Theoretical Model for Ostwald Ripening of Nanoparticles with Size-Linear Capture Coefficients.

Area of Science:

• Materials Science
• Physical Chemistry
• Nanotechnology

Background:

• Ostwald ripening is a well-studied phenomenon in 3D and 2D systems, crucial for surface nanoisland and nanodroplet evolution.
• Typically, adatom capture coefficients for nanoparticles scale with size 's' as sα, with α < 1.

Purpose of the Study:

• To theoretically investigate Ostwald ripening in nanoparticles where capture coefficients scale linearly with size (α=1).
• To analyze the resulting size distributions and their scaling properties, particularly after material influx cessation.

Main Methods:

• Development of a theoretical model for Ostwald ripening with linear scaling capture coefficients.
• Derivation of analytical solutions for nanoparticle size distributions using Lifshitz-Slezov scaled variables.
• Application of the Family-Vicsek scaling hypothesis.

Main Results:

• Obtained analytical solutions for size (s) and radius (R) distributions, showing they are monotonically decreasing.
• Confirmed that these distributions satisfy normalization conditions for various Lifshitz-Slezov constants.
• Demonstrated adherence to the Family-Vicsek scaling hypothesis even without material influx.

Conclusions:

• The linear scaling model provides a valid framework for understanding Ostwald ripening under specific conditions.
• The derived monotonically decreasing size distributions accurately model experimental data, as shown with gold nanoparticles used in nanowire catalysis.