Tunable Fractal Morphogenesis in Reaction-Diffusion Crystallization: From Dendrites to Compact Aggregates

Fractal growth in reaction-diffusion frameworks (RDF) offers a powerful paradigm for understanding self-assembly in chemical and materials systems. However, its connection to diffusion-limited aggregation (DLA) remains underexplored. Here, we present the first quantitative demonstration of RDF-driven fractal crystallization of benzoic acid (BA), revealing a direct correlation among fractal dimension, diffusion rate, and gel-matrix chemistry. In gelatin-based systems, BA crystallizes into dendritic structures that conform to classical DLA behavior, with fractal dimensions converging toward ∼1.71 to 1.74 at high supersaturation. Complementary characterization by powder X-ray diffraction and scanning electron microscope confirms consistent crystal structure across growth zones, while systematic peak shifts indicate uniform tensile macrostrain embedded during rapid, diffusion-limited growth. In contrast, agar-based systems yield spherulitic morphologies, underscoring the critical influence of gel-network interactions on crystallization pathways. Monte Carlo simulations of DLA in a concentric geometry further demonstrate that experimental fractal dimension trends map directly onto variations in effective sticking coefficients, indicating that supersaturation gradients modulate particle adhesion in the diffusion-controlled regime. Moreover, reverse-phase diffusion experiments reveal that slower diffusion promotes branch thickening and reduced fractal dimensions. These findings establish RDF crystallization as a versatile platform for engineering fractal architectures, offering new strategies for hierarchical material design, biomimetic crystallization, and soft-matter self-assembly.