Fotoenergetikada nanostrukturali yarimo‘tkazgich materiallar II xalqaro ilmiy anjumani

QUANTUM-SIZE EFFECTS IN POLYMER COMPOSITE
MATERIALS CONTAINING METAL NANOPARTICLES 
 
A.V. Umarov
1
., I. Balberg
2
., U. Abdurakhmanov
3
,
A.G. Daminov
2 
, D. Saidkulov
3

Tashkent state transport university
1
, Tashkent, Uzbekistan 
Racah Institute of Physics
2
, Jerusalem, Israel, 
National university of Uzbekistan named after Ulugbek 
3
, Tashkent, Uzbekistan 
E-mail: [e-mail] 
The interest in nanomaterials is explained by the fact that a decrease in the 
size of fillers in composite materials to nanometer sizes leads to the manifestation 
of so-called “quantum size effects” in them, when the sizes of fillers are 
comparable to the de Broglie wavelength of electrons, phonons and excitons. One 
of the main reasons for the change in the physical and chemical properties of small 
particles as their size decreases is an increase in the relative fraction of "surface" 
atoms in other conditions (coordination number, symmetry of the local 

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Fotoenergetikada nanostrukturali yarimo‘tkazgich materiallar

II xalqaro ilmiy anjumani 
 
19-20 noyabr 2021 yil 
51 
environment, etc.) than atoms inside the bulk phase. From the energetic point of 
view, a decrease in the particle size leads to an increase in the role of surface 
energy. In other words, only the "inner" atoms will form a continuous energy zone, 
while the energy levels of the outer (surface) atoms will be discrete and clearly 
expressed. This is one of the main provisions of the theory of dimensional 
quantization. This effect is most pronounced for semiconductor nanoparticles with 
a large exciton radius. 
Therefore, the development of composite ceramic and polymer materials 
containing metal nanoparticles or semiconductor nanoparticles, the study of their 
electrical and optical properties is very important. 
By the method of thermal decomposition of metal formate, composite 
materials were obtained, which are metal-containing nanoparticles stabilized in the 
bulk of matrices of ceramics and polymers, and the dependences of their electrical 
conductivity (σ) and dielectric constant (ε) on the volume content of metal 
nanoparticles (V) were investigated [1-5]. 
It was found that the percolation-like behavior of σ and ε, which is observed 
when metal particles have a size of 1-3 μm (fine particles), is replaced by another 
behavior characterized by an additional contribution to σ and ε below the 
percolation threshold, when the Ni particles have a size of ≤ 10 nm (nanoparticles). 
It is shown that this feature of the behavior of σ and ε in the indicated composites 
is consistent with the spatial-structural hierarchical model of composites proposed 
by Balberg et al. [6] 
As shown in [6], in composites in which the contribution to the electrical 
conductivity from the tunneling of charge carriers between neighboring particles is 
observed, there are two percolation thresholds. One of them is observed at high V 
values; it is the percolation threshold Vc determined above. Another threshold 
(additional percolation Vcd) is observed at low V values; it is the critical fractional 
volume of metal particles that initiates the first infinite cluster of tunnel-coupled 
conductors. For the studied composites containing nickel nanoparticles, the 
percolation tunneling process is the reason for the “low” percolation threshold 
Vcd, which determines the behavior of electrical conductivity and dielectric 
constant in the region below the classical percolation threshold [1,3]. 
The temperature dependence of σ for the composites under study has a 
semiconductor character. In order to understand the nature of the temperature 
dependence of electrical conductivity in such systems, one should study their 
structure. From a physical point of view, the formation of the studied composites 
containing metal nanoparticles can be considered as a consequence of the doping 
of the initial dielectric with metal nanoparticles, similar to doped compensated 
semiconductors. This means that electronic states appear in the band gap of the 
initial ceramic and polymer, similar to impurity levels. An increase in the volume 
content of metal nanoparticles affects not only the concentration, but also their size 
distribution. If this representation is correct, then the conduction mechanism in 

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