Percolation Threshold and Luminescence in Films of Binary Mixtures of Spherical Particles Covered with Quantum Dots

  • N. V. Bondar Institute of Physics, Nat. Acad. of Sci. of Ukraine
  • M. S. Brodyn Institute of Physics, Nat. Acad. of Sci. of Ukraine
  • N. A. Matveevska Institute for Single Crystals, Nat. Acad. of Sci. of Ukraine
  • T. Beynik Institute for Single Crystals, Nat. Acad. of Sci. of Ukraine
Keywords: quantum dots, films, luminescence


The results of experimental studies of films fabricated on the basis of binary mixtures consisting of bare submicron silica particles (SPs) and silica particles covered with CdS quantum dots (NPs) are reported. The performed analysis concerns various coverage degrees and various SP-to-NP concentration ratios. By analyzing the sedimentation time and the absorption and luminescence spectra of the NP and SP aqueous suspensions and their mixtures, two exciton percolation thresholds are revealed: quasi-two-dimensional (2D) and bulk (3D) ones. The former arises in an ensemble of CdS quantum dots on the SiO2 surface at a critical coverage value, when the wave function of excitons spans over the whole surface of NPs. The latter occurs in the binary-film plane at the critical concentration of NPs in the binary mixture. The phase transition is found to take place only if the system is above the both thresholds, which is confirmed by the optical spectra of the specimens.


D. Stauffer, A. Aharony. Introduction to Percolation Theory (Taylor and Francis, 1992) [ISBN: 0748400273].

N. Johner, C. Grimaldi, I. Balberg, P. Ryser. Transport exponent in a three-dimensional continuum tunnelingpercolation model. Phys. Rev. B 77, 174204 (2008).

I. Balberg, J. Jedrzejewski, E. Savir. Electrical transport in three-dimensional ensembles of silicon quantum dots. Phys. Rev. B 83, 035318 (2011).

I. Balberg. Electrical transport mechanisms in threedimensional ensembles of silicon quantum dots. J. Appl. Phys. 110, 061301 (2011).

A. Coniglio, U. De Angelis, A. Forlani, G. Lauro. Distribution of physical clusters. J. Phys. A 10, 219 (1977).

A. Coniglio, U. De Angelis, A. Forlani. Pair connectedness and cluster size. J. Phys A 10, 1123 (1977).

G.H. Wu, Y.C. Chiew. Selective particle clustering and percolation in binary mixtures of randomly centered spheres. J. Chem. Phys. 90, 5024 (1989).

E. Dickinson. Simple statistical thermodynamic model of the heteroaggregation and gelation of dispersions and emulsions. J. Colloid Interf. Sci. 356, 196 (2011).

Y.C. Chiew, E.D. Glandt. Percolation behaviour of permeable and of adhesive spheres. J. Phys. A 16, 2599 (1983).

N. Seaton, E.D. Glandt. Aggregation and percolation in a system of adhesive spheres. J. Chem. Phys. 86, 4668 (1987).

J. Wang, I.L. McLaughlin, M. Silber. Percolation in binary mixtures with strong attraction between unlike particles. J. Phys.: Condens. Matter 3, 5603 (1991).

Y.C. Chiew, G. Stell, E.D. Gland. Clustering and percolation in multicomponent systems of randomly centered and permeable spheres. J. Chem Phys. 83, 761 (1985).

A.L.R. Bug, S.A. Safran, G.S Grest, I. Webman. Do interactions raise or lower a percolation threshold? Phys. Rev. Lett. 55, 1896 (1985).

K.S. Deepa, S.K. Nisha, P. Parameswaran, M.S. Sebastian, J. James. Effect of conductivity of filler on the percolation threshold of composites. Appl. Phys. Lett. 94, 142902 (2009).

B. Nettelblad, E. M˚artensson, C. Onneby, U. G¨afvert, ¨ A. Gustafsson. Two percolation thresholds due to geometrical effects: experimental and simulated results. J. Phys. D 36, 399 (2003).

H.E. Roman. A continuum percolation model for dispersed ionic conductors. J. Phys.: Condens. Matter 2, 3909 (1990).

E. Roman, A. Bunde, W. Dieterich. Conductivity of dispersed ionic conductors: A percolation model with two critical points. Phys. Rev. B 34, 3439 (1986).

N.V. Bondar, M.S. Brodin, N.A. Matveevskaya. Photoluminescence and exciton confinement in porous disordered films. Fiz. Tekh. Poluprovodn. 50, 369 (2016) (in Russian).

N.V. Bondar, M.S. Brodyn. Spectroscopy of semiconductor quantum dots. Physica E 42, 1549 (2010).

N.V. Bondar, M.S. Brodin, N.A. Matveevskaya. Quantumsize effect and exciton percolation in porous and disordered films on the basis of spherical "core/shell" elements. Ukr. Fiz. Zh. 60, 649 (2015) (in Ukrainian).

Z. Adamczyk. Particles at Interfaces: Interactions, Deposition, Structure (Academic Press, 2006) [ISBN: 9780123705419].

M. Alonso, M. Satoh, K. Miyanami. The effect of random positioning on the packing of particles adhering to the surface of a central particle. Powder Technol. 62, 35 (1990).

D. Scott, Ch.A. Tout. Nearest neighbour analysis of random distributions on a sphere. Mon. Not. R. Astron. Soc. 241, 109 (1989).

R. Hogg. Collision efficiency factors for polymer flocculation. J. Colloid Interf. Sci. 102, 232 (1984).

D. Bouvard, F.F. Lange. Relation between percolation and particle coordination in binary powder mixtures. Acta Metal. Mater. 39, 3083 (1991).

R.M. German. Coordination number changes during powder densification. Powder Tech. 253, 368 (2003).

C.L. Feng, A.B. Yu. Quantification of the relationship between porosity and interparticle forces for the packing of wet uniform spheres. J. Colloid Interf. Sci. 231, 136 (2000).

Semiconductor Nanocrystals: From Basic Principles to Applications, edited by A.L. Efros, D.L. Lockwood, L. Tsybeskov (Springer, 2003) [ISBN: 978-1441934024].

K.S. Deepa, M.T. Sebastian, J. James. Effect of interparticle distance and interfacial area on the properties of insulator-conductor composites. Appl. Phys. Lett. 91, 202904 (2007).

A. Oleinikova, N. Smolin, I. Brovchenko, A. Geiger, R. Winter. Formation of spanning water networks on protein surfaces via 2D percolation transition. J. Phys. Chem. B 109, 1988 (2005).

How to Cite
Bondar, N., Brodyn, M., Matveevska, N., & Beynik, T. (2018). Percolation Threshold and Luminescence in Films of Binary Mixtures of Spherical Particles Covered with Quantum Dots. Ukrainian Journal of Physics, 62(10), 874.
Solid matter