本論文探討經由膠體粒子在水滴上聚結所形成的網絡對水滴的彈性強度的貢獻。 利用布朗動力學模擬來模擬膠體粒子在水滴上的聚結， 我們研究在不同大小的水滴以及不同粒子濃度上形成的網絡的彈性。 對於粒子濃度比較高的水滴， 粒子在水滴上形成對彈性有貢獻的網 絡的機率相對較高。 當粒子濃度高於某個臨界濃度時， 水滴的彈性係數增加的非常快。 雖然這個現象在一開始被認為是跟 rigidity percolation 問題有關， 但是模擬的結果卻指出膠體在水滴上的聚結其實是凝膠化過程(gelation)。 因為我們發現對於比較大的水滴， 膠體所形成的網絡在比較低的粒子濃度就可以對彈性產生貢獻， 並且經由 finite-size scaling 的分析我們推斷當水滴半徑為無限大時， 在任意有限的粒子濃度下水滴的彈性皆不為零。 類似的現象也可以在二維凝膠化過程過程中被發現。 再者， 因為這些由膠體粒子所形的的網絡的 fractal dimension 都小於2， 於是我們總結由膠體力子在水滴上形成的彈性網絡的問題屬於凝膠化過程。 Inspired by the experiment of the fabrication of colloidosome carried out by Dinsmore et al. [1], we are interested in the mechanical strength of the network formed by the aggregation of colloids on a water droplet. Brownian dynamics simulation is applied to simulate slippery diffusion-limited cluster aggregation (slippery DLCA) of nanoparticles on a micron-sized droplet. We study the elasticity of the network on droplets of different sizes and different surface concentration of particles. For higher concentration of particle on the droplet, there is a greater probability for network to be formed. The elastic modulus increases rapidly after the surface concentration of the particle is greater than some critical concentration. However, we find that although this phenomenon is related to rigidity percolation problem, the simulation result actually indicates that rigidity problem of the aggregate formed by slippery DLCA of nanoparticles on a droplet belongs to a gelation problem. This is because for a larger droplet, the elastic modulus becomes nonzero at lower surface concentration C and finite-size scaling analysis indicates that it should be nonzero at any finite C for a droplet of infinite radius. Similar behavior is also observed in gelation process in flat space. Furthermore, the fractal dimension of the aggregates formed through this simulation is smaller than 2. Therefore we conclude that rigidity problem of the aggregate formed by slippery DLCA of nanoparticles on a droplet belongs to gelation problem.
