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Simulation of Batch Nanoparticle Growth by the Generalized Diffusional Model

Wen, Tianlong, Zhang, Xiaochen, Zhang, Dainan, Zhang, Chong, Wen, Qiye, Zhang, Huaiwu, Zhong, Zhiyong
Journal of physical chemistry 2018 v.122 no.47 pp. 27070-27081
Ostwald ripening, adsorption, diffusivity, equations, models, nanoparticles, variance
Diffusional growth in solution is the most efficient method to grow monodisperse colloidal nanoparticles. Instead of calculating for a single nanoparticle, here the growth of an ensemble of nanoparticles has been numerically simulated by the generalized growth rate of nanoparticles, which has been deduced in our previous work from the very fundamental laws and equations. By doing that, the dynamic interaction among nanoparticles through monomer attachment and detachment can be clearly revealed. The constant and diminishing monomer concentrations have been simulated separately and compared together. The simulations give the growth dynamics of batch nanoparticles across a broad range of conditions, where diffusivity, adsorption, and concentration of monomers play a significant role. The relations between the average radius and time, the variance and time, and the variance and average radius have been obtained for different growth conditions. The average radius–time curve can be well-fitted to E[R] = E[R₀] + αtⁿ and E[R] = E[R₀] + (RS – E[R₀])Langevin(βt) for constant and diminishing monomer concentrations, respectively. By simulation, many hidden details about diffusional growth have been unveiled, such as the details of Ostwald ripening and the role of monomer concentration.