Shengli Oilfield Co., Ltd, SINOPEC, Dongying 257015, Shandong, China.
J Phys Chem B. 2010 Sep 30;114(38):12293-7. doi: 10.1021/jp1023179.
The probability and dimension of the simple macromolecular knots over a wide range of temperatures corresponding from good to poor solvents are investigated by Monte Carlo simulation. Macromolecular knots are modeled as rings of self-avoiding walks on a simple cubic lattice with the nearest neighbor attractions. We found that there is a minimum probability for the unknotted ring at a certain temperature. The size dependence of trivial, trefoil, and figure-eight knots on chain lengths and temperatures is presented. The simulation results for the size dependence on the knot's complication in different solvents are in good qualitative agreement with prediction of the scaling model proposed by Grosberg et al. The critical exponent for long chain is independent of the knot types based on the simulation results, although the mean square radius of gyration is influenced significantly by the knot types for a shorter length macromolecular ring. We calculated the ratio of the topological invariant p of trefoil knot and figure-eight knot and found that the ratio is approaching to 1.3 with the increasing of the chain length.
通过蒙特卡罗模拟研究了从良溶剂到不良溶剂的广泛温度范围内简单高分子纽结的概率和尺寸。高分子纽结被建模为简单立方晶格上的自回避行走的环，具有最近邻吸引力。我们发现，在某一温度下，无纽结环的概率存在最小值。呈现了 trivial、三叶形和 8 字结的尺寸依赖性与链长和温度的关系。不同溶剂中纽结复杂度的尺寸依赖性的模拟结果与 Grosberg 等人提出的标度模型的预测具有良好的定性一致性。基于模拟结果，长链的临界指数与纽结类型无关，尽管对于较短长度的高分子环，均方回转半径受到纽结类型的显著影响。我们计算了三叶形纽结和 8 字纽结的拓扑不变量 p 的比值，发现随着链长的增加，比值趋近于 1.3。
