Polimer Çözeltilerinde Statik Işık Saçılmasının Simülasyon Temelli Bir İncelemesi: Rayleigh, Mie, Debye ve Guinier Modellerinin Araştırılması

Yıl 2025, Cilt: 8 Sayı: 1, 1 - 13, 15.06.2025

Ali Özhan Akyüz , Kazım Kumaş

https://doi.org/10.53448/akuumubd.1662307

Öz

Bu çalışmada, bir polimer çözeltisindeki polimer parçacıklarının saçılma davranışı simülasyon temelli bir yaklaşımla incelenmiştir. 635 nm dalga boyuna sahip bir lazer kaynağı kullanılmış ve saçılma, açıları 0° ile 175° aralığında hesaplanmıştır. Çözücü ve polimer parçacıklarının kırılma indisleri sırasıyla 1.33 (su için tipik) ve 1.59 (polimerler için yaygın) olarak ayarlanmıştır. Hidrodinamik çaptan tahmin edilen jirasyon yarıçapı 58.5 nm olarak alınmıştır. Saçılma davranışını analiz etmek için dört model—Rayleigh, Mie, Debye ve Guinier uygulanmıştır. Küçük parçacıklar için geçerli olan Rayleigh saçılması, 0°'de düşük bir yoğunlukla başlamış ve 100°'ye kadar artan açıyla azalmış, ardından daha yüksek açılarda simetrik olarak artmıştır. Daha büyük parçacıklar için uygun olan Mie saçılması, 0°'de en yüksek yoğunluğu göstermiş ve açı arttıkça keskin bir şekilde azalmıştır. Debye saçılması, normalleştirilmiş 1.0 yoğunluğuyla başlamış ve açıyla birlikte düzgün bir şekilde azalarak polimer zincirlerinin rastgele sarmal yapısını analiz etmedeki etkinliğini göstermiştir. Öte yandan, Guinier yaklaşımı düşük açılarda etkili olmuş ve yoğunluk açı arttıkça üstel olarak azalmıştır, bu da onu parçacık boyutunu belirlemede kullanışlı bir yöntem haline getirmiştir. Bu karşılaştırma, her bir modelin açısal bağımlılıklarını ve uygulama alanlarını vurgulamıştır. Mie saçılması büyük parçacıklar için, Debye saçılması polimer zincirleri için, Rayleigh saçılması küçük parçacıklar için ve Guinier yaklaşımı düşük açılarda parçacık boyutunu ve jirasyon yarıçapını belirlemek için en uygun bulunmuştur. Bu çalışma, polimer çözeltilerinin saçılma davranışını anlamada bu modellerin güçlü ve zayıf yönlerini ortaya koymaktadır.

Anahtar Kelimeler

Debye modeli, Guinier modeli, Mie modeli, Polimer çözeltileri, Statik ışık saçılması

A Simulation-Based Study of Static Light Scattering in Polymer Solutions: Exploring Rayleigh, Mie, Debye, and Guinier Models

Öz

This study investigated the scattering behavior of polymer particles in a solvent using a simulation-based approach. A laser source with a wavelength of 635 nm was employed, and scattering angles were calculated within the range of 0° to 175°. The refractive indices of the solvent and polymer particles were set to 1.33 (typical for water) and 1.59 (commonly observed for polymers), respectively. The radius of gyration, estimated from the hydrodynamic diameter, was taken as 58.5 nm. Four models—Rayleigh, Mie, Debye, and Guinier—were applied to analyze the scattering behavior. Rayleigh scattering, valid for small particles, started with a lower intensity at 0° and decreased with increasing angle up to 100°, after which it symmetrically increased at higher angles. Mie scattering, suitable for larger particles, exhibited the highest intensity at 0° and sharply decreased as the angle increased. Debye scattering began with a normalized intensity of 1.0 and decreased smoothly with angle, demonstrating its effectiveness in analyzing the random coil structure of polymer chains. On the other hand, the Guinier approximation was most effective at low angles, where the intensity decreased exponentially with increasing angle, making it a useful method for determining particle size. This comparison highlighted the angular dependencies and application areas of each model. Mie scattering was found to be most appropriate for large particles, Debye scattering for polymer chains, Rayleigh scattering for small particles, and the Guinier approximation for determining particle size and radius of gyration at low angles. This study underscores the strengths and limitations of these models in understanding the scattering behavior of polymer solutions.

Anahtar Kelimeler

Debye model, Guinier model, Mie model, Polymer solutions, Rayleigh model, Static light scattering

Kaynakça

• Balderas-Cabrera, C. and Castillo, R. 2024. Mie scattering theory applied to light scattering of large nonhomogeneous colloidal spheres. The Journal of Chemical Physics, 161(8), 084903.
• Bunge, C. A., Kruglov, R. and Poisel, H. 2006. Rayleigh and Mie scattering in polymer optical fibers. Journal of lightwave technology, 24(8), 3137-3146.
• Cheong, S. W. and Woon, K. L. 2011. Modeling of light extraction efficiency of scattering thin film using Mie scattering. Optica Applicata, 41(1), 217-223.
• Findik, F. 2025. Polymeric materials and their applications. Sustainable Engineering and Innovation, 7(1), 15-40.
• Fischer, B. and Abetz, V. 2018. Determination of thermodynamic and structural quantities of polymers by scattering techniques. Pure and Applied Chemistry, 90(6), 955-968.
• Hammouda, B. 2010. A new Guinier–Porod model. Applied Crystallography, 43(4), 716-719.
• He, G. S., Qin, H. Y. and Zheng, Q. 2009. Rayleigh, Mie and Tyndall scatterings of polystyrene microspheres in water: Wavelength, size, and angle dependences. Journal of Applied Physics, 105(2).
• Horvath, H. 2009. Gustav Mie and the scattering and absorption of light by particles: Historical developments and basics. Journal of Quantitative Spectroscopy and Radiative Transfer, 110(11), 787-799.
• Hsissou, R. 2021. Review on epoxy polymers and its composites as potential anticorrosive coatings for carbon steel in 3.5% NaCl solution: Computational approaches. Journal of molecular liquids, 336, 116307.
• Jonasz, M. and Fournier, G. 2011. Light scattering by particles in water: theoretical and experimental foundations. Elsevier.
• Jones, A. R. 1999. Light scattering for particle characterization. Progress in Energy and Combustion Science, 25(1), 1-53.
• Ma, C., Tang, Z., Zhang, J. and Ye, Q. 2007. Monte Carlo simulation of light multiple scattering in polymers. Chinese Journal of Computational Physics, 24(4), 457.
• Mansuri, S. S., Patil, H. S., Nunse, D. K., Jumde, S. M., Gupta, P. R., Talele, S. G. and Borse, L. B. 2025. Polymer and Plastic Fundamentals and Its Connecting with Current Environmental, Biomedical, and Pharmaceutical Engineering. In Sustainability in Polymer Technology and Plastic Engineering (pp. 117-255). Apple Academic Press.
• Marangoni, A. G. and Pensini, E. 2025. Practical analysis of diffuse scattering patterns of inhomogeneous liquids. Physics of Fluids, 37(3).
• Matson, J. B., Steele, A. Q., Mase, J. D. and Schulz, M. D. 2024. Polymer characterization by size-exclusion chromatography with multi-angle light scattering (SEC-MALS): a tutorial review. Polymer Chemistry, 15(3), 127-142.
• Miles, R. B., Lempert, W. R. and Forkey, J. N. 2001. Laser Rayleigh scattering. Measurement Science and Technology, 12(5), R33.
• Minton, A. P. 2016. Recent applications of light scattering measurement in the biological and biopharmaceutical sciences. Analytical Biochemistry, 501, 4-22.
• Molnár, J., Sepsi, Ö., Erdei, G., Lenk, S., Ujhelyi, F. and Menyhárd, A. 2020. Modeling of light scattering and haze in semicrystalline polymers. Journal of Polymer Science, 58(13), 1787-1795.
• Scardi, P., Billinge, S. J., Neder, R. and Cervellino, A. 2016. Celebrating 100 years of the Debye scattering equation. Foundations of Crystallography, 72(6), 589-590.
• Schärtl, W. 2007. Light scattering from polymer solutions and nanoparticle dispersions. Springer Science and Business Media.
• Schure, M. R. and Palkar, S. A. 2002. Accuracy estimation of multiangle light scattering detectors utilized for polydisperse particle characterization with field-flow fractionation techniques: a simulation study. Analytical chemistry, 74(3), 684-695.
• Shen, J. and Wang, H. 2010. Calculation of Debye series expansion of light scattering. Applied Optics, 49(13), 2422-2428.
• Su, G., Guan, M. and Su, M. 2025. Laser diffraction modeling based on laser and particle behaviour statistics for particle size characterization. Journal of Quantitative Spectroscopy and Radiative Transfer, 109381.
• Svaneborg, C. and Pedersen, J. S. 2004. Monte Carlo simulations and analysis of scattering from neutral and polyelectrolyte polymer and polymer-like systems. Current Opinion in Colloid and Interface Science, 8(6), 507-514.
• Tacx, J. C. and Iedema, P. D. 2017. Simulating light scattering behavior of branched molecules. Macromolecular Theory and Simulations, 26(6), 1700058.
• Takahashi, K. 2020. Advanced reference materials for the characterization of molecular size and weight. Journal of Physics: Materials, 3(4), 042002.
• Thakkar, A. and Bhattacharya, S. 2025. Advancing Structure-Property Insights of Poly (Lactic-co-Glycolic Acids): A Mini Review on the Biodegradable Polymers Applications in Drug Delivery. Journal of Macromolecular Science, Part B, 1-15.
• Wei, Y. and Hore, M. J. 2021. Characterizing polymer structure with small-angle neutron scattering: A Tutorial. Journal of Applied Physics, 129(17).
• Wieder, T. and Fuess, H. 1997. A generalized Debye scattering equation. Zeitschrift für Naturforschung A, 52(5), 386-392.
• Wolf, S. and Voshchinnikov, N. V. 2004. Mie scattering by ensembles of particles with very large size parameters. Computer Physics Communications, 162(2), 113-123.
• Wyatt, P. J. 1993. Light scattering and the absolute characterization of macromolecules. Analytica Chimica Acta, 272(1), 1-40.
• Xu, R. 2001. Particle characterization: light scattering methods (Vol. 13). Springer Science and Business Media.
• Zhang, H., Zhang, F. and Yuan, R. 2020. Applications of natural polymer-based hydrogels in the food industry. In Hydrogels based on natural polymers (pp. 357-410). Elsevier.
• Zheng, W. and Best, R. B. 2018. An extended Guinier analysis for intrinsically disordered proteins. Journal of Molecular Biology, 430(16), 2540-2553.