管子模型在高分子纽结体系中的构建和应用  

Tube model for polymer knots:establishment and applications

作　　者：代亮 Liang Dai(Department of Physics,City University of Hong Kong,Hong Kong 999077,China;Shenzhen Research Institute of City University of Hong Kong,Shenzhen 518057,China)

机构地区：[1]香港城市大学物理系,中国香港999077 [2]香港城市大学深圳研究院,深圳518057

出　　处：《中国科学：化学》2023年第4期693-707,共15页SCIENTIA SINICA Chimica

基　　金：国家自然科学基金(编号:22273080,21973080)资助项目。

摘　　要：纽结是链状物中的常见现象,既存在于耳机线等宏观物体,也存在于微观链状分子,包括DNA和蛋白质.近年来,实验观察到高分子纽结能显著改变力学、流变、催化、生物功能等性质,但是对高分子纽结的理论认识和解析推导较少,导致对纽结现象机理理解不足.理论研究的难点在于,纽结构象空间复杂,难以用统计物理理论进行严格解析推导.为解决该问题,我们发展纽结管子模型对纽结体系进行理论简化,将纽结问题转化成管子限制问题,使理论推导变得可行.基于该管子模型,结合蒙特卡洛模拟、分子动力学模拟、链生长法以及特定管子生成算法,我们将理论模型中的管子实物化、可视化和定量化,并得到管子形状和直径等参数.我们发现纽结管子是优美协调的心形.另外,基于该管子模型,结合受限链的标度行为,我们推导各种条件下高分子纽结的自由能、概率、纽结大小分布等性质,与模拟和实验结果吻合.在本专题论述中,我们将介绍本课题组近几年得到的高分子纽结研究结果.Knotting is a common phenomenon of linear objects,including macroscopic chains,e.g.,earphone cables,and microscopic objects,e.g.,DNA,proteins,and other polymers.In recent years,experiments have demonstrated that knotting dramatically affects mechanical,rheological,and catalytic properties as well as biological functions.However,the theoretical understanding and analytical calculation of polymer knots remain little,which prevents us from revealing the mechanisms underlying knotting phenomena.The difficulty in developing the theory for polymer knots is that the conformational space of polymer knots is too complex,and it is almost impossible to directly derive knotting properties from statistical mechanics.To overcome this difficulty,we developed the tube theory(model)for polymer knots.The tube model converts the knotting problem to a confinement problem,which makes the analytical derivation possible.We visualized,materialized,and quantified the tubes for polymer knots using Monte Carlo,molecular dynamics,PERM simulations,and tube-building algorithm.Accordingly,we obtained the tube shape and tube diameters.We found that the knot tubes usually assume a beautiful heart shape.Based on the tube model and the scaling relationships of confined polymers,we derived the free energy of knots,knotting probability and knot sizes under various conditions,which agree with simulation and experimental results.In the review,we will describe our recent results of polymer knots using the tube model.

关 键 词：高分子纽结 链缠结 管子模型 标度定律 蒙特卡洛模拟 分子动力学模拟 

分 类 号：O631[理学—高分子化学]