Quintero Yenny Cardona, Nagarajan Ramanathan
U.S. Army DEVCOM Soldier Center, 15 General Greene Avenue, Natick, Massachusetts01760, United States.
Langmuir. 2023 Jan 31;39(4):1425-1433. doi: 10.1021/acs.langmuir.2c02704. Epub 2023 Jan 18.
Platonic micelles have been defined as structurally precise amphiphilic aggregates with discrete aggregation numbers corresponding to the close packing of spherical caps (representing head groups) on a sphere (representing hydrophobic core), analogous to the Tammes problem in geometry. Here, we use DFT to explore how an actual molecule behaves compared to the idealized picture based on the Tammes problem by also considering the packing of the tails. We modeled micelles of aggregation numbers 4 to 8 generated from the calix[4]arene amphiphile, PACaL3, with the tails forming a close-packed configuration while the headgroups are arranged as in Platonic solids. The DFT calculations reveal that tail packing overwhelmingly influences the equilibrium aggregation number. While the DFT prediction of a PACaL3 micelle of aggregation number 6 agrees with the scattering experiments of the Sakurai group, DFT calculations also suggest small concentrations of micelles of aggregation number 7. More interestingly, DFT calculations reveal that PACaL3 micelle formation occurs even though less than 20% of the hydrophobic tail surface is removed from contact with water, in contrast to the roughly 80% removal observed for classical surfactant micelles. While the close-packed head groups model predicts higher coverage of the hydrophobic surface for aggregation numbers 4 and 6 compared to 5 and 7, the DFT calculations also accounting for tail packing show that the surface coverage for aggregation numbers 5 and 7 is practically no different than that for aggregation number 4. Finally, although both the close-packed head groups model and the DFT calculations agree that the exposed hydrophobic surface area controls the equilibrium micelle aggregation number, the DFT calculations demonstrate how this exposed hydrophobic area is overwhelmingly determined by the tail group packing and not just by the close packing of head groups.
柏拉图式胶束被定义为结构精确的两亲性聚集体，其离散聚集数对应于球体（代表疏水核心）上球形帽（代表头基）的紧密堆积，类似于几何学中的塔姆斯问题。在此，我们使用密度泛函理论（DFT）来探究与基于塔姆斯问题的理想化图像相比，实际分子的行为，同时也考虑尾部的堆积情况。我们对由杯[4]芳烃两亲物PACaL3生成的聚集数为4至8的胶束进行了建模，尾部形成紧密堆积构型，而头基则按柏拉图立体排列。DFT计算表明，尾部堆积对平衡聚集数有压倒性影响。虽然DFT预测聚集数为6的PACaL3胶束与樱井小组的散射实验结果一致，但DFT计算也表明存在少量聚集数为7的胶束。更有趣的是，DFT计算表明，即使只有不到20%的疏水尾部表面与水脱离接触，PACaL3胶束仍会形成，这与经典表面活性剂胶束中约80%的表面脱离情况形成对比。虽然紧密堆积头基模型预测聚集数为4和6时疏水表面的覆盖率高于聚集数为5和7时，但考虑尾部堆积的DFT计算表明，聚集数为5和7时的表面覆盖率与聚集数为4时实际上并无差异。最后，尽管紧密堆积头基模型和DFT计算都认为暴露的疏水表面积控制着平衡胶束聚集数，但DFT计算表明，这种暴露的疏水面积主要由尾部基团堆积决定，而不仅仅取决于头基的紧密堆积。
