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Yan Wang

A FRACTAL MODEL FOR THE CRYSTALLIZATION KINETICS

ABSTRACT
The Kolmogorov-Johnson-Mehl-Avrami equation is wildly applied in the crystallization kinetics, and Avrami exponent involved in the equation plays an important role in crystallization process. Here we show that the Kolmogorov-Johnson-Mehl-Avrami equation can be obtained by a fractal crystallization model, and the exponent is explained as the fractal dimension in time, which depends upon the chain length and molecule weight.
KEYWORDS
KJMA model，isothermal crystallization, fractal calculus, fractal derivative
PAPER SUBMITTED: 1970-01-01
PAPER REVISED: 2020-06-12
PAPER ACCEPTED: 2020-06-16
PUBLISHED ONLINE: 2021-01-31
DOI REFERENCE: https://doi.org/10.2298/TSCI191212027W
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2021, VOLUME 25, ISSUE Issue 2, PAGES [1313 - 1315]
REFERENCES
  1. Tian, D., et al., Self-Assembly of Macromolecules in a Long and Narrow Tube, Thermal Science, 22 (2018), 4, pp. 1659-1664
  2. Tian, D., et al., Macromolecule Orientation in Nanofibers, Nanomaterials, 8 (2018), 11, 918
  3. Tian, D., He, J. H., Macromolecular Electrospinning: Basic Concept and Preliminary Experiment, Results in Physics, 11 (2018), Dec., pp. 740-742
  4. Tian, D., et al., Geometrical Potential and Nanofiber Membrane's Highly Selective Adsorption Property, Adsorption Science and Technology, 37 (2019), 5-6, pp. 367-388
  5. Jin, X., et al., Low Frequency of a Deforming Capillary Vibration, Part 1: Mathematical Model, Journal of Low Frequency Noise Vibration and Active Control, 38 (2019), 3-4, pp. 1676-1680
  6. Yang, Z., et al., On the Cross-Section of Shaped Fibers in the Dry Spinning Process: Physical Explanation by the Geometric Potential Theory, Results in Physics, 14 (2019), Sept., 102347
  7. Li, X. X., He, J. H., Nanoscale Adhesion and Attachment Oscillation under the Geometric Potential - Part 1: The Formation Mechanism of Nanofiber Membrane in the Electrospinning, Results in Physics, 12 (2019), Mar., pp. 1405-1410
  8. Kolmogorov, A. N., On the Statistical Theory of Crystallization of Metals, Ivz. Akad. Nauk. SSSR, Ser. Mat., 3 (1937), pp. 355-359
  9. Johnson, W. A., Mehl, R. F., Reaction Kinetics in Processes of Nucleation and Growth, Trans. Am. Inst. Min. (Metall.) Engs, 135 (1939), pp. 416-442
  10. Avrami, M. J., Kinetics of Phase Change, I General Theory, Phys. Chem., 7 (1939), 12, pp. 1103-1112
  11. Elabbar, A. A., On the Application of the KJMA Equation on the Analysis of Isothermal Crystallization Kinetics, Materials Chemistry and Physics, 238 (2019), Dec., 121896
  12. Yousefzade, O., et al., Crystallization Kinetics of Chain Extended Poly(L-lactide)s Having Different Molecular Structures, Materials Chemistry and Physics, 240 (2020), Jan., 122217
  13. Hassanzadeh, N., et al., An Investigation of Crystallization Kinetics of the Na3MnCO3PO4 Cathode Material, Synthesized by the Hydrothermal Method, Materials Chemistry and Physics, 214 (2018), Aug., pp. 73-79
  14. Ain, Q. T., He, J. H., On Two-Scale Dimension and Its Applications, Thermal Science, 23 (2019), 3B, pp. 1707-1712
  15. He, J. H., Ji, F. Y., Two-Scale Mathematics and Fractional Calculus for Thermodynamics, Thermal Science, 23 (2019), 4, pp. 2131-2133
  16. He, J. H., Fractal Calculus and Its Geometrical Explanation, Results Phys., 10 (2018), Sept., p. 272-276
  17. He, C. H., et al., Taylor Series Solution for Fractal Bratu-Type Equation Arising in Electrospinning Process, Fractals, 28 (2020), 1, 2050011
  18. He, J. H., The Simplest Approach to Non-Linear Oscillators, Results in Physics, 15 (2019), Dec., 102546
  19. He, J. H., A Simple Approach to 1-D Convection-Diffusion Equation and Its Fractional Modification for E Reaction Arising in Rotating Disk Electrodes, Journal of Electroanalytical Chemistry, 854 (2019), Dec., 113565
  20. He, J. H., A Fractal Variational Theory for 1-D Compressible Flow in a Microgravity Space, Fractals, 28 (2020), 02, 2050024
  21. He, J. H., Variational Principle for the Generalized KdV-Burgers Equation with Fractal Derivatives for Shallow Water Waves, Journal Appl. Comput. Mech., 6 (2020), 4, pp. 735-740
  22. Liu, H. Y., et al., A Fractal Rate Model for Adsorption Kinetics at Solid/Solution Interface, Thermal Science, 23 (2019), 4, pp. 2477-2480
  23. Wang, K. L., et al., A Remark on Wang's Fractal Variational Principle, Fractals, 27 (2019), 8, 1950134
  24. Wang, Q. L., et al., Fractal Calculus and Its Application Explanation of Biomechanism of Polar Bear Hairs, Fractals, 27 (2019), 5, 1992001
  25. Wang, Y., Deng, Q. G., Fractal Derivative Model for Tsunami Travelling, Fractals, 27 (2019), 1, 1950017
  26. Wang, Y., A Variational Formulation for Anisotropic Wave Traveling in a Porous Medium, Fractals, 27 (2019), 4, 19500476
  27. Wang, Y., et al., A Fractal Derivative Model for Snow's Thermal Insulation Property, Thermal Science, 23 (2019), 4, pp. 2351-2354
  28. Nottale, L., On Time in Microphysics, Comptes Rendus de L. Acad. Sci., Ser II, 306 (1988), 5, pp. 341-346
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A fractal model for the crystallization kinetics

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence