Efficient approach to nucleation and growth dynamics: stationary diffusion flux model

Area of Science:

• Physics
• Physical Chemistry
• Materials Science

Background:

• Understanding cluster evolution is crucial for nucleation and growth phenomena.
• Existing models often face computational challenges or limitations in applicability.
• The induction time for cluster formation is a key factor in modeling dynamics.

Purpose of the Study:

• To propose a new, computationally efficient model for cluster evolution.
• To approximate the diffusion flux in the Fokker-Planck equation for improved modeling.
• To ensure the model's applicability across various cluster sizes and formation processes.

Main Methods:

• Developed a closed-form expression for diffusion flux by approximating the nonstationary Fokker-Planck equation.
• Utilized the steady-state solution of the Zeldovich-Frenkel equation for approximation.
• Validated the model against experimental data from a nucleation pulse experiment.

Main Results:

• The proposed stationary diffusion flux model is valid for all cluster sizes.
• The model demonstrates computational efficiency.
• Excellent agreement was observed between the model and the Becker-Döring equations for a nucleation pulse experiment.

Conclusions:

• The new model provides an accurate and efficient description of cluster evolution.
• The approximation is justified by the small induction time of cluster formation.
• The model is broadly applicable to diverse cluster formation processes.