V. G. Dubrovskii, “Dispersion of scale-invariant size-distribution functions”, Pisma v Zhurnal Tekhnicheskoi Fiziki, 2017, Volume 43, Issue 9,Pages <nobr>3

Dispersion of scale-invariant size-distribution functions

V. G. Dubrovskii^abc

^a Federal State Budgetary Institution of Higher Education and Science Saint Petersburg National Research Academic University of the Russian Academy of Sciences, St. Petersburg
^b Ioffe Institute, St. Petersburg
^c St. Petersburg National Research University of Information Technologies, Mechanics and Optics

Abstract: It is shown that the size-distribution function of nanostructures, which obeys scale invariance (scaling), always displays a dispersion proportional to the square of the average size. Theoretical analysis is carried out for the shape and dispersion of a biparametric scale-invariant distribution describing the growth of homogeneous or heterogeneous nanoobjects with monomer capture rates proportional to their size. It is found that the Gaussian distribution is replaced by a broader and asymmetric distribution upon a decrease in the nucleation probability.

Received: 24.11.2016

DOI: 10.21883/PJTF.2017.09.44570.16584