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51PH-O-1
Bruggeman approximation and nanostructures agglomeration two-scale model
V. Krasovskii1, L. Apresyan1, T. Vlasova1, S. Rasmagin1, V. Kryshtob1, V. Pustovoy1 1Prokhorov General physics institute, Russian Academy of Sciences, Laser physics, Moscow, Russian Federation
The Bruggemapn approximation [1], also known as the effective medium approximation (EMA), is one of the main heuristic approaches in the photonics of composite materials, making it possible to obtain reasonable estimates for various physical phenomena in randomly inhomogeneous systems without finding exact solutions to the problem (so-called homogenization theory [2]). An important advantage of this approximation is the possibility of describing the occurrence of a percolation threshold, which is absent when using simple forms of perturbation theory [3]. In the literature, several versions of generalizations of this approximation, initially describing isotropic inclusions, were proposed for the case of composites with anisotropic particles [4-6], in which ellipsoids appear instead of spherical particles. Each of them has its own expression for the percolation threshold, and the choice of the optimal model can be different for different specific tasks. When creating composite optical materials, the problem of uniform distribution of fillers in the matrix volume is essential. This problem is especially important in the case of nano-composites, since nanoparticles often have a pronounced tendency to agglomerate. This paper compares several forms of these generalizations of the EMA, after which one of them is used to construct a two-scale agglomeration model, similar to that proposed in [7]. In this model, the initial filler nanoparticles are divided into two parts: "free" and "agglomerated", i.e. clot-forming agglomerates. At the same time, to describe both agglomerates and "free" particles, the EMA approximation in the ellipsoid model is used twice, but with different depolarization tensors. As a result, it appears that agglomeration can both increase or decrease the percolation threshold as compared with the case of a completely homogeneous distribution of filler particles. This work was supported by Russan Foundation of Basic Research Grant No 18-02-00786 and Program of RAS presidium I.7P.
References
[1] D.A.G. Bruggema, Ann. Phys. (23) 636-664 (1935). DOI: 10.1002/andp.19354160705.
[2] L.A.Apresyan, Light & Engineering, 27 (1) 4-14 (2019). DOI: 10.33383/2018-094.
[3] Milton G.W. The Theory of Composites. Cambridge Univ. Press, 2004.
[4] Sihvola A. Electromagnetic Mixing Formulas and Applications, Electromagnetic Wave Series 47, London: IEE Publishing, 1999.
[5] T. W. Noh, P. H. Song, and A. J. Sievers, Phys. Rev. B (44) 5459 -5464 (1991). DOI: 10.1103/PhysRevB.44.5459.
[6] D. Stroud and A. Kazaryan, Phys. Rev. B (53) 7076 (1996). DOI: 10.1103/PhysRevB.53.7076.
[7] Y. Wang, J.W.Shan, G.J.Weng, J. Appl. Phys. (118) 065101 (2006). DOI: 10.1063/1.4928293.
