近年來，各國際期刊陸續發表了許多關於膠體在二維介面上理論與實驗的相關研究。實驗上，發現膠體於介面上有穩定的叢聚形成，且膠體間具有長程的作用力。理論方面，眾說紛紜，探討長程作用的來源。歸納主要三種基本的作用力: (1)凡德瓦爾斯力(van der Waals force)；(2)毛細張力(capillary force)；(3)靜電力(electrostatic force)。由此三種作用力為出發點，並且利用基因演算法(Genetic Algorithm， GA)及Basin Hopping Method (BH)作雙重比較，尋求最低能量的結構。本論文預測的最穩定結構與實驗普遍觀測的結果相吻合，更試圖歸納整理二維叢集系統幾何結構的圖像描述方法。進一步，些微地改變膠體粒徑的分配(原本所有的膠體具有一樣的半徑)，有趣的現象也一一出現了！

Recent experimental efforts on charged colloids trapped at the fluid/water interface have witnessed the formation of colloid-clusters. It was observed in these studies that the average inter-colloidal distance is surprisingly large on the order of approximately and often greater than 3 μm much farther than that in bulk colloidal dispersion. The mechanism giving rise to these mesoscopic structures remains an unclear puzzle unquestionably due to some kind of a long-range attractive force which is certainly not of van der Waals origin. In this work, we analyze theoretically the three main contributions, namely, the electrostatic (screened Yukawa and dipolar), van der Waals and capillary potentials, to the total energy of a two dimensional (2D) charged colloids spread on the fluid/water interface. Among them, we pay due attention to the capillary potential and consider it as a dominant source causing the long-range attraction. Realistically, we choose to study charged colloids possessing the same radius equal approximately to 10 μm and consult recent theoretical and experimental works for a reasonable estimation of other interfacial related quantities such as the charge of a surface colloid , Debye screening length,..etc which are indispensable in a colloid-cluster calculation. By appealing to two state-of-the-art optimization algorithms, we calculate the 2D colloid-clusters by searching their lowest energies. Our results show that the optimized total energies yield mesoscopic structures in close resemblance to surface colloid-clusters trappped at the fluid/water interface. Prevalently, we see primary clusetrs that include singlet, doublet, triplet and quadruplet occupying deeply in the cluster core center. For the range of cluster size studied here, we find, in particular, regularity in the growth pattern in three qualitative repeated sequences. As the number of colloids increases, we notice furthermore that the triangular and centered hexagonal clusters and their respective sequence are two common core clusters. Also, our predicted large clusters show tendency towards circular geometries similar to those observed experimentally.

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