Mass fractal dimension from 2D microscopy images via an aggregation model with variable compactness.

Area of Science:

• Colloid and Surface Science
• Materials Science
• Image Analysis

Background:

• Microscopy image analysis is crucial for understanding colloidal aggregate and agglomerate size and structure.
• Colloid structure is typically quantified by mass fractal dimension (Df), distinct from the 2D fractal dimension (d) derived from images.
• A gap exists in relating 2D image-derived dimensions to 3D structural properties.

Purpose of the Study:

• To establish a relationship between the 2D fractal dimension (d) from images and the 3D mass fractal dimension (Df) of colloidal aggregates.
• To utilize a morphological aggregation model for this cross-dimensional analysis.
• To investigate the influence of colloidal suspension composition on aggregate density.

Main Methods:

• Application of a recent morphological aggregation model.
• Analysis of scanning transmission electron microscopy (STEM) images of boehmite colloidal suspensions.
• Computation of the 2D fractal dimension (d) from microscopy images.

Main Results:

• A correlation was found between the 2D image fractal dimension (d) and the 3D mass fractal dimension (Df).
• The computed 2D fractal dimension (d) showed good agreement with small-angle X-ray scattering (SAXS) data and existing literature.
• Observed behavior of 'd' across varying acid and base concentrations validated the model's applicability.

Conclusions:

• The established relationship between 'd' and 'Df' provides a valuable tool for characterizing colloidal aggregates.
• This method allows for the study of how suspension composition impacts the density of colloidal aggregates and agglomerates.
• The findings offer a novel approach to inferring 3D structural properties from 2D microscopy data in colloid science.