奈米粒子─有機混成材料(Nanoparticle–organic hybrid materials)是一種無溶劑的奈米複合材料,由無機中心核與嫁接在表面的有機高分子刷組成。實驗上,高分子尺寸和表面接枝密度的多分散性(Polydispersity)已經顯示會影響鄰近高分子刷之間的交纏程度。為了透過理論預測多分散性在奈米粒子─有機混成材料的粒子間相互作用力的效果,我們以雙成分的高分子刷作為起點,並利用密度泛函理論(Density-functional theory)推導出熱力學平衡情形下的性質,例如兩種高分子的機率分布。具體而言,我們考慮了兩種不同的雙成分系統:一是兩種種類高分子刷均勻混合且固定接枝密度的情形;二是兩種不同分子鍊長與不同接枝密度的情況。這些不同的情形能夠展現各式多分散性的物理系統的特性。
Nanoparticle–organic hybrid materials (NOHMs) are a solvent-free nanocomposite composed of inorganic cores and tethered polymeric brushes. Experimentally, polydispersity in the polymer size and variations in the surface grafting density have shown to impact the degree of interdigitation between neighboring brushes. In order to theoretically predict the effects of polydispersity on the interparticle interactions in NOHMs, we consider bidisperse polymer brushes as a starting point, and formulate a density-functional theory for the equilibrium thermodynamic properties such as probability distributions of the two polymers. Specifically, we consider two different bidisperse systems: One for brushes uniformly mixed with two species at a fixed grafting density and the other for brushes with distinct chain lengths and grafting densities. These different scenarios would represent various extents of polydispersity in physical systems.