Diffusion-Limited Growth of a Spherical Nanocrystal in a Finite Space

Kinetic analysis of the growth behavior of perovskite CsPbBr3 nanocrystals in a microfluidic system

Understanding the growth behavior of nanoparticles and semiconductor nanocrystals under dynamic environments is of profound importance in controlling the sizes and uniformity of the prepared nanoparticles and semiconductor nanocrystals. In this work, we develop a relation between the bandgap (the photoluminescence peak wavelength) of semiconductor nanocrystals and the total flow rate for the synthesis of semiconductor nanocrystals in microfluidic systems under the framework of the quantum confinement effect without the contribution of Coulomb interaction. Using this relation, we analyze the growth behavior of CsPbBr₃ nanocrystals synthesized in a microfluidic system by an antisolvent method in the temperature range of 303 to 363 K. The results demonstrate that the square of the average size of the CsPbBr₃ nanocrystals is inversely proportional to the total flow rate and support the developed relation. The activation energy for the rate process controlling the growth of the CsPbBr₃ nanocrystals in the microfluidic system is 2.05 kJ mol^-1. Increasing the synthesis temperature widens the size distribution of the CsPbBr₃ NCs prepared in the microfluidic system. The method developed in this work provides a simple approach to use photoluminescent characteristics to in situ monitor and analyze the growth of semiconductor nanocrystals under dynamic environments.

Modeling analysis of the growth of a cubic crystal in a finite space

The applications of semiconductor nanocrystals in optoelectronics are based on the unique characteristic of quantum confinement. There is great interest to tailor the performance of optoelectronic nanodevices and systems through the control of the sizes of nanocrystals. In this work, we develop a general mathematical formulation for the growth of a crystal/particle in a liquid solution, which takes account of the combinational effect of diffusion-limited growth and reaction-limited growth, and formulate the growth equations for the size of a cubic crystal grown under three different scenarios - isothermal and isochoric conditions, isothermal growth with the evaporation and/or extraction of the solvent and isochoric growth with continuous change in temperature. For the growth of a cubic crystal under isothermal and isochoric conditions, there are three growth stages - linear growth, nonlinear growth and plateau, and the growth rate in the stage of linear growth and the final size of the cubic crystal are dependent on the degree of supersaturation. For the growth of multi-crystals with a Gaussian distribution of crystal sizes, the change of the monomer concentration in a liquid solution is dependent on the change rates of average size and the standard deviation of the crystal sizes.