The Prefactor of Fractal Aggregates

Area of Science:

• Physical Chemistry
• Materials Science
• Complex Systems

Background:

• Fractal aggregates are ubiquitous in nature and technology.
• Understanding their scaling relationships is crucial for predicting material properties.
• Diffusion Limited Aggregation (DLA) and Diffusion Limited Cluster Aggregation (DLCA) are key models for fractal growth.

Purpose of the Study:

• To determine the prefactor k0 in the fractal aggregate scaling relationship N = k0(Rg/a)Df.
• To investigate the behavior of k0 across various spatial dimensions (2, 3, 4, and 5).
• To analyze the relationship between k0 and the fractal dimension Df for different aggregation processes.

Main Methods:

• Simulations of DLA and DLCA processes in 2D, 3D, 4D, and 5D.
• Analysis of the scaling relationship N = k0(Rg/a)Df to extract k0 and Df.
• Statistical analysis to determine uncertainties in k0 and Df values.

Main Results:

• The prefactor k0 was determined for DLA and DLCA in dimensions 2 through 5.
• For 3D DLCA aggregates, k0 = 1.19 ± 0.1 with Df = 1.82 ± 0.04.
• A uniform trend was observed between the prefactor k0 and the fractal dimension Df across all aggregation types and dimensions.

Conclusions:

• The prefactor k0 exhibits consistent behavior with the fractal dimension Df, irrespective of the aggregation mechanism or spatial dimension.
• These findings support theoretical models attempting to explain k0 trends based on small N limits or sphere packing.
• The study provides valuable quantitative data for fractal aggregate modeling and applications.