摘 要
我們的三維蒙第卡羅模擬將以鍵振盪模型來探究柔性與半柔性的高分子刷平衡結構及諸多性質。在我們的模擬結果中，長柔性的高分子刷與自洽場理論所預測的行為大致相符，在低覆蓋率時，拋物線形式的分子刷在接近基板時有剝離層的出現，但是在高覆蓋率的時候由於接近基板處的高分子密度而使得剝離層消失。長柔性分子刷的高度正比於 ， 為分子鏈長度， 為覆蓋率。在短鍵的情形 ，分子刷高度大約正比於 ，這是由於一非線性的伸張能量所造成， 。對半柔性的分子鏈而言，分子刷高度可以分為兩項，一項為 ，此項與分子鍵強度 有關，另一項為 ，則與分子鍵強度無關， 比 小很多，而類似的結果，也在端點分子間距離出現。
此外，我們也討論了分子刷系統的均向─針向相變，當我們改變覆蓋率、分子鏈長度及分子鍵強度時，我們發現分子刷系統的均向─針向相變為一連續的相變。分子鍵的角度分布也在不同溫度時被量測，最後，我們將討論局部的覆蓋變異將對分子密度分布所造成的影響。

Abstract
Three dimensional Monde-Carlo simulations of flexible and semi-flexible polymer brushes at various coverage are carried out to study their equilibrium structure and attendant properties by using the bond fluctuation model. Our simulation results of long flexible polymer brushes are in general consistent with predictions of the self-consistent field theory. At low grafting densities, a parabolic brush with a depletion layer near the substrate is observed, while the depletion layer disappears and the monomer density near the substrate is enhanced due to the compression of monomers outside this region at high grafting densities. The brush height of long flexible polymers is proportional to where is the number of monomers per chain and is the grafting density. For short chains , the brush height is roughly proportional to , which indicates a nonlinear stretching energy . For semi-flexible chains, the brush height can be decomposed into a term depending on the chain stiffness and the other term independent of the stiffness. is found much smaller than . Similar results have been found for the end to end distance of the chains. Moreover, we study the isotropic-to-nematic transition of polymer brushes by varying the grafting density , chain length , and the chain stiffness. The isotropic-to-nematic transition of polymer brush is found to be a continuous phase transition from our simulation results. The angular distribution of polymer bonds has also been measured at various temperature. Finally, we discuss the effects of fluctuation of local grafting density on the monomer density distribution.

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