scholarly journals Reply to “A Comparison of the Stochastic and Deterministic Approaches in a Nucleation–Growth Type Model of Nanoparticle Formation”

2021 ◽  
Author(s):  
James D. Martin
Keyword(s):  
Type Model ◽  
Growth Type ◽  
Nanoparticle Formation ◽  
Nucleation Growth

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

2021 ◽  
Author(s):  
Rebeka Szabó ◽  
Gábor Lente
Keyword(s):  
Analytical Solutions ◽  
Kinetic Models ◽  
Average Particle Size ◽  
Experimental Studies ◽  
Chemical Species ◽  
Average Particle ◽  
Growth Type ◽  
Nanoparticle Formation ◽  
Spontaneous Nucleation ◽  
Nucleation Growth

AbstractIn 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.

scholarly journals Coarsening Process of Nucleation-Growth Type Phase-Separated Particles in Binary Germanate Glasses

1990 ◽  
Vol 31 (9) ◽  
pp. 766-771 ◽  
Author(s):  
Kunihiko Nakashima ◽  
Koichi Hayashi ◽  
Kenji Morinaga
Keyword(s):  
Growth Type ◽  
Type Phase ◽  
Germanate Glasses ◽  
Nucleation Growth

Flight Control of a Twin-Rotor Type Model Helicopter Based on First-Order Approximate Linearization

2014 ◽  
Vol 134 (9) ◽  
pp. 1269-1270 ◽  
Author(s):  
Hiroki Noma ◽  
Shun Tanabe ◽  
Takao Sato ◽  
Nozomu Araki ◽  
Yasuo Konishi
Keyword(s):  
Flight Control ◽  
Type Model ◽  
First Order ◽  
Model Helicopter ◽  
Approximate Linearization ◽  
Twin Rotor ◽  
Rotor Type

QUASI-ONE-DIMENSIONAL SEPARATION TYPE MODEL OF PSEUDO-SHOCK IN A DUCT

2013 ◽  
Vol 44 (5) ◽  
pp. 639-664 ◽  
Author(s):  
Evgeniy Aleksandrovich Meshcheryakov ◽  
Violetta Vasilievna Yashina
Keyword(s):  
Type Model ◽  
One Dimensional
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