Moon Seungju, Al-Ghoul Mazen
Department of Chemistry, American University of Beirut, P.O. Box 11-0236, Riad El-Solh, 1107 2020 Beirut, Lebanon.
ACS Omega. 2025 Aug 5;10(34):38629-38639. doi: 10.1021/acsomega.5c03338. eCollection 2025 Sep 2.
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.
反应扩散框架（RDF）中的分形生长为理解化学和材料系统中的自组装提供了一个强大的范例。然而，它与扩散限制聚集（DLA）的联系仍未得到充分探索。在这里，我们首次定量证明了RDF驱动的苯甲酸（BA）分形结晶，揭示了分形维数、扩散速率和凝胶基质化学之间存在直接关联。在基于明胶的系统中，BA结晶成符合经典DLA行为的树枝状结构，在高过饱和度下分形维数趋向于~1.71至1.74。通过粉末X射线衍射和扫描电子显微镜进行的补充表征证实了整个生长区域晶体结构的一致性，而系统的峰移表明在快速的扩散限制生长过程中嵌入了均匀的拉伸宏观应变。相比之下，基于琼脂的系统产生球晶形态，突出了凝胶网络相互作用对结晶途径的关键影响。在同心几何结构中对DLA进行的蒙特卡罗模拟进一步表明，实验分形维数趋势直接映射到有效粘附系数的变化上，这表明过饱和度梯度在扩散控制区域调节颗粒粘附。此外，反相扩散实验表明，较慢的扩散会促进分支变粗并降低分形维数。这些发现将RDF结晶确立为用于构建分形结构的通用平台，为分级材料设计、仿生结晶和软物质自组装提供了新策略。
