2019/01/31 by C. Fanelli, Claudia Fanelli, Vincent Cregan +5
Chemistry · Earth and Planetary Sciences · Materials Science · Mathematics · Physics and Astronomy · #Applied mathematics #Biological system #Chemistry #Computer science #Gold and Silver Nanoparticles Synthesis and Applications #Materials science #Mathematics #Nanocrystal #Nanotechnology #Ostwald ripening #Particle (ecology) #Particle number #Particle size #Particle system #Physical chemistry #Physics #Precipitation #Process (computing) #Quantum Dots Synthesis And Properties #RADIUS #Range (aeronautics) #Simple (philosophy) #Statistical physics #Thermodynamics #cond-mat.mes-hall #nanoparticles nucleation surface interactions
paper · pdf · doi:10.1016/j.ijheatmasstransfer.2020.120643
published as International Journal of Heat and Mass Transfer, 165, 120643 (2021)
arxiv created 2019/02/15 · openalex created_date 2019/02/21 · openalex publication_date 2020/11/09 · arxiv updated 2020/11/17 · openalex updated_date 2026/08/05
A mathematical model to describe the growth of an arbitrarily large number of nanocrystals from solution is presented. First, the model for a single particle is developed. By non-dimensionalising the system we are able to determine the dominant terms and reduce it to the standard pseudo-steady approximation. The range of applicability and further reductions are discussed. An approximate analytical solution is also presented. The one particle model is then generalised to N well dispersed particles. By setting N=2 we are able to investigate in detail the process of Ostwald ripening. The various models, the N particle, single particle and the analytical solution are compared against experimental data, all showing excellent agreement. By allowing N to increase we show that the single particle model may be considered as representing the average radius of a system with a large number of particles. Following a similar argument the N=2 model could describe an initially bimodal distribution. The mathematical solution clearly shows the effect of problem parameters on the growth process and, significantly, that there is a single controlling group. The model provides a simple way to understand nanocrystal growth and hence to guide and optimise the process.