Simulation of Melt Viscosity Effect on the Rate of Solidification in Polymer

Jaka Fajar Fatriansyah(1), Hanindito Haidar Satrio(2*), Muhammad Joshua Yuriansyah Barmaki(3), Arbi Irsyad Fikri(4), Mochamad Chalid(5)

(1) Department of Metallurgical and Materials Engineering, Faculty of Engineering, Universitas Indonesia, Kampus Depok, West Java 16424, Indonesia
(2) Department of Metallurgical and Materials Engineering, Faculty of Engineering, Universitas Indonesia, Kampus Depok, West Java 16424, Indonesia
(3) Department of Metallurgical and Materials Engineering, Faculty of Engineering, Universitas Indonesia, Kampus Depok, West Java 16424, Indonesia
(4) Department of Metallurgical and Materials Engineering, Faculty of Engineering, Universitas Indonesia, Kampus Depok, West Java 16424, Indonesia
(5) Department of Metallurgical and Materials Engineering, Faculty of Engineering, Universitas Indonesia, Kampus Depok, West Java 16424, Indonesia
(*) Corresponding Author


Phase field model has been successfully derived from ordinary metal phase field equation to simulate the behavior of semi-crystalline polymer solidification phenomenon. To obtain the polymer phase field model, a non-conserved phase field equation can be expanded to include the unique polymer parameters, which do not exist in metals, for example, polymer melt viscosity and diffusion coefficient. In order to expand this model, we include free energy density and non-local free energy density based on Harrowel-Oxtoby and Ginzburg-Landau theorem for polymers. The expansion principle for a higher order of binary phase field parameter was employed to obtain fully modified phase field equation. To optimize the final properties of the products, the solidification phenomenon in polymers is very important. Here, we use our modified equation to investigate the effect of melt viscosity on the rate of solidification by employing ordinary differential equation numerical methods. It was found that the rate of solidification is related to the melting temperature and the kinetic coefficient.


polymer; solidification; phase field

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[1] International Organization for Standardization: Plastic Europe, The plastic industry Berlin,, accessed on August 20, 2012.

[2] Corinaldesi, V., Donnini, J., and Nardinocchi, A., 2015, Lightweight plasters containing plastic waste for sustainable and energy-efficient building, Constr. Build. Mater., 94, 337–345.

[3] Atzeni, E., Iuliano, L., Minetola, P., and Salmi, A., 2010, Redesign and cost estimation of rapid manufactured plastic parts, Rapid Prototyping J., 16 (5), 308–317.

[4] Firdaus, D.F., Masrudin, Lestari, D.A., Arbi, M.R., and Chalid, M., 2015, Structure and compatibility study of modified polyurethane/Fe3O4 nanocomposite for shape memory materials, Indones. J. Chem., 15 (2), 130–140

[5] Chalid, M., Heeres, H.J., and Broekhuis, A.A., 2015, Structure-mechanical and thermal properties relationship of novel γ-valerolactone-based polyurethanes, Polym. Plast. Technol. Eng., 54 (3), 234–245

[6] Faruk, O., Bledzki, A.K., and Fink, H-P., 2014, Progress report on natural fiber reinforced composites, Macromol. Mater. Eng., 299 (1), 9–26.

[7] Chalid, M., Rahman, A., Ferdian, R., Nofrijon, and Priyono, B., 2015, On the tensile properties of polylactide (PLA)/Arenga pinnata "ijuk" fibre composite, Macromol. Symp., 353 (1), 108–114.

[8] Chalid, M., Yuanita, E., and Pratama, J., 2015, Study of alkalization to the crystallinity and the thermal behavior of Arenga pinnata “ijuk” fibers-based poly(lactic acid) (PLA) biocomposite, Mater. Sci. Forum, 827, 326-331

[9] Yuanita, E., Pratama, J., and Chalid, M., 2017, Preparation of micro fibrillated cellulose based on Arenga pinnata ‘ijuk’ fibre for nucleating agent of polypropylene: Characterization, optimization and feasibility study, Macromol. Symp., 371 (1), 61–68.

[10] Feng, L., Laderman, B., Sacanna, S., and Chaikin, P., 2015, Re-entrant solidification in polymer–colloid mixtures as a consequence of competing entropic and enthalpic attractions, Nat. Mater., 14 (1), 61–65.

[11] Boutaous, M., Zinet, M., Boyard, N., and Bailleul, J.L., 2016, “Phase Change Kinetics within Process Conditions and Coupling with Heat Transfer” in Heat Transfer in Polymer Composite Materials: Forming Processes, Eds., Boyard, N., John Wiley & Sons, Inc., 121–155.

[12] Le Goff, R., Poutot, G., Delaunay, D., Fulchiron, R., and Koscher, E., 2005, Study and modeling of heat transfer during the solidification of semi-crystalline polymers, Int. J. Heat Mass Transfer, 48 (25-26), 5417–5430.

[13] Lovinger, A.J., and Cais, R.E., 1984, Structure and morphology of poly(trifluoroethylene), Macromolecules, 17 (10), 1939–1945.

[14] Micheletti, A., and Burger, M., 2001, Stochastic and deterministic simulation of nonisothermal crystallization of polymers, J. Math. Chem., 30 (2), 169–193.

[15] Raabe, D., and Godara, A., 2005, Mesoscale simulation of the kinetics and topology of spherulite growth during crystallization of isotactic polypropylene (iPP) by using a cellular automaton, Modell. Simul. Mater. Sci. Eng., 13 (5), 733–751.

[16] Xu, H., Matkar, R., and Kyu, T., 2005, Phase-field modeling on morphological landscape of isotactic polystyrene single crystal, Phys. Rev. E: Stat. Nonlinear Soft Matter Phys., 72, 011804.

[17] Warren, J.A., Kobayashi, R., Lobkovsky, A.E., and Carter, W.C., 2003, Extending phase field models of solidification to polycrystalline materials, Acta Mater., 51 (20), 6035–6058.

[18] Collins, J.B., and Levine, H., 1985, Diffuse interface model of diffusion-limited crystal growth, Phys. Rev. B: Condens. Matter, 31 (9), 6119–6122.

[19] Wheeler, A.A., Boettinger, W.J., and McFadden, G.B., 1992, Phase-field model for isothermal phase transition in binary alloys, Phys. Rev. A: At. Mol. Opt. Phys., 45 (10), 7424–7439.

[20] Zhu, J., Lu, X., Balieu, R., and Kringos, N., 2016, Modelling and numerical simulation of phase separation in polymer modified bitumen by phase field method, Mater. Des., 107, 322–332.

[21] Morris, P.J., 2005, Polymer Pioneers: A Popular History of the Science and Technology of Large Molecules, Chemical Heritage Foundation, Philadelphia, PA 19106, USA, 76.

[22] Kaiser, W., 2011, Kunststoffchemie für Ingenieure Von der Synthese bis zur Anwendung, 3rd ed., Carl Hanser Verlag GmbH & Co. KG, München.

[23] Provatas, N., and Elder, K., 2005, “Ising Model of Magnetism” in Phase-Field Methods in Material Science and Engineering, Wiley-VCH, New York, 11–14.

[24] Harrowell, P.R., and Oxtoby, D.W., 1987, On the interaction between order and a moving interface: Dynamical disordering and anisotropic growth rates, J. Chem. Phys., 86, 2932–2942.


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