| Summary: | 碩士 === 淡江大學 === 物理學系碩士班 === 101 === Cooperative jointed chain (CJC) model is a basic model to describe the property of semiflexible polymer. We use the exact enumeration method to study the effect of constraints on the mechanical properties of a CJC with finite length. We fix the direction of both ends of a one-dimensional chain, calculate the relationship between force and relative extension, and compare them with the existed results of an infinite long chain. In 1D case, fixing (directed to left or right) or freeing (in randomly) both ends of the chain result in nine possible situations in which three are degenerate. Our results show that with increasing length of chain, in all cases the results get closer and closer to the result of infinite long chain. But there are three types of results for short chain, i.e., the relative extensions become very close, smaller or larger than that of an infinite long chain. When force is small, the extension with free ends is closest to the result of a infinite long chain. Meanwhile, fixing both ends to left results in smallest extension, and fixing both ends to right leads to largest extension. We have done all results from N=3 to N=200 with N being the length of chain. Our results show that when N>100, effects of constraint conditions (fixed both ends of the bar) affected can be disregard.
We use the exact enumeration method to study two two-dimensional models of semiflexible polymer. One of models is the CJC model, and the other is a model with intrinsic curvature c. CJC model has only one parameter which is bending rigidity k1, but the second model has two parameters which are bending rigidity k2 and intrinsic curvature. We found that when c is negative, the second model is equivalent to the CJC model. When c is positive but small, the second model is also equivalent to the CJC model. Here the “equivalence” means that for any k2 and c, we can always find a k1 such that the relative extensions and the <yN2> both models are the same, where yN is the component of position vector of the right end, and the mean energies of two models are differed by a constant only. Therefore, in these cases, the second model can be replaced completely by CJC. We also find that in equivalent state and with a given k2, k1 and c have linear relation.
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