Radiation-responsive polymers: a novel spectral approach to investigate ultrahigh molecular weight polyethylene modifications using Grunwald-Letnikov and Caputo fractional order derivatives
DOI:
https://doi.org/10.31349/RevMexFis.71.011005Keywords:
Grünwald-Letnikov fractional order derivatives; ATR-FTIR spectroscopy; UHMWPE; principal component analysis; Caputo ¨ fractional order derivativesAbstract
The impact of gamma radiation on Ultrahigh Molecular Weight Polyethylene (UHMWPE) using fractional differential transformations of FTIR spectra has been probed during the current study. The gamma irradiated samples of UHMWPE for doses of 0, 25, and 50 kGy have been tested with FTIR spectroscopy, and subsequent to testing each spectrum has been analyzed with fraction order differentiation ranging from 0.5 to 1. The exhibited significant shifts in absorbance due to radiation-induced physical and chemical changes, including C=C unsaturation, C=O carbonyl absorption, and variations in CH2 bending and stretching frequencies are clearly evident even at the lowest order of applied transformation. The weak bands in spectral regions 800 − 1100 cm−1 because of gamma radiation caused peak splitting in the 800 − 1100 cm−1 region, attributed to the conversion of vinyl groups into vinylidene and trans-vinylene groups, have also been observed at all orders of applied transformations. It is, therefore, fractional differential transformations thus proved to be a potential methodology for in depth spectra analysis of radiation responsive polymers like UHMWPE with a minimal information loss during the transformation. This is also confirmed by sensitivity and specificity analysis that demonstrated that lower-order transformations are effective for accurate spectral characterization.
References
L. Silva, Q. Martins, A. Ribas, D. Oliveira, R. Lima, and J. Santos, Raman and FTIR spectroscopy experimental and theoretical in magnetic nanoemulsion from Carapa Guianensis Aublet, Rev. Mex. Fis., 69 (2023) 051003, https://doi.org/10.31349/RevMexFis.69.051003
A. Souigat, Z. Korichi, and M. T. Meftah, Solution of the fractional diffusion equation by using Caputo-Fabrizio derivative: application to intrinsic arsenic diffusion in germanium, Rev. Mex. Fis. 70 (2024) 010501 1, https://doi.org/10.31349/RevMexFis.70.010501
M. Irfan et al., Raman spectroscopy and electrical properties of polypyrrole doped dodecylbenzene sulfonic acid/Y2O3 composites, Rev. Mex. Fis. 70 (2024) 010502 1, https://doi.org/10.31349/RevMexFis.70.010502
M. M. Saeed, M. S. Mehmood, and M. Muhammad, Spectroscopic analysis of residual radicals of gamma sterilized UHMWPE with fractional order differential operators, Rev. Mex. Fis. 70 (2024) 011001, https://doi.org/10.31349/RevMexFis.70.011001
M. S. Mehmood et al., Assessment of γ-sterilization and/or cross linking effects on orthopedic biomaterial using optical diffuse reflectance spectroscopy, Optik 144 (2017) 387, https://doi.org/10.1016/j.ijleo.2017.06.127
M. S. Mehmood et al., UHMWPE band-gap properties-II: Effect of post e-beam irradiation real time shelf aging in air, Radiat. Phys. Chem. 159 (2019) 231, https://doi.org/10.1016/j.radphyschem.2019.02.045
M. S. Mehmood et al., Mueller matrix polarimetry for characterization of E-Beam irradiated Uhmwpe, Radiat. Phys. Chem. 166 (2020) 108503, https://doi.org/10.1016/j.radphyschem.2019.108503
R. Caponetto, Fractional order systems: modeling and control applications. (World Scientific, 2010). https://doi.org/10.1142/7709
A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and applications of fractional differential equations. (Elsevier, 2006)
S. Saberhaghparvar and H. Panahi, Initial value problem for a Caputo space-time fractional Schrödinger equation for the delta potential, Rev. Mex. Fis. 68 (2022) 040703, https://doi.org/10.31349/RevMexFis.68.040703
C. Li, D. Qian, Y. J. D. D. i. N. Chen, and Society, On Riemann-Liouville and caputo derivatives, 2011 (2011) 562494, https://doi.org/10.1155/2011/562494
A. Atangana and J. F. Gómez-Aguilar, Numerical approximation of Riemann-Liouville definition of fractional derivative: From Riemann-Liouville to Atangana-Baleanu, Numer. Methods Partial Differ. Equ. 34 (2018) 1502, https://doi.org/10.1002/num.22195
D. A. Murio, Stable numerical evaluation of Grünwald-Letnikov fractional derivatives applied to a fractional IHCP, Inverse Problems in Science and Engineering, 17 (2009) 229, https://doi.org/10.1080/17415970802082872
Z. Odibat and Computation, Approximations of fractional integrals and Caputo fractional derivatives, 178 (2006) 527, https://doi.org/10.1016/j.amc.2005.11.072
W. Jiang, C. Huang, and X. Deng, A new probability transformation method based on a correlation coefficient of belief functions, Int. J. Intell. Syst. 34 (2019) 1337, https://doi.org/10.1002/int.22098
M. S. Mehmood, A. Sanawar, N. Siddiqui, and T. J. P. B. Yasin, Quantification of silane grafting efficacy, weak IR vibration bands and percentage crystallinity in post e-beam irradiated UHMWPE, Polym. Bull. 74 (2017) 213, https://doi.org/10.1007/s00289-016-1709-0
M. S. Khurshid, M. S. Mehmood, and M. Zubair, Ultrahigh Molecular Weight Polyethylene and Graphene Oxide (UHMWPE/GO) Nano-composites for EMI Shielding, in Handbook of Polymer and Ceramic Nanotechnology: (Springer, 2021), pp. 1243-1267. https://doi.org/10.1007/978-3-030-40513-782
M. S. Mehmood and M. N. Mehmood, Ultrahigh Molecular Weight Polyethylene and Silane (UHMWPE/Silane) Hybrids: Radiation Modifications and Characterization, in Handbook of Polymer and Ceramic Nanotechnology: (Springer, 2021), pp. 1377-1393. https://doi.org/10.1007/978-3-030-40513-784
M. Slouf et al., Structural changes of UHMWPE after e-beam irradiation and thermal treatment, 85 (2008) 240, https://doi.org/10.1002/jbm.b.30942
L. Costa, I. Carpentieri, P. J. P. D. Bracco, and Stability, Post electron-beam irradiation oxidation of orthopaedic Ultra-High Molecular Weight Polyethylene (UHMWPE) stabilized with vitamin E, Polym. Degrad. Stab. 94 (2009) 1542, https://doi.org/10.1016/j.polymdegradstab.2009.04.023
L. Costa, I. Carpentieri, P. Bracco, Post electron-beam irradiation oxidation of orthopaedic UHMWPE, Polym. Degrad. Stab. 93 (2008) 1695, https://doi.org/10.1016/j.polymdegradstab.2008.06.003
S. Liu et al., Study on the post-irradiation oxidation of polyethylenes using EPR and FTIR technique, Polym. Degrad. Stab. 196 (2022) 109846, https://doi.org/10.1016/j.polymdegradstab.2022.109846
M. M. Saeed, M. Muddassar, M. S. Mehmood, H. M. J. R. P. Musharaf, and Chemistry, Diffuse reflectance spectroscopy of γ-irradiated UHMWPE: A novel fractional order based filters approach for accessing the radiation modification, Radiat. Phys. Chem. 197 (2022) 110163, https://doi.org/10.1016/j.radphyschem.2022.110163
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 M. Mudassir Saeed, M. Muddassar, M. Sajjad Mehmood, N. Siddiqui
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Authors retain copyright and grant the Revista Mexicana de Física right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
