Smoluchowski equations for linker-mediated irreversible aggregation.

Area of Science:

• Physical Chemistry
• Materials Science
• Chemical Engineering

Background:

• Aggregation phenomena are crucial in various scientific fields.
• Understanding linker-mediated aggregation requires explicit consideration of both particles and linkers.
• Existing models often simplify the complex interactions involved.

Purpose of the Study:

• To develop a generalized Smoluchowski framework for studying linker-mediated aggregation.
• To explicitly account for particles, linkers, and their interactions.
• To identify key tunable parameters governing aggregation dynamics.

Main Methods:

• Developed a generalized Smoluchowski framework with irreversible bonds and limited diffusion aggregation.
• Utilized a kernel analogous to single-component diffusive aggregation.
• Employed a scaling hypothesis for analytical solutions of Smoluchowski equations.
• Performed numerical simulations of a lattice model to validate the hypothesis.

Main Results:

• Identified three experimentally tunable factors influencing aggregation dynamics: diffusion coefficient ratio, relative particle-linker numbers, and linker-particle bonding capacity.
• The scaling hypothesis simplifies cluster site availability.
• Obtained results for asymptotic limits, bonding probabilities, and cluster size distribution.

Conclusions:

• The developed framework accurately models linker-mediated aggregation.
• Findings are consistent with existing experimental results.
• The study provides insights into previously unexplained experimental observations in aggregation science.