Full analytical solution of a nucleation-growth type kinetic model of nanoparticle formation

Rebeka Szabó, G. Lente

Research output: Contribution to journalArticle

Abstract

The analytical solution of a specific kinetic model describing nanoparticle formation is presented. The model starts from a monomer unit, two of which combine in a slow second-order seed formation reaction. The other process is second-order particle growth between a particle and a monomer unit, the rate constant of which is proportional to the mass of the growing nanoparticle. Exact analytical solutions are derived for the time dependence of the concentrations of all different kinds of nanoparticles. The average number of monomer units, the average size and polydispersity is also given by exact formulas. It is shown that the final size distribution of nanoparticles is described by a monotonically decreasing function under all conditions. Possibilities for the comparison of these modeling results with actual experimental data are also considered.

Original languageEnglish
JournalJournal of Mathematical Chemistry
DOIs
Publication statusAccepted/In press - Jan 1 2018

Fingerprint

Kinetic Model
Nucleation
Nanoparticles
Analytical Solution
Kinetics
Monomers
Unit
Polydispersity
Time Dependence
Rate Constant
Seed
Rate constants
Directly proportional
Experimental Data
Modeling
Model

Keywords

  • Analytical solution
  • Kinetics
  • Moments
  • Nanoparticle growth

ASJC Scopus subject areas

  • Chemistry(all)
  • Applied Mathematics

Cite this

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AB - The analytical solution of a specific kinetic model describing nanoparticle formation is presented. The model starts from a monomer unit, two of which combine in a slow second-order seed formation reaction. The other process is second-order particle growth between a particle and a monomer unit, the rate constant of which is proportional to the mass of the growing nanoparticle. Exact analytical solutions are derived for the time dependence of the concentrations of all different kinds of nanoparticles. The average number of monomer units, the average size and polydispersity is also given by exact formulas. It is shown that the final size distribution of nanoparticles is described by a monotonically decreasing function under all conditions. Possibilities for the comparison of these modeling results with actual experimental data are also considered.

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