Small-Angle Scattering from Weakly Correlated Nanoscale Mass Fractal Aggregates
Abstract
:1. Introduction
2. Theoretical Background
3. Results and Discussion
3.1. A Unified Guinier–Porod Model with Spherical Correlations
3.2. Application to DLA Fractals
4. Conclusions
Funding
Conflicts of Interest
References
- Bica, I.; Anitas, E.M. Magnetodielectric effects in membranes based on magnetorheological bio-suspensions. Mater. Des. 2018, 155, 317–324. [Google Scholar] [CrossRef]
- Andrzejewski, J.; Przyszczypkowski, P.; Szostak, M. Development and characterization of poly(ethylene terephthalate) based injection molded self-reinforced composites. Direct reinforcement by overmolding the composite inserts. Mater. Des. 2018, 153, 273–286. [Google Scholar] [CrossRef]
- Ramírez-Herrera, C.A.; Gonzalez, H.; Torre, F.d.l.; Benitez, L.; Cabañas-Moreno, J.G.; Lozano, K. Electrical Properties and Electromagnetic Interference Shielding Effectiveness of Interlayered Systems Composed by Carbon Nanotube Filled Carbon Nanofiber Mats and Polymer Composites. Nanomaterials 2019, 9, 238. [Google Scholar] [CrossRef] [PubMed]
- Vedrtnam, A. Novel method for improving fatigue behavior of carbon fiber reinforced epoxy composite. Compos. Part B Eng. 2019, 157, 305–321. [Google Scholar] [CrossRef]
- Bica, I.; Anitas, E.M. Magnetic flux density effect on electrical properties and visco-elastic state of magnetoactive tissues. Compos. Part B Eng. 2019, 159, 13–19. [Google Scholar] [CrossRef]
- Bica, I.; Anitas, E.; Averis, L. Tensions and deformations in composites based on polyurethane elastomer and magnetorheological suspension: Effects of the magnetic field. J. Ind. Eng. Chem. 2015, 28, 86–90. [Google Scholar] [CrossRef]
- Bica, I.; Anitas, E.M. Magnetic field intensity and graphene concentration effects on electrical and rheological properties of MREs-based membranes. Smart Mater. Struct. 2017, 26, 105038. [Google Scholar] [CrossRef]
- Bica, I.; Anitas, E.M.; Lu, Q.; Choi, H.J. Effect of magnetic field intensity and γ-Fe2O3 nanoparticle additive on electrical conductivity and viscosity of magnetorheological carbonyl iron suspension-based membranes. Smart Mater. Struct. 2018, 27, 095021. [Google Scholar] [CrossRef]
- Bica, I.; Anitas, E. Magnetic field intensity and γ-Fe2O3 concentration effects on the dielectric properties of magnetodielectric tissues. Mat. Sci. Eng. B 2018, 236–237, 125–131. [Google Scholar] [CrossRef]
- Naskar, A.K.; Keum, J.K.; Boeman, R.G. Polymer matrix nanocomposites for automotive structural components. Nat. Nanotechnol. 2016, 11, 1026–1030. [Google Scholar] [CrossRef] [PubMed]
- Pitchan, M.K.; Bhowmik, S.; Balachandran, M.; Abraham, M. Process optimization of functionalized MWCNT/polyetherimide nanocomposites for aerospace application. Mater. Des. 2017, 127, 193–203. [Google Scholar] [CrossRef]
- Calisi, N.; Salvo, P.; Melai, B.; Paoletti, C.; Pucci, A.; Di Francesco, F. Effects of thermal annealing on SEBS/MWCNTs temperature-sensitive nanocomposites for the measurement of skin temperature. Mater. Chem. Phys. 2017, 186, 456–461. [Google Scholar] [CrossRef]
- Borenstein, A.; Hanna, O.; Attias, R.; Luski, S.; Brousse, T.; Aurbach, D. Carbon-based composite materials for supercapacitor electrodes: A review. J. Mater. Chem. A 2017, 5, 12653–12672. [Google Scholar] [CrossRef]
- Ramesh, M. Flax (Linum usitatissimum L.) fibre reinforced polymer composite materials: A review on preparation, properties and prospects. Prog. Mater. Sci. 2019, 102, 109–166. [Google Scholar] [CrossRef]
- Zhang, M.Q.; Rong, M.Z.; Yu, S.L.; Wetzel, B.; Friedrich, K. Improvement of Tribological Performance of Epoxy by the Addition of Irradiation Grafted Nano-Inorganic Particles. Macromol. Mat. Eng. 2002, 287, 111–115. [Google Scholar] [CrossRef]
- Huang, Y.Y.; Terentjev, E.M. Dispersion of Carbon Nanotubes: Mixing, Sonication, Stabilization, and Composite Properties. Polymers 2012, 4, 275–295. [Google Scholar] [CrossRef]
- Garusinghe, U.M.; Raghuwanshi, V.S.; Batchelor, W.; Garnier, G. Water Resistant Cellulose—Titanium Dioxide Composites for Photocatalysis. Sci. Rep. 2018, 8, 2306. [Google Scholar] [CrossRef] [PubMed]
- Tancredi, P.; Moscoso Londoño, O.; Rivas Rojas, P.C.; Knobel, M.; Socolovsky, L.M. Step-by-step synthesis of iron-oxide nanoparticles attached to graphene oxide: A study on the composite properties and architecture. Mater. Res. Bull. 2018, 107, 255–263. [Google Scholar] [CrossRef]
- Mandelbrot, B.B. The Fractal Geometry of Nature; W.H. Freeman: New York, NY, USA, 1982; p. 460. [Google Scholar]
- Feigin, L.A.; Svergun, D.I. Structure Analysis by Small-Angle X-ray and Neutron Scattering; Springer: Boston, MA, USA, 1987; p. 335. [Google Scholar]
- Gille, W. Particle and Particle Systems Characterization: Small-Angle Scattering (SAS) Applications, 1st ed.; CRC Press: Boca Raton, FL, USA, 2013; p. 336. [Google Scholar]
- Hammouda, B. A new Guinier–Porod model. J. Appl. Cryst. 2010, 43, 716–719. [Google Scholar] [CrossRef]
- Schaefer, D.W.; Justice, R.S. How Nano Are Nanocomposites? Macromolecules 2007, 40, 8501–8517. [Google Scholar] [CrossRef]
- Teixeira, J. Small-angle scattering by fractal systems. J. Appl. Cryst. 1988, 21, 781–785. [Google Scholar] [CrossRef]
- Martin, J.E.; Hurd, A.J. Scattering from fractals. J. Appl. Cryst. 1987, 20, 61–78. [Google Scholar] [CrossRef]
- Schmidt, P.W. Small-angle scattering studies of disordered, porous and fractal systems. J. Appl. Cryst. 1991, 24, 414–435. [Google Scholar] [CrossRef]
- Beaucage, G. Approximations Leading to a Unified Exponential/Power-Law Approach to Small-Angle Scattering. J. Appl. Cryst. 1995, 28, 717–728. [Google Scholar] [CrossRef]
- Beaucage, G. Small-Angle Scattering from Polymeric Mass Fractals of Arbitrary Mass-Fractal Dimension. J. Appl. Cryst. 1996, 29, 134–146. [Google Scholar] [CrossRef]
- Beaucage, G.; Schaefer, D.W. Structural studies of complex systems using small-angle scattering: A unified Guinier/power-law approach. J. Non-Cryst. Sol. 1994, 172, 805. [Google Scholar] [CrossRef]
- Guinier, A.; Fournet, G. Small-Angle Scattering of X-rays; John Wiley & Sons, Inc.: New York, NY, USA, 1955; p. 56. [Google Scholar]
- Hammouda, B. Analysis of the Beaucage model. J. Appl. Cryst. 2010, 43, 1474–1478. [Google Scholar] [CrossRef]
- Seager, C.R.; Mason, T.G. Slippery diffusion-limited aggregation. Phys. Rev. E 2007, 75, 011406. [Google Scholar] [CrossRef]
- Anitas, E.M. Microscale Fragmentation and Small-Angle Scattering from Mass Fractals. Adv. Cond. Matter Phys. 2015, 2015, 501281. [Google Scholar] [CrossRef]
- Hammouda, B. Probing Nanoscale Structures—The SANS Toolbox; NIST: Gaithersburg, MD, USA, 2016; p. 332.
- Liu, Y.L.; Hsu, C.Y.; Wei, W.L.; Jeng, R.J. Preparation and thermal properties of epoxy-silica nanocomposites from nanoscale colloidal silica. Polymer 2003, 44, 5159–5167. [Google Scholar] [CrossRef]
- Zhang, H.; Tang, L.C.; Zhang, Z.; Friedrich, K.; Sprenger, S. Fracture behaviours of in situ silica nanoparticle-filled epoxy at different temperatures. Polymer 2008, 49, 3816–3825. [Google Scholar] [CrossRef]
© 2019 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Mircea Anitas, E. Small-Angle Scattering from Weakly Correlated Nanoscale Mass Fractal Aggregates. Nanomaterials 2019, 9, 648. https://doi.org/10.3390/nano9040648
Mircea Anitas E. Small-Angle Scattering from Weakly Correlated Nanoscale Mass Fractal Aggregates. Nanomaterials. 2019; 9(4):648. https://doi.org/10.3390/nano9040648
Chicago/Turabian StyleMircea Anitas, Eugen. 2019. "Small-Angle Scattering from Weakly Correlated Nanoscale Mass Fractal Aggregates" Nanomaterials 9, no. 4: 648. https://doi.org/10.3390/nano9040648