on a well-known relation in radiation heat transfer theory. At last, parametric numerical studies were performed using the calculated extinction and absorption characteristics of the polymer where also the boundary conditions and the thermal-physical properties of the polymer were kept identical. The numerical studies were done employing a preliminary radiation heat transfer model. The computations were performed using in-house developed radiation heat transfer algorithm -RAYHEAT- which is built based on ray-tracing method and Beer-Lambert Law. Thanks to the numerical analyses, the effect of optical scattering, as a numerical input, was analyzed regarding the predicted temperature profiles. The combined experimental and numerical analyses demonstrated the importance of the optical scattering considering the identification of thermo-optical properties, accuracy of the numerical inputs and their effects on the temperature profile predictions.
The PE samples prepared for the calorimetric and optical analyses
Sample thickness (mm)
0.42, 0.90 and 1.82
The determination of the Xc (%) was carried out using a Perkin-Elmer DSC 8000. For the each DSC scan, a piece of material with a mass of 2.5 mg was cut from the compressed samples. In order to determine the crystallinity that is induced by to the two different cooling steps, the melting endotherms were used for the calculations of Xc (%). The heating scan was performed at 20 °C/min at a temperature range of 20 °C to 180 °C. Apart from obtaining information on Xc (%), the melting temperature (Tm) of the polymer were also determined thanks to the analyses.
As aforementioned, two groups of samples with different crystallinity, but with identical material and thickness, were prepared. Thanks to this step, the difference in the optical characteristics of the samples could be related to the difference in their Xc (%).After the initial analyses were done using the first and second group of samples, the third group was used in order to analyze how strong scattering exists in the PE polymer adopting two different transmittance measurements.
Results and discussion
Experimental analyses between crystallinity and optical characteristics
As explained in Section 2, the first and the second group of samples were prepared with the identical material and thickness but with different crystallinity induced by the two different cooling conditions. The actual cooling rate of the samples was not determined for both the cooling conditions as the focus of this study is to analyze the relation between optical properties of PE and its microcrystalline structure, represented here by different Xc (%).
A numerical approach for modeling IR-radiation heat transfer for semi-crystalline polymers
In order to analyze how the optical scattering affects the temperature predictions in 3D medium, parametric numerical studies were carried out adopting a preliminary numerical approach. In this section, using the optical properties obtained from the two-step experimental analyses, two different thermo-optical properties were proposed which were used as a numerical input for the parametric numerical studies.
For the numerical studies, a two-step computation was employed where ∇.qr is computed using an in-house developed radiation heat transfer algorithm - RAYHEAT - and the ∇.qr is used as heat source input in the commercial Finite Element Analysis (FEA) software -COMSOL Multiphysics- to compute the temperature in a 3D geometry. RAYHEAT is a MATLAB-based code which simulates radiation heat transfer using geometrical optics that is based on ray tracing method. Therefore, spectral and direction dependency of the emitted radiation from an IR-lamp are taken into account. Although there are other approaches for modelling radiation transfer, it was demonstrated by Jensen et al.  that ray tracing is one of the most accurate method in comparison to the other approaches revealed in literature. In RAYHEAT, the change in the direction of a propagated radiation is only assumed at the surface of a heated medium. Therefore, radiation attenuation in a medium is modeled adopting Beer-Lambert Law as stated in Eq. 4. The accuracy of the algorithm was demonstrated in [5, 39] considering a non-scattering (Dλ = 0), optically homogeneous and cold medium for low-crystalline PET. Detailed information on the computation algorithm and the theoretical background of the model can be found in .
Although 3D temperature profile may not be predicted closely in the highly crystalline PE polymer medium due to the simplifications adopted at this step the parametric numerical analyses demonstrate how the optical scattering may cause to change the predicted temperature, even for a heating case with a single IR-lamp. Considering the fact that the IR-heating step of various thermoforming processes of semi-crystalline polymers is performed using multiple heat source, the difference between the real and the estimated temperature profile may be much more significant.
In the current study, the effect of the microcrystalline structure on the thermo-optical properties of PE was experimentally analyzed. The analyses demonstrated that the effect of crystallinity on the transmission was significant considering NIR range, whereas a slight effect was observed in MIR range. Even an increase of 5% of the Xc (%) caused a decrease of nearly 50% of the Tλ-directional in the spectral range around 1 μm. Considering IR-heating assisted thermoforming processes, it is crucial to take into account this coupled effect as the maximum emission wavelength of a typical IR heater is close to this spectral range. In addition, the crystallinity does not only affect the transmission through the material but also causes a change in the reflection characteristics as it was also determined that a slight change in crystallinity is somewhat effective on the reflectance levels in NIR range. As the change in the crystalline structure has much greater impact in NIR range than MIR range, the relation between the wavelength of the transmitted light and the size of spherulite or crystalline lamellae may have a key role to change the scattering behavior and therefore the thermo-optical parameters. In other words, the wavelength-dependent effect of crystallinity on the transmittance opens a discussion about the fact that the relation between scatterer size and the wavelength play the key role to affect optical characteristics, particularly transmission due to the optical heterogeneity and scattering of the light. It may therefore be concluded that the change in the thermo-optical characteristics of the PE samples may not be addressed by the Xc (%) itself but its microcrystalline morphology, which may defined by the spherulites or their substructures such as lamallae.
The experimental analyses on the transmission characteristics of the polymer were extended adopting comparative experimental measurements on the transmission behavior of the polymer. Tλ-directional and Tλ-hemispherical of the identical samples were determined and, the amount of the scattered radiative flux was estimated. These measurements also allowed estimating the βλ and κλ of the polymer that were calculated based on a well-known relation in radiation heat transfer theory. At last, two different models were simulated adopting an identical boundary conditions and numerical inputs but, with two different thermo-optical properties obtained through the comparative experimental analyses. The parametric numerical studies were carried out adopting a preliminary model based on an in-house developed radiation heat transfer algorithm, named as RAYHEAT. Thanks to the numerical analyses the effect of optical scattering, as a numerical input, was analyzed regarding to the predicted through-thickness temperature profiles. Although the analyses are not indicative of the accuracy of the absorbed radiation energy in the polymer medium, and therefore the predicted temperature distributions, it highlights how temperature predictions may differ if the optical scattering phenomenon in semi-crystalline thermoplastics is ignored. The Tλ-hemispherical measurements clearly revealed that the amount of radiative flux that could not be detected in the Tλ-directional measurements are not absorbed by the polymer medium, but scattered and transmitted. It may therefore be concluded that the computation-1 performed using the βλ provides relatively more realistic temperature predictions. As a consequence, the absorption characteristics obtained via Tλ-directional measurements may require a special attention if an optically heterogeneous medium is considered. Otherwise the thermo-optical properties obtained from such measurements may cause to adopt an erroneous numerical input where temperature predictions may be overestimated due to the incapability of detecting the scattered and transmitted amount of radiative flux. In addition, it is required to model the change in the direction of the scattered radiation in such optically heterogeneous polymer medium for accurate absorbed radiation predictions. In future work, a predictive model will be built including the change in radiation direction induced by optical scattering. The coupled relation between microcrystalline structure and optical characteristics of the polymer will be studied further in order to model optical scattering as a function of microcrystalline structure of the semi-crystalline polymer.
The authors declare that they have no conflict of interest.
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