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

Szabó, Rebeka; Lente, Gábor

doi:10.1007/s10910-018-0975-5

Cited by 14 publications

(29 citation statements)

References 32 publications

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“…As in our initial study [25], it is useful to introduce dimensionless (or scaled) physical properties to simplify the differential equation somewhat. This process does not limit the general nature of the results obtained in any way.…”

Section: Resultsmentioning

confidence: 99%

“…The case n = 2 here bears some special practical relevance [4,5,17]. In our previous publication that was solely dedicated to this particular system [25], lengthy derivations were developed to show that the analytical solution is: For higher values of n, the successive solution procedure could not even be started as no explicit formulas were gained for c n at n ≥ 3.…”

Section: Resultsmentioning

confidence: 99%

“…Particle size average and distribution in the final state In experimental studies of nanoparticle formation, the average particle size is the most common property that is used to characterize the process. As shown previously [25], the average number of monomeric units (N) in the nanoparticles formed can be simply calculated as the ration of the first and the zeroth moments:…”

Section: Resultsmentioning

confidence: 99%

“…In our previous article [25], we showed that the analytical solution of a non-lumped kinetic model is still possible despite the fact that it has an infinite number of concentration variables. The model itself was based on pervious experimental results and theoretical considerations [4,5,[26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

“…This paper will first state a general nucleation-growth type kinetic model, than identify the cases in which finding a symbolic solution is feasible. In two cases in addition to the one already known [25], the full solution is presented. In a number of other cases, some partial solutions are available.…”

Section: Introductionmentioning

confidence: 99%

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General nucleation-growth type kinetic models of nanoparticle formation: possibilities of finding analytical solutions

Szabó

Lente

2021

J Math Chem

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In this work, analytical solutions for the time dependences for the concentration of each chemical species are determined in a class of nucleation-growth type kinetic models of nanoparticle formation. These models have an infinitely large number of dependent variables and describe the studied process without approximations. Symbolic solutions are found for the mass kernel (where reactivity is directly proportional to the mass of a nanoparticle) and the diffusion kernel (where reactivity is independent of the size of the nanoparticle). The results show that the average particle size is primarily determined by the type of the kernel function and the ratio of the rate constants of spontaneous nucleation and particle growth. The final distribution of nanoparticle sizes is a continuously decreasing function in each studied case. Furthermore, the time dependences of the concentrations of monomeric units show the induction behavior that has already been observed in many experimental studies.

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Section: Resultsmentioning

confidence: 99%