Fractal nature of fat crystal networks

Abstract

The quantification of microstructure in fat crystal networks is studied using the relationship of the shear elastic modulus ${(G}^{\prime })$ to the volume fraction of solid fat (Φ) via the mass fractal dimension (D) of the network. Results from application of a scaling theory (weak-link regime theory), developed for colloidal gels, to the microstructure of fat crystal networks are presented and discussed. A method to measure mass fractal dimensions and chemical length exponents or backbone fractal dimensions (x) from in situ polarized light microscope (PLM) images of the microstructural network of fat crystals is developed and applied to the fat systems studied. Fractal dimensions measured from in situ PLM images of the various fat systems are in good agreement with fractal dimensions measured using rheological measurements and the weak-link regime theory (percent deviations range from 0.40% to 2.50%). The crystallization behavior of the various fat systems is studied using differential scanning calorimetry, and the potential for altering $G^{\prime }$ by changing crystallization conditions using the fractal dimension of the network as an indicator is discussed.