Predictive model for diffusion-limited aggregation kinetics of nanocolloids under high concentration

Area of Science:

• Colloid and Surface Science
• Chemical Engineering
• Materials Science

Background:

• Smoluchowski's equation is foundational for diffusion-limited aggregation kinetics but fails at high concentrations.
• Accurate modeling of concentrated colloidal systems is crucial for understanding gelation and material properties.

Purpose of the Study:

• To develop and validate a corrected aggregation kernel for Smoluchowski's equation applicable to concentrated colloidal suspensions.
• To investigate the concentration-dependent effects on diffusion-limited aggregation kinetics.

Main Methods:

• A corrected aggregation kernel was derived using Richards' trapping theory.
• The corrected kernel was implemented in a population-balance equations (PBE) model.
• PBE predictions were validated against Brownian dynamics (BD) simulations for particle volume fractions up to 30%.

Main Results:

• The corrected aggregation kernel accurately reproduced BD simulation results across all tested concentrations.
• The model successfully predicted the time to reach the gel point in concentrated suspensions.
• Classical Smoluchowski theory significantly underestimated aggregation rates and delayed gelation onset at higher concentrations.

Conclusions:

• The proposed corrected aggregation kernel effectively models diffusion-limited aggregation in concentrated colloidal systems.
• This approach provides a more accurate framework for predicting aggregation kinetics and gelation compared to classical theory.
• The findings have implications for controlling and understanding aggregation phenomena in various applications.